Abstract:
This invention will provide a method of determining nondestructively, the purity or composition of an unknown material sample, such as, for example a sample of gold or silver of unknown purity. Their forms can be a: casting, bullion, coupon or disc (a coin), as well as some jewelry, such as gold or silver rings with signet surfaces. The method involves subjecting one of the large surfaces of the sample of known thickness to an elevated or a cold temperature, relative to the initial temperature of the sample, and comparing the time-varying temperature pattern during finite lengths of time at the same surface thereof, or at the opposite surface, with that of a known and identically-sized standard subjected to the equivalent conditions. The temperature of said surfaces or opposite surfaces can be monitored during the time the heat or cold pulse, or constant temperature is applied and/or after withdrawal. The test specimens are such that their areal dimensions are large compared to their thicknesses, thus qualifying as ‘slabs’. In order to detect a particular adulterant the method may require a dual-test procedure: The first is an application of a pulse of constant heat and the second, if necessary, is an application of constant temperature. Furthermore, during the time the conditions are applied the slopes of the time-varying temperature patterns can be determined, the decay curves, after such conditions are removed, and their slopes can also be realized. Such information will provide a further check on the authenticity of the test item.

Description:
FIELD OF THE INVENTION  
         [0001]    The present invention relates to the nondestructive determination of the composition of a material when comparing the thermal properties of a sample of the material with the thermal properties of a standard of a similar material, said standard or substitute having a desired composition.  
           [0002]    The invention herein described has use for nondestructive qualitative determination of composition of a variety of materials and its use is discussed mostly with reference to precious metals, such as gold and silver.  
         BACKGROUND OF THE INVENTION AND PRIOR ART  
       Background  
         [0003]    The rise in trading in recent years of precious metals, such as gold and silver, as commodities, and the rise in their unit prices has increased the need for an economical, fail-safe mechanism for determining nondestructively, the purity of such materials. Since gold, like silver, is often transferred or sold by persons not particularly knowledgeable about such precious metals to one of greater knowledge, it is important that some way be found to detect forgeries and ascertain the purity of such precious metals that avoids the costly and time consuming methods, several of which are outlined below, a way that is nondestructive, fast and accurate. By way of background, much of what follows was paraphrased from  The collector&#39;s Dictionary of the Silver and Gold of Great Britain and North America,  Michael Clayton, World Publishing Company, 1971.  
           [0004]    Pure gold is extremely heavy in proportion to its cubic volume and also very soft (malleable), and if pure, is referred to as ‘24 carat’. Silver is not so malleable and only approximately half the weight of a piece of gold of similar cubic measurement. Both are too soft to use in their pure form and must be hardened by the admixture of base metals, usually copper, though silver may be used with gold. If both silver and copper are added to gold it becomes pale and green in color. The fact that adding a 50 percent alloy of copper to silver retains a silvery appearance can easily lead to fraud without protection. In general, the best proportions of gold and alloy are 22 parts pure gold to 2 parts alloy, but this can be varied so that 18, 15, 12, or 9 carats (or parts) are balanced by an alloy making up 24 parts. These balanced fractions of pure gold and alloys are legally used and obviously the less pure gold parts, the cheaper the finished product. With silver, only two standards are permitted in Great Britain, 925 parts out of 1000 as normal Sterling standard and 958.3 parts as the higher Britannia standard. By the same measurement, 18 carat gold is the equivalent of 750 parts fine gold to 1000 (24 carats). For most of the English gold coinage and all since 1672, the fineness has never been below 22 carats (916.66 parts gold to the 1000). Since the nineteenth century in the United States, the coin standard is 900 parts pure silver to 100 parts alloy.  
           [0005]    In order to protect the buyer of gold and silver, a system of testing, or assaying, and checking the quality and standards of an object is necessary. This can be done by comparison (touch), weight, or chemical means. The first demands considerable visual skill as the object to be tested and a piece of known quality have both to be stroked across a piece of basanite, a hard flint-like slate, and the resulting streaks compared. In the second test, weight, small portions of the object to be assayed are scraped from each piece, wrapped in lead (lead and silver are also used to wrap gold) and heated in a bone-ash crucible. As the heat is applied lead and other base metals oxidize and are absorbed by the crucible, known as a ‘cupel’; the balance is then weighed and compared with the weight of the original scrapings.  
           [0006]    In the case of gold, which is also wrapped in silver, a further process is required whereby the silver is finally removed by placing it in hot nitric acid. This method was first recorded in 1495. If on completion of these tests, the gold or the silver are found to be below the lowest permitted standards, the marks which would guarantee their quality, ‘hall-marks’, as they are known, are withheld and the objects under examination are crushed and returned to the maker. The third is a simple method and applicable only to silver, but requires some reasonable idea of the quality of the metal being tested. This involves the dissolving of the weighed scrapings, also known as ‘diet’, in nitric acid and the addition of a standard solution of sodium chloride (common salt); at a certain point the cloudy liquid clears and silver chloride is precipitated. A comparison of the original weight of the silver sample and the quantity of saline solution required to do this, enables the fineness of the metal to be assessed.  
           [0007]    Historically, as indicated above there are a number of methods used to determine the composition of metallic materials that can be classified as comparative as well as destructive. A comparative method is one, as the name implies, that requires a comparison to a known reference material. A destructive test is as the name implies and needs no explanation. The descriptions of pertinent testing methods that follows are all comparative tests and are categorized as ‘destructive’ or ‘nondestructive’. The following paragraphs, under the heading “Prior Art”, discuss appropriate examples of these.  
         Prior Art  
         [0008]    Destructive Tests  
           [0009]    Some of the more modern methods, than those described above, that have been developed and in use today to determine alloy content of metallic materials are: optical emission spectrography, spectrometry, x-ray fluorescence spectrometry, atomic absorption spectrometry, plasma emission spectrometry and combustometric analysis to determine particular elements. Such methods usually require a sample from the test piece, and thus are somewhat destructive.  
