Quantitative analysis device, analysis method and analysis procedure for amorphous phase

Abstract

The present invention provides a quantitative analysis device that can more easily perform quantitative analysis on a non-crystalline phase and a sample. The quantitative analysis device for the non-crystalline phase includes a powder diffraction pattern acquisition unit, a qualitative analysis result acquisition unit, a fitting function acquisition unit for acquiring a fitting function for one or more crystalline phases, a full-image fitting unit for performing a powder diffraction pattern of the sample using the acquired fitting function, and a weight ratio calculation unit for calculating the weight ratio of an non-crystalline phase and one or more crystalline phases, wherein the fitting function for the one or more crystalline phases is one of a first fitting function using an integral intensity obtained by full-image decomposition, a second fitting function using an integral intensity obtained by observation or calculation, and a third fitting function using a distributed intensity obtained by observation or calculation, and the third fitting function is used for the non-crystalline phase.

Description

Technical Field

[0001] The present invention relates to a quantitative analysis device, a quantitative analysis method and a quantitative analysis program of an amorphous phase for quantitatively analyzing each component of a sample based on a sample powder diffraction pattern, and particularly to quantitative analysis of a sample containing an amorphous component. Background Art

[0002] When the sample is a mixture sample containing an amorphous phase and one or more crystalline phases, the powder diffraction pattern of the sample is obtained by measuring using, for example, an X-ray diffraction device. The powder diffraction pattern of a certain crystalline phase is inherent to its crystalline phase, and the powder diffraction pattern of the sample is a powder diffraction pattern obtained by adding the powder diffraction patterns of an amorphous phase and one or more crystalline phases contained in the sample based on the content. In addition, in this specification, the crystalline phase is a crystalline pure substance solid having a chemical composition and a crystal structure. The amorphous phase is a pure substance solid, which refers to a substance that does not have long-range order like a crystalline substance, but has short-range order.

[0003] Qualitative analysis is to analyze what kind of substances are present in a sample. Quantitative analysis is to analyze what amount ratios of substances contained in a sample exist. Here, as a prerequisite for quantitative analysis, qualitative analysis of substances contained in the sample has been completed.

[0004] It is difficult to analyze the powder diffraction pattern of the amorphous phase (amorphous phase halo). Therefore, for example, as disclosed in Non-Patent Document 1, a conventional method is to add a standard material (SRM) to the sample when the sample contains an amorphous phase (amorphous component), and perform quantitative analysis of the amorphous phase based on the powder diffraction pattern of the standard material.

[0005] Prior art literature.

[0006] Non-patent literature.

[0007] Non-patent literature 1: G. DeLa Torre, S. Bruque and MAG Aranda, "Rietveld quantitative amorphous content analysis", J. Appl. Cryst., 2001, 50, pp. 196-202

[0008] Non-patent document 2: Hideo Toraya "A new method for quantitative phase analysis using X-ray powder diffraction: direct derivation of weight fractions from observed integrated intensities and chemical compositions of individual phases", J.Appl.Cryst., 2016, pp. 49, 1508-1516

[0009] Non-patent document 3: Hideo Toraya, "Quantitative phase analysis using observed integrated intensities and chemical composition data of individual crystalline phases: quantification of materials with indefinite chemical compositions", J.Appl.Cryst., 2017, pp. 50, 820-829

[0010] Non-patent document 4: Alexander, LE & Klug, HP, Anal. Chem., 1948, p. 20, pp. 886-889.

[0011] Non-patent document 5: Chung, FH, "Quantitative Interpretation of X-ray Diffraction Patterns of Mixtures. I. Matrix-Flushing Method for Quantitative Multicomponent Analysis", J. Appl. Cryst., 1974, pp. 7, 519-525

[0012] Non-patent document 6: Chung, FH, "Quantitative Interpretation of X-ray Diffraction Patterns of Mixtures. II. Adiabatic Principle of X-ray Diffraction Analysis of Mixtures", J. Appl. Cryst., 1974, pp. 7, 526-531

[0013] Non-patent document 7: Werner, P.-E., Salome, S., Malmros, G., and Thomas, JO, "Quantitative Analysis of Multicomponent Powders by Full-Profile Refinement of Guinier-Hagg X-ray Film Data", J. Appl. Cryst., 1979, pp. 12, 107-109

[0014] Non-patent literature 8: Hill, RJ and Howard, CJ, "Quantitative Phase Analysis from Neutron Powder Diffraction Data Using the Rietveld Method", J. Appl. Cryst., 1987, p. 20, pp. 467-474

[0015] Non-patent literature 9: Toraya, H. and Tsusaka S., "Quantitative Phase Analysis using the Whole-Powder-Pattern Decomposition Method. I. Solution from Knowledge of Chemical Compositions", J. Appl. Cryst., 1995, 28, 392-399

[0016] Non-Patent Literature 10: Smith, DK, Johnson, GG Jr., Scheible, A., Wims, AM, Johnson, JLand Ullmann, G., "Quantitative X-Ray Powder Diffraction Method Using the Full Diffraction Pattern", Power Diffr., 1987, pp. 2, 73-77

[0017] Non-patent literature 11: Scarlett, NVY and Madsen, IC, "Quantification of phases with partial or no known crystal structure", Powder Diffraction, 2006, pp. 21, 278-284 Summary of the invention

[0018] Problem that the invention aims to solve

[0019] However, by adding standard substances to the sample, the number of steps for quantitative analysis increases abnormally, and the sample itself becomes different from the original due to the addition of standard substances. As a result of in-depth research, the inventors found that by adopting the DD method (Direct Derivation Method), quantitative analysis can be performed even when the sample contains an amorphous phase. The DD method is described below.

[0020] The IC formula (Intensity-Composion formula) used in the present invention is described in Non-Patent Documents 2 and 3. The IC formula is described below. Assuming that a powder sample contains K (K is an integer greater than 2) crystal phases, the integrated intensity of the j (j is an integer greater than 1) diffraction line of the k (k is an integer greater than 1 and less than K) crystal phase is I jk In the case of X-ray powder diffraction with an optical system based on Bragg-Brentano geometry, the integrated intensity I of each diffraction line (the jth diffraction line of the kth crystal phase) in the powder diffraction pattern of the sample is jk It is given by the mathematical formula 1 shown below.

[0021] [Mathematical formula 1]

[0022]

[0023] In equation 1, I0 is the incident X-ray intensity, V kis the volume fraction of the kth crystalline phase, Q is a constant including physical constants such as incident X-ray intensity and light speed and optical system parameters, μ is the linear absorption coefficient of the powder sample, and U k is the unit cell volume of the kth crystalline phase, m jk is the multiplicity of reflection, F jk is the crystal structure factor. jk Using the Lorentz deflection factor Lp jk (Lorentz-polarization factor: Lp factor) and the factor related to the width of the light receiving slit (sinθ jk ), is defined by the mathematical formula 2 shown below.

