Patent Publication Number: US-2023135441-A1

Title: Abrasive particles having particular shapes and methods of forming such particles

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     This application is a continuation of and claims priority under 35 U.S.C. § 120 to U.S. Non-Provisional patent application Ser. No. 16/859,336, entitled “ABRASIVE PARTICLES HAVING PARTICULAR SHAPES AND METHODS OF FORMING SUCH PARTICLES,” naming inventors Anuj SETH, et al., filed on Apr. 27, 2020, which is a continuation of and claims priority under 35 U.S.C. § 120 to U.S. Non-Provisional patent application Ser. No. 16/202,801, entitled “ABRASIVE PARTICLES HAVING PARTICULAR SHAPES AND METHODS OF FORMING SUCH PARTICLES,” naming inventors Anuj SETH, et al., filed on Nov. 28, 2018, now U.S. Pat. No. 10,668,598, which is a continuation of and claims priority under 35 U.S.C. § 120 to U.S. Non-Provisional patent application Ser. No. 15/261,142, entitled “ABRASIVE PARTICLES HAVING PARTICULAR SHAPES AND METHODS OF FORMING SUCH PARTICLES,” naming inventors Anuj SETH, et al., filed on Sep. 9, 2016, now U.S. Pat. No. 10,179,391, which is a continuation of and claims priority under 35 U.S.C. § 120 to U.S. Non-Provisional patent application Ser. No. 14/231,019, entitled “ABRASIVE PARTICLES HAVING PARTICULAR SHAPES AND METHODS OF FORMING SUCH PARTICLES,” naming inventors Anuj SETH, et al., filed on Mar. 31, 2014, now U.S. Pat. No. 9,457,453, which claims priority under 35 U.S.C. § 119(e) to and the benefit of U.S. Provisional Patent Application No. 61/806,741 entitled “ABRASIVE PARTICLES HAVING PARTICULAR SHAPES AND METHODS OF FORMING SUCH PARTICLES,” naming inventors Anuj SETH, et al., filed on Mar. 29, 2013, of which these applications are assigned to the current assignee hereof and incorporated herein by reference in their entireties. 
    
