JP2002039971A - Simple method for determining zirconia crystal phase ratio by x-ray diffraction pattern - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for quickly and highly accurately determine ratios of crystal phases in a zirconia crystal. SOLUTION: According to this simple method for determining the ratio of each of monoclinic, tetragonal and cubic crystal phases in the zirconia crystal, an actual measurement X-ray diffraction pattern of the crystal to be determined is simulated with the use of an X-ray diffraction pattern of each of monoclinic, tetragonal and cubic crystals preliminarily measured to be a standard, and the ratio is calculated from the obtained parameter ratio.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for quickly and accurately determining the proportion of each crystal phase in a zirconia crystal by using an X-ray diffraction pattern.

[0002]

2. Description of the Related Art Zirconia ceramics have high fracture toughness,
Because of its excellent physical, chemical, and mechanical properties such as high strength, low thermal conductivity, good thermal shock resistance, corrosion resistance, chemical resistance, and high-temperature conductivity, it is used as various structural materials.

One of the factors affecting these characteristics is
There is a crystal structure. Pure zirconia has a crystal structure that is stabilized by temperature, and zirconia ceramics and its raw material powders are mixed with various crystal stabilizers such as yttrium oxide to provide the desired properties at the operating temperature. The structure is stabilized. Therefore, it is necessary to rapidly and accurately analyze the raw material powder and the crystal phase ratio of zirconia ceramics in product management and development studies for adding new functions or improving conventional characteristics.

[0004] Zirconia generally has three stable crystal phases, monoclinic, tetragonal, and cubic, and these crystal information is reflected in the X-ray diffraction pattern. At present, there are two methods for quantifying the crystalline phase ratio of zirconia using X-ray diffraction patterns.

[0005] One is a very quick method which is obtained from the ratio of the intensity of the diffraction peak characteristic of each crystal phase.

However, in this method, the diffraction patterns of tetragonal and cubic cannot be separated, and the ratio of the monoclinic phase can be determined, but the ratio of the tetragonal and cubic phases cannot be determined. There is a disadvantage that.

As a second method, there is a Rietveld analysis method for simulating an X-ray diffraction pattern based on crystallographic theory. According to this method, the ratio of each of the monoclinic, tetragonal, and cubic crystal phases can be determined with high accuracy.

However, this Rietveld analysis method uses S /
Since a high-precision X-ray diffraction pattern with good N is required, there is a problem that the measurement time for one sample is very long, about 10 hours, and the efficiency is low. In addition, the simulation requires a high degree of specialized knowledge of crystallography, so that there is a problem that the number of people who can perform the simulation is very limited. Further, there is a problem that the simulation itself takes time.

[0009]

SUMMARY OF THE INVENTION An object of the present invention is to solve the above-mentioned problems and to provide a method for quickly and accurately determining the ratio of the crystal phase in zirconia crystals.

[0010]

Means for Solving the Problems The inventors of the present invention have conducted intensive studies to solve the above-mentioned problems, and as a result, the proportion of each of the monoclinic, tetragonal, and cubic crystal phases in the zirconia crystal was measured in advance. Actual measurement of the crystal to be quantified using the X-ray diffraction pattern of each of the standard monoclinic, tetragonal, and cubic crystals
By simulating a line diffraction pattern and calculating the obtained parameter ratios, it was found that the respective crystal phase ratios in the zirconia crystal could be obtained simply and with high accuracy, and the present invention was completed.

More specifically, in the method for determining the crystal phase ratio in the zirconia crystal from the X-ray diffraction pattern,
And the corresponding diffraction positions of the X-ray diffraction pattern of the target crystal and the combined X-ray intensity given by the linear combination of the X-ray intensities at the same diffraction position of each of the X-ray diffraction patterns of the three standard crystal phases In the simulation that minimizes the difference from the measured X-ray intensity in the above, parameters a, b, and c are determined so as to minimize the residual sum of squares shown in Expression 7, and the respective crystal phase ratios in the zirconia crystal are determined. The present invention relates to a method of quantification, that is, a multiple regression analysis method, and further relates to determining each crystal phase ratio by Expressions 8 to 10.

