JP2008070331A - Method and device for analyzing sample having a plurality of crystalline phases - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To simultaneously determine the percentage of each crystalline phase and crystallite size, regarding a sample having a plurality of crystal phases, in a short time. <P>SOLUTION: In this analysis method of the sample, an actual diffraction pattern of an analyzed sample is obtained by X-ray diffraction measurement, various parameters contained in an approximate calculation formula are made precise by Rietvelt-analyzing the diffraction measurement result, and the percentage (mass percentage χ) and crystallite size (crystallite diameter p) of the analyzed sample are calculated, based on the precise parameter values. In applying at least first precision processing to secondary profile parameters of the various parameters, parameters U, X and Y, of the secondary profile parameters, affect the calculation result of the percentage of each crystal phase by a relatively large amount, and crystallite size are made precise under the constraint condition, with Us, Xs and Ys of each crystal phase being respectively identical. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a technique for analyzing a crystal structure of a sample having a plurality of crystal phases by using a so-called Rietveld analysis.

Conventionally, an analysis method called Rietveld analysis is known as an analysis method for specifying a crystal structure of a substance having a plurality of crystal phases. In this Rietveld analysis, first, the measured diffraction pattern of the sample to be analyzed is obtained by the X-ray diffraction method, and the measured diffraction pattern is included in the approximate calculation formula so as to match the calculated diffraction pattern based on the approximate calculation formula. The so-called pattern fitting analysis method is used to refine various parameters. When various parameters are refined in this way, the ratio of a plurality of crystal phases (for example, monoclinic phase, tetragonal crystal, cubic crystal), the size of each crystallite ( Crystallite diameter) can be calculated.
JP 9-297112 A

  However, in the Rietveld analysis method as described above, since the parameters included in the approximate calculation formula are correlated with each other, the refinement of the parameters (measured diffraction pattern and calculated diffraction pattern based on the approximate calculation formula and Depending on the procedure for obtaining parameters so that they match, even if the refinement of a certain parameter succeeds, other parameters converge to meaningless values (the refinement fails). I woke up often. For this reason, there is a problem that the ratio of each crystal phase and the crystallite size cannot be obtained simultaneously, and the time required for the analysis process increases.

  The present invention has been made in view of the above circumstances, and an object of the present invention is to simultaneously obtain the ratio of each crystal phase and the crystallite size in a short time for a sample having a plurality of crystal phases.

In order to solve the above problems, the present invention is a method for analyzing a sample having a plurality of crystal phases, and includes a first step of obtaining an actually measured diffraction pattern of a sample to be analyzed using an X-ray diffractometer, The following parameters (1) and (2) included in the approximate calculation formula so that the actually measured diffraction pattern obtained in the first step matches the calculated diffraction pattern based on the approximate calculation formula;
“(1) The following parameters as secondary profile parameters,
・ Parameters U, Y, Ye regarding spread of profile due to lattice distortion
-Parameters P, X, Xe regarding the spread of the profile due to the effect of crystallite size,
・ Parameters V, W, which depend mainly on the X-ray diffractometer and optical system
(2) Parameters other than the above-mentioned secondary profile parameters, including scale factor parameters and lattice constants "
The ratio of each crystal phase in the sample to be analyzed and the crystallite size based on the value of a specific parameter among the parameters refined by the Rietveld analysis. In the second step, the various parameters are refined a plurality of times, and at least the first precision of the secondary profile parameter among the various parameters is calculated. The parameters U, X, and Y that have a relatively large influence on the calculation results of the ratio of crystal phases and the crystallite size when the crystallization process is performed are the same for U, X, and Y of each crystal phase. It is characterized by refinement under the constraint condition (Claim 1).

