Abstract:
Methods for measuring expansion of a test sample. One method includes establishing a diffraction slit between two blades, with the position of at least one of the blades being dependent upon the length of a test sample of material. As the temperature of the sample changes, the width of the slit changes. Light is projected through the slit onto a target and an diffraction pattern is measured. Changes in the light diffraction pattern correspond to the thermal expansion of the sample. Another method includes establishing a diffraction slit between two blades, with the position of at least one of the blades being dependent upon a length along a test sample of material. As a load is applied to the test sample, the width of the slit changes. Changes in the light diffraction pattern correspond to Young&#39;s Modulus for the sample.

Description:
FIELD 
     The claimed technology relates generally to measuring the expansion of materials and more specifically to a method and devices for accurately measuring the expansion of materials resulting from changes in temperature, mechanical stress, or other causes. 
     BACKGROUND 
     Materials may change their size and shape such as by expanding or contracting when subjected to various forces such as heat, mechanical stress, electricity, and the like. Most materials expand when heated, for example, and the amount and rate of this expansion must be considered when designing devices which will be subjected to temperature changes. The coefficient of linear thermal expansion represents the ratio of change of length to the actual (original) length per degree temperature change. Typically, this ratio is expressed as the fractional change in length of a material per degree of temperature change. Engineering and construction applications where temperature changes are expected must take the expansion and contraction of materials into account. 
     The coefficient of thermal expansion of a material can be measured with the use of a dilatometer. Dilatometers typically consist of a heat source, such as a furnace, and a means for measuring the expansion of the material being tested. Capacity dilatometers measure the expansion of a material using capacitor having one movable and/or flexible plate. Expansion of the material being tested moves the plate relative to the fixed plate thereby changing the capacitance of the capacitor. The change in capacitance is then used to calculate the change in distance between the capacitor&#39;s plates which is equal to the change in the length of the material being measured. Other dilatometers measure the expansion of the sample material using a strain gauge. 
     Most commercially available dilatometers are large and expensive pieces of equipment. Additionally, many are equipped with heat sources capable of reaching temperatures in excess of 1000° Celsius making them unsuitable for certain applications such as educational science labs. There remains a need for a less expensive but highly accurate means for determining the coefficient of thermal expansion of materials. Additionally, there is also a need for the ability to accurately measure very small changes in the size of materials when they are subjected to a variety of stresses other than temperature changes. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram of wave diffraction through a single slit. 
         FIG. 2  is a front view of one embodiment of a device for measuring the thermal expansion of a material. 
         FIG. 3  is a partial cut away view of another embodiment of a device for measuring the thermal expansion of a material. 
         FIG. 4  is top plan view of the embodiment of the device shown in  FIG. 3 . 
         FIG. 5  is a perspective view of device shown in  FIG. 3 . 
         FIG. 6  is a front view of another embodiment of a device for measuring the thermal expansion of a material. 
         FIG. 7  is a partial cut away view of still another embodiment of a device for measuring the thermal expansion of a material. 
         FIG. 8  is a front view of an embodiment of a device for measuring the expansion of a material. 
         FIG. 9  is a front view of an embodiment of an apparatus for measuring the Young&#39;s Modulus of a material. 
         FIG. 10  is one embodiment of an apparatus for measuring the expansion of a liquid. 
         FIG. 11  is another embodiment of an apparatus for measuring the expansion of a liquid. 
     
    
    
     DESCRIPTION 
     For the purposes of promoting an understanding of the principles of the claimed technology and presenting its currently understood best mode of operation, reference will now be made to the embodiments illustrated in the drawings and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope of the claimed technology is thereby intended, with such alterations and further modifications in the illustrated device and such further applications of the principles of the claimed technology as illustrated therein being contemplated as would normally occur to one skilled in the art to which the claimed technology relates. 
     The phenomenon of diffraction can be observed when waves pass through a narrow aperture. As shown in  FIG. 1 , one example of diffraction occurs when light  10  passes through a narrow opening  15  having a width w. In this and other drawings, width w is depicted as being relatively large for the sake of clarity. In practice, the actual slit width is typically very small. After the waves  10  pass through the opening  15 , they behave as if there were a single point source at the location of the opening and form a semi-circular diffraction pattern of ripples. This configuration is known as single-slit diffraction  25 . As the width of the slit w becomes smaller relative to the wavelength λ of the light (i.e., w/λ approaches zero) the opening behaves more like a point source and diffraction increases. 
     If the diffracted light  20  is projected onto a screen  30  which is at a distance D from the slit  15 , an interference or diffraction pattern  35  is formed. Diffraction pattern  35  is shown in an exaggerated fashion as a series of blocks for the sake of clarity. The distance between repeating points in the diffraction pattern, or fringe width, is represented as z. The relationship between the fringe width, the distance between the slit and the screen D, the slit width w, and the wavelength λ of light passing through the slit is expressed in the equation:
 
zw=λD   1
 
When solved for w, this relationship can be used to calculate the width of an opening by measuring the fringe width z resulting from passing light of a known wavelength λ through a slit at a known distance D from a screen.
 