           [0010]    A primary example of a destructive test is the standard prescribed by the American Society for Testing and Materials, (ASTM) Test Method B 562-95, “Standard Specification for Refined Gold”. This test method examines samples taken from the melt before pouring the casting of gold. The standard utilizes, for 99.5 percent purity, a test method for chemical analysis by cupellation fire assay. If there is a disagreement between the manufacturer and the purchaser the specified test will then be in accordance with ASTM Test Method E 1446, “Test method for Chemical Analysis of Refined Gold by Direct Current Plasma Emission Spectroscopy.” 
           [0011]    The standard for testing silver, which is also destructive, is that given by the ASTM Test Method B 413-89, “Standard Specification for Refined Silver”. This method requires that the samples be taken from bars by drilling six holes and the chemical composition is determined in accordance with ASTM Test Method E 378 “Test Method for Spectrographic Analysis of Silver by the Powder Technique”.  
           [0012]    Portable electronic gold testers that measure the carat value of gold are also available, such as those described in U.S. Pat. Nos. 4,799,999 and 5,218,303, authored by Medvinsky and Radomyshelsky. These patents describe a method for determining the assay of gold alloy, utilizing an electrochemical process. The specimen gold is wetted by an electrolyte, and a small current anodizes the surface of the specimen for a metered period of time. A potential sensing device is then applied to the charged surface, and a potential decay is observed. The potential decay information is compared with empirical data and by interpolating the potential with the empirical data a determination of the carat quality of the gold alloy may be determined. This same method may be used for other precious metals, employing different electrolytes, empirical standards, and potentiometers.  
           [0013]    There are two additional patents, U.S. Pat. Nos. 5,128,016 and 5,080,766, authored by Moment and Nelson, that essentially utilize the same technique with some variation as those indicated above.  
           [0014]    The criticism of these gold testing devices are that they are slightly destructive, are surface sensitive only, will not detect plating or gold overlay, and will leave a mark on items that are of 14 carat or less.  
           [0015]    Nondestructive Tests  
           [0016]    There are several methods of nondestructively discriminating between bodies having similar appearances but of slightly different composition or even of different material. In one instance the relatively old technique of eddy current testing is utilized to attempt to separate higher grade from lower grade materials. This method principally compares the subsurface electrical conductivity, synonymous with thermal conductivity, and magnetic permeability of a resulting read-out wave form of the higher grade standard material to that of the sample. The conductivity of gold and a mixture of gold with an adulterant will be very similar, as will silver and a mixture of silver with an adulterant, and thus the sensitivity of the eddy current technique will not be sufficient to separate such forgeries. Also, if a tungsten body, which has the same density as gold, is gold plated at a surface depth deeper than the subsurface penetration of the eddy current, then this test method will not discriminate between pure gold and the forgery.  
           [0017]    In another instance U.S. Pat. No. 4,255,962, issued to Ashman, teaches a method of distinguishing a simulated diamond from a natural diamond by utilizing a probe which applies a pulse of heat to the surface of the sample in an air environment and during the occurrence of thermal equilibrium the same probe detects the change in temperature. This change in temperature is related to the thermal conductivity of the sample. Since the thermal conductivity of natural diamond is at least an order of magnitude greater than a simulated diamond, such as cubic zirconia, it is readily detected. This method, however, is not sensitive enough to detect the slight change in thermal conductivity between: pure gold and a forgery or pure silver and a forgery.  
           [0018]    Another example of a nondestructive test method is described in U.S. Pat. No. 3,981,175, which was issued to Hammond, III and Baratta. In accordance with that patent, the device is a nondestructive counterfeit gold bar and silver bar detection system based upon heat transfer principles. Regarding the testing of gold the principle entails the application of identical finite suddenly applied controlled heat pulses at a first region which is one end of an elongated gold bar of specific dimensions and of known purity, used as a standard, and a geometrically identical test bar. The system is completely enclosed in an insulating medium. The temperatures, which are measured at a second region at the far end of each bar are not only dependent upon the thermal properties of each bar, but upon its length and the length of the test time. Those thermal properties, which in gold are unique, are specific heat, thermal conductivity and density; the combination of these properties is defined as thermal diffusivity. Since these properties in gold are singular, the temperature at the second region, i.e., the end opposite from that which is suddenly pulsed by a quantity of heat, will usually be at a higher temperature in a given time than that of a bar of a particular length less pure than the standard gold bar of the same length. Because of the large differences in thermal properties of gold and an alloyed gold sample, temperature measurements conducted at the far end will reveal differences.  
           [0019]    The general heat transfer equation for the aforementioned situation is given in the following:  
           [0020]    If heat (e.g., a square wave pulse of indefinite duration) is applied to one end of a gold bar, at x=L, the general equation given in U.S. Pat. No. 3,981,175 for the temperature T(x,t) at any distance x along the bar&#39;s length is:  
             T ( x,t )= QL/k{αt/L   2 +(3 x   2   −L   2 )/6 L   2 −2/π 2 Σ m=1   ∞ (−1) m   /m   2 [exp(−α m   2 π 2   t/L   2 )]cos( mπx/L )}  (1)  
           [0021]    Where: Q is the suddenly applied constant heat flux applied over an area BTU/sec-ft 2 ) of the bar, at x=L, L is length in feet, k is the thermal conductivity (BTU/sec-ft-F), α=k/ρc, and is the thermal diffusivity in ft 2 /sec, c is the specific heat (BTU/lb-F), ρ is the density in lbs/ft 3 , t is time in seconds, x is the distance in feet along the length of the sample and T(x,t) is temperature in degrees F. Note at x=0, at the far end there is no flow of heat because of the insulation, See Carslaw and Jaeger  conduction Heat in Solids , Oxford Press, 1950.  
           [0022]    The nondestructive testing of silver bars described in U.S. Pat. No. 3,981,175 is essentially the same as that indicated above except rather than employing a pulse of heat a constant temperature source is applied. Silver has the highest thermal diffusivity of any known material and the equation for the temperature along the bar length is dependent upon thermal diffusivity. Therefore, as a function of time, the silver bar will attain a higher far end temperature than any other material. The equation for the temperature at the far end is given in the following:  
               T        (   t   )       =     2        T   0            ∑     n   =   0     ∞              (     -   1     )     n          {     1   -     erf        [         (       2      n     +   1     )     /   2            (     α                   t   /     L   2         )       1   /   2         ]         }                   (   2   )                               
 
           [0023]    Where T 0  is the applied constant temperature above ambient and erf is the standard definition of the error function; well tabulated in many references.  