[0012]

(Equation 6)

A, b, c: parameters 2θ: measured diffraction angle (°) in X-ray diffraction pattern I (synthetic (2θ)): synthetic X-ray intensity at 2θ of X-ray diffraction pattern I (monoclinic (2θ) ): X-ray intensity at 2θ of X-ray diffraction pattern of standard monoclinic crystal I (tetragonal (2θ)): X-ray intensity at 2θ of X-ray diffraction pattern of standard tetragonal crystal I (cubic (2θ)) : X-ray intensity at 2θ of X-ray diffraction pattern of standard cubic crystal

[0014]

(Equation 7)

I (target crystal (2θ)): X-ray intensity at 2θ of the X-ray diffraction pattern of the target crystal where 2θ = Start + k × Step (k = 0,1,2... N−
1) Start: Minimum 2θ of measured X-ray diffraction pattern k: Number of each X-ray intensity of measured X-ray diffraction pattern 2θ = S
Number when counting from low angle to high angle with tart as 0 n: Total number of data points of measured X-ray diffraction pattern Step: Measurement step angle of measured X-ray diffraction pattern

[0016]

(Equation 8)

W1 (monoclinic): ratio of monoclinic phase of standard monoclinic crystal (%) W2 (monoclinic): ratio of monoclinic phase of standard tetragonal crystal (%) W3 (monoclinic) ): Ratio of monoclinic phase of standard cubic crystal (%)

[0018]

(Equation 9)

W1 (tetragonal): ratio of tetragonal phase of standard monoclinic crystal (%) W2 (tetragonal): ratio of tetragonal phase of standard tetragonal crystal (%) W3 (tetragonal): standard cubic Of tetragonal phase of polycrystalline (%)

[0020]

(Equation 10)

W1 (cubic): ratio of cubic phase of standard monoclinic crystal (%) W2 (cubic): ratio of cubic phase of standard tetragonal crystal (%) W3 (cubic): standard cubic The present invention will be described in detail below.

The sample to be treated in the method of the present invention is not particularly limited as long as it contains zirconia crystal as a main component, and yttrium oxide, calcium oxide, cerium oxide or the like is added as a crystal stabilizer. It can also be applied to various partially stabilized zirconia. The form of the target sample is not particularly limited as long as it can perform X-ray diffraction pattern measurement, and may be in a powder state or a sintered state.

Monoclinic, tetragonal,
The ratio of each crystal phase is determined for the cubic crystal sample, and there is no particular limitation as long as the ratio of the crystal phase ratio is not equal between the standard samples. Those having a crystal phase ratio of 90% or more are desirable.

The respective crystal phase ratios of the present invention are defined by the following formulas (α), (β), and (γ).

Monoclinic phase = 100 × (Wm) / (Wm + Wt + Wc) (α) Tetragonal phase = 100 × (Wt) / (Wm + Wt + Wc) β) Cubic phase = 100 × (Wc) / (Wm + Wt + Wc) (γ) (Wm, Wt, and Wc in the formula are monoclinic, tetragonal, and cubic, respectively, in the sample.) Hereinafter, specific embodiments of the present invention will be described, but the present invention is not limited thereto.

1) Measurement of X-ray Diffraction Pattern The X-ray diffraction patterns of each of the standard monoclinic, tetragonal, and cubic crystal phases and the crystal sample to be quantified are measured. An X-ray diffraction pattern measuring device is a normal X-ray diffraction pattern.
There is no particular limitation as long as it is a line diffraction apparatus, but an apparatus capable of step scanning is desirable. The region of the X-ray diffraction pattern to be used is not particularly limited, but 2θ is from 20 ° to 90 °.
Is desirable. Further, the measurement interval and the measurement time at each measurement point are not particularly limited, but are preferably about 0.04 ° to 1 ° and about 1 second to 4 seconds, respectively.

