JP2013134169A - Crystal phase quantitative method using x-ray diffraction - Google Patents

Abstract

PROBLEM TO BE SOLVED: To simply measure a content of a substance composing a material by using an X-ray diffraction method.SOLUTION: First of all, X-ray diffraction intensities Iof respective crystalline phases in a reference sample in which contents of a plurality of crystalline phases are known are measured as reference intensities (step S1). Then X-ray diffraction intensities Iof respective crystalline phases in a sample to be quantitated are measured as quantitative intensities (step S2). Then a value obtained by dividing the quantitative intensity Iof each crystalline phase by the reference intensity Iof each crystalline phase and multiplying the divided value of each crystalline phase by a mass ratio Wof each crystalline phase in the reference sample is calculated as an index value of each crystalline phase and a value obtained by dividing the index value of each crystalline phase by the sum of index values of all the crystalline phases is simultaneously calculated as the content of each crystalline phase in the sample to be quantitated (step S3).

Description

  The present invention quantifies a crystalline phase using X-ray diffraction that measures the content of a plurality of crystalline phases (hereinafter sometimes referred to as crystalline phases) in a sample to be quantified using an X-ray diffraction method. Regarding the method.

  In general, in various materials such as inorganic materials, metal materials, chemicals, and chemical products, the abundance of substances constituting the materials dominates the material characteristics. For this reason, the quantification method of the substance which comprises material is an important elemental technique for material development, product quality assurance, and quality control. Methods for quantifying substances constituting a material are roughly classified into a technique for measuring the abundance of elements constituting the material and a technique for measuring the abundance of substances such as compounds and molecules constituting the material.

When the sample to be quantified is crystalline, the abundance of a substance constituting the sample to be quantified can be measured using an X-ray diffraction method (see Non-Patent Document 1). Specifically, the X-ray diffraction intensity I _i of the crystalline phase i in the sample to be quantified containing a plurality of crystalline phases is represented by the following formula (1). In Formula (1), K _i represents a constant specific to the crystalline phase i, W _i represents the mass ratio of the crystalline phase i, and (μ / ρ) represents the average mass absorption coefficient of the sample to be quantified. Show. Therefore, by measuring the X-ray diffraction intensity I _i of the crystalline phase i using the X-ray diffraction method, the mass ratio W _i of the crystalline phase i in the sample to be determined can be obtained.

As is apparent from equation (1), even if the mass ratio W _i of the crystalline phase i in the quantitative samples are the same, the mass ratio of other crystalline phases are different, of the quantitative sample Since the average mass absorption coefficient changes, the X-ray diffraction intensity I _i of the crystalline phase i changes. For this reason, there are various methods in the quantification method using the X-ray diffraction method depending on how the average mass absorption coefficient that differs for each sample to be quantified is corrected. Specifically, the quantification method using the X-ray diffraction method is based on the case where a pure substance of a substance (test substance) whose mass ratio is to be measured (a test substance) or a test sample whose mass ratio of the test substance is known can be obtained. It can be roughly classified into two cases when it cannot be done.

That is, when a pure substance of a test substance or a sample to be measured whose mass ratio of the test substance is known can be obtained, a constant mass of an internal standard substance is mixed with the test substance with a known mass ratio, and By using the X-ray diffraction intensity ratio with the internal standard substance for quantification, it is possible to exclude an average mass absorption coefficient that differs for each sample to be quantified (internal standard method, standard addition method). Moreover, several of the quantitative samples with different mixing ratio of the crystalline phase i ₁ and the crystalline phase i ₂ were prepared, and X-ray diffraction intensity I ₁ of the crystalline phase i ₁ crystalline phase i ₂ X by determining the ratio between the line diffraction intensity I _2, it is also possible to exclude the average mass absorption coefficient differs for each target quantitation sample (direct comparison method).

  On the other hand, when a sample to be measured is not available, a pure substance of the test substance or a mass ratio of the test substance is not available, the theory is calculated from the X-ray diffraction intensity measured by the X-ray diffraction method and the structure model of the sample to be measured. In general, the Rietveld method is used to obtain the mass ratio of the test substance based on the X-ray diffraction intensity calculated on the basis of the X-ray diffraction intensity.