           [0024]    The method of U.S. Pat. No. 3,981,175 requires that the standard and test sample be completely insulated and the further restrictions are that: The standard and test sample must be elongated bars of the same particular length, and temperatures at the far end of each bar must be taken over same particular time interval after the heat is applied, depending on the length of the bar.  
           [0025]    Yet another example of a nondestructive test method to detect fraudulent precious metal bars is revealed in U.S. Pat. No. 4,381,154, issued to Hammond, III. It was found that of all possible forgeries, a non-alloyed tungsten forgery of gold, i.e., an insert of tungsten within the gold bar, is the most difficult to detect because the density and heat-capacity of tungsten and gold are virtually identical (a less difficult forgery to detect is an alloyed forgery wherein its composition is generally uniform throughout). Thus, an improvement in accuracy over the previous U.S. Pat. No. 3,981,175 was required at that time. This improvement consists mainly of increasing the accuracy of the detection system by providing and controlling heat into the test chamber resulting in equilibrium, termed “dynamic insulation” by the author; accurate heater control and using a compensated infrared sensor to measure the temperature at the far end opposite the heated end of the sample. Also the author claimed that this method allowed the determination of the density, thermal conductivity and and heat capacity of a given material.  
           [0026]    Although the improved techniques adopted in U.S. Pat. No. 4,381,154 will enhance the the sensitivity of this test method, it still requires that the test piece be an elongated bar of specific dimensions and additional temperature sensors, controls and electronic instrumentation compared to the method of prescribed in U.S. Pat. No. 3,981,175. It is also noted that the present day infrared temperature sensors can readily determine temperatures to an accuracy within 0.10 C. over a wide range of temperatures (see the paper by J. M. Looney, JR., and F. Pompei, Medical Electronics, 1989), thus superseding the method proposed in U.S. Pat. No. 4,381,154.  
           [0027]    An additional improvement is described in U.S. Pat. No. 4,385,843 granted to Hammond, III, whereby an induction heater is employed to provide a pulse of heat to a bar of precious metal to determine if it has the purity of composition within a given range of variance. Heat is induced at one end of the bar using an induction heater powered by a high frequency power source, and the time versus temperature response at the other end of the bar is monitored. This device was employed, according to the author, to circumvent the problems associated with contact heaters. However, present day lasers or infrared heat sources will accomplish the same goal.  
           [0028]    A more recent U.S. Pat. No. 5,052,819, was issued to Baratta; this document taught a method of nondestructively identifying materials and fraudulent carbon steel fasteners. This invention compared the characteristic temperature-time curve of a standard fastener to a test fastener by simultaneously providing a pulse of heat to both fasteners and measuring the temperatures at their heated ends. However this patent required an insulated receptacle and specified that the standard and test sample be restricted to elongated bars.  
         SUMMARY  
         [0029]    The device will provide, broadly, a method of determining nondestructively, the purity or composition of an unknown material sample, such as, for example a sample of gold or silver of unknown purity. The form of the sample can be the shape of a casting, a bullion, a coupon or a disc (a coin). The procedure involves first subjecting one of the large surfaces of the sample of known thickness to an elevated or a cold temperature relative to the initial temperature of the sample and comparing the time-varying temperature pattern at the same surface thereof, or at the opposite surface during finite lengths of time with that of a known and identically-sized standard subjected to the equivalent or the same conditions for an interval of time of the same finite length. The temperature of said surface or the opposite surface can be monitored during the time the heat or cold pulse, or constant temperature is applied and/or after withdrawal. A second test in the form of the application of constant temperature may be required, dependent upon a particular adulterant; this is referred to as a dual test. In addition, the slopes of the time-varying temperature patterns during the time the condition is applied and/or after it is withdrawn can also be determined.  
           [0030]    Several shapes of jewelry, such as gold or silver rings with partially flat surfaces, such as signets, can also be tested using the same processes as those indicated above.  
           [0031]    The objects of the present invention are to provide improvements over U.S. Pat. No. 3,981,175 by Hammond, III and Baratta for the nondestructive comparison of the composition of an unknown material sample to the composition of a known material sample and provide a mechanism for such a nondestructive comparison determination, and one that can be operated by persons with only a small amount of technical training.  
           [0032]    Such improvements over the present state-of-the art consist of eliminating the need for a specified sample shape such as an elongated bar, as well as a completely insulated environment and allowing testing of samples whose surfaces are exposed to a medium, and the use of both contacting and non-contacting heating units; and noncontacting temperature sensing elements. Further improvement is realized by examining: the slope of the temperature-time curves, the decay of the temperature-time curves after the heat or cold pulse, or constant temperature is removed, as well as the slope of the decay curve. Such improvements are applicable to field operations.  
           [0033]    The improved invention described herein allows for the temperature measurements at either the large surfaces at which the heat or cold pulse, or constant temperature is applied or at the opposite surfaces of the standard and the sample. In this way, a comparison of temperature differences between the standard and the test sample definitively reveals the temperature differences such that the fraudulent bullion, coupons, coins, and certain shaped jewelry can be determined. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0034]    Other and further objects, advantages and features of the invention will be apparent to those skilled in the art from the following description thereof, taken in connection with accompanying drawings, in which:  
         [0035]    [0035]FIG. 1 is a diagrammatic representation, partly block diagram in form and the portions of the apparatus shown being partly cut away, of a system adapted to effect nondestructive determination of the composition of a material sample in the form of bullion, a coupon, or a disc;  
         [0036]    [0036]FIG. 2 shows in block diagram form a part of the system of FIG. 1, but slightly modified;  
         [0037]    [0037]FIG. 3 shows in block diagram form another modified version of a part of the system of FIG. 1;  
         [0038]    [0038]FIG. 4 shows a modification of the system shown in FIG. 1:  
         [0039]    [0039]FIG. 5 shows a modification of the system shown in FIG. 4;  
         [0040]    [0040]FIG. 6 shows a modification of the system shown in FIG. 5;  
         [0041]    [0041]FIG. 7 schematically shows a partly cut-away system to determine the purity of a material sample in the form of a ring;  
         [0042]    [0042]FIG. 8 shows a modification of the system shown in FIG. 5; and  
         [0043]    [0043]FIG. 9 shows a modification of FIG. 6. 