2) Digitization of Diffraction Patterns The X-ray diffraction patterns of the standard crystal sample and the target crystal sample are compiled into data points in which the measured 2θ and the measured X-ray intensity are paired.
The number of data points is determined by the operation range of measurement 2θ and the increment of 2θ.

For example, when the measurement 2θ range is from 20 ° to 90 ° and the interval is 0.04 °, the number of data points is 1750.

The data of the X-ray diffraction pattern used in the simulation of the present invention may be used by extracting a plurality of all or a part of the measured diffraction pattern.

Further, the pre-processing of the data used for the simulation is not particularly limited, but a method of making the width of the maximum intensity and the minimum intensity constant in a specific region, and a method of keeping the width of the maximum intensity and the minimum intensity constant in all the regions. Is desirable. Here, the specific region is a region including one or more diffraction peaks in a diffraction pattern used for the simulation.

3) Minimization of the residual sum of squares of the X-ray intensity of the target crystal and the synthetic X-ray intensity This operation corresponds to the simulation operation of the present invention.

By substituting the X-ray intensity of each 2θ obtained in 2) for the target crystal and the standard sample into the above equation 7, the X-ray diffraction pattern of the target crystal and each X-ray intensity of the synthetic X-ray diffraction pattern are calculated. The residual sum of squares is obtained, and the parameters a, b, and c of the above-described Expression 6 that minimize this value are obtained.

This simulation calculation is based on the statistical analysis method.
One method is multiple regression analysis.

That is, the X-ray diffraction patterns of the monoclinic, tetragonal, and cubic standard crystal samples are defined as explanatory variable 1, explanatory variable 2, and explanatory variable 3, respectively. By performing multiple regression analysis calculations using the corresponding X-ray intensity as the objective variable and the value of each variable, the regression coefficients of the explanatory variables 1, 2, and 3 can be used as the regression coefficients of the parameters a, b, and c.
Is obtained.

4) Calculation of Crystalline Phase Ratio The values of a, b, and c obtained in 3) are calculated by the above-mentioned equations (8), (9) and (1).
By substituting 0, each crystal phase ratio of the target crystal can be obtained. Here, when each standard crystal sample used is a single crystal, Expressions 8, 9, and 10 are very simple expressions, and Expressions 11, 9 and
The parameters a, b, and c are simply represented as shown by 12 and 13.
Is the ratio of

[0036]

[Equation 11]

[0037]

(Equation 12)

[0038]

(Equation 13)

By simulating the X-ray diffraction pattern of the target crystal using the X-ray diffraction pattern of the standard sample measured in advance as described above, the monoclinic, tetragonal, and cubic crystal phase ratios can be calculated. Can be obtained simply and accurately.

[0040]

EXAMPLES The present invention will be described in more detail with reference to the following Examples, but it should not be construed that the invention is limited thereto.

In the following examples, ZrO ₂ powders having a Y ₂ O ₃ content of 0, 4, and 8 mol% were used as standard samples comprising monoclinic, tetragonal, and cubic single crystals, respectively. Except for the unknown sample 9, an unknown sample was used in which a Y ₂ O ₃ -containing partially stabilized ZrO ₂ powder having a known crystal phase ratio was mixed at an arbitrary ratio.

Table 1 shows the crystal phase ratios of the standard sample and the unknown sample.
Shown in The measurement of the X-ray diffraction pattern is 2θ in accordance with the usual method.
The range from 0.2 to 80 ° was measured in increments of 0.04 °. Therefore, the number of data points is 1496. The measurement time is about 5 per sample.
It took 0 minutes.

Example 1 1) Measurement of X-ray diffraction patterns of standard sample and unknown sample The X-ray diffraction patterns of the standard sample and unknown sample 1 shown in Table 1 were measured.

2) Digitization of Diffraction Patterns The X-ray diffraction patterns of the standard crystal sample and the target crystal sample were collected into data points obtained by measuring 2θ and X-ray intensity. Each data point was normalized to 10000.