     
       
         
           
             
               
                 
                   w 
                   = 
                   
                     
                       λ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       D 
                     
                     z 
                   
                 
               
               
                 2 
               
             
           
         
       
     
     Changes in the diffraction pattern observed as a change in the value of z result from very small changes in the width of the slit opening. Consequently, very accurate measurements of the expansion and/or contraction of a material can be made by relating the change in length of a sample material to changes in slit width and observing the diffraction patterns resulting from projecting light of a known wavelength through the slit and onto a screen. 
     The linear coefficient of thermal expansion a represents the ratio of change of length of a material with respect to a change in temperature and can be expressed as: 
                   α   =       1   ℓ     ·       ℓ   -     ℓ   °         T   -     T   °                 3             
Where l∘ is the initial length of the material being measured at initial temperature T∘, and l is the length of the material being measured at temperature T.
 
     Coupling the expansion of a sample material to changes in the width of a narrow slit through which light is passing can be used to measure the coefficient of thermal expansion of the sample material. That is, where l−l∘ is equal to the difference between two slit widths (w−w∘), changes in the diffraction pattern resulting from light of a known wavelength passing through the slit can be measured and used to calculate the coefficient of thermal expansion of the sample material. Where l−l∘=w−w∘, substituting single slit diffraction equation solved for w produces: 
                     ℓ   -     ℓ   °       =         λ   ⁢           ⁢   D     z     -       λ   ⁢           ⁢   D       z   °               4             
Where λ is the wavelength of the light, D is the distance between the screen and the slit, z is the fringe width resulting from slit width w and z∘ is the fringe width resulting from slit width w∘. Substituting the right hand side of this equation into the previous equation for calculating the coefficient of thermal expansion and simplifying results in:
 
                   α   =         λ   ⁢           ⁢   D       ℓ   °       ·         1   z     -     1   z         T   -     T   °                 5             
This equation can be used to calculate the linear coefficient of thermal expansion α for a sample material.
 
       FIG. 2  shows one example of a device  40  for measuring the linear coefficient of thermal expansion of a sample material using changes in the diffraction pattern resulting from light passing through a narrow slit where changes in the width of the slit correspond to changes in the length of the sample material. Device  40  comprises a thin strip of the material to be tested  42  formed generally into a U shape having two substantially parallel arm portions  44 ,  45  and having a bottom portion of length t which is substantially perpendicular to arm portions  44 ,  45 . Sample  42  may be bent, cast, molded, or otherwise suitably formed into the desired shape. Attached to each arm portion  44 ,  45  is a bracket  46 ,  47 , respectively, which is substantially parallel to the bottom portion of sample  42 . Brackets  46 ,  47  may be made out of wood, ceramic, plastic, glass, composite, alloy, or some other suitable material that has a relatively low coefficient of thermal expansion. Optionally, brackets  46 ,  47  are coated with a sealant, insulation, or other material to isolate them from moisture and changes in temperature. 
     A slit blade  48 ,  49  is adjustably mounted to each bracket  46 ,  47 , respectively. The blades  48 ,  49  are configured and arranged so as to form a slit  50  having a uniform width w. In this particular example, each blade  48 ,  49  includes an adjustment screw  52 ,  53  which allows the width w of slit  50  to be adjusted as desired. The blades  48 ,  49  may be made of the same or different material as the brackets such as metal alloy, glass, ceramic, plastic, and the like. Optionally, blades  48 ,  49  are coated with a material which protects them from moisture and changes in temperature. 
     As the temperature of the sample material changes, any resulting changes in the length l of the bottom portion  42  of the material are reflected in changes in the width w of slit  50 . For example, if the sample material is heated, bottom portion  42  will expand and increase in length. As the length of bottom portion  42  increases, arm portions  44 ,  45  are urged apart thereby moving brackets  46 ,  47  apart and increasing the width w of slit  50 . Device  40  is configured so that the increase in the length of bottom portion  42  is equal to the increase in the width of slit  50 , i.e., l−l∘=w−w∘. By passing light of a known wavelength λ through slit  50  before and after heating the sample, changes in the diffraction pattern can be measured to obtain values for the fringe width z∘ at the initial temperature T∘ as well as the fringe width z at the final temperature T. The initial length l∘ of bottom portion  42  and the distance D to the screen where the diffraction pattern is projected can be measured. Once these values are obtained, equation 5 can be used as previously discussed to obtain a value for the coefficient of thermal expansion of the sample material. 
     Alternatively, a series of measurements of fringe widths z can be taken at different temperatures and the results plotted on a graph. On a graph of the reciprocal of fringe width (1/z) plotted as a function of temperature T, the slope of a line is: 
                   Slope   =       αℓ   °       λ   ⁢           ⁢   D             6             
Solving this equation for the coefficient of thermal expansion α yields:
 