X-ray diffraction handbook, Rigaku Corporation, February 21, 2000, 3rd edition, pages 62-71

  However, when measuring the mass ratio of a test substance using the internal standard method or standard addition method, the sample to be quantified must be powdered in order to uniformly mix the internal standard substance with the sample to be quantified. Sample preparation may be difficult or impossible. For example, when quantifying the corrosion product generated on the surface of the steel material, it is necessary to separate the corrosion product from the steel material, and alteration of the corrosion product at this time may be a problem. In addition, it is very difficult to powder a material with very high hardness such as sintered ceramics. Furthermore, it takes time to create a calibration curve for each test substance to be quantified.

  In addition, when quantification is performed using the direct comparison method, it is not necessary to mix the internal standard substance with the sample to be quantified, but the applicable sample to be quantified is limited to a two-component system or a calibration curve for each component. It takes time to create. In addition, when measuring the mass ratio of the test substance using the Rietveld method, it takes time to input parameters for the theoretical calculation for each sample, and the profile of the theoretical calculation diffraction pattern for the X-ray diffraction pattern of the sample to be determined. Advanced knowledge such as fitting know-how is required.

  For the above reasons, there are limits to the application of quantitative methods using X-ray diffraction to a wide range of general materials, and there are many restrictions even when used industrially for purposes such as quality assurance and quality control. Occurs. For this reason, provision of the technique which can measure easily the abundance of the substance which comprises material using X-ray diffraction method was anticipated.

  The present invention has been made in view of the above problems, and its purpose is to provide a crystal phase using X-ray diffraction that can easily measure the content of a substance constituting the material using an X-ray diffraction method. It is to provide a quantitative method.

  In order to solve the above-described problems and achieve the object, the method for quantifying a crystalline phase using X-ray diffraction according to the first aspect of the present invention provides a method for determining the content of a plurality of crystalline phases in each reference sample. A step of measuring the X-ray diffraction intensity of the crystalline phase as a reference intensity, a step of measuring the X-ray diffraction intensity of each crystalline phase in the sample to be quantified as a quantitative intensity, and the quantitative intensity of each crystalline phase for each crystalline substance Dividing by the reference intensity of the phase and multiplying the divided value of each crystalline phase by the content of each crystalline phase in the reference sample as an index value for each crystalline phase; and The ratio of the index values is used as the ratio of the content of each crystalline phase in the sample to be quantified, or the value obtained by dividing the index value of each crystalline phase by the sum of the index values of all crystalline phases Calculating at a time as the content of each crystalline phase in Characterized in that it comprises a.

  In order to solve the above-described problems and achieve the object, the method for quantifying a crystalline phase using X-ray diffraction according to the second aspect of the present invention provides each of the reference samples in which the contents of the plurality of crystalline phases are known. A step of measuring the X-ray diffraction intensity of the crystalline phase as a reference intensity, a step of measuring the X-ray diffraction intensity of each crystalline phase in the sample to be quantified as a quantitative intensity, and optionally one crystalline phase, a standard crystal In each sample to be quantified and reference sample, the ratio of the quantitative strength of each crystalline phase to the quantitative strength of the standard crystalline phase is determined as the relative strength of the crystalline phase, and for each crystalline phase, The value obtained by dividing the relative intensity in the sample to be measured by the relative intensity in the reference sample multiplied by the ratio of the content of each crystalline phase in the reference sample to the standard crystalline phase in the reference sample is the standard for each crystalline phase in the sample to be measured. Crystalline phase Characterized in that it comprises the steps of: calculating a ratio of the content against.

  The crystal phase quantification method using X-ray diffraction according to the present invention is characterized in that, in the above invention, the reference intensity of each crystalline phase is calculated by theoretical calculation.