[0024] [Mathematical formula 2]

[0025]

[0026] In addition, the above-mentioned mathematical formula 2 assumes the case where an optical system in which a one-dimensional detector is placed on the diffraction side. Of course, the form is different in an optical system in which a monochromator is arranged on the diffraction side.

[0027] Equivalent to the volume percentage V of the irradiated volume k The weight factor (W k ) by changing the volume percentage V k Multiply by the material density d of the kth crystal phase k (=Z k M k / U k ), calculated as W k =V k d k Volume percentage V k V k =W k U k / (Z k M k ), Mathematical formula 1 is transformed into the following mathematical formula 3. In addition, Z k is the number of chemical formula units (i.e., the number of atoms or molecules in the kth crystal phase), M k It is the chemical formula weight.

[0028] [Mathematical formula 3]

[0029]

[0030] When multiplying both sides of equation 3 by G jk , when added to the kth crystal phase, the mathematical formula 4 shown below is obtained.

[0031] [Formula 4]

[0032]

[0033] Among them, N k is the number of diffraction lines of the kth crystalline phase (therefore, j is greater than 1, N k The following integers). k Ideally, it is the total number of diffraction lines of the kth crystalline phase. However, the range of 2θ of the powder diffraction pattern actually observed is limited. Therefore, and represents the total, N k It can also be the number of diffraction lines within the range of 2θ selected by the user. The range of 2θ only needs to fully include the number of diffraction lines required for quantitative analysis. In addition, although it actually exists, there can also be diffraction lines that are not included in the sum as needed.

[0034] The brackets on the right side of Formula 4 correspond to the height of the peak at the origin of the Patterson function. If the peak height is approximated by the integral value of the peak, its amount is equal to the number of electrons (n) belonging to each atom in the chemical formula unit. jk ) squared and then added together. Therefore, if the proportionality constant is set to C, the following mathematical formula 5 holds true.

[0035] [Formula 5]

[0036]

[0037] Here, N k A is the total number of atoms in the chemical formula unit of the kth crystal phase. In addition, the material parameter a k It is defined by the following mathematical formula 6.

[0038] [Mathematical formula 6]

[0039]

[0040] Here, the material parameter a k It is a physical quantity specific to the crystal phase (substance). Therefore, the material parameter can also be called the crystal phase factor. In addition, the parameter S is defined by the following mathematical formula 7:k .

[0041] [Mathematical formula 7]

[0042]

[0043] By weight factor W k The weight ratio of the K crystal phases contained in the sample can be calculated. Here, the weight ratio of the K crystal phases can be calculated as W1:W2:…:W K In addition, a part of the K crystal phases can be selected to find their weight ratio. In addition, when the sample does not include amorphous components, all the crystal phases included in the sample are qualitatively analyzed, and the sum of 1 to K can be used for k. k Therefore, the weight percentage of the kth crystal phase W k It can be expressed by the mathematical formula 8 shown below.

[0044] [Mathematical formula 8]

[0045]

[0046] For equation 4, if the weight factor W k Convert and substitute into equation 5, equation 6 and equation 7. According to equation 8, the weight percentage w is k The calculation is performed using the following formula 9. In addition, formula 9 is an IC formula.

[0047] [Mathematical formula 9]

[0048]

[0049] The material parameter a shown in the IC formula (Equation 9) k It is a physical quantity unique to the crystal phase (substance). Therefore, the material parameter can be called the crystal phase factor. If the chemical composition of the crystal phase is determined by qualitative analysis, the material parameter a can be obtained. k In addition, even when a sample contains a crystal phase with an uncertain chemical composition (uncertain crystal phase), it is sometimes possible to estimate the material parameter a of the substance. k In addition, even when the sample contains an amorphous phase, if the chemical composition of the amorphous phase is determined, the material parameter a is calculated. k .

[0050] The parameter S shown in the IC formula (Equation 9) k It is a physical quantity obtained by measurement (observation). As shown in Mathematical Formula 7, if the integrated intensity I of each diffraction line is obtained by measurement, jk , then find the parameter S kThrough qualitative analysis, the K crystal phases contained in the sample are determined. If the peak position (2θ) of the powder diffraction pattern of each crystal phase is known, it is possible to determine which of the K crystal phases the multiple diffraction lines appearing in the powder diffraction pattern belong to. In addition, when there are overlapping diffraction lines with two or more overlapping diffraction lines, the parameter S of each crystal phase can be calculated by a simple method by, for example, equally distributing the integrated intensity of the overlapping diffraction lines or distributing them according to the volume percentage. k .

[0051] However, in order to perform quantitative analysis with higher accuracy, it is desirable to obtain the parameter Sk with high accuracy by fitting the calculated powder diffraction pattern to the observed powder diffraction pattern of the sample. As a quantitative analysis technique using X-ray powder diffraction, there is the WPPF (Whole-Powder Pattern Fitting) method. In the WPPF method, the powder diffraction pattern of the observed sample is generally fitted with the calculated pattern as a whole to optimize various parameters using the least double method. Next, the key points in the WPPF method are described.

[0052] As described in non-patent document 4, internal (and external) standards are known as methods with high accuracy. In addition, a simple quantitative method is known for calculating the weight ratio of a crystalline phase based on the ratio of a databased RIR (Reference Intensity Ratio) value to the strongest peak intensity. RIR quantitative methods using RIR values ​​are disclosed in non-patent document 5 and non-patent document 6. A Rietveld (Rietveld analysis) method using the full distribution intensity within a measurement angle range is known. A quantitative method using the Rietveld method is disclosed in non-patent document 7 and non-patent document 8. In addition, a Whole-Power Pattern Decomposition (WPPD) method is known for quantifying based on a proportional factor multiplied by the observed integrated intensity of each crystalline phase. A quantitative method using the whole-power pattern decomposition method is disclosed in non-patent document 9. In addition, non-patent document 10 discloses a full-pattern fitting method for quantitative analysis by fitting the powder diffraction pattern of a sample (from which the background intensity is removed) as the distribution intensity, without the need to pre-process the distribution intensity of the powder diffraction pattern based on previous data.

[0053] The internal (and external) standard method requires obtaining a sample of a single crystalline phase of each of the multiple crystalline phases contained in the sample and making a calibration line, so there is a problem of lack of versatility and rapidity. In the RIR quantitative method using RIR values, databased RIR values ​​are required. In the Rietveld method, the crystal structure parameters of the multiple crystalline phases contained in the powder sample are required. In the full-image decomposition method, it is necessary to obtain a sample of a single crystalline phase. As a Rietveld method that can be applied when the structural parameters of a part of the multiple crystalline phases cannot be obtained, it is known to use a method of using RIR values ​​for crystalline phases whose structural parameters cannot be obtained, or the PONKCS method, etc. The PONKCS method is disclosed in non-patent document 11. However, in any method, when the structural parameters cannot be obtained, the RIR value is measured in the RIR quantitative method, or a sample of a single crystalline phase or an approximate sample is obtained as reference data in the PONKCS method.

