Patent Publication Number: US-2021180174-A1

Title: Applied magnetic field synthesis and processing of iron nitride magnetic materials

Description:
RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 15/840,747, filed Dec. 13, 2017, which is a continuation of U.S. patent application Ser. No. 14/754,284, filed Jun. 29, 2015, which claims the benefit of U.S. Provisional Patent Application No. 62/019,046, filed Jun. 30, 2014, each of which is incorporated herein by reference in its entirety. 
    
    
     This invention was made with government support under ARPA-E 0472-1595 awarded by the Dept. of Energy. The government has certain rights in the invention. 
    
    
     TECHNICAL FIELD 
     The disclosure relates to techniques for forming iron nitride magnetic materials. 
     BACKGROUND 
     Permanent magnets can provide high efficiency and reliability for renewable energy technologies, including electrical vehicles and wind turbines, etc. Because rare earth permanent magnets have supply constraints and high price, a new magnet with more abundant and less strategically important elements is desired to replace rare earth magnets. 
     SUMMARY 
     The α″-Fe 16 N 2  phase is a promising candidate for rare-earth-free magnets. In this disclosure, techniques including annealing iron nitride materials in the presence of an applied magnetic field have been used to enhance the Fe 16 N 2  phase formation in iron nitride materials. Increased volume fractions of the Fe 16 N 2  phase may improve the magnetic properties of the iron nitride magnetic materials. Improved magnetic properties may include, for example, coercivity, magnetization, and magnetic orientation. In some examples, the applied magnetic field may be at least 0.2 Tesla (T). The temperature at which the magnetic field annealing is performed may at least partially depend upon further elemental additions to the iron nitride base composition and the approach used to initially synthesize the iron nitride base composition. In some examples, the magnetic field may be at least about 0.2 T, at least about 2 T, at least about 2.5 T, at least about 6 T, at least about 7 T, at least about 8 T, at least about 9 T, at least about 10 T, or higher. In some examples, the magnetic field is between about 5 T and about 10 T. In other examples, the magnetic field is between about 8 T and about 10 T. 
     In one example, the disclosure describes a method including annealing a material including iron and nitrogen in the presence of an applied magnetic field to form at least one Fe 16 N 2  phase domain, wherein the applied magnetic field has a strength of at least about 0.2 Tesla (T). 
     In another example, the disclosure describes an apparatus configured to perform any of the techniques described herein. 
     In another example, the disclosure describes a material formed by any of the techniques described herein. 
     In an additional example, the disclosure describes a bulk permanent magnet formed by any of the techniques described herein. 
     The details of one or more examples are set forth in the accompanying drawings and the description below. Other features, objects, and advantages will be apparent from the description and drawings, and from the claims. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a flow diagram illustrating another example technique for forming an iron nitride permanent magnet. 
         FIG. 2  is a flow diagram illustrating an example technique for forming an iron nitride permanent magnet. 
         FIG. 3  is a chart illustrating x-ray diffraction spectra of an example Fe—N rod sample before and after quenching. 
         FIG. 4  is a chart illustrating x-ray diffraction spectra of an example Fe—N rod sample after annealing, with and without an applied high magnetic field. 
         FIG. 5  is a chart illustrating magnetization curves of an example bulk Fe—N rod sample, measured by a SQUID at room temperature after annealing with and without an applied 9 T magnetic field. 
         FIG. 6  is a chart illustrating magnetization curves of example bulk Fe—N rod samples, measured by a SQUID after annealing with and without an applied 9 T magnetic field. 
         FIG. 7  is a chart illustrating x-ray diffraction spectra of example Fe—N rod samples after annealing, with and without an applied high magnetic field. 
         FIG. 8A  is a chart illustrating magnetization curves of an example as-nitrided Fe 16 N 2 -based nanoscale powder, measured at room temperature before and after annealing. 
         FIG. 8B  is a chart illustrating magnetization curves of an example as-nitrided Fe 16 N 2 -based nanoscale powder, measured at room temperature before and after annealing with an applied 9 T magnetic field. 
         FIG. 9A  is a chart illustrating a magnetization curve of an example gallium arsenide substrate coated with films of iron, silver and iron nitride, measured at room temperature after annealing. 
         FIG. 9B  is a chart illustrating a magnetization curve of an example gallium arsenide substrate coated with films of iron, silver and iron nitride, measured at room temperature after annealing with an applied 9 T high magnetic field. 
         FIG. 9C  is a chart illustrating a magnetization curve of an example gallium arsenide substrate coated with films of iron, silver and iron nitride, measured at room temperature after annealing with an applied 9 T high magnetic field at a temperature higher than the example thin-film structure of  FIG. 9B . 
         FIG. 10  is a chart illustrating a magnetization curve of an example iron nitride sample prepared by ball milling, nitriding, and annealing with and without an applied 9 T high magnetic field. 
         FIG. 11  is a chart x-ray diffraction spectra of example Fe—N material after annealing, with and without an applied 9 T high magnetic field. 
     
    
    