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0044]    In the description of the preferred embodiments that now follows, the invention is first discussed with reference to a system for determining nondestructively the composition of an unknown sample in various forms and, to simplify the explanation, the samples taken up are precious metals, gold and silver, but it will be kept in mind that most aspects of the system discussed with respect to such materials may also apply to other materials not having unique thermal properties as those of gold or silver.  
         [0045]    It is noted that in the descriptions that follow where reference is made to the application or discontinuance of heat to the various bodies, it is understood to be equally applicable to cryogenic operations as well, which can be accomplished, for example, by the application of chilled objects of defined sizes or with liquids or liquified gases in contact with the sample and the standard for comparison. However, this is not repeated in each case for the sake of brevity.  
         [0046]    As previously mentioned in the discussion of U.S. Pat. No. 3,981,175 in the prior art, the shapes of the standard and the sample were required to be in the form of an elongated bars of specific dimensions where both were insulated. The formulation in the aforementioned patent is given by Carslaw and Jaeger supra. These authors, as well as A. B. Newman and L. Green in their paper entitled “The Temperature History and Rate of Heat loss of an Electrically Heated Slab,” in Transactions of the Electrochemical Society, Vol. LXVI, 1934, also indicate that if the four edges of a slab are large compared to their thickness, then heat flow toward the edges may be neglected. Therefore, if these dimensions are so large compared to the thickness, such as bullion, coupons and discs (coins), and most importantly, these cases can be considered from the view of thermodynamic analysis as approaching slabs, then the general aforementioned heat transfer equations, equations (1) and (2), can also be applied to the bodies of interest here, e.g., bullion, coupons, discs (coins), as well as certain shapes of jewelry, which will be discussed later.  
         [0047]    Turning now to FIG. 1, which is a partly cut-away schematic of the apparatus for such nondestructive determination of gold bullion, a coupon, or a coin sample. Gold bullion, including gold coupons, have large width and length dimensions and gold coins have large diameters compared to their thicknesses. To qualify as a ‘slab’ the ratio of the edge dimensions, i.e., length, width or diameter, to the thickness can be approximately 3/1 or greater. Sample  1  is of unknown composition which is compared with a standard gold bullion, coupon or coin  2  of known composition. Although in FIG. 1 and subsequent figures, the sample and standard are shown as bullion, it is understood that the concepts as now explained are equally applicable to coupons, discs (coins) and in some instances jewelry. An electric-resistance heater  3 , making contact over the full bottom surface of sample  1 , which is insulated from the environment by insulation  13 , applies a sudden pulse of constant energy and at the same time an identical electric-resistance heater  4 , which is insulated from the environment by insulation  14 , applies a sudden pulse of constant energy over the full bottom surface of the standard  2 , thereby providing the same time-varying temperature patterns in the sample and the standard. Simultaneously, with or at a predetermined time after the heat is applied and for a predetermined time interval, or after the heat has been shut off and for a predetermined time interval, the temperature or time-varying temperature patterns of the sample, and the standard are sensed or noted and compared. The sensing functions are provided by infrared temperature sensor  9  focused on a spot  15  located at the middle of the top surface of sample  1  by a focal lens  5  and an infrared temperature sensor  10  located at the middle of the top surface of standard  2  focused on a spot  16  by a focal lens  7 , both operatively disposed to sense the time-varying temperatures of the sample and the standard, thus providing as output an electrical signal that is a function of the time-varying temperature. Rather than utilize contacting temperature sensors as in U.S. Pat. No. 3,981,175, non-contacting infrared temperature sensors  9  and  10  are employed; a further improvement.  
         [0048]    The top surface of sample  1  is insulated from the environment by insulation  11 , which also encloses temperature sensor  9  and focal lens  5 . Also, the upper surface of the standard  2  is insulated from the environment by insulation  12 , which also encloses temperature sensor  10  and focal lens  7 . As previously explained, the edges of the sample and the standard need not be insulated because they behave thermodynamically as heated slabs; this is an important embodiment. Each pair of heating means, as well as the sample  1  and standard  2  are well distanced from each other so as to eliminate thermodynamic interference between the two systems. The two electrical signals are connected as inputs to a difference amplifier  20  which notes any difference between the two electrical signals due to a temperature differential and amplifies the same.  
         [0049]    In FIG. 2, a comparator  21  is connected to receive an output from the difference amplifier  20 A and is connected to an alarm  22  which is activated in those instances in which the content of sample  1  varies from that of the standard  2 , or to a recorder  23 . As FIG. 1 shows, and to complete the electric circuitry of FIG. 1 by which sample purity is evaluated or analyzed, the heaters  3  and  4  are electrically energized through a switch  24  from an electrical power supply  25 . The sequencing and timing of the events in the system are provided by a timer means  26 .  
         [0050]    In the apparatus shown by FIG. 1, the heating elements  3  and  4  are in contact with the bottom of sample  1  and sample  2 , respectively, and temperature sensors  9  and  10  are focused on the top surfaces of the unknown sample  1  and the standard  2 , respectively, as noted above. The thickness of the the sample  1  and the standard  2  must be known. This can be readily accomplished through exterior means by physical measurement, or for example done through additional instrumentation and sensors built into the testing apparatus (this is not shown in FIG. 1 since it is not necessary to the understanding of the concept).  
         [0051]    Each heater means  3  and  4  should be of a type that provides, in this instance, controlled constant heat input to the sample  1  of unknown purity and to the gold standard  2 , as opposed to a constant temperature source (the later case is subsequently discussed); the heat thus applied is a controlled amount and the heating elements  3  and  4 , by their physical nature, each have low heat capacity so that all of the heat generated therein is transferred to the sample  1  and the standard  2 .  
