Systems and methods for calibration of gas specific gravity meters and gas adsorption analyzers - Patents.com

Abstract

A system and method for calibrating a gas density gauge utilizing a custom volumetric reference standard is disclosed. The custom volumetric reference standard may include a material. The material may include low CTE and highly accurate dimensions. The material may have a high aspect ratio reference shape that corresponds to the interior area of ​​a custom-fabricated sample cup. The custom volumetric reference standard may include a defined number of inclusions, high purity, and / or a precisely known density of the material. The custom volumetric reference standard may include a known volume.

Description

[Technical field]

[0001] (CROSS REFERENCE TO RELATED APPLICATIONS) This application claims the benefit of U.S. Provisional Patent Application No. 63 / 180,692, filed April 28, 2021.

[0002] (Cited by reference) The disclosure of U.S. Provisional Patent Application No. 63 / 180,692, filed April 28, 2021, is hereby incorporated by reference for all purposes as if set forth in its entirety.

[0003] (Technical field) In one aspect, the present disclosure is directed to systems and methods for calibration of measurement devices, and more particularly, for calibration of gas pycnometers or gas sorption analyzers (referred to herein as pycnometer devices) utilizing custom volumetric reference standard materials with low coefficients of thermal expansion. Other aspects are also described. [Background technology]

[0004] (background) Gas pycnometers are used to non-destructively measure the volume of various materials, such as powders, slurries, porous materials, etc., and determine their various properties, such as the true density of the material being measured; similarly, gas sorption analyzers are used to non-destructively measure the amount of fluid that can be adsorbed by powders and porous materials. However, to ensure accurate measurement and determination of the volume and density of the material or adsorbed fluid, pycnometer devices rely on being accurately calibrated using known reference volume standards. Heretofore, reference volume standards have been sold that are formed for use with a specific size sample cup, container, or chamber of a particular measurement device. Typically, these reference volume standards are formed from metals, such as tungsten carbide or stainless steel, and molded as spheres, so that they can be machined within desired tolerances and in specific sizes designed to fit such specific size sample containers / cups. However, these reference volume standards are typically very expensive to produce due to the high precision required in their machining, making it difficult and generally prohibitively expensive to provide customers with a wide variety of different size / shape containers and / or customized sample measurement solutions. Still further, if such conventional reference volume standards are mishandled or damaged, e.g., dropped so as to affect / change their dimensions or roundness even slightly, the reference volume standards may become inaccurate and would need to be replaced. In addition, the coefficient of thermal expansion (CTE) and density of these volume reference standards are also generally relatively high, e.g., tungsten carbide has a CTE of 5.5 μm / m-°C and a density of at least 15 g / cc, while stainless steel has a CTE of 17.5 μm / m-°C with a density of about 7.9 g / cc. The high CTE of such materials means that they tend to undergo expansion in response to exposure to higher temperatures and, at least indirectly, pressure, which expansion affects the volume of the volumetric reference standards and must therefore be taken into account during volumetric calibration.

[0005] Thus, the present disclosure is directed to embodiments of systems and methods for calibrating specific gravity measuring devices that address the above-mentioned and other related and unrelated problems in the related art. Summary of the Invention [Means for solving the problem]

[0006] (summary) Briefly, the present disclosure includes systems and methods for calibrating measurement systems, such as gas pycnometers or gas sorption analyzers. In some aspects, the systems and methods may be adapted to calibrate gas pycnometers or gas sorption analyzers utilizing custom shaped sample cups, secondary sample cups, containers, or sample chambers. Such calibration may utilize volumetric reference standards formed from a variety of materials that exhibit low coefficients of thermal expansion (CTE), can be produced with high dimensional and / or density accuracy, may incorporate sample chambers of a variety of different sizes and / or configurations, and may provide a volumetric reference standard that will have a volume that is determinable with high accuracy to enable calibration of the gas pycnometer. Such materials may also be produced at substantially lower cost compared to conventional volumetric reference standard materials without substantially affecting their reference volume calculations, and may be produced in a variety of different and / or customizable sizes and / or configurations, and with known and / or low content, known high purity, and / or known density. Thus, by utilizing such materials, gas density meters that utilize customer defined or otherwise custom configured sample cups or chambers can be accurately calibrated.

[0007] Thus, in one aspect, the present disclosure is directed to a method for calibrating a gas pycnometer. The method may include placing a custom volumetric reference standard in a sample cup or sample chamber, the custom volumetric reference standard being formed from a ceramic or optical glass material having a low coefficient of thermal expansion, for example, less than 5.5-6.0 μm / m-°C, in embodiments within the range of about 0.005 μm / m-°C to about 4.5 μm / m-°C or 0.05 μm / m-°C to about 3.0 μm / m-°C, and having a known volume with an accuracy of ±0.00005 inches (50 microinches). The custom volumetric reference standard will further be formed with a configuration or reference geometry adapted to substantially match the configuration or dimensions of the sample cup or container that will be placed in the sample chamber of the gas pycnometer, and the gas introduced into the sample chamber. In another embodiment, the custom volumetric reference standard will further be formed with a volume adapted to substantially match the volume of the sample to be measured or analyzed. In such an embodiment, the gas pycnometer can be operated without a sample cup or container, and the reference standard can have a selected known shape (including known dimensions of length, width, and depth) and volume for calibration of the gas pycnometer without a sample cup or container required. For example, a custom volumetric reference standard need not be formed as a sphere, but can be formed with a selected reference shape, such as, but not limited to, a disk, cylinder, cone, frustum, or other shape.

[0008] After the pressure and temperature of the gas in the sample chamber reach pressure and / or temperature equilibrium, a first pressure in the sample chamber is measured. Gas from the sample chamber is then allowed to flow into the expansion chamber until it is filled, after which a second pressure in the sample chamber is measured. The volume of the custom volumetric reference standard is determined based on the first measured pressure and the second measured pressure after expansion of the gas. This measured volume of the custom volumetric reference standard is then compared to the known volume of the custom volumetric reference standard, and an adjustment to the average calibration volume of the sample chamber will be made based on the comparison.