    
     BACKGROUND 
     Field of the Disclosure 
     The following is directed to abrasive articles, and particularly, methods of forming abrasive articles. 
     Description of the Related Art 
     Abrasive particles and abrasive articles made incorporating abrasive particles are useful for various material removal operations including grinding, finishing, and polishing. Depending upon the type of abrasive material, such abrasive particles can be useful in shaping or grinding a wide variety of materials and surfaces in the manufacturing of goods. Certain types of abrasive particles have been formulated to date that have particular geometries, such as triangular shaped abrasive particles and abrasive articles incorporating such objects. See, for example, U.S. Pat. Nos. 5,201,916; 5,366,523; and 5,984,988. 
     Some basic technologies that have been employed to produce abrasive particles having a specified shape are (1) fusion, (2) sintering, and (3) chemical ceramic. In the fusion process, abrasive particles can be shaped by a chill roll, the face of which may or may not be engraved, a mold into which molten material is poured, or a heat sink material immersed in an aluminum oxide melt. See, for example, U.S. Pat. No. 3,377,660, disclosing a process comprising the steps of flowing molten abrasive material from a furnace onto a cool rotating casting cylinder, rapidly solidifying the material to form a thin semisolid curved sheet, densifying the semisolid material with a pressure roll, and then partially fracturing the strip of semisolid material by reversing its curvature by pulling it away from the cylinder with a rapidly driven cooled conveyor. 
     In the sintering process, abrasive particles can be formed from refractory powders having a particle size of 45 micrometers or less in diameter. Binders can be added to the powders along with a lubricant and a suitable solvent, e.g., water. The resulting mixtures or slurries can be shaped into platelets or rods of various lengths and diameters. See, for example, U.S. Pat. No. 3,079,242, which discloses a method of making abrasive particles from calcined bauxite material comprising the steps of (1) reducing the material to a fine powder, (2) compacting under affirmative pressure and forming the fine particles of said powder into grain sized agglomerations, and (3) sintering the agglomerations of particles at a temperature below the fusion temperature of the bauxite to induce limited recrystallization of the particles, whereby abrasive grains are produced directly to size. 
     Chemical ceramic technology involves: converting a colloidal dispersion or hydrosol (sometimes called a sol), optionally in a mixture, with solutions of other metal oxide precursors, to a gel; drying; and firing to obtain a ceramic material. See, for example, U.S. Pat. Nos. 4,744,802 and 4,848,041. 
     Still, there remains a need in the industry for improving performance, life, and efficacy of abrasive particles, and the abrasive articles that employ abrasive particles. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present disclosure may be better understood, and its numerous features and advantages made apparent to those skilled in the art by referencing the accompanying drawings. 
         FIG.  1 A  includes a top view illustration of a portion of an abrasive article according to an embodiment. 
         FIG.  1 B  includes a cross-sectional illustration of a portion of an abrasive article in accordance with an embodiment. 
         FIG.  1 C  includes a cross-sectional illustration of a portion of an abrasive article in accordance with an embodiment. 
         FIG.  1 D  includes a cross-sectional illustration of a portion of an abrasive article in accordance with an embodiment. 
         FIG.  2 A  includes a top view illustration of a portion of an abrasive article including shaped abrasive particles in accordance with an embodiment. 
         FIG.  2 B  includes a perspective view of a shaped abrasive particle on an abrasive article in accordance with an embodiment. 
         FIG.  3 A  includes a top view illustration of a portion of an abrasive article in accordance with an embodiment. 
         FIG.  3 B  includes a perspective view illustration of a portion of an abrasive article including shaped abrasive particles having predetermined orientation characteristics relative to a grinding direction in accordance with an embodiment. 
         FIG.  4    includes a top view illustration of a portion of an abrasive article in accordance with an embodiment. 
         FIG.  5    includes a top view of a portion of an abrasive article in accordance with an embodiment. 
         FIG.  6    includes a top view illustration of a portion of an abrasive article in accordance with an embodiment. 
         FIG.  7 A  includes a top view illustration of a portion of an abrasive article in accordance with an embodiment. 
         FIG.  7 B  includes a perspective view illustration of a portion of an abrasive article in accordance with an embodiment. 
         FIG.  8 A  includes a perspective view illustration of a shaped abrasive particle in accordance with an embodiment. 
         FIG.  8 B  includes a cross-sectional illustration of the shaped abrasive particle of  FIG.  8 A . 
         FIG.  8 C  includes a side-view illustration of a shaped abrasive particle according to an embodiment. 
         FIG.  9    includes an illustration of a portion of an alignment structure according to an embodiment. 
         FIG.  10    includes an illustration of a portion of an alignment structure according to an embodiment. 
         FIG.  11    includes an illustration of a portion of an alignment structure according to an embodiment. 
         FIG.  12    includes an illustration of a portion of an alignment structure according to an embodiment. 
         FIG.  13    includes an illustration of a portion of an alignment structure including discrete contact regions comprising an adhesive in accordance with an embodiment. 
         FIGS.  14 A- 14 H  include top down views of portions of tools for forming abrasive articles having various patterned alignment structures including discrete contact regions of an adhesive material according to embodiments herein. 
         FIG.  15    includes an illustration of a system for forming an abrasive article according to an embodiment. 
         FIG.  16    includes an illustration of a system for forming an abrasive article according to an embodiment. 
         FIGS.  17 A- 17 C  include illustrations of systems for forming an abrasive article according to an embodiment. 
         FIG.  18    includes an illustration of a system for forming an abrasive article according to an embodiment. 
         FIG.  19    includes an illustration of a system for forming an abrasive article according to an embodiment. 
         FIG.  20 A  includes an image of a tool used to form an abrasive article according to an embodiment. 
         FIG.  20 B  includes an image of a tool used to form an abrasive article according to an embodiment. 
         FIG.  20 C  includes an image of a portion of an abrasive article according to an embodiment. 
         FIG.  21    includes a plot of normal force (N) versus cut number for Sample A and Sample B according to the grinding test of Example 1. 
         FIG.  22    includes an image of a portion of an exemplary sample according to an embodiment. 
         FIG.  23    includes an image of a portion of a conventional sample. 
         FIG.  24    includes a plot of up grains/cm 2  and total number of grains/cm 2  for two conventional samples and three sample representative of embodiments. 
         FIGS.  25 - 27    include illustrations of plots of locations of shaped abrasive particles to form non-shadowing arrangements according to embodiments. 
         FIG.  28    is an illustration of a rotary screen printing embodiment. 
         FIG.  29    is a top down view illustration of a plurality of shaped abrasive particles located on a plurality discrete adhesive regions according to an embodiment. 
         FIG.  30    is an illustration of a plurality of discrete adhesive target locations and a plurality of discrete adhesive strike locations according to an embodiment. 
         FIG.  31    is a flow diagram of a process for making a coated abrasive according to an embodiment. 
         FIG.  32    is an illustration of a phyllotactic non-shadowing distribution embodiment. 
         FIG.  33    is an illustration of a rotogravure-type printing embodiment. 
         FIG.  34 A  is a photograph of a discontinuous distribution of adhesive contact regions where the make coat does not contain any abrasive particles. 
         FIG.  34 B  is a photograph of the same discontinuous distribution of adhesive contact regions as shown in  FIG.  34 A  after abrasive particles have been disposed on the discontinuous distribution of adhesive contact regions. 
         FIG.  34 C  is a photograph of the abrasive particle covered discontinuous distribution of adhesive contact regions shown in  FIG.  34 B  after a continuous size coat has been applied. 
         FIG.  35 A  is an image of a conventional coated abrasive, which shows a mixture of upright shaped abrasive particles and tipped over shaped abrasive particles. 
         FIG.  35 B  is an image of an inventive coated abrasive embodiment, which shows a majority of upright shaped abrasive particles and very few tipped over shaped abrasive particles. 
         FIG.  36    is graph comparing abrasive particle concentration and orientation (i.e., upright abrasive grains) of a conventional coated abrasive and an inventive coated abrasive embodiment. 
         FIG.  37    is a photograph of an inventive coated abrasive embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     The following is directed to: methods of forming and using shaped abrasive particles, features of shaped abrasive particles; methods of forming and using abrasive articles that include shaped abrasive particles; and features of abrasive articles. The shaped abrasive particles may be used in various abrasive articles, including for example bonded abrasive articles, coated abrasive articles, and the like. In particular instances, the abrasive articles of embodiments herein can be coated abrasive articles defined by a single layer of abrasive grains, and more particularly a discontinuous, single layer of shaped abrasive particles, which may be bonded or coupled to a backing and used to remove material from workpieces. Notably, the shaped abrasive particles can be placed in a controlled manner such that the shaped abrasive particles define a predetermined distribution relative to each other. 
     Methods of Forming Shaped Abrasive Particles 
     Various methods may be employed to form shaped abrasive particles. For example, the shaped abrasive particles may be formed using techniques such as extrusion, molding, screen printing, rolling, melting, pressing, casting, segmenting, sectioning, and a combination thereof. In certain instances, the shaped abrasive particles may be formed from a mixture, which may include a ceramic material and a liquid. In particular instances, the mixture may be a gel formed of a ceramic powder material and a liquid, wherein the gel can be characterized as a shape-stable material having the ability to substantially hold a given shape even in the green (i.e., unfired) state. In accordance with an embodiment, the gel can be formed of the ceramic powder material as an integrated network of discrete particles. 
     The mixture may contain a certain content of solid material, liquid material, and additives such that it has suitable rheological characteristics for forming the shaped abrasive particles. That is, in certain instances, the mixture can have a certain viscosity, and more particularly, suitable rheological characteristics that facilitate formation a dimensionally stable phase of material. A dimensionally stable phase of material is a material that can be formed to have a particular shape and substantially maintain the shape such that the shape is present in the finally-formed object. 
     According to a particular embodiment, the mixture can be formed to have a particular content of solid material, such as the ceramic powder material. For example, in one embodiment, the mixture can have a solids content of at least about 25 wt %, such as at least about 35 wt %, or even at least about 38 wt % for the total weight of the mixture. Still, in at least one non-limiting embodiment, the solid content of the mixture can be not greater than about 75 wt % such as not greater than about 70 wt %, not greater than about 65 wt %, not greater than about 55 wt %, not greater than about 45 wt %, or not greater than about 42 wt %. It will be appreciated that the content of the solids materials in the mixture can be within a range between any of the minimum and maximum percentages noted above. 
     According to one embodiment, the ceramic powder material can include an oxide, a nitride, a carbide, a boride, an oxycarbide, an oxynitride, and a combination thereof. In particular instances, the ceramic material can include alumina. More specifically, the ceramic material may include a boehmite material, which may be a precursor of alpha alumina. The term “boehmite” is generally used herein to denote alumina hydrates including mineral boehmite, typically being Al 2 O 3 H 2 O and having a water content on the order of 15%, as well as pseudoboehmite, having a water content higher than 15%, such as 20-38% by weight. It is noted that boehmite (including pseudoboehmite) has a particular and identifiable crystal structure, and accordingly unique X-ray diffraction pattern, and as such, is distinguished from other aluminous materials including other hydrated aluminas such as ATH (aluminum trihydroxide) a common precursor material used herein for the fabrication of boehmite particulate materials. 
     Furthermore, the mixture can be formed to have a particular content of liquid material. Some suitable liquids may include water. In accordance with one embodiment, the mixture can be formed to have a liquid content less than the solids content of the mixture. In more particular instances, the mixture can have a liquid content of at least about 25 wt %, such as at least about 35 wt %, at least about 45 wt %, at least about 50 wt %, or even at least about 58 wt % for the total weight of the mixture. Still, in at least one non-limiting embodiment, the liquid content of the mixture can be not greater than about 75 wt %, such as not greater than about 70 wt %, not greater than about 65 wt %, not greater than about 62 wt %, or even not greater than about 60 wt %. It will be appreciated that the content of the liquid in the mixture can be within a range between any of the minimum and maximum percentages noted above. 
     Furthermore, for certain processes, the mixture may have a particular storage modulus. For example, the mixture can have a storage modulus of at least about 1×10 4  Pa, such as at least about 4×10 4  Pa, or even at least about 5×10 4  Pa. However, in at least one non-limiting embodiment, the mixture may have a storage modulus of not greater than about 1×10 7  Pa, such as not greater than about 2×10 6  Pa. It will be appreciated that the storage modulus of the mixture  101  can be within a range between any of the minimum and maximum values noted above. 
     The storage modulus can be measured via a parallel plate system using ARES or AR-G2 rotational rheometers, with Peltier plate temperature control systems. For testing, the mixture can be extruded within a gap between two plates that are set to be approximately 8 mm apart from each other. After extruding the gel into the gap, the distance between the two plates defining the gap is reduced to 2 mm until the mixture completely fills the gap between the plates. After wiping away excess mixture, the gap is decreased by 0.1 mm and the test is initiated. The test is an oscillation strain sweep test conducted with instrument settings of a strain range between 01% to 100%, at 6.28 rad/s (1 Hz), using 25 mm parallel plate and recording 10 points per decade. Within 1 hour after the test completes, lower the gap again by 0.1 mm and repeat the test. The test can be repeated at least 6 times. The first test may differ from the second and third tests. Only the results from the second and third tests for each specimen should be reported. 
     Furthermore, to facilitate processing and forming shaped abrasive particles according to embodiments herein, the mixture can have a particular viscosity. For example, the mixture can have a viscosity of at least about 4×10 3  Pa s, at least about 5×10 3  Pa s, at least about 6×10 3  Pa s, at least about 8×10 3  Pa s, at least about 10×10 3  Pa s, at least about 20×10 3  Pa s, at least about 30×10 3  Pa s, at least about 40×10 3  Pa s, at least about 50×10 3  Pa s, at least about 60×10 3  Pa s, at least about 65×10 3  Pa s. In at least one non-limiting embodiment, the mixture may have a viscosity of not greater than about 100×10 3  Pa s, not greater than about 95×10 3  Pa s, not greater than about 90×10 3  Pa s, or even not greater than about 85×10 3  Pa s. It will be appreciated that the viscosity of the mixture can be within a range between any of the minimum and maximum values noted above. The viscosity can be measured in the same manner as the storage modulus as described above. 
     Moreover, the mixture can be formed to have a particular content of organic materials, including for example, organic additives that can be distinct from the liquid, to facilitate processing and formation of shaped abrasive particles according to the embodiments herein. Some suitable organic additives can include stabilizers, binders, such as fructose, sucrose, lactose, glucose, UV curable resins, and the like. 
     Notably, the embodiments herein may utilize a mixture that can be distinct from slurries used in conventional forming operations. For example, the content of organic materials, within the mixture, particularly, any of the organic additives noted above, may be a minor amount as compared to other components within the mixture. In at least one embodiment, the mixture can be formed to have not greater than about 30 wt % organic material for the total weight of the mixture. In other instances, the amount of organic materials may be less, such as not greater than about 15 wt %, not greater than about 10 wt %, or even not greater than about 5 wt %. Still, in at least one non-limiting embodiment, the amount of organic materials within the mixture can be at least about 0.01 wt %, such as at least about 0.5 wt % for the total weight of the mixture. It will be appreciated that the amount of organic materials in the mixture can be within a range between any of the minimum and maximum values noted above. 
     Moreover, the mixture can be formed to have a particular content of acid or base distinct from the liquid, to facilitate processing and formation of shaped abrasive particles according to the embodiments herein. Some suitable acids or bases can include nitric acid, sulfuric acid, citric acid, chloric acid, tartaric acid, phosphoric acid, ammonium nitrate, ammonium citrate. According to one particular embodiment, the mixture can have a pH of less than about 5, and more particularly, within a range between about 2 and about 4, using a nitric acid additive. 
     According to one particular method of forming, the mixture can be used to form shaped abrasive particles via a screen printing process. Generally, a screen printing process may include extrusion of the mixture from a die into openings of a screen in an application zone. A substrate combination including a screen having openings and a belt underlying the screen can be translated under the die and the mixture can be delivered into the openings of the screen. The mixture contained in the openings can be later extracted from the openings of the screen and contained on the belt. The resulting shaped portions of mixture can be precursor shaped abrasive particles. 
     In accordance with an embodiment, the screen can have one or more openings having a predetermined two-dimensional shape, which may facilitate formation of shaped abrasive particles having substantially the same two-dimensional shape. It will be appreciated that there may be features of the shaped abrasive particles that may not be replicated from the shape of the opening. According to one embodiment, the opening can have various shapes, for example, a polygon, an ellipsoid, a numeral, a Greek alphabet letter, a Latin alphabet letter, a Russian alphabet character, a Kanji character, a complex shape including a combination of polygonal shapes, and a combination thereof. In particular instances, the openings may have two-dimensional polygonal shape such as, a triangle, a rectangle, a quadrilateral, a pentagon, a hexagon, a heptagon, an octagon, a nonagon, a decagon, and a combination thereof. 
     Notably, the mixture can be forced through the screen in rapid fashion, such that the average residence time of the mixture within the openings can be less than about 2 minutes, less than about 1 minute, less than about 40 seconds, or even less than about 20 seconds. In particular non-limiting embodiments, the mixture may be substantially unaltered during printing as it travels through the screen openings, thus experiencing no change in the amount of components from the original mixture, and may experience no appreciable drying in the openings of the screen. 
     The belt and/or the screen may be translated at a particular rate to facilitate processing. For example, the belt and/or the screen may be translated at a rate of at least about 3 cm/s. In other embodiments, the rate of translation of the belt and/or the screen may be greater, such as at least about 4 cm/s, at least about 6 cm/s, at least about 8 cm/s, or even at least about 10 cm/s. For certain processes according to embodiments herein, the rate of translation of the belt as compared to the rate of extrusion of the mixture may be controlled to facilitate proper processing. 
     Certain processing parameters may be controlled to facilitate features of the precursor shaped abrasive particles (i.e., the particles resulting from the shaping process) and the finally-formed shaped abrasive particles described herein. Some exemplary process parameters can include a release distance defining a point of separation between the screen and the belt relative to a point within the application zone, a viscosity of the mixture, a storage modulus of the mixture, mechanical properties of components within the application zone, thickness of the screen, rigidity of the screen, a solid content of the mixture, a carrier content of the mixture, a release angle between the belt and screen, a translation speed, a temperature, a content of release agent on the belt or on the surfaces of the openings of the screen, a pressure exerted on the mixture to facilitate extrusion, a speed of the belt, and a combination thereof. 
     After completing the shaping process, the resultant precursor shaped abrasive particles may be translated through a series of zones, wherein additional treatments can occur. Some suitable exemplary additional treatments can include drying, heating, curing, reacting, radiating, mixing, stirring, agitating, planarizing, calcining, sintering, comminuting, sieving, doping, and a combination thereof. According to one embodiment, the precursory shaped abrasive particles may be translated through an optional shaping zone, wherein at least one exterior surface of the particles may be further shaped. Additionally or alternatively, the precursor shaped abrasive particles may be translated through an application zone wherein a dopant material can be applied to at least one exterior surface of the precursor shaped abrasive particles. A dopant material may be applied utilizing various methods including for example, spraying, dipping, depositing, impregnating, transferring, punching, cutting, pressing, crushing, and any combination thereof. In particular instances, the application zone may utilize a spray nozzle, or a combination of spray nozzles to spray dopant material onto the precursor shaped abrasive particles. 
     In accordance with an embodiment, applying a dopant material can include the application of a particular material, such as a precursor. Some exemplary precursor materials can include a dopant material to be incorporated into the finally-formed shaped abrasive particles. For example, the metal salt can include an element or compound that is the precursor to the dopant material (e.g., a metal element). It will be appreciated that the salt may be in liquid form, such as in a mixture or solution comprising the salt and liquid carrier. The salt may include nitrogen, and more particularly, can include a nitrate. In other embodiments, the salt can be a chloride, sulfate, phosphate, and a combination thereof. In one embodiment, the salt can include a metal nitrate, and more particularly, consist essentially of a metal nitrate. 
     In one embodiment, the dopant material can include an element or compound such as an alkali element, alkaline earth element, rare earth element, hafnium, zirconium, niobium, tantalum, molybdenum, vanadium, or a combination thereof. In one particular embodiment, the dopant material includes an element or compound including an element such as lithium, sodium, potassium, magnesium, calcium, strontium, barium, scandium, yttrium, lanthanum, cesium, praseodymium, niobium, hafnium, zirconium, tantalum, molybdenum, vanadium, chromium, cobalt, iron, germanium, manganese, nickel, titanium, zinc, and a combination thereof. 
     In particular instances, the process of applying a dopant material can include select placement of the dopant material on an exterior surface of a precursor shaped abrasive particle. For example, the process of applying a dopant material can include the application of a dopant material to an upper surface or a bottom surface of the precursor shaped abrasive particles. In still another embodiment, one or more side surfaces of the precursor shaped abrasive particles can be treated such that a dopant material is applied thereto. It will be appreciated that various methods may be used to apply the dopant material to various exterior surfaces of the precursor shaped abrasive particles. For example, a spraying process may be used to apply a dopant material to an upper surface or side surface of the precursor shaped abrasive particles. Still, in an alternative embodiment, a dopant material may be applied to the bottom surface of the precursor shaped abrasive particles through a process such as dipping, depositing, impregnating, or a combination thereof. It will be appreciated that a surface of the belt may be treated with dopant material to facilitate a transfer of the dopant material to a bottom surface of precursor shaped abrasive particles. 
     And further, the precursor shaped abrasive particles may be translated on the belt through a post-forming zone, wherein a variety of processes, including for example, drying, may be conducted on the precursor shaped abrasive particles as described in embodiments herein. Various processes may be conducted in the post-forming zone, including treating of the precursor shaped abrasive particles. In one embodiment, the post-forming zone can include a heating process, wherein the precursor shaped abrasive particles may be dried. Drying may include removal of a particular content of material, including volatiles, such as water. In accordance with an embodiment, the drying process can be conducted at a drying temperature of not greater than about 300° C., such as not greater than about 280° C., or even not greater than about 250° C. Still, in one non-limiting embodiment, the drying process may be conducted at a drying temperature of at least about 50° C. It will be appreciated that the drying temperature may be within a range between any of the minimum and maximum temperatures noted above. Furthermore, the precursor shaped abrasive particles may be translated through the post-forming zone at a particular rate, such as at least about 0.2 feet/min (0.06 m/min) and not greater than about 8 feet/min (2.4 m/min). 
     In accordance with an embodiment, the process of forming shaped abrasive particles may further comprise a sintering process. For certain processes of embodiments herein, sintering can be conducted after collecting the precursor shaped abrasive particles from the belt. Alternatively, the sintering may be a process that is conducted while the precursor shaped abrasive particles are on the belt. Sintering of the precursor shaped abrasive particles may be utilized to densify the particles, which are generally in a green state. In a particular instance, the sintering process can facilitate the formation of a high-temperature phase of the ceramic material. For example, in one embodiment, the precursor shaped abrasive particles may be sintered such that a high-temperature phase of alumina, such as alpha alumina is formed. In one instance, a shaped abrasive particle can comprise at least about 90 wt % alpha alumina for the total weight of the particle. In other instances, the content of alpha alumina may be greater, such that the shaped abrasive particle may consist essentially of alpha alumina. 
     Shaped Abrasive Particles 
     The shaped abrasive particles can be formed to have various shapes. In general, the shaped abrasive particles may be formed to have a shape approximating shaping components used in the forming process. For example, a shaped abrasive particle may have a predetermined two-dimensional shape as viewed in any two dimensions of the three dimension shape, and particularly in a dimension defined by the length and width of the particle. Some exemplary two-dimensional shapes can include a polygon, an ellipsoid, a numeral, a Greek alphabet letter, a Latin alphabet letter, a Russian alphabet character, a Kanji character, a complex shape including a combination of polygonal shapes, and a combination thereof. In particular instances, the shaped abrasive particle may have two-dimensional polygonal shape such as, a triangle, a rectangle, a quadrilateral, a pentagon, a hexagon, a heptagon, an octagon, a nonagon, a decagon, and a combination thereof. 
     In one particular aspect, the shaped abrasive particles may be formed to have a shape as illustrated in  FIG.  8 A .  FIG.  8 A  includes a perspective view illustration of a shaped abrasive particle in accordance with an embodiment. Additionally,  FIG.  8 B  includes a cross-sectional illustration of the shaped abrasive particle of  FIG.  8 A . The body  801  includes an upper surface  803  a bottom major surface  804  opposite the upper surface  803 . The upper surface  803  and the bottom surface  804  can be separated from each other by side surfaces  805 ,  806 , and  807 . As illustrated, the body  801  of the shaped abrasive particle  800  can have a generally triangular shape as viewed in a plane of the upper surface  803 . In particular, the body  801  can have a length (Lmiddle) as shown in  FIG.  8 B , which may be measured at the bottom surface  804  of the body  801  and extending from a corner at the bottom surface corresponding to corner  813  at the top surface through a midpoint  881  of the body  801  to a midpoint at the opposite edge of the body corresponding to the edge  814  at the upper surface of the body. Alternatively, the body can be defined by a second length or profile length (Lp), which is the measure of the dimension of the body from a side view at the upper surface  803  from a first corner  813  to an adjacent corner  812 . Notably, the dimension of Lmiddle can be a length defining a distance between a height at a corner (hc) and a height at a midpoint edge (hm) opposite the corner. The dimension Lp can be a profile length along a side of the particle defining the distance between h1 and h2 (as explained herein). Reference herein to the length can be reference to either Lmiddle or Lp. 
     The body  801  can further include a width (w) that is the longest dimension of the body and extending along a side. The shaped abrasive particle can further include a height (h), which may be a dimension of the shaped abrasive particle extending in a direction perpendicular to the length and width in a direction defined by a side surface of the body  801 . Notably, as will be described in more detail herein, the body  801  can be defined by various heights depending upon the location on the body. In specific instances, the width can be greater than or equal to the length, the length can be greater than or equal to the height, and the width can be greater than or equal to the height. 
     Moreover, reference herein to any dimensional characteristic (e.g., h1, h2, hi, w, Lmiddle, Lp, and the like) can be reference to a dimension of a single particle of a batch. Alternatively, any reference to any of the dimensional characteristics can refer to a median value or an average value derived from analysis of a suitable sampling of particles from a batch. Unless stated explicitly, reference herein to a dimensional characteristic can be considered reference to a median value that is a based on a statistically significant value derived from a sample size of suitable number of particles of a batch. Notably, for certain embodiments herein, the sample size can include at least 40 randomly selected particles from a batch of particles. A batch of particles may be a group of particles that are collected from a single process run, and more particularly, may include an amount of shaped abrasive particles suitable for forming a commercial grade abrasive product, such as at least about 20 lbs of particles. 
     In accordance with an embodiment, the body  801  of the shaped abrasive particle can have a first corner height (hc) at a first region of the body defined by a corner  813 . Notably, the corner  813  may represent the point of greatest height on the body  801 ; however, the height at the corner  813  does not necessarily represent the point of greatest height on the body  801 . The corner  813  can be defined as a point or region on the body  301  defined by the joining of the upper surface  803  and two side surfaces  805  and  807 . The body  801  may further include other corners, spaced apart from each other, including for example, corner  811  and corner  812 . As further illustrated, the body  801  can include edges  814 ,  815 , and  816  that can be separated from each other by the corners  811 ,  812 , and  813 . The edge  814  can be defined by an intersection of the upper surface  803  with the side surface  806 . The edge  815  can be defined by an intersection of the upper surface  803  and side surface  805  between corners  811  and  813 . The edge  816  can be defined by an intersection of the upper surface  803  and side surface  807  between corners  812  and  813 . 
     As further illustrated, the body  801  can include a second midpoint height (hm) at a second end of the body  801 , which can be defined by a region at the midpoint of the edge  814 , which can be opposite the first end defined by the corner  813 . The axis  850  can extend between the two ends of the body  801 .  FIG.  8 B  is a cross-sectional illustration of the body  801  along the axis  850 , which can extend through a midpoint  881  of the body  801  along the dimension of length (Lmiddle) between the corner  813  and the midpoint of the edge  814 . 
     In accordance with an embodiment, the shaped abrasive particles of the embodiments herein, including for example, the particle of  FIGS.  8 A and  8 B  can have an average difference in height, which is a measure of the difference between hc and hm. For convention herein, average difference in height will be generally identified as hc-hm, however it is defined an absolute value of the difference and it will be appreciated that average difference in height may be calculated as hm-hc when the height of the body  801  at the midpoint of the edge  814  is greater than the height at the corner  813 . More particularly, the average difference in height can be calculated based upon a plurality of shaped abrasive particles from a suitable sample size, such as at least 40 particles from a batch as defined herein. The heights hc and hm of the particles can be measured using a STIL (Sciences et Techniques Industrielles de la Lumiere—France) Micro Measure 3D Surface Profilometer (white light (LED) chromatic aberration technique) and the average difference in height can be calculated based on the average values of hc and hm from the sample. 
     As illustrated in  FIG.  8 B , in one particular embodiment, the body  801  of the shaped abrasive particle may have an average difference in height at different locations at the body. The body can have an average difference in height, which can be the absolute value of [hc−hm] between the first corner height (hc) and the second midpoint height (hm) is at least about 20 microns. It will be appreciated that average difference in height may be calculated as hm-hc when the height of the body  801  at a midpoint of the edge is greater than the height at an opposite corner. In other instances, the average difference in height [hc-hm], can be at least about 25 microns, at least about 30 microns, at least about 36 microns, at least about 40 microns, at least about 60 microns, such as at least about 65 microns, at least about 70 microns, at least about 75 microns, at least about 80 microns, at least about 90 microns, or even at least about 100 microns. In one non-limiting embodiment, the average difference in height can be not greater than about 300 microns, such as not greater than about 250 microns, not greater than about 220 microns, or even not greater than about 180 microns. It will be appreciated that the average difference in height can be within a range between any of the minimum and maximum values noted above. 
     Moreover, it will be appreciated that the average difference in height can be based upon an average value of hc. For example, the average height of the body at the corners (Ahc) can be calculated by measuring the height of the body at all corners and averaging the values, and may be distinct from a single value of height at one corner (hc). Accordingly, the average difference in height may be given by the absolute value of the equation [Ahc−hi], wherein hi is the interior height which can be the smallest dimension of height of the body as measured along a dimension between any corner and opposite midpoint edge on the body. Furthermore, it will be appreciated that the average difference in height can be calculated using a median interior height (Mhi) calculated from a suitable sample size of a batch of shaped abrasive particles and an average height at the corners for all particles in the sample size. Accordingly, the average difference in height may be given by the absolute value of the equation [Ahc−Mhi]. 
     In particular instances, the body  801  can be formed to have a primary aspect ratio, which is a ratio expressed as width:length, wherein the length may be Lmidddle, having a value of at least 1:1. In other instances, the body can be formed such that the primary aspect ratio (w:l) is at least about 1.5:1, such as at least about 2:1, at least about 4:1, or even at least about 5:1. Still, in other instances, the abrasive particle can be formed such that the body has a primary aspect ratio that is not greater than about 10:1, such as not greater than 9:1, not greater than about 8:1, or even not greater than about 5:1. It will be appreciated that the body  801  can have a primary aspect ratio within a range between any of the ratios noted above. Furthermore, it will be appreciated that reference herein to a height is the maximum height measurable of the abrasive particle. It will be described later that the abrasive particle may have different heights at different positions within the body  801 . 
     In addition to the primary aspect ratio, the abrasive particle can be formed such that the body  801  comprises a secondary aspect ratio, which can be defined as a ratio of length:height, wherein the length may be Lmiddle and the height is an interior height (hi). In certain instances, the secondary aspect ratio can be within a range between about 5:1 and about 1:3, such as between about 4:1 and about 1:2, or even between about 3:1 and about 1:2. It will be appreciated that the same ratio may be measured using median values (e.g., median length and interior median height) for a batch of particles. 
     In accordance with another embodiment, the abrasive particle can be formed such that the body  801  comprises a tertiary aspect ratio, defined by the ratio width:height, wherein the height is an interior height (hi). The tertiary aspect ratio of the body  801  can be within a range between about 10:1 and about 1.5:1, such as between 8:1 and about 1.5:1, such as between about 6:1 and about 1.5:1, or even between about 4:1 and about 1.5:1. It will be appreciated that the same ratio may be measured using median values (e.g., median length, median middle length, and/or interior median height) for a batch of particles. 
     According to one embodiment, the body  801  of the shaped abrasive particle can have particular dimensions, which may facilitate improved performance. For example, in one instance, the body can have an interior height (hi), which can be the smallest dimension of height of the body as measured along a dimension between any corner and opposite midpoint edge on the body. In particular instances, wherein the body is a generally triangular two-dimensional shape, the interior height (hi) may be the smallest dimension of height (i.e., measure between the bottom surface  804  and the upper surface  805 ) of the body for three measurements taken between each of the three corners and the opposite midpoint edges. The interior height (hi) of the body of a shaped abrasive particle is illustrated in  FIG.  8 B . According to one embodiment, the interior height (hi) can be at least about 28% of the width (w). The height (hi) of any particle may be measured by sectioning or mounting and grinding the shaped abrasive particle and viewing in a manner sufficient (e.g., light microscope or SEM) to determine the smallest height (hi) within the interior of the body  801 . In one particular embodiment, the height (hi) can be at least about 29% of the width, such as at least about 30%, or even at least about 33% of the width of the body. For one non-limiting embodiment, the height (hi) of the body can be not greater than about 80% of the width, such as not greater than about 76%, not greater than about 73%, not greater than about 70%, not greater than about 68% of the width, not greater than about 56% of the width, not greater than about 48% of the width, or even not greater than about 40% of the width. It will be appreciated that the height (hi) of the body can be within a range between any of the above noted minimum and maximum percentages. 
     A batch of shaped abrasive particles can be fabricated, wherein the median interior height value (Mhi) can be controlled, which may facilitate improved performance. In particular, the median internal height (hi) of a batch can be related to a median width of the shaped abrasive particles of the batch in the same manner as described above. Notably, the median interior height (Mhi) can be at least about 28%, such as at least about 29%, at least about 30%, or even at least about 33% of the median width of the shaped abrasive particles of the batch. For one non-limiting embodiment, the median interior height (Mhi) of the body can be not greater than about 80%, such as not greater than about 76%, not greater than about 73%, not greater than about 70%, not greater than about 68% of the width, not greater than about 56% of the width, not greater than about 48% of the width, or even not greater than about 40% of the median width. It will be appreciated that the median interior height (Mhi) of the body can be within a range between any of the above noted minimum and maximum percentages. 
     Furthermore, the batch of shaped abrasive particles may exhibit improved dimensional uniformity as measured by the standard deviation of a dimensional characteristic from a suitable sample size. According to one embodiment, the shaped abrasive particles can have an interior height variation (Vhi), which can be calculated as the standard deviation of interior height (hi) for a suitable sample size of particles from a batch. According to one embodiment, the interior height variation can be not greater than about 60 microns, such as not greater than about 58 microns, not greater than about 56 microns, or even not greater than about 54 microns. In one non-limiting embodiment, the interior height variation (Vhi) can be at least about 2 microns. It will be appreciated that the interior height variation of the body can be within a range between any of the above noted minimum and maximum values. 
     For another embodiment, the body of the shaped abrasive particle can have an interior height (hi) of at least about 400 microns. More particularly, the height may be at least about 450 microns, such as at least about 475 microns, or even at least about 500 microns. In still one more non-limiting embodiment, the height of the body can be not greater than about 3 mm, such as not greater than about 2 mm, not greater than about 1.5 mm, not greater than about 1 mm, not greater than about 800 microns. It will be appreciated that the height of the body can be within a range between any of the above noted minimum and maximum values. Moreover, it will be appreciated that the above range of values can be representative of a median interior height (Mhi) value for a batch of shaped abrasive particles. 
     For certain embodiments herein, the body of the shaped abrasive particle can have particular dimensions, including for example, a width≥length, a length≥height, and a width≥height. More particularly, the body  801  of the shaped abrasive particle can have a width (w) of at least about 600 microns, such as at least about 700 microns, at least about 800 microns, or even at least about 900 microns. In one non-limiting instance, the body can have a width of not greater than about 4 mm, such as not greater than about 3 mm, not greater than about 2.5 mm, or even not greater than about 2 mm. It will be appreciated that the width of the body can be within a range between any of the above noted minimum and maximum values. Moreover, it will be appreciated that the above range of values can be representative of a median width (Mw) for a batch of shaped abrasive particles. 
     The body  801  of the shaped abrasive particle can have particular dimensions, including for example, a length (L middle or Lp) of at least about 0.4 mm, such as at least about 0.6 mm, at least about 0.8 mm, or even at least about 0.9 mm. Still, for at least one non-limiting embodiment, the body  801  can have a length of not greater than about 4 mm, such as not greater than about 3 mm, not greater than about 2.5 mm, or even not greater than about 2 mm. It will be appreciated that the length of the body  801  can be within a range between any of the above noted minimum and maximum values. Moreover, it will be appreciated that the above range of values can be representative of a median length (Ml), which may be more particularly, a median middle length (MLmiddle) or median profile length (MLp) for a batch of shaped abrasive particles. 
     The shaped abrasive particle can have a body  801  having a particular amount of dishing, wherein the dishing value (d) can be defined as a ratio between an average height of the body  801  at the corners (Ahc) as compared to smallest dimension of height of the body at the interior (hi). The average height of the body  801  at the corners (Ahc) can be calculated by measuring the height of the body at all corners and averaging the values, and may be distinct from a single value of height at one corner (hc). The average height of the body  801  at the corners or at the interior can be measured using a STIL (Sciences et Techniques Industrielles de la Lumiere—France) Micro Measure 3D Surface Profilometer (white light (LED) chromatic aberration technique). Alternatively, the dishing may be based upon a median height of the particles at the corner (Mhc) calculated from a suitable sampling of particles from a batch. Likewise, the interior height (hi) can be a median interior height (Mhi) derived from a suitable sampling of shaped abrasive particles from a batch. According to one embodiment, the dishing value (d) can be not greater than about 2, such as not greater than about 1.9, not greater than about 1.8, not greater than about 1.7, not greater than about 1.6, or even not greater than about 1.5. Still, in at least one non-limiting embodiment, the dishing value (d) can be at least about 0.9, such as at least about 1.0. It will be appreciated that the dishing ratio can be within a range between any of the minimum and maximum values noted above. Moreover, it will be appreciated that the above dishing values can be representative of a median dishing value (Md) for a batch of shaped abrasive particles. 
     The shaped abrasive particles of the embodiments herein, including for example, the body  801  of the particle of  FIG.  8 A  can have a bottom surface  804  defining a bottom area (A b ). In particular instances the bottom surface  304  can be the largest surface of the body  801 . The bottom surface can have a surface area defined as the bottom area (A b ) that is greater than the surface area of the upper surface  803 . Additionally, the body  801  can have a cross-sectional midpoint area (A m ) defining an area of a plane perpendicular to the bottom area and extending through a midpoint  881  (a between the top and bottom surfaces) of the particle. In certain instances, the body  801  can have an area ratio of bottom area to midpoint area (A b /A m ) of not greater than about 6. In more particular instances, the area ratio can be not greater than about 5.5, such as not greater than about 5, not greater than about 4.5, not greater than about 4, not greater than about 3.5, or even not greater than about 3. Still, in one non-limiting embodiment, the area ratio may be at least about 1.1, such as at least about 1.3, or even at least about 1.8. It will be appreciated that the area ratio can be within a range between any of the minimum and maximum values noted above. Moreover, it will be appreciated that the above area ratios can be representative of a median area ratio for a batch of shaped abrasive particles. 
     Furthermore the shaped abrasive particles of the embodiments herein, including for example, the particle of  FIG.  8 B  can have a normalized height difference of at least about 0.3. The normalized height difference can be defined by the absolute value of the equation [(hc-hm)/(hi)]. In other embodiments, the normalized height difference can be not greater than about 0.26, such as not greater than about 0.22, or even not greater than about 0.19. Still, in one particular embodiment, the normalized height difference can be at least about 0.04, such as at least about 0.05, at least about 0.06. It will be appreciated that the normalized height difference can be within a range between any of the minimum and maximum values noted above. Moreover, it will be appreciated that the above normalized height values can be representative of a median normalized height value for a batch of shaped abrasive particles. 
     In another instance, the body  801  can have a profile ratio of at least about 0.04, wherein the profile ratio is defined as a ratio of the average difference in height [hc−hm] to the length (Lmiddle) of the shaped abrasive particle, defined as the absolute value of [(hc−hm)/(Lmiddle)]. It will be appreciated that the length (Lmiddle) of the body can be the distance across the body  801  as illustrated in  FIG.  8 B . Moreover, the length may be an average or median length calculated from a suitable sampling of particles from a batch of shaped abrasive particles as defined herein. According to a particular embodiment, the profile ratio can be at least about 0.05, at least about 0.06, at least about 0.07, at least about 0.08, or even at least about 0.09. Still, in one non-limiting embodiment, the profile ratio can be not greater than about 0.3, such as not greater than about 0.2, not greater than about 0.18, not greater than about 0.16, or even not greater than about 0.14. It will be appreciated that the profile ratio can be within a range between any of the minimum and maximum values noted above. Moreover, it will be appreciated that the above profile ratio can be representative of a median profile ratio for a batch of shaped abrasive particles. 
     According to another embodiment, the body  801  can have a particular rake angle, which may be defined as an angle between the bottom surface  804  and a side surface  805 ,  806  or  807  of the body. For example, the rake angle may be within a range between about 1° and about 80°. For other particles herein, the rake angle can be within a range between about 5° and 55°, such as between about 10° and about 50°, between about 15° and 50°, or even between about 20° and 50°. Formation of an abrasive particle having such a rake angle can improve the abrading capabilities of the abrasive particle. Notably, the rake angle can be within a range between any two rake angles noted above. 
     According to another embodiment, the shaped abrasive particles herein, including for example the particles of  FIGS.  8 A and  8 B  can have an ellipsoidal region  817  in the upper surface  803  of the body  801 . The ellipsoidal region  817  can be defined by a trench region  818  that can extend around the upper surface  803  and define the ellipsoidal region  817 . The ellipsoidal region  817  can encompass the midpoint  881 . Moreover, it is thought that the ellipsoidal region  817  defined in the upper surface can be an artifact of the forming process, and may be formed as a result of the stresses imposed on the mixture during formation of the shaped abrasive particles according to the methods described herein. 
     The shaped abrasive particle can be formed such that the body includes a crystalline material, and more particularly, a polycrystalline material. Notably, the polycrystalline material can include abrasive grains. In one embodiment, the body can be essentially free of an organic material, including for example, a binder. More particularly, the body can consist essentially of a polycrystalline material. 
     In one aspect, the body of the shaped abrasive particle can be an agglomerate including a plurality of abrasive particles, grit, and/or grains bonded to each other to form the body  801  of the abrasive particle  800 . Suitable abrasive grains can include nitrides, oxides, carbides, borides, oxynitrides, oxyborides, diamond, superabrasives (e.g., cBN) and a combination thereof. In particular instances, the abrasive grains can include an oxide compound or complex, such as aluminum oxide, zirconium oxide, titanium oxide, yttrium oxide, chromium oxide, strontium oxide, silicon oxide, and a combination thereof. In one particular instance, the abrasive particle  800  is formed such that the abrasive grains forming the body  800  include alumina, and more particularly, may consist essentially of alumina. In an alternative embodiment, the shaped abrasive particles can include geosets, including for example, polycrystalline compacts of abrasive or superabrasive materials including a binder phase, which may include a metal, metal alloy, super alloy, cermet, and a combination thereof. Some exemplary binder materials can include cobalt, tungsten, and a combination thereof. 
     The abrasive grains (i.e., crystallites) contained within the body may have an average grain size that is generally not greater than about 100 microns. In other embodiments, the average grain size can be less, such as not greater than about 80 microns, not greater than about 50 microns, not greater than about 30 microns, not greater than about 20 microns, not greater than about 10 microns, or even not greater than about 1 micron. Still, the average grain size of the abrasive grains contained within the body can be at least about 0.01 microns, such as at least about 0.05 microns, such as at least about 0.08 microns, at least about 0.1 microns, or even at least about 1 micron. It will be appreciated that the abrasive grains can have an average grain size within a range between any of the minimum and maximum values noted above. 
     In accordance with certain embodiments, the abrasive particle can be a composite article including at least two different types of abrasive grains within the body. It will be appreciated that different types of abrasive grains are abrasive grains having different compositions with regard to each other. For example, the body can be formed such that is includes at least two different types of abrasive grains, wherein the two different types of abrasive grains can be nitrides, oxides, carbides, borides, oxynitrides, oxyborides, diamond, and a combination thereof. 
     In accordance with an embodiment, the abrasive particle  800  can have an average particle size, as measured by the largest dimension measurable on the body  801 , of at least about 100 microns. In fact, the abrasive particle  800  can have an average particle size of at least about 150 microns, such as at least about 200 microns, at least about 300 microns, at least about 400 microns, at least about 500 microns, at least about 600 microns, at least about 700 microns, at least about 800 microns, or even at least about 900 microns. Still, the abrasive particle  800  can have an average particle size that is not greater than about 5 mm, such as not greater than about 3 mm, not greater than about 2 mm, or even not greater than about 1.5 mm. It will be appreciated that the abrasive particle  100  can have an average particle size within a range between any of the minimum and maximum values noted above. 
     The shaped abrasive particles of the embodiments herein can have a percent flashing that may facilitate improved performance. Notably, the flashing defines an area of the particle as viewed along one side, such as illustrated in  FIG.  8 C , wherein the flashing extends from a side surface of the body within the boxes  888  and  889 . The flashing can represent tapered regions proximate to the upper surface and bottom surface of the body. The flashing can be measured as the percentage of area of the body along the side surface contained within a box extending between an innermost point of the side surface (e.g.,  891 ) and an outermost point (e.g.,  892 ) on the side surface of the body. In one particular instance, the body can have a particular content of flashing, which can be the percentage of area of the body contained within the boxes  888  and  889  compared to the total area of the body contained within boxes  888 ,  889 , and  890 . According to one embodiment, the percent flashing (f) of the body can be at least about 10%. In another embodiment, the percent flashing can be greater, such as at least about 12%, such as at least about 14%, at least about 16%, at least about 18%, or even at least about 20%. Still, in a non-limiting embodiment, the percent flashing of the body can be controlled and may be not greater than about 45%, such as not greater than about 40%, or even not greater than about 36%. It will be appreciated that the percent flashing of the body can be within a range between any of the above minimum and maximum percentages. Moreover, it will be appreciated that the above flashing percentages can be representative of an average flashing percentage or a median flashing percentage for a batch of shaped abrasive particles. 
     The percent flashing can be measured by mounting the shaped abrasive particle on its side and viewing the body at the side to generate a black and white image, such as illustrated in  FIG.  8 C . A suitable program for creating and analyzing images including the calculation of the flashing can be ImageJ software. The percentage flashing can be calculated by determining the area of the body  801  in the boxes  888  and  889  compared to the total area of the body as viewed at the side (total shaded area), including the area in the center  890  and within the boxes  888  and  889 . Such a procedure can be completed for a suitable sampling of particles to generate average, median, and/or and standard deviation values. 
     A batch of shaped abrasive particles according to embodiments herein may exhibit improved dimensional uniformity as measured by the standard deviation of a dimensional characteristic from a suitable sample size. According to one embodiment, the shaped abrasive particles can have a flashing variation (Vf), which can be calculated as the standard deviation of flashing percentage (f) for a suitable sample size of particles from a batch. According to one embodiment, the flashing variation can be not greater than about 5.5%, such as not greater than about 5.3%, not greater than about 5%, or not greater than about 4.8%, not greater than about 4.6%, or even not greater than about 4.4%. In one non-limiting embodiment, the flashing variation (Vf) can be at least about 0.1%. It will be appreciated that the flashing variation can be within a range between any of the minimum and maximum percentages noted above. 
     The shaped abrasive particles of the embodiments herein can have a height (hi) and flashing multiplier value (hiF) of at least 4000, wherein hiF=(hi)(f), an “hi” represents a minimum interior height of the body as described above and “f” represents the percent flashing. In one particular instance, the height and flashing multiplier value (hiF) of the body can be greater, such as at least about 4500 micron %, at least about 5000 micron %, at least about 6000 micron %, at least about 7000 micron %, or even at least about 8000 micron %. Still, in one non-limiting embodiment, the height and flashing multiplier value can be not greater than about 45000 micron %, such as not greater than about 30000 micron %, not greater than about 25000 micron %, not greater than about 20000 micron %, or even not greater than about 18000 micron %. It will be appreciated that the height and flashing multiplier value of the body can be within a range between any of the above minimum and maximum values. Moreover, it will be appreciated that the above multiplier value can be representative of a median multiplier value (MhiF) for a batch of shaped abrasive particles. 
     The shaped abrasive particles of the embodiments herein can have a dishing (d) and flashing (F) multiplier value (dF) as calculated by the equation dF=(d)(F), wherein dF is not greater than about 90%, “d” represents the dishing value, and “f” represents the percentage flashing of the body. In one particular instance, the dishing (d) and flashing (F) multiplier value (dF) of the body can be not greater than about 70%, such as not greater than about 60%, not greater than about 55%, not greater than about 48%, not greater than about 46%. Still, in one non-limiting embodiment, the dishing (d) and flashing (F) multiplier value (dF) can be at least about 10%, such as at least about 15%, at least about 20%, at least about 22%, at least about 24%, or even at least about 26%. It will be appreciated that the dishing (d) and flashing (F) multiplier value (dF) of the body can be within a range between any of the above minimum and maximum values. Moreover, it will be appreciated that the above multiplier value can be representative of a median multiplier value (MdF) for a batch of shaped abrasive particles. 
     The shaped abrasive particles of the embodiments herein can have a height and dishing ratio (hi/d) as calculated by the equation hi/d=(hi)/(d), wherein hi/d is not greater than about 1000, “hi” represents a minimum interior height as described above, and “d” represents the dishing of the body. In one particular instance, the ratio (hi/d) of the body can be not greater than about 900 microns, not greater than about 800 microns, not greater than about 700 microns, or even not greater than about 650 microns. Still, in one non-limiting embodiment, the ratio (hi/d), can be at least about 10 microns, such as at least about 50 microns, at least about 100 microns, at least about 150 microns, at least about 200 microns, at least about 250 microns, or even at least about 275 microns. It will be appreciated that the ratio (hi/d) of the body can be within a range between any of the above minimum and maximum values. Moreover, it will be appreciated that the above height and dishing ratio can be representative of a median height and dishing ratio (Mhi/d) for a batch of shaped abrasive particles. 
     Abrasive Articles 
       FIG.  1 A  includes a top view illustration of a portion of an abrasive article according to an embodiment. As illustrated, the abrasive article  100  can include a backing  101 . The backing  101  can comprise an organic material, inorganic material, and a combination thereof. In certain instances, the backing  101  can comprise a woven material. However, the backing  101  may be made of a non-woven material. Particularly suitable backing materials can include organic materials, including polymers, and particularly, polyester, polyurethane, polypropylene, polyimides such as KAPTON from DuPont, and paper. Some suitable inorganic materials can include metals, metal alloys, and particularly, foils of copper, aluminum, steel, and a combination thereof. It will be appreciated that the abrasive article  100  can include other components, including for example adhesive layers (e.g. make coat, size coat, front fill, etc.), which will be discussed in more detail herein. 
     As further illustrated, the abrasive article  100  can include a shaped abrasive particle  102  overlying the backing  101 , and more particularly, coupled to the backing  101 . Notably, the shaped abrasive particle  102  can be placed at a first, predetermined position  112  on the backing  101 . As further illustrated, the abrasive article  100  can further include a shaped abrasive particle  103  that may be overlying the backing  101 , and more particularly, coupled to the backing  101  in a second, predetermined position  113 . The abrasive article  100  can further include a shaped abrasive particle  104  overlying the backing  101 , and more particularly, coupled to the backing  101  in a third, predetermined position  114 . As further illustrated in  FIG.  1 A , the abrasive article  100  can further include a shaped abrasive particle  105  overlying the backing  101 , and more particularly, coupled to the backing  101  in a fourth, predetermined position  115 . As further illustrated, the abrasive article  100  can include a shaped abrasive particle overlying the backing  101 , and more particularly, coupled to the backing  101  in a fifth, predetermined position  116 . It will be appreciated that any of the shaped abrasive particles described herein may be coupled to the backing  101  via one or more adhesive layers as described herein. 
     In accordance with an embodiment, the shaped abrasive particle  102  can have a first composition. For example, the first composition can comprise a crystalline material. In one particular embodiment, the first composition can comprise a ceramic material, such as an oxide, carbide, nitride, boride, oxynitride, oxycarbide, and a combination thereof. More particularly, the first composition may consist essentially of a ceramic, such that it may consist essentially of an oxide, carbide, nitride, boride, oxynitride, oxycarbide, and a combination thereof. Still, in an alternative embodiment, the first composition can comprise a superabrasive material. Still in other embodiments, the first composition can comprise a single phase material, and more particularly may consist essentially of a single phase material. Notably, the first composition may be a single phase polycrystalline material. In specific instances, the first composition may have limited binder content, such that the first composition may have not greater than about 1% binder material. Some suitable exemplary binder materials can include organic materials, and more particularly, polymer containing compounds. More notably, the first composition may be essentially free of binder material and may be essentially free of an organic material. In accordance with one embodiment, the first composition can comprise alumina, and more particularly, may consist essentially of alumina, such as alpha alumina. 
     Still, in yet another aspect, the shaped abrasive particle  102  can have a first composition that can be a composite including at least two different types of abrasive grains within the body. It will be appreciated that different types of abrasive grains are abrasive grains having different compositions with regard to each other. For example, the body can be formed such that is comprises at least two different types of abrasive grains, wherein the two different types of abrasive grains can be nitrides, oxides, carbides, borides, oxynitrides, oxyborides, diamond, and a combination thereof. 
     In one embodiment, the first composition may include a dopant material, wherein the dopant material is present in a minor amount. Some suitable exemplary dopant materials can comprise an element or compound such as an alkali element, alkaline earth element, rare earth element, hafnium, zirconium, niobium, tantalum, molybdenum, vanadium, or a combination thereof. In one particular embodiment, the dopant material comprises an element or compound including an element such as lithium, sodium, potassium, magnesium, calcium, strontium, barium, scandium, yttrium, lanthanum, cesium, praseodymium, niobium, hafnium, zirconium, tantalum, molybdenum, vanadium, chromium, cobalt, iron, germanium, manganese, nickel, titanium, zinc, and a combination thereof. 
     The second shaped abrasive particle  103  may have a second composition. In certain instances, the second composition of the second shaped abrasive particle  103  may be substantially the same as the first composition of the first shaped abrasive particle  102 . More particularly, the second composition may be essentially the same as the first composition. Still, in an alternative embodiment, the second composition of the second shaped abrasive particle  103  may be significantly different that the first composition of the first shaped abrasive particle  102 . It will be appreciated that the second composition can comprise any of the materials, elements, and compounds described in accordance with the first composition. 
     In accordance with an embodiment, and as further illustrated in  FIG.  1 A , the first shaped abrasive particle  102  and second shaped abrasive particle  103  may be arranged in a pre-determined distribution relative to each other. 
     A predetermined distribution can be defined by a combination of predetermined positions on a backing that are purposefully selected. A predetermined distribution can comprise a pattern, design, sequence, array, or arrangement. In a particular embodiment predetermined positions can define an array, such as a two-dimensional array, or a multidimensional array. An array can have short range order defined by a unit, or group, of shaped abrasive particles. An array can also be a pattern, having long range order including regular and repetitive units linked together, such that the arrangement may be symmetrical and/or predictable; however, it should be noted that a predictable arrangement is not necessarily a repeating arrangement (i.e., an array or pattern or arrangement can be both predictable and non-repeating). An array may have an order that can be predicted by a mathematical formula. It will be appreciated that two-dimensional arrays can be formed in the shape of polygons, ellipsis, ornamental indicia, product indicia, or other designs. A predetermined distribution can also include a non-shadowing arrangement. A non-shadowing arrangement can comprise a controlled, non-uniform distribution; a controlled uniform distribution; or a combination thereof. In particular instances, a non-shadowing arrangement can comprise a radial pattern, a spiral pattern, a phyllotactic pattern, an asymmetric pattern, a self-avoiding random distribution, or a combination thereof. Non-shadowing arrangements can include a particular arrangement of abrasive particles (i.e., a particular arrangement of shaped abrasive particles, standard abrasive particles, or a combination thereof) and/or diluent particles, relative to each other, wherein the abrasive particles, diluent particles, or both, can have a degree of overlap. The degree of overlap of the abrasive particles during an initial phase of a material removal operation is not greater than about 25%, such as not greater than about 20%, not greater than about 15%, not greater than about 10%, or even not greater than about 5%. In particular instances, a non-shadowing arrangement can comprise a distribution of abrasive particles wherein upon engagement with a workpiece during an initial stage of a material removal operation, essentially none of the abrasive particles engage the region of the surface of the workpiece. 
     The predetermined distribution can be partially, substantially, or fully asymmetric. The predetermined distribution can overlie the entire abrasive article, can cover substantially the entire abrasive article (i.e. greater than 50% but less than 100%), overlie multiple portions of the abrasive article, or overlie a fraction of the abrasive article (i.e., less than 50% of the surface area of the article). 
     As used herein, “a phyllotactic pattern” means a pattern related to phyllotaxis. Phyllotaxis is the arrangement of lateral organs such as leaves, flowers, scales, florets, and seeds in many kinds of plants. Many phyllotactic patterns are marked by the naturally occurring phenomenon of conspicuous patterns having arcs, spirals, and whorls. The pattern of seeds in the head of a sunflower is an example of this phenomenon. An additional example of a phyllotactic pattern is the arrangement of scales about the axis of a pinecone or pineapple. In a specific embodiment, the predetermined distribution conforms to a phyllotactic pattern that describes the arrangement of the scales of a pineapple and which conforms to the below mathematical model for describing the packing of circles on the surface of a cylinder. According to the below model, all components lie on a single generative helix generally characterized by the formula (1.1) 
       φ= n*α, r =const,  H=h*n,   (1.1)
 
     where:
         n is the ordering number of a scale, counting from the bottom of the cylinder;   φ, r, and H are the cylindrical coordinates of the nth scale;   α is the divergence angle between two consecutive scales (assumed to be constant, e.g., 137.5281 degrees); and   h is the vertical distance between two consecutive scales (measured along the main axis of the cylinder).       