[0054] Conventionally, crystallographic data such as experimentally obtained calibration lines (internal standard method), RIR values, crystal structure parameters (Rietveld method) etc. are required. However, a quantitative analysis method is desired that can perform quantitative analysis by full pattern fitting of the powder diffraction pattern of a sample in a simpler method.

[0055] The present invention is made in view of the above-mentioned problems, and its purpose is to provide a quantitative analysis device for an amorphous phase, a quantitative analysis method for an amorphous phase, and a quantitative analysis program for an amorphous phase, which can more easily perform quantitative analysis on samples containing one amorphous phase and one or more crystalline phases.

[0056] Means used to solve problems

[0057] (1) In order to solve the above-mentioned problems, the quantitative analysis device of the amorphous phase of the present invention performs quantitative analysis on the amorphous phase contained in the sample according to the powder diffraction pattern of the sample, and is characterized in that it includes: a powder diffraction pattern acquisition unit, which acquires the powder diffraction pattern of the sample; a qualitative analysis result acquisition unit, which acquires information of an amorphous phase and one or more crystalline phases contained in the sample; a fitting function acquisition unit, which acquires fitting functions respectively for the one or more crystalline phases; a full-image fitting unit, which performs full-image fitting on the powder diffraction pattern of the sample using the fitting functions respectively for the one amorphous phase and the one or more crystalline phases, and acquires fitting results; and a weight ratio calculation unit, which calculates the weight ratio of the one amorphous phase and the one or more crystalline phases based on the fitting results, wherein the fitting functions respectively for the one or more crystalline phases are one of a first fitting function, a second fitting function, and a third fitting function, the first fitting function uses the integrated intensity obtained by full-image decomposition, the second fitting function uses the integrated intensity obtained by observation or calculation, the third fitting function uses the distribution intensity obtained by observation or calculation, and the fitting function for the one amorphous phase is the third fitting function.

[0058] (2) In the quantitative analysis device for an amorphous phase described in (1) above, it is preferred that the weight ratio calculation unit calculates the weight percentage using an IC formula.

[0059] (3) The quantitative analysis device for an amorphous phase described in (1) or (2) above preferably selects either the first fitting function or the second fitting function for at least one of the one or more crystalline phases.

[0060] (4) The quantitative analysis method of the amorphous phase of the present invention performs quantitative analysis on the amorphous phase contained in the sample according to the powder diffraction pattern of the sample, preferably comprising a powder diffraction pattern obtaining step, obtaining the powder diffraction pattern of the sample; a qualitative analysis result obtaining step, obtaining information of an amorphous phase and one or more crystalline phases contained in the sample; a fitting function obtaining step, obtaining fitting functions respectively for the one or more crystalline phases; a full-image fitting step, using the fitting functions respectively for the one amorphous phase and the one or more crystalline phases, performing full-image fitting on the powder diffraction pattern of the sample to obtain a fitting result; and a weight ratio calculation step, calculating the weight ratio of the one amorphous phase and the one or more crystalline phases based on the fitting result, wherein the fitting function respectively for the one or more crystalline phases is a fitting function selected from a first fitting function, a second fitting function, and a third fitting function, the first fitting function uses the integrated intensity obtained by full-image decomposition, the second fitting function uses the integrated intensity obtained by observation or calculation, the third fitting function uses the distribution intensity obtained by observation or calculation, and the fitting function for the one amorphous phase is the third fitting function.

[0061] (5) The quantitative analysis program of the amorphous phase of the present invention performs quantitative analysis on the amorphous phase contained in the sample based on the powder diffraction pattern of the sample, and preferably enables the computer to function as the following units: a powder diffraction pattern acquisition unit, which acquires the powder diffraction pattern of the sample; a qualitative analysis result acquisition unit, which acquires information on an amorphous phase and one or more crystalline phases contained in the sample; a fitting function acquisition unit, which acquires fitting functions respectively for the one or more crystalline phases; a full-image fitting unit, which uses the fitting functions respectively for the one amorphous phase and the one or more crystalline phases to perform full-image fitting on the powder diffraction pattern of the sample to obtain a fitting result; and a weight ratio calculation unit, which calculates the weight ratio of the one amorphous phase and the one or more crystalline phases based on the fitting result, wherein the fitting function respectively for the one or more crystalline phases is a fitting function selected from the first fitting function, the second fitting function, and the third fitting function, the first fitting function uses the integrated intensity obtained by full-image decomposition, the second fitting function uses the integrated intensity obtained by observation or calculation, the third fitting function uses the distribution intensity obtained by observation or calculation, and the fitting function for the one amorphous phase is the third fitting function.

[0062] Effects of the Invention

[0063] According to the present invention, a quantitative analysis device, a quantitative analysis method and a quantitative analysis program of an amorphous phase are provided, which can more easily perform quantitative analysis of a sample containing an amorphous phase and one or more crystalline phases. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 It is a block diagram showing the structure of the quantitative analysis device of the amorphous phase according to the first embodiment of the present invention.

[0065] Figure 2 This is a flowchart showing the quantitative analysis method of the amorphous phase according to the first embodiment of the present invention.

[0066] Figure 3 FIG. 1 is a diagram showing a sample used in an example of the amorphous phase quantitative analysis method according to the first embodiment of the present invention.

[0067] Figure 4A This is a diagram showing the fitting result of step S4 of this embodiment for single-component crystalline phase SiO 2 .

[0068] Figure 4B This is a diagram showing the fitting result of step S4 of this embodiment for single-component crystalline phase GeO 2 .

[0069] Figure 5 This is a diagram showing an observed powder diffraction pattern of a measured single-component amorphous phase.

[0070] Figure 6 This is a diagram showing the observed powder diffraction pattern of the measured single-component amorphous GeO2 and the background intensity of the crystalline GeO2.

[0071] Figure 7 1 is a diagram showing an observed powder diffraction pattern of single-component amorphous GeO 2 after treatment.

[0072] Figure 8 It is a diagram showing the results of quantitative analysis in an example of the quantitative analysis method of the amorphous phase according to the first embodiment of the present invention.

[0073] Fig. 9 This is a diagram showing a sample used in an example of a quantitative analysis method of an amorphous phase according to the second embodiment of the present invention.

[0074] Fig. 10A 3 is a diagram showing the fitting result of two crystal phases in the three-component system sample in step S4 of this embodiment.

[0075] Fig. 10B 3 is a diagram showing the fitting results of the three crystal phases in the four-component system sample in step S4 of this embodiment.

[0076] Fig.11A This is a diagram showing the results of quantitative analysis in an example of the quantitative analysis method of the amorphous phase according to the second embodiment of the present invention.