                   α   =         (   Slope   )     ⁢   λ   ⁢           ⁢   D       ℓ   °             7             
By measuring the slope from the graph, an accurate value of α may be calculated. Optionally, the graphing and measurement may be automated using a microcomputer or similar device so that multiple measurements may be obtained quickly and the slope of a best-fit line from the resulting graph generated automatically.
 
     One example of an apparatus  52  for measuring the coefficient of thermal expansion of a material is shown in  FIG. 3 . In this particular example, a device  55  similar to that described in  FIG. 2  is heated by immersing the device  55  in a water bath  58 . The water bath comprises a tank  54  heated by means of a hotplate  56  and monitored using a thermometer  60 . In other examples, the device may be heated using a furnace, oven, electrical resistance heater, or any other suitable heat source as desired and the temperature monitored using other monitoring means such as a thermocouple. Optionally, the water bath may be cooled rather than heated to measure the contraction of the sample material rather than the expansion. The water bath may be replaced by alcohol, ethylene glycol, or any other suitable substance having a freezing point lower than water if measurements below 0° Celsius are desired. Operation of apparatus  52  is similar to that previously described with respect to  FIG. 2 . 
       FIG. 4  is a top plan view of the apparatus  52  shown in  FIG. 3 . The water bath  58 , tank  54 , hotplate  56 , and thermometer  60  have been omitted from this view for the sake of clarity. A light source having a known wavelength  70 , in this particular example a laser, projects a beam of light  72  through the slit  62  of device  55 . The light is diffracted and the diffracted light  74  strikes a screen  76  disposed at a known distance D from the slit  62 . The resulting diffraction pattern  78  can be used to measure the fringe distance z and changes in the fringe distance caused by changes in the width w of slit  62  resulting from the expansion and/or contraction of the sample material used in device  55  can then be used to calculate the coefficient of thermal expansion of the sample material using the method and equations previously described. Apparatus  55  is shown in perspective in  FIG. 5 . Optionally, screen  76  further includes a scale or series of measuring marks inscribed or drawn on its surface to aide in the measurement of the fringe width z. In other embodiments, screen  76  is made of a photosensitive material or device which can automatically detect a diffraction pattern projected onto its surface and is operatively connected to a computer or other device such that the fringe distance z can be automatically measured and any changes in fringe distance automatically calculated. 
       FIG. 6  is a front view of another embodiment of a device  80  for measuring changes in the length of a sample material. In this example, device  80  includes arm portions  82 ,  84  made of a material similar to or the same as the brackets  88 ,  90 . In this particular example, only the bottom portion  86  of the device is made from the sample material. This particular configuration might be used when the sample material is a substance that is not easily bent, molded, or otherwise shaped into a suitable configuration other than a flat bar or rod. 
     Another example of an apparatus  92  is shown in  FIG. 7 . In this particular example, the liquid bath  95  used to heat the device  98  is contained in a tank  94  equipped with a lid  96 . The lid  96  protects the slit blades  100 ,  102  of the device  98  from any deleterious effects caused by being directly exposed to heat or moisture from the liquid bath. 
       FIG. 8  shows yet another device  178  suitable for measuring small changes in the length of a sample material  182  using the diffraction method and equations previously described. In this particular example, device  178  comprises a pair of movable brackets  180 ,  188 , where each bracket includes a slit blade portion  190 ,  192 , respectively, and a sample face portion  184 ,  186 , respectively. The brackets are configured and arranged so that slit blades  190 ,  192  are disposed so as to form a slit  194  having a width w and sample face portions  184 ,  186  are disposed at a distance s from one another. The brackets are also configured and arranged so as to be freely moving and so that movement caused by a force exerted on the sample face portions  184 ,  186  is transmitted through the brackets and results in an equal movement of the slit blades  190 ,  192 . That is, any change in the value of s results in an equal change in the value of w. 
     The disclosed method can be used to measure changes in length arising from causes other than heating. For example, the disclosed method can be used to measure the change in length in a sample material caused by an applied force which can be used to calculate Young&#39;s Modulus for the material. Young&#39;s Modulus is a measure of the stiffness of a material expressed as the ratio of the rate of change of stress to strain. 
                   Y   =       F   ⁢           ⁢     ℓ   °           A   °     ⁡     (     ℓ   -     ℓ   °       )               8             
Where Y is Young&#39;s Modulus, F is the applied force, l∘ is the original length of the object, A∘ is the original cross-sectional area of the object, and l is the length of the object under stress.
 