     The pattern described by formula (1.1) is shown in  FIG.  32   , and is sometimes referred to herein as a “pineapple pattern”. In a specific embodiment, the divergence angle (α) can be in a range from 135.918365° to 138.139542°. 
     Furthermore, according to one embodiment, a non-shadowing arrangement can include a microunit, which may be defined as a smallest arrangement of shaped abrasive particles relative to each other. The microunit may repeat a plurality of times across at least a portion of the surface of the abrasive article. A non-shadowing arrangement may further include a macrounit, which can include a plurality of microunits. In particular instances, the macrounit may have a plurality of microunits arranged in a predetermined distribution relative to each other and repeating a plurality of times with the non-shadowing arrangement. Abrasive articles of the embodiments herein can include one or more microunits. Furthermore, it will be appreciated that the abrasive articles of the embodiments herein can include one or more macrounits. In certain embodiments, the macrounits may be arranged in a uniform distribution having a predictable order. Still, in other instances, the macrounits may be arranged in a non-uniform distribution, which may include a random distribution, having no predictable long range or short range order. 
     Referring briefly to  FIGS.  25 - 27   , different non-shadowing arrangements are illustrated. In particular,  FIG.  25    includes an illustration of a non-shadowing arrangement, wherein the locations  2501  represent predetermined positions to be occupied by one or more shaped abrasive particles, diluent particles, and a combination thereof. The locations  2501  may be defined as positions on X and Y axes as illustrated. Moreover, the locations  2506  and  2507  can define a microunit  2520 . Furthermore,  2506  and  2509  may define a microunit  2521 . As further illustrated, the microunits may be repeated across the surface of at least a portion of the article and define a macrounit  2530 . 
       FIG.  26    includes an illustration of a non-shadowing arrangement, wherein the locations (shown as dots on the X and Y axes) represent predetermined positions to be occupied by one or more shaped abrasive particles, diluent particles, and a combination thereof. In one embodiment, the locations  2601  and  2602  can define a microunit  2620 . Furthermore, locations  2603 ,  2604 , and  2605  can define a microunit  2621 . As further illustrated, the microunits may be repeated across the surface of at least a portion of the article and define at least one macrounit  2630 . It will be appreciated, as illustrated, other macrounits may exist. 
       FIG.  27    includes an illustration of a non-shadowing arrangement, wherein the locations (shown as dots on the X and Y axes) represent predetermined positions to be occupied by one or more shaped abrasive particles, diluent particles, and a combination thereof. In one embodiment, the locations  2701  and  2702  can define a microunit  2720 . Furthermore, locations  2701  and  2703  can define a microunit  2721 . As further illustrated, the microunits may be repeated across the surface of at least a portion of the article and define at least one macrounit.  2730 . 
     A predetermined distribution between shaped abrasive particles can also be defined by at least one of a predetermined orientation characteristic of each of the shaped abrasive particles. Exemplary predetermined orientation characteristics can include a predetermined rotational orientation, a predetermined lateral orientation, a predetermined longitudinal orientation, a predetermined vertical orientation, a predetermined tip height, and a combination thereof. The backing  101  can be defined by a longitudinal axis  180  that extends along and defines a length of the backing  101  and a lateral axis  181  that extends along and defines a width of a backing  101 . 
     In accordance with an embodiment, the shaped abrasive particle  102  can be located in a first, predetermined position  112  defined by a particular first lateral position relative to the lateral axis of  181  of the backing  101 . Furthermore, the shaped abrasive particle  103  may have a second, predetermined position defined by a second lateral position relative to the lateral axis  181  of the backing  101 . Notably, the shaped abrasive particles  102  and  103  may be spaced apart from each other by a lateral space  121 , defined as a smallest distance between the two adjacent shaped abrasive particles  102  and  103  as measured along a lateral plane  184  parallel to the lateral axis  181  of the backing  101 . In accordance with an embodiment, the lateral space  121  can be greater than 0, such that some distance exists between the shaped abrasive particles  102  and  103 . However, while not illustrated, it will be appreciated that the lateral space  121  can be 0, allowing for contact and even overlap between portions of adjacent shaped abrasive particle. 
     In other embodiments, the lateral space  121  can be at least about 0.1 (w), wherein w represents the width of the shaped abrasive particle  102 . According to an embodiment, the width of the shaped abrasive particle is the longest dimension of the body extending along a side. In another embodiment, the lateral space  121  can be at least about 0.2( w ), such as at least about 0.5(w), at least about 1(w), at least about 2(w), or even greater. Still, in at least one non-limiting embodiment, the lateral space  121  can be not greater than about 100(w), not greater than about 50(w), or even not greater than about 20(w). It will be appreciated that the lateral space  121  can be within a range between any of the minimum and maximum values noted above. Control of the lateral space between adjacent shaped abrasive particles may facilitate improved grinding performance of the abrasive article. 
     In accordance with an embodiment, the shaped abrasive particle  102  can be in a first, predetermined position  112  defined by a first longitudinal position relative to a longitudinal axis  180  of the backing  101 . Furthermore, the shaped abrasive particle  104  may be located at a third, predetermined position  114  defined by a second longitudinal position relative to the longitudinal axis  180  of the backing  101 . Further, as illustrated, a longitudinal space  123  may exist between the shaped abrasive particles  102  and  104 , which can be defined as a smallest distance between the two adjacent shaped abrasive particles  102  and  104  as measured in a direction parallel to the longitudinal axis  180 . In accordance with an embodiment, the longitudinal space  123  can be greater than 0. Still, while not illustrated, it will be appreciated that the longitudinal space  123  can be 0, such that the adjacent shaped abrasive particles are touching, or even overlapping each other. 
     In other instances, the longitudinal space  123  can be at least about 0.1(w), wherein w is the width of the shaped abrasive particle as described herein. In other more particular instances, the longitudinal space can be at least about 0.2(w), at least about 0.5(w), at least about 1(w), or even at least about 2(w). Still, the longitudinal space  123  may be not greater than about 100(w), such as not greater than about 50(w), or even not greater than about 20(w). It will be appreciated that the longitudinal space  123  can be within a range between any of the above minimum and maximum values. Control of the longitudinal space between adjacent shaped abrasive particles may facilitate improved grinding performance of the abrasive article. 
     In accordance with an embodiment, the shaped abrasive particles may be placed in a predetermined distribution, wherein a particular relationship exists between the lateral space  121  and longitudinal space  123 . For example, in one embodiment the lateral space  121  can be greater than the longitudinal space  123 . Still, in another non-limiting embodiment, the longitudinal space  123  may be greater than the lateral space  121 . Still, in yet another embodiment, the shaped abrasive particles may be placed on the backing such that the lateral space  121  and longitudinal space  123  are essentially the same relative to each other. Control of the relative relationship between the longitudinal space and lateral space may facilitate improved grinding performance. 
     As further illustrated, a longitudinal space  124  may exist between the shaped abrasive particles  104  and  105 . Moreover, the predetermined distribution may be formed such that a particular relationship can exist between the longitudinal space  123  and longitudinal space  124 . For example, the longitudinal space  123  can be different than the longitudinal space  124 . Alternatively, the longitudinal space  123  can be essentially the same at the longitudinal space  124 . Control of the relative difference between longitudinal spaces of different abrasive particles may facilitate improved grinding performance of the abrasive article. 
     Furthermore, the predetermined distribution of shaped abrasive particles on the abrasive article  100  can be such that the lateral space  121  can have a particular relationship relative to the lateral space  122 . For example, in one embodiment the lateral space  121  can be essentially the same as the lateral space  122 . Alternatively, the predetermined distribution of shaped abrasive particles on the abrasive article  100  can be controlled such that the lateral space  121  is different than the lateral space  122 . Control of the relative difference between lateral spaces of different abrasive particles may facilitate improved grinding performance of the abrasive article. 
       FIG.  1 B  includes a side view illustration of a portion of an abrasive article in accordance with an embodiment. As illustrated, the abrasive article  100  can include a shaped abrasive particle  102  overlying the backing  101  and a shaped abrasive particle  104  spaced apart from the shaped abrasive particle  102  overlying the backing  101 . In accordance with an embodiment, the shaped abrasive particle  102  can be coupled to the backing  101  via the adhesive layer  151 . Furthermore or alternatively, the shaped abrasive particle  102  can be coupled to the backing  101  via the adhesive layer  152 . It will be appreciated that any of the shaped abrasive particles described herein may be coupled to the backing  101  via one or more adhesive layers as described herein. 
     In accordance with an embodiment, the abrasive article  100  can include an adhesive layer  151  overlying the backing. In accordance with one embodiment, the adhesive layer  151  can include a make coat. The make coat can be overlying the surface of the backing  101  and surrounding at least a portion of the shaped abrasive particles  102  and  104 . Abrasive articles of the embodiments herein can further include an adhesive layer  152  overlying the adhesive layer  151  and the backing  101  and surrounding at least a portion of the shaped abrasive particles  102  and  104 . The adhesive layer  152  may be a size coat in particular instances. 
     A polymer formulation may be used to form any of a variety of the adhesive layers  151  or  152  of the abrasive article, which can include but not limited to, a frontfill, a pre-size coat, a make coat, a size coat, and/or a supersize coat. When used to form the frontfill, the polymer formulation generally includes a polymer resin, fibrillated fibers (preferably in the form of pulp), filler material, and other optional additives. Suitable formulations for some frontfill embodiments can include material such as a phenolic resin, wollastonite filler, defoamer, surfactant, a fibrillated fiber, and a balance of water. Suitable polymeric resin materials include curable resins selected from thermally curable resins including phenolic resins, urea/formaldehyde resins, phenolic/latex resins, as well as combinations of such resins. Other suitable polymeric resin materials may also include radiation curable resins, such as those resins curable using electron beam, UV radiation, or visible light, such as epoxy resins, acrylated oligomers of acrylated epoxy resins, polyester resins, acrylated urethanes and polyester acrylates and acrylated monomers including monoacrylated, multiacrylated monomers. The formulation can also comprise a nonreactive thermoplastic resin binder which can enhance the self-sharpening characteristics of the deposited abrasive composites by enhancing the erodability. Examples of such thermoplastic resin include polypropylene glycol, polyethylene glycol, and polyoxypropylene-polyoxyethene block copolymer, etc. Use of a frontfill on the backing can improve the uniformity of the surface, for suitable application of the make coat and improved application and orientation of shaped abrasive particles in a predetermined orientation. 
     Either of the adhesive layers  151  and  152  can be applied to the surface of the backing  101  in a single process, or alternatively, the shaped abrasive particles  102  and  104  can be combined with a material of one of the adhesive layers  151  or  152  and applied as a mixture to the surface of the backing  101 . Suitable materials of the adhesive layer  151  for use as a make coat can include organic materials, particularly polymeric materials, including for example, polyesters, epoxy resins, polyurethanes, polyamides, polyacrylates, polymethacrylates, poly vinyl chlorides, polyethylene, polysiloxane, silicones, cellulose acetates, nitrocellulose, natural rubber, starch, shellac, and mixtures thereof. In one embodiment, the adhesive layer  151  can include a polyester resin. The coated backing  101  can then be heated in order to cure the resin and the abrasive particulate material to the substrate. In general, the coated backing  101  can be heated to a temperature of between about 100° C. to less than about 250° C. during this curing process. 
     The adhesive layer  152  may be formed on the abrasive article, which may be in the form of a size coat. In accordance with a particular embodiment, the adhesive layer  152  can be a size coat formed to overlie and bond the shaped abrasive particles  102  and  104  in place relative to the backing  101 . The adhesive layer  152  can include an organic material, may be made essentially of a polymeric material, and notably, can use polyesters, epoxy resins, polyurethanes, polyamides, polyacrylates, polymethacrylates, poly vinyl chlorides, polyethylene, polysiloxane, silicones, cellulose acetates, nitrocellulose, natural rubber, starch, shellac, and mixtures thereof. 
     It will be appreciated, that while not illustrated, the abrasive article can include diluent abrasive particles different than the shaped abrasive particles  104  and  105 . For example, the diluent particles can differ from the shaped abrasive particles  102  and  104  in composition, two-dimensional shape, three-dimensional shape, size, and a combination thereof. For example, the abrasive particles  507  can represent conventional, crushed abrasive grit having random shapes. 
     The abrasive particles  507  may have a median particle size less than the median particle size of the shaped abrasive particles  505 . 
     As further illustrated, the shaped abrasive particle  102  can be oriented in a side orientation relative to the backing  101 , wherein a side surface  171  of the shaped abrasive particle  102  can be in direct contact with the backing  101  or at least a surface of the shaped abrasive particle  102  closest to the upper surface of the backing  101 . In accordance with an embodiment, the shaped abrasive particle  102  can have a vertical orientation defined by a tilt angle (A T1 )  136  between a major surface  172  of the shaped abrasive particle  102  and a major surface  161  of the backing  101 . The tilt angle  136  can be defined as the smallest angle or acute angle between the surface  172  of the shaped abrasive particle  102  and the upper surface  161  of the backing  101 . In accordance with an embodiment, the shaped abrasive particle  102  can be placed in a position having a predetermined vertical orientation. In accordance with an embodiment, the tilt angle  136  can be at least about 2°, such as at least about 5°, at least about 10°, at least about 15°, at least about 20°, at least about 25°, at least about 30°, at least about 35°, at least about 40°, at least about 45°, at least about 50°, at least about 55°, at least about 60°, at least about 70°, at least about 80°, or even at least about 85°. Still, the tilt angle  136  may be not greater than about 90°, such as not greater than about 85°, not greater than about 80°, not greater than about 75°, not greater than about 70°, not greater than about 65°, not greater than about 60°, such as not greater than about 55°, not greater than about 50°, not greater than about 45°, not greater than about 40°, not greater than about 35°, not greater than about 30°, not greater than about 25°, not greater than about 20°, such as not greater than about 15°, not greater than about 10°, or even not greater than about 5°. It will be appreciated that the tilt angle  136  can be within a range between any of the above minimum and maximum degrees. 
     As further illustrated, the abrasive article  100  can include a shaped abrasive particle  104  in a side orientation, wherein a side surface  171  of the shaped abrasive particle  104  is in direct contact with or closest to an upper surface  161  of the backing  101 . In accordance with an embodiment, the shaped abrasive particle  104  can be in a position having a predetermined vertical orientation defined by a second tilt angle (A T2 )  137  defining an angle between a major surface  172  of the shaped abrasive particle  104  and the upper surface  161  of the backing  101 . The tilt angle  137  may be defined as the smallest angle between a major surface  172  of the shaped abrasive particle  104  and an upper surface  161  of the backing  101 . Moreover, the tilt angle  137  can have a value of at least about 2°, such as at least about 5°, at least about 10°, at least about 15°, at least about 20°, at least about 25°, at least about 30°, at least about 35°, at least about 40°, at least about 45°, at least about 50°, at least about 55°, at least about 60°, at least about 70°, at least about 80°, or even at least about 85°. Still, the tilt angle  136  may be not greater than about 90°, such as not greater than about 85°, not greater than about 80°, not greater than about 75°, not greater than about 70°, not greater than about 65°, not greater than about 60°, such as not greater than about 55°, not greater than about 50°, not greater than about 45°, not greater than about 40°, not greater than about 35°, not greater than about 30°, not greater than about 25°, not greater than about 20°, such as not greater than about 15°, not greater than about 10°, or even not greater than about 5°. It will be appreciated that the tilt angle  136  can be within a range between any of the above minimum and maximum degrees. 
     In accordance with an embodiment, the shaped abrasive particle  102  can have a pre-determined vertical orientation that is the same as the predetermined vertical orientation of the shaped abrasive particle  104 . Alternatively, the abrasive article  100  may be formed such that the predetermined vertical orientation of the shaped abrasive particle  102  can be different than the predetermined vertical orientation of the shaped abrasive particle  104 . 
     In accordance with an embodiment, the shaped abrasive particles  102  and  104  may be placed on the backing such that they have different predetermined vertical orientations defined by a vertical orientation difference. The vertical orientation difference can be the absolute value of the difference between the tilt angle  136  and the tilt angle  137 . In accordance with an embodiment, the vertical orientation difference can be at least about 2°, such as at least about 5°, at least about 10°, at least about 15°, at least about 20°, at least about 25°, at least about 30°, at least about 35°, at least about 40°, at least about 45°, at least about 50°, at least about 55°, at least about 60°, at least about 70°, at least about 80°, or even at least about 85°. Still, the vertical orientation difference may be not greater than about 90°, such as not greater than about 85°, not greater than about 80°, not greater than about 75°, not greater than about 70°, not greater than about 65°, not greater than about 60°, such as not greater than about 55°, not greater than about 50°, not greater than about 45°, not greater than about 40°, not greater than about 35°, not greater than about 30°, not greater than about 25°, not greater than about 20°, such as not greater than about 15°, not greater than about 10°, or even not greater than about 5°. It will be appreciated that the vertical orientation difference can be within a range between any of the above minimum and maximum degrees. Control of the vertical orientation difference between shaped abrasive particles of the abrasive article  100  may facilitate improved grinding performance. 
     As further illustrated, the shaped abrasive particles can be placed on the backing to have a predetermined tip height. For example, the predetermined tip height (h T1 )  138  of the shaped abrasive particle  102  can be the greatest distance between an upper surface of the backing  161  and an uppermost surface  143  of the shaped abrasive particle  102 . In particular, the predetermined tip height  138  of the shaped abrasive particle  102  can define the greatest distance above the upper surface of the backing  161  that the shaped abrasive particle  102  extends. As further illustrated, the shaped abrasive particle  104  can have a predetermined tip height (h T2 )  139  defined as the distance between the upper surface  161  of the backing  101  and an uppermost surface  144  of the shaped abrasive particle  104 . Measurements may be evaluated via X-ray, confocal microscopy CT, micromeasure, white-light interferometry, and a combination thereof. 
     In accordance with an embodiment, the shaped abrasive particle  102  can be placed on the backing  101  to have a predetermined tip height  138  that can be different that than predetermined tip height  139  of the shaped abrasive particle  104 . Notably, the difference in the predetermined tip height (Δh T ) can be defined as the difference between the average tip height  138  and average tip height  139 . In accordance with an embodiment, the difference in the predetermined tip height can be at least about 0.01(w), wherein (w) is the width of the shaped abrasive particle as described herein. In other instances, the tip height difference can be at least about 0.05(w), at least about 0.1(w), at least about 0.2(w), at least about 0.4(w), at least about 0.5(w), at least about 0.6(w), at least about 0.7(w), or even at least about 0.8(w). Still, in one non-limiting embodiment, the tip height difference can be not greater than about 2(w). It will be appreciated that the difference in tip height can be in a range between any of the minimum and maximum values noted above. Control of the average tip height and more particularly the difference in average tip height, between shaped abrasive particles of the abrasive article  100  can facilitate improved grinding performance. 
     While reference herein is made to shaped abrasive particles having a difference in average tip height, it will be appreciated that the shaped abrasive particles of the abrasive articles may have a same average tip height such that there is essentially no difference between the average tip height between the shaped abrasive particles. For example, as described herein, shaped abrasive particles of a group may be positioned on the abrasive article such that the vertical tip height of each of the shaped abrasive particles of the group is substantially the same. 
       FIG.  1 C  includes a cross-sectional illustration of a portion of an abrasive article in accordance with an embodiment. As illustrated, the shaped abrasive particles  102  and  104  can be oriented in a flat orientation relative to the backing  101 , wherein at least a portion of a major surface  174 , and particular the major surface having the largest surface area (i.e., the bottom surface  174  opposite the upper major surface  172 ), of the shaped abrasive particles  102  and  104  can be in direct contact with the backing  101 . Alternatively, in a flat orientation, a portion of the major surface  174  may not be in direct contact with the backing  101 , but may be the surface of the shaped abrasive particle closest to the upper surface  161  of the backing  101 . 
       FIG.  1 D  includes a cross-sectional illustration of a portion of an abrasive article in accordance with an embodiment. As illustrated, the shaped abrasive particles  102  and  104  can be oriented in an inverted orientation relative to the backing  101 , wherein at least a portion of a major surface  172  (i.e., the upper major surface  172 ) of the shaped abrasive particles  102  and  104  can be in direct contact with the backing  101 . Alternatively, in an inverted orientation, a portion of the major surface  172  may not be in direct contact with the backing  101 , but may be the surface of the shaped abrasive particle closest to the upper surface  161  of the backing  101 . 
       FIG.  2 A  includes a top view illustration of a portion of an abrasive article including shaped abrasive particles in accordance with an embodiment. As illustrated, the abrasive article can include a shaped abrasive particle  102  overlying the backing  101  in a first position having a first rotational orientation relative to a lateral axis  181  defining the width of the backing  101  and perpendicular to a longitudinal axis  181 . In particular, the shaped abrasive particle  102  can have a predetermined rotational orientation defined by a first rotational angle between a lateral plane  184  parallel to the lateral axis  181  and a dimension of the shaped abrasive particle  102 . Notably, reference herein to a dimension can be reference to a bisecting axis  231  of the shaped abrasive particle extending through a center point  221  of the shaped abrasive particle  102  along a surface (e.g., a side or an edge) connected to (directly or indirectly) the backing  101 . Accordingly, in the context of a shaped abrasive particle positioned in a side orientation, (see,  FIG.  1 B ), the bisecting axis  231  extends through a center point  221  and in the direction of the width (w) of a side  171  closest to the surface  181  of the backing  101 . Moreover, the predetermined rotational orientation can be defined as the smallest angle  201  with the lateral plane  184  extending through the center point  221 . As illustrated in  FIG.  2 A , the shaped abrasive particle  102  can have a predetermined rotational angle defined as the smallest angle between a bisecting axis  231  and the lateral plane  184 . In accordance with an embodiment, the rotational angle  201  can be 0°. In other embodiments, the rotational angle can be greater, such as at least about 2°, at least about 5°, at least about 10°, at least about 15°, at least about 20°, at least about 25°, at least about 30°, at least about 35°, at least about 40°, at least about 45°, at least about 50°, at least about 55°, at least about 60°, at least about 70°, at least about 80°, or even at least about 85°. Still, the predetermined rotational orientation as defined by the rotational angle  201  may be not greater than about 90°, such as not greater than about 85°, not greater than about 80°, not greater than about 75°, not greater than about 70°, not greater than about 65°, not greater than about 60°, such as not greater than about 55°, not greater than about 50°, not greater than about 45°, not greater than about 40°, not greater than about 35°, not greater than about 30°, not greater than about 25°, not greater than about 20°, such as not greater than about 15°, not greater than about 10°, or even not greater than about 5°. It will be appreciated that the predetermined rotational orientation can be within a range between any of the above minimum and maximum degrees. 
     As further illustrated in  FIG.  2 A , the shaped abrasive particle  103  can be at a position  113  overlying the backing  101  and having a predetermined rotational orientation. Notably, the predetermined rotational orientation of the shaped abrasive particle  103  can characterized as the smallest angle between the lateral plane  184  parallel to the lateral axis  181  and a dimension defined by a bisecting axis  232  of the shaped abrasive particle  103  extending through a center point  222  of the shaped abrasive particle  102  in the direction of the width (w) of a side closest to the surface  181  of the backing  101 . In accordance with an embodiment, the rotational angle  208  can be 0°. In other embodiments, the rotational angle  208  can be greater, such as at least about 2°, at least about 5°, at least about 10°, at least about 15°, at least about 20°, at least about 25°, at least about 30°, at least about 35°, at least about 40°, at least about 45°, at least about 50°, at least about 55°, at least about 60°, at least about 70°, at least about 80°, or even at least about 85°. Still, the predetermined rotational orientation as defined by the rotational angle  208  may be not greater than about 90°, such as not greater than about 85°, not greater than about 80°, not greater than about 75°, not greater than about 70°, not greater than about 65°, not greater than about 60°, such as not greater than about 55°, not greater than about 50°, not greater than about 45°, not greater than about 40°, not greater than about 35°, not greater than about 30°, not greater than about 25°, not greater than about 20°, such as not greater than about 15°, not greater than about 10°, or even not greater than about 5°. It will be appreciated that the predetermined rotational orientation can be within a range between any of the above minimum and maximum degrees. 
     In accordance with an embodiment, the shaped abrasive particle  102  can have a predetermined rotational orientation as defined by the rotational angle  201  that is different that the predetermined rotational orientation of the shaped abrasive particle  103  as defined by the rotational angle  208 . In particular, the difference between the rotational angle  201  and rotational angle  208  between the shaped abrasive particles  102  and  103  can define a predetermined rotational orientation difference. In particular instances, the predetermined rotational orientation difference can be 0°. In other instances, the predetermined rotation orientation difference between any two shaped abrasive particles can be greater, such as at least about 1°, at least about 3°, at least about 5°, at least about 10°, at least about 15°, at least about 20°, at least about 25°, at least about 30°, at least about 35°, at least about 40°, at least about 45°, at least about 50°, at least about 55°, at least about 60°, at least about 70°, at least about 80°, or even at least about 85°. Still, the predetermined rotational orientation difference between any two shaped abrasive particles may be not greater than about 90°, such as not greater than about 85°, not greater than about 80°, not greater than about 75°, not greater than about 70°, not greater than about 65°, not greater than about 60°, such as not greater than about 55°, not greater than about 50°, not greater than about 45°, not greater than about 40°, not greater than about 35°, not greater than about 30°, not greater than about 25°, not greater than about 20°, such as not greater than about 15°, not greater than about 10°, or even not greater than about 5°. It will be appreciated that the predetermined rotational orientation difference can be within a range between any of the above minimum and maximum values. 
       FIG.  2 B  includes a perspective view illustration of a portion of an abrasive article including a shaped abrasive particle in accordance with an embodiment. As illustrated, the abrasive article can include a shaped abrasive particle  102  overlying the backing  101  in a first position  112  having a first rotational orientation relative to a lateral axis  181  defining the width of the backing  101 . Certain aspects of a shaped abrasive particles predetermined orientation characteristics may be described by relation to a x, y, z three-dimensional axis as illustrated. For example, the predetermined longitudinal orientation of the shaped abrasive particle  102  may be defined by the position of the shaped abrasive particle on the y-axis, which extends parallel to the longitudinal axis  180  of the backing  101 . Moreover, the predetermined lateral orientation of the shaped abrasive particle  102  may be defined by the position of the shaped abrasive particle on the x-axis, which extends parallel to the lateral axis  181  of the backing  101 . Furthermore, the predetermined rotational orientation of the shaped abrasive particle  102  may be defined as the rotational angle  102  between the x-axis, which corresponds to an axis or plane parallel to the lateral axis  181  and the bisecting axis  231  of the shaped abrasive particle  102  extending through the center point  221  of the side  171  shaped abrasive particle  102  connected to (directly or indirectly) the backing  101 . As generally illustrated, the shaped abrasive particle  102  can further have a predetermined vertical orientation and predetermined tip height as described herein. Notably, the controlled placement of a plurality of shaped abrasive particles that facilitates control of the predetermined orientation characteristics described herein is a highly involved process, which has not previously been contemplated or deployed in the industry. 
     For simplicity of explanation, the embodiments herein reference certain features relative to a plane defined by X, Y, and Z directions. However, it is appreciated and contemplated that abrasive articles can have other shapes (e.g., coated abrasive belts defining an ellipsoidal or looped geometry or even coated abrasive sanding disks having an annular-shaped backing). The description of the features herein is not limited to planar configurations of abrasive articles and the features described herein are applicable to abrasive articles of any geometry. In such instances wherein the backing has a circular geometry, the longitudinal axis and lateral axis can be two diameters extending through the center point of the backing and having an orthogonal relationship relative to each other. 
       FIG.  3 A  includes a top view illustration of a portion of an abrasive article  300  in accordance with an embodiment. As illustrated, the abrasive article  300  can include a first group  301  of shaped abrasive particles, including shaped abrasive particles  311 ,  312 ,  313 , and  314  ( 311 - 314 ). As used herein, a group can refer to a plurality of shaped abrasive particles have at least one (or a combination of) predetermined orientation characteristic that is the same for each of the shaped abrasive particles. Exemplary predetermined orientation characteristics can include a predetermined rotational orientation, a predetermined lateral orientation, a predetermined longitudinal orientation, a predetermined vertical orientation, and a predetermined tip height. For example, the first group  301  of shaped abrasive particles includes a plurality of shaped abrasive particles having substantially the same predetermined rotational orientation with respect to each other. As further illustrated, the abrasive article  300  can include another group  303  including a plurality of shaped abrasive particles, including for example shaped abrasive particles  321 ,  322 ,  323 , and  324  ( 321 - 324 ). As illustrated, the group  303  can include a plurality of shaped abrasive particles having a same predetermined rotational orientation. Furthermore, at least a portion of the shaped abrasive particles of the group  303  can have a same predetermined lateral orientation with respect to each other (e.g., shaped abrasive particles  321  and  322  and shaped abrasive particles  323  and  324 ). Moreover, at least a portion of the shaped abrasive particles of the group  303  can have a same predetermined longitudinal orientation with respect to each other (e.g., shaped abrasive particles  321  and  324  and shaped abrasive particles  322  and  323 ). 