     DETAILED DESCRIPTION 
     The present disclosure describes the synthesis and processing of Fe—N magnetic materials under application of magnetic fields for facilitating the transformation of Fe 8 N phase to Fe 16 N 2  phase, thus potentially increasing the volume ratio of Fe 16 N 2  and improving magnetic properties of the magnetic material, including, for example, at least one of saturation magnetization, coercivity, remnant magnetization, or the like. The disclosure describes techniques including annealing a material including iron and nitrogen in the presence of a magnetic field greater than about 0.2 T. The presence of the magnetic field may facilitate transformation of iron nitride disordered phases into Fe 16 N 2  phase. In some examples, the strength of the high magnetic field may be at least about 0.2 T, at least about 2 T, at least about 2.5 T, at least about 6 T, at least about 7 T, at least about 8 T, at least about 9 T, at least about 10 T, or higher. In some examples, the magnetic field is between about 0.2 T and about 10 T, or between about 2 and about 10 T, or between about 2.5 T and about 9 T, or between about 5 T and about 10 T, or between about 8 T and about 10 T. 
     In some examples, the material including iron and nitrogen may be annealed at a temperature between about 100° C. and about 250° C., such as between about 120° C. and about 250° C., for between about 10 hours to about 100 hours, while being exposed to the magnetic field. For example, the material including iron and nitrogen may be annealed at a temperature between about 120° C. and 200° C. for between about 10 hours to about 100 hours, while being exposed to the magnetic field. The atmosphere in which the material may be annealed may include, for example, vacuum, air, or liquid, such as oil. According to this disclosure, the material including iron and nitrogen may be annealed at a temperature of between about 150° C. and 160° C. for about 20 hours, while being exposed to the magnetic field. In other examples, for instance when the material including iron and nitrogen further includes at least one dopant, the material may be annealed at a temperature as high as about 250° C. for between about 10 hours and 100 hours, while being exposed to the magnetic field. The disclosure also describes an apparatus configured to perform the techniques disclosed herein, and materials that may be formed by the techniques described in this disclosure. 
     Annealing a material including iron and nitrogen in the presence of an applied magnetic field may facilitate the phase transformation for iron nitride magnetic materials, including iron nitride bulk samples, thin film samples, and nanoparticle (powder) samples. In some examples, the iron nitride magnetic materials additionally may include at least one dopant. For example, the dopant may include at least one metal dopant (e.g. Al, Mn, Ti, La, Co, Cr, Ni, rare earth metals, and combinations thereof), and/or at least one non-metal dopant (e.g., B, C, O, P, Si, and combinations thereof). The dopant may be incorporated in the iron nitride material or may be coated on the iron nitride material. In some examples, the temperature at which the material is annealed may vary based on the identity of one or more dopants in the material. 
     In some examples, radio waves generated by a radio frequency source (for example, radio waves having a power of between about 100 watts (W) and about 1000 W and a frequency between about 13.56 megahertz (MHz) and about 1.8 gigahertz (GHz) may be applied to assist annealing of the material including iron and nitrogen in the presence of a magnetic field, to facilitate formation of Fe 16 N 2  phase in the material. 
     Additionally or alternatively, in some examples, an ultrasonic wave (for example, ultrasonic waves having a power of between about 50 W and 1000 W) may be applied to assist annealing of the material including iron and nitrogen in the presence of a magnetic field, to facilitate formation of Fe 16 N 2  phase in the material. 
     In some examples, in addition to annealing the material including iron and nitrogen in the presence of an applied magnetic field, the techniques described herein may include solutionizing a material including iron and nitrogen in the presence of an applied magnetic field. During solutionizing, the material including iron and nitrogen may be brought to a temperature above the upper critical temperature to form a solution. For example, bulk FeN pellet materials, such as gamma-phase Fe—N(austenite), may be solutionized in an applied magnetic field at a high temperature, for example, at about 750° C. for about 15 minutes. Applying a magnetic field during solutionizing may shift the Fe—N phase equilibria, which may facilitate Fe 16 N 2  phase formation during subsequent annealing. In some examples, after solutionizing, the material may be quenched, which may be accomplished inside or outside of the applied magnetic field. In some examples, the quenching may include multiple steps, such as quenching in water followed by placing the iron nitride materials at liquid nitrogen temperature for about 20 hours (h) to aid in conversion of any retained austenite Fe phase to Fe 8 N martensite. After quenching, the iron nitride material may be annealed in the presence of the applied magnetic field. 
     The crystalline texture of the iron nitride material relative to the direction of the applied magnetic field also may affect the conversion of iron nitride to Fe 16 N 2  phase during annealing of the iron nitride materials in the presence of an applied magnetic field. By annealing a specific crystalline texture in a predetermined orientation relative to the direction of the applied magnetic field, external magnetic force (Zeeman energy) can facilitate the phase transformation from body-centered cubic (bcc) to body-centered tetragonal (bct). 
     An example technique of this disclosure includes nitridizing a material including iron in the presence of an applied magnetic field to form an iron-nitride-containing material ( 12 ), and annealing the iron-nitride-containing material in the presence of the applied magnetic field to form at least one Fe 16 N 2  phase domain ( 14 ), as shown in  FIG. 1 . The applied magnetic field may be applied at different strengths, as described above. For example, the applied magnetic field may have a strength of at least about 0.2 T, at least about 2 T, at least about 2.5 T, at least about 6 T, at least about 7 T, at least about 8 T, at least about 9 T, at least about 10 T, or higher. In some examples, the applied magnetic field may have a strength of between about 0.2 T and about 10 T, or between about 2 and about 10 T, or between about 2.5 T and about 9 T, or between about 5 T and about 10 T, or between about 8 T and about 10 T. 
     The magnetic field may be constant or a pulse field. The on/off ratio of pulse field may be between about 0.1% (percentage of pulse “on” duration divided by the inverse of the pulse frequency) up to about 90%. The frequency of pulse field may be between several Hz and several MHz. 
     In some examples, nitridizing of a material including iron (e.g., an iron-based powder or iron-based nanoscale powder) may be performed at a relatively low temperature, for example, between about 100° C. and 250° C. Example materials including iron include iron oxide, iron carbide, or iron-metal solid solutions. In some examples, the temperature of nitridization may depend on the addition of dopants to the material including iron to yield improved magnetic properties. Such dopants may include, for example, Al, Mn, Ti, La, Co, Cr, Ni, rare earth metals, or combinations thereof. In some examples, nitridizing (or nitriding) may be performed in NH 3  gas, H 2  gas, N 2  gas, or mixtures thereof. Fe8N may or may not form as an intermediate during the synthesis of Fe 16 N 2  according to this technique. 
     In some examples, nitridizing the material and annealing the iron-nitride-containing material may occur together in situ, in the presence of the applied magnetic field, to form at least one Fe 16 N 2  phase domain. In some examples, an example technique also may include, prior to nitridizing the material including iron, reducing the material, where reduction of the material occurs in situ in the presence of the applied magnetic field. Reduction of the material including iron may remove oxygen from the material including iron, such as by reaction of oxygen with at least one of Ca, Al, or Na. The reducing of material including iron also may include exposing the material to NH 3  gas, H 2  gas, N 2  gas, or mixtures thereof. For example, a carbon-coated iron powder may be reduced in hydrogen gas for about 1 hour at a temperature of between about 375° C. and about 425° C., such as about 390° C., prior to nitridizing the powder. 
     The annealing of iron-nitride-containing materials formed from nitridizing a material including iron (e.g., iron nanoscale powder), and the various conditions associated with annealing, may be similar to or the same as annealing in a high magnetic field described with respect to other examples described herein of annealing a material including iron and nitrogen. Likewise, techniques of annealing the iron-nitride-containing materials may also include treatment with radio waves, ultrasonic waves, and addition of various dopants to the materials as described herein. Phase transformations (e.g., transformation of an α′-Fe 8 N phase in the iron-nitride-containing material to an α″-Fe 16 N 2  phase), anticipated yields of transformation, and the volume of certain iron-nitride phases in iron-nitride-containing material, also may be similar to or the same for iron-nitride containing materials formed by nitridization techniques, as with respect to other examples described herein, such as the processing of Fe—N rod samples. Moreover, interactions between the applied magnetic field and the crystalline matrix of iron-nitride-containing material of the described technique (e.g., such materials formed by nitridization of iron powder), also may be similar to or the same as those interactions disclosed regarding materials including iron and nitrogen, such as processed Fe—N rod samples. 