[0009] In an embodiment, the custom volumetric reference standard will be constructed from a material with a low CTE, such as lithium aluminosilicate glass ceramic. In some embodiments, the custom volumetric reference standard may be constructed from optical glass materials, such as sapphire, silicon, and fused silica. Other ceramic, glass, and / or similar crystalline materials with a CTE of less than 6 μm / m-°C, in some embodiments less than about 3 μm / m-°C, including crystalline materials that can be grown or lab-formed in a desired custom reference shape to fit a customer-defined / custom sample cup or container, can also be used. The custom volumetric reference standard may further include a defined number of inclusions or high purity, which allows the density to be known to a high degree of accuracy. In another aspect, a mishandled custom volumetric reference standard may be reusable after cleaning and / or reweighing.

[0010] In another aspect, the sample cup or sample chamber may be a custom shape. The custom shape may include or have a high aspect ratio. The sample cup or sample chamber may be configured to accept a custom volumetric reference standard having a variety of configurations, including, but not limited to, a thin disk, a long rod, a cylinder, a sphere, or other configurations. The sample cup or sample chamber may be made of the same low CTE material as the custom reference volume standard.

[0011] Another aspect of the present disclosure is directed to a system for calibration of a gas spectrometer. The system may include one or more sample cups, sample chambers, or containers that may be used with the gas spectrometer and may be of various sizes and / or shapes, including customer-defined shapes and sizes. The system would further include one or more high aspect ratio custom volumetric reference standards, each of which may be formed to match such various or customized sizes and / or shapes of sample cups, sample chambers, or containers with high dimensional accuracy. The system would include a controller configured to calibrate the gas spectrometer utilizing the custom volumetric reference standards when inserted into the sample cup and to calibrate the average volume of the gas spectrometer.

[0012] In another aspect, when a high aspect ratio custom volumetric reference standard is inserted into a sample cup, the high aspect ratio can occupy approximately 90% of the sample cup, sample chamber, or container.

[0013] Another aspect of the present disclosure is directed to a custom volumetric reference standard for the calibration of gas density meters, which will comprise a material with low CTE and highly accurate dimensions. The reference shape of the custom volumetric reference standard can be adapted to correspond to the inner surface area of ​​the custom sample cup. The custom volumetric reference standard may also contain a defined number of inclusions or be made of high purity and will have a known volume, as this may allow the density of the standard to be known with high accuracy.

[0014] Another aspect of the present disclosure is directed to the calibration of devices used to determine adsorption isotherms. In particular, in embodiments, the present disclosure is directed to or provides nanometer-based adsorption instruments that utilize pressure, temperature, and a calibrated volume or volumes for the determination of the volume occupied by the test material, and also the total amount of fluid, typically vapor, in the calibrated volume at known pressure and temperature. Calibration of such devices can be performed in a manner substantially identical or similar to that of gas pycnometers. Both pycnometers and adsorption devices require a reference volume with reasonably well-defined and thermally stable dimensions, and both devices can achieve more precise calibration if temperature dependence is minimized.

[0015] Another aspect of the present disclosure is directed to determining the coefficient of thermal expansion (CTE) for known or unknown materials. A specific gravity measuring device with high accuracy calibration can be used to determine the volume displaced by a sample under a series of different test conditions. As an example, in one embodiment, the displaced volume of the sample can be evaluated at several temperatures ranging from below ambient to above ambient, and the CTE of the sample can then be calculated from the displaced volume as a function of temperature. The CTE is calculated as the linear or volumetric change in dimension per degree of temperature change from a reference temperature in degrees Celsius, the reference temperature being about 20°C.

[0016] Another aspect of the present disclosure is directed to the use of low CTE materials as reference standards that may be used for the calibration of measurement devices requiring precise linear displacement calibration, such as those used for packed bed permeability measurements, or for determining the density of powders or objects packed into a powder bed, and / or for determining packed bed length in cylindrical devices with well-defined diameters. Typically, tool steel pins or other cylindrical steel cylinders with dimensions ranging from 20 to 60 + / - 0.01 mm may be used to calibrate linear displacement devices. As an example and for reference, a (17.3 x 10 -6A 50 mm long stainless steel 304 rod (having a CTE of +0.022 mm / °C) would have a length change of +0.022 mm. In such a case, the calibration accuracy may be improved to minimize the effect of thermal expansion of the traditional tool steel reference standard such that the effect of possible thermal expansion on the volumetric calibration of a linear displacement device may be substantially eliminated by using a low CTE material.