     As further illustrated, the abrasive article can include a group  305 . The group  305  can include a plurality of shaped abrasive particles, including shaped abrasive particles  331 ,  332 , and  333  ( 331 - 333 ) having at least one common predetermined orientation characteristic. As illustrated in the embodiment of  FIG.  3 A , the plurality of shaped abrasive particles within the group  305  can have a same predetermined rotational orientation with respect to each other. Furthermore, at least a portion of the plurality of shaped abrasive particles of the group  305  can have a same predetermined lateral orientation with respect to each other (e.g., shaped abrasive particles  332  and  333 ). In addition, at least a portion of the plurality of shaped abrasive particles of the group  305  can have a same predetermined longitudinal orientation with respect to each other. Utilization of groups of shaped abrasive particles, and particularly, a combination of groups of shaped abrasive particles having the features described herein may facilitate improved performance of the abrasive article. 
     As further illustrated, the abrasive article  300  can include groups  301 ,  303 , and  305 , which may be separated by channel regions  307  and  308  extending between the groups  301 ,  303 ,  305 . In particular instances, the channel regions can be regions on the abrasive article that can be substantially free of shaped abrasive particles. Moreover, the channel regions  307  and  308  may be configured to move liquid between the groups  301 ,  303 , and  305 , which may improve swarf removal and grinding performance of the abrasive article. The channel regions  307  and  308  can be predetermined regions on the surface of the shaped abrasive article. The channel regions  307  and  308  may define dedicated regions between groups  301 ,  303 , and  305  that are different, and more particularly, greater in width and/or length, than the longitudinal space or lateral space between adjacent shaped abrasive particles in the groups  301 ,  303 , and  305 . 
     The channel regions  307  and  308  can extend along a direction that is parallel or perpendicular to the longitudinal axis  180  or parallel or perpendicular to the lateral axis  181  of the backing  101 . In particular instances, the channel regions  307  and  308  can have axes,  351  and  352  respectively, extending along a center of the channel regions  307  and  308  and along a longitudinal dimension of the channel regions  307  and  308  can have a predetermined angle relative to the longitudinal axis  380  of the backing  101 . Moreover, the axes  351  and  352  of the channel regions  307  and  308  may form a predetermined angle relative to the lateral axis  181  of the backing  101 . Controlled orientation of the channel regions may facilitate improved performance of the abrasive article. 
     Furthermore, the channel regions  307  and  308  may be formed such that they have a predetermined orientation relative to the direction of grinding  350 . For example, the channel regions  307  and  308  can extend along a direction that is parallel or perpendicular to the direction of grinding  350 . In particular instances, the channel regions  307  and  308  can have axes,  351  and  352  respectively, extending along a center of the channel regions  307  and  308  and along a longitudinal dimension of the channel regions  307  and  308  can have a predetermined angle relative to the direction of grinding  350 . Controlled orientation of the channel regions may facilitate improved performance of the abrasive article. 
     For at least one embodiment, as illustrated the group  301  can include a plurality of shaped abrasive particles, wherein at least a portion of the plurality of shaped abrasive particles in the group  301  can define a pattern  315 . As illustrated, the plurality of shaped abrasive particles  311 - 314  can be arranged with respect to each other in a predetermined distribution that further defines a two-dimensional array, such as in the form of a quadrilateral, as viewed top-down. An array is a pattern having short range order defined by a unit arrangement of shaped abrasive particles and further having long range order including regular and repetitive units linked together. It will be appreciated that other two-dimensional arrays can be formed, including other polygonal shapes, ellipsis, ornamental indicia, product indicia, or other designs. As further illustrated, the group  303  can include the plurality of shaped abrasive particles  321 - 324  that can also be arranged in a pattern  325  defining a quadrilateral two-dimensional array. Furthermore, the group  305  can include a plurality of shaped abrasive particles  331 - 334  which can be arranged with respect to each other to define a predetermined distribution in the form of a triangular pattern  335 . 
     In accordance with an embodiment, the plurality of shaped abrasive particles of a group  301  may define a pattern that is different than the shaped abrasive particles of another group (e.g., group  303  or  305 ). For example, the shaped abrasive particles of the group  301  may define a pattern  315  that is different than the pattern  335  of the group  305  with respect to the orientation on the backing  101 . Moreover, the shaped abrasive particles of the group  301  may define a pattern  315  that has a first orientation relative to the direction of grinding  350  as compared to the orientation of the pattern of a second group (e.g.,  303  or  305 ) relative to the direction of grinding  350 . 
     Notably, any one of the groups ( 301 ,  303 , or  305 ) of the shaped abrasive particles can have a pattern defining one or more vectors (e.g.,  361  or  362  of group  305 ) that can have a particular orientation relative to the direction of grinding. In particular, the shaped abrasive particles of a group can have a predetermined orientation characteristic that define a pattern of the group, which may further define one or more vectors of the pattern. In an exemplary embodiment, the vectors  361  and  362  of the pattern  335  can be controlled to form a predetermined angle relative to the grinding direction  350 . The vectors  361  and  362  may have various orientations including for example, a parallel orientation, perpendicular orientation, or even a non-orthogonal or non-parallel orientation (i.e., angled to define an acute angle or obtuse angle) relative to the grinding direction  350 . 
     In accordance with an embodiment, the plurality of shaped abrasive particles of the first group  301  can have at least one predetermined orientation characteristic that is different than the plurality of shaped abrasive particles in another group (e.g.  303  or  305 ). For example, at least a portion of the shaped abrasive particles of the group  301  can have a predetermined rotational orientation that is different than the predetermined rotational orientation of at least a portion of the shaped abrasive particles of the group  303 . Still, in one particular aspect, all of the shaped abrasive particles of the group  301  can have a predetermined rotational orientation that is different than the predetermined rotational orientation of all of the shaped abrasive particles of the group  303 . 
     In accordance with another embodiment, at least a portion of the shaped abrasive particles of the group  301  can have a predetermined lateral orientation that is different than the predetermined lateral orientation of at least a portion of the shaped abrasive particles of the group  303 . For yet another embodiment, all of the shaped abrasive particles of the group  301  can have a predetermined lateral orientation that is different than the predetermined lateral orientation of all of the shaped abrasive particles of the group  303 . 
     Moreover, in another embodiment, at least a portion of the shaped abrasive particles of the group  301  can have a predetermined longitudinal orientation that may be different than the predetermined longitudinal orientation of at least a portion of the shaped abrasive particles of the group  303 . For another embodiment, all of the shaped abrasive particles of the group  301  can have a predetermined longitudinal orientation that may be different than the predetermined longitudinal orientation of all of the shaped abrasive particles of the group  303 . 
     Furthermore, at least a portion of the shaped abrasive particles of the group  301  can have a predetermined vertical orientation that is different than the predetermined vertical orientation of at least a portion of the shaped abrasive particles of the group  303 . Still, for one aspect, all of the shaped abrasive particles of the group  301  can have a predetermined vertical orientation that is different than the predetermined vertical orientation of all of the shaped abrasive particles of the group  303 . 
     Moreover, in one embodiment, at least a portion of the shaped abrasive particles of the group  301  may have a predetermined tip height that is different than the predetermined tip height of at least a portion of the shaped abrasive particles of the group  303 . In yet another particular embodiment, all of the shaped abrasive particles of the group  301  may have a predetermined tip height that is different than the predetermined tip height of all of the shaped abrasive particles of the group  303 . 
     It will be appreciated that any number of groups may be included in the abrasive article creating various regions on the abrasive article having predetermined orientation characteristics. Moreover, each of the groups can be different from each other as described in the foregoing for the groups  301  and  303 . 
     As described in one or more embodiments herein, the shaped abrasive particles can be arranged in a predetermined distribution defined by predetermined positions on the backing. More notably, the predetermined distribution can define a non-shadowing arrangement between two or more shaped abrasive particles. For example, in one particular embodiment, the abrasive article can include a first shaped abrasive particle in a first predetermined position and a second shaped abrasive particle in a second predetermined position, such that the first and second shaped abrasive particle define a non-shadowing arrangement relative to each other. A non-shadowing arrangement can be defined by an arrangement of the shaped abrasive particles such that they are configured to make initial contact with the workpiece at separate locations on the workpiece and limiting or avoiding an initial overlap in the location of initial material removal on the workpiece. A non-shadowing arrangement can facilitate improved grinding performance. In one particular embodiment, the first shaped abrasive particle can be part of a group defined by a plurality of shaped abrasive particles, and the second shaped abrasive particle can be part of a second group defined by a plurality of shaped abrasive particles. The first group can define a first row on the backing and the second group can define a second row on the backing, and each of the shaped abrasive particles of the second group can be staggered relative to each of the shaped abrasive particles of the first group, thus defining a particular non-shadowing arrangement. 
       FIG.  3 B  includes a perspective view illustration of a portion of an abrasive article including shaped abrasive particles having predetermined orientation characteristics relative to a grinding direction in accordance with an embodiment. In one embodiment, the abrasive article can include a shaped abrasive particle  102  having a predetermined orientation relative to another shaped abrasive particle  103  and/or relative to a grinding direction  385 . Control of one or a combination of predetermined orientation characteristics relative to the grinding direction  385  may facilitate improved grinding performance of the abrasive article. The grinding direction  385  may be an intended direction of movement of the abrasive article relative to a workpiece in a material removal operation. In particular instances, the grinding direction  385  may be related to the dimensions of the backing  101 . For example, in one embodiment, the grinding direction  385  may be substantially perpendicular to the lateral axis  181  of the backing and substantially parallel to the longitudinal axis  180  of the backing  101 . The predetermined orientation characteristics of the shaped abrasive particle  102  may define an initial contact surface of the shaped abrasive particle  102  with a workpiece. For example, the shaped abrasive particle  102  can have a major surfaces  363  and  364 , and side surfaces  365  and  366  extending between the major surfaces  363  and  364 . The predetermined orientation characteristics of the shaped abrasive particle  102  can position the particle such that the major surface  363  is configured to make initial contact with a workpiece before the other surfaces of the shaped abrasive particle  102 . Such an orientation may be considered a frontal orientation relative to the grinding direction  385 . More particularly, the shaped abrasive particle  102  can have a bisecting axis  231  having a particular orientation relative to the grinding direction. For example, as illustrated, the vector of the grinding direction  385  and the bisecting axis  231  are substantially perpendicular to each other. It will be appreciated that just as any range of predetermined rotational orientations are contemplated for a shaped abrasive particle, any range of orientations of the shaped abrasive particles relative to the grinding direction  385  are contemplated and can be utilized. 
     The shaped abrasive particle  103  can have different predetermined orientation characteristics relative to the shaped abrasive particle  102  and the grinding direction  385 . As illustrated, the shaped abrasive particle  103  can include major surfaces  391  and  392 , which can be joined by side surfaces  371  and  372 . Moreover, as illustrated, the shaped abrasive particle  103  can have a bisecting axis  373  forming a particular angle relative to the vector of the grinding direction  385 . As illustrated, the bisecting axis  373  of the shaped abrasive particle  103  can have a substantially parallel orientation with the grinding direction  385  such that the angle between the bisecting axis  373  and the grinding direction  385  is essentially 0 degrees. Accordingly, the predetermined orientation characteristics of the shaped abrasive particle facilitate initial contact of the side surface  372  with a workpiece before any of the other surfaces of the shaped abrasive particle. Such an orientation of the shaped abrasive particle  103  may be considered a sideways orientation relative to the grinding direction  385 . 
     It will be appreciated that the abrasive article can include one or more groups of shaped abrasive particles that can be arranged in a predetermined distribution relative to each other, and more particularly can have distinct predetermined orientation characteristics that define groups of shaped abrasive particles. The groups of shaped abrasive particles, as described herein, can have a predetermined orientation relative to a grinding direction. Moreover, the abrasive articles herein can have one or more groups of shaped abrasive particles, each of the groups having a different predetermined orientation relative to a grinding direction. Utilization of groups of shaped abrasive particles having different predetermined orientations relative to a grinding direction can facilitate improved performance of the abrasive article. 
       FIG.  4    includes a top view illustration of a portion of an abrasive article in accordance with an embodiment. In particular, the abrasive article  400  can include a first group  401  including a plurality of shaped abrasive particles. As illustrated, the shaped abrasive particles can be arranged relative to each other to define a predetermined distribution. More particularly, the predetermined distribution can be in the form of a pattern  423  as viewed top-down, and more particularly defining a triangular shaped two-dimensional array. As further illustrated, the group  401  can be arranged on the abrasive article  400  defining a predetermined macro-shape  431  overlying the backing  101 . In accordance with an embodiment, the macro-shape  431  can have a particular two-dimensional shape as viewed top-down. Some exemplary two-dimensional shapes can include polygons, ellipsoids, numerals, Greek alphabet characters, Latin alphabet characters, Russian alphabet characters, Arabic alphabet characters, Kanji characters, complex shapes, designs, any a combination thereof. In particular instances, the formation of a group having a particular macro-shape may facilitate improved performance of the abrasive article. 
     As further illustrated, the abrasive article  400  can include a group  404  including a plurality of shaped abrasive particles which can be arranged on the surface of the backing  101  to define a predetermined distribution. Notably, the predetermined distribution can include an arrangement of the plurality of the shaped abrasive particles that define a pattern, and more particularly, a generally quadrilateral pattern  424 . As illustrated, the group  404  can define a macro-shape  434  on the surface of the abrasive article  400 . In one embodiment, the macro-shape  434  of the group  404  can have a two-dimensional shape as viewed top down, including for example a polygonal shape, and more particularly, a generally quadrilateral (diamond) shape as viewed top down on the surface of the abrasive article  400 . In the illustrated embodiment of  FIG.  4   , the group  401  can have a macro-shape  431  that is substantially the same as the macro-shape  434  of the group  404 . However, it will be appreciated that in other embodiments, various different groups can be used on the surface of the abrasive article, and more particularly wherein each of the different groups has a different macro-shape. 
     As further illustrated, the abrasive article can include groups  401 ,  402 ,  403 , and  404  which can be separated by channel regions  422  and  421  extending between the groups  401 - 404 . In particular instances, the channel region can be substantially free of shaped abrasive particles. Moreover, the channel regions  421  and  422  may be configured to move liquid between the groups  401 - 404  and further improve swarf removal and grinding performance of the abrasive article. Furthermore, in a certain embodiment, the abrasive article  400  can include channel regions  421  and  422  extending between groups  401 - 404 , wherein the channel regions  421  and  422  can be patterned on the surface of the abrasive article  400 . In particular instances, the channel regions  421  and  422  can represent a regular and repeating array of features extending along a surface of the abrasive article. 
       FIG.  5    includes a top view of a portion of an abrasive article in accordance with an embodiment. Notably, the abrasive article  500  can include shaped abrasive particles  501  overlying, and more particularly, coupled to the backing  101 . In at least one embodiment, the abrasive articles of the embodiments herein, can include a row  511  of shaped abrasive particles. The row  511  can include a group of shaped abrasive particles  501 , wherein each of the shaped abrasive particles  501  within the row  511  can have a same predetermined lateral orientation with respect to each other. In particular, as illustrated, each of the shaped abrasive particles  501  of the row  511  can have a same predetermined lateral orientation with respect to the lateral axis  551 . Moreover, each of the shaped abrasive particles  501  of the first row  511  may be part of a group and thus having at least one other predetermined orientation characteristic that is the same relative to each other. For example, each of the shaped abrasive particles  501  of the row  511  can be part of a group having a same predetermined vertical orientation, and may define a vertical company. In at least another embodiment, each of the shaped abrasive particles  501  of the row  511  can be part of a group having a same predetermined rotational orientation, and may define a rotational company. Moreover, each of the shaped abrasive particles  501  of the row  511  can be part of a group having a same predetermined tip height with respect to each other, and may define a tip height company. Moreover, as illustrated, the abrasive article  500  can include a plurality of groups in the orientation of the row  511 , which may be spaced apart from each other along the longitudinal axis  180 , and more particularly, separated from each other by other intervening rows, including for example, rows  521 ,  531 , and  541 . 
     As further illustrated in  FIG.  5   , the abrasive article  500  can include shaped abrasive particles  502  which may be arranged relative to each other to define a row  521 . The row  521  of shaped abrasive particles  502  can include any of the features described in accordance with the row  511 . Notably, the shaped abrasive particles  502  of the row  521  may have a same predetermined lateral orientation with respect to each other. Furthermore, the shaped abrasive particles  502  of the row  521  may have at least one predetermined orientation characteristic that is different than a predetermined orientation characteristic of any one the shaped abrasive particles  501  of the row  511 . For example, as illustrated, each of the shaped abrasive particles  502  of the row  521  can have a same predetermined rotational orientation that is different than the predetermined rotational orientation of each of the shaped abrasive particles  501  of the row  511 . 
     In accordance with another embodiment, the abrasive article  500  can include shaped abrasive particles  503  arranged relative to each other and defining a row  531 . The row  531  can have any of the characteristics as described in accordance with other embodiments, particularly with respect to row  511  or row  521 . Furthermore, as illustrated, each of the shaped abrasive particles  503  within the row  531  can have at least one predetermined orientation characteristic that is the same with respect to each other. Moreover, each of the shaped abrasive particles  503  within the row  531  can have at least one predetermined orientation characteristic that is different than a predetermined orientation characteristic relative to any one of the shaped abrasive particles  501  of row  511  or the shaped abrasive particles  502  of row  521 . Notably, as illustrated, each of the shaped abrasive particles  503  of row  531  can have a same predetermined rotational orientation that is different with respect to the predetermined rotational orientation of the shaped abrasive particles  501  and row  511  and the predetermined rotational orientation of the shaped abrasive particles  502  and row  521 . 
     As further illustrated, the abrasive article  500  can include shaped abrasive particles  504  arranged relative to each other and defining a row  541  on the surface of the abrasive article  500 . As illustrated, each of the shaped abrasive particles  504  and the row  541  can have at least one of the same predetermined orientation characteristic. Furthermore, in accordance with an embodiment, each of the shaped abrasive particles  504  can have at least one of the same predetermined orientation characteristic, such as a predetermined rotational orientation that is different than the predetermined rotational orientation of any of the shaped abrasive particles  501  of row  511 , the shaped abrasive particles  502  of the row  521 , and the shaped abrasive particles  503  of the row  531 . 
     As further illustrated, the abrasive article  500  can include a column  561  of shaped abrasive particles including at least one shaped abrasive particle from each of the rows  511 ,  521 ,  531 , and  541 . Notably, each of the shaped abrasive particles within the column  561  can share at least one predetermined orientation characteristic, and more particularly at least a predetermined longitudinal orientation with respect to each other. As such, each of the shaped abrasive particles within the column  561  can have a predetermined longitudinal orientation with respect to each other and a longitudinal plane  562 . In certain instances, the arrangement of shaped abrasive particles in groups, which can include the arrangement of shaped abrasive particles in rows, columns, vertical companies, rotational companies, and tip height companies can facilitate improved performance of the abrasive article. 
       FIG.  6    includes a top view illustration of a portion of an abrasive article in accordance with an embodiment. Notably, the abrasive article  600  can include shaped abrasive particles  601  that can be arranged relative to each other to define a column  621  extending along a longitudinal plane  651  and having at least one of the same predetermined orientation characteristics relative to each other. For example, each of the shaped abrasive particles  601  of the company  621  can have a same predetermined longitudinal orientation with respect to each other and the longitudinal axis  651 . It will be appreciated that the shaped abrasive particles  601  of the column  621  can share at least one other predetermined orientation characteristic, including for example a same predetermined rotational orientation with respect to each other. 
     As further illustrated, the abrasive article  600  can include shaped abrasive particles  602  arranged relative to each other on the backing  101  and defining a column  622  with respect to each other along a longitudinal plane  652 . It will be appreciated that the shaped abrasive particles  602  of the column  622  can share at least one other predetermined orientation characteristic, including for example a same predetermined rotational orientation with respect to each other. Still, each of the shaped abrasive particles  602  of the column  622  can define a group having at least one predetermined orientation characteristic different than at least one predetermined orientation characteristic of at least one of the shaped abrasive particles  621  of the column  621 . More particularly, each of the shaped abrasive particles  602  of the column  622  can define a group having a combination of predetermined orientation characteristics different than a combination of predetermined orientation characteristics of the shaped abrasive particles  601  of the column  621 . 
     Furthermore, as illustrated, the abrasive article  600  can include shaped abrasive particles  603  having a same predetermined longitudinal orientation with respect to each other along the a longitudinal plane  653  on the backing  101  and defining a column  623 . Still, each of the shaped abrasive particles  603  of the column  623  can define a group having at least one predetermined orientation characteristic different than at least one predetermined orientation characteristic of at least one of the shaped abrasive particles  621  of the column  621  and the shaped abrasive particles  602  of the column  622 . More particularly, each of the shaped abrasive particles  603  of the column  623  can define a group having a combination of predetermined orientation characteristics different than a combination of predetermined orientation characteristics of the shaped abrasive particles  601  of the column  621  and the shaped abrasive particles  602  of the column  622 . 
       FIG.  7 A  includes a top down view of a portion of an abrasive article in accordance with an embodiment. In particular instances, the abrasive articles herein may further include orientation regions that facilitate placement of shaped abrasive particles in the predetermined orientations. The orientation regions can be coupled to the backing  101  of the abrasive article. Alternatively, the orientation regions can be part of an adhesive layer, including for example a make coat or a size coat. In still another embodiment, the orientation regions can be overlying the backing  101  or even more particularly integrated with the backing  101 . 
     As illustrated in  FIG.  7 A , the abrasive article  700  can include shaped abrasive particles  701 ,  702 ,  703 , ( 701 - 703 ) and each of the shaped abrasive particles  701 - 703  can be coupled with a respective orientation region  721 ,  722 , and  723  ( 721 - 723 ). In accordance with an embodiment, the orientation region  721  can be configured to define at least one (or a combination of) predetermined orientation characteristic of the shaped abrasive particle  701 . For example, the orientation region  721  can be configured to define a predetermined rotational orientation, a predetermined lateral orientation, a predetermined longitudinal orientation, a predetermined vertical orientation, a predetermined tip height, and a combination thereof with respect to the shaped abrasive particle  701 . Furthermore, in a particular embodiment, the orientation regions  721 ,  722  and  723  can be associated with a plurality of shaped abrasive particles  701 - 703  and can define a group  791 . 
     According to one embodiment, the orientation regions  721 - 723  can be associated with an alignment structure, and more particularly, part of an alignment structure (e.g., discrete contact regions) as described in more detail herein. The orientation regions  721 - 723  can be integrated within any of the components of the abrasive article, including for example, the backing  101  or adhesive layers, and thus may be considered contact regions as described in more detail herein. Alternatively, the orientation regions  721 - 723  can be associated with an alignment structure use in forming the abrasive article, which may be a separate component from the backing and integrated within the abrasive article, and which may not necessarily form a contact region associated with the abrasive article. 
     As further illustrated, the abrasive article  700  can further include shaped abrasive particles  704 ,  705 ,  706  ( 704 - 706 ), wherein each of the shaped abrasive particles  704 - 706  can be associated with an orientation region  724 ,  725 ,  726 , respectively. The orientation regions  724 - 726  can be configured to control at least one predetermined orientation characteristic of the shaped abrasive particles  704 - 706 . Moreover, the orientation regions  724 - 726  can be configured to define a group  792  of shaped abrasive particle  704 - 706 . In accordance with an embodiment, the orientation regions  724 - 726  can be spaced apart from the orientation regions  721 - 723 . More particularly the orientation regions  724 - 726  can be configured to define a group  792  having at least one predetermined orientation characteristic that is different than a predetermined orientation characteristic of the shaped abrasive particles  701 - 703  of the group  791 . 
       FIG.  7 B  includes an illustration of a portion of an abrasive article according to an embodiment. In particular,  FIG.  7 B  includes an illustration of particular embodiments of alignment structures and contact regions that may be utilized and configured to facilitate at least one predetermined orientation characteristic of one or more shaped abrasive particles associated with the alignment structure and contact regions. 
       FIG.  7 B  includes a portion of an abrasive article including a backing  101  a first group  791  of shaped abrasive particles  701  and  702  overlying the backing  101 , a second group  792  of shaped abrasive particles  704  and  705  overlying the backing  101 , a third group  793  of shaped abrasive particles  744  and  745  overlying the backing  101 , and a fourth group  794  of shaped abrasive particles  746  and  747  overlying the backing  101 . It will be appreciated that while various and multiple different groups  791 ,  792 ,  793 , and  794  are illustrated, the illustration is in no way limiting and the abrasive articles of the embodiments herein can include any number and arrangement of groups. 
     The abrasive article of  FIG.  7 B  further includes an alignment structure  761  having a first contact region  721  and a second contact region  722 . The alignment structure  761  can be used to facilitate placement of the shaped abrasive particles  701  and  702  in desired orientations on the backing and relative to each other. The alignment structure  761  of the embodiments herein can be a permanent part of the abrasive article. For example, the alignment structure  761  can include contact regions  721  and  722 , which can overlie the backing  101 , and in some instances, directly contact the backing  101 . In particular instances, the alignment structure  761  may be integral with the abrasive article, and may overlie the backing, underlie an adhesive layer overlying the backing, or even be integral part of one or more adhesive layers overlying the backing. 
     According to one embodiment, the alignment structure  761  can be configured to deliver and in particular instances, temporarily or permanently hold the shaped abrasive particle  701  at a first position  771 . In particular instances, such as illustrated in  FIG.  7 B , the alignment structure  761  can include a contact region  721 , which can have a particular two-dimensional shape as viewed top down and defined by the width of the contact region (w cr ) and the length of the contact region (l cr ), wherein the length is the longest dimension of the contact region  721 . According to at least one embodiment, the contact region can be formed to have a shape (e.g., a two-dimensional shape), which may facilitate controlled orientation of the shaped abrasive particle  701 . More particularly, the contact region  721  can have a two-dimensional shape configured to control one or more (e.g., at least two of) a particular predetermined orientation characteristic, including for example, a predetermined rotational orientation, a predetermined lateral orientation, and a predetermined longitudinal orientation. 
     In particular instances, the contact regions  721  and  722  can be formed to have controlled two-dimensional shapes that may facilitate a predetermined rotational orientation of the corresponding shaped abrasive particles  701  and  702 . For example, the contact region  721  can have a controlled and predetermined two-dimensional shape configured to determine a predetermined rotational orientation of the shaped abrasive particle  701 . Moreover, the contact region  722  can have a controlled and predetermined two-dimensional shape configured to determine a predetermined rotational orientation of the shaped abrasive particle  702 . 
     As illustrated, the alignment structure can include a plurality of discrete contact regions  721  and  722 , wherein each of the contact regions  721  and  722  can be configured to deliver, and temporarily or permanently hold, one or more shaped abrasive particles. In some instances, the alignment structure can include a web, a fibrous material, a mesh, a solid structure having openings, a belt, a roller, a patterned material, a discontinuous layer of material, a patterned adhesive material, and a combination thereof. 
     The plurality of contact regions  721  and  722  can define at least one of the predetermined rotational orientation of a shaped abrasive particle, a predetermined rotational orientation difference between at least two shaped abrasive particles, the predetermined longitudinal orientation of a shaped abrasive particle, a longitudinal space between two shaped abrasive particles, the predetermined lateral orientation, a lateral space between two shaped abrasive particles, a predetermined vertical orientation, a predetermined vertical orientation difference between two shaped abrasive particles, a predetermined tip height, a predetermined tip height difference between two shaped abrasive particles. In particular instances, as illustrated in  FIG.  7 B , the plurality of discrete contact regions can include a first contact region  721  and a second contact region  722  distinct from the first contact region  721 . While the contact regions  721  and  722  are illustrated as having the same general shape relative to each other, as will become evident in based on further embodiments described herein, the first contact region  721  and second contact region  722  can be formed to have different two-dimensional shapes. Furthermore, while not illustrated, it will be appreciated that alignment structures of the embodiments herein can include first and second contact regions configured to deliver and contain shaped abrasive particles in different predetermined rotational orientations with respect to each other. 