     The iron nitride materials formed by the techniques described herein may be used as magnetic materials in a variety of applications, including, for example, bulk permanent magnets. Bulk permanent magnets may include a minimum dimension of at least about 0.1 mm. In some examples, the iron nitride materials that are annealed in the presence of an applied magnetic field may be bulk materials (have a minimum dimension of at least about 0.1 mm). In other examples, iron nitride materials that are annealed in the presence of the applied magnetic field may not be bulk materials (may have a minimum dimension less than about 0.1 mm), and the iron nitride materials may be consolidated with other iron nitride materials to form bulk permanent magnets. Examples of techniques that may be used to consolidate iron nitride magnetic materials are described, for example, in International Patent Application Number PCT/US2012/051382, filed on Aug. 17, 2012, and titled “IRON NITRIDE PERMANENT MAGNET AND TECHNIQUE FOR FORMING IRON NITRIDE PERMANENT MAGNET,” the entire content of which is incorporated herein by reference. 
     For example, iron nitride materials may be arranged such that the &lt;001&gt; axes of the respective iron nitride materials are substantially aligned. Aligning the &lt;001&gt; axes of the respective iron nitride materials may provide uniaxial magnetic anisotropy to a bulk magnetic material, such as a permanent magnet, formed by joining the iron nitride materials. 
     The multiple iron nitride materials may be compressed using, for example, cold compression or hot compression. In some examples, the temperature at which the compression is performed may be below about 300° C., as Fe 16 N 2  may begin to degrade above about 300° C. The compression may be performed at a pressure and for a time sufficient to join the multiple iron nitride materials into a substantially unitary bulk magnetic material, such as a permanent magnet. 
     Any number of iron nitride materials may be pressed together to form a bulk magnetic material, such as a permanent magnet. In some examples, the bulk magnetic material has a size such that a minimum dimension is at least 0.1 mm. In some examples, the bulk magnetic material has a size in at least one dimension of at least 1 mm. In some examples, the bulk magnetic material has a size in at least one dimension of at least 1 cm. 
     Other examples of techniques that may be used to consolidate iron nitride magnetic materials are described in International Patent Application Number PCT/US2014/015104, filed on Feb. 6, 2014, and titled “IRON NITRIDE PERMANENT MAGNET AND TECHNIQUE FOR FORMING IRON NITRIDE PERMANENT MAGNET,” the entire content of which is incorporated herein by reference. For example, iron nitride materials may be sintered to form a bulk magnetic material. In some examples, For example, a plurality of iron nitride materials (which include Fe 16 N 2  phase domains) may be mixed or interleaved with a plurality of workpieces (e.g., sheets, particles, or the like) that include iron or nonmagnetic materials. The iron nitride materials may be arranged so the &lt;001&gt; axes of the respective iron nitride materials are substantially aligned. Aligning the &lt;001&gt; axes of the respective iron nitride materials may provide uniaxial magnetic anisotropy to the bulk magnetic material. 
     Then, the iron nitride materials (alone or with iron or nonmagnetic materials) may be pressed together and sintered. The sintering pressure, temperature and duration may be selected to mechanically join the iron nitride materials while maintaining the crystal structure of the iron nitride materials (e.g., as including the Fe 16 N 2  phase domains). Thus, in some examples, the sintering step may be performed at a relatively low temperature. For example, the sintering temperature may be below about 250° C., such as between about 120° C. and about 250° C., between about 150° C. and about 250° C., between about 120° C. and about 200° C., between about 150° C. and about 200° C., or about 150° C. The sintering pressure may be between, for example, about 0.2 gigapascal (GPa) and about 10 GPa. The sintering time may be at least about 5 hours, such as at least about 20 hours, or between about 5 hours and about 100 hours, or between about 20 hours and about 100 hours, or about 40 hours. The sintering time, temperature, and pressure may be affected by the materials in iron nitride materials that include iron or nonmagnetic materials. The sintering may be performed in an ambient atmosphere, a nitrogen atmosphere, a vacuum, or another inert atmosphere. 
     Other examples of techniques that may be used to consolidate iron nitride magnetic materials are described in International Patent Application Number PCT/US2014/015104, filed on Feb. 6, 2014, and titled “IRON NITRIDE PERMANENT MAGNET AND TECHNIQUE FOR FORMING IRON NITRIDE PERMANENT MAGNET,” the entire content of which is incorporated herein by reference. For example, tin (Sn) may be disposed on a surface of at least iron nitride material including at least one Fe 16 N 2  phase domain, such as a first workpiece and a second workpiece. Crystallite and atomic migration may cause the Sn to agglomerate. The first workpiece and the second workpiece then may be pressed together and heated to form an iron-tin (Fe—Sn) alloy. The Fe—Sn alloy may be annealed at a temperature between about 150° C. and about 400° C. to join the first workpiece and the second workpiece. In some examples, the annealing temperature may be sufficiently low that magnetic properties of the first workpiece and the second workpiece (e.g., magnetization of the at least one Fe 16 N 2  and proportion of Fe 16 N 2  phase domains within the workpieces and) may be substantially unchanged. In some examples, rather than Sn being used to join the iron nitride materials including at least one Fe 16 N 2  phase domain, Cu, Zn, or Ag may be used. 
     In some examples, &lt;001&gt; crystal axes of the respective iron nitride materials may be substantially aligned. Aligning the &lt;001&gt; crystal axes of the respective iron nitride materials may provide uniaxial magnetic anisotropy to the magnet formed from iron nitride materials. 
     As another example, a plurality of iron nitride materials including at least one Fe 16 N 2  phase domain may be disposed adjacent to each other, with &lt;001&gt; crystal axes substantially aligned. This may provide uniaxial magnetic anisotropy to the magnet formed from the iron nitride materials. Ferromagnetic particles may disposed within a resin or other adhesive, such as natural or synthetic resins, including ion-exchange resins, such as those available under the trade designation Amberlite™, from The Dow Chemical Company, Midland, Mich.; epoxies, such as Bismaleimide-Triazine (BT)-Epoxy; a polyacrylonitrile; a polyester; a silicone; a prepolymer; a polyvinyl buryral; urea-formaldehyde, or the like. The filled resin or other adhesive may then be used to substantially fully encapsulate the plurality of iron nitride materials including at least one Fe 16 N 2  phase domain. In some examples, the resin or other adhesive may be cured to bond the plurality of iron nitride materials to each other. 
     The ferromagnetic particles may be magnetically coupled to Fe 16 N 2  hard magnetic material within the plurality of iron nitride materials via exchange spring coupling. Exchange spring coupling may effectively harden the magnetically soft ferromagnetic particles and provide magnetic properties for the bulk material similar to those of a bulk material consisting essentially of Fe 16 N 2 . To achieve exchange spring coupling throughout the volume of the magnetic material, the Fe 16 N 2  domains may be distributed throughout the bulk magnetic material, e.g., at a nanometer or micrometer scale. In some examples, magnetic materials including Fe 16 N 2  domains and domains of ferromagnetic particles and resin or other adhesive may include a volume fraction of Fe 16 N 2  domains of less than about 40 volume percent (vol. %) of the entire bulk magnetic material. The ferromagnetic particles  144  may include, for example, Fe, FeCo, Fe 8 N, or combinations thereof. 
     As another example, a compression shock apparatus may be used to generate a compression shock, which joins the iron nitride materials. Again, a plurality of iron nitride materials may be disposed adjacent to each other, with &lt;001&gt; crystal axes substantially aligned. At least some ferromagnetic particles may be disposed between adjacent iron nitride materials. In some examples, shock compression may include placing the iron nitride materials between parallel plates. The iron nitride materials may be cooled by flowing liquid nitrogen through conduit coupled to a back side of one or both of the parallel plates, e.g., to a temperature below 0 qC. A gas gun may be used to impact one of the parallel plates with a burst of gas at a high velocity, such as about 850 m/s. In some examples, the gas gun may have a diameter between about 40 mm and about 80 mm. After the shock compression, the ferromagnetic particles may be magnetically coupled to Fe 16 N 2  hard magnetic material within the plurality of iron nitride materials via exchange spring coupling. 
     As another example, a conductive coil through which a current may be applied, which generates an electromagnetic field may be used to join iron nitride materials. The current may be generated in a pulse to generate an electromagnetic force, which may help to consolidate the iron nitride materials. In some examples, ferromagnetic particles may be disposed about the iron nitride materials. In some examples, the iron nitride materials may be disposed within an electrically conductive tube or container within the bore of a conductive coil. The conductive coil may be pulsed with a high electrical current to produce a magnetic field in the bore of the conductive coil that, in turn, induces electrical currents in the electrically conductive tube or container. The induced currents interact with the magnetic field generated by the conductive coil to produce an inwardly acting magnetic force that collapses the electrically conductive tube or container. The collapsing electromagnetic container or tube transmits a force to the iron nitride materials and joins the iron nitride materials. After the consolidation of the iron nitride materials with the ferromagnetic particles (if present), the ferromagnetic particles may be magnetically coupled to Fe 16 N 2  hard magnetic material within the iron nitride materials via exchange spring coupling. In some examples, this technique may be used to produce workpieces that have at least one of cylindrical symmetry, a high aspect-ratio, or a net shape (a shape corresponding to a desired final shape of the workpiece). 