  According to the method for quantifying a crystalline phase using X-ray diffraction according to the present invention, the quantitative intensity and reference intensity of X-ray diffraction with a plurality of different plane indices are measured for one or more crystalline phases in the above invention, For each surface index, determine the value obtained by dividing the quantitative strength by the reference strength, then determine the average value of the division values obtained for each surface index, and then calculate the average value for each crystalline phase in the reference sample. A value obtained by multiplying the content of is calculated as an index value of the crystalline phase.

  According to the crystal phase quantification method using X-ray diffraction according to the present invention, the content of a substance constituting the material can be easily measured using the X-ray diffraction method.

FIG. 1 is a flowchart showing the flow of a crystal phase determination method using X-ray diffraction according to an embodiment of the present invention.

  Hereinafter, a flow of a crystal phase determination method using X-ray diffraction according to an embodiment of the present invention will be described with reference to the drawings. The crystal phase quantification method using X-ray diffraction according to an embodiment of the present invention is applicable even if there is a crystalline phase or an amorphous phase that is not subject to quantification other than the crystalline phase that is subject to quantification. It can be applied regardless. Hereinafter, what is described as a crystalline phase is a crystalline phase to be quantified, and does not include a crystalline phase that is not to be quantified. Hereinafter, the content of the crystalline phase indicates the content of each crystalline phase with respect to the entire crystalline phase to be quantified (the sum of the crystalline phases to be quantified).

[Concept of the present invention]
First, the concept of the present invention will be described.

If the material constituting the sample to be quantified is all crystalline, or the amorphous component in the sample to be quantified is not an important constituent material, the content of only the crystalline phase in the sample to be quantified If it is sufficient to measure the ratio of each crystalline substance to the sum of the crystalline phases) or the ratio of the content, the method of the present invention can be used. In Equation (1), the constant K _{i of} each test component (each crystalline phase to be quantified) i, the X-ray diffraction intensity I _i of each test component i, and each test component i We can represent the relationship between the weight ratio W _i. Further, when the above-described mathematical expression (1) is modified, the constant K _i can be expressed as the following mathematical expression (2). (Μ / ρ) in the formula (2) is an average mass absorption coefficient of the sample to be quantified. Further, the mass ratio W _si of each test component i in the reference sample, the X-ray diffraction intensity I _si of each test component i, and the constant K _i satisfy the relationship represented by the following mathematical formula (3). Note that (μ / ρ) _s in Equation (3) represents the average mass absorption coefficient of the reference sample.

On the other hand, the mass ratio W _i of the test components i of the quantitative sample can be expressed as Equation (4) shown below from Equation (1). Therefore, by substituting Equation (3) for the constant K _i in Equation (4), the mass ratio W _i of the test component i in the sample to be quantified is expressed as Equation (5) below. The Further, in this case, (μ / ρ) / (μ / ρ) _s in the formula (5) is determined by the sample to be quantified and the reference sample, and is a constant regardless of the type of the test component i. By expressing it as a constant a, the mass ratio W _i of each test component i in the sample to be measured can be expressed as the following formula (6).

From the above, when all of the plurality of test components contained in the sample to be quantified are in the crystalline phase, or the content rate of only the crystalline phase in the sample to be quantified (of the crystalline phase to be quantified). If it is sufficient to measure the ratio of each crystalline substance to the sum) or the content ratio, the X-ray diffraction intensity I of the reference sample whose mass ratio W _si of the test component i is known, as shown in Equation (6) _{Let si} be the reference intensity, the mass ratio W _si be the reference mass ratio, divide the X-ray diffraction intensity I _i of the test component i in the sample to be quantified by the reference intensity I _si and divide the divided value by the reference mass ratio W _si . The multiplied value is calculated as the index value of each test component i, and the value obtained by dividing the index value of each test component i by the sum of the index values of all the test components i is calculated as the content rate of the test component i. . Or the ratio of the content rate of each test component can be calculated | required with the ratio of the index value of each test component.