     In one particular embodiment, the contact regions  721  and  722  can have a two-dimensional shape selected from the group consisting of polygons, ellipsoids, numerals, crosses, multi-armed polygons, Greek alphabet characters, Latin alphabet characters, Russian alphabet characters, Arabic alphabet characters, rectangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon, and a combination thereof. Moreover, while the contact regions  721  and  722  are illustrated as having substantially the same two-dimensional shape, it will be appreciated, that in alternative embodiments, the contact regions  721  and  722  can have different two-dimensional shapes. Two-dimensional shapes are the shapes of the contact regions  721  and  722  as viewed in the plane of the length and width of the contact regions, which may be the same plane defined by the upper surface of the backing. 
     Moreover, it will be appreciated that the alignment structure  761  may be a temporary part of the abrasive article. For example, the alignment structure  761  can represent a template or other object that temporarily fixes the shaped abrasive particles at the contact regions, facilitating placement of the shaped abrasive particles in a desired position having one or more predetermined orientation characteristics. After placement of the shaped abrasive particles, the alignment structure may be removed leaving the shaped abrasive particle on the backing in the predetermined positions. 
     According to one particular embodiment, the alignment structure  761  can be a discontinuous layer of material including the plurality of contact regions  721  and  722  that may be made of an adhesive material. In more particular instances, the contact region  721  can be configured to adhere at least one shaped abrasive particle. In other embodiments, the contact region  721  can be formed to adhere more than one shaped abrasive particle. It will be appreciated that according to at least one embodiment, the adhesive material can include an organic material, and more particularly, at least one resin material. 
     Furthermore, the plurality of contact regions  721  and  722  can be arranged on the surface of the backing  101  to define a predetermined distribution of contact regions. The predetermined distribution of contact regions can have any characteristic of predetermined distributions described herein. In particular, the predetermined distribution of contact regions can define a controlled, non-shadow arrangement. The predetermined distribution of contact regions can define and substantially correspond to a same predetermined distribution of shaped abrasive particles on the backing, wherein each contact region can define a position of a shaped abrasive particle. 
     As illustrated, in certain instances, the contact regions  721  and  722  can be spaced apart from each other. In at least one embodiment, the contact regions  721  and  722  can be spaced apart from each other by a distance  731 . The distance  731  between contact regions  721  and  722  is generally the smallest distance between adjacent contact regions  721  and  722  in a direction parallel to the lateral axis  181  or longitudinal axis  180 . 
     In an alternative embodiment, the plurality of discrete contact regions  721  and  722  can be openings in a structure, such as a substrate. For example, each of the contact regions  721  and  722  can be openings in a template that is used to temporarily place the shaped abrasive particles in particular positions on the backing  101 . The plurality of openings can extend partially or entirely through the thickness of the alignment structure. Alternatively, the contact regions  7821  and  722  can be openings in a structure, such as a substrate or layer that is permanently part of the backing and final abrasive article. The openings can have particular cross-sectional shapes that may be complementary to a cross-sectional shape of the shaped abrasive particles to facilitate placement of the shaped abrasive particles in predetermined positions and with one or more predetermined orientation characteristics. 
     Moreover, according to an embodiment, the alignment structure can include a plurality of discrete contact regions separated by non-contact regions, wherein the non-contact regions are regions distinct from the discrete contact regions and may be substantially free of the shaped abrasive particles. In one embodiment, the non-contact regions can define regions configured to be essentially free of adhesive material and separating contract regions  721  and  722 . In one particular embodiment, the non-contact region can define regions configured to be essentially free of shaped abrasive particles. 
     Various methods may be utilized for form an alignment structure and the discrete contact regions, including but not limited to process such as coating, spraying, depositing, printing, etching, masking, removing, molding, casting, stamping, heating, curing, tacking, pinning, fixing, pressing, rolling, stitching, adhering, irradiating, and a combination thereof. In particular instances, wherein the alignment structure is in the form of a discontinuous layer of adhesive material, which can include a plurality of discrete contact regions including an adhesive material spaced apart from each other by non-contact regions, the forming process can include a selective deposition of the adhesive material. 
     As illustrated and noted above,  FIG.  7 B  further includes a second group  792  of shaped abrasive particles  704  and  705  overlying the backing  101 . The second group  792  can be associated with an alignment structure  762 , which can include a first contact region  724  and a second contact region  725 . The alignment structure  762  can be used to facilitate placement of the shaped abrasive particles  704  and  705  in desired orientations on the backing  101  and relative to each other. As noted herein, the alignment structure  762  can have any of the characteristics of alignment structures described herein. It will be appreciated that the alignment structure  762  can be a permanent or temporary part of the final abrasive article. The alignment structure  762  may be integral with the abrasive article, and may overlie the backing  101 , underlie an adhesive layer overlying the backing  101 , or even be integral part of one or more adhesive layers overlying the backing  101 . 
     According to one embodiment, the alignment structure  762  can be configured to deliver and in particular instances, temporarily or permanently hold the shaped abrasive particle  704  at a first position  773 . In particular instances, such as illustrated in  FIG.  7 B , the alignment structure  762  can include a contact region  724 , which can have a particular two-dimensional shape as viewed top down and defined by the width of the contact region (w cr ) and the length of the contact region (l cr ), wherein the length is the longest dimension of the contact region  724 . 
     According to at least one embodiment, the contact region  724  can be formed to have a shape (e.g., a two-dimensional shape), which may facilitate controlled orientation of the shaped abrasive particle  704 . More particularly, the contact region  724  can have a two-dimensional shape configured to control one or more (e.g., at least two of) a particular predetermined orientation characteristic, including for example, a predetermined rotational orientation, a predetermined lateral orientation, and a predetermined longitudinal orientation. In at least one embodiment, the contact region  724  can be formed to have a two-dimensional shape, wherein the dimensions of the contact region  724  (e.g., length and/or width) substantially correspond to and are substantially the same as dimensions of the shaped abrasive particle  704 , thereby facilitating positioning of the shaped abrasive particle at the position  772  and facilitating one or a combination of predetermined orientation characteristics of the shaped abrasive particle  704 . Furthermore, according to an embodiment, the alignment structure  762  can include a plurality of contact regions having controlled two-dimensional shapes configured to facilitate and control one or more predetermined orientation characteristics of associated shaped abrasive particles. 
     As further illustrated, and according to an embodiment, the alignment structure  762  can be configured to deliver and in particular instances, temporarily or permanently hold the shaped abrasive particle  705  at a second position  774 . In particular instances, such as illustrated in  FIG.  7 B , the alignment structure  762  can include a contact region  725 , which can have a particular two-dimensional shape as viewed top down and defined by the width of the contact region (w cr ) and the length of the contact region (l cr ), wherein the length is the longest dimension of the contact region  725 . Notably, the contact regions  724  and  725  of the alignment structure can have a different orientation relative to the contact regions  721  and  722  of the alignment structure  761  to facilitate different predetermine orientation characteristics between the shaped abrasive particles  701  and  702  of the group  791  and the shaped abrasive particles  704  and  705  of the group  792 . 
     As illustrated and noted above,  FIG.  7 B  further includes a third group  793  of shaped abrasive particles  744  and  745  overlying the backing  101 . The third group  793  can be associated with an alignment structure  763 , which can include a first contact region  754  and a second contact region  755 . The alignment structure  763  can be used to facilitate placement of the shaped abrasive particles  744  and  745  in desired orientations on the backing  101  and relative to each other. As noted herein, the alignment structure  763  can have any of the characteristics of alignment structures described herein. It will be appreciated that the alignment structure  763  can be a permanent or temporary part of the final abrasive article. The alignment structure  763  may be integral with the abrasive article, and may overlie the backing  101 , underlie an adhesive layer overlying the backing  101 , or even be integral part of one or more adhesive layers overlying the backing  101 . 
     According to one embodiment, the alignment structure  763  can be configured to deliver and in particular instances, temporarily or permanently hold the shaped abrasive particle  744  at a first position  775 . Likewise, as illustrated, the alignment structure  763  can be configured to deliver and in particular instances, temporarily or permanently hold the shaped abrasive particle  745  at a second position  776 . 
     In particular instances, such as illustrated in  FIG.  7 B , the alignment structure  763  can include a contact region  754 , which can have a particular two-dimensional shape as viewed top down. As illustrated, the contact region  754  can have a circular two-dimensional shape, which can be defined in part by a diameter (d cr ). 
     According to at least one embodiment, the contact region  754  can be formed to have a shape (e.g., a two-dimensional shape), which may facilitate controlled orientation of the shaped abrasive particle  744 . More particularly, the contact region  754  can have a two-dimensional shape configured to control one or more (e.g., at least two of) a particular predetermined orientation characteristic, including for example, a predetermined rotational orientation, a predetermined lateral orientation, and a predetermined longitudinal orientation. In at least one alternative embodiment as illustrated, the contact region  754  can have a circular shape, which may facilitate some freedom of a predetermined rotational orientation. For example, in comparison of the shaped abrasive particles  744  and  745 , each of which are associated with the contact regions  754  and  755 , respectively, and further wherein each of the contact regions  754  and  755  have circular two-dimensional shapes, the shaped abrasive particles  744  and  745  have different predetermined rotational orientations with respect to each other. The circular two-dimensional shape of the contact regions  754  and  755  may facilitate a preferential side orientation of the shaped abrasive particles  744  and  745 , while also allowing for a degree of freedom in at least one predetermined orientation characteristic (i.e., a predetermined rotational orientation) with respect to each other. 
     It will be appreciated, that in at least one embodiment, a dimensions of the contact region  754  (e.g., diameter) may substantially correspond to and may be substantially the same as a dimension of the shaped abrasive particle  744  (e.g., a length of a side surface), which may facilitate positioning of the shaped abrasive particle  744  at the position  775  and facilitating one or a combination of predetermined orientation characteristics of the shaped abrasive particle  744 . Furthermore, according to an embodiment, the alignment structure  763  can include a plurality of contact regions having controlled two-dimensional shapes configured to facilitate and control one or more predetermined orientation characteristics of associated shaped abrasive particles. It will be appreciated, that while the foregoing alignment structure  763  includes contact regions  754  and  755  having substantially similar shapes, the alignment structure  763  can include a plurality of contact regions having a plurality of different two-dimensional shapes. 
     As illustrated and noted above,  FIG.  7 B  further includes a fourth group  794  of shaped abrasive particles  746  and  747  overlying the backing  101 . The fourth group  794  can be associated with an alignment structure  764 , which can include a first contact region  756  and a second contact region  757 . The alignment structure  764  can be used to facilitate placement of the shaped abrasive particles  746  and  747  in desired orientations on the backing  101  and relative to each other. As noted herein, the alignment structure  764  can have any of the characteristics of alignment structures described herein. It will be appreciated that the alignment structure  764  can be a permanent or temporary part of the final abrasive article. The alignment structure  764  may be integral with the abrasive article, and may overlie the backing  101 , underlie an adhesive layer overlying the backing  101 , or even be integral part of one or more adhesive layers overlying the backing  101 . 
     According to one embodiment, the alignment structure  764  can be configured to deliver and in particular instances, temporarily or permanently hold the shaped abrasive particle  746  at a first position  777 . Likewise, as illustrated, the alignment structure  764  can be configured to deliver and in particular instances, temporarily or permanently hold the shaped abrasive particle  747  at a second position  778 . 
     In particular instances, such as illustrated in  FIG.  7 B , the alignment structure  763  can include a contact region  756 , which can have a particular two-dimensional shape as viewed top down. As illustrated, the contact region  756  can have a cross-like two-dimensional shape, which can be defined in part by a length (l cr ). 
     According to at least one embodiment, the contact region  756  can be formed to have a shape (e.g., a two-dimensional shape), which may facilitate controlled orientation of the shaped abrasive particle  746 . More particularly, the contact region  756  can have a two-dimensional shape configured to control one or more (e.g., at least two of) a particular predetermined orientation characteristic, including for example, a predetermined rotational orientation, a predetermined lateral orientation, and a predetermined longitudinal orientation. In at least one alternative embodiment as illustrated, the contact region  756  can have a cross-shaped two-dimensional shape, which may facilitate some freedom of a predetermined rotational orientation of the shaped abrasive particle  746 . 
     For example, in comparison of the shaped abrasive particles  746  and  747 , each of which are associated with the contact regions  756  and  757 , respectively, and further wherein each of the contact regions  756  and  757  have cross-shaped two-dimensional shapes, the shaped abrasive particles  746  and  747  can have different predetermined rotational orientations with respect to each other. The cross-shaped two-dimensional shapes of the contact regions  756  and  757  may facilitate a preferential side orientation of the shaped abrasive particles  746  and  747 , while also allowing for a degree of freedom in at least one predetermined orientation characteristic (i.e., a predetermined rotational orientation) with respect to each other. As illustrated, the shaped abrasive particles  746  and  747  are oriented substantially perpendicular to each other. The cross-shaped two-dimensional shape of the contact regions  756  and  757  facilitates generally two preferred predetermined rotational orientations of shaped abrasive particles, each of which are associated with the direction of the arms of the cross-shaped contact regions  756  and  757 , and each of the two orientations are illustrated by the shaped abrasive particles  746  and  747 . 
     It will be appreciated, that in at least one embodiment, a dimensions of the contact region  756  (e.g., length) may substantially correspond to and may be substantially the same as a dimension of the shaped abrasive particle  746  (e.g., a length of a side surface), which may facilitate positioning of the shaped abrasive particle  746  at the position  777  and facilitating one or a combination of predetermined orientation characteristics of the shaped abrasive particle  746 . Furthermore, according to an embodiment, the alignment structure  764  can include a plurality of contact regions having controlled two-dimensional shapes configured to facilitate and control one or more predetermined orientation characteristics of associated shaped abrasive particles. It will be appreciated, that while the foregoing alignment structure  764  includes contact regions  756  and  757  having substantially similar shapes, the alignment structure  764  can include a plurality of contact regions having a plurality of different two-dimensional shapes. 
     An abrasive article can have a number of discrete contact regions. The number of contact regions can influence the amount of abrasive particles adhered to the abrasive article, which in turn can influence the abrasive performance of the abrasive article. In an embodiment the number of contact regions can be specific or variable. In an embodiment, the number of contact regions can be least 1, such as at least 5, at least 10, at least 100, at least 500, at least 1000, at least 2000, at least 5000, at least 7500, at least 10,000; at least 15,000; at least 17,000; at least 20,000; at least 30,000; at least 40,000; or at least 50,000. In an embodiment, the number of contact regions can be not greater than 100,000; such as not greater than 90,000; not greater than 80,000, not greater than 70,000; not greater than 60,000; not greater than 50,000; not greater than 40,000; not greater than 30,000, or not greater than 20,000. It will be appreciated that the number of contact regions can be in a range of any maximum or minimum value indicated above. In a specific embodiment the number of contact regions is in a range from 1000 to 50,000; such as 5,000 to 40,000, such as 10,000 to 17,000. In a specific embodiment, the number of contact regions is 10,000. In another specific embodiment, the number of contact regions is 17,000. 
     As stated elsewhere herein, the size of an individual contact region, and similarly an adhesive region size, can be specific or variable. In an embodiment, the size of a contact region can be defined by its average area or average diameter (polygon or circular). 
     In an embodiment, a contact region can have an average area of at least 0.01 mm 2 , such as at least 0.02 mm 2 , at least 0.05 mm 2 , at least 0.1 mm 2 , at least 0.2 mm 2 , at least 0.3 mm 2 , at least 0.4 mm 2 , at least 0.5 mm 2 , at least 0.60 mm 2 , at least 0.70 mm 2 , at least 0.80 mm 2 , at least 0.90 mm 2 , or at least 1 mm 2 . In an embodiment, a contact region can have an average area not greater than 800 cm 2 , such as not greater than 500 cm 2 , not greater than 200 cm 2 , not greater than 100 cm 2 , not greater than 10 cm 2 , not greater than 5 cm 2 , or not greater than 3.5 cm 2 . It will be appreciated that the number of adhesive regions can be in a range of any maximum or minimum value indicated above. In average area of a contact region is in a range from 0.1 mm 2  to 100 cm 2 ; such as 0.1 mm 2  to 10 cm 2 . In a specific embodiment, the average area of a contact region is in a range from 0.1 mm 2  to 20 mm 2 . 
     In an embodiment, a contact region can have an average diameter of at least 0.3 mm, such as at least 0.05 mm, at least 0.06 mm, at least 0.7 mm, at least 0.8 mm, at least 0.9 mm, or at least 1 mm. In an embodiment, a contact region can have an average diameter not greater than 40 cm, such as not greater than 30 cm, not greater than 20 cm, not greater than 15 cm, not greater than 10 cm, not greater than 5 cm, or not greater than 3.5 cm. It will be appreciated that the number of adhesive regions can be in a range of any maximum or minimum value indicated above. In average diameter of a contact region is in a range from 0.1 mm to 40 cm; such as 0.1 mm to 10 cm. In a specific embodiment, the average diameter of a contact region is in a range from 0.1 mm to 20 mm. 
     Methods and Systems for Forming Abrasive Articles 
     The foregoing has described abrasive articles of the embodiments having predetermined distributions of shaped abrasive particles. The following describes various methods used to form such abrasive articles of the embodiments herein. It will be appreciated that any of the methods and systems described herein can be used in combination to facilitate the formation of an abrasive article according to an embodiment. 
     According to one embodiment, a method of forming an abrasive article includes placing a shaped abrasive particle on the backing in a first position defined by one or more predetermined orientation characteristics. In particular, the method of placing the shaped abrasive particle can include a templating process. A templating process may make use of an alignment structure, which may be configured to hold (temporarily or permanently) one or more shaped abrasive particles in a predetermined orientation and deliver the one or more shaped abrasive particles onto the abrasive article in a predetermined position defined having one or more predetermined orientation characteristics. 
     According to one embodiment, the alignment structure can be various structures, including but not limited to, a web, a fibrous material, a mesh, a solid structure having openings, a belt, a roller, a patterned material, a discontinuous layer of material, a patterned adhesive material, and a combination thereof. In one particular embodiment, the alignment structure can include a discrete contact region configured to hold a shaped abrasive particle. In certain other instances, the alignment structure can include a plurality of discrete contact regions spaced apart from each other and configured to hold a plurality of shaped abrasive particles. For certain embodiments herein, a discrete contact region can be configured to temporarily hold a shaped abrasive particle and place the first shaped abrasive particle at a predetermined position on the abrasive article. Alternatively, in another embodiment, the discrete contact region can be configured to permanently hold a first shaped abrasive particle and place the first shaped abrasive particle at the first position. Notably, for embodiments utilizing a permanent hold between the discrete contact region and the shaped abrasive particle, the alignment structure may be integrated within the finished abrasive article. 
     Some exemplary alignments structures according to embodiments herein are illustrated in  FIGS.  9 - 11   .  FIG.  9    includes an illustration of a portion of an alignment structure according to an embodiment. In particular, the alignment structure  900  can be in the form of web or mesh including fibers  901  and  902  overlapping each other. In particular, the alignment structure  900  can include discrete contact regions  904 ,  905 , and  906 , which may be defined by a plurality of intersections of objects of the alignment structure. In the particular illustrated embodiment, the discrete contact regions  904 - 906  can be defined by an intersection of the fibers  901  and  902 , and more particularly, a joint between the two fibers  901  and  902 , configured to hold the shaped abrasive particles  911 ,  912 , and  913 . According to certain embodiments, the alignment structure can further include discrete contact regions  904 - 906  that can include an adhesive material to facilitate placement and holding of the shaped abrasive particles  911 - 913 . 
     As will be appreciated, the construction and arrangement of the fibers  901  and  902  can facilitate control of the discrete contact regions  904 - 906  and further can facilitate control of one or more predetermined orientation characteristics of the shaped abrasive particles on the abrasive article. For example, the discrete contact regions  904 - 906  can be configured to define at least one of a predetermined rotational orientation of a shaped abrasive particle, a predetermined rotational orientation difference between at least two shaped abrasive particles, a predetermined longitudinal orientation of a shaped abrasive particle, a longitudinal space between two shaped abrasive particles, a predetermined lateral orientation, a lateral space between two shaped abrasive particles, a predetermined vertical orientation of a shaped abrasive particle, a predetermined vertical orientation difference between two shaped abrasive particles, a predetermined tip height orientation of a shaped abrasive particle, a predetermined tip height difference between two shaped abrasive particles, and a combination thereof. 
       FIG.  10    includes an illustration of a portion of an alignment structure according to an embodiment. In particular, the alignment structure  1000  can be in the form of a belt  1001  having discrete contact regions  1002  and  1003  configured to engage and hold the shaped abrasive particles  1011  and  1012 . According to an embodiment, the alignment structure  1000  can include discrete contact regions  1002  and  1003  in the form of openings in the alignment structure. Each of the openings can a shape configured to hold one or more shaped abrasive particles. Notably, each of the openings can have a shape configured to hold one or more shaped abrasive particles in a predetermined position to facilitate placement of the one or more shaped abrasive particles on the backing in a predetermined position with one or more predetermined orientation characteristics. In at least one embodiment, the openings defining the discrete contact regions  1002  and  1003  can have a cross-sectional shape complementary to a cross-sectional shape of the shaped abrasive particles. Moreover, in certain instances, the openings defining the discrete contact regions can extend through an entire thickness of the alignment structure (i.e., belt  1001 ). 
     In yet another embodiment, the alignment structure can include discrete contact regions defined by openings, wherein the openings extend partially through the entire thickness of the alignment structure. For example,  FIG.  11    includes an illustration of a portion of an alignment structure according to an embodiment. Notably, the alignment structure  1100  can be in the form of a thicker structure wherein the openings defining the discrete contact regions  1102  and  1103  configured to hold the shaped abrasive particles  1111  and  1112  do not extend through the entire thickness of the substrate  1101 . 
       FIG.  12    includes an illustration of a portion of an alignment structure according to an embodiment. Notably, the alignment structure  1200  can be in the form of a roller  1201  having openings  1203  in the exterior surface and defining the discrete contact regions. The discrete contact regions  1203  can have particular dimensions configured to facilitate holding of the shaped abrasive particles  1204  in the roller  1201  until a portion of the shaped abrasive particles are contacted to the abrasive article  1201 . Upon contact with the abrasive article  1201 , the shaped abrasive particles  1204  can be released from the roller  1201  and delivered to the abrasive article  1201  in a particular position defined by one or more predetermined orientation characteristics. Accordingly, the shape and orientation of the openings  1203  on the roller  1201 , the position of the roller  1201  relative to the abrasive article  1201 , the rate of translation of the roller  1201  relative to the abrasive article  1201  may be controlled to facilitate positioning of the shaped abrasive particles  1204  in a predetermined distribution. 
     Various processing steps may be utilized to facilitate the placement of the shaped abrasive particles on the alignment structure. Suitable processes can include, but are not limited to, vibration, adhesion, electromagnetic attraction, patterning, printing, pressure differential, roll coat, gravity drop, and a combination thereof. Moreover, particular devices may be used to facilitate orientation of the shaped abrasive particles on the alignment structure, including for example, cams, acoustics, and a combination thereof. 
     In yet another embodiment, the alignment structure can be in the form of a layer of adhesive material. Notably, the alignment structure can be in the form of a discontinuous layer of adhesive portions, wherein the adhesive portions define discrete contact regions configured to hold (temporarily or permanently) one or more shaped abrasive particles. According to one embodiment, the discrete contact regions can include an adhesive, and more particularly, the discrete contact regions are defined by a layer of adhesive, and still more particularly, each of the discrete contact regions are defined by a discrete adhesive region. In certain instances, the adhesive can include a resin, and more particularly, can include a material for use as a make coat as described in embodiments herein. Moreover, the discrete contact regions can define a predetermined distribution relative to each other, and can further define positions of the shaped abrasive particles on the abrasive article. Furthermore, the discrete contact regions comprising the adhesive can be arranged in a predetermined distribution, which is substantially the same as a predetermined distribution of shaped abrasive particles overlying the backing. In one particular instance, the discrete contact regions comprising the adhesive can be arranged in a predetermined distribution, can be configured to hold a shaped abrasive particle, and further can define at least one of a predetermined orientation characteristic for each shaped abrasive particle. 
     In an embodiment the number of adhesive regions can be specific or variable. In an embodiment, the number of adhesive regions can be least 1, such as at least 5, at least 10, at least 100, at least 500, at least 1000, at least 2000, at least 5000, at least 7500, at least 10,000; at least 15,000; at least 17,000; at least 20,000; at least 30,000; at least 40,000; or at least 50,000. In an embodiment, the number of adhesive regions can be not greater than 100,000; such as not greater than 90,000; not greater than 80,000, not greater than 70,000; not greater than 60,000; not greater than 50,000; not greater than 40,000; not greater than 30,000, or not greater than 20,000. It will be appreciated that the number of adhesive regions can be in a range of any maximum or minimum value indicated above. In a specific embodiment the number of adhesive regions is in a range from 1000 to 50,000; such as 5,000 to 40,000, such as 10,000 to 17,000. In a specific embodiment, the number of adhesive regions is 10,000. In another specific embodiment, the number of adhesive regions is 17,000. 
       FIG.  13    includes an illustration of a portion of an alignment structure including discrete contact regions comprising an adhesive in accordance with an embodiment. As illustrated, the alignment structure  1300  can include a first discrete contact region  1301  comprising a discrete region of adhesive and configured to couple a shaped abrasive particle. The alignment structure  1300  can also include a second discrete contact region  1302  and a third discrete contact region  1303 . According to one embodiment, at least the first discrete contact region  1301  can have a width (w)  1304  related to at least one dimension of the shaped abrasive particle, which may facilitate positioning of the shaped abrasive particle in a particular orientation relative to the backing. For example, certain suitable orientations relative to the backing can include a side orientation, a flat orientation, and inverted orientation. According to a particular embodiment, the first discrete contact region  1301  can have a width (w)  1304  related to a height (h) of the shaped abrasive particle to facilitate a side orientation of the shaped abrasive particle. It will be appreciated that reference herein to a height can be reference to an average height or median height of a suitable sample size of a batch of shaped abrasive particles. For example, the width  1304  of the first discrete contact region  1301  can be not greater than the height of the shaped abrasive particle. In other instances, the width  1304  of the first discrete contact region  1301  can be not greater than about 0.99(h), such as not greater than about 0.95(h), not greater than about 0.9(h), not greater than about 0.85(h), not greater than about 0.8(h), not greater than about 0.75(h), or even not greater than about 0.5(h). Still, in one non-limiting embodiment, the width  1304  of the first discrete contact region  1301  can be at least about 0.1(h), at least about 0.3(h), or even at least about 0.5(h). It will be appreciated that the width  1304  of the first discrete contact region  1301  can be within a range between any of the minimum and maximum values noted above. 
     In accordance with a particular embodiment, the first discrete contact region  1301  can be spaced apart from the second discrete contact region  1302  via a longitudinal gap  1305 , which is a measure of the shortest distance between immediately adjacent discrete contact regions  1301  and  1302  in a direction parallel to the longitudinal axis  180  of the backing  101 . In particular, control of the longitudinal gap  1305  may facilitate control of the predetermined distribution of the shaped abrasive particles on the surface of the abrasive article, which may facilitate improved performance. According to one embodiment, the longitudinal gap  1305  can be related to a dimension of one or a sampling of shaped abrasive particle. For example, the longitudinal gap  1305  can be at least equal to a width (w) of a shaped abrasive particle, wherein the width is a measure of the longest side of the particle as described herein. It will be appreciated that reference herein to a width (w) of the shaped abrasive particle can be reference to an average width or median width of a suitable sample size of a batch of shaped abrasive particles. In a particular instance, the longitudinal gap  1305  can be greater than the width, such as at least about 1.1(w), at least about 1.2 (w), at least about 1.5(w), at least about 2(w), at least about 2.5(w), at least about 3(w) or even at least about 4(w). Still, in one non-limiting embodiment, the longitudinal gap  1305  can be not greater than about 10(w), not greater than about 9(w), not greater than about 8(w), or even not greater than about 5(w). It will be appreciated that the longitudinal gap  1305  can be within a range between any of the minimum and maximum values noted above. 
     In accordance with a particular embodiment, the second discrete contact region  1302  can be spaced apart from the third discrete contact region  1303  via a lateral gap  1306 , which is a measure of the shortest distance between immediately adjacent discrete contact regions  1302  and  1303  in a direction parallel to the lateral axis  181  of the backing  101 . In particular, control of the lateral gap  1306  may facilitate control of the predetermined distribution of the shaped abrasive particles on the surface of the abrasive article, which may facilitate improved performance. According to one embodiment, the lateral gap  1306  can be related to a dimension of one or a sampling of shaped abrasive particle. For example, the lateral gap  1306  can be at least equal to a width (w) of a shaped abrasive particle, wherein the width is a measure of the longest side of the particle as described herein. It will be appreciated that reference herein to a width (w) of the shaped abrasive particle can be reference to an average width or median width of a suitable sample size of a batch of shaped abrasive particles. In a particular instance, the lateral gap  1306  can be less than the width of the shaped abrasive particle. Still, in other instances, the lateral gap  1306  can be greater than the width of the shaped abrasive particle. According to one aspect, the lateral gap  1306  can be zero. In yet another aspect, the lateral gap  1306  can be at least about 0.1(w), at least about 0.5 (w), at least about 0.8(w), at least about 1(w), at least about 2 (w), at least about 3(w) or even at least about 4(w). Still, in one non-limiting embodiment, the lateral gap  1306  may be not greater than about 100(w), not greater than about 50(w), not greater than about 20(w), or even not greater than about 10(w). It will be appreciated that the lateral gap  1306  can be within a range between any of the minimum and maximum values noted above. 
