JPH02176453A - Data processing method in x-ray diffraction measurement - Google Patents

Abstract

PURPOSE:To improve measuring accuracy of the diameter of a crystal grain or lattice strain by determining a plurality of coefficients in the expression of relations with regard to the integrated widths of the peaks of diffraction angles and diffraction lines in an X-ray diffraction apparatus, and thereby comparing the integrated widths of a specimen to be measured and that of computation. CONSTITUTION:A standard specimen having the adequate diameter of a crystal grain without lattice strain is used, and an angle is scanned for an X-ray detector D. The intensity of the X rays with respect to a diffraction angle theta, i.e. the output of a rate meter R, is stored in a memory M. Integrated widths H1-H5 of about five peaks of the stored data are obtained and substituted into an expression H=a tan<2>theta+b tantheta+c. The expression is solved, and the coefficients (a), (b) and (c) are determined and stored in the memory M. A specimen to be measured is used, and the integrated widths H are computed for the diffraction peaks specified by the data from the meter R by the same way as the standard specimen. Then, the integrated width H0 of the standard specimen for the specified diffraction peak is computed by said expression. The result is compared with the width H, and the diameter of the grain and the lattice strain are computed. Therefore, the accuracy can be improved in comparison with the computation using a half value in a conventional method.

Description

DETAILED DESCRIPTION OF THE INVENTION (Field of Industrial Application) The present invention relates to a data processing method in an X-ray diffraction apparatus.

(Prior art) When measuring the crystal grain size or lattice strain of a sample using an X-ray diffraction device, conventionally, the half-value width of the diffraction peak was generally determined
The method used is to compare this with the half-width of the corresponding diffraction peak in a standard sample. However, the actually measured diffraction
The shape of the peak of the line deviates slightly from the ideal shape due to the influence of noise, etc., and the half-width includes the deviation of this peak shape from the ideal shape, and is used to measure the diameter of crystal grains. This appears as an error in the value.

(Problems to be Solved by the Invention) The present invention aims to improve the data processing method when measuring the diameter of crystal grains or lattice strain of a sample in an X-ray diffraction apparatus, thereby increasing measurement accuracy.

(Means for Solving the Problem) In an X-ray diffraction device, the relationship function between the diffraction angle θ and the integral width of the diffraction peak is expressed by a formula including a plurality of coefficients, and in this formula,
Determine the above coefficient by substituting the integral width of multiple diffraction line peaks actually measured using a standard sample, and use the determined function of the above coefficient for the diffraction angle of any diffraction line peak in the sample to be measured. Using the integral width calculated as the integral width of the diffraction line peak of the standard sample for that diffraction line peak,
The integral widths of the diffraction line peaks of the measured samples were compared.

(Function) The integral width is the value obtained by dividing the area of the peak by the peak height in any measuring device in which the measured output has a peak with respect to the independent variable. For example, if the peak is triangular, the integral width is the value of the peak base. It is 1/2 of the width of the peak, which coincides with the half value, and is a value representing the width of the peak. This integral width integrates the peak with respect to the independent variable, so
The error in the measured output corresponding to the value will be averaged,
It is a more accurate width value that characterizes a peak than the half-width. Therefore, in data processing in the measurement of diffraction X-rays, measurement accuracy can be improved by using the integral width instead of the conventionally used half-width. When a diffraction line is measured using an X-ray diffraction device, the peak width of the diffraction line becomes a function of the diffraction angle due to the characteristics of the diffraction phenomenon and the characteristics of the X-ray diffraction device. This function also varies depending on the sample, but the basic form of the function is constant, and the coefficients included in the function vary depending on the device and sample. This function form can generally be approximated with sufficient accuracy in the form (= (21tan θ + btan θ 10), where the integral width is H), where a, b, and c are coefficients determined by the equipment and sample. By actually measuring the integral width for some diffraction lines and substituting it into the above formula, the coefficients a, b, and c can be determined, so the integral width of the standard sample for any diffraction line can be calculated from the above formula.This calculation By comparing the obtained integral width with the actually measured integral width of an arbitrary diffraction line of the sample to be measured, the size of crystal grains or lattice strain can be determined.

(Example) FIG. 1 shows an example of an apparatus for carrying out the invention.

This device is an X-ray diffraction device, where G is a goniometer;
X is an X-ray source, D is an X-ray detector, and S is a sample. The output of the X-ray detector is sent to the data processing bag R via the rate meter R.
It is taken into memory M in tc.

FIG. 2 is a flowchart showing the operation of data processing device C. When the sample S is rotated by an angle θ using the apparatus shown in Figure 1,
The line detector rotates by an angle of 2θ in conjunction. The data processing device sends a pulse signal to a goniometer drive circuit (not shown) to drive the pulse motor, rotates the sample S, and rotates the sample S at a rotation angle of θ.
The pulses sent to the drive circuit are counted and detected, and the output of the rate meter R is taken into the memory M using this angle data as address designation data for the memory. The operating sequence is explained with reference to Fig. 2. Using a standard sample, that is, a sample with no lattice distortion and an appropriate crystal grain size, the X-ray detector is angularly scanned, and the X-ray intensity with respect to the diffraction angle θ, that is, the rate meter R is measured. The output of is taken into the memory M (a), and the integral width of 5 (not necessarily 5, it is better to have a larger number) peaks specified in advance for the taken data is determined (see). To calculate this integral width, find the peak center height of the specified peak (which can be specified by the diffraction angle or the specified number from the innermost diffraction peak), determine the half-width, and calculate the height of the peak center. Calculate by integrating the X-ray intensity of one peak over an angular range of, for example, five times the half width on both high and low angles around the diffraction angle, and dividing the integrated value by the peak height.Next, specify When the integral widths for the five peaks obtained are Hl, H2, H3, H4, and H5, these values are expressed as H= (21tan"θ+btanθ+c) - (
Substitute H in 1) to create five equations, solve them, determine coefficients a, b, and c, and store them in memory M (c). In this calculation, there are three unknowns, and the equation is Since there are 5, a, b, and c are determined by the least squares method. By introducing the least squares method, the errors in the measured integral widths of the individual peaks are averaged, improving the accuracy of coefficient determination. After the preparation operation is completed,
Wait until the sample to be measured is set, and once the sample to be measured is set, start the measurement operation. The measurement operation is the same as for the standard sample, and the diffraction X-ray intensity data is imported into the memory M using the rotation angle θ of the sample as addressing data.2)
Start data processing operation. Data processing calculates the integral width for the designated diffraction peak (e). This calculation is performed in the same manner as in step (b) above. Next, calculate the integral width of the diffraction peak of the standard sample with respect to the specified diffraction peak. This calculation is described in (1) above.
H is calculated by entering the values determined in step (c) into a, b, and c of the equation, and substituting the diffraction angle θ of the designated diffraction line peak of the sample to be measured. The crystal grain size or lattice strain is calculated by comparing the integral width H of the designated diffraction peak of the measured sample obtained in this way with the corresponding integral width Ho of the diffraction peak of the standard sample. Finish the action.

(Effects of the Invention) According to the present invention, the crystal grain diameter and lattice strain, which were conventionally calculated from the half-width, can now be calculated using the integral width, making it possible to further improve measurement accuracy.

[Brief explanation of the drawing]

FIG. 1 is a block diagram of an example of an apparatus for carrying out the method of the present invention, and FIG. 2 is a flowchart of the operation of the apparatus. G: goniometer, X: X-ray source, D: X-ray detector