Of course, it is within the scope of the present invention to use a calculation method that is mathematically equivalent to the above as shown below, regardless of the calculation method. That is, any one crystalline phase is selected as a standard crystalline phase (standard test component j), and in each of the sample to be quantified and the reference sample, the quantitative strengths I _i and I _si of each crystalline phase are determined. The ratio of the crystalline phase to the quantitative strength I _j I _{sj is} determined as the relative strength R _i (= I _i / I _j ), R _si (= I _si / I _sj ) of the crystalline phase, and for each crystalline phase, The value obtained by multiplying the relative intensity R _{i of the} sample to be quantified by the relative intensity R _si of the reference sample multiplied by the ratio of the content ratio of each crystalline phase in the reference sample to the standard crystalline phase (W _si / W _sj ). It can also be calculated as the ratio of the content of each crystalline phase to the reference crystalline phase in the sample to be determined.

As the reference intensity I _si , either an actual measurement value or a theoretical calculation value may be used. Further, as the mass ratio W _si of the test component i, even if the mass ratio of the test component i in the reference sample is unknown, the ratio of the test component i in the reference sample to the sum of all the test components, Alternatively, if the ratio between test components is known, it can be used. In addition, as described above, the method of the present invention allows the crystalline phase not to be quantified in addition to the crystalline phase to be quantified in the sample to be quantified. When the X-ray diffraction peak does not overlap with the X-ray diffraction peak of the crystalline phase to be quantified, the crystalline phase to be quantified can be obtained by applying the method of the present invention only to the crystalline phase to be quantified. It can use as a method of calculating | requiring the ratio or content rate of a content rate.

According to such a crystal phase quantification method using X-ray diffraction according to the present invention, an internal standard substance is unnecessary, and it is not necessary to prepare a calibration curve. Even when the reference intensity I _si is calculated by theoretical calculation, it is only necessary to once calculate the X-ray diffraction intensity when the pure substance of the test substance is mixed. Therefore, according to the crystal phase quantification method using X-ray diffraction according to the present invention, the content rate of substances constituting the material can be easily measured using the X-ray diffraction method.

In the crystal phase quantification method using X-ray diffraction according to the present invention, simpler quantification is possible by using an equal amount mixture of the test component i as a reference sample. That is, in an equal amount mixture of the test component i, the mass ratios W _i of the test components _i are equal, so the ratio of the X-ray diffraction intensity I _i between the test components i corresponds to the ratio of the constant K _i. It will be. Specifically, since (μ / ρ) _s / W _si is a constant in an equal mixture of the test component i, if this is expressed as a constant b in the above-described equation (3), the constant K _i is shown below. It is expressed as Equation (7). Thus, by substituting Equation (7) for the constant K _i in Equation (1), the mass ratio W _i of the test component i is expressed as Equation (8) below.

Since (μ / ρ) / b in Equation (8) is a constant, by expressing this as a constant c, the mass ratio W _i of the test component i is expressed as shown in Equation (9) below. . Therefore, the X-ray diffraction intensity of the test component i in the sample to be measured is divided by the X-ray diffraction intensity of the test component i in the reference sample by using an equal mixture of the test component i as the reference sample. The division value is calculated as the index value of each test component i, and the value obtained by dividing the index value of each test component i by the sum of the index values of all the test components i is calculated as the content rate of the test component i. be able to. Moreover, the ratio of the content rate of each test component can be obtained from the ratio of the index values of each test component.

  As the X-ray diffraction peak used for quantification, it is desirable to use an X-ray diffraction peak that does not overlap with the X-ray diffraction peaks of other test components and has high intensity. A plurality of X-ray diffraction peaks used for quantification may be used for each test component i. In other words, if the sample intensity is different from the ideal peak intensity ratio of the non-oriented sample, the accuracy of the quantitative value will decrease, but the use of multiple diffraction peaks can reduce the effect of the sample orientation. There is. At this time, for one or more crystalline phases, the quantitative intensity and the reference intensity of X-ray diffraction with a plurality of different plane indices are measured, and a value obtained by dividing the quantitative intensity by the reference intensity in each plane index is obtained. Then, an average value of the division values in each plane index can be obtained, and then a value obtained by multiplying the average value by the content of each crystalline phase in the reference sample can be calculated as an index value of the crystalline phase.