     The first discrete contact region  1301  can be formed on an upper major surface of a backing using various methods, including for example, printing, patterning, gravure rolling, etching, removing, coating, depositing, and a combination thereof.  FIGS.  14 A- 14 H  include top down views of portions of tools for forming abrasive articles having various patterned alignment structures including discrete contact regions of an adhesive material according to embodiments herein. In particular instances, the tools can include a templating structure that can be contacted to the backing and transfer the patterned alignment structure to the backing. In one particular embodiment, the tool can be a gravure roller having a patterned alignment structure comprising discrete contact regions of adhesive material that can be rolled over a backing to transfer the patterned alignment structure to the backing. After which, shaped abrasive particles can be placed on the backing in the regions corresponding to the discrete contact regions.  FIG.  33    illustrates a gravure roller embodiment having a patterned alignment structure comprising a pattern of open cells on the roller surface capable of pick up and transfer of adhesive material to form discrete contact regions of adhesive material on a backing.  FIG.  32    is an illustration of a phyllotactic non-shadowing pattern (“pineapple pattern”) suitable for use on a gravure roller embodiment or other rotary printing embodiment.  FIG.  34 A  is a photograph of a discontinuous distribution of adhesive contact regions comprised of a make coat that does not contain any abrasive particles.  FIG.  34 B  is a photograph of the same discontinuous distribution of adhesive contact regions as shown in  FIG.  34 A  after abrasive particles have been disposed on the discontinuous distribution of adhesive contact regions.  FIG.  34 C  is a photograph of the abrasive particle covered discontinuous distribution of adhesive contact regions shown in  FIG.  34 B  after a continuous size coat has been applied. 
     In at least one particular aspect, an abrasive article of an embodiment can including forming a patterned structure comprising an adhesive on at least a portion of the backing. Notably, in one instance, the patterned structure can be in the form of a patterned make coat. The patterned make coat can be a discontinuous layer including at least one adhesive region overlying the backing, a second adhesive region overlying the backing separate from the first adhesive region, and at least one exposed region between the first and second adhesive regions. The at least one exposed region can be essentially free of adhesive material and represent a gap in the make coat. In one embodiment, the patterned make coat can be in the form of an array of adhesive regions coordinated relative to each other in a predetermined distribution. The formation of the patterned make coat with a predetermined distribution of adhesive regions on the backing can facilitate placement of the shaped abrasive grains in a predetermined distribution, and particularly, the predetermined distribution of the adhesive regions of the patterned make coat can correspond to the positions of the shaped abrasive particles, wherein each of the shaped abrasive particles can be adhered to the backing at the adhesive regions, and thus correspond to the predetermined distribution of shaped abrasive particles on the backing. Moreover, in at least one embodiment, essentially no shaped abrasive particles of the plurality of shaped abrasive particles are overlying the exposed regions. Furthermore, it will be appreciated that a single adhesive region can be shaped and sized to accommodate a single shaped abrasive particle. However, in an alternative embodiment, an adhesive region can be shaped and sized to accommodate a plurality of shaped abrasive particles. 
     As already stated, a make coat can be selectively applied to a backing such that a portion of the backing surface is not covered with any make coat material. Any portion not covered by make coat, though, can be partially to fully covered by another coating layer such as a size coat or supersize coat. Alternatively, portions of the backing surface can be free of any overlying coatings (i.e., “bare” portions). A portion of the backing surface not covered with make coat material can be defined as a fraction of the total surface of the backing. Similarly, a portion of the backing surface not covered with any overlying coating can be defined as a fraction of the total surface of the backing. It will be appreciated that the total contact area for the abrasive article is based on the sum of the discrete contact areas (i.e., the sum of all the discrete contact areas and can be equal to the fraction of the total surface area of the backing that is covered with make coat. 
     In an embodiment, the portion of the backing covered by make coat material can range from 0.01 to 1.0 of the total backing surface. In a specific embodiment, the portion of the total area of the backing surface covered by make coat material can range from 0.05 to 0.9 of the total backing surface, such as 0.1 to 0.8 of the total backing surface. In a specific embodiment, the portion of the total backing surface covered by make coat material is in a range from 0.1 to 0.6 of the total backing surface, such as 0.15 to 0.55, such as 0.16 to 0.16 to 0.5 of the total backing surface. 
     In an embodiment, the portion of the backing surface not covered by any overlying coating material (i.e., “bare” surface) can range from 0.0 to 0.99 of the total backing surface. In a specific embodiment, the portion of the backing surface that is bare can range from 0.1 to 0.95 of the total backing surface, such as 0.2 to 0.9 of the total backing surface. In a specific embodiment, the bare portion of the backing surface is in a range from 0.4 to 0.85 of the total backing surface. 
     Various processes may be utilized in the formation of a patterned structure, including for example, a patterned make coat. In one embodiment, the process can include selectively depositing the make coat. In yet another embodiment, the process can include selectively removing at least a portion of the make coat. Some exemplary processes can include coating, spraying, rolling, printing, masking, irradiating, etching, and a combination thereof. According to a particular embodiment, forming the patterned make coat can include providing a patterned make coat on a first structure and transferring the patterned make coat to at least a portion of the backing. For example, a gravure roller may be provided with a patterned make coat layer, and the roller can be translated over at least a portion of the backing and transferring the patterned make coat from the roller surface to the surface of the backing. 
     Methods of Applying Adhesive Coating 
     In an embodiment, an adhesive layer can be applied by a screen printing process. The screen printing process can be a discrete adhesive layer application process, a semi-continuous adhesive layer application process, a continuous adhesive layer application process, or combinations thereof. In an embodiment, the application process includes the use of a rotary screen. In a particular embodiment, a rotary screen can be in the form of a hollow cylinder, or drum, having a plurality of apertures located on the wall of the cylinder or drum. An aperture, or combination of apertures, can correspond to the desired location of a discrete contact region, or a combination of discrete contact regions. A discrete contact region can include one, or more, discrete adhesive regions. In a particular embodiment, a contact region includes a plurality of discrete adhesive regions. The adhesive regions can be arranged in the form of a non-shadowing pattern. 
     Methods of Making 
       FIG.  31    illustrates a flow diagram for a method  3100  of making an abrasive article, such as shown in  FIG.  32   . In step  3101 , applying an adhesive layer to the backing occurs. The adhesive layer can be a polymeric binder composition (i.e., polymeric resin) corresponding to a make layer  3202  (i.e., make resin), disposed over a major surface  3204  of a backing  3206  in a plurality of discrete areas, such as discrete contact areas or discrete adhesive regions  3208 . The discrete adhesive regions can be arranged so as to provide a random, semi-random, or ordered distribution. An exemplary distribution is a non-shadowing distribution as shown in  FIGS.  25 ,  26 ,  27 , and  32   . Disposing (applying) abrasive particles  3210  onto the discrete adhesive regions of the make resin next occurs in step  3103 . In step  3105 , curing the make resin at least partially to fully occurs to provide the abrasive article. Optionally, a functional powder, such as a mineral powder, can be applied over the entire coated backing and then be removed from those areas not containing the make resin. Optionally, A size coat  3212  (i.e., size resin) can then be preferentially applied over the abrasive particles and the make resin. The size coat can be in contact with open areas  3214  of the backing (i.e., areas where make resin has not been applied), in contact with areas where the make resin has been applied, or combinations thereof. In a specific embodiment, the size resin is applied over the make resin in a manner such that it does not completely cover the make resin and does not extend beyond the make resin. Optionally, curing of the size resin then occurs to provide the abrasive article. In and embodiment, when applying an adhesive layer to the backing, particularly as a make layer, the make resin can contain suitable additives and fillers but does not contain any abrasive particles (i.e., the make resin is not an abrasive slurry). In a specific embodiment, the adhesive resin is a make resin and does not contain any abrasive particles. Further, it will be noted that although the discrete adhesive regions can be arranged as a discontinuous non-shadowing distribution, such as a make coat having a discontinuous non-shadowing distribution, that any size coat that is optionally applied over the make coat can be continuous or discontinuous, just as any supersize coat that is optionally applied over the size coat can be continuous or discontinuous. In a specific embodiment, a size coat and a supersize coat are both discontinuous and are applied so that the size coat and supersize coat match the make coat distribution. In another specific embodiment, a size coat and a supersize coat are both discontinuous and are applied so that the size coat and supersize coat partially match the make coat distribution. In another specific embodiment, a continuous size coat is applied over the discontinuous make coat and a discontinuous supersize coat is applied over the size coat. In another specific embodiment, a discontinuous size coat is applied over the discontinuous make coat (either matching or partially matching the make coat) and a continuous supersize coat is applied over the size coat. 
     The selective application of a make resin and a size resin can be achieved using contact coating and printing methods, non-contact coating and printing methods, transfer contact coating and printing methods, or a combination thereof. Suitable methods include mounting a template, such as a stencil or screen, against the backing of the article to mask off areas of the backing that are not to be coated. A screen printing process can be a discrete adhesive application process, a semi-continuous adhesive application process, a continuous adhesive application process, or combinations thereof. In an embodiment, the application process can include the use of a rotary screen. In a particular embodiment, a rotary screen  2801  can be in the form of a hollow cylinder, or drum, having a plurality of apertures  2803  located on the wall of the cylinder or drum. In an embodiment, an aperture or combination of apertures can be located in the wall of the rotary screen. The apertures can correspond to one or more discrete contact regions, including one or more discrete adhesive regions  2805 . 
     In an embodiment the number of apertures can be specific or variable. In an embodiment, the number of apertures can be least 1, such as at least 5, at least 10, at least 100, at least 500, at least 1000, at least 2000, at least 5000, at least 7500, at least 10,000; at least 15,000; at least 17,000; at least 20,000; at least 30,000; at least 40,000; or at least 50,000. In an embodiment, the number of apertures can be not greater than 100,000; such as not greater than 90,000; not greater than 80,000, not greater than 70,000; not greater than 60,000; not greater than 50,000; not greater than 40,000; not greater than 30,000, or not greater than 20,000. It will be appreciated that the number of apertures can be in a range of any maximum or minimum value indicated above. In a specific embodiment the number of apertures is in a range from 1000 to 50,000; such as 5,000 to 40,000, such as 10,000 to 17,000. In a specific embodiment, the number of apertures is 10,000. In another specific embodiment, the number of apertures is 17,000. 
     A rotary screen process can include an open squeegee system or a closed squeegee system. In a specific embodiment, the rotary screen process includes a closed squeegee system  2809 . The rotary screen can be filled with the adhesive resin  2811  (i.e., polymeric resin for use in one or more specific coating layers, such as make resin, size resin) and the squeegee, or the like, can be used to guide the resin through the apertures. Closed rotary squeegee systems can have a number of advantages over other coating and printing systems. For instance, rotary screen printing systems allow the screen and the backing material to run at the same speed, thus reducing friction, at times marked by there being no friction, between the screen and the backing material. Additionally, tension on the backing material is reduced, allowing more delicate or sensitive backing materials, such as much thinner backing materials or open backing materials to be coated effectively. Also, rotary screen printing systems can reduce or eliminate the pressure required to push an adhesive material through the apertures of the rotary screen, which allows for enhanced control of the thickness of the adhesive material applied to the backing. In an embodiment, the thickness of the adhesive material is precisely controlled and applied at a thickness that promotes at least about 55%, at least about 60%, at least about 65%, at least about 70%, at least about 75%, at least about 80%, at least about 85%, at least about 90%, or at least about 95% of the abrasive particles have tips that are upright. The thickness of the adhesive material can be the thickness of the make layer alone, or can be the thickness in combination with the size layer. The thickness of the adhesive layer can be adversely affected by penetration into the backing material. The penetration of the adhesive material into the backing material can be reduced, if desired, so as to control strike-through of the adhesive material and selectively control the flexibility of the backing material, also known as the “hand” of the backing material, when dealing with a fabric backing. Another benefit of a rotary screen printing system is that the shape of adhesive material deposited onto the backing will be less disturbed, thus discontinuous distributions of make coat resin, such as a discontinuous distributions of dots, stripes, or the like as described herein will have a more controlled shape, thus providing sharply defined coating areas, or images, on the substrate. Embodiments of suitable rotary screen processes that include a closed squeegee system can include Specific STORK printing machines makes and models. An illustration of a rotary screen process system is shown in  FIG.  28   .  FIG.  32    is an illustration of a phyllotactic non-shadowing pattern suitable for use on a rotary screen printing embodiment. 
     Phyllotactic 
     In an embodiment, the adhesive layer can have a substantially uniform thickness. The thickness can be less than the d 50  height of the abrasive particle. The thickness can be less than 50% of the height of the abrasive particle, such as less than 45%, such as less than 40%, such as less than 35%, such as less than 30%, such as less than 25%, such as less than 20%, such as less than 15%, such as less than 10%, such as less than 5%, such as less than 4%, such as less than 3%, such as less than 2%, such as less than 1%, such as less than 0.5%. 
     In an embodiment, the width of the discrete adhesive contact regions can be the same or different. In an embodiment, the width of the discrete adhesive contact region is substantially equal to the d 50  width of the at least one abrasive particle. 
     In an alternate embodiment, stencil printing can be used, such as by use of a frame to support a resin-blocking stencil. The stencil can be a woven or nonwoven material. The stencil can form open areas allowing the transfer of resin to produce a sharply-defined image onto a substrate. A roller or squeegee can be moved across the screen stencil, forcing or pumping the resin or slurry through the open areas in the stencil, such as open areas in the mesh of a woven stencil. 
     Screen printing can also include a stencil method of print making in which a design is imposed on a screen of silk or other fine mesh, wherein portions of the backing that are desired to be blank areas, or open areas, are coated with an impermeable substance, and the resin or slurry is forced through the mesh onto the printing surface (i.e., the desired backing or substrate). Printing of low profile and high fidelity features can be enabled by screen printing. 
     An alternate embodiment includes a contact method that includes a combination of screen printing and stencil printing, where a woven mesh is used to support a stencil. The stencil includes open areas of mesh through which resin (adhesive) can be deposited in a desired distribution, such as a pattern of discrete areas onto the backing material. The resin can be applied as a make coat, a size coat, a supersize coat, or other coating layer known in the art, or combinations thereof. 
     In an alternate embodiment, a method can include an inkjet-type printing and other technologies capable of selectively coating patterns onto the backing without need for a template. 
     Another suitable method, is a continuous kiss coating operation where the adhesive material (make coat or size coat) is coated over the backing material by passing the backing material between a delivery roll and a nip roll. Such a method can be well suited for coating a size coat over abrasive particles by passing the backing sheet between a delivery roll and a nip roll. Optionally, the adhesive resin can be metered directly onto the delivery roll. The final coated material can then be cured to provide the completed article.  FIG.  33    illustrates a gravure roller embodiment having a patterned alignment structure comprising a pattern of open cells on the roller surface capable of pick up and transfer of adhesive material to form discrete contact regions of adhesive material on a backing during a kiss coating operation.  FIG.  32    is an illustration of a phyllotactic non-shadowing pattern suitable for use on a gravure roller embodiment or other rotary printing embodiment.  FIG.  34 A  is a photograph of a discontinuous distribution of adhesive contact regions comprised of a make coat that does not contain any abrasive particles.  FIG.  34 B  is a photograph of the same discontinuous distribution of adhesive contact regions as shown in  FIG.  34 A  after abrasive particles have been disposed on the discontinuous distribution of adhesive contact regions.  FIG.  34 C  is a photograph of the abrasive particle covered discontinuous distribution of adhesive contact regions shown in  FIG.  34 B  after a continuous size coat has been applied. 
     A rotary screen for preparing a patterned coated abrasive article can include a generally cylindrical body and a plurality of perforations extending through the body. Alternatively a stencil for preparing a patterned coated abrasive article can include a generally planar body and a plurality of perforations extending through the body. Optionally, a frame can surround the stencil partially or completely. 
     A screen or stencil can be made from any material generally known in the art, such as a natural fiber, polymer, metal, ceramic, composite, or combinations thereof. The material can be of any desired dimension. In an embodiment, the screen is preferably thin. In an embodiment, combinations of metal and woven plastics are used. Metal stencils can be etched in one or more patterns, or a combination of patterns. Other suitable screen and stencil materials include polyester films, such as those having a thickness ranging from 1 to 20 mils (0.076 to 0.51 millimeters), more preferably ranging from 3 to 7 mils (0.13 to 0.25 millimeters). 
     As mentioned above, a rotary screen can be advantageously used to provide precisely defined coating patterns. In an embodiment, a layer of make resin is selectively applied to the backing by rotatively overlaying the rotary screen above the backing at a desired distance (to determine the thickness of the coat) and applying the make resin through the rotary screen. The make resin can be applied in a single pass or multiple passes using a squeegee, doctor blade, or other blade-like device. 
     The viscosity of the make resin can be manipulated to be in a range that is sufficiently high so that distortion of the overall distribution pattern, as well as the individual adhesive contact regions (e.g., dots, stripes, etc.) is minimized, and in some embodiments eliminated (i.e., not detectable). 
     Adhesive Spacing 
     The adhesive application methods described above can be used to impart one or more desirable orientation characteristics for the discrete adhesive regions or to establish one or more desirable predetermined distributions of the discrete adhesive regions. A predetermined distribution between discrete adhesive regions can also be defined by at least one of a predetermined orientation characteristic of each of the discrete adhesive regions. Exemplary predetermined orientation characteristics can include a predetermined rotational orientation, a predetermined lateral orientation, a predetermined longitudinal orientation, a predetermined vertical orientation, and combinations thereof. 
     As shown in  FIG.  29   , in an embodiment, the backing  2901  can be defined by a longitudinal axis  2980  that extends along and defines a length of the backing  2901  and a lateral axis  2981  that extends along and defines a width of a backing  2901 . The discrete adhesive region  2902  can be located in a first, predetermined position  2912  defined by a particular first lateral position relative to the lateral axis of  2981  of the backing  2901 . Furthermore, the discrete adhesive region  2903  can have a second, predetermined position defined by a second lateral position relative to the lateral axis  2981  of the backing  2901 . Notably, the discrete adhesive regions  2902  and  2903  can be spaced apart from each other by a lateral space  2921 , defined as a smallest distance between the two adjacent discrete adhesive regions  2902  and  2903  as measured along a lateral plane  2984  parallel to the lateral axis  2981  of the backing  2901 . In accordance with an embodiment, the lateral space  2921  can be greater than zero (0), such that some distance exists between the discrete adhesive regions  2902  and  2903 . However, while not illustrated, it will be appreciated that the lateral space  2921  can be zero (0), allowing for contact and even overlap between portions of adjacent discrete adhesive regions. 
     In other embodiments, the lateral space  2921  can be at least about 0.1 (w), wherein w represents the width of the discrete adhesive region  2902 . According to an embodiment, the width of the discrete adhesive region is the longest dimension of the body extending along a side. In another embodiment, the lateral space  2921  can be at least about 0.2(w), such as at least about 0.5(w), at least about 1(w), at least about 2(w), or even greater. Still, in at least one non-limiting embodiment, the lateral space  2921  can be not greater than about 100(w), not greater than about 50(w), or even not greater than about 20(w). It will be appreciated that the lateral space  2921  can be within a range between any of the minimum and maximum values noted above. Control of the lateral space between adjacent discrete adhesive regions can facilitate improved grinding performance of the abrasive article. 
     In accordance with an embodiment, the discrete adhesive region  2902  can be in a first, predetermined position  2912  defined by a first longitudinal position relative to a longitudinal axis  2980  of the backing  2901 . Furthermore, the discrete adhesive region  2904  can be located at a third, predetermined position  2914  defined by a second longitudinal position relative to the longitudinal axis  2980  of the backing  2901 . Further, as illustrated, a longitudinal space  2923  can exist between the discrete adhesive regions  2902  and  2904 , which can be defined as a smallest distance between the two adjacent discrete adhesive regions  2902  and  2904  as measured in a direction parallel to the longitudinal axis  2980 . In accordance with an embodiment, the longitudinal space  2923  can be greater than zero (0). Still, while not illustrated, it will be appreciated that the longitudinal space  2923  can be zero (0), such that the adjacent discrete adhesive regions are touching, or even overlapping each other. 
     In other instances, the longitudinal space  2923  can be at least about 0.1(w), wherein w is the width of the discrete adhesive region as described herein. In other more particular instances, the longitudinal space can be at least about 0.2(w), at least about 0.5(w), at least about 1(w), or even at least about 2(w). Still, the longitudinal space  2923  may be not greater than about 100(w), such as not greater than about 50(w), or even not greater than about 20(w). It will be appreciated that the longitudinal space  2923  can be within a range between any of the above minimum and maximum values. Control of the longitudinal space between adjacent discrete adhesive regions may facilitate improved grinding performance of the abrasive article. 
     In accordance with an embodiment, the discrete adhesive regions may be placed in a predetermined distribution, wherein a particular relationship exists between the lateral space  2921  and longitudinal space  2923 . For example, in one embodiment the lateral space  2921  can be greater than the longitudinal space  2923 . Still, in another non-limiting embodiment, the longitudinal space  2923  may be greater than the lateral space  2921 . Still, in yet another embodiment, the discrete adhesive regions may be placed on the backing such that the lateral space  2921  and longitudinal space  2923  are essentially the same relative to each other. Control of the relative relationship between the longitudinal space and lateral space may facilitate improved grinding performance. 
     In accordance with an embodiment, the discrete adhesive region  2905  may be located at a fourth, predetermined position  2915  defined by a third longitudinal position relative to the longitudinal axis  2980  of the backing  2901 . Further, as illustrated, a longitudinal space  2925  may exist between the discrete adhesive regions  2902  and  2905 , which can be defined as a smallest distance between the two adjacent discrete adhesive regions  2902  and  2905  as measured in a direction parallel to the longitudinal axis  2980 . In accordance with an embodiment, the longitudinal space  2925  can be greater than zero (0). Still, while not illustrated, it will be appreciated that the longitudinal space  2925  can be zero (0), such that the adjacent discrete adhesive regions are touching, or even overlapping each other. 
     In other instances, the longitudinal space  2925  can be at least about 0.1(w), wherein w is the width of the discrete adhesive region as described herein. In other more particular instances, the longitudinal space can be at least about 0.2(w), at least about 0.5(w), at least about 1(w), or even at least about 2(w). Still, the longitudinal space  2925  may be not greater than about 100(w), such as not greater than about 50(w), or even not greater than about 20(w). It will be appreciated that the longitudinal space  2925  can be within a range between any of the above minimum and maximum values. Control of the longitudinal space between adjacent discrete adhesive regions may facilitate improved grinding performance of the abrasive article. 
     As further illustrated, a longitudinal space  2924  may exist between the discrete adhesive regions  2904  and  2905 . Moreover, the predetermined distribution may be formed such that a particular relationship can exist between the longitudinal space  2923  and longitudinal space  2924 . For example, the longitudinal space  2923  can be different than the longitudinal space  2924 . Alternatively, the longitudinal space  2923  can be essentially the same at the longitudinal space  2924 . Control of the relative difference between longitudinal spaces of different abrasive particles may facilitate improved grinding performance of the abrasive article. As further illustrated, a longitudinal space  2927  may exist between the discrete adhesive regions  2903  and  2906 . Moreover, the predetermined distribution may be formed such that a particular relationship can exist between the longitudinal space  2927  and longitudinal space  2926 . For example, the longitudinal space  2927  can be different than the longitudinal space  2926 . Alternatively, the longitudinal space  2927  can be essentially the same at the longitudinal space  2926 . Still further, the longitudinal space  2927  can be different than, or essentially the same as, the longitudinal space  2923 . Likewise, the longitudinal space  2928  can be different than, or essentially the same as, the longitudinal space  2924 . Control of the relative difference between longitudinal spaces of different abrasive particles may facilitate improved grinding performance of the abrasive article. 
     Furthermore, the predetermined distribution of shaped abrasive particles on the abrasive article  2900  can be such that the lateral space  2921  can have a particular relationship relative to the lateral space  2922 . For example, in one embodiment the lateral space  2921  can be essentially the same as the lateral space  2922 . Alternatively, the predetermined distribution of shaped abrasive particles on the abrasive article  2900  can be controlled such that the lateral space  2921  is different than the lateral space  2922 . Control of the relative difference between lateral spaces of different abrasive particles may facilitate improved grinding performance of the abrasive article. 
     As further illustrated, a longitudinal space  2926  may exist between the discrete adhesive regions  2903  and  2906 . Moreover, the predetermined distribution may be formed such that a particular relationship can exist between the longitudinal space  2925  and longitudinal space  2926 . For example, the longitudinal space  2925  can be different than the longitudinal space  2926 . Alternatively, the longitudinal space  2925  can be essentially the same at the longitudinal space  2926 . Control of the relative difference between longitudinal spaces of different abrasive particles may facilitate improved grinding performance of the abrasive article. In addition to the latitudinal spacing and longitudinal spacing already described herein, the spacing between discrete contact regions, discrete adhesive regions, or abrasive particles can also be described as having a particular or variable “adjacent spacing” wherein said adjacent spacing need not be strictly latitudinal or longitudinal (but can be the shortest distance that extends between adjacent discrete contact regions, discrete adhesive regions, or abrasive particles even if at an oblique angle. Adjacent spacing can be constant or variable. 
     In an embodiment adjacent spacing can be defined as a fraction of abrasive particle length, abrasive particle width, discrete contact area length, discrete contact area width, discrete adhesive region length, adhesive region width, or combinations thereof. In an embodiment, adjacent spacing is defined as a fraction of abrasive particle length (l). In an embodiment, adjacent spacing is at least 0.5(l), such as at least 0.5(l), at least 0.6(l), at least 0.7(l), at least 1.0(l), or at least 1.1(l). In an embodiment, the adjacent spacing is not greater than 10(l), such is not greater than 9(l), not greater than 8(l), not greater than 7(l), not greater than 6(l), not greater than 5(l), not greater than 4(l), or not greater than 3(l). It will be appreciated that the adjacent spacing can be in a range of any maximum or minimum value indicated above. In an embodiment, adjacent spacing is in a range from 0.5(l) to  3 ( l ), such as 1(l) to 2.5(l), such as 1.25(l) to 2.25(l), such as 1.25(l) to 1.7 5(l), such as 1.5(l) to 1.6(l). 
     In an embodiment, the adjacent spacing is at least 0.2 mm, such as at least 0.3 mm, such as at least 0.4 mm, such as at least 0.5 mm, such as at least 0.6 mm, such as at least 0.7 mm, such as at least 1.0 mm. In an embodiment, adjacent spacing can be not greater than 4.0 mm, such as not greater than 3.5 mm, not greater than 2.8 mm, or not greater than 2.5 mm. It will be appreciated that the adjacent spacing can be in arrange of any maximum or minimum value indicated above. In a particular embodiment, the adjacent spacing is in a range from 1.4 mm to 2.8 mm. 
     In an embodiment, the adjacent spacing tween discrete contact areas can be at least about 0.1 (W), where in W is the with of the discrete adhesive region as described herein. 
     It will be appreciated that abrasive particles, such as embodiments of shaped abrasive particles described herein, can be disposed on the discrete adhesive regions described above. The number of abrasive particles disposed on a discrete adhesive region can be from 1 to n, where n=1 to 3. The number of abrasive particles disposed per discrete abrasive region can be the same or different. Furthermore, a predetermined distribution of shaped abrasive particles can be defined by the predetermined distribution of discrete adhesive regions to which they are relatively adhered. A predetermined distribution of discrete adhesive regions can also be defined by the precision and accuracy of the actual placement of a discrete adhesive region (i.e., an adhesive strike location) with respect to its intended target location (i.e., adhesive target location), and more precisely defined by the precision and accuracy of the placement of the center (or centroid) of an adhesive strike area compared to the center (or centroid) of the intended adhesive target area. The difference in distance between the adhesive target location and the adhesive strike location is the differential distance. Control of the differential distance can facilitate improved grinding performance of the abrasive article. As explained in greater detail below, control of the differential distance can be defined by one or more of several well known measures of variability, such as Range, Interquartile Range, Variance, and Standard Deviation, among others. 