         [0052]    If the temperature is measured at x=0, the surface opposite from the heated surface, equation (1) becomes:  
           T ( t )= QL/k{αt/L   2 −1/6−2/π 2 Σ m=1   ∞ (−1) m   /m   2 [exp(−α m   2 π 2   t/L   2 )]}  (1A)  
         [0053]    If an attempt is made to counterfeit a sample, the weight W in pounds and the thickness L in feet, would be dependent upon its size. Thus, equation (1A) becomes:  
           T ( t )= q/W{t/c−L   2 ρ/6 k− 2 L   2 ρ/π 2   kΣ   m=1   ∞ (−1) m   /m   2 [exp(−α m   2 π 2   t/L   2 )]}  (1B)  
         [0054]    Where: q is the suddenly applied constant heat flux in BTU/sec and all other terms are as previously defined.  
         [0055]    For proof of the purity of the sample it is sufficient that at all times during the test interval, the measured temperature of the suspected counterfeit bullion, or coupon, or coin sample be as high as that of the known gold standard (or a recording thereof). If the sample in question has the same purity as the standard, then it will be as hot as or hotter than the standard for comparison. This is subject to several restrictions and possible errors which are taken up in the next paragraph.  
         [0056]    Use of equation (1B) requires that the ratio q sa /W sa =q st /W st  (wherein q sa  and q st  are the heat inputs to the sample and standard of respective weights W sa  and W st ) must be kept within acceptable tolerance. The test is as good as the exactitude with which the thicknesses and weights are known. It may be impracticable to match thicknesses and weights of the test sample and the standard for comparison. However, neither is it necessary that the standard actually be present at the time the sample is tested nor is it necessary that a difference amplifier be employed since present day computers can readily discriminate between the temperature-time signatures and determine differences. Thus, in FIG. 3, one input to the computer  27  allows the measured thickness and weight of the sample and has stored within it the signatures of an equivalent standard, see Senturia et al, U.S. Pat. No. 3,747,755, which is incorporated by reference. Note the measurement of thickness and weight can be integral to the test device (for simplicity this is not shown in FIG. 1) and automatically programmed into the computer  27 , as shown in FIG. 3, or be manually programmed. The second input, the time-varying temperature patterns of the sample, are converted to electric signals as before and are fed to a sensor amplifier  28  and thence to an analog-to-digital converter  29 , the output of the converter being connected as the second input back to the computer  27 . The two signatures, one from the standard and the other from the sample, are compared by the computer; filed and recorded for viewing, and connected to an alarm  22 A.  
         [0057]    The embodiment indicated in the partly cut-away schematic, FIG. 4, shows as before the heating element  3 A, within the insulation  13 A, in full contact with the bottom surface of the test sample  1 A and the top surface of the sample  1 A is insulated by insulation  11 A from the environment. If the temperature is measured at the middle of the heated surface at x=L of the sample, as indicated by the sensor  9 A with focusing element  5 A focused on a spot  17 , then equation (1) becomes:  
           T ( x,t )= QL/k{αt/L   2 +1/3−2/π 2  Σ m=1   ∞ (−1) m   /m   2 [exp(−α m   2 π 2   t/L   2 )]cos( m π)}  (1C)  
         [0058]    The temperature sensor  9 A is operatively disposed to sense the time-varying temperatures at the lower surface of sample  1 A and thus provide as an output an electrical signal that is a function of the time-varying temperature. For this situation, only the thicknesses of test sample  1 A is needed and its weight need not be known. As before, the thickness of the test sample  1 A can be predetermined by physical measurement or a sensor built into the system with supplementary instrumentation. This is neither shown nor discussed here and is not further mentioned with reference to subsequently described systems, because it is not necessary to the understanding of the present concepts.  
         [0059]    It is noted that the heating element  3 A, shown in FIG. 4, can easily be replaced by either a focused laser or a focused infrared heater and equation 1C above will still be applicable. The definition of Q is defined by the knowledge of the area of the spot at which the heater is focused.  
         [0060]    Note also, that the physical system associated with the standard is not shown in FIG. 4, nor need it be, because as already explained in the description of FIG. 1, an electronic signal representative of the standard&#39;s temperature-time signature, i.e., temperature-time curve, can readily be built into the electronics of the system; this was included in the discussions of FIGS. 2 and 3. Therefore, subsequent discussions of related embodiments and figures will include only the physical system associated with the sample to be tested.  
         [0061]    As stated in U.S. Pat. No. 3,981,175 most adulterated samples will be cooler than the pure gold standard at the far end when x=0 (also at the heated end at x=L), but not always. In the course of the work leading to and arising from the aforementioned patent it was necessary to adjust the length of the sample and standard, which were in the form of rods, and the time of the test in order that an adulterated sample would always be cooler than the standard. In this work that choice is not available because the thickness, L, for bullion, coupons and discs (coins) are all different and fixed. For example, Handy and Harmon Corporation produce gold bullion that range from a thickness of {fraction (3/16)} inch (4.76 mm) to 1½ inches (38.10 mm) and gold coupons that range from 0.039 inch (0.99 mm) to {fraction (1/16)} inch (1.59 mm). Consequently, not all adulterated gold samples, when applying either Equation (1A), (1B) or (1C) were cooler than the gold standard after applying a pulse of heat for a given time interval.  
         [0062]    The reason for this is that there appears to be an optimum combination of thermal properties as they occur in equation (1), and related equations (1A), (1B) and (1C), as a function of thickness and length of test time. These properties, important in controlling the transmission of heat through the body and thus the temperature, are: thermal conductivity, k, and thermal diffusivity, α; where α is defined as k/ρc, ρ being the density and c the specific heat. The thermal properties of gold and those elements most likely to be used as adulterants are presented in Table I below:  
                                                     TABLE I                           ρ   c   k   α       Elements   lb/ft 3     BTU/lb-F   BTU/hr-ft-F   ft 2 /hr                                Gold (Au)   1204.860   0.031   183.159   4.936       Copper (Cu)   559.355   0.092   231.693   4.483       Silver (Ag)   655.494   0.056   247.872   6.729       Lead (Pb)   705.436   0.031   20.396   0.948       Tungsten (W)   1204.860   0.032   100.535   2.591                  
 
         [0063]    Ratios of from 50% gold (Au) and 50% adulterants, each of: copper (Cu), silver (Ag), lead (Pb) or tungsten (W), to ratios of 99.5% Au and 0.5% adulterants, each of Cu, Ag, Pb or W in bullion thicknesses from {fraction (3/16)} inch (4.76 mm) to 1½ inches (38.10 mm) and coupons and coin of from 0.039 inch (0.95 mm) to {fraction (1/16)} inch (1.67 mm) were examined. A linear relationship was used to estimate the thermal properties of the various ratios of adulterants examined. White and yellow gold samples of 14, 15, 18 and 22 carats were also tested and compared to pure gold (24 carat).  