[0077] Fig. 11BThis is a diagram showing the results of quantitative analysis in an example of the quantitative analysis method of the amorphous phase according to the second embodiment of the present invention. DETAILED DESCRIPTION

[0078] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In addition, in order to explain more clearly, the accompanying drawings sometimes schematically show dimensions, shapes, etc. compared to actual embodiments, but this is only an example and does not limit the interpretation of the present invention. In addition, in this specification and each figure, for elements related to existing drawings and the same as those described, the same reference numerals are sometimes used, and detailed descriptions are appropriately omitted.

[0079] [First embodiment]

[0080] Figure 1 1 is a block diagram showing the structure of the quantitative analysis device 1 of the amorphous phase according to the first embodiment of the present invention. The quantitative analysis method of the amorphous phase of the embodiment is performed by the quantitative analysis device 1 of the amorphous phase of the embodiment. That is, the quantitative analysis device 1 of the amorphous phase of the embodiment is a device that can easily perform quantitative analysis of a sample using the quantitative analysis method of the amorphous phase of the embodiment.

[0081] The quantitative analysis device 1 of the amorphous phase of this embodiment includes an analysis unit 2, an information input unit 3, an information output unit 4 and a storage unit 5. The quantitative analysis device 1 of the amorphous phase is implemented by a commonly used computer, and although not shown in the figure, it also includes ROM (Read Only Memory) and RAM (Random Access Memory), and ROM and RAM constitute the internal memory of the computer. The storage unit 5 is a storage medium, which can be composed of a semiconductor memory, a hard disk or any other storage medium. Here, the storage unit 5 is arranged inside the computer, but it can also be arranged outside the computer. In addition, the storage unit 5 can be a single body, but it can also be a plurality of storage media. The quantitative analysis device 1 of the amorphous phase is connected to the X-ray diffraction device 11 and the input device 13. The X-ray diffraction device 11 measures the X-ray diffraction data of the sample by performing X-ray diffraction measurement on the sample in the shape of a powder, and outputs the measured X-ray diffraction data to the information input unit 3 of the quantitative analysis device 1 of the amorphous phase. The input device 13 is implemented by a keyboard, a mouse, a touch panel, etc. The information input unit 3 is an interface connected to the X-ray diffraction device 11 and the input device 13. The analysis unit 2 obtains the X-ray diffraction data from the information input unit 3, performs preprocessing on the X-ray diffraction data, and generates a powder diffraction pattern of the sample. Here, preprocessing refers to processing such as smoothing of the data and removal of the Kα2 component. The powder diffraction pattern generated by the analysis unit 2 is input to the storage unit 5 and stored. In addition, the X-ray diffraction device 11 includes an analysis unit (data processing unit), which generates a powder diffraction pattern of the sample by preprocessing the X-ray diffraction data measured by the analysis unit of the X-ray diffraction device 11, and outputs the powder diffraction pattern of the sample to the information input unit 3 of the quantitative analysis device 1 of the amorphous phase. The analysis unit 2 obtains the powder diffraction pattern of the sample from the storage unit 5 (or the information input unit 3), and based on the powder diffraction pattern, performs quantitative analysis on the crystalline phase contained in the sample, and outputs the weight ratio of the quantitatively analyzed crystalline phase to the information output unit 4 as an analysis result. The information output unit 4 is an interface connected to the display device 12 , outputs the weight ratio of the crystal phase to the display device 12 , and displays the analysis result of the quantitative analysis on the display device 12 .

[0082] Figure 2 : is a flowchart showing the quantitative analysis method of the amorphous phase of this embodiment. The analysis unit 2 of the quantitative analysis device 1 of the amorphous phase includes a powder diffraction pattern acquisition unit 21, a qualitative analysis result acquisition unit 22, a fitting function acquisition unit 23, a full-image fitting unit 24 and a weight ratio calculation unit 25, which are units for executing each step of the quantitative analysis method of the amorphous phase described below. In addition, the quantitative analysis program of the amorphous phase of this embodiment is a program for causing a computer to function as each unit.

[0083] [Step S1: Powder diffraction pattern acquisition step]

[0084] Obtain a powder diffraction pattern of the sample (S1: powder diffraction pattern obtaining step). The powder diffraction pattern of the sample is stored in the storage unit 5. Alternatively, as described above, the X-ray diffraction device 11 may include an analysis unit (data processing unit) that preprocesses the X-ray diffraction data of the measured sample to generate a powder diffraction pattern of the sample, and outputs the powder diffraction pattern of the sample to the information input unit 3 of the quantitative identification device 1. The analysis unit 2 of the quantitative identification device 1 obtains the powder diffraction pattern of the sample from the storage unit 5 (or the information input unit 3). The powder diffraction pattern is a spectrum in which the horizontal axis represents the diffraction angle 2θ of the peak position and the vertical axis represents the intensity of the diffracted X-ray. Here, the diffraction angle 2θ is the angle between the direction of the incident X-ray and the direction of the diffracted X-ray. In addition, the X-ray diffraction data of the sample measured by the X-ray diffraction device 11 can be input into the information input unit 3 or stored in the storage unit 5. At this time, the analysis unit 2 obtains the X-ray diffraction data of the sample from the information input unit 3 or the storage unit 5, performs preprocessing on the X-ray diffraction data of the sample, and generates a powder diffraction pattern of the sample.

[0085] [Step S2: Qualitative analysis result acquisition step]

[0086] Obtain information about one amorphous phase and one or more crystalline phases contained in the sample (S2: qualitative analysis result acquisition step). The analysis unit 2 identifies the crystalline phase based on the position and intensity of the diffraction line (peak) of the powder diffraction pattern of the sample obtained in step S1. That is, through qualitative analysis, obtain information about one or more crystalline phases contained in the sample. Here, the information of the crystalline phase includes its chemical composition, information related to the polymorph when its crystalline phase has a polymorph with different crystal structures, and multiple peak positions of the powder diffraction pattern of the crystalline phase. It can also further include the intensity at multiple peak positions of the powder diffraction pattern of the crystalline phase.

[0087] The analysis unit 2 performs a qualitative analysis on the sample based on the peak position and peak intensity of the powder diffraction pattern of the sample obtained in step S1 to obtain information on multiple crystalline phases contained in the sample. However, it is not limited to this, and the information input unit 3 may also obtain information on multiple crystalline phases contained in the sample as a result of the qualitative analysis of the sample from the input device 13. In addition, by implementing other known qualitative analyses, information on one amorphous phase is obtained. Here, the information on one amorphous phase includes its chemical composition.

[0088] [Step S3: Fitting function acquisition step]

[0089] Obtain fitting functions for one or more crystal phases contained in the sample (S3: fitting function acquisition step). Based on the powder diffraction pattern of the sample obtained in step S1 and the information of one or more crystal phases obtained in step S2, the user decides to use a fitting function selected from the first fitting function to the third fitting function to perform fitting for each powder diffraction pattern of the one or more crystal phases. The user uses the input device 13 to input the fitting functions used for the multiple crystal phases. The analysis unit 2 obtains the fitting functions for the multiple crystal phases input to the input device 13 from the information input unit 3. In addition, the third fitting function is used for the powder diffraction pattern (amorphous phase halo) of an amorphous phase.