     In any of the above examples, other techniques for assisting consolidation of a plurality of workpieces including at least one  Fe16N2  phase domain may be used, such as pressure, electric pulse, spark, applied external magnetic fields, a radio frequency signal, laser heating, infrared heating, for the like. Each of these example techniques for joining a plurality of workpieces including at least one Fe 16 N 2  phase domain may include relatively low temperatures such that the temperatures use may leave the Fe 16 N 2  phase domains substantially unmodified (e.g., by converting Fe 16 N 2  phase domains to other types of iron nitride). 
     In some examples, the disclosure describes techniques for forming a magnet including Fe 16 N 2  phase domains from a powder including iron nitride. By using iron nitride-containing raw materials to form the permanent magnet including Fe 16 N 2  phase domains, further nitriding of iron may be avoided, which may reduce a cost of forming the permanent magnet including Fe 16 N 2  phase domains, e.g., compared to techniques which include nitriding pure iron. 
     In some examples, the disclosure describes a technique for forming an iron nitride permanent magnet.  FIG. 2  is a flow diagram illustrating an example technique for forming an iron nitride permanent magnet. The technique of  FIG. 2  includes forming a material including a mixture of iron and nitrogen ( 16 ). Examples of techniques that may be used to form materials including a mixture of iron and nitrogen are described, for example, in International Patent Application Number PCT/US2012/051382, filed on Aug. 17, 2012, and titled “IRON NITRIDE PERMANENT MAGNET AND TECHNIQUE FOR FORMING IRON NITRIDE PERMANENT MAGNET,” the entire content of which is incorporated herein by reference. For example, an iron material may be strained along a direction substantially parallel (e.g., parallel or nearly parallel) to a &lt;001&gt; axis of at least one iron crystal in the iron material. The strain may be exerted on the iron material using a variety of strain inducing apparatuses. For example, a first end and a second end of iron material may received by (e.g., wound around) a first roller and a second roller, respectively, and the rollers may be rotated in opposite directions to exert a tensile force on the iron material. In other examples, opposite ends of the iron material may be gripped in mechanical grips, e.g., clamps, and the mechanical grips may be moved away from each other to exert a tensile force on the iron material. The iron material may be strained between about 0.3% and about 7%. 
     As the iron material is strained, the iron material may be nitridized. During nitridizing, the iron material may be heated and exposed to a nitrogen source. For example, the iron material may be heated to a temperature between about 125° C. and about 600° C. for between about 2 hours and about 9 hours. The nitrogen source may include, for example, diatomic nitrogen (N 2 ), ammonia (NH 3 ), or urea, and may be supplied in gas phase or liquid phase. Regardless of the technique used to nitridize the iron material, in some examples, the nitrogen may be diffused into the iron material to a concentration of between about 8 atomic percent (at. %) and about 14 at. %, such as about 11 at. %. 
     Other examples of techniques that may be used to form materials including a mixture of iron and nitrogen are described, for example, in International Patent Application Number PCT/US2014/015104, filed on Feb. 6, 2014, and titled “IRON NITRIDE PERMANENT MAGNET AND TECHNIQUE FOR FORMING IRON NITRIDE PERMANENT MAGNET,” the entire content of which is incorporated herein by reference. For example, N+ ions may be implanted in an iron material using ion implantation. The iron material may include a plurality of iron crystals. In some examples, the plurality of iron crystals may have crystal axes oriented in substantially the same direction. For example, a major surface of the iron material may be parallel to the (110) surfaces of all or substantially all of the iron crystals. In other examples, a major surface of the iron material may be parallel to another surface of all or substantially all of the iron crystals. By using an iron material in which all or substantially all of the iron crystals have substantially aligned crystal axes, anisotropy formed when forming the Fe 8 N and Fe 16 N 2  phases may be substantially aligned. 
     In some examples, the iron material includes a foil. The iron material may define a thickness on the order of hundreds of nanometers to millimeters. In some examples, the iron material may define a thickness between about 500 nanometers (nm) and about 1 millimeter (mm). The thickness of the iron material may affect the parameters used for ion implantation and annealing of the iron material. 
     Prior to implantation of N+ ions in the iron material, the iron material may be positioned on a surface of a silicon substrate or a gallium arsenide (GaAs) substrate. In some examples, the iron material may be position on the (111) surface of a (single crystal) silicon substrate, although any crystalline orientation may be used. 
     The average depth to which the N+ ions are implanted in the iron material may depend upon the energy to which the N+ ions are accelerated. The implant energy used to implant the N+ ions may be selected based at least in part on the thickness of the iron material. The implant energy also may be selected to implant the N+ ions without doing overly significant damage to the iron material, including the crystal lattice of the iron crystals in the iron material. For example, while higher implant energies may allow implantation of the N+ ions at a greater average depth, higher implant energies may increase the damage to the iron material, including damaging the crystal lattice of the iron crystals and ablating some of the iron atoms due to the impact of the N+ ions. 
     Additionally, the fluency of N+ ions may be selected to implant a desired dose of N+ ions within the iron material. In some examples, the fluency of N+ ions may be selected to implant approximately stoichiometric number of N+ ions within the iron material. The stoichiometric ratio of iron to nitrogen in Fe 16 N 2  is 8:1. Thus, the approximate number of iron atoms in the iron material may be determined, and a number of N+ ions equal to approximately ⅛ (12.5%) of the iron atoms may be implanted in the iron material, such as between about 8 at. % and about 15 at. %. The temperature of the iron material during the ion implantation also may be controlled. In some examples, the temperature of the iron material may be between about room temperature and about 500 qC. 
     Other examples of techniques that may be used to form materials including a mixture of iron and nitrogen are described, for example, in International Patent Application No. PCT/US2014/043902, filed Jun. 24, 2014, and titled “IRON NITRIDE MATERIALS AND MAGNETS INCLUDING IRON NITRIDE MATERIALS,” which claims the benefit of U.S. Provisional Patent Application No. 61/935,516, filed Feb. 4, 2014, and titled “IRON NITRIDE MATERIALS AND MAGNETS INCLUDING IRON NITRIDE MATERIALS.” The entire contents of International Patent Application No. PCT/US2014/043902 and U.S. Provisional Patent Application No. 61/935,516 are incorporated herein by reference. For example, iron materials may be milled in the presence of a nitrogen source to form iron-nitride containing particles. The milling apparatus may include, for example, a rolling mode milling apparatus, a stirring mode milling apparatus, or a vibration mode milling apparatus. In some examples, the iron material may include substantially pure iron (e.g., iron with less than about 10 atomic percent (at. %) dopants or impurities). In some examples, the dopants or impurities may include oxygen or iron oxide. The iron material may be provided in any suitable form, including, for example, a powder or relatively small particles. In some examples, an average size of particles in the iron material may be less than about 100 micrometers (μm). 
     The nitrogen source may include ammonium nitrate (NH 4 NO 3 ) or an amide-containing material, such as a liquid amide or a solution containing an amide, or hydrazine or a solution containing hydrazine. Amides include a C—N—H bond and hydrazine includes an N—N bond. Ammonium nitrate, amides and hydrazine may serve as a nitrogen donor for forming the powder including iron nitride. Example amides include carbamide ((NH 2 ) 2 CO; also referred to as urea), methanamide, benzamide, and acetamide, although any amide may be used. 
     In some examples, the milling apparatus may also contain a catalyst, such as Co, Ni, or both, which may catalyze the nitriding of the iron material. The bin of the milling apparatus may be rotated at a rate sufficient to cause mixing of the components in the bin (e.g., the milling spheres, the iron material, the nitrogen source, and, optionally, the catalyst) and cause the milling spheres to mill the iron material. In some examples, the bin may be rotated at a rotational speed of about 500 revolutions per minute (rpm) to about 2000 rpm, such as between about 600 rpm and about 650 rpm, about 600 rpm, or about 650 rpm. Milling may be performed for a predetermined time selected to allow nitriding of the iron material and milling of the iron material (and nitridized iron containing material) to a predetermined size distribution. In some examples, milling may be performed for a time between about 1 hour and about 100 hours, such as between about 1 hour and about 20 hours, or about 20 hours, or about 24 hours. In some examples, the milling apparatus may be stopped for about 10 minutes after each 10 hours of milling to allow the milling apparatus, the iron material, the nitrogen source, and, if present, the catalyst to cool. 
     As another example, a mixture of iron and nitrogen may be formed by melting a mixture including iron and nitrogen to form a molten iron nitride-containing mixture. The mixture including iron and nitrogen may include, for example, including an approximately 8:1 iron-to-nitrogen atomic ratio. For example, the mixture may include between about 8 atomic percent (at. %) and about 15 at. % nitrogen, with a balance iron, other elements, and dopants. As another example, the mixture may include between about 10 at. % and about 13 at. % nitrogen, or about 11.1 at. % nitrogen. 