         [0064]    The samples that defeated the test set forth in equation (1), because of their particular combination of thermal properties and required thicknesses, were composed of the adulterant Pb. However, when these same samples were tested in accordance with equation (2), where a constant temperature T 0  was applied for a given time period, they were cooler than the gold standard. The basic reason for this is that pure gold has a higher thermal diffusivity, α, than any of the aforementioned admixtures of gold samples with the exception of a silver admixture. Therefore, with the use of the two tests, referred here as the dual test method, i.e., application of both general equations (1) and (2), discrimination between the pure standard and the adulterated sample of at least 99.5 percent purity will be realized.  
         [0065]    With further reference to equation (2); pure silver has the highest thermal diffusivity of any known metallic material, and thus as a function of time, fine silver bullion of up to 3¼ inch (82.55 mm), including coin of up to 99.5 percent purity will attain a higher far end temperature than any other admixture. The U.S. Standard of 90 percent silver, the Sterling Standard of 92.5 percent purity and the Britannia Standard of 95.83 percent purity, can also be used as successful paradigms for comparison. Therefore, it is sufficient that at any time during the test, the temperature of the known silver bullion, coupon or coin (or a recording thereof) be as low as or lower than that of the suspected forgery, for certainty that the sample in question is either as pure or purer than the standard. This is subject to restrictions and several possible errors, as now discussed.  
         [0066]    The constant temperature T 0  in equation (2), which can be applied by the use of a heat sink for a defined time, must be identical for the sample and the standard. The test is as good as the exactitude with which the thicknesses of the bullion, coupons and discs (coins) are known. The thermal diffusivity of silver is very high compared to most materials, as shown in Table I. (Those elements shown in Table I as possible adulterants of gold are also candidates likely to be used as forgeries of silver.) As in the case of the gold test, the thickness of the sample L in equation (2), is very important for the sensitivity of the test. Nevertheless, lower thickness values can be compensated for by more sensitive instrumentation and amplification of temperature differences.  
         [0067]    Further embodiments can be realized by determining the slopes of the temperature-time curves; these objectives can readily obtained by taking the first derivative of the various appropriate equations. This is accomplished in the following:  
         [0068]    Differentiating equation (1), the general equation applicable to FIGS. 1 and 4, we obtain:  
           dT/dt=Q/ρcL{ 1+2Σ m=1   ∞ (−1) m  exp(−α m   2 π 2   t/L   2   t )cos( mπx/L )}  (3)  
         [0069]    However, at both x=0 and x=L equation (3) reduces to:  
           dT/dt=Q/ρcL   (3A)  
         [0070]    Similarly, equation (1B) reduces to:  
           dT/dt=q/Wc   (3B)  
         [0071]    To determine the slope of a system where constant temperature is applied and where the system is completely enclosed in an insulated medium or as shown in FIG. 1, differentiation of equation (2), with x=0, will result in the following:  
           dT/dt=T   0   L /(πα t   3 ) ½ Σ n=0   ∞ (−1) n (2 n+ 1)exp[−(2 n+ 1) 2 /4α t/L   2 ]  (4)  
         [0072]    If in the system shown in FIGS. 1 and 4 the heat is turned off, referred here as the decay rate, the temperature of the slab becomes:  
           T=Qt/ρcL   (5)  
         [0073]    Differentiating equation (5) gives the slope of the decay rate as:  
           dT/dt=Q/ρcL   (5A)  
         [0074]    Equations (3), (3A), (3B), (5) and (5A) provide a further check on the authenticity of the previously described gold and silver bullion, coupons, and discs. Using the dual test method indicated by equations (3A) and (4), the slopes for the constant heat and constant temperature applications, respectively, will provide a further check on the authenticity of the sample. Although the formulations for the decay rate and its slope for the constant temperature application are not presented here, nevertheless, such tests appropriately combined with those indicated by equations (5) and (5A), will provide a further check on the authenticity of the previously described gold and silver bullion, coupons, and discs.  
         [0075]    Appropriate instrumentation can be employed with the use of the above mentioned tests and equations providing guidelines. For example, additional instrumentation, such as a differentiator (not shown), can be added between the sensor amplifier  28  and the A/D convertor  29  to the circuitry in FIG. 3 to differentiate the temperature-time signal from the sample transducer to obtain slope versus time signals analogous to equations (3A), (3B) and (4). These signatures can then be compared to the appropriately stored data in the computer  27 ; filed and recorded for viewing, and connected to the alarm  22 A. Alternatively, rather than include a differentiator in the circuitry, the computer can numerically differentiate the digitized temperature-time signal from the A/D converter  29  and thus the process will proceed as aforementioned.  
         [0076]    The decay rate versus time signatures can also be obtained by simply retaining the electric signal from the sample transducer  9  after the heating element  3  in FIG. 1 has been shut off. The process for the attainment of the decay rate versus time signatures will proceed as aforementioned and the slope of same would then proceed as previously described in the above paragraph.  
         [0077]    If the areal dimensions of the test item are relatively large compared to its thickness, then another embodiment and improvement, schematically shown in FIGS. 5 and 6, is realized, i.e., exposure of the sample at x=0 to the environment.  