[Quantification method of crystal phase using X-ray diffraction]
Next, with reference to FIG. 1, a method for quantifying a crystal phase using X-ray diffraction, which is an embodiment of the present invention, will be described. FIG. 1 is a flowchart showing the flow of a crystal phase determination method using X-ray diffraction according to an embodiment of the present invention.

In the crystal phase quantification method using X-ray diffraction which is one embodiment of the present invention, first, each crystal in a reference sample in which the content ratio of a plurality of crystalline phases (quantitative substance, test substance) is known. The X-ray diffraction intensity I _si of the mass phase is measured as a reference intensity (step S1). Next, the X-ray diffraction intensity I _i of each crystalline phase in the sample to be quantified is measured as the quantitative intensity (step S2). Then, the quantitative strength I _i of each crystalline phase is divided by the reference strength I _si of each crystalline phase, and the divided value of each crystalline phase is the mass ratio (or content) W _si of each crystalline phase in the reference sample. Is calculated as the index value of each crystalline phase, and the ratio of the index values of each crystalline phase is used as the ratio of the content ratio of each crystalline phase, or the index value of each crystalline phase is the total crystal A value obtained by dividing by the sum of the index values of the quality phase is calculated at once as the content of each crystalline phase in the sample to be quantified (step S3).

  According to the crystal phase quantification method using X-ray diffraction as one embodiment of the present invention, an internal standard substance is unnecessary, and it is not necessary to prepare a calibration curve. Further, even when the X-ray diffraction intensity of the reference sample is calculated by theoretical calculation, it is only necessary to once calculate the X-ray diffraction intensity when the pure substance of the quantitative substance is mixed. Therefore, according to the crystal phase quantification method using X-ray diffraction which is one embodiment of the present invention, the content of a plurality of crystalline phases constituting the material is easily measured using the X-ray diffraction method. be able to.

[Example 1]
Anatase (Anatase), rutile (Rutile), and titanium nitride (TiN) were mixed in the ratios shown in Table 1 below to prepare an equivalent mixture sample and a sample to be quantified. In order to reduce the orientation of the sample as much as possible, the X-ray diffraction pattern of each sample prepared by filling the sample holder with the sample being applied with as little pressure as possible was measured by in-plane rotation of the sample by the θ-2θ method. CuKα rays were used as the X-ray source. For the determination, 101, 110, and 200 reflections were used for anatase, rutile, and titanium nitride, respectively. However, the reflection used for quantification is not limited to this. Table 1 below shows the X-ray diffraction intensities of the equivalent mixture sample and the sample to be determined. The quantitative values of anatase, rutile, and titanium nitride in the sample to be quantified are the X-ray diffraction intensities of Anatase, rutile, and titanium nitride in the equivalence mixture sample, respectively, As, Rs, and Ts. , Rutile, and titanium nitride were calculated by the following mathematical formulas (10) to (12) as Ai, Ri, and Ti, respectively.

  As shown in Table 1, the quantitative values calculated by the quantitative method according to the present invention are in good agreement with the mixing ratio of each component. Thus, it was confirmed that according to the crystal phase quantification method using X-ray diffraction according to the present invention, the content of the substance constituting the material can be easily measured using the X-ray diffraction method.

[Example 2]
Depending on the sample, the probability of the quantitative value may decrease due to the sample orientation.In this case, as shown below, the influence of the sample orientation may be reduced by using multiple diffraction lines. is there. Specifically, in Example 2, anatase (Anatase), rutile (Rutile), and titanium nitride (TiN) were mixed in the ratios shown in Table 2 to prepare an equal mixture sample and a test sample. For the test sample of Example 2, the sample preparation method that avoids sample orientation as in Example 1 was not used. The X-ray diffraction patterns of these test materials were measured by the θ-2θ method. In Example 2, the sample was not rotated in the sample plane except for an equal amount of the mixed sample. CuKα rays were used as the X-ray source. Anatase, rutile, and titanium nitride were quantified using 101, 110, and 200 reflections, respectively. Since rutile was particularly affected by sample orientation, quantification was also performed using three diffraction lines 101 and 111 in addition to 110. Measurement conditions and reflection used for quantification are not limited to these. Table 2 shows the diffraction intensities of the equivalent mixture sample and the test sample.