     In some examples, the mixture including iron and nitrogen may include at least one type of iron nitride, such as, for example, FeN, Fe 2 N (e.g., ξ-Fe 2 N), Fe 3 N (e.g., ε-Fe 3 N), Fe 4 N (e.g., γ′-Fe 4 N and/or γ-Fe 4 N), Fe 2 N 6 , Fe 8 N, Fe 16 N 2 , or FeN x  (where x is between about 0.05 and about 0.5), in addition to iron and/or nitrogen. In some examples, the mixture including iron and nitrogen may have a purity (e.g., collective iron and nitrogen content) of at least 92 atomic percent (at. %). 
     In some examples, the iron and nitrogen may be melted by heating the mixture at a temperature above about 1500° C. In some examples, the mixture including iron and nitrogen may be heated in a furnace using a radio frequency (RF) induction coil. In examples in which a bulk iron nitride-containing material is used, the furnace may be heated at a temperature greater than about 1600° C. In examples in which an iron-nitride containing powder is used, the furnace may be heated at a temperature greater than about 2000° C. 
     Once the mixture including iron and nitrogen is molten, the mixture may be subjected to a casting, quenching, and pressing process to form iron nitride material. In some examples, the casting, quenching, and pressing process may be continuous, as opposed to a batch process. The molten mixture including iron and nitrogen may be deposited in a mold, which may shape the mixture including iron and nitrogen into a predetermined shape, such as at least one wire, ribbon, or other article having length that is greater than its width or diameter. During the casting process, the temperature of the mold may be maintained at a temperature between about 650° C. and about 1200° C., depending on the casting speed. The casting process can be conducted in air, a nitrogen environment, an inert environment, a partial vacuum, a full vacuum, or any combination thereof. The casting process can be at any pressure, for example, between about 0.1 GPa and about 20 GPa. In some examples, the casting process can be assisted by a straining field, a temperature field, a pressure field, a magnetic field, an electrical field, or any combination thereof. 
     After casting is complete or while the casting process is being completed, the mixture including iron and nitrogen may be quenched to set the crystalline structure and phase composition of the iron-nitride containing material. In some examples, during the quenching process, the workpieces may be heated to a temperature above 650° C. for between about 0.5 hour and about 20 hours. In some examples, the temperature of the workpieces may be dropped abruptly below the martensite temperature of the workpiece alloy (Ms). For example, for Fe 16 N 2 , the martensite temperature (Ms) is about 250° C. The medium used for quenching can include a liquid, such as water, brine (with a salt concentration between about 1% and about 30%), a non-aqueous liquid or solution such as an oil, or liquid nitrogen. In other examples, the quenching medium can include a gas, such as nitrogen gas with a flow rate between about 1 sccm and about 1000 sccm. In other examples, the quenching medium can include a solid, such as salt, sand, or the like. In some examples, the workpieces including iron and nitrogen may be cooled at a rate of greater than 50° C. per second during the quenching process. In some examples, the casting process can be assisted by a magnetic field and/or an electrical field. 
     After quenching is complete, the iron nitride material may be pressed to achieve the predetermined size of the iron nitride material. During the pressing process, the temperature of the iron nitride material may be maintained below about 250° C., and the iron nitride material may be exposed to a pressure between about 5 tons and 50 tons, depending on the desired final dimension (e.g., thickness or diameter) of the iron nitride material. When the pressing process is complete, the iron nitride material may be in the shape of a workpiece with a dimension in one or more axis between about 0.001 mm and about 50 mm (e.g., a diameter between about 0.1 mm and about 50 mm for a wire or a thickness between about 0.001 mm and about 5 mm for a ribbon). The iron nitride workpiece may include at least one Fe 8 N iron nitride phase domain. 
     Regardless of the technique by which the iron nitride material is formed, the technique of  FIG. 2  also includes annealing the material including iron and nitrogen in the presence of an applied magnetic field ( 18 ). The applied magnetic field may be applied at different strengths, as described above. For example, the applied magnetic field may have a strength of at least about 0.2 T, at least about 2 T, at least about 2.5 T, at least about 6 T, at least about 7 T, at least about 8 T, at least about 9 T, at least about 10 T, or higher. In some examples, the applied magnetic field may have a strength of between about 0.2 T and about 10 T, or between about 2 and about 10 T, or between about 2.5 T and about 9 T, or between about 5 T and about 10 T, or between about 8 T and about 10 T. As an example, the material including iron and nitrogen may be annealed at a temperature of between about 100° C. and 200° C. for between about 10 hours to about 100 hours, while being exposed to the magnetic field. In some examples, the material including iron and nitrogen may be annealed at a temperature of about 150° C. and about 160° C. for between about 10 hours and about 30 hours, such as about 20 hours, while being exposed to the magnetic field. In other examples, for instance when the material including iron and nitrogen further includes at least one dopant, the material may be annealed at a temperature as high as about 250° C. for between about 10 hours and 100 hours, while being exposed to the magnetic field. The atmosphere in which material including iron and nitrogen, or iron-nitride containing materials, may be annealed may include, for example, vacuum, air, or liquid, such as oil. 
     Clause 1: A method comprising annealing a material including iron and nitrogen in the presence of an applied magnetic field to form at least one Fe 16 N 2  phase domain, wherein the applied magnetic field has a strength of at least about 0.2 Tesla (T). 
     Clause 2: The method of clause 1, wherein the strength of the high magnetic field is greater than about 2.5 T. 
     Clause 3: The method of clause 1, wherein the strength of the high magnetic field is about 9 T. 
     Clause 4: The method of clause 1, wherein the strength of the high magnetic field is greater than about 9 T. 
     Clause 5: The method of any one of clauses 1 to 4, wherein annealing the material comprises heating the material at a temperature of between about 120° C. to about 200° C. for between about 10 hours and about 100 hours. 
     Clause 6: The method of any one of clauses 1 to 4, wherein annealing the material comprises heating the material at a temperature between about 150° and about 160° C. for about 20 hours. 
     Clause 7: The method of any one of clauses 1 to 6, further comprising exposing the material to a radio wave, wherein the radio wave has a power of between about 100 W and about 1000 W, and a frequency of between about 13.56 MHz and about 1.8 GHz. 
     Clause 8: The method of any one of clauses 1 to 6, further comprising exposing the material to an ultrasonic wave, wherein the ultrasonic wave has a power of between about 50 W and about 1000 W. 
     Clause 9: The method of any one of clauses 1 to 8, wherein the material comprises at least one of a pellet, rod, thin film, nanoparticle, powder, or nanoscale powder. 
     Clause 10: The method of any one of clauses 1 to 9, wherein the material further comprises at least one dopant. 
     Clause 11: The method of clause 10, wherein the at least one dopant comprises at least one of Al, Mn, La, Cr, Co, Ti, Ni, or a rare earth metal. 
     Clause 12: The method of clause 10 or 11, wherein the at least one dopant comprises at least one of B, C, P, Si, or O. 
     Clause 13: The method of any one of clauses 10 to 12, wherein annealing the material comprises heating the material at a temperature of between about 100° C. to about 250° C. for between about 10 hours and about 100 hours. 
     Clause 14: The method of any one of clauses 1 to 13, wherein annealing the material in the presence of the applied magnetic field transforms an α′-Fe 8 N phase in the material to an α″-Fe 16 N 2  phase. 
     Clause 15: The method of clause 14, wherein a transformation yield of the α′-Fe 8 N phase to the α″-Fe 16 N 2  phase is at least 70%. 
     Clause 16: The method of any one of clauses 1 to 15, wherein, after annealing, the α″-Fe 16 N 2  phase in the material is at least 20% of the material by volume. 
     Clause 17: The method of any one of clauses 1 to 16, wherein the applied magnetic field is applied in substantial alignment with a c axis of at least one iron crystal in the material. 
     Clause 18: The method of any one of clauses 1 to 17, wherein annealing the material reassembles a plurality of nitrogen atoms of the material from a disordered state to an ordered state within a crystalline matrix of the material. 
     Clause 19: The method of any one of clauses 1 to 18, wherein annealing the material in the presence of the applied magnetic field modifies a phase of iron nitride in the material and a crystalline orientation of the iron nitride. 
     Clause 20: The method of any of clauses 1 to 19, further comprising: prior to annealing the material, solutionizing the material in the presence of an applied magnetic field with a strength of at least about 0.2 T; and after solutionizing the material, quenching the material. 
     Clause 21: The method of clause 20, wherein quenching the material comprises exposing the material to liquid nitrogen for about 20 hours. 
     Clause 22: The method of clause 20 or 21, wherein solutionizing the material comprises solutionizing the material in the presence of an applied magnetic field with a strength of at least about 9 T magnetic field at about 750° C. 
     Clause 23: The method of any one of clauses 20 to 22, wherein quenching the material comprises quenching the material with water outside the presence of the magnetic field applied during solutionization. 
     Clause 24: The method of any one of clauses 20 to 22, wherein quenching the material with water comprises quenching the material with water within the presence of the magnetic field applied during solutionization. 