         [0078]    The general heat transfer equation for the body shown in FIGS. 5 and 6, i.e., constant heat flux Q applied at x=L and whose opposite surface is exposed to a medium, is:  
           T ( x,t )= Q/k{ 1/ h+x− 2 Σ n=1   ∞  exp(−αβ 2   n   t )cos[( L−x )β n ](β 2   n   +h   2 )/(β 2   n   [h+L (β 2   n   +h   2 )])}  (6)  
         [0079]    Where the thermal constants are as previously defined and h=H/k; H is the coefficient of heat transfer as a function of temperature in BTU/sec- ft 2 -F and β n , n=1, 2, 3 . . . , are the positive roots of the transcendental equation β tan βL=h. (See Carslaw and Jaeger  conduction Heat in Solids,  Oxford Press, 1950).  
         [0080]    Returning to FIG. 5, the sample  1 B being testing has its upper surface free of insulation. The sample  1 B is placed on an insulated bed  13 B enclosing a non-contacting heat source such as a laser or infrared heat source  30  and a focusing means  31 , which is concentrated on a known small area  32  at the mid-lower surface of a bullion, coupon or a coin  1 B. The sensing function is provided by infrared temperature sensor  9 B focused by a focusing means  5 B on a spot  15 A directly in line with spot  32 . The temperature sensor  9 B is operatively disposed to sense the time-varying temperatures at the upper surface of sample  1 B and thus provide as an output an electrical signal that is a function of the time-varying temperature. For this situation, only the thicknesses of test sample is needed and its weight need not be known.  
         [0081]    When the temperature is measured at x=0, as indicated in FIG. 5, equation (6) becomes:  
           T ( x,t )= Q/k{ 1/ h− 2Σ n=1   ∞  exp(−αβ 2   n   t )cos( Lβ   n )(β 2   n   +h   2 )/(β 2   n   [h+L (β 2   n   +h   2 )])}  (6A)  
         [0082]    A variation of FIG. 5 shows a partly cut-away schematic, FIG. 6, where again the sample  1 C is placed on an insulated bed  13 C with the noncontacting laser or infrared heater  30 A being focused by focusing means  31 A which is concentrated on a small known area  32 A at the mid-lower surface of a bullion, coupon or a coin. The sample being tested has its upper surface free of insulation and the temperature is sensed by an infrared temperature sensor  9 C focused by a focusing means  5 C at the lower surface on the spot  32 A.  
         [0083]    When the temperature is measured at x=L, the same surface at which the heat is applied, as depicted in FIG. 6, equation (6) becomes:  
           T ( x,t )= Q/k{ 1/ h+L− 2Σ n=1   ∞  exp(−αβ 2   n   t )(β 2   n   +h   2 )/(β 2   n   [h+L (β 2   n   +h   2 )])}  (6B)  
         [0084]    A similar situation as that described above for FIG. 5, where instead of a sudden pulse of heat, a constant temperature source T(t) is applied to silver bullion or disc (coin); the formula for this case, given by the same authors, is:  
           T=T   0 {1/(1+ hL )−2Σ n=1   ∞  exp(−αγ 2   n   t )sin( Lγ   n )(γ n   2   +h   2 )/(γ n   [h+L (γ 2   n   +h   2 ])  (7)  
         [0085]    Where γ n , n=1, 2, 3 . . . , are the positive roots of the transcendental equation γ cot γL+h=0.  
         [0086]    Equations (6A) and (6B) were employed to determine the temperature differences between the idealized gold standard and adulterated gold samples at the surfaces opposite the application of constant heat at x=0 and at the heated surfaces at x=L, respectively. The value of H used was 1.30 to 1.70 BTU/hr-ft 2 -F, obtained from  Heat Transmission , McGraw-Hill, 2nd ed., 1942, for polished surfaces in still air with small temperature differences. The thermal properties of the elements used were those given in Table I, as well as the same percent variation previously utilized when applying equation (1). Results of testing the samples according to equations (6A) and (6B), again indicated only the sample containing Pb defeated the test comprised of the previously mentioned thicknesses of bullion, coupon and coin at both x=0 and x=L. Nevertheless, when these samples containing variations of Pb were tested in accordance to equation (7), where constant temperature was applied for a given time period at x=L and the temperature measured at x=0, they were cooler than the idealized pure gold standard tested under the same circumstances. Thus the dual method, wherein the first test will generally discriminate between an idealized gold standard and most adulterated samples; those compositions comprised of gold and lead that defeat the first test can be retested, as indicated, and successfully determined to be less than the idealized gold standard.  
         [0087]    Additional embodiments can be realized by determining the slopes of the temperature-time curves; again these objectives can readily be obtained by taking the first derivative of the various appropriate equations. This is accomplished in the following:  
         [0088]    Again by differentiating equation (6A), which is applicable to FIG. 5 when x=0:  
           dT/dt= 2 Q/ρcΣ   n=1   ∞  exp(−αβ 2   n   t )cos( Lβ   n )(β 2   n   +h   2 )/[ h+L (β 2   n   +h   2 )],  (8)  
         [0089]    and differentiating equation (6B), where x=L, which is appropriate for FIG. 6:  
           dT/dt= 2 Q/ρc Σ   n=1   ∞  exp(−αβ 2   n   t )(β 2   n   +h   2 )/[ h+L (β 2   n   +h   2 )]  (9)  
         [0090]    The slope at x=0 opposite to the surface which is exposed to the environment and at which a constant application of temperature is applied, analogous to FIG. 5, is obtained by differentiating equation (7):  
           dT/dt= 2  T   0  αΣ n=1   ∞ γ n  exp(−αγ 2   n   t )sin( Lγ   n )(γ n   2   +h   2 )/[ h+L (γ 2   n   +h   2 )]  (10)  
         [0091]    Equations (8), (9) and (10) with the use of the dual test method, also provide a further check on the authenticity where appropriately applied to the previously described gold and silver bullion, coupons, and discs.  
         [0092]    The formulations are not presented for the decay rates and their slopes after the removal of the sudden heat pulse application and after the removal of constant temperature application, appropriate to FIGS. 5 and 6. Nevertheless, such tests along with the use of the dual test method and the suitable instrumentation, previously described, can be employed to provide a further check on the authenticity of the gold and silver bullion, coupons, and discs.  