FIGS. 1, 2, 3, and 4 show the data of the standard sample and the unknown sample 1 after the standardization.

As apparent from FIGS. 2 and 3, the diffraction patterns of the tetragonal system and the cubic system are very similar, and a specific diffraction angle is obtained.
It can be seen that the ratio between the two cannot be calculated using the X-ray intensity at 2θ.

3) Minimization of the residual sum of squares of the X-ray intensity of the target crystal and the synthetic X-ray intensity (multiple regression analysis) The synthetic X-ray intensity was calculated using the data of the standard crystals shown in FIGS. Were calculated, and the above equation parameters a, b, and c were determined so that the residual sum of squares with the data of FIG. 4 as the target crystal was minimized.

Specifically, monoclinic, tetragonal,
A multiple regression analysis was performed using the X-ray intensity of the cubic crystal as an explanatory variable and the X-ray intensity of the target crystal as an objective variable, and a regression coefficient corresponding to each parameter was obtained.

In the case of this multiple regression analysis calculation, the number of explanatory variables was 3, and the number of data was 1496 points corresponding to the number of measurement points. A = 0.064, b = 0.42, c = 0.59 from multiple regression analysis calculations
was gotten.

4) Calculation of Crystalline Phase Ratio The values of a, b, and c obtained in 3) are calculated by the above equations (11), (12),
13 and each crystal phase is monoclinic = 6%, tetragonal = 39
%, Cubic = 55%.

The quantitative results and the crystal phase ratios calculated from the mixing ratios shown in Table 1 are in good agreement with each other, and it can be seen that the respective crystal phase ratios can be determined favorably by this method.

[0052]

[Table 1]

Example 2 The crystal phase ratios of the unknown samples 2 to 8 were determined in the same manner as in Example 1, and the crystal phase ratios calculated from the mixing ratios for each crystal phase and the crystal phase ratios obtained by the method of the present invention. Figure 5 shows the relationship
6 and 7. The correlation coefficient between the quantitative value of monoclinic, tetragonal, and cubic and the crystal phase ratio calculated from the mixture ratio is
0.989, 0.998, 0.934 are high and in good correlation,
It is understood that the crystal phase ratio can be easily determined by the method of the present invention.

Example 3 The crystal phase ratio of the unknown sample 9 was determined in the same manner as in Example 1, and a comparison with the result of the conventional Rietveld analysis is shown in Table 2.

[0055]

[Table 2]

The results obtained by the method of the present invention are in good agreement with the results of the conventional Rietveld analysis method, and the quantitative values of the method of the present invention are found to be almost as accurate as the conventional Rietveld analysis method. Was.

In the Rietveld analysis, it took 15 hours including measurement and analysis. However, in the method of the present invention, it takes only 1.5 hours to measure and calculate a quantitative value, which is 1/10 of the conventional Rietveld analysis method. It was found that the method of the present invention was a very quick and simple method. In the conventional method using the peak intensity ratio, since the diffraction peaks of the tetragonal system and the cubic system overlap, it is not possible to determine the ratio of each crystal phase.

[0058]

As described above in detail, according to the present invention, the measured X-ray diffraction patterns of the crystals to be quantified using the standard X-ray diffraction patterns of monoclinic, tetragonal and cubic crystals. Is calculated, and the three parameter phases in zirconia can be quickly and accurately determined by calculating the obtained parameter ratios.

[Brief description of the drawings]

FIG. 1 shows the results of Example 1. In a graph obtained by digitizing the X-ray diffraction pattern of a monoclinic crystal of a standard sample and digitizing the result, the X axis indicates the diffraction angle, and the Y axis indicates the X-ray diffraction intensity.

FIG. 2 shows the results of Example 1. Standard sample tetragonal X
X is a graph obtained by digitizing the X-ray diffraction pattern and standardizing it.
The axis is the diffraction angle, and the Y axis is the diffracted X-ray intensity.

FIG. 3 shows the results of Example 1. Cubic X of the standard sample
X is a graph obtained by digitizing the X-ray diffraction pattern and standardizing it.
The axis is the diffraction angle, and the Y axis is the diffracted X-ray intensity.