  Here, the diffraction intensities of anatase, rutile, and titanium nitride in the equivalent mixed sample are As, Rs, and Ts, respectively, and the diffraction intensities of anatase, rutile, and titanium nitride in the test sample are respectively Ai, Ri, and Ti, Quantitative values of anatase, rutile, and titanium nitride in the test sample were calculated by Equations (10) to (12). Regarding rutile, the results of quantification using only 110 reflection as diffraction lines and the results of quantification using three diffraction lines (110 reflection, 101 reflection, and 111 reflection) are shown in Table 3. When three diffraction lines are used, three Ri / Rs in each case are obtained, and an average of them is defined as Ri / Rs of rutile, and anatase, rutile, and The quantitative value of titanium nitride was calculated.

  In Example 2, as shown in Table 3, when only the rutile 110 reflection was used, a discrepancy between the quantitative value and the actual mixing ratio was recognized due to the influence of the sample orientation. On the other hand, when three rutile reflections were used, a quantitative value that closely matched the mixing ratio was obtained. From the above, according to the method of the present invention, the internal standard substance is not mixed with the test sample, the profile fitting is not performed on the X-ray diffraction pattern of the test sample, and It was confirmed that quantification was possible without preparing a calibration curve.

Claims (4)

A method for quantifying a crystalline phase using X-ray diffraction that measures the content of a plurality of crystalline phases in a sample to be quantified using an X-ray diffraction method,
Measuring the X-ray diffraction intensity of each crystalline phase in a reference sample having a known content of a plurality of crystalline phases as a reference intensity;
Measuring the X-ray diffraction intensity of each crystalline phase in the sample to be quantified as a quantitative intensity;
The index value of each crystalline phase is obtained by dividing the quantitative strength of each crystalline phase by the reference strength of each crystalline phase and multiplying the divided value of each crystalline phase by the content of each crystalline phase in the reference sample. As a step of calculating as
The ratio of the index values of each crystalline phase is the ratio of the content of each crystalline phase in the sample to be quantified, or the value obtained by dividing the index value of each crystalline phase by the sum of the index values of all crystalline phases Calculating at a time as the content of each crystalline phase in the sample to be quantified,
A method for quantifying a crystal phase using X-ray diffraction, which comprises: A method for quantifying a crystalline phase using X-ray diffraction that measures the content of a plurality of crystalline phases in a sample to be quantified using an X-ray diffraction method,
Measuring the X-ray diffraction intensity of each crystalline phase in a reference sample having a known content of a plurality of crystalline phases as a reference intensity;
Measuring the X-ray diffraction intensity of each crystalline phase in the sample to be quantified as a quantitative intensity;
Arbitrarily select one crystalline phase as the standard crystalline phase, and in each of the sample to be quantified and the reference sample, the ratio of the quantitative strength of each crystalline phase to the quantitative strength of the standard crystalline phase Obtained as relative strength, and for each crystalline phase, the value obtained by dividing the relative strength in the sample to be quantified by the relative strength in the reference sample multiplied by the ratio of the content ratio of each crystalline phase in the reference sample to the reference crystalline phase Calculating the ratio of the content of each crystalline phase to the reference crystalline phase in the sample to be quantified;
A method for quantifying a crystal phase using X-ray diffraction, which comprises:   3. The method for quantifying a crystalline phase using X-ray diffraction according to claim 1, wherein the reference intensity of each crystalline phase is calculated by theoretical calculation.   For one or more crystalline phases, measure the quantitative intensity and the reference intensity of X-ray diffraction with a plurality of different plane indices, and determine the value obtained by dividing the quantitative intensity by the reference intensity in each plane index; An average value of division values in each plane index is obtained, and then a value obtained by multiplying the average value by the content of each crystalline phase in the reference sample is calculated as an index value of the crystalline phase. Item 4. A method for quantifying a crystal phase using X-ray diffraction according to Item 1 or 3.

Images