[0090] The first to third fitting functions will be described below. The fitting function y(2θ) representing the powder diffraction pattern of the entire sample can be regarded as the background intensity y(2θ) back and y(2θ) representing the powder diffraction pattern of each of K (K is an integer greater than or equal to 2) crystal phases (kth crystal phase: k is an integer greater than or equal to 1 and less than or equal to K) k When the powder diffraction patterns of the entire sample overlap, the fitting function y(2θ) of the powder diffraction pattern of the entire sample is expressed by the mathematical formula 10 shown below.

[0091] [Formula 10]

[0092]

[0093] In this embodiment, the sample includes 1 amorphous phase and K-1 crystalline phases. For example, the fitting function y(2θ) representing the powder diffraction pattern of the kth (k is an integer of 1≤k≤K-1) crystalline phase is k The fitting function y(2θ) of the powder diffraction pattern representing one amorphous phase (amorphous phase halo) is used as the fitting function y(2θ) of the powder diffraction pattern representing the Kth crystalline phase. K Therefore, in this embodiment, the fitting function y(2θ) representing the powder diffraction pattern of the entire sample can also be expressed by Mathematical Formula 10.

[0094] The fitting function y(2θ) representing the powder diffraction pattern of each crystalline phase k With various labels, it becomes a fitting function. The first fitting function uses the integrated intensity obtained by full-image decomposition based on the Pawley method and is represented by Mathematical Formula 11 shown below.

[0095] [Mathematical formula 11]

[0096] y(2θ) k =∑ j I jk P(2θ) jk ···(11)

[0097] Here, P(2θ) jk P(2θ) is a normalized distribution function that describes the distribution shape. Although P(2θ) is defined by [-∞, +∞] using, for example, a pseudo-Voigt function or the like, it can actually be considered to have values ​​only before and after the peak position of each diffraction line.

[0098] The second fitting function uses observed or calculated integrated intensity input from the outside and is expressed by Mathematical Formula 12 shown below.

[0099] [Mathematical formula 12]

[0100] y(2θ) k =∑ j Sc k I′ jk P(2θ) jk ···(12)

[0101] Here, Sc k is the scaling factor, given by I jk =Sc k I' jk Definition. The integrated intensity set {I' jk} can be an integrated intensity set measured (or calculated) for a single-phase sample of the kth crystal phase, or a function of the crystal structure parameters. In the fitting, the fixed integrated intensity set {I' jk}, instead, let the scaling factor Sc k Precision.

[0102] The third fitting function is based on the observed or calculated distribution intensity input from the outside, and is represented by Mathematical Formula 13 shown below.

[0103] [Mathematical formula 13]

[0104] y(2θ) k =Sc k y(2θ)′ k ···(13)

[0105] Here, Sc k Same as the second fitting function, it is the scaling factor. y(2θ)' k It can be the integrated intensity of the k-th powder diffraction pattern measured (or calculated) separately for a single-phase sample of the k-th crystalline phase, or it can be calculated on the spot when fitting based on the crystal structure parameters. In the fitting, the distribution intensity y(2θ)' representing the k-th powder diffraction pattern is fixed. k , instead, let the scaling factor Sc k Precision.

[0106] The user decides which of the first to third fitting functions to use to fit the powder diffraction patterns of one or more crystalline phases based on the powder diffraction pattern of the sample and the information of one or more crystalline phases. When the crystallinity of the crystalline phase is high and the symmetry of the crystal is relatively high, the first fitting function is preferably selected. On the contrary, for a crystalline phase with low crystal symmetry and a complex diffraction pattern consisting of multiple peaks, the second fitting function or the third fitting function is preferably used. In particular, when the crystallinity is low and the peak distribution collapses, the third fitting function is used. In addition, as previously described, the third fitting function is used for the fitting function of an amorphous phase.

[0107] [Step S4: Full-image fitting step]

[0108] Using the fitting functions for the amorphous phase and one or more crystalline phases obtained in step S3, the powder diffraction pattern of the sample is subjected to full-image fitting to obtain a fitting result (S4: full-image fitting step). Here, the fitting function used for full-image fitting is mathematical formula 10, which represents the fitting function y(2θ) of the powder diffraction pattern of the kth (integer 1≤k≤K-1) crystalline phase described in mathematical formula 10: k is any one of the first to third fitting functions. In addition, the fitting function y(2θ) representing the powder diffraction pattern of the Kth (k=K) crystal phase (the Kth crystal phase is an amorphous phase) is k is the third fitting function.

[0109] When the first fitting function is used, the parameters of the model required to calculate the shape of the distribution are (a) the parameter that determines the half-value width (FWHM), (b) the parameter that determines the shape of the distribution, and (c) the lattice constant of the kth crystal phase. In addition, when the first fitting function is used, the integral intensity I is not required. jk The initial value of .

[0110] When the second fitting function is used, the parameters of the model required to calculate the shape of the distribution are the same as when the first fitting function is used, including (a) to (c) above, but also include predetermined parameters of the integrated intensity and the scaling factor. As mentioned above, the parameters of the integrated intensity are fixed in the fitting.

[0111] When the third fitting function is used, the parameters of the model required to calculate the shape of the distribution are data representing the distribution intensity y(2θ)' of the observed or calculated powder diffraction pattern of the kth crystalline phase minus the background intensity, and a scaling factor. It represents the powder diffraction pattern of the observed or calculated kth crystalline phase minus the background intensity. As previously described, in the fitting, the distribution intensity y(2θ)' of the powder diffraction pattern representing the kth crystalline phase is fixed.

[0112] In addition, even when any one of the first to third fitting functions is used, as described in Mathematical Formula 10, the background intensity y(2θ) is required to be back These parameters are optimized by fitting and the results are obtained.

[0113] [Step S5: Weight ratio calculation step]

[0114] Based on the fitting result obtained in step S4, the weight ratio of the plurality of phases is calculated (weight ratio calculation step).

[0115] When the first fitting function is used, the mathematical formula 7 is used to calculate the integral intensity I jk Calculate the parameter S of the kth crystal phase k .

[0116] When the second fitting function is used, the following mathematical formula 14 is used, through the proportional factor S ck and integrated intensity I' jk To calculate the parameter S of the kth crystal phase k .

[0117] [Formula 14]

[0118]

[0119] When the third fitting function is used, the parameter S of the kth crystal phase is calculated using the following mathematical formula 15: k .

[0120] [Mathematical formula 15]

[0121]

[0122] The following is an explanation of the derivation of equation 15. G defined by equation 2 jk It can be considered as a continuous function G(2θ) relative to the diffraction angle 2θ. When G(2θ) is multiplied on both sides of equation 11, and the finite 2θ range [2θ L , 2θ H ] is integrated, the following mathematical formula 16 is obtained. In addition, the integral value of this integral is set to Y k Here, the 2θ range may be such that it sufficiently includes the number of diffraction lines required for the above-mentioned quantitative analysis.