[0017] Still other aspects and advantages of these and other embodiments are discussed in detail herein. It should also be understood that both the foregoing information and the following detailed description are merely illustrative examples of the various aspects and embodiments, and are intended to provide an overview or framework for understanding the nature and characteristics of the various aspects and embodiments disclosed herein. Thus, these and other objects, in addition to the advantages and features of the present disclosure disclosed herein, will become apparent through the following description and reference to the accompanying drawings. It should also be understood that the features of the various embodiments described herein are not mutually exclusive and may exist in various combinations and permutations. The present invention provides, for example, the following: (Item 1) 1. A method for calibrating a specific gravity measuring device, comprising: (a) placing a custom volumetric reference standard into a sample chamber, the custom volumetric reference standard comprising a material with a low coefficient of thermal expansion (CTE), including at least one of a lithium aluminosilicate glass ceramic, sapphire, silicon, fused silica, or a combination thereof; (b) determining a determined volume of the custom volumetric reference standard based on the pressure measurement from the specific gravity measuring device and the known volume of the sample chamber; (c) comparing the determined volume of the custom volumetric reference standard to a known volume of the custom volumetric reference standard; (d) adjusting an average calibration volume for the sample chamber based on a comparison of the determined volume of the custom volumetric reference standard to the known volume of the custom volumetric reference standard; A method comprising: (Item 2) 2. The method of claim 1, wherein the sample chamber comprises a custom shape. (Item 3) 2. The method of claim 1, further comprising obtaining the custom volumetric standard, the custom volumetric standard comprising a defined number of inclusions. (Item 4) 2. The method of claim 1, wherein if the custom volumetric reference standard is mishandled, the custom volumetric reference standard is reusable after cleaning and reweighing. (Item 5) After calibration of the specific gravity measuring device, placing a test material in a sample chamber and measuring a volume of the test material at a plurality of temperatures, and measuring the volume of the test material as a function of temperature; determining a coefficient of thermal expansion for the test material; The method of claim 1, further comprising: (Item 6) 2. The method of claim 1, wherein placing the custom volumetric reference standard in a sample chamber includes placing the custom volumetric reference standard in a sample cup and positioning the sample cup in the sample chamber prior to calibration. (Item 7) Determining the volume of the custom volumetric reference standard further comprises: (a) providing a gas to a sample chamber; (b) measuring a first pressure in the sample chamber after the sample chamber is filled with gas; and (c) after the pressure and temperature in the sample chamber reach equilibrium, opening a valve to allow the gas to flow from the sample chamber to an expansion chamber; (d) measuring a second pressure in the sample chamber after the expansion chamber is filled with the gas; and (e) determining a volume of the custom volumetric reference standard based on the first pressure, the second pressure, and known specifications of the sample chamber; The method according to item 6, comprising: (Item 8) A custom volumetric reference standard for calibration of a gas density instrument, comprising: (a) a material comprising a CTE of about 0.007 μm / m-°C to about 6.0 μm / m-°C; (b) the precisely determined density of said material and the weight of said material; (c) a selected reference shape having a known width, length, depth, or volume, or a combination thereof; A custom volumetric reference standard. (Item 9) Item 9. The custom volumetric reference standard of item 8, wherein the material comprises a lithium aluminosilicate glass ceramic. (Item 10) 9. The custom volumetric reference standard of claim 8, wherein the material comprises fused silica. (Item 11) 9. The custom volumetric reference standard of item 8, wherein the material comprises single crystal silicon. (Item 12) 9. The custom volumetric reference standard of claim 8, wherein the material comprises sapphire. (Item 13) 9. The custom volumetric reference standard according to item 8, wherein the reference shape comprises a cylindrical shape. (Item 14) 9. The custom volumetric reference standard according to item 8, wherein the reference shape comprises a disk shape. (Item 15) 9. The custom volumetric reference standard according to item 8, wherein the reference shape comprises a spherical shape. (Item 16) 9. The custom volumetric reference standard of item 8, wherein the reference shape of the custom volumetric reference standard is selected to substantially correspond to a shape of a sample cup configured to be received within a sample chamber of a gas density meter for calibration. (Item 17) 9. The custom volumetric reference standard of item 8, wherein the reference shape comprises a high aspect ratio shape. (Item 18) 9. The custom volumetric reference standard of item 8, wherein the reference shape comprises selected geometric dimensions that are accurate to within about one millimeter. (Item 19) 9. The custom volumetric reference standard of item 8, wherein the reference shape comprises selected feature dimensions that are accurate to within about 1 micrometer. (Item 20) 9. The custom volumetric reference standard of item 8, further comprising a material having a defined number of inclusions of said material or of known high purity. [Brief description of the drawings]

[0018] It should be understood that for simplicity and clarity of illustration, elements illustrated in the figures have not necessarily been drawn to scale. For example, the dimensions of some elements may be exaggerated relative to other elements. These and other features, aspects, and advantages of the present disclosure will become better understood with respect to the following description, aspects, and accompanying drawings. It should be noted, however, that the drawings only illustrate some embodiments of the present disclosure and therefore should not be considered as limiting the scope of the present disclosure. Embodiments incorporating the teachings of the present disclosure are shown and described with respect to the drawings herein.

[0019] [Figure 1] 1A and 1B are schematic diagrams of a gas pycnometer for determining the volume and density of a material in accordance with the present disclosure.

[0020] [Diagram 2] 2A and 2B are schematic diagrams of a sample chamber of a gas pycnometer including a custom volumetric reference standard according to the present disclosure, FIG 2C is a schematic diagram of the custom volumetric reference standard of FIG 2A and FIG 2B, and FIG 2D and FIG 2E are schematic diagrams of exemplary custom volumetric reference standards having alternative shapes according to the present disclosure.

[0021] [Diagram 3] FIG. 3 is a flow diagram of a process that may be implemented to calibrate a gas density meter in accordance with the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0022] The use of the same reference symbols in different drawings indicates similar or identical items.

[0023] (Detailed Description) The following description combined with the figures is provided to aid in understanding the teachings disclosed herein. The description focuses on the implementation and embodiments of the present teachings and is provided to aid in explaining the present teachings. This focus should not be interpreted as a limitation of the scope or applicability of the present teachings. In a manner in which the features and advantages of the embodiments of the systems and methods disclosed herein, as well as others that will become apparent, may be more fully understood, a more particular description of the embodiments of the systems and methods briefly summarized above may be obtained by reference to the following detailed description of those embodiments, one or more of which are further illustrated in the accompanying drawings, which form a part of this specification. However, it should be noted that the drawings only illustrate various embodiments of the systems and methods disclosed herein, and therefore should not be considered as limiting the scope of the systems and methods disclosed herein, as this may include other effective embodiments as well.