     One example of a device which can be used to determine Young&#39;s Modulus is shown in  FIG. 9 . In this particular example, a wire  198  having a known cross-sectional area A∘ is attached to a surface  200 . A weight  202  having a known mass is attached to the wire  198  opposite the surface  200 . Attached at some point along the wire  198  are two brackets  204 ,  206  to which slit blades  208 ,  210 , respectively, are mounted. The brackets  204 ,  206  and slit blades  208 ,  210  are configured so that a slit  212  of the desired width is created between the blades. Weight  202  applies a known force to wire  198  which causes a lengthening of the wire. This lengthening can be measured by observing changes in the diffraction patterns created by light of a known wavelength passing through slit  212  using the method previously described. The change in length ΔL of the wire  198  between brackets  204  and  206  can then be used to calculate the Young&#39;s Modulus Y of the wire. In other examples, devices according to the disclosed method for calculating the Young&#39;s Modulus of a material are configured so that the sample material is disposed generally horizontally and a force is applied using a mechanical means such as a screw, pneumatic piston, or the like rather than gravity. 
     An example of a device  220  for measuring the expansion and/or contraction of a liquid is shown in  FIG. 10 . In this particular example, a sample liquid is placed in a piston  222  having a known volume. The piston  222  is operably connected to a slit blade  224 , while a second slit blade  226  is fixably mounted to a surface  228 . The piston  222  is configured and arranged so that the slit blades  224 ,  226  are disposed at a distance w thereby forming a slit  230 . The piston  222  is then heated using a suitable heating means. As the liquid is heated and expands, the slit blades  224 ,  226  are urged closer together thereby decreasing w and causing changes to the diffraction pattern of light passing through the slit  230 . The previously described method is particularly suited to measuring the very small changes in volume which result from heating most liquids. 
     A dual piston arrangement of a device  240  for measuring changes in the volume of a liquid is shown in  FIG. 11 . In this example, a chamber  242  is equipped with two pistons  244 ,  246  which are operably connected to slit blades  248 ,  250 , respectively, so that movement of the pistons results in corresponding movement of the slit blades. The chamber and pistons are configured and arranged so that the slit blades  248 ,  250  are disposed at a distance w from one another thereby forming a slit  252 . The chamber  242  is filled with a sample liquid and then heated using a suitable heating means. As the liquid is heated and expands, the slit blades  248 ,  250 , are urged closer together thereby decreasing w and causing changes to the diffraction pattern of light passing through the slit  252 . 
     The preceding descriptions of devices represent a limited number of examples of using the disclosed method of measuring changes in the size of objects through changes in diffraction patterns. The disclosed method can easily be adapted to measure other types of small changes in the dimensions of materials using similar devices. In addition to thermal expansion, thermal contraction, and Young&#39;s Modulus previously discussed, changes in size caused by humidity (i.e., moisture expansion) as well as changes in size caused by the application of an electric current (i.e., piezoelectricity) could also be measured. 
     While the claimed technology has been illustrated and described in detail in the drawings and foregoing description, the same is to be considered as illustrative and not restrictive in character. It is understood that the embodiments have been shown and described in the foregoing specification in satisfaction of the best mode and enablement requirements. It is understood that one of ordinary skill in the art could readily make a nigh-infinite number of insubstantial changes and modifications to the above-described embodiments and that it would be impractical to attempt to describe all such embodiment variations in the present specification. Accordingly, it is understood that all changes and modifications that come within the spirit of the claimed technology are desired to be protected.