     In accordance with an embodiment,  FIG.  30    illustrates a predetermined, or controlled, distribution  3000  of discrete adhesive regions with respect to their intended target locations. As shown, the predetermined distribution of discrete adhesive regions  3000  can include a first adhesive target area  3002  and a first adhesive strike area  3004 . The relationship between the first adhesive target area  3002  and the first adhesive strike area  3004  can be defined by a first differential distance  3001  between the adhesive target location  3003  (i.e., the center or centroid of the first adhesive target area) and the adhesive strike location  3005  (i.e., the center or centroid of the first adhesive strike area). Preferably, the differential distance will be equal to zero, but in actuality will likely be an acceptably small value. In an embodiment, the first differential distance  3001  can be zero (0), or an acceptable distance greater than zero, such that some distance can exist between locations  3003  and  3005 . Further, as illustrated, the first differential distance  3001  can be less than the length or width, or diameter of either the first adhesive strike area  3004  or the first adhesive target area  3002 , allowing for contact and even overlap between portions of the first adhesive strike area  3004  and the first adhesive target area  3002 . Moreover, while not illustrated, it will be appreciated that the first differential distance  3001  can be zero (0), indicating completely accurate placement of the first adhesive strike area  3004  on the first adhesive target area  3002 . 
     In an embodiment, the first differential distance  3001  can be less than about 0.1 (d), wherein (d) represents the diameter of the first adhesive strike area  3004 . the diameter of the adhesive strike area is the longest dimension of the strike area, including for non-circular shapes, extending through its center. In an embodiment, the differential distance  3001  can be less than about 5(d), such as less than about 2(d), less than about 1(d) less than about 0.5(d), less than about 0.2(d), or even less than about 0.1 (d). It will be appreciated that the first differential distance  3001  can be within a range between any of the minimum and maximum values noted above. Control of the differential distance between the adhesive strike area and the adhesive target area can facilitate improved grinding performance of the abrasive article. 
     In an embodiment, a predetermined, or controlled, distribution  3000  can also include a second adhesive target area  3006  and a second adhesive strike area  3008 . Similar to the first adhesive target area and first adhesive strike area, the relationship between the second adhesive target area  3006  and the second adhesive strike area  3008  can be defined by a second differential distance  3010  between the second adhesive target location  3007  and the adhesive strike location  3009 . Preferably, the second differential distance will be equal to zero, but in actuality will likely be an acceptably small value. In an embodiment, the second differential distance  3010  can be zero (0), or an acceptable distance greater than zero, such that some distance can exist between locations  3007  and  3009 . As illustrated, the second differential distance  3010  can be less than the length or width, or diameter of either the second adhesive strike area  3008  or the second adhesive target area  3006 , allowing for contact and even overlap between portions of the second adhesive strike area  3006  and the second adhesive target area  3006 . Moreover, while not illustrated, it will be appreciated that the second differential distance  3010  can be zero (0), indicating completely accurate placement of the second adhesive strike area  3008  on the second adhesive target area  3006 . 
     Similarly, the predetermined distribution  3000  of adhesive areas can also include three or more adhesive target areas and three or more adhesive strike areas, such as a third adhesive target area  3011  and a third adhesive strike area  3013 , or a plurality of other target areas and strike areas as illustrated in  FIG.  30   . 
     Further with regard to the differential distance, such as the first differential distance  3001 , second differential distance  3010 , or any other of the plurality of differential distances can be defined as a vector, having a magnitude (i.e., distance or length) and a direction (or degree of rotation). As illustrated in  FIG.  30   , the first differential distance  3001  and the second differential distance  3010  have substantially similar or identical vectors. However, it is considered within the scope of the invention that the magnitude of differential distances can be the same or different, including direction or degree of rotation. For instance, A first differential distance  3001  and a second differential distance  3010  can have the same magnitude (length) but can have different directions. Similarly, a first differential distance  3001  and a second differential distance  3010  can have the same direction or degree of rotation, but they can have different magnitudes. In either case, as described in greater detail below, vector measurement is but one of several methods available for determining the accuracy, precision, and variability of placement of an adhesive strike area with respect to an adhesive target area. 
     As mentioned previously, adhesive contact regions that are applied with a high level of control (i.e., high accuracy, high precision, low variability) can facilitate improved grinding performance of the abrasive article. In an embodiment, a substantial number (greater than 50%) of the adhesive contact regions are applied “on target”, i.e., such that the magnitude and direction (or degree of rotation) of the differential distance between an adhesive strike area and an adhesive target area is zero or an acceptably small value. In an embodiment the number of adhesive contact regions that are “on target” in a given sample area (such as 1 square meter) is at least about 55%, such as at least about 60%, at least about 65%, at least about 68%, at least about 70%, at least about 75%, at least about 80%, at least about 85%, at least about 90%, at least about 95%, at least about %, at least about 98%, at least about 99%, at least about 99.5%, or even about 100% (all measured values are within an acceptable limit). In another embodiment, the accuracy and precision of the application and placement of the adhesive contact areas (as defined by the differential distance between the adhesive target location and adhesive strike location) can be measured as a percentage of adhesive contact regions that are “on target” within a standard deviation. In an embodiment, the number of adhesive contact regions that are “on target” within a standard deviation is at least at least about 65%, at least about 68%, at least about 70%, at least about 75%, at least about 80%, at least about 85%, at least about 90%, at least about 95%, at least about 97%, at least about 98%, at least about 99%, at least about 99.5%, or even about 100% (all measured values are within an acceptable limit). In another embodiment, at least a specific number or percentage of adhesive contact regions have a differential distance that is within one standard deviation of the mean differential distance of the sample population. In a specific embodiment, at least about 68% of the population (or alternatively a sample of the population) of adhesive contact regions are within one (1) standard deviation of the mean differential distance of the population or sample population. In another embodiment, at least about 70%, at least about 75%, at least about 80%, at least about 85%, at least about %, at least about 95%, at least about 97%, at least about 98%, at least about 99%, at least about 0.5%, or even about 100% (all measured values are within an acceptable limit) of adhesive contact regions are within one (1) standard deviation of the mean differential distance of the population or sample population. 
     Lateral Spacing 
     As mentioned previously, the adhesive contact regions can be spaced apart from each other by a lateral space, defined as a smallest distance between two adjacent adhesive contact regions as measured along a lateral plane parallel to the lateral axis of the backing upon which the adhesive contact regions are disposed. In an embodiment,*the lateral spacing between adhesive contact regions can exhibit a high level of control (i.e., high accuracy, high precision, low variability). In an embodiment, a substantial number (greater than 50%) of the adhesive contact regions are applied “on target” such that the difference between the lateral spacing of adjacent adhesive contact areas is zero or an acceptably small value. In an embodiment at least about 55% such as at least about 60%, at least about 65%, at least about 68%, at least about 70%, at least about 75%, at least about 80%, at least about 85%, at least about 90%, at least about 95%, at least about %, at least about 98%, at least about 99%, at least about 99.5%, or even about 100% (all measured values are within an acceptable limit) of the lateral spacing between the adjacent adhesive contact regions is within 2.5 standard deviations of the mean. In another embodiment, at least about 65% of a sample population of the lateral spacing between adjacent adhesive contact areas will be within 2.5 standard deviation of the mean, such as within 2.25 standard deviations, within 2.0 standard deviations, within 1.75, standard deviations, within 1.5 standard deviations, within 1.25 standard deviations, or within 1.0 standard deviations of the mean. It will be appreciated that alternative ranges can be constructed by using the above combinations of percentages and deviations from the mean. 
     Longitudinal Spacing 
     As mentioned previously, the adhesive contact regions can be spaced apart from each other by a longitudinal space, defined as a smallest distance between two adjacent adhesive contact regions as measured along a longitudinal plane parallel to the longitudinal axis of the backing upon which the adhesive contact regions are disposed. In an embodiment, the longitudinal spacing between adhesive contact regions can exhibit a high level of control (i.e., high accuracy, high precision, low variability). In an embodiment, a substantial number (greater than 50%) of the adhesive contact regions are applied “on target” such that the difference between the longitudinal spacing of adjacent adhesive contact areas is zero or an acceptably small value. In an embodiment at least about 55% such as at least about 60%, at least about 65%, at least about 68%, at least about 70%, at least about 75%, at least about 80%, at least about 85%, at least about 90%, at least about 95%, at least about %, at least about 98%, at least about 99%, at least about 99.5%, or even about 100% (all measured values are within an acceptable limit) of the longitudinal spacing between the adjacent adhesive contact regions is within 2.5 standard deviations of the mean. In another embodiment, at least about 65% of a sample population of the longitudinal spacing between adjacent adhesive contact areas will be within 2.5 standard deviation of the mean, such as within 2.25 standard deviations, within 2.0 standard deviations, within 1.75, standard deviations, within 1.5 standard deviations, within 1.25 standard deviations, or within 1.0 standard deviations of the mean. It will be appreciated that alternative ranges can be constructed by using the above combinations of percentages and deviations from the mean. 
     As mentioned above, at least one abrasive particle can be disposed on an adhesive contact region. Similar to the lateral spacing and longitudinal spacing between adjacent adhesive contact areas, a lateral spacing and longitudinal spacing can exist between the at least one abrasive particles disposed on the adjacent contact regions. 
     In an embodiment, the lateral spacing between the at least one abrasive particles can exhibit a high level of control (i.e., high accuracy, high precision, low variability). In an embodiment, a substantial number (greater than 50%) of the at least one abrasive particles are applied “on target” such that the difference between the lateral spacing of the at least one abrasive particles is zero or an acceptably small value. In an embodiment at least about 55% such as at least about 60%, at least about 65%, at least about 68%, at least about 70%, at least about 75%, at least about 80%, at least about 85%, at least about 90%, at least about 95%, at least about %, at least about 98%, at least about 99%, at least about 99.5%, or even about 100% (all measured values are within an acceptable limit) of the lateral spacing between the adjacent at least one abrasive particles is within 2.5 standard deviations of the mean. In another embodiment, at least about 65% of a sample population of the lateral spacing between the at least one abrasive particles will be within 2.5 standard deviation of the mean, such as within 2.25 standard deviations, within 2.0 standard deviations, within 1.75, standard deviations, within 1.5 standard deviations, within 1.25 standard deviations, or within 1.0 standard deviations of the mean. It will be appreciated that alternative ranges can be constructed by using the above combinations of percentages and deviations from the mean. 
     As mentioned previously, the at least one abrasive particles can be spaced apart from each other by a longitudinal space, defined as a smallest distance between the at least one abrasive particles as measured along a longitudinal plane parallel to the longitudinal axis of the backing upon which the at least one abrasive particles are disposed. In an embodiment, the longitudinal spacing between the at least one abrasive particles can exhibit a high level of control (i.e., high accuracy, high precision, low variability). In an embodiment, a substantial number or percentage (greater than 50%) of the at least one abrasive particles are applied “on target” such that the difference between the longitudinal spacing of the at least one abrasive particles is zero or an acceptably small value. In an embodiment at least about 55% such as at least about 60%, at least about 65%, at least about 68%, at least about 70%, at least about 75%, at least about 80%, at least about 85%, at least about 90%, at least about 95%, at least about %, at least about 98%, at least about 99%, at least about 99.5%, or even about 100% (all measured values are within an acceptable limit) of the longitudinal spacing between the at least one abrasive particles is within 2.5 standard deviations of the mean. In another embodiment, at least about 65% of a sample population of the longitudinal spacing between adjacent adhesive contact areas will be within 2.5 standard deviation of the mean, such as within 2.25 standard deviations, within 2.0 standard deviations, within 1.75, standard deviations, within 1.5 standard deviations, within 1.25 standard deviations, or within 1.0 standard deviations of the mean. It will be appreciated that alternative ranges can be constructed by using the above combinations of percentages and deviations from the mean. 
     High accuracy, high precision, low variability placement of adhesive contact regions can directly contribute to improved abrasive performance of the abrasive article by directly improving accuracy, precision, an lower variability in the placement of abrasive particles, as well as, promoting efficient swarf removal. It will be appreciated that several different measures of variability related to the location of the predetermined distribution of the adhesive contact regions can be evaluated. Such measures can include well known statistical analytical measures including variability, standard deviation, interquartile range, range, mean difference, median absolute deviation, average absolute deviation, distance standard deviation, coefficient of variation, quartile coefficient of dispersion, relative mean difference, variance, variance-to-mean ratio, or combinations thereof. For instance, the ratio for the variance-to-mean cannot be greater than 35%, such as not greater than 30%, such as not greater than 20%. Whichever tool is utilized, the purpose for analysis is to measure the accuracy and precision of embodiments that can be defined by the location of a predetermined distribution of adhesive strike areas with respect to adhesive target areas. As used herein, “precision” and “precise” are terms meaning the degree to which repeated measurements under unchanged conditions reveal the same results. As used herein, “accuracy” and “accurate” are terms meaning the degree of closeness of a measurement to its actual, or target, value. 
     Abrasive particles can be disposed on an adhesive layer (e.g., make layer, size layer, or other layer of the abrasive article) using a suitable deposition method, such as electrostatic coating process, gravity drop coating, and all other abrasive particle deposition processes described herein. During electrostatic coating, the abrasive particles are applied in an electric field, allowing the particles to be advantageously aligned with their long axes normal to the major surface. In another embodiment, the abrasive particles are coated over the entire surface of the make coat that has been applied to the backing. In another embodiment, the abrasive particles are applied to only a portion of the make coat that has been applied to the backing. abrasive particles will preferentially bond to the areas coated with the make resin. 
     As mentioned previously, the shaped abrasive particles may be disposed on the adhesive contact region such that the footprint of the abrasive particle can substantially be the same as the discrete adhesive contact region. Thus the lateral and longitudinal spacing between the adjacent adhesive contact regions and associated abrasive particles can be controlled. 
     In accordance with one embodiment, the process of delivering shaped abrasive particles to the abrasive article can include expelling the first shaped abrasive particle from an opening within the alignment structure. Some suitable exemplary methods for expelling can include applying a force on the shaped abrasive particle and removing it from the alignment structure. For example, in certain instances, the shaped abrasive particle can be contained in the alignment structure and expelled from the alignment structure using gravity, electrostatic attraction, surface tension, pressure differential, mechanical force, magnetic force, agitation, vibration, and a combination thereof. In at least one embodiment, the shaped abrasive particles can be contained in the alignment structure until a surface of the shaped abrasive particles are contacted to a surface of the backing, which may include an adhesive material, and the shaped abrasive particles are removed from the alignment structure and delivered to a predetermined position on the backing. 
     According to another aspect, the shaped abrasive particles can be delivered to the surface of the abrasive article in a controlled manner by sliding the shaped abrasive particles along a pathway. For example, in one embodiment, the shaped abrasive particles can be delivered to a predetermined position on the backing by sliding the abrasive particles down a pathway and through an opening via gravity.  FIG.  15    includes an illustration of a system according to an embodiment. Notably, the system  1500  can include a hopper  1502  configured to contain a content of shaped abrasive particles  1503  and deliver the shaped abrasive particles  1503  to a surface of a backing  1501  that can be translated under the hopper  1502 . As illustrated, the shaped abrasive particles  1503  can be delivered down a pathway  1504  attached to the hopper  1502  and delivered to a surface of the backing  1501  in a controlled manner to form a coated abrasive article including shaped abrasive particles arranged in a predetermined distribution relative to each other. In particular instances, the pathway  1504  can be sized and shaped to deliver a particular number of shaped abrasive particles at a particular rate to facilitate the formation of the predetermined distribution of shaped abrasive particles. Furthermore, the hopper  1502  and the pathway  1504  may be movable relative to the backing  1501  to facilitate the formation of select predetermined distributions of shaped abrasive particles. 
     Moreover, the backing  1501  may further be translated over a vibrating table  1506  that can agitate or vibrate the backing  1501  and the shaped abrasive particles contained on the backing  1501  to facilitate improved orientation of the shaped abrasive particles. 
     In yet another embodiment, the shaped abrasive particles can be delivered to a predetermined position by expelling individual shaped abrasive particles on to the backing via a throwing process. In the throwing process, shaped abrasive particles may be accelerate and expelled from a container at a rate sufficient to hold the abrasive particles at a predetermined position on the backing. For example,  FIG.  16    includes an illustration of a system using a throwing process, wherein shaped abrasive particles  1602  are expelled from a throwing unit  1603  that can accelerate the shaped abrasive particles via a force (e.g., pressure differential) and deliver the shaped abrasive particles  1602  from the throwing unit  1603  down a pathway  1605 , which may be attached to the throwing unit  1603  and onto a backing  1601  in a predetermined position. The backing  1601  may be translated under the throwing unit  1603 , such that after initial placement, the shaped abrasive particles  1602  can undergo a curing process that may cure an adhesive material on the surface of the backing  1601  and hold the shaped abrasive particles  1602  in their predetermined positions. 
       FIG.  17 A  includes an illustration of an alternative throwing process in accordance with an embodiment. Notably, the throwing process can include expelling a shaped abrasive particle  1702  from a throwing unit  1703  over a gap  1708  to facilitate placement of the shaped abrasive particle  1702  on the backing in a predetermined position. It will be appreciated that the force of expelling, the orientation of the shaped abrasive particle  1702  upon being expelled, the orientation of the throwing unit  1703  relative the backing  1701 , and the gap  1708  may be controlled and adjusted to adjust the predetermined position of the shaped abrasive particle  1702  and the predetermined distribution of shaped abrasive particles  1702  on the backing  1701  relative to each other. It will be appreciated that the abrasive article  1701  may include an adhesive material  1712  on a portion of the surface to facilitate adherence between the shaped abrasive particles  1702  and the abrasive article  1701 . 
     In particular instances, the shaped abrasive particles  1702  can be formed to have a coating. The coating can be overlying at least portion of the exterior surface of the shaped abrasive particles  1702 . In one particular embodiment, the coating can include an organic material, and more particularly, a polymer, and still more particularly an adhesive material. The coating comprising an adhesive material may facilitate attachment of the shaped abrasive particles  1702  to the backing  1701 . 
       FIG.  17 B  includes an illustration of an alternative throwing process in accordance with an embodiment. In particular, the embodiment of  FIG.  17 B  details a particular throwing unit  1721  configured to direct the shaped abrasive particles  1702  at the abrasive article  1701 . According to an embodiment, the throwing unit  1721  can include a hopper  1723  configured to contain a plurality of shaped abrasive particles  1702 . Furthermore, the hopper  1723  can be configured to deliver one or more shaped abrasive particles  1702  in a controlled manner to an acceleration zone  1725 , wherein the shaped abrasive particles  1702  are accelerated and directed toward the abrasive article  1701 . In one particular embodiment, the throwing unit  1721  can include a system  1722  utilizing a pressurized fluid, such as a controlled gas stream or air knife unit, to facilitate the acceleration of the shaped abrasive particles  1702  in the acceleration zone  1725 . As further illustrated, the throwing unit  1721  may utilize a slide  1726  configured to generally direct the shaped abrasive particles  1702  toward the abrasive article  1701 . In one embodiment, the throwing unit  1731  and/or the slide  1726  can be moveable between a plurality of positions and configured to facilitate delivery of individual shaped abrasive particles to particular positions on the abrasive article, thus facilitating the formation of the predetermined distribution of shaped abrasive particles. 
       FIG.  17 A  includes an illustration of an alternative throwing process in accordance with an embodiment. In the illustrated embodiment of  FIG.  17 C  details an alternative throwing unit  1731  configured to direct the shaped abrasive particles  1702  at the abrasive article  1701 . According to an embodiment, the throwing unit  1731  can include a hopper  1734  configured to contain a plurality of shaped abrasive particles  1702  and deliver one or more shaped abrasive particles  1702  in a controlled manner to an acceleration zone  1735 , wherein the shaped abrasive particles  1702  are accelerated and directed toward the abrasive article  1701 . In one particular embodiment, the throwing unit  1731  can include a spindle  1732  that may be rotated around an axis and configured to rotate a stage  1733  at a particular rate of revolutions. The shaped abrasive particles  1702  can be delivered from the hopper  1734  to the stage  1733  and accelerated at a particular from the stage  1733  toward the abrasive article  1701 . As will be appreciated, the rate of rotation of the spindle  1732  may be controlled to control the predetermined distribution of shaped abrasive particles  1702  on the abrasive article  1701 . Furthermore, the throwing unit  1731  can be moveable between a plurality of positions and configured to facilitate delivery of individual shaped abrasive particles to particular positions on the abrasive article, thus facilitating the formation of the predetermined distribution of shaped abrasive particles. 
     According to another embodiment, the process of delivering the shaped abrasive particles in a predetermined position on the abrasive article and forming an abrasive article having a plurality of shaped abrasive particles in a predetermined distribution relative to each other can include the application of magnetic force.  FIG.  18    includes an illustration of a system according to an embodiment. The system  1800  can include a hopper  1801  configured to contain a plurality of shaped abrasive particles  1802  and deliver the shaped abrasive particles  1802  to a first translating belt  1803 . 
     As illustrated, the shaped abrasive particles  1802  can be translated along the belt  1803  to an alignment structure  1805  configured to contain each of the shaped abrasive particles at a discrete contact region. According to one embodiment, the shaped abrasive particles  1802  can be transferred from the belt  1803  to the alignment structure  1805  via a transfer roller  1804 . In particular instances, the transfer roller  1804  may utilize a magnet to facilitate controlled removal of the shaped abrasive particles  1802  from the belt  1803  to the alignment structure  1805 . The provision of a coating comprising a magnetic material may facilitate the use of the transfer roller  1804  with magnetic capabilities. 
     The shaped abrasive particles  1802  and can be delivered from the alignment structure  1805  to a predetermined position on the backing  1807 . As illustrated, the backing  1807  may be translated on a separate belt and from the alignment structure  1805  and contact the alignment structure to facilitate the transfer of the shaped abrasive particles  1802  from the alignment structure  1805  to the backing  1807 . 
     In still another embodiment, the process of delivering the shaped abrasive particles in a predetermined position on the abrasive article and forming an abrasive article having a plurality of shaped abrasive particles in a predetermined distribution relative to each other can include the use of an array of magnets.  FIG.  19    includes an illustration of a system for forming an abrasive article according to an embodiment. In particular, the system  1900  can include shaped abrasive particles  1902  contained within an alignment structure  1901 . As illustrated, the system  1900  can include an array of magnets  1905 , which can include a plurality of magnets arranged in a predetermined distribution relative to the backing  1906 . According to an embodiment, the array of magnets  1905  can be arranged in a predetermined distribution that can be substantially the same as the predetermined distribution of shaped abrasive particles on the backing. 
     Moreover, each of the magnets of the array of magnets  1905  can be moveable between a first position and a second position, which can facilitate control of the shape of the array of magnets  1905  and further facilitate control of the predetermined distribution of the magnets and the predetermined distribution of shaped abrasive particles  1902  on the backing. According to one embodiment, the array of magnets  1905  can be changed to facilitate control of one or more predetermined orientation characteristics of the shaped abrasive particles  1902  on the abrasive article. 
     Furthermore, each of the magnets of the array of magnets  1905  may be operable between a first state and a second state, wherein a first state can be associated with a first magnetic strength (e.g., an on state) and the second state can be associated with a second magnetic strength (e.g., an off state). Control of the state of each of the magnets can facilitate selective delivery of shaped abrasive particles to particular regions of the backing  1906  and further facilitate control of the predetermined distribution. According to one embodiment, the state of the magnets of the array of magnets  1905  can be changed to facilitate control of one or more predetermined orientation characteristics of the shaped abrasive particles  1902  on the abrasive article. 
       FIG.  20 A  includes an image of a tool used to form an abrasive article in accordance with an embodiment. Notably, the tool  2051  can include a substrate, which may be an alignment structure having openings  2052  defining discrete contact regions configured to contain shaped abrasive particles and assist in the transfer and placement of shaped abrasive particles on a finally-formed abrasive article. As illustrated, the openings  2052  can be arranged in a predetermined distribution relative to each other on alignment structure. In particular, the openings  2052  can be arranged in one or more groups  2053  having a predetermined distribution relative to each other, which can facilitate the placement of the shaped abrasive particles on the abrasive article in a predetermined distribution defined by one or more predetermined orientation characteristics. In particular, the tool  2051  can include a group  2053  defined by a row of openings  2052 . Alternatively, the tool  2051  may have a group  2055  defined by all of the openings  2052  illustrated, since each of the openings have substantially the same predetermined rotational orientation relative to the substrate. 
       FIG.  20 B  includes an image of a tool used to form an abrasive article according to an embodiment. Notably, as illustrated in  FIG.  20 B , shaped abrasive particles  2001  are contained in the tool  2051  of  FIG.  20 A , and more particularly, the tool  2051  can be an alignment structure, wherein each of the openings  2052  contains a single shaped abrasive particle  2001 . In particular, the shaped abrasive particles  2001  can have a triangular two-dimensional shaped, as viewed top-down. Moreover, the shaped abrasive particles  2001  can be placed into the openings  2052  such that a tip of the shaped abrasive particle extends into and through the openings  2052  to the opposite side of the tool  2051 . The openings  2052  can be sized and shaped such that they substantially complement at least a portion (if not the entire) contour of the shaped abrasive particles  2001  and hold them in a position defined by one or more predetermined orientation characteristics in the tool  2051 , which will facilitate transfer of the shaped abrasive particles  2001  from the tool  2051  to a backing while maintaining the predetermined orientation characteristics. As illustrated, the shaped abrasive particles  2001  can be contained within the openings  2052  such that at least a portion of the surfaces of the shaped abrasive particles  2001  extends above the surface of the tool  2051 , which may facilitate transfer of the shaped abrasive particles  2001  from the openings  2052  to a backing. 
     As illustrated, the shaped abrasive particles  2001  can define a group  2002 . The group  2002  can have a predetermined distribution of shaped abrasive particles  2001 , wherein each of the shaped abrasive particles has substantially the same predetermined rotational orientation. Moreover, each of the shaped abrasive particles  2001  has substantially the same predetermined vertical orientation and predetermined tip height orientation. Furthermore, the group  2002  includes multiple rows (e.g.,  2005 ,  2006 , and  2007 ) oriented in a plane parallel to a lateral axis  2081  of the tool  2051 . Moreover, within the group  2002 , smaller groups (e.g.,  2012 ,  2013 , and  2014 ) of the shaped abrasive particles  2001  may exist, wherein the shaped abrasive particles  2001  share a same difference in a combination of a predetermined lateral orientation and predetermined longitudinal orientation relative to each other. Notably, the shaped abrasive particle  2001  of the groups  2012 ,  2013 , and  2014  can be oriented in raked columns, wherein the group extends at an angle to the longitudinal axis  2080  of the tool  2051 , however, the shaped abrasive particles  2001  can have substantially a same difference in the predetermined longitudinal orientation and predetermined lateral orientation relative to each other. As also illustrated, the predetermined distribution of shaped abrasive particles  2001  can defines a pattern, which may be considered a triangular pattern  2011 . Moreover, the group  2002  can be arranged such that the boundary of the group defines a two-dimensional macro-shape of a quadrilateral (see dotted line). 
       FIG.  20 C  includes an image of a portion of an abrasive article according to an embodiment. In particular, the abrasive article  2060  includes a backing  2061  and a plurality of shaped abrasive particles  2001 , which were transferred from the openings  2052  of the tool  2051  to the backing  2061 . As illustrated, the predetermined distribution of the openings  2052  of the tool can correspond to the predetermined distribution of shaped abrasive particles  2001  of the group  2062  contained on the backing  2061 . The predetermined distribution of shaped abrasive particles  2001  can be defined by one or more predetermined orientation characteristics. Moreover, as evidence from  FIG.  20 C , the shaped abrasive particles  2001  can be arranged in groups that substantially correspond to the groups of the shaped abrasive particles of  FIG.  20 B , when the shaped abrasive particles  2001  were contained in the tool  2051 . 
     For certain abrasive articles herein, at least about 75% of the plurality of shaped abrasive particles on the abrasive article can have a predetermined orientation relative to the backing, including for example a side orientation as described in embodiments herein. Still, the percentage may be greater, such as at least about 77%, at least about 80%, at least about 81%, or even at least about 82%. And for one non-limiting embodiment, an abrasive article may be formed using the shaped abrasive particles herein, wherein not greater than about 99% of the total content of shaped abrasive particles have a predetermined side orientation. It will be appreciated that reference herein to percentages of shaped abrasive particles in a predetermined orientation is based upon a statistically relevant number of shaped abrasive particles and a random sampling of the total content of shaped abrasive particles. 
     To determine the percentage of particles in a predetermined orientation, a 2D microfocus x-ray image of the abrasive article is obtained using a CT scan machine run in the conditions of Table 1 below. The X-ray 2D imaging was conducted using Quality Assurance software. A specimen mounting fixture utilizes a plastic frame with a 4″×4″ window and an 00.5″ solid metallic rod, the top part of which is half flattened with two screws to fix the frame. Prior to imaging, a specimen was clipped over one side of the frame where the screw heads were faced with the incidence direction of the X-rays ( FIG.  1 ( b ) ). Then five regions within the 4″×4″ window area are selected for imaging at 120 kV/80 μA. Each 2D projection was recorded with the X-ray off-set/gain corrections and at a magnification. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                   
                 Field of view 
                   