[0024] 1A and 1B are schematic diagrams of a gas pycnometer for measuring the volume and density of a material. In general, such a gas pycnometer 100 can be used to measure the volume of a material or sample 110 with a high degree of accuracy. The principles of the present disclosure are also applicable to gas adsorption analyzers or other similar measurement devices.

[0025] By way of illustration and example, in an embodiment relating to the use of a gas pycnometer such as that shown in FIGS. 1A-1B to measure the volume of a material, a sample 110 is added to the sample chamber 106 of the gas pycnometer or gas adsorption analyzer 100. In an embodiment, the sample 110 will be added to a sample cup 108 that is placed in the sample chamber 106. However, it will be understood by those skilled in the art that a sample cup or other container need not necessarily be used and that a sample may be tested by placing it directly in the sample chamber without the use of a sample cup. In yet other embodiments, a secondary sample cup may also be utilized in addition to the sample cup. If a sample cup 108 is utilized, once the sample cup 108 is placed in the sample chamber 106 or once the sample 110 is placed directly in the sample chamber 106, the valve 102 is opened (FIG. 1A) to allow gas to flow into the sample chamber 106 through the pipeline 104. The pipeline 104 may also be referred to as piping or tubing. Once the sample chamber 106 is filled and the pressure and temperature within the sample chamber 106 reach equilibrium, pressure and temperature measurements are taken. Pressure may be determined via a pressure transducer or pressure gauge 114 connected to and / or in fluid communication with the sample cup 108 or sample chamber 106 via pipeline 112. Temperature may be measured via a thermocouple (not shown) or similar measurement. After initial values ​​for temperature and pressure have been determined, valve 102 may be closed and valve 118 may be opened (FIG. 1B) to allow gas to flow through pipeline 116 to expansion chamber 122.

[0026] The expansion chamber 122 is monitored as it fills with gas from the sample chamber 106. Once the expansion chamber 122 is filled and the pressure and temperature reach equilibrium, a second measurement of the sample chamber 106 is determined, for example, via a pressure transducer or pressure gauge 114. Using the first and second pressure measurements, a controller of the gas pycnometer can determine the actual volume of the sample material.

[0027] As described, prior to use, the gas pycnometer 100 must be calibrated using a volumetric reference standard to accurately calculate the volume of the material sample. The volumetric reference standard may be a solid object and will have a known volume, a known mass, and / or a known density. So far, spherical volumetric reference standards made of tungsten carbide or stainless steel have been used. However, such volumetric reference standards made of tungsten carbide or stainless steel are expensive to produce and possess a high CTE such that they tend to expand significantly under higher temperatures and, at least indirectly, under pressure (e.g., an increase in pressure, which causes a further increase in temperature), and the expansion must be stabilized and taken into account in calibrating the volume of the sample chamber. Furthermore, it is difficult and expensive to produce custom volumetric reference standards with shapes other than spheres, such as, for example, thin disks, cylinders, rods, stackable materials, or other shapes of dense and hard materials such as, but not limited to, tungsten carbide or stainless steel, and such volumetric reference standards can be easily damaged. Thus, customer needs / desires for further variations in sample chamber size and shape, which in turn require further customization of volumetric standards, have generally remained limited and / or substantially unmet.

[0028] In an embodiment, the gas pycnometer 100 or the custom sample cup of the gas pycnometer 100 may include or be included with a custom volumetric reference standard. The custom volumetric reference standard may correspond in shape and size to an indentation in the custom sample cup, or may correspond or resemble in size and / or volume to the sample to be measured or analyzed. The custom volumetric reference standard may be constructed from a low CTE material. The custom volumetric reference standard may be produced in a variety of reference shapes and sizes. The reference shapes and sizes may be produced to a high level of dimensional accuracy (e.g., with geometry accurate to about 1 micrometer to about 1.0 millimeter, although greater or lesser dimensional accuracy may also be used). For example, the custom volumetric reference standard may be produced to an accuracy of ±50 microinches relative to the diameter and thickness of the custom volumetric reference standard. Additionally, the custom volumetric reference standard may be polished such that deviations from flatness and smoothness may be assumed to be negligible. Based on such characteristics, the resulting volume uncertainty may be ±0.00016 cm 3 ~±0.00092cm 3 Such low CTE materials can result in stable custom volumetric reference standards that undergo a small amount of thermal expansion and are capable of withstanding high heat due to the low CTE qualities of the low CTE materials. The low CTE materials can also be low cost, even when compared to the cost of tungsten carbide or stainless steel.

[0029] 2A and 2B are schematic diagrams of a sample chamber 202 of a gas pycnometer including a custom volumetric reference standard 206 (FIGS. 2A-2C) according to the present disclosure. According to an embodiment of the present disclosure, a different and / or custom sample cup 204 or chamber is utilized, so that a volumetric reference standard for calibration of a gas pycnometer utilizing such a different, custom designed sample cup or chamber may be customized, such as, for example, a custom reference standard 206. In particular, the custom volumetric reference standard of the present disclosure may include materials such as ceramic-based materials, glass materials, or other types of materials, including various optical crystal structured materials, that possess low CTE and provide cost-efficient production / formation with high accuracy dimensions for all sides of any desired fiducial shape. Materials used to generate the custom volumetric reference standard 206 may include sapphire material, silicon or single crystal silicon, fused silica, borosilicate, titanium silicate glass (e.g., Corning® ULE® glass (ultra-low expansion glass), and / or lithium aluminosilicate glass ceramic (e.g., Zerodur®). Other materials exhibiting similar properties may also be utilized. Such custom volumetric reference standard materials can be formed as sheets, cut and polished to size and / or shape, or grown and polished as crystalline structures.