  According to the present invention, X-ray diffraction measurement is performed to obtain an actual diffraction pattern of the sample to be analyzed, and the diffraction measurement result is subjected to Rietveld analysis to refine various parameters included in the approximate calculation formula. In the sample analysis method in which the ratio of each crystal phase and the crystallite size in the sample to be analyzed are calculated from the converted parameter values, at least the first of the secondary profile parameters among the various parameters When performing the refinement process, among the secondary profile parameters, parameters U, X, and Y that have a relatively large effect on the calculation result of the ratio of crystal phases and the crystallite size are used as the values of U of each crystal phase, X Since refinement is performed under the constraint that Y and Y are the same, the first refinement process is given such a constraint. And unlike the case of performing no, the parameter U, X, at least a portion of Y is (fail refinement) converge to become meaningless values can be effectively prevented. As a result, both the ratio of each crystal phase and the crystallite size in the sample to be analyzed can be calculated at a time, and the time required to calculate these values can be effectively shortened.

  In the second step, it is preferable that the parameters U, X, and Y are refined under the constraint conditions, and then U, X, and Y of each crystal phase are refined independently.

  In this way, the parameters U, X, and Y, which should originally take different values, are independently converged to appropriate values while preventing the parameters U, X, and Y from converging to meaningless values. be able to.

  In the above method, at least before the second step, X-ray diffraction measurement is performed on a standard sample whose crystal structure is known in advance, and diffraction data of the standard sample obtained thereby is subjected to Rietveld analysis. The parameters V and W depending on the X-ray diffractometer and the like are extracted from the analysis result, the Rietveld analysis of the sample to be analyzed in the second step is performed, and the values of the parameters V and W are templated in advance. It is preferable to carry out the process in a state where it is input to a file.

  In this way, a standard sample whose crystal structure is known in advance is analyzed to extract the values of parameters V and W depending on the diffractometer and the like. When Rietveld analysis is performed, it is possible to obtain accurate values of the parameters V and W that change according to the model of the diffraction device, the optical system, the deterioration of the device, and the like, and reflect the value of this parameter. By starting the Rietveld analysis of the sample to be analyzed in this state, it becomes possible to perform more accurate and quick analysis processing.

The present invention also relates to an analyzer for a sample having a plurality of crystal phases, an X-ray diffractometer that performs X-ray diffraction measurement on the sample to be analyzed, and an actual diffraction of the sample to be analyzed from the X-ray diffractometer. The following parameters (1) and (2) included in the approximate calculation formula are obtained so that a pattern is obtained and the actually measured diffraction pattern matches the calculated diffraction pattern based on the approximate calculation formula;
“(1) The following parameters as secondary profile parameters,
・ Parameters U, Y, Ye regarding spread of profile due to lattice distortion
-Parameters P, X, Xe regarding the spread of the profile due to the effect of crystallite size,
・ Parameters V, W, which depend mainly on the X-ray diffractometer and optical system
(2) Parameters other than the above-mentioned secondary profile parameters, including scale factor parameters and lattice constants "
Rietveld analysis is performed to refine each of the parameters, and the ratio of each crystal phase and crystallite size in the sample to be analyzed are calculated based on the values of specific parameters among the parameters refined by the Rietveld analysis. An analysis device, and the analysis device repeatedly performs the refinement processing of the various parameters a plurality of times, and performs at least the first refinement processing on the secondary profile parameter among the various parameters. Refine the parameters U, X, and Y that have a relatively large effect on the calculation results of the ratio and crystallite size of each crystal phase under the constraint that the U, X, and Y of each crystal phase are the same. It is comprised so that it may carry out (Claim 4).

  According to the sample analyzing apparatus of the present invention, the ratio of each crystal phase and the crystallite size can be simultaneously obtained in a short time.

  As described above, according to the present invention, the ratio of each crystal phase and the crystallite size of a sample having a plurality of crystal phases can be simultaneously obtained in a short time.

  First, an outline of Rietveld analysis will be described. As described above, Rietveld analysis uses an analysis method called pattern fitting in which a calculated diffraction pattern based on an approximate calculation formula is applied to an actually measured diffraction pattern obtained by an X-ray diffraction method.

As an approximate expression of the diffraction pattern, a profile function representing the spectral intensity at each diffraction angle; Φ (2θ _i −2θ _K ) is used. In the parentheses, 2θ _i represents the diffraction angle at the i-th measurement point, and θ _K represents the angle of the peak position of the diffraction pattern. Specifically, as this profile function, a function called a pseudo-Forked function or a Pearson VII function is generally used. Here, the analysis method using the pseudo-Forked function is briefly described.