     Clause 25: The method of clause 20, wherein solutionizing the material comprises solutionizing the material at about 900° C. 
     Clause 26: The method of any one of clauses 1 to 25, wherein, prior to solutionizing, the concentration of nitrogen in the material is between about 8 atomic percent (at. %) and about 9 at. %. 
     Clause 27: A method comprising: nitridizing a material including iron in the presence of an applied magnetic field to form an iron-nitride-containing material; and annealing the iron-nitride-containing material in the presence of the applied magnetic field to form at least one Fe 16 N 2  phase domain, wherein the applied magnetic field has a strength of at least about 0.2 Tesla (T). 
     Clause 28: The method of clause 27, wherein the material including iron comprises an iron-based powder or iron-based nanoscale powder. 
     Clause 29: The method of clause 27 or 28, wherein the material comprises at least one of an iron oxide, iron carbide, iron chloride, or iron-metal solid solution. 
     Clause 30: The method of any one of clauses 27 to 29, wherein nitridizing the material and annealing the iron-nitride-containing material to form at least one Fe 16 N 2  phase domain occur in situ in the presence of the applied magnetic field. 
     Clause 31: The method of any of clauses 27 to 30, further comprising, prior to nitridizing the material, reducing the material, wherein reduction of the material occurs in situ in the presence of the applied magnetic field. 
     Clause 32: The method of clause 31, wherein reducing the material comprises reducing the material in at least one of hydrogen, nitrogen, or ammonia gas. 
     Clause 33: The method of clause 31, wherein reducing the material comprises reducing a carbon-coated iron powder in hydrogen gas for about 1 hour at a temperature of about 390° C. 
     Clause 34: The method of any one of clauses 27 to 33, wherein the strength of the high magnetic field is greater than about 2.5 T. 
     Clause 35: The method of any one of clauses 27 to 33, wherein the strength of the high magnetic field is about 9 T. 
     Clause 36: The method of any one of clauses 27 to 33, wherein the strength of the high magnetic field is greater than about 9 T. 
     Clause 37: The method of any one of clauses 27 to 36, wherein annealing the iron-nitride-containing material comprises heating the iron-nitride-containing material at a temperature of between about 100° C. to about 250° C. for between about 10 hours and about 100 hours. 
     Clause 38: The method of any one of clauses 27 to 36, wherein annealing the iron-nitride-containing material comprises heating the material at a temperature between about 150° and 160° C. for about 20 hours. 
     Clause 39: The method of any one of clauses 27 to 38, further comprising exposing the iron-nitride-containing material to a radio wave, wherein the radio wave has a power of between about 100 W and about 1000 W, and a frequency of between about 13.56 MHz and about 1.8 GHz. 
     Clause 40: The method of any one of clauses 27 to 38, further comprising exposing the iron-nitride-containing material to an ultrasonic wave, wherein the ultrasonic wave has a power of between about 50 W and about 1000 W. 
     Clause 41: The method of any one of clauses 27 to 40, wherein the iron-nitride-containing material further comprises at least one dopant. 
     Clause 42: The method of clause 41, wherein the at least one dopant comprises at least one of Al, Mn, La, Cr, Co, Ti, Ni, or a rare earth metal. 
     Clause 43: The method of clause 41 or 42, wherein the at least one dopant comprises at least one of B, C, P, Si, or O. 
     Clause 44: The method of any one of clauses 27 to 43, wherein annealing the iron-nitride-containing material in the presence of the applied magnetic field transforms an α′-Fe 8 N phase in the iron-nitride-containing material to an α″-Fe 16 N 2  phase. 
     Clause 45: The method of clause 44, wherein a transformation yield of the α′-Fe 8 N phase to the α″-Fe 16 N 2  phase is at least 70%. 
     Clause 46: The method of any one of clauses 27 to 45, wherein, after annealing, the α″-Fe 16 N 2  phase in the iron-nitride-containing material is at least 20% of the iron-nitride-containing material by volume. 
     Clause 47: The method of any one of clauses 27 to 46, wherein the applied magnetic field is applied in substantial alignment with a c axis of at least one iron crystal in the iron-nitride-containing material. 
     Clause 48: The method of any one of clauses 27 to 47, wherein annealing the iron-nitride-containing material reassembles a plurality of nitrogen atoms of the iron-nitride-containing material from a disordered state to an ordered state within a crystalline matrix of the iron-nitride-containing material. 
     Clause 49: The method of any of clauses 27 to 48, wherein annealing the iron-nitride-containing material in the presence of the applied magnetic field modifies a phase of iron nitride in the iron-nitride-containing material and a crystalline orientation of the iron nitride. 
     Clause 50: An apparatus configured to perform any one of the methods of clauses 1 to 49. 
     Clause 51: A material formed by the method of any one of clauses 1 to 49. 
     Clause 52: A bulk permanent magnet formed by the method of any one of claims  1  to  49 . 
     EXAMPLES 
     Example 1 
     A bulk Fe—N pellet containing between about 8 atomic percent (at. %) and about 9 at. % N was synthesized using a cold crucible high temperature melting of iron in the presence of urea. Further details regarding cold crucible processing may be found, for example, in International Patent Application Number PCT/US2012/051382, filed on Aug. 17, 2012, and titled “IRON NITRIDE PERMANENT MAGNET AND TECHNIQUE FOR FORMING IRON NITRIDE PERMANENT MAGNET,” the entire content of which is incorporated herein by reference. The Fe—N rod samples were about 10 millimeters (mm) in length, having a square cross-section of 1 mm per side. The surface of the rod was shiny, with no surface treatment having been applied during the following steps, with the nitrogen concentration measured by Auger Electron Spectroscopy (AES). 
       FIG. 3  is a chart illustrating x-ray diffraction spectra of Fe—N rod samples before solutionizing and quenching (upper spectrum) and after solutonizing at 660° C. for 4 h and quenching (lower spectrum). The strongest diffraction line in the upper spectrum is (110), which indicates the Fe—N bulk samples possess (110) preferred orientation. Before solutionizing and quenching, the sample is a solid mixture of Fe and N so that the main phase at this time is Fe. However, a small peak of Fe 4 N(200) appeared, as shown in the upper spectrum of  FIG. 3 , which was generated during Fe—N rod preparation. 
     The bulk Fe—N pellets were then solutionized at about 660° C. for about 4 hours and quenched in water. As shown in  FIG. 3 , the Fe 8 N phase appeared after quenching, with a 28% volume ratio calculated with respect to the Fe 8 N(202) peak. An oxide line, Fe 3 O 4 (121), also appeared with a 6% volume ratio, arising from the preparation stage. The Fe volume ratio was estimated to be 54%, with the remaining 12% being Fe 4 N. Therefore, after solutionizing and quenching, the FeN rod samples exhibit a mixture primarily of of bcc Fe and body-centered tetragonal (bct) Fe 8 N phases. 
     Based on standard diffraction intensity data for an iron nitride powder sample without any orientation, the ratio of diffraction intensities between Fe 8 N(202) and Fe 8 N(112) peaks in an XRD spectrum should be 100:1; however, the ratio observed in the sample of this example was about 1:1.5. The observed ratio of diffraction intensities between Fe 8 N(202) and Fe 8 N(004) was nearly the same as the ratio predicted by the standard data for iron nitride powder. These observations indicate that the b axis lies out of the sample plane, while a and c axes lie in the sample plane. 
     The bulk Fe—N pellet samples were then annealed at about 150° C. for about 20 hours. For one sample, the annealing was performed without applying a magnetic field. For a second sample, the material was re-solutionized at 750° C. for 15 minutes in a 9 T magnetic field, quenched, stored in liquid N2 for 20 h to help promote Fe 8 N formation. Annealing to form Fe 16 N 2  was then performed at 150° C. for 20 h with an applied field of about 9 T. The magnetic field was applied in plane in order to minimize the eddy current and the demagnetization factor. 
       FIG. 4  is a chart illustrating x-ray diffraction spectra of iron nitride rod samples after annealing, with and without an applied high magnetic field. Annealing without an applied magnetic field yielded a structure indicated by x-ray diffraction to include 54% iron, 10% of the highly magnetic ordered Fe 16 N 2  phase 18% of disordered Fe 8 N phase, 12% Fe 4 N phase, and 6% Fe 3 O 4  phase (top spectrum of  FIG. 4 ). 
       FIG. 4  shows that annealing the iron nitride bulk material in the presence of the applied magnetic field modified the phase constitution and crystalline orientation of the iron nitride bulk material. The Fe 16 N 2  content increased in the samples upon high field annealing, while both the Fe 16 N 2  (002) and Fe 8 N (004) peaks increased in intensity. Table 1 presents data with respect to the iron nitride rod samples prepared by normal annealing without an applied high magnetic field, as compared to iron nitride rod samples prepared by annealing with an applied magnetic field. The total amount of Fe 16 N 2  and Fe 8 N in the high field anneal sample (28%) matched the total Fe 16 N 2  and Fe 8 N content of the sample annealed outside of the field (28%), which may suggest that solutionizing and quenching samples in a high magnetic field may not significantly affect the resulting Fe—N structure, as compared to solutionizing and quenching outside of a high magnetic field. However, the intensities of Fe 8 N and Fe 16 N 2  compounds presented in the compared samples are different, which may be attributed to the influence of the applied high magnetic field during the 150° C. annealing step. The volume ratios of different elements or compounds with and without high field assistance are listed in Table 1. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Volume ratio 
                 Volume ratio 
               