[0123] [Formula 16]

[0124]

[0125] As mentioned above, the distribution function P(2θ) jkIt can have values ​​only before and after the peak position of each diffraction line, and G(2θ) multiplied by it will not produce a large difference even if it has a certain value within this range. In addition, the distribution function P(2θ) jk is normalized to ∫P(2θ) jk d(2θ)=1. Therefore, it can be considered that Y k The parameter S shown in equation 7 k Therefore, Mathematical formula 15 is derived from Mathematical formula 13 and Mathematical formula 16. The fitting function for the amorphous phase is set to the third fitting function, but in this case, it can be considered that Mathematical formula 15 can be directly applied to the distribution intensity of the amorphous phase.

[0126] As mentioned above, if the chemical composition of the crystalline phase or amorphous phase is determined by qualitative analysis, the material parameter a is obtained. k In addition, even if the sample contains a crystal phase with an uncertain chemical composition (uncertain crystal phase), it is sometimes possible to infer the material parameter a of the substance. k In addition, even if the sample contains an amorphous phase, the amorphous phase also has material parameters a k Therefore, using the material parameter a k , and the parameter S obtained by the fitting result obtained in step S4 k , calculate the weight factor W of the kth crystal phase k .

[0127] Therefore, the weight factor W can be used k To calculate the weight ratio of multiple crystal phases contained in the sample. In addition, the weight percentage w of the kth crystal phase can be calculated using Mathematical Formula 8 or IC Formula (Mathematical Formula 9): k .

[0128] In the quantitative analysis method of the amorphous phase of this embodiment, there is no process of adding standard substances required in the prior art, and a quantitative analysis with high reliability can be performed by a simple method. In addition, in the prior art, by adding standard substances to the sample, the sample is changed from the original state to a different state (a mixed state with the addition of standard substances), but in this embodiment, it is not necessary to change the state of the sample.

[0129] Next, an example in which a mixture sample including one amorphous phase (amorphous component) is quantitatively analyzed using the quantitative analysis method of the amorphous phase according to this embodiment will be described.

[0130] Figure 3 : is a diagram showing a sample used in the quantitative analysis method of the amorphous phase of this embodiment. Figure 3As shown, the sample consists of an amorphous phase and a crystalline phase. There are multiple types (16 types), but they are all two-component systems. The samples are combinations of any crystalline component of SiO2 or GeO2 and any amorphous component of SiO2 or GeO2 (4 series of 2×2: series 1 to series 4). In addition, the mixing ratios of the crystalline component and the amorphous component are (a) 20:80, (b) 40:60, (c) 60:40, and (d) 80:20. That is, there are 16 types of 4 series × 4 composition ratios of the sample. Material parameter a of SiO2 k =0.1545, material parameter a of GeO2 k =0.09079. Whether it is a crystalline phase or an amorphous phase, if it is the same substance (such as SiO2), the material parameter a k By processing 4 types of systems, it is possible to process both systems in which the material parameters ak of the two components are the same and systems in which the material parameters ak of the two components are greatly different.

[0131] Figure 4A This is a diagram showing the fitting result of step S4 of this embodiment for single-component crystalline phase SiO 2. Figure 4B 2 is a diagram showing the fitting result of step S4 of this embodiment for single-component crystalline phase GeO2. The first fitting function is selected for the fitting functions of crystalline phase SiO2 and crystalline phase GeO2. Figure 4A and Figure 4B The diffraction pattern shown in the upper part of is a calculated powder diffraction pattern obtained by fitting, and the peak positions are indicated by vertical lines. Figure 4A and Figure 4B The figure shown in the lower part of is the residual pattern of the calculated powder diffraction pattern subtracted from the observed powder diffraction pattern. The peaks seen in the residual pattern are very small and the pattern fitting was done with high accuracy.

[0132] Figure 5 is an observed powder diffraction pattern showing the measured single-component amorphous phase. Figure 5 In the figure, the observed powder diffraction pattern (amorphous halo) of the single-component amorphous phase SiO2 is represented as curve A, and the observed powder diffraction pattern (amorphous halo) of the single-component amorphous phase GeO2 is represented as curve B. Figure 5 The observed powder diffraction pattern shown is consistent with Figure 4A and Figure 4B By comparison, it can be seen that the powder diffraction pattern of the amorphous phase is also particularly different in shape from the powder diffraction pattern of the crystalline phase.

[0133] Figure 6 The observed powder diffraction pattern of the single-component amorphous GeO2 and the background intensity y(2θ) of the crystalline GeO2 are calculated. back Figure represented together. Figure 6The curve B shown is Figure 5 Curve B shown is the observed powder diffraction pattern of single-component amorphous GeO2. Figure 6 The curve BG shown is the calculated background intensity y(2θ) obtained by full-graph fitting of the single-component crystalline GeO2. back .

[0134] Figure 7 This is a diagram showing the observed powder diffraction pattern of single-component amorphous GeO2 after treatment. Figure 7 The curve shown is from Figure 6 Curve B shown minus Figure 6 The above curve is obtained by the curve BG shown in FIG. That is, the processing mentioned here is the BG (Background) processing. The same processing is also performed on the amorphous phase SiO2. In addition, it is assumed here that "the background intensity of the crystalline phase (crystalline) and the amorphous phase (amorphous material) of the same composition measured under the same experimental conditions is the same".

[0135] In the quantitative analysis method of the amorphous phase of this embodiment, a sample of a two-component system is processed. When the sample consists of an amorphous phase and a crystalline phase, the background intensity y(2θ) is adjusted by performing full-image fitting on the observed powder diffraction pattern. back By optimizing the background parameter in the , the integral intensity parameter or scale factor in the calculated powder diffraction pattern of a crystalline phase, and the scale factor of the powder diffraction pattern of an amorphous phase (amorphous halo), the intensity contribution S of a crystalline phase can be calculated. k and the strength contribution of an amorphous phase S K (One amorphous substance is k=K=2) In this embodiment, mixed samples of four composition ratios are prepared for each of the four series, and quantitative analysis is performed on each of them as described above.

[0136] Figure 8 1 is a diagram showing the results of quantitative analysis in the first example of this embodiment. The results of quantitative analysis for a total of 16 types of samples of four series and four composition ratios are shown. Figure 8 The horizontal axis is the weight percentage w of the crystalline component weighed when the sample was prepared. k The vertical axis is the weight percentage w of the crystalline component obtained by quantitative analysis of the crystalline component. k In addition, for reference, the weight percentage w of the pure amorphous phase is also shown. k (=0) and the weight percentage of pure crystalline phase w k (=100%). Figure 8 As shown, although there are sometimes errors of some magnitude in some systems, for the material parameter a k Mixed substances with large differences have the same value of substance parameter a kAs with mixed substances, the analysis results are obtained along an almost ideal proportional curve (y=x).