  The pseudo-Forked function as the profile function is expressed by the following mathematical formula 1. That is, the pseudo-Forked function according to the following formula 1 is a function configured by adding the Lorentz function (the first term on the right side of the formula 1) and the Gaussian function (the second term on the right side of the formula 1).

Here, Δ2θ _iK = 2θ _i −2θ _K. Η and H _K are called primary profile parameters, η represents the fraction of the Lorentz component, and H _K represents the full width at half maximum.

The fraction η of the Lorentz component can be approximated by the following Equation 2, which is a polynomial in the ratio of the half width H _KL of the Lorentz component to the full width at half maximum H _K.

Further, assuming that the full width at half maximum H _{KG of the} Gaussian component, the full width at half maximum H _K is approximated by the following mathematical formula 3, which is a polynomial including the full width at half maximum H _KG of the Gaussian component and the full width at half maximum H _{KL of the} Lorentz component. Can do.

Therefore, if the half-value width H _{KL of} the Lorentz component and the half-value width H _{KG of the} Gaussian component are obtained, the primary profile parameters η and H _K , and the profile function Φ (Δ2θ _iK ) can be obtained. However, the H _KL, H _KG is changes according to the theta _K, it is necessary to equation representing the theta _K dependent of H _KL, H _KG. The formula for that can be expressed by the following formulas 4 and 5.

In these mathematical formulas 4 and 5, U, V, W, P, X, Xe, Y, and Ye are called secondary profile parameters, and each has a physical meaning. Specifically, U, Y, and Ye are parameters relating to profile spreading caused by lattice distortion, and P, X, and Xe are parameters relating to profile spreading caused by crystallite size effects. Further, V and W are parameters that are independent of the crystallinity of the sample and have different values mainly depending on the diffraction device and the optical system. Incidentally, phi _K in Equation 5, the inverse vector of the most significant reflection of anisotropic spread ^{_{(h a · a * + k}} a · b * + l a · c *), substantially in reflection K (Bragg reflection intensity It represents the acute angle formed by the reciprocal lattice vector (h ^* a ^* + k ^* b ^* + l ^* c ^* ) of the reflecting reflection number K).

In Rietveld analysis, the second-order profile parameters; U, V, W, P, X, Xe, Y, and Ye are subjected to refinement processing based on the nonlinear least square method, and the calculated diffraction patterns (Equations 1 to 5). (Calculated value based on the above) and the actually measured diffraction pattern (residual sum of squares) is determined to be minimized. In addition, although detailed explanation is omitted, a more detailed calculation formula of Rietveld analysis includes a scale factor parameter s and lattice constants (a, b, c, α, β, γ), atomic coordinates (x, y, z), background parameters (b ₀ , b ₁ , b ₂ ,...), etc. are included, and the values of these parameters are processed in the same manner as described above. Is now required.

  For example, in the diffraction data shown in FIG. 1, the scale factor parameter s out of the various parameters can be obtained by matching the height h of the peak position with the measured diffraction pattern, and half of the peak height h. By combining the peak width w (half-value width) at the height position, X (half-value width parameter), which is one of the secondary profile parameters, can be obtained.

The scale factor parameter s is proportional to the amount of each phase component (tetragonal or cubic). Therefore, if the mass fraction of a certain crystal phase component i is χ _i , this mass fraction χ _i can be obtained by the following formula 6.

Here, s _i is a scale factor parameter of each crystal phase component, Z _i is the number of chemical formulas per unit cell (per crystal) of each crystal phase component, M _i is the chemical formula amount of each crystal phase component, and V _i is It is the volume per unit cell of each crystal phase component.

When the crystallite diameter of the crystal phase component i is p _i , the crystallite diameter p _i can be obtained by the following formula 7 (Scherrer formula) including the half width parameter X _i of the component.

  Here, K is the Scherrer constant (0.9), and λ is the wavelength of the X-ray used.