               
                   
                 (Normal annealing) 
                 (High field annealing) 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Fe 
                 54% 
                 54% 
               
               
                   
                 Fe 16 N 2   
                 10% 
                 22% 
               
               
                   
                 Fe 8 N 
                 18% 
                  6% 
               
               
                   
                 Fe 4 N 
                 12% 
                 12% 
               
               
                   
                 Fe 3 O 4   
                  6% 
                  6% 
               
               
                   
                   
               
            
           
         
       
     
     The data in Table 1 shows that the volume ratios of Fe, Fe 4 N and Fe 3 O 4  remain the substantially same under the different annealing conditions. This consistency may indicate that additional solutionizing at about 750° C. under an applied high magnetic field followed by liquid nitrogen quenching (without such a field) has little or no influence on these phases, as compared to normal annealing in the present example. In some examples, additional solutionizing at about 750° C. in an applied high magnetic field may be beneficial for samples with higher nitrogen levels than the about 8 to about 9 at. % range of the present example, as the solutionizing in a high magnetic field may shift the phase equilibria to permit higher levels of N in the precursor austentic Fe phase, which can yield a higher yield percentage of Fe 8 N upon quenching. 
     However, the volume ratio of α″-Fe 16 N 2  phase after high field annealing at 150° C. for 20 h in the presence of a 9 T high magnetic field is higher than that by annealing at 150° C. for 20 h without a high magnetic field having been applied. The increment of the α″-Fe 16 N 2  phase may be derived from the α′ Fe 8 N phase. The total volume ratio of α′-Fe 8 N and α″-Fe 16 N 2  was about 28% after solutionizing and quenching ( FIG. 3 ). After annealing without an applied magnetic field, the α′-Fe 8 N and α″-Fe 16 N 2  phases are present in the sample at 18% and 10% by volume, respectively. This result indicates that only 35% ( 10/28) of Fe 8 N transformed into the α″-Fe 16 N 2  phase with annealing at 150° C. for 20 h without an applied magnetic field. On the other hand, for the sample annealed at about 150° C. for about 20 h in the presence of an applied magnetic field of 9 T, the α′-Fe 8 N and α″-Fe 16 N 2  phases are present at 6% and 22% by volume respectively, corresponding to a 78% yield in ( 22/28) transforming from the α′-Fe 8 N phase to the α″-Fe 16 N 2  phase. This result demonstrates that application of a high magnetic field during annealing promotes the phase transformation from α′-Fe 8 N to α″-Fe 16 N 2 . 
     As shown by the peak intensities of the spectra presented in  FIG. 4 , the effect of the applied high magnetic field on different phases present in the Fe—N rod samples may be categorized in three ways, namely, intensity enhancement, intensity decrement, and no difference, as listed in Table 2. 
     
       
         
           
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Phase (Intensity 
                 Phase (Intensity 
                   
               
               
                 decreased after high 
                 enhanced after high 
               
               
                 field annealing) 
                 field annealing) 
                 Phase without difference 
               
               
                   
               
             
            
               
                 Fe (110) 
                 Fe (200) 
                 Fe (211) 
               
               
                 Fe 8 N (112) 
                 Fe 16 N 2  (004) 
                 Fe 16 N 2  (301) 
               
               
                 Fe 8 N (202) 
                 Fe 16 N 2  (002) 
                 Fe 4 N (200) 
               
               
                   
                   
                 Fe 3 O 4  (121) 
               
               
                   
                   
                 Fe 4 N (100) 
               
               
                   
               
            
           
         
       
     
       FIG. 5  is a chart illustrating magnetization curves of bulk Fe—N rod samples, measured by a superconducting quantum interference device (SQUID) magnetometer at room temperature after 150° C. annealing for 20 h with and without an applied 9 T high magnetic field. The magnetization curves were measured at 300 K using the SQUID magnetometer (Quantum Design MPMS-XP) in a magnetic field of −2 T≤B≤+2 T, where B is the magnetic induction or magnetic flux density. The sample weights were determined with an ultra-micro balance (Mettler UMT-2). As shown in  FIG. 5 , the saturation magnetization of the iron nitride material annealed without an applied magnetic field, measured at room temperature, was about 218 emu/g, which is in excess of that of pure Fe, but the coercivity was very low, with a value of only about 45 Oe. The iron nitride annealed in the presence of an applied magnetic field has enhanced magnetic properties compared the sample annealed in the absence of an applied magnetic field, as shown in  FIG. 5 . The saturation magnetization (M s ) of the sample annealed in the presence of a 9 T magnetic field increased to 227 emu/g, and the coercivity increased to about 376 Oe. Table 3 summarized the results illustrated in  FIG. 5 . 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 3 
               
               
                   
                   
               
               
                   
                 Normal Annealing 
                 Magnetic Field Annealing 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 M s  (emu/g) 
                 218 
                 227 
               
               
                 Coercivity (Oe) 
                 45 
                 376 
               
               
                   
               
            
           
         
       
     