FIG. 4 shows the results of Example 1. In the graph obtained by digitizing the X-ray diffraction pattern of the unknown sample 1, the X-axis is the diffraction angle, and the Y-axis is the diffraction X-ray intensity.

FIG. 5 shows the results of Example 2. The X axis shows the ratio of the monoclinic phase calculated from the mixing ratio, and the Y axis shows the crystal phase ratio of the monoclinic phase quantified by the method of the present invention.

FIG. 6 shows the results of Example 2. The X-axis shows the ratio of the tetragonal phase calculated from the mixing ratio, and the Y-axis shows the crystal phase ratio of the tetragonal phase determined by the method of the present invention.

FIG. 7 shows the results of Example 2. The X-axis shows the ratio of the cubic phase calculated from the mixing ratio, and the Y-axis shows the ratio of the cubic phase determined by the method of the present invention.

Claims (3)

[Claims] 1. A method for quantifying the monoclinic, tetragonal, and cubic crystal phase ratios in zirconia crystal, wherein X-rays of standard monoclinic, tetragonal, and cubic crystals are measured in advance. Actual measurement of crystal to be quantified using diffraction pattern X
A simple method for quantifying the proportion of each crystal phase in a zirconia crystal, characterized by simulating a line diffraction pattern and calculating from a parameter ratio obtained. 2. A simulation is performed with a composite X-ray intensity given by a linear combination of X-ray intensities at the same diffraction position of each X-ray diffraction pattern of three standard crystal phases represented by the following formula 1. Regarding the measured X-ray intensity at the corresponding diffraction position of the X-ray diffraction pattern of the crystal, each parameter a, such that the residual sum of squares shown by the following equation 2 is minimized:
The simple method for determining the proportion of each crystal phase in a zirconia crystal according to claim 1, which is a technique for obtaining b and c. (Equation 1) a, b, c: parameters 2θ: measured diffraction angle (°) in X-ray diffraction pattern I (synthetic (2θ)): synthetic X-ray intensity at 2θ of X-ray diffraction pattern I (monoclinic (2θ)): standard X-ray intensity at 2θ of X-ray diffraction pattern of monoclinic crystal I (tetragonal (2θ)): X-ray intensity at 2θ of X-ray diffraction pattern of standard tetragonal crystal I (cubic (2θ)): standard cubic -Ray intensity at 2θ of the X-ray diffraction pattern of the crystalline crystal I (target crystal (2θ)): X-ray intensity at 2θ of the X-ray diffraction pattern of the target crystal where 2θ = Start + k × Step (k = 0,1,2... N−
1) Start: Minimum 2θ of measured X-ray diffraction pattern k: Number of each X-ray intensity of measured X-ray diffraction pattern 2θ = S
Number when counting from low angle to high angle with tart as 0 n: Total number of data points of measured X-ray diffraction pattern Step: Measurement step angle of measured X-ray diffraction pattern 3. The parameter ratio is obtained by calculating the values of the parameters a, b, and c obtained by the simulation according to claim 2.
3. A simplified method for quantitatively determining the proportion of each crystal phase in the zirconia crystal according to claim 1 obtained by substituting the values into W1 (monoclinic): ratio of monoclinic phase of standard monoclinic crystal (%) W2 (monoclinic): ratio of monoclinic phase of standard tetragonal crystal (%) W3 (monoclinic): Ratio of monoclinic phase of standard cubic crystal (%) W1 (tetragonal): ratio of tetragonal phase of standard monoclinic crystal (%) W2 (tetragonal): ratio of tetragonal phase of standard tetragonal crystal (%) W3 (tetragonal): standard cubic crystal Ratio of tetragonal phase (%) W1 (cubic): ratio of cubic phase of standard monoclinic crystal (%) W2 (cubic): ratio of cubic phase of standard tetragonal crystal (%) W3 (cubic): standard cubic crystal Cubic phase ratio (%)