  As described above, in Rietveld analysis, various parameters are refined so as to make the calculated diffraction pattern coincide with the actually measured diffraction pattern. The mass fraction χ of each crystal phase and the crystallite diameter p of each crystal phase can be calculated from the value of a specific parameter among the refined parameters.

  Next, a specific procedure for obtaining the ratio of each crystal phase and the crystallite size in a short time using such a Rietveld analysis will be described based on the process diagrams shown in FIGS. In the following procedure, “RIETAN-2000” is used as the analysis software.

  First, X-ray diffraction measurement is performed on a standard sample whose crystal structure is known in advance, and the diffraction data obtained thereby is subjected to Rietveld analysis (steps S1 and S3). Specifically, X-ray diffractometry is performed on the standard sample using an X-ray diffractometer, and diffraction data obtained thereby is input to an analyzer equipped with analysis software “RIETAN-2000”. This analysis apparatus is caused to execute Rietveld analysis of the data. Then, from the analysis result, parameters V and W depending on the diffraction device are extracted from the secondary profile parameters (step S5). The values of the parameters V and W depending on the diffraction device are used in Rietveld analysis for the sample to be analyzed which will be described later. The parameters V and W depending on the diffraction device can be used as they are if the same device is used. In such a case, the step here is omitted. Is also possible. However, since it may change slightly depending on the deterioration of the apparatus and the stability of X-rays, it is desirable to obtain accurate V and W from the analysis result of the standard sample as described above.

  Next, X-ray diffraction measurement is performed on the sample to be analyzed in the same manner as Step S1 (Step S7). The parameters V and W depending on the device extracted in step S5 are input to a template file (initial value of preset calculation data) prepared in the analysis device (step S9). The Rietveld analysis of the X-ray diffraction measurement data of the sample to be analyzed is executed by the analysis device (step S11).

  FIG. 3 shows a specific procedure for Rietveld analysis of the sample to be analyzed. Here, first, the analysis apparatus is caused to execute a process of refining U of the secondary profile parameters under the constraint that U of each crystal phase is the same (step S13). That is, after adding a conditional expression “U of the first phase” = “U of the second phase” =... To the calculation program, the U of each phase is refined. Note that the process of refining a specific parameter in this way is performed in a state where all other parameters are fixed.

  Next, the analysis apparatus is caused to execute a process of refining X and Y of the secondary profile parameters under the constraint that X and Y of each crystal phase are the same (step S15). That is, the conditional expressions “X of the first phase” = “X of the second phase” = ··· and “Y of the first phase” = “Y of the second phase” = ··· are added to the arithmetic program. Above, refine each phase X and Y respectively. At this time, the X refinement process and the Y refinement process are performed simultaneously.

  As in steps S13 and S15, U, X, and Y of the secondary profile parameters are refined under the constraint that U, X, and Y of each phase are the same. Since the parameters U, X, and Y of the above are parameters that tend to fluctuate compared to other secondary profile parameters, if they are refined separately without giving the above-mentioned constraints, they are correlated. This is because parameters may influence each other and any parameter may converge to a meaningless value. If any of the parameters U, X, and Y converges to meaningless values in this way, the ratio of each crystal phase and the value of the crystallite size calculated in the steps described later are increased from the appropriate values. It will shift. That is, these parameters U, X, and Y can be said to be parameters that greatly affect the calculation results of the ratio of crystal phases and the crystallite size. On the other hand, for other secondary profile parameters, there is almost no such concern. Therefore, for the purpose of preventing the divergence of parameters (convergence to meaningless values) as described above, temporarily Do not refine. For example, the parameters P, Xe, and Ye (these parameters are usually parameters for inputting a numerical value of zero) are finely adjusted by the refinement process and hardly change. Also, the parameters V and W depending on the diffractometer etc. have a small fluctuation range. In particular, if the accurate V and W obtained by analyzing the standard sample as described above are input in advance, the fluctuations are almost the same. Never do.

  After U, X, and Y are refined as described above, parameters other than the secondary profile parameters, that is, the scale factor parameter s and the lattice constants (a, b, c, α, β, γ), etc. The parameters are refined (step S17).