[0137] [Second Embodiment]

[0138] Fig. 9 The sample used in the quantitative analysis method of the amorphous phase in the second embodiment of the present invention is shown. The sample used in this embodiment is composed of one amorphous phase and multiple crystalline phases, and quantitative analysis is performed on the sample consisting of one amorphous phase and two crystalline phases (three-component system) and one amorphous phase and three crystalline phases (four-component system). That is, Fig. 9 As shown, the three-component system sample is composed of crystalline GeO2, crystalline ZnO and amorphous SiO2, and the four-component system sample is composed of crystalline GeO2, crystalline ZnO, crystalline α-Al2O3 and amorphous SiO2.

[0139] The samples used for quantitative analysis are designed to have a weight percentage of each component w k The weight percentage of each component of the three-component system sample actually prepared is w k In the order of crystalline GeO2, crystalline ZnO and amorphous SiO2, w1=33.479%, w2=33.416%, w3=33.105%. The weight percentage wk of each component of the four-component system sample actually made is w1=25.076%, w2=24.925%, w3=25.121%, and w4=24.878% in the order of crystalline GeO2, crystalline ZnO, crystalline α-Al2O3 and amorphous SiO2. The main measurement conditions are that an X-ray diffraction device with an output of 9kW of the X-ray source is used, the sample is of powder specification, the voltage and current of the detector used for measurement are 45kV and 200mA respectively, the depth of the sample holder is 0.5mm, and a scattering protector (height 2mm) is used to prevent scattered rays. In this embodiment, in step S4, the background intensity y(2θ) back Also optimized (precise) together.

[0140] In step 3 of the second embodiment, it is determined that the first fitting function is used for two crystal phases in the three-component system sample and three crystal phases in the four-component system sample, but the present invention is not limited to this.

[0141] In step S4, each parameter is refined by fitting, but it is desirable to refine it in stages. First, in the initial cycle, the parameter of the integrated intensity of the crystal phase (I jk ), the scaling factor of the amorphous phase (S ck) and background intensity parameters are refined. Second, in subsequent cycles, in addition to the above parameters, other parameters (lattice constants of each crystalline phase, zero point correction, 2θ correction of amorphous scattering curves, UVW parameters of each crystalline phase, etc.) are refined at the same time.

[0142] Fig. 10A : is a figure which shows the fitting result of step S4 of this embodiment performed on two crystal phases in the three-component system sample. Fig. 10B : is a figure which shows the fitting result of step S4 of this embodiment performed on three crystal phases in the four-component system sample. Fig.11A and Fig. 11B It is a figure which shows the result of the quantitative analysis of the second example of this embodiment. Fig.11A and Fig. 11B The quantitative analysis results of the three-component system sample and the quantitative analysis results of the four-component system sample are shown respectively. Fig. 10A and Fig. 10B The diffraction pattern shown in the upper part is a calculated powder diffraction pattern obtained by fitting, and the peak positions are respectively indicated by vertical lines. Fig. 10A and Fig. 10B The figure shown at the bottom of is the residual graph. Fig. 10A and Fig. 10B As shown in , the peaks seen in the residual plot are very small and the graph fitting is performed with high accuracy. Fig.11A and Fig. 11B As shown in FIG. 1 , the full-image fitting is performed for the entire domain of the 2θ analysis range (a) 3° to 125° and (i) 3° to 100°. In addition, when the 2θ analysis range is (a) and (i), the weight percentage w is respectively expressed for each of them. k The error (w1~w3 or w4), the root mean squared error (RMSE), the R value (R wp ), and chi-square (χ 2 ) Yes. In addition, the parameter for background intensity is added to the parameters to be refined in the full image fit.

[0143] Investigation Fig.11A and Fig. 11B The mass analysis results are shown. Regarding the analysis range of 2θ, it is found that the analysis error in the range of (i) 3° to 100° is smaller than that in the range of (a) 3° to 125°. In addition, high-precision analysis results were obtained in both the three-component system sample and the four-component system sample, demonstrating the effectiveness of the quantitative analysis of this embodiment (quantitative analysis of samples containing amorphous components). In both the three-component system sample and the four-component system sample, analysis results with small errors were obtained by refining the parameters of the background intensity, demonstrating the effectiveness of the quantitative analysis of this embodiment.

[0144] In the first embodiment, the parameters of the background intensity are also refined in step S4, but are not limited thereto. When the chemical compositions of an amorphous phase and a crystalline phase of a two-component sample are the same, it can be assumed that the background intensity of the amorphous phase is the same as the background intensity of the crystalline phase. In this case, full-image fitting can be performed more easily.

[0145] The above describes the quantitative analysis device of the amorphous phase, the quantitative analysis method of the amorphous phase, and the quantitative analysis program of the amorphous phase according to the embodiment of the present invention. The present invention is not limited to the above embodiment and can be widely used. For example, the powder diffraction pattern in the above embodiment is obtained by X-ray diffraction measurement, but is not limited to this, and can also be obtained by other measurements such as neutron diffraction measurement. In addition, the discrimination of the diffraction lines contained in the powder diffraction pattern, the distribution of the intensity of overlapping or close diffraction lines, etc., can consider various approximations as needed. In the quantitative analysis method of the amorphous phase in the above embodiment, the weight ratio of multiple crystalline phases is calculated, but other quantitative ratios such as molar ratio can also be calculated based on such weight ratio.

[0146] In the above-mentioned embodiment, the function for one or more crystalline phases is set as the first fitting function, but it is not limited thereto. Since the fitting function for an amorphous phase is the third fitting function, when selecting the third fitting function for at least one of the one or more crystalline phases, that is, the first fitting function or the second fitting function, multiple fitting functions are simultaneously included in the fitting function, which can play an unprecedented outstanding effect. In addition, when the sample contains multiple crystalline phases, two or more fitting functions from the first fitting function to the third fitting function can also be selected for the multiple crystalline phases. Including multiple fitting functions in the fitting function at the same time can play an unprecedented outstanding effect.