       FIG. 6  is a chart illustrating magnetization curves of bulk Fe—N rod samples, measured by a SQUID magnetometer at room temperature. The samples presented in the chart of  FIG. 6  were manufactured according to the same methods described with respect to  FIGS. 3-5 , with the Fe—N rod samples being solutionized at about 660° C. for 4 h and quenched. One sample was annealed at 160° C. for 20 h with no applied magnetic field, while another sample was annealed at 160° C. for 20 with an applied 9 T magnetic field. The magnetization curves were measured at 300 K using the SQUID magnetometer (Quantum Design MPMS-XP) in a magnetic field cycling between-10,000 Oe and +10,000 Oe. The sample weights were determined with an ultra-micro balance (Mettler UMT-2). As shown in  FIG. 4 , the saturation magnetization of the iron nitride material annealed without an applied magnetic field, measured at room temperature, was about 202 emu/g, with coercivity of 57 Oe. The Fe—N rod sample annealed in the presence of an applied 9 T magnetic field showed an increased coercivity (H c ) of 397 Oe, and an increased M s  of 231 emu/g. These results illustrate the beneficial effect of 9 T annealing for improved conversion of Fe 8 N to Fe 16 N 2  with increased saturation magnetization and coercivity properties in a bulk form Fe—N magnet. This high magnetic field annealing technique can be applied to Fe—N materials made by other methods, which may yield higher initial fractions of Fe 8 N phase than the examples presented herein, with enhanced conversion of Fe 8 N to the desired Fe 16 N 2  magnetic phase. 
       FIG. 7  is a chart illustrating x-ray diffraction spectra of example Fe—N rod samples after annealing, with and without an applied high magnetic field. The spectra shown in  FIG. 7  were taken from Fe—N rod samples prepared according to a method similar to that described with respect to the samples of  FIGS. 3-5 . The Fe—N rod samples shown in  FIG. 7  were solutionized at about 660° C. for about 4 hours then quenched. One sample was annealed at about 160° C. for about 20 hours with no applied magnetic field (the upper spectrum of  FIG. 7 , at the point of the x axis equaling zero). Another sample was annealed at about 160° C. for about 20 hours with an applied 9 T magnetic field (the lower spectrum of  FIG. 7 , at the point of the x axis equaling zero). The spectra of the Fe—N rod samples shown in  FIG. 7  also include a strain effect. For example, a strain energy accumulated inside the Fe—N rods may suppress further progress of the phase transformation from α′-Fe 8 N to α″-Fe 16 N 2  to some degree, yet contribute to an increase in the saturation magnetization of the samples. 
     These examples show that annealing in the presence of a 9 T applied magnetic field may enhance magnetic properties of bulk FeN rod samples by modifying the phase constitution and crystalline orientation of the rod samples after annealing. The yield of phase transformation from α′-Fe 8 N to α″-Fe 16 N 2  was increased to 78% by annealing in the presence of the applied magnetic field. There are four different phases and three phase transformations during preparation of α″-Fe 16 N 2 , namely α→ →α′→α″. Applied magnetic fields have been used to increase the fraction of the α′ phase transformed from   phase. In this disclosure, the effect of ultra-high field annealing on the α′→α″ phase transformation is demonstrated. The final percentage of α″ may depend on the transforming rate of  →α′ and α′→α″. An applied magnetic field can improve the transformation of  →α′ to 92%. Based on the transformation efficiency from  →α′ and from α′→α″, it is anticipated that a volume percentage of α″ of 72% may be obtained an applied magnetic field is used during both transformations. 
     While not wishing to be bound by any theory, the mechanism of the magnetic field effects on the FeN phase formation may be understood based on the free energy of the material. At the beginning α′ phase, nitrogen atoms are arranged in a disordered manner on octahedral sites along the c axis of the iron crystal. The phase transformation into α″ corresponds to nitrogen having reassembled in an ordered manner. However, the transformation may not occur easily due to the strain effect. In this example, strain effect means an accumulation of strain energy inside of the sample, which can suppress any further progress of the phase transformation. For iron nitride material, the main contribution of strain energy accumulation comes from the quenching stage, since the martensitic transformation from fcc to bct includes an accompanying atomic volume increase. This accumulation of strain energy may hinder the following α′→α″ transformation. In fact, the rate of transformation from α′→α″ under any reported annealing process without an applied magnetic field may be only 35%. 
     The direction of the strain effect is related to the matrix orientation. As shown in  FIG. 3 , the main matrix orientation is (110). Analysis of relative intensities of different peaks indicates that the b axis lies out of the sample plane, while the a and c axes lie in the sample plane. Accordingly, the in-plane 9 T field is perpendicular to the b axis. This may account for the decrease of Fe(110) intensity and increase of Fe(200) during annealing, as shown in  FIG. 4 . Based on the above analysis, an applied high magnetic field in the plane can reduce the strain effect and therefore, increase α′→α″ transformation. Since the magnetic field was aligned with the FeN(001) orientation, Gibbs free energy on the elongated c axis is decreased and assists in Fe 16 N 2 (004) and Fe 16 N 2 (002) phase formation. 
     Example 2 
     A nanoscale powder based on the Fe 16 N 2  phase (70% Fe 16 N 2 , 17% Fe, and 13% Fe x (C,N) where x=2 to 4) was synthesized by reduction of nominal 25 nm carbon coated Fe powder at about 390° C. for about 1 hour while exposing the powder to hydrogen gas, followed by NH 3  nitridation at about 160° C. for about 21 hours. This material yielded a room temperature saturation magnetization (M s ) value of about 232 emu/g and a coervicity of about 216 Oe. Annealing this powder at about 150° C. for about 20 hours in vacuum resulted in a decrease in saturation magnetization to about 146 emu/g, a decrease of nearly 40%, and a coercivity of about 169 Oe.  FIG. 8A  is a chart illustrating magnetization curves of the example Fe 16 N 2 -based nanoscale powder, measured at room temperature before and after annealing. 
     A similar nanoscale iron nitride powder was annealed in vacuum at about 150° C. for about 20 hours while being exposed to a 9 T magnetic field.  FIG. 8B  is a chart illustrating magnetization curves of the example Fe 16 N 2 -based nanoscale powder, measured at room temperature before and after annealing with the applied 9 T magnetic field. Annealing in the presence of the magnetic field resulted in an approximately four-fold increase in coercivity over the as-nitrided starting powder, and a quintuple increase over the powder annealed without the magnetic field, to 880 Oe, as shown at  FIG. 8B . Although the saturation magnetization (M s ) decreased by about 25% from the saturation magnetization of the as-nitrided material, this decrease is compensated for by the increase in coercivity. 
     Example 3 
     A three layer thin film was deposited on a gallium arsenide (GaAs) substrate using reactive sputtering. The three layers included a first layer including iron with a thickness of about 5 nm, a second layer including silver with a thickness of about 40 nm and a third, top layer including iron nitride with a thickness of about 20 nm. The top layer of iron nitride may form as Fe 8 N as the layer quenches during deposition on the example (or any other) substrate. One sample was annealed at about 150° C. for about 20 hours, without being exposed to an applied magnetic field.  FIG. 9A  is a chart illustrating a magnetization curve of a gallium arsenide substrate coated with films of iron, silver and iron nitride, measured at room temperature after annealing. Values of M s =1330 emu/cc, H s =5830 Oe, and H c =357 Oe were obtained. 
     A second thin film sample, prepared as described above in this Example, was annealed at about 150° C. for about 20 hours while being exposed to an applied magnetic field of about 9 T.  FIG. 9B  is a chart illustrating a magnetization curve of a gallium arsenide substrate coated with films of iron, silver and iron nitride, measured at room temperature after annealing with an applied 9 T high magnetic field. Values of M s =1609 emu/cc, H s =8500 Oe, and H c =273 Oe were obtained, as shown at  FIG. 9B . 
       FIG. 9C  is a chart illustrating a magnetization curve of a gallium arsenide substrate coated with films of iron, silver and iron nitride, prepared as described above in this Example and measured at room temperature after annealing with an applied 9 T high magnetic field at a temperature higher than the example thin-film structure of  FIG. 9B . When a third sample was annealed at higher temperature, about 200° C., for about 20 hours while being exposed to an applied magnetic field of about 9 T, the magnetic properties of the materials degraded, due to thermal breakdown of the Fe 16 N 2  phase (see  FIG. 9C ). In this example, values of M s =1215 emu/cc, H s =1200 Oe, and H c =183 Oe were obtained 
     Overall, these examples illustrate that synthesis of iron nitride based magnetic materials within an applied magnetic field, or annealing of iron nitride magnetic materials in an applied magnetic field, can significantly enhance both Fe 16 N 2  content and coercivity, resulting in iron nitride magnetic materials with improved energy products. 
     Example 4 
     A powder based on the Fe 16 N 2  phase was synthesized by ball milling (in a Retsch® Planetary Ball Mill PM 100 available from Verder Scientific Inc., Haan, Germany) iron powder with an average particle diameter between about 30 micrometers and 40 micrometers in the presence of ammonium nitride for about 60 hours to nitridize the iron particles. Some particles were annealed at a temperature of about 160° C. for about 24 hours without applying a magnetic field, while some particles were annealed at a temperature of about 160° C. for about 24 hours while a 9 T magnetic field was applied.  FIG. 10  is a chart illustrating a magnetization curve of an example iron nitride sample prepared by ball milling, nitriding, and annealing with and without an applied 9 T high magnetic field. As  FIG. 10  illustrates, the particles annealed without an applied magnetic field had a coercivity of about 160 Oe and a M s  value of about 175 emu/g. The particles annealed in the presence an applied 9 T magnetic field had a coercivity of about 520 Oe and a M s  value of about 207 emu/g.  FIG. 11  is a chart x-ray diffraction spectra of example Fe—N material after annealing, with and without an applied 9 T high magnetic field. 
     Various examples have been described. These and other examples are within the scope of the following claims.