  Then, the process returns to the refinement process of the secondary profile parameter again, and this time, the U of each phase is refined independently (step S19). Specifically, after the U of the first phase and the U of the second phase are refined separately one by one, this separately refined U of each phase is now applied to all phases. Refine at the same time.

  Next, X and Y of each crystal phase are refined independently (step S21). Specifically, the first phase X and Y, the second phase X and Y,... Are refined separately one by one, and then the separately refined X and Y of each phase are obtained. Now refine all phases simultaneously.

  After U, X, and Y are refined independently as described above, parameters other than the secondary profile parameters, that is, the scale factor parameter s and the lattice constants (a, b, c, α, β, The parameters such as γ) are refined again (step S23).

  This time, V and W of the secondary profile parameters are refined (step S25). Note that these parameters V and W are parameters that mainly depend on the diffraction device and the like and are not related to the type of crystal phase, and therefore should have the same value in each crystal phase. Therefore, the parameters V and W are refined under the constraint that Vs and Ws of each phase are the same. This is the same when V and W are refined in other steps. Then, the process proceeds to the next step S27, and the scale factor parameter s and the lattice constants (a, b, c, α, β, γ), which are parameters other than the secondary profile parameters, are refined again.

  Next, all secondary profile parameters U, V, W, P, X, Xe, Y, Ye are refined (step S29). Among these, for X, Xe, Y, and Ye, in order to increase the precision of refinement, it is avoided to perform all the processes simultaneously. Specifically, Xe and Ye are fixed and X and Y are refined (or refined in the reverse order), or X and Xe are fixed and Y and Ye are refined (or vice versa). )).

  When the processing of step S29 is completed, after confirming that the reliability factor of Rietveld analysis (a measure for estimating the degree of analysis progress and the degree of coincidence between the actual measurement pattern and the calculation pattern) is reduced to some extent, All parameters, that is, secondary profile parameters and other parameters are refined (step S31). At this time, the number of parameters to be refined is gradually increased. For example, first refine the lattice constant, then refine the lattice constant and atomic coordinates, then refine the lattice parameters, atomic coordinates, and background parameters, and so on. Let the process proceed gradually. The Rietveld analysis process based on the process diagram of FIG. 3 as described above is executed until the required accuracy is obtained while repeating the process of each step or returning to the upstream step as necessary. The

  As a result of the above processing, if it can be confirmed that the reliability factor is sufficiently small and various parameters have been refined with sufficient accuracy, that is, the Rietveld analysis has been successfully completed, FIG. Returning to the process diagram, the mass fraction χ and crystallite of each crystal phase based on the scale factor parameter s of the refined parameters and the value of X (half-width parameter) of the secondary profile parameters. Each of the diameters p is calculated (step S33). Specifically, by substituting the value of the scale factor parameter s of each crystal phase into the above Equation 6, the mass fraction χ of each crystal phase is calculated, and the value of the half-width parameter X of each crystal phase is By substituting into Equation 7 (Scherrer's formula), a process of calculating the crystallite diameter p of each crystal phase is executed.

  As described above, the X-ray diffraction measurement is performed to obtain the actual diffraction pattern of the sample to be analyzed, and the diffraction measurement result is subjected to Rietveld analysis to refine the various parameters included in the approximate calculation formula. In the sample analysis method for calculating the ratio (mass fraction χ) and crystallite size (crystallite diameter p) of each crystal phase in the sample to be analyzed from the values of the parameters, When performing at least the first refinement process on the secondary profile parameters, among the secondary profile parameters, parameters U, X, and Y that have a relatively large influence on the calculation result of the ratio of crystal phases and the crystallite size. Is refined under the constraint that U, X, and Y of each crystal phase are the same (step S in the process diagram). 3 and step S15), unlike the case where the first refinement process is performed without giving such a constraint, at least a part of the parameters U, X, and Y converge to meaningless values ( Can be effectively prevented. That is, since the parameters U, X, and Y are in a state of being greatly deviated from the appropriate values in the first stage before the refinement, the first refinement process is performed without giving the above constraint conditions. As a result, there is a high possibility that at least some of the parameters U, X, and Y will converge to meaningless values (because the parameters are correlated with each other, if one parameter is suddenly refined, Parameters are greatly affected and converge to meaningless values). If parameter refinement fails in this way, both the ratio of each crystal phase and the crystallite size cannot be calculated properly, and Rietveld analysis needs to be performed again. On the other hand, when at least the first refinement process is performed under a predetermined constraint as described above, both the ratio of each crystal phase and the crystallite size are avoided by avoiding the above situation. Since it can be calculated at once, the time required to calculate these values can be effectively shortened.