[0030] In such an example, a gas pycnometer having a custom sample cup 204 or chamber defined by a customer may be utilized. As an example, in one embodiment, the custom sample cup 204 may be configured with a thin disk-shaped indentation 204a (FIG. 2B) for holding various samples. Various other shapes may also be desired for the indentation of the custom sample cup. Additionally, the custom sample cup 204 may be made of the same material (e.g., a low CTE material) as the custom volumetric reference standard 206. To calibrate the gas pycnometer, the thin disk-shaped custom volumetric reference standard 206 may be utilized. Other reference shapes may be considered for the custom reference standard based on the indentation shape of the custom sample cup and / or based on the shape or volume of the sample to be measured or analyzed. As shown in FIG. 2B, the custom volumetric reference standard 206 may be inserted or placed into the indentation 204a of the custom sample cup 204, which may then be placed or inserted into the sample chamber 202, and the assembly process may be performed as discussed above.

[0031] The thin disk-shaped custom volumetric reference standard 206 would be constructed to occupy up to 90% of the custom sample cup 204, as described above, including a material having a CTE that would be less than about 5.5 μm / m-° C. Because the CTE of such a custom volumetric reference standard 206 would be low, the custom reference standard 206 would exhibit minimal thermal-based expansion as hot gases flow into the sample chamber 202 or sample cup 204. Furthermore, the temperature of the custom volumetric reference standard 206 would not be an issue due to such nature. In embodiments, the CTE of such a custom volumetric reference standard 206 may be from about 0.005 to about 5.5-6.0 μm / m-°C, from about 0.007 μm / m-°C to about 4.5 μm / m-°C, from about 0.007 μm / m-°C to about 4.0 μm / m-°C, 0.05 μm / m-°C to about 4.0 μm / m-°C, 0.05 μm / m-°C to about 3.5 μm / m-°C, 0.005 μm / m-°C to about 3.0 μm / m-°C, 0.05 μm / m-°C to about 2.5 μm / m-°C, or other variations. For example, materials such as lithium aluminosilicate glass ceramics can have a CTE of about 0.007 μm / m-° C. to about 0.05 μm / m-° C., fused silica materials can have a CTE of about 0.6 μm / m-° C., silicon and / or single crystal silicon materials can have a CTE of about 2.6 μm / m-° C., while sapphire crystalline materials can have a CTE of about 5 to about 7 μm / m-° C. See Table 1 for additional details and a comparison of the described custom volumetric standard materials to conventional volumetric standard materials.

[0032] [Table 1]

[0033] The custom volumetric reference standard 206 may also include or be formed with reference shapes other than the disk shape shown. For example, the custom volumetric reference standard 206 may be a sphere, an ellipse, an oval, a cone, a frustum, and / or any other reference shape that can fit within the custom sample cup 204 or sample chamber 202 and fill sufficient space within the custom sample cup 204 or sample chamber 202. Furthermore, the custom volumetric reference standard 206, in contrast to tungsten carbide or stainless steel, may exhibit little or no damage if mishandled. For example, because the custom standard is constructed with a selected low CTE, its density can generally be considered constant within a given temperature range, and therefore the mass of the custom reference standard is known, if the custom volumetric reference standard 206 is mishandled, e.g., touched without gloves or dropped, rather than discarding the custom volumetric reference standard 206, the custom volumetric reference standard 206 may be cleaned or polished and / or re-weighed, and use of the custom volumetric reference standard 206 may continue. Additionally, some of the materials selected for construction of the custom volumetric reference standard (e.g., Zerodur) are defined with very few inclusions, meaning that the density is substantially constant throughout the object.

[0034] A variety of other custom sample cups other than the illustrated custom sample cup 204 may also be defined. Such shapes may include disk-shaped areas, portions, or indentations of different sizes, as well as elongated vertical rod or cylindrical areas, portions, or indentations. For a user to define a custom shaped sample cup, a corresponding custom volumetric reference standard with a selected reference shape configured to fit within the custom shaped sample cup may be generated for calibration purposes.

[0035] The custom volumetric reference standard 206 may be a high aspect ratio reference shape because the custom sample cup 204 may include a narrow or shallow indentation, or an elongated vertical rod, or a cylindrical shaped area configured to receive a sample and perform an accurate calibration. As used herein, "high aspect ratio" or "high aspect ratio reference shape" may refer to the ratio of different dimensions of a reference shape. Such a ratio may include one dimension that is several times larger than the other dimension utilized in the ratio. For example, the aspect ratio of a cylinder or disk may be expressed as the height (h) 210 of the cylinder or disk divided by the diameter (d) 212 of the cylinder or disk, e.g., h:d. A high aspect ratio cylinder or disk may include a cylinder or disk with a height several times larger, e.g., three times larger, four times larger, five times larger, or even multiples larger than the diameter of the cylinder or disk, or a diameter several times larger than the height of the cylinder or disk. Custom volumetric reference standards may be produced in a variety of sizes and / or shapes. For example, an alternative custom volumetric reference standard 206' having a cylindrical or rod shape (eg, with a high aspect ratio) is shown in FIG. 2D, and an alternative custom volumetric reference standard 206'' having a spherical shape is shown in FIG. 2E.

[0036] As described, to properly calibrate a specific gravity instrument, such custom volumetric standards may be of known volume and include a high level of dimensional accuracy. For example, custom volumetric standards may be produced with 50 microinch accuracy for diameter and thickness. Additionally, custom volumetric standards may be polished until flat and smooth. Such polishing may allow deviations in the surface of the custom volumetric standard, such as non-uniformity and / or roughness, to be negligible. Such production methods may result in measurements of ±0.00016 cm. 3 ~±0.00092cm 3 This can result in a volume uncertainty of

[0037] Producing custom fiducial shapes, e.g., high aspect ratio fiducial shapes, from tungsten carbide or stainless steel is difficult and expensive, and achieving high dimensional accuracy is generally an expensive procedure in common calibration materials such as metals. Alternative low CTE materials used for custom volumetric reference standards, e.g., sapphire materials, silicon or single crystal silicon, fused silica, and / or lithium aluminosilicate glass ceramics, may result in quicker, less difficult, and / or highly accurate manufacturing, thus lowering the cost of custom volumetric reference standards. Because custom volumetric reference standards have an engineered low CTE, their density can be considered constant within a given temperature range, such that only their mass is needed to figure out the volume. This means that dimensional accuracy of the object is not necessarily required for volume calculations. In addition, optical glass surfaces are typically fabricated and inspected to a higher precision than metal objects, and the tolerances on the surface finish quality of a typical glass surface can range from 5 nm RMS (typical quality) to 2 nm RMS (precision quality) to 0.5 nm RMS (high quality) versus a high quality metal surface finish of 28 nm RMS (ISO grade N1 roughness).