         [0093]    Heretofore, there has been no simple, viable method of nondestructively determining the purity of gold or silver jewelry, such as rings or other shapes. Jewelry items, whose shapes are analogous to bullion already depicted, for example FIGS.  4  or  5 , i.e., signets of gold or silver rings, or other shapes that conform to the ratio previously mentioned of unknown fineness for which it is desired to know their carat or silver purity can also be examined by the method already described. If the gold or silver rings have signet portions or even other shapes in which their dimensions, such as widths and lengths or diameters that are a ratio of approximately 3/1 or greater compared to their thicknesses, then these test items can be considered as slabs when pulsed by a suddenly applied constant heat source or the application of a constant temperature and compared to a standard tested under the same circumstances.  
         [0094]    The calibration of the standard can be attained by simply fabricating the jewel item from the desired fineness for comparison. A gold standard, being considered either 24, 22, 18, 14 or even 9 carat gold, or a Sterling or Britannia Standard from which the temperature-time signature of the exact replica of the test sample having already been attained. As indicated previously the temperature-time signature of the standard can readily be built into the system instrumentation and need not be discussed further.  
         [0095]    Analogous to the systems shown in FIGS. 1 and 5, is the aforementioned gold or silver ring sample  40 , shown in FIG. 7, which can be slipped over an insulated semi-tapered mandrel  41 . The sample being tested has its upper surface and edges free of insulation. The heating function can be supplied by a laser or an infrared heater ( 30 B) focused by a focusing means ( 31 B) on to a small known area  32 B at the mid-lower surface of the signet and the sensing function is provided by an infrared temperature sensor  9 D and a focusing means  5 D. The temperature sensor is operatively disposed to sense the time-varying temperatures at the small known area  32 B of the signet; the signet being exposed to the environment and thus provides as output an electrical signal that is a function of the time-varying temperature. For this situation, only the thicknesses of the signet portion of the test sample is needed, but its weight need not be known.  
         [0096]    Additional variations of FIG. 7 can be envisioned: With the heating function within the insulated semi-tapered mandrel and focused on the mid-inside surface of the signet and measure the temperature at the same location, similar to FIG. 6, or the heating function focused on the mid-outside surface of the signet and the temperature measured at the same location or on the inside mid-surface of the signet.  
         [0097]    It was found that the dual test according to equations ( 6 A) and ( 6 B), as well as equation (7), as described above, were successfully applied to a gold ring, such as that shown in FIG. 7, having 14, 18 and 24 carat alloys, which were used as standards to discriminate between such alloys and determine their carat content. Also in all cases, the adulterants of silver tested according to equation (7) showed lower temperature-time responses than those of pure silver and the U.S., Sterling and Britannia Standards.  
         [0098]    Equations (8), (9) and (10), with the use of the dual test method, also provide a further check on the authenticity where appropriately applied to the above described gold and silver jewelry.  
         [0099]    Again as previously mentioned, the formulations are not presented for the decay rates and their slopes after the removal of the sudden heat pulse application and after the removal of constant temperature application, appropriate to FIG. 7. Nevertheless, such tests along with the use of the dual test method and the suitable instrumentation, previously described, can be employed to provide a further check on the authenticity of the above described gold and silver jewelry.  
         [0100]    Test samples that are not insulated, as schematically depicted in FIGS. 8 and 9, can also be tested even though the formulation is not presented here. Nevertheless, the results will be similar to those cases already described but the magnitudes of the resulting temperatures will be mitigated. However, with present day instrumentation the signals can be readily amplified such that the difference between the standard and the test sample will  3 be measurable. Turning to FIG. 8, the test sample  1 D is place on supports  33  with the noncontacting laser or infrared heater  30 C being focused by focusing means  31 C which are concentrated on a small known area  32 C at the mid-lower surface of a bullion, coupon or a coin  1 D. The sample  1 D has at its upper surface an infrared temperature sensor  9 E and focusing means  5 E focused on a spot  15 B opposite  32 C, and as before the temperature sensor  9 E and its focusing means  5 E detect the temperature-time response of the sample which is compared to the temperature-time signature of the standard having been tested under the exact conditions as the test sample  1 D for comparison.  
         [0101]    Now turning to FIG. 9, the test sample  1 E is place on supports  33 A with the noncontacting laser or infrared heater  30 D being focused by focusing means  31 D which are concentrated on a small known area  32 D at the mid-upper surface of a bullion, coupon or a coin  1 E. The sample  1 E being testing also has at its upper surface an infrared temperature sensor  9 F and focusing means  5 F and the temperature sensor is focused on the small area  32 D and it detects the temperature-time response of the test sample  1 E which is compared to the temperature-time response signature of the standard having been tested under the exact conditions as the test sample for comparison.  
         [0102]    Again, other embodiments can be described as jewelry samples, whose shapes are analogous to the bullion depicted in FIGS. 8 and 9, i.e., the signets of gold rings or silver rings of unknown fineness for which it is desired to know their carat or silver purity. The aforementioned gold or silver ring samples are suspended in air by gripping them at locations opposite from the signets. The sample being tested has at its lower surface, analogous to FIG. 8, an infrared heater or laser focused on a spot of known area in the middle of the signet and the sensing function is provided by an infrared temperature sensor focused on the top surface of the signet opposite to the focused heater. The alternative system, which is analogous to FIG. 9, would have the sample being tested at its upper surface with an infrared heater or laser focused on a spot of known area at the middle of the signet and the sensing function, provided by an infrared temperature sensor and is focused on a the same spot on the upper surface. The temperature sensors are operatively disposed to sense the time-varying temperatures at their respective surfaces of the signets, which is exposed to the environment and thus provides as output electrical signals that are a function of the time-varying temperature which is compared to the temperature-time signature of the standard having been tested under the exact conditions as the test sample for comparison.  
         [0103]    For the situations described above, i.,e., FIGS. 8 and 9, and the similar systems such as the jewelry test sample, only the thicknesses of the bullion and signet portion of the rings are needed, but their weights need not be known. It is further noted that even though the formulation, i.e., temperature-time signatures, slopes versus time signatures, decay rate and slopes of the decay rate versus time signatures for both sudden heat pulse application and for constant temperature application are not presented, nevertheless, such tests along with with the use of the dual test method and the suitable instrumentation previously described can be employed to provide a further check on the authenticity of the previously described gold and silver bullion, coupons, discs and jewelry.