  Further, as in the above embodiment, when the parameters U, X, Y are refined under the constraints as described above, U, X, Y of each crystal phase is refined independently. (Steps S19 and S21 in the process diagram), the parameters U, X, and Y, which should originally take different values, while preventing the parameters U, X, and Y from converging to meaningless values, respectively. There is an advantage that it can be independently converged to an appropriate value.

  Further, as in the above-described embodiment, a standard sample whose crystal structure is known in advance is analyzed to extract the values of parameters V and W depending on the diffraction apparatus and the like, and these parameter values are input to a template file in advance. When the Rietveld analysis of the sample to be analyzed is performed, it is possible to obtain accurate values of the parameters V and W that change according to the model of the diffraction device, the deterioration of the device, etc., and the value of this parameter By starting the Rietveld analysis of the sample to be analyzed in a state reflecting the above, it becomes possible to perform more accurate and quick analysis processing.

  In the above-described embodiment, the actual diffraction pattern is obtained using the X-ray diffraction measurement method, and the analysis is performed based on the diffraction data. However, the analysis method according to the present invention is obtained by the X-ray diffraction measurement method. The present invention is not limited to the obtained diffraction data, and can be used to analyze data obtained by a diffraction method using other radiation (for example, neutron beam).

  Rietveld analysis was performed under the following conditions by the method shown in FIGS.

Standard sample: CeO ₂
- the analyzed sample ... zirconium - cerium composite oxide _{(Zr x Ce y Nd z O} w)
・ X-ray diffractometer used: RINT2500 manufactured by Rigaku
・ Analysis software used for Rietveld analysis… RIETAN2000
-Profile function used: Thomson, Cox, Hasting pseudo-forked function

  In the present embodiment, in the process diagram of FIG. 3, after the processes of steps S13 to S17 are repeated three times, the processes of steps S19 to S23 are repeated three times, then the processes of steps S25 and S27 are performed, and steps S19 to S23 are performed again. After that, the processes of steps S29 and S31 were finally performed. And by performing an analysis in such a procedure, results as shown in FIGS. 4 to 7 were obtained according to the stage of the analysis. In the figure, Rwp and Rp are reliability factors (R factors), and S is a reliability factor that represents the fit of the entire pattern as one of the reliability factors. The value and the calculated value are in good agreement. Among these, the value of the reliability factor S should be 2.0 or less, more preferably 1.5 or less, and a highly accurate analysis is performed by repeating the refinement process until this value is reached. Can do. In addition, since the zirconium-cerium double oxide, which is the sample to be analyzed, has only two crystal phases, cubic and tetragonal, the mass ratio and the crystallite diameter are described for these two crystal phases in the figure. Has been.

  From the results of FIGS. 4 to 7, as the analysis step proceeds, the residual between the calculated value and the actually measured value converges within a certain range, and the reliability factor (Rwp, Rp, S ) Is decreasing. And since the value of the reliability factor S is 1.5 or less (1.42) in the final state of FIG. 7, it can be said that the analysis with sufficiently high accuracy has succeeded. Note that the cubic crystallite diameter and the tetragonal crystallite diameter are the same in the state of FIG. 5 because the secondary profile parameters are the same in each phase until the time of FIG. 5 (step S15). This is because the analysis is performed under the constraint condition.