[0038] Custom volumetric reference standards may also contain a known number or amount of inclusions or be of known high purity (e.g., high level of homogeneity). As an example, an inclusion can be generally defined as any air bubble with a diameter >300 μm, although other diameters / variations can also be used. Inclusions and purity can be related to the density of the custom volumetric reference material. Thus, if the number or purity of inclusions is known, the density is known or can be determined with high accuracy. Such inclusions can affect any volume measurements and potentially provide an inaccurate calibration. Some materials may not be considered based on such inclusions. For some of the potential materials, a maximum number of inclusions may be specified during manufacturing. Other materials may also be pure and contain no or few inclusions. Exemplary materials include silicon, graphite, and diamond, and other carbon lattice materials, and materials that form crystalline structures. Class 0 Zerodur has an average of 100 cm 3 It is specified to have one inclusion per

[0039] Based on such purity, it is expected that weighing such custom volumetric reference standards 206 can be directly translatable to known densities, and therefore volumes, with a very high degree of accuracy. Furthermore, such materials can be produced in such reference shapes more quickly and accurately than their other counterparts.

[0040] FIG. 3 is a flow diagram of a process as implemented to calibrate a gas density meter according to the present disclosure. Method 300 may be implemented in a computing device or controller of a gas density meter. The components of FIGS. 1A-2B may be utilized in such method 300. Unless otherwise specified, the actions of method 300 may be completed in a gas density meter. Specifically, method 300 may be included in one or more programs, protocols, or instructions that are loaded into the memory of a computing device or controller of a gas density meter. The order in which the operations are described is not intended to be construed as a limitation, and any number of the described blocks may be combined in any order and / or in parallel to implement the method.

[0041] As used herein, a "computing device" may refer to an electronic device that includes or is connected to one or more processors and non-transitory machine-readable storage media, including, for example, but not limited to, a controller of a gas density meter or other device, a desktop computer, a microcontroller connected to a memory, a server, an edge server, a processor, and a memory, as would be understood by one of ordinary skill in the art. As used herein, a "non-transitory machine-readable storage medium" or "memory" may be any electronic, magnetic, optical, or other physical storage device for containing or storing information, such as executable instructions, data, and the like. For example, any machine-readable storage medium described herein may be any of random access memory (RAM), volatile memory, non-volatile memory, flash memory, a storage drive (e.g., a hard drive), a solid-state drive, any type of storage disk, and the like, or a combination thereof. As described, a memory may store or include instructions executable by a processor. As used herein, a "processor" may include, for example, one processor or multiple processors contained within a single device or distributed across multiple computing devices. The processor may be at least one of a central processing unit (CPU), a semiconductor-based microprocessor, a graphics processing unit (GPU), a field programmable gate array (FPGA) for reading and executing instructions, a real-time processor (RTP), an application specific integrated circuit (ASIC), other electronic circuitry suitable for reading and executing instructions stored on a machine-readable storage medium, or a combination thereof.

[0042] At block 302, a custom-shaped volumetric reference standard may be inserted into the sample cup. The custom-shaped volumetric reference standard may be based on the custom-shaped sample cup. For example, the custom-shaped volumetric reference standard may be a flat thin disk, an elongated rod, and / or other custom reference shape that is not typically used in gas pycnometers. In such an example, the custom-shaped volumetric reference standard may correspond to an interior area or portion of the custom-shaped sample cup. In another example, a user may define a shape for the sample cup based on a material that the user may want to measure. Based on the specifications for the sample cup, a custom-shaped volumetric reference standard may be generated and included with the sample cup separately from, but not within, the sample cup. In other words, when a customer receives such a gas pycnometer, the custom-shaped sample cup and the custom-shaped volumetric reference standard may be contained in separate, protected packaging to prevent damage. Additionally, the sample cup or sample chamber may be made of a material from a specification selected by the user or customer. In other embodiments, the material may be metal or the same material as the custom-shaped volumetric standard. In certain examples, utilizing the same low CTE material for the sample cup or sample chamber as that of the custom volumetric reference standard may eliminate or reduce any effect of the sample cup on the measured volume over temperature. In embodiments, the custom shaped volumetric reference standard and / or sample cup may have any suitable shape.

[0043] A custom shaped sample cup may be inserted into the sample chamber at block 304. A user may insert the custom shaped sample cup into the sample chamber after inserting the custom shaped volumetric reference standard or before inserting the custom shaped volumetric reference standard.

[0044] In block 306, after the custom-shaped sample cup is inserted into the sample chamber and the lid of the gas pycnometer is closed or sealed, the controller or computing device of the gas pycnometer may actuate a valve to bring and / or transport gas into the sample chamber and / or the custom-shaped sample cup. In block 308, the controller or computing device may check or determine whether the sample chamber or the custom-shaped sample cup is filled with gas. Once the sample chamber or the custom-shaped sample cup is filled with gas, the controller or computing device may measure a first pressure in block 310. The first pressure may be measured via a pressure gauge or pressure transducer disposed in the gas pycnometer and in fluid communication with the sample chamber and / or the custom-shaped sample cup.