Claims

1. A quantitative analysis device for an amorphous phase, which performs quantitative analysis on the amorphous phase contained in a sample through a powder diffraction pattern of the sample, characterized in that: include: A powder diffraction pattern obtaining unit, which obtains the powder diffraction pattern of the sample; A qualitative analysis result obtaining unit is used to obtain information of an amorphous phase and one or more crystalline phases contained in the sample; A fitting function obtaining unit, which obtains fitting functions respectively for the one or more crystal phases; A full-image fitting unit, using the fitting functions for the one amorphous phase and the one or more crystalline phases respectively, performs full-image fitting on the powder diffraction pattern of the sample to obtain a fitting result; as well as A weight ratio calculation unit calculates a weight ratio of the amorphous phase and the one or more crystalline phases based on the fitting result, The fitting function for each of the one or more crystalline phases is a fitting function selected from a first fitting function, a second fitting function, and a third fitting function, wherein the first fitting function uses an integrated intensity obtained by full-image decomposition, the second fitting function uses an integrated intensity obtained by observation or calculation, and the third fitting function uses a distributed intensity obtained by observation or calculation. The fitting function for the one amorphous phase is the third fitting function, The sample includes 1 amorphous phase and K-1 crystalline phases, and the fitting function y(2θ) representing the powder diffraction pattern of the kth crystalline phase is k The fitting function y(2θ) representing the powder diffraction pattern of the Kth crystalline phase is used as the fitting function y(2θ) representing the powder diffraction pattern of the amorphous phase. K To process, where k is an integer of 1≤k≤K-1; P(2θ) jk is the standardized distribution function that describes the shape of the distribution, y(2θ)'k represents the distribution intensity of the kth powder diffraction pattern additionally measured or calculated for a single-phase sample of the kth crystalline phase, Sc k is the scaling factor, I jk and I' jk is the integrated intensity, given by I jk =Sc k I' jk definition, The first fitting function y(2θ) K It is expressed by the following mathematical formula 11: [Mathematical formula 11] y(2θ) k =∑ j I jk P(2θ) jk (11) The second fitting function y(2θ) K It is expressed by the following mathematical formula 12: [Mathematical formula 12] y(2θ) k =∑ j Sc k I′ jk P(2θ) jk ···(12) The third fitting function y(2θ) K It is expressed by the following mathematical formula 13: [Mathematical formula 13] y(2θ) k =Sc k y(2θ)′ k ···(13)。 2. The quantitative analysis device for amorphous phase according to claim 1, characterized in that: The weight ratio calculation unit calculates the weight percentage using the IC formula.

3. The quantitative analysis device for amorphous phase according to claim 1 or 2, characterized in that: For at least one of the one or more crystal phases, any one of the first fitting function or the second fitting function is selected.

4. A quantitative analysis method of an amorphous phase, which quantitatively analyzes the amorphous phase contained in the sample through a powder diffraction pattern of the sample, characterized in that: include: A powder diffraction pattern obtaining step, obtaining a powder diffraction pattern of the sample; A qualitative analysis result obtaining step, obtaining information of an amorphous phase and one or more crystalline phases contained in the sample; A fitting function obtaining step, obtaining fitting functions respectively for the one or more crystal phases; A full-image fitting step, using the fitting functions for the one amorphous phase and the one or more crystalline phases respectively, performing full-image fitting on the powder diffraction pattern of the sample to obtain a fitting result; as well as a weight ratio calculation step, calculating the weight ratio of the amorphous phase and the one or more crystalline phases based on the fitting result, The fitting function for each of the one or more crystalline phases is a fitting function selected from a first fitting function, a second fitting function, and a third fitting function, wherein the first fitting function uses an integrated intensity obtained by full-image decomposition, the second fitting function uses an integrated intensity obtained by observation or calculation, and the third fitting function uses a distributed intensity obtained by observation or calculation. The fitting function for the one amorphous phase is the third fitting function, The sample includes 1 amorphous phase and K-1 crystalline phases, and the fitting function y(2θ) representing the powder diffraction pattern of the kth crystalline phase is k The fitting function y(2θ) representing the powder diffraction pattern of the Kth crystalline phase is used as the fitting function y(2θ) representing the powder diffraction pattern of the amorphous phase. K To process, where k is an integer of 1≤k≤K-1; P(2θ) jk is the standardized distribution function that describes the shape of the distribution, y(2θ)'k represents the distribution intensity of the kth powder diffraction pattern additionally measured or calculated for a single-phase sample of the kth crystalline phase, Sc k is the scaling factor, I jk and I' jk is the integrated intensity, given by I jk -Sc k I' jk definition, Among them, the first fitting function y(2θ) K The integrated intensity obtained by full-image decomposition based on the Pawley method is used and is expressed by the following mathematical formula 11: [Mathematical formula 11] y(2θ) k =∑ j I jk P(2θ) jk (11) The second fitting function y(2θ) K It is expressed by the following mathematical formula 12: [Mathematical formula 12] y(2θ) k =∑ j Sc k I′ jk P(2θ) jk ···(12) The third fitting function y(2θ) K It is expressed by the following mathematical formula 13: [Mathematical formula 13] y(2θ) k =Sc k y(2θ)′ k ···(13)。 5. A storage medium having recorded thereon a quantitative analysis program of an amorphous phase, wherein the quantitative analysis program of an amorphous phase performs a quantitative analysis on an amorphous phase contained in a sample through a powder diffraction pattern of the sample, characterized in that: Make the computer function as the following unit: A powder diffraction pattern obtaining unit, which obtains the powder diffraction pattern of the sample; A qualitative analysis result obtaining unit is used to obtain information of an amorphous phase and one or more crystalline phases contained in the sample; A fitting function obtaining unit, which obtains fitting functions respectively for the one or more crystal phases; A full-image fitting unit, using the fitting functions for the one amorphous phase and the one or more crystalline phases respectively, performs full-image fitting on the powder diffraction pattern of the sample to obtain a fitting result; as well as A weight ratio calculation unit calculates a weight ratio of the amorphous phase and the one or more crystalline phases based on the fitting result, The fitting function for each of the one or more crystalline phases is a fitting function selected from a first fitting function, a second fitting function, and a third fitting function, wherein the first fitting function uses an integrated intensity obtained by full-image decomposition, the second fitting function uses an integrated intensity obtained by observation or calculation, and the third fitting function uses a distributed intensity obtained by observation or calculation. The fitting function for the one amorphous phase is the third fitting function, The sample includes 1 amorphous phase and K-1 crystalline phases, and the fitting function y(2θ) representing the powder diffraction pattern of the kth crystalline phase is k The fitting function y(2θ) representing the powder diffraction pattern of the Kth crystalline phase is used as the fitting function y(2θ) representing the powder diffraction pattern of the amorphous phase. K To process, where k is an integer of 1≤k≤K-1; P(2θ) jk is the standardized distribution function that describes the shape of the distribution, y(2θ)'k represents the distribution intensity of the kth powder diffraction pattern additionally measured or calculated for a single-phase sample of the kth crystalline phase, Sc k is the scaling factor, I jk and I' jk is the integrated intensity, given by I jk =Sc k I' jk definition, The first fitting function y(2θ) K It is expressed by the following mathematical formula 11: [Mathematical formula 11] y(2θ) k =∑ j I jk P(2θ) jk (11) The second fitting function y(2θ) K It is expressed by the following mathematical formula 12: [Mathematical formula 12] y(2θ) k =∑ j Sc k I′ jk P(2θ) jk ···(12) The third fitting function y(2θ) K It is expressed by the following mathematical formula 13: [Mathematical formula 13] y(2θ) k =Sc k y(2θ)′ k ···(13)。

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