               
               
                 Voltage 
                 Current 
                   
                 per image 
                 Exposure 
               
               
                 (kV) 
                 (μA) 
                 Magnification 
                 (mm × mm) 
                 time 
               
               
                   
               
             
            
               
                 120 
                 80 
                 15X 
                 16.2 × 13.0 
                 500 ms/2.0 fps 
               
               
                   
               
            
           
         
       
     
     The image is then imported and analyzed using the ImageJ program, wherein different orientations are assigned values according to Table 2 below. 
     
       
         
           
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Cell marker 
                   
               
               
                 type 
                 Comments 
               
               
                   
               
             
            
               
                 1 
                 Grains on the perimeter of the image, partially exposed - 
               
               
                   
                 standing in a side orientation (e.g., particles standing 
               
               
                   
                 on their side surface) 
               
               
                 2 
                 Grains on the perimeter of the image, partially exposed - 
               
               
                   
                 down orientation (i.e., particles in a flat orientation 
               
               
                   
                 or inverted orientation) 
               
               
                 3 
                 Grains on the image, completely exposed - standing in a 
               
               
                   
                 side orientation 
               
               
                 4 
                 Grains on the image, completely exposed - down 
               
               
                 5 
                 Grains on the image, completely exposed - standing slanted 
               
               
                   
                 (between standing vertical and down at a 45 degree angle) 
               
               
                   
               
            
           
         
       
     
     Three calculations are then performed as provided below in Table 3. After conducting the calculations the percentage of shaped abrasive particles in a side orientation per square centimeter can be derived. Notably, a particle having a side orientation is a particle having a vertical orientation, as defined by the angle between a major surface of the shaped abrasive particle and the surface of the backing, wherein the angle is 45 degrees or greater. Accordingly, a shaped abrasive particle having an angle of 45 degrees or greater is considered standing or having a side orientation, a shaped abrasive particle having an angle of 45 degrees is considered standing slanted, and a shaped abrasive particle having an angle of less than 45 degrees is considered having a down orientation. 
     
       
         
           
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                 5) Parameter 
                 Protocol* 
               
               
                   
               
             
            
               
                 % grains up 
                 ((0.5 × 1) + 3 + 5)/(1 + 2 + 3 + 4 + 5) 
               
               
                 Total # of grains per cm 2   
                 (1 + 2 + 3 + 4 + 5) 
               
               
                 # of grains up per cm 2   
                 (% grains up × Total # of grains per cm 2   
               
               
                   
               
               
                 *These are all normalized with respect to the representative area of the image. 
               
               
                 + - A scale factor of 0.5 was applied to account for the fact that they are not completely present in the image. 
               
            
           
         
       
     
     Furthermore, the abrasive articles made with the shaped abrasive particles can utilize various contents of the shaped abrasive particles. For example, the abrasive articles can be coated abrasive articles including a single layer of the shaped abrasive particles in an open-coat configuration or a closed coat configuration. However, it has been discovered, quite unexpectedly, that the shaped abrasive particles demonstrate superior results in an open coat configuration. For example, the plurality of shaped abrasive particles can define an open coat abrasive product having a coating density of shaped abrasive particles of not greater than about 70 particles/cm 2 . In other instances, the density of shaped abrasive particle per square centimeter of the abrasive article may be not greater than about 65 particles/cm 2 , such as not greater than about 60 particles/cm 2 , not greater than about 55 particles/cm 2 , or even not greater than about 50 particles/cm 2 . Still, in one non-limiting embodiment, the density of the open coat coated abrasive using the shaped abrasive particle herein can be at least about 5 particles/cm 2 , or even at least about 10 particles/cm 2 . It will be appreciated that the density of shaped abrasive particles per square centimeter of abrasive article can be within a range between any of the above minimum and maximum values. 
     In certain instances, the abrasive article can have an open coat density of a coating not greater than about 50% of abrasive particle covering the exterior abrasive surface of the article. In other embodiments, the percentage coating of the abrasive particles relative to the total area of the abrasive surface can be not greater than about 40%, not greater than about 30%, not greater than about 25%, or even not greater than about 20%. Still, in one non-limiting embodiment, the percentage coating of the abrasive particles relative to the total area of the abrasive surface can be at least about 5%, such as at least about 10%, at least about 15%, at least about 20%, at least about 25%, at least about 30%, at least about 35%, or even at least about 40%. It will be appreciated that the percent coverage of shaped abrasive particles for the total area of abrasive surface can be within a range between any of the above minimum and maximum values. 
     Some abrasive articles may have a particular content of abrasive particles for a length (e.g., ream) of the backing. For example, in one embodiment, the abrasive article may utilize a normalized weight of shaped abrasive particles of at least about 10 lbs/ream (148 grams/m 2 ), at least about 15 lbs/ream, at least about 20 lbs/ream, such as at least about 25 lbs/ream, or even at least about 30 lbs/ream. Still, in one non-limiting embodiment, the abrasive articles can include a normalized weight of shaped abrasive particles of not greater than about 60 lbs/ream (890 grams/m 2 ), such as not greater than about 50 lbs/ream, or even not greater than about 45 lbs/ream. It will be appreciated that the abrasive articles of the embodiments herein can utilize a normalized weight of shaped abrasive particle within a range between any of the above minimum and maximum values. 
     Applicants have observed that certain abrasive article embodiments according to the teachings herein exhibit a beneficial amount of make coat material (aka the “make weight”) compared to the amount of abrasive particles (aka the “grain weight”) disposed on the backing. In an embodiment, the ratio of the make weight to the grain weight can be constant or variable. In an embodiment, the ratio of make weight to grain weight can be in a range of 1:40 to 1:1, such as 1:40 to 1:1.3, such as 1:25 to 1:2, such as 1:20 to 1:5. In a particular embodiment the ratio of make weight to grain weight is in a range of 1:20 to 1:9. 
     In an embodiment, the make weight can be at least 0.1 pound per ream, such as at least 0.2 pounds per ream, at least 0.3 pounds per ream, at least 0.4 pounds per ream, at least 0.5 pounds per ream, at least 0.6 pounds per ream, at least 0.7 pounds per ream, at least 0.8 pounds per ream, at least 0.9 pounds per ream, or at least 1.0 pound per ream. In an embodiment the make weight can be not greater than 40 pounds per ream, such as not greater than 35 pounds per ream, not greater than 30 pounds per ream, not greater than 28 pounds per ream, not greater than 25 pounds per ream, not greater than 20 pounds per ream, or not greater than 15 pounds per ream. It will be appreciated that make weight can be in a range of any of the maximum and minimum values given above. In specific embodiment, the make weight can be in a range of 0.5 pounds per ream to 20 pounds per ream, such as 0.6 pounds per ream to 15 pounds per ream, such as 0.7 pounds per ream to 10 pounds per ream. In a particular embodiment, the make weight is in a range of 0.5 pounds per ream to 5 pounds per ream. 
     In certain instances, the abrasive articles can be used on particular workpieces. A suitable exemplary workpiece can include an inorganic material, an organic material, a natural material, and a combination thereof. According to a particular embodiment, the workpiece can include a metal or metal alloy, such as an iron-based material, a nickel-based material, and the like. In one embodiment, the workpiece can be steel, and more particularly, can consist essentially of stainless steel (e.g., 304 stainless steel). 
     Example 1 
     A grinding test is conducted to evaluate the effect of orientation of a shaped abrasive grain relative to a grinding direction. In the test, a first set of shaped abrasive particles (Sample A) are oriented in frontal orientation relative to the grinding direction. Turning briefly to  FIG.  3 B , the shaped abrasive particle  102  has a frontal orientation grinding direction  385 , such that the major surface  363  defines a plane substantially perpendicular to the grinding direction, and more particularly, the bisecting axis  231  of the shaped abrasive particle  102  is substantially perpendicular to the grinding direction  385 . Sample A was mounted on a holder in a frontal orientation relative to a workpiece of austenitic stainless steel. The wheel speed and work speed were maintained at 22 m/s and 16 mm/s respectively. The depth of cut can be selected between 0 and 30 micron. Each test consisted of 15 passes across the 8 inch long workpiece. For each test, 10 repeat samples were run and the results were analyzed and averaged. The change in the cross-sectional area of the groove from beginning to the end of the scratch length was measured to determine the grit wear. 
     A second set of samples (Sample B) are also tested according to the grinding test described above for Sample A. Notably, however, the shaped abrasive particles of Sample B have a sideways orientation on the backing relative to the grinding direction. Turning briefly to  FIG.  3 B , the shaped abrasive particle  103  is illustrated as having a sideways orientation relative to the grinding direction  385 . As illustrated, the shaped abrasive particle  103  can include major surfaces  391  and  392 , which can be joined by side surfaces  371  and  372 , and the shaped abrasive particle  103  can have a bisecting axis  373  forming a particular angle relative to the vector of the grinding direction  385 . As illustrated, the bisecting axis  373  of the shaped abrasive particle  103  can have a substantially parallel orientation with the grinding direction  385 , such that the angle between the bisecting axis  373  and the grinding direction  385  is essentially 0 degrees. Accordingly, the sideways orientation of the shaped abrasive particle  103  may facilitate initial contact of the side surface  372  with a workpiece before any of the other surfaces of the shaped abrasive particle  103 . 
       FIG.  21    includes a plot of normal force (N) versus cut number for Sample A and Sample B according to the grinding test of Example 1.  FIG.  21    illustrates the normal force necessary to conduct grinding of the workpiece with the shaped abrasive particles of the representative samples A and B for multiple passes or cuts. As illustrated, the normal force of Sample A is initially lower than the normal force of Sample B. However, as the testing continues, the normal force of Sample A exceeds the normal force of Sample B. Accordingly, in some instances an abrasive article may utilize a combination of different orientations (e.g., frontal orientation and sideways orientation) of the shaped abrasive particles relative to an intended grinding direction to facilitate improved grinding performance. In particular, as illustrated in  FIG.  21   , a combination of orientations of shaped abrasive particles relative to a grinding direction may facilitate lower normal forces throughout the life of the abrasive article, improved grinding efficiency, and greater useable life of the abrasive article. 
     Example 2 
     Five samples are analyzed to compare the orientation of shaped abrasive particles. Three samples (Samples S1, S2 and S3) are made according to an embodiment. Sample S1 was made using at template and contacting process. The abrasive particles were disposed into and held in place by a template having a desired predetermined abrasive particle distribution. A backing substrate having a continuous make coat was contacted with the abrasive particles so that the abrasive particles were adhered to the make coat in the desired predetermined abrasive particle distribution. Samples S2 and S3 were made using a continuous electrostatic projection process. Shaped abrasive particles were projected onto a backing substrate having a discontinuous make coat. The make coat was previously applied as a predetermined distribution of a nonshadowing pattern of discrete circular adhesive contact areas (also called herein make coat “spots”). The pattern was phyllotactic pattern conforming to formula 1.1, described herein, (also called the pineapple pattern). The make coat for S2 and S3 comprised 17,000 circular adhesive contact regions distributed over the surface of the backing material. The make weight for the abrasive sample S2 and S3 was approximately 0.84 pounds per ream. The grain weight for samples S2 and S3 was approximately 17.7 pounds per ream. An image of the S2 and S3 sample is shown in  FIG.  37   . Image analysis was conducted to determine various spatial properties concerning the pattern. The average size of the adhesive contact areas (i.e. the make coat spots) was approximately 1.097 mm 2 . The adjacent spacing between the make coat spots was approximately 2.238 mm. The ratio of area covered with make coat to the area not covered with make coat was 0.1763 (i.e., approximately 17.6% of the backing surface was covered with make coat). 
       FIG.  22    includes an image of a portion of Sample S1 using a 2D microfocus X-ray via a CT scan machine according to the conditions described herein. Two other samples (Samples CS1 and CS2) are representative of conventional abrasive products including shaped abrasive particles. Samples CS1 and CS2 are commercially available from 3M as Cubitron II. Sample S1 included shaped grains commercially available from 3M as Cubitron II. Inventive samples S2 and S3 included next generation shaped abrasive particles available from Saint-Gobain Abrasives.  FIG.  23    includes an image of a portion of Sample CS2 using 2D microfocus X-ray via a CT scan machine according to the conditions described herein. Each of the samples is evaluated according to the conditions described herein for evaluating the orientation of shaped abrasive particles via X-ray analysis. 
       FIG.  24    includes a plot of up grains/cm 2  and total number of grains/cm 2  for each of the comparative samples (Sample CS1 and Sample CS2) and the inventive samples (Samples S1, S2, and S3). It should be noted that sample CS1 and CS2 are different trials of the same belt. The grinding machine broke down after CS1 was tested and had to be repaired and recalibrated. The comparative sample was again run and reported as CS2. The values for CS1 are included because they do appear to still be instructive; however, the more apt comparison is between the values for CS2 and S1, S2, and -S3, which were all tested under the same exact grinding conditions. As illustrated, Samples CS1 and CS2 demonstrate a significantly fewer number of shaped abrasive particles oriented in a side orientation (i.e., upright orientation) as compared to Samples S1, S2, and S3. In particular, Sample S1 demonstrated all shaped abrasive particles (i.e., 100%) measured were oriented in a side orientation (i.e., 100% of the shaped abrasive particles were upright with grinding tips “up”), while only 72 percent of the total number of shaped abrasive particles of CS2 had a side orientation (i.e. only 72% of the shaped abrasive particles were in an upright position with grinding tips up). Further, 100% of the shaped abrasive particles of sample S1 were in a controlled rotational alignment. Inventive samples S2 and S3 also show a superior number of shaped abrasive particles in an upright position with grinding tips up as compared to C2. As evidenced, state-of-the-art conventional abrasive articles (C2) using shaped abrasive particles have not achieved the precision of orientation of the presently described abrasive articles. 
     Example 3 
     Another inventive coated abrasive embodiment was prepared in a similar manner to S2 and S3. The make coat was applied according to a discontinuous, non-shadowing distribution following the pineapple pattern; however the total number of discrete adhesive contact regions was 10,000. The make weight was approximately 1.6 lbs/ream and the grain weight was approximately 19.2 lbs/ream. Shaped abrasive particles (Cubitron II), as described above in Example 2, were then applied to the make coat contact regions. The inventive coated abrasive had an abrasive particle density (abrasive grain density) of 19 grains/cm 2 . X-ray analysis was conducted, similar to Example 2 above, to evaluate the orientation of the shaped abrasive particles of the inventive embodiment and a conventional comparative coated abrasive product.  FIG.  35 A  is exemplary of the comparative product.  FIG.  35   . B is exemplary of the inventive embodiment. A graphical representation of the results of the orientation analysis is presented by  FIG.  36   . The inventive embodiment had a surprisingly improved amount of abrasive grains, 89%, in an upright position, whereas the comparative example only had 72% of the abrasive grains in an upright position. 
     The present application represents a departure from the state of the art. While the industry has recognized that shaped abrasive particles may be formed through processes such as molding and screen printing, the processes of the embodiments herein are distinct from such processes. Notably, the embodiments herein include a combination of process features facilitating the formation of batches of shaped abrasive particle having particular features. Moreover, the abrasive articles of the embodiments herein can have a particular combination of features distinct from other abrasive articles including, but not limited to, a predetermined distribution of shaped abrasive particles, utilization of a combination of predetermined orientation characteristics, groups, rows, columns, companies, macro-shapes, channel regions, aspects of the shaped abrasive particles, including but not limited to, aspect ratio, composition, additives, two-dimensional shape, three-dimensional shape, difference in height, difference in height profile, flashing percentage, height, dishing, half life change of specific grinding energy, and a combination thereof. And in fact, the abrasive articles of embodiments herein may facilitate improved grinding performance. While the industry has generally recognized that certain abrasive articles may be formed having an order to certain abrasive units, such abrasive units have traditionally been limited to abrasive composites that can be easily molded via a binder system, or using traditional abrasive or superabrasive grits. The industry has not contemplated or developed systems for forming abrasive articles from shaped abrasive particles having predetermined orientation characteristics as described herein. Manipulation of shaped abrasive particles in order to effectively control predetermined orientation characteristics is a non-trivial matter, having exponentially improved control of particles in three-space, which is not disclosed or suggested in the art. Reference herein to the term “the same” will be understood to mean substantially the same. 
     Item 1. A coated abrasive article comprising a backing; an adhesive layer disposed in a discontinuous distribution on at least a portion of the backing, wherein the discontinuous distribution comprises a plurality of adhesive contact regions having at least one of a lateral spacing or a longitudinal spacing between each of the adhesive contact regions; and at least one abrasive particle disposed on a majority of the adhesive contact regions, the abrasive particle having a tip, and there being at least one of a lateral spacing or a longitudinal spacing between each of the abrasive particles, and wherein at least 65% of the at least one of a lateral spacing and a longitudinal spacing between the tips of the abrasive particles is within 2.5 standard deviations of the mean. 
     Item 2. The coated abrasive article of item 1, wherein at least 55% of the abrasive particle tips are upright. 
     Item 3. The coated abrasive article of item 1, wherein the ratio of the variance to the mean is not greater than 35%. 
     Item 4. The coated abrasive article of item 1, wherein the discontinuous distribution is a non-shadowing pattern, a controlled non-uniform pattern, a semi-random pattern, a random pattern, a regular pattern, an alternating pattern, or combinations thereof. 
     Item 5. The coated abrasive article of item 2, wherein the at least one abrasive particle disposed on the majority of adhesive contact regions comprises a first shaped abrasive particle coupled to a first adhesive contact region in a first position; and a second shaped abrasive particle coupled to a second adhesive contact region; wherein the first shaped abrasive particle and second shaped abrasive particle are arranged in a controlled, non-shadowing arrangement relative to each other, the controlled, non-shadowing arrangement comprising at least two of a predetermined rotational orientation, a predetermined lateral orientation, and a predetermined longitudinal orientation. 
     Item 6. The coated abrasive article of item 1, wherein at least 65% of the at least one of the lateral spacing and the longitudinal spacing between the adhesive contact regions is within 2.5 standard deviations of the mean. 
     Item 7. The coated abrasive article of item 1, wherein the adhesive layer has a substantially uniform thickness that is less than the d50 height of the at least one abrasive particle. 
     Item 8. The coated abrasive article of item 1, wherein the width of each of the discrete adhesive contact regions is substantially equal to the d50 width of the at least one abrasive particle. 
     Item 9. The coated abrasive article of item 1 further comprising: 
     a second adhesive layer disposed in a discontinuous distribution over the first adhesive layer,
 
wherein the second adhesive layer covers a smaller surface area than the first adhesive layer and does not extend beyond the first adhesive layer.
 
     Item 10. The coated abrasive article of item 1, 5, or 9, wherein at least one abrasive particle is disposed on each adhesive contact region. 
     Item 11. A method of making a coated abrasive article comprising applying an adhesive composition to a backing using a continuous screen printing process, wherein the adhesive composition is applied as a discontinuous distribution comprising a plurality of discrete adhesive contact regions having at least one of a lateral spacing and a longitudinal spacing between each of the adhesive contact regions, disposing at least one abrasive particle onto each of the discrete adhesive contact regions, the abrasive particle having a tip and there being at least one of a lateral spacing or a longitudinal spacing between each of the abrasive particles and curing the binder composition. 
     Item 12. The method of item 11, wherein at least 65% of the at least one of a lateral spacing and a longitudinal spacing between the tips of the adhesive particle is within 2.5 standard deviations of the mean. 
     Item 13. A coated abrasive article comprising a backing; a make coat disposed on the backing in a predetermined distribution; and a plurality of shaped abrasive particles, wherein the predetermined distribution comprises a discontinuous pattern of a plurality of discrete contact regions, wherein at least one shaped abrasive particle of the plurality of shaped abrasive particles is disposed on each of the discrete contact regions, and wherein the ratio of make weight to grain weight is in a range of 1:40 to 1:1. 
     Item 14. A coated abrasive article comprising a backing; a make coat disposed on the backing in a predetermined distribution; and a plurality of shaped abrasive particles, wherein the predetermined distribution comprises a discontinuous pattern of a plurality of discrete contact regions, wherein at least one shaped abrasive particle of the plurality of shaped abrasive particles is disposed on each of the discrete contact regions, and wherein the number of discrete contact regions is in a range of 1000 to 40,000, and wherein greater than 50% of the shaped abrasive particles are in an upright position. 
     Item 15. The coated abrasive article of item 14, wherein the discrete contact regions have an adjacent spacing in a range of 0.5 to 3 times the average length of the shaped abrasive particle. 
     Item 16. The coated abrasive article of item 14, wherein the discrete contact regions have an adjacent spacing in a range of 0.2 mm to 2.2 mm. 
     Item 17. The coated abrasive article of item 14, wherein the discontinuous make coat covers at least 1% to 95% of the backing. 
     Item 18. The coated abrasive article of item 14, wherein the discrete contact regions have an average diameter in a range of 0.3 mm to 20 mm. 
     Item 19. The coated abrasive article of item 14, wherein 4% to 85% of the backing is bare. 
     Item 20. The coated abrasive article of item 14, wherein greater than 75% of the shaped abrasive particles are in an upright position. 
     The above-disclosed subject matter is to be considered illustrative, and not restrictive, and the appended items are intended to cover all such modifications, enhancements, and other embodiments, which fall within the true scope of the present invention. Thus, to the maximum extent allowed by law, the scope of the present invention is to be determined by the broadest permissible interpretation of the following items and their equivalents, and shall not be restricted or limited by the foregoing detailed description. 
     The Abstract of the Disclosure is provided to comply with Patent Law and is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the items. In addition, in the foregoing Detailed Description of the Drawings, various features may be grouped together or described in a single embodiment for the purpose of streamlining the disclosure. This disclosure is not to be interpreted as reflecting an intention that the itemed embodiments require more features than are expressly recited in each item. Rather, as the following items reflect, inventive subject matter may be directed to less than all features of any of the disclosed embodiments. Thus, the following items are incorporated into the Detailed Description of the Drawings, with each item standing on its own as defining separately itemed subject matter.