[0045] After the first pressure is determined, in block 312, the controller or computing device may determine whether the pressure and / or temperature in the sample chamber and / or custom shaped sample cup have reached an equilibrium state. In such an embodiment, the gas pycnometer may include a temperature sensor in addition to the pressure gauge or transducer. Once the pressure and / or temperature in the sample chamber and / or custom shaped sample cup have reached an equilibrium state and are not exhibiting further changes, in block 314, the controller or computing device may actuate a valve to the expansion chamber. Additionally, the valve to the sample chamber and / or custom shaped sample cup may be actuated to close and prevent gas from continuing to flow.

[0046] In block 316, the controller or computing device may determine whether the expansion chamber is filled. If the expansion chamber is not filled, the controller or computing device may continue to check the pressure of the expansion chamber and / or the sample chamber. After the expansion chamber is filled, the controller or computing device may measure the pressure of or at the sample chamber and / or the custom-shaped sample cup. After determining the second pressure in block 318, the controller or computing device may determine the volume of the custom-shaped volumetric reference standard in block 320. In block 322, the controller or computing device may compare the determined volume to the known volume of the custom-shaped volumetric reference standard. Based on such comparison, the controller or computing device may adjust the calibration volume of the gas specific gravity meter (block 324).

[0047] In addition, once the gas pycnometer or gas sorption analyzer is calibrated, it can be used to measure the volume of additional other, known or unknown materials at multiple temperatures and determine the thermal expansion coefficient for the additional materials as a function of temperature based on the test results at multiple temperatures. The volume of the displaced sample can be evaluated at several temperatures ranging from below ambient to above ambient, and the CTE of the sample can then be calculated from the displaced volume as a function of temperature. The CTE is calculated as the linear change in dimension per degree of temperature change from a reference temperature in degrees Celsius. By way of example only, in some embodiments, the reference temperature can be about 20° C., but the reference temperature can vary depending on the material being tested.

[0048] The foregoing description generally illustrates and describes various embodiments of the present disclosure. However, it will be understood by those skilled in the art that various changes and modifications may be made to the above-discussed structures of the present disclosure without departing from the spirit and scope of the present disclosure as disclosed herein, and it is intended that all matters contained in the above description or shown in the accompanying drawings should be interpreted as illustrative and not in a limiting sense. Furthermore, the scope of the present disclosure shall be interpreted as covering various modifications, combinations, additions, alterations, etc. to the above and above-described embodiments, and shall be considered to be within the scope of the present disclosure. Thus, various features and characteristics of the present disclosure as discussed herein may be selectively substituted for and applied to other illustrated and unillustrated embodiments of the present disclosure, and numerous variations, modifications, and additions may also be made thereto without departing from the spirit and scope of the present invention, as described in the accompanying aspects. (Item 1) 1. A method for calibrating a specific gravity measuring device, comprising: (a) selecting a custom volumetric reference standard having a known volume selected to substantially match a volume of at least one sample to be measured by the specific gravity measuring device, the custom volumetric reference standard being formed with a high aspect ratio fiducial feature, having a low coefficient of thermal expansion (CTE), and comprising a material including at least one of a lithium aluminosilicate glass ceramic, sapphire, silicon, fused silica, or a combination thereof; (b) placing the custom volumetric reference standard into a sample chamber of the specific gravity measuring device; (c) determining a measured volume of the custom volumetric reference standard based on the difference in pressure of gas introduced into the specific gravity measuring device and the known volume of the sample chamber; (d) comparing the measured volume of the custom volumetric standard to the known volume of the custom volumetric standard; (e) adjusting an average calibration volume for the sample chamber based on a comparison of the measured volume of the custom volumetric reference standard to the known volume of the custom volumetric reference standard; A method comprising: (Item 3) 2. The method of claim 1, further comprising obtaining the custom volumetric standard, the custom volumetric standard comprising a defined average number of inclusions. (Item 4) 2. The method of claim 1, further comprising washing and reweighing the custom volumetric standard to determine a new known volume of the custom volumetric standard if the custom volumetric standard is mishandled. (Item 6) 2. The method of claim 1, wherein placing the custom volumetric reference standard in the sample chamber includes placing the custom volumetric reference standard in a sample cup and positioning the sample cup in the sample chamber prior to calibration. (Item 7) Determining the measured volume of the custom volumetric reference standard further comprises: (a) supplying the gas to a sample chamber; (b) measuring a first pressure of the gas in the sample chamber after the sample chamber is filled with the gas; and (c) after the pressure and temperature in the sample chamber reach equilibrium, opening a valve to allow the gas to flow from the sample chamber to an expansion chamber; (d) measuring a second pressure of the gas in the sample chamber after the expansion chamber is filled with the gas; and (e) determining the measured volume of the custom volumetric reference standard based on the first pressure, the second pressure, and the known volume of the sample chamber; The method according to item 6, comprising: (Item 8) A custom volumetric reference standard for calibration of a gas density instrument, comprising: (a) a ceramic or optical glass material having a CTE of about 0.007 μm / m-°C to about 6.0 μm / m-°C; (b) the known density of said material and the weight of said material; (c) a known volume selected to substantially match the volume of the selected sample material; (d) A selected nominal shape having a known width, length, depth, or combination thereof, and a defined number of inclusions; A custom volumetric reference standard. (Item 9) Item 9. The custom volumetric reference standard of item 8, wherein the material comprises a lithium aluminosilicate glass ceramic. (Item 10) 9. The custom volumetric reference standard of item 8, wherein the material comprises fused silica. (Item 11) 9. The custom volumetric reference standard of item 8, wherein the material comprises single crystal silicon. (Item 12) Item 9. The custom volumetric reference standard of item 8, wherein the material comprises sapphire. (Item 13) 9. The custom volumetric reference standard according to item 8, wherein the reference shape comprises a cylindrical shape. (Item 14) 9. The custom volumetric reference standard according to item 8, wherein the reference shape comprises a disk shape. (Item 15) 9. The custom volumetric reference standard according to item 8, wherein the reference shape comprises a spherical shape. (Item 16) 9. The custom volumetric reference standard of item 8, wherein the reference shape of the custom volumetric reference standard is selected to substantially correspond to a shape of a sample cup configured to be received within a sample chamber of a gas density meter for calibration. (Item 17) 9. The custom volumetric reference standard according to item 8, wherein the reference shapes include high aspect ratio shapes. (Item 20) The above specified number of contents of the above material is 100 cm 3 9. The custom volumetric standard of claim 8, having an average number of inclusions of about 1 inclusion or less per volume. (Item 21) 9. The custom volumetric reference standard of item 8, wherein the reference shape comprises a cylinder or disk having a diameter and a height that is at least about three times the diameter. (Item 22) Item 9. The custom volumetric reference standard of item 8, wherein the material comprises a lithium aluminosilicate glass ceramic having a CTE of less than about 1.0 μm / m-° C. (Item 23) 2. The method of claim 1, further comprising obtaining the custom volumetric reference standard, the custom volumetric reference standard comprising an optical or ceramic material formed as a sheet or grown crystalline structure and polished to a selected size and / or shape.