It is a graph with the horizontal axis representing the diffraction angle and the vertical axis representing the spectral intensity, and is a diagram for explaining an analysis method of Rietveld analysis. It is process drawing for demonstrating the analysis method concerning one Embodiment of this invention. It is a figure for demonstrating the specific content of the Rietveld analysis of the to-be-analyzed sample performed in the process drawing of FIG. It is a figure (analysis pattern figure) for showing the coincidence degree of the measured value of a X-ray diffraction pattern, and the calculated value by Rietveld analysis, and has shown the state before performing a parameter refinement process. FIG. 5 is an analysis pattern diagram in a state where the analysis processing has progressed to some extent from the time of FIG. 4. FIG. 6 is an analysis pattern diagram in a state in which the analysis processing has further progressed from the time of FIG. 5. It is an analysis pattern figure in the state where the Rietveld analysis was completed.

Claims (4)

A method for analyzing a sample having a plurality of crystal phases,
A first step of obtaining an actually measured diffraction pattern of the sample to be analyzed using an X-ray diffractometer;
The following parameters (1) and (2) included in the approximate calculation formula so that the actually measured diffraction pattern obtained in the first step matches the calculated diffraction pattern based on the approximate calculation formula;
“(1) The following parameters as secondary profile parameters,
・ Parameters U, Y, Ye regarding spread of profile due to lattice distortion
-Parameters P, X, Xe regarding the spread of the profile due to the effect of crystallite size,
・ Parameters V, W, which depend mainly on the X-ray diffractometer and optical system
(2) Parameters other than the above-mentioned secondary profile parameters, including scale factor parameters and lattice constants "
A second step of performing a Rietveld analysis to refine each of the above,
A third step of calculating a ratio and a crystallite size of each crystal phase in the sample to be analyzed based on a value of a specific parameter among parameters refined by the Rietveld analysis,
In the second step, the refinement process of the various parameters is repeated a plurality of times, and at least when the first refinement process is performed on the secondary profile parameter among the various parameters, The parameters U, X, and Y that have a relatively large effect on the calculation results of the ratio and the crystallite size are refined under the constraint that U, X, and Y of each crystal phase are the same. A method for analyzing a sample having a plurality of crystal phases. The method for analyzing a sample having a plurality of crystal phases according to claim 1,
In the second step, the parameters U, X, and Y are refined under the constraint conditions, and then U, X, and Y of each crystal phase are refined independently. A method for analyzing a sample having The method for analyzing a sample having a plurality of crystal phases according to claim 1 or 2,
At least before the second step, X-ray diffraction measurement is performed on a standard sample whose crystal structure is known in advance, and diffraction data of the standard sample obtained thereby is subjected to Rietveld analysis. Extracting the parameters V and W depending on the X-ray diffractometer etc.
A method for analyzing a sample having a plurality of crystal phases, wherein the Rietveld analysis of the sample to be analyzed in the second step is performed in a state where the values of the parameters V and W are previously input to a template file. An apparatus for analyzing a sample having a plurality of crystal phases,
An X-ray diffractometer that performs X-ray diffraction measurement on the sample to be analyzed;
The measured diffraction pattern of the sample to be analyzed is obtained from the X-ray diffractometer, and the measured diffraction pattern and the calculated diffraction pattern based on the approximate calculation formula are made to coincide with each other, the following (1) Parameter (2);
“(1) The following parameters as secondary profile parameters,
・ Parameters U, Y, Ye regarding spread of profile due to lattice distortion
-Parameters P, X, Xe regarding the spread of the profile due to the effect of crystallite size,
・ Parameters V, W, which depend mainly on the X-ray diffractometer and optical system
(2) Parameters other than the above-mentioned secondary profile parameters, including scale factor parameters and lattice constants "
Rietveld analysis is performed to refine each of the parameters, and the ratio of each crystal phase and crystallite size in the sample to be analyzed are calculated based on the values of specific parameters among the parameters refined by the Rietveld analysis. With an analysis device,
The analysis apparatus repeatedly performs the refinement process of the various parameters a plurality of times, and when performing at least the first refinement process on the secondary profile parameter among the various parameters, The parameters U, X, and Y that have a relatively large effect on the calculation result of the crystallite size are refined under the constraint that the crystal phases U, X, and Y are the same. An analysis apparatus for a sample having a plurality of crystal phases.

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