Claims

1. 1. A method for calibrating a specific gravity measuring device, comprising: (a) selecting a custom volumetric reference standard having a known volume selected to substantially match a volume of at least one sample to be measured by the specific gravity measuring device, the custom volumetric reference standard being formed with a high aspect ratio reference shape, the custom volumetric reference standard comprising a material having a low coefficient of thermal expansion (CTE), the material including at least one of a lithium aluminosilicate glass ceramic, sapphire, silicon, fused silica, or a combination thereof; (b) placing the custom volumetric reference standard into a sample chamber of the specific gravity measuring device; (c) determining a measured volume of the custom volumetric reference standard based on a pressure differential of a gas introduced into the specific gravity measuring device and the known volume of the sample chamber; (d) comparing the determined volume of the custom volumetric reference standard to the known volume of the custom volumetric reference standard; (e) correcting a calibration volume for the sample chamber by calculating an average of a plurality of pressure measurements and updating a stored calibration volume, the correcting being based on a comparison of the measured volume of the custom volumetric reference standard to the known volume of the custom volumetric reference standard; The method includes:

2. The method of claim 1, further comprising obtaining the custom volumetric standard, the custom volumetric standard comprising a specified average number of inclusions.

3. The method of claim 1, further comprising cleaning and reweighing the custom volumetric standard to determine a new known volume of the custom volumetric standard if the custom volumetric standard is mishandled.

4. 2. The method of claim 1, wherein placing the custom volumetric reference standard in the sample chamber comprises placing the custom volumetric reference standard in a sample cup and positioning the sample cup in the sample chamber prior to calibrating.

5. Determining a volume of the custom volumetric reference standard comprises: (a) supplying the gas to the sample chamber; (b) measuring a first pressure of the gas in the sample chamber after the sample chamber is filled with the gas; and (c) after the pressure and temperature in the sample chamber reach equilibrium, opening a valve to allow the gas to flow from the sample chamber to an expansion chamber; (d) measuring a second pressure of the gas in the sample chamber after the expansion chamber is filled with the gas; and (e) determining the measured volume of the custom volumetric reference standard based on the first pressure of the gas in the sample chamber and the second pressure of the gas in the sample chamber and the known volume of the sample chamber; The method of claim 4 further comprising:

6. A custom volumetric reference standard for calibration of a gas density instrument, comprising: (a) a ceramic or optical glass material having a CTE of 0.007 μm·m −1 ·K −1 to 6.0 μm·m −1 ·K −1; (b) a known density of the ceramic or optical glass material and a weight of the ceramic or optical glass material; (c) a known volume selected to substantially correspond to the volume of the selected sample material; and (d) a selected reference shape having a known width, a known length, a known depth, or a combination thereof and a prescribed number of inclusions; Custom volumetric reference standard with.

7. 7. The custom volumetric reference standard of claim 6, wherein the ceramic or optical glass material comprises a lithium aluminosilicate glass ceramic.

8. 7. The custom volumetric reference standard of claim 6, wherein the ceramic or optical glass material comprises fused silica.

9. 7. The custom volumetric reference standard of claim 6, wherein the ceramic or optical glass material comprises single crystal silicon.

10. 7. The custom volumetric reference standard of claim 6, wherein the ceramic or optical glass material comprises sapphire.

11. The custom volumetric reference standard of claim 6 , wherein the reference shape comprises a cylindrical shape.

12. The custom volumetric reference standard of claim 6 , wherein the reference shape comprises a disk shape.

13. The custom volumetric reference standard of claim 6 , wherein the reference shape comprises a spherical shape.

14. 7. The custom volumetric reference standard of claim 6, wherein the reference shape of the custom volumetric reference standard is selected to substantially correspond to a shape of a sample cup configured to be received within a sample chamber of a gas density meter for calibration.

15. 7. The custom volumetric reference standard of claim 6, wherein the defined number of inclusions in the ceramic or optical glass material comprises an average number of inclusions of less than 1 inclusion per 100 cm3.

16. The custom volumetric reference standard of claim 6, wherein the reference shape includes a cylinder or disk, the cylinder or disk having a diameter and a height that is at least approximately three times the diameter.

17. The custom volumetric reference standard of claim 6, wherein the ceramic or optical glass material comprises a lithium aluminosilicate glass ceramic having a CTE less than 1.0 μm·m −1 ·K −1 .

18. The method of claim 1, further comprising obtaining the custom volumetric reference standard, the custom volumetric reference standard comprising an optical or ceramic material formed as a sheet or grown crystal structure and polished to a selected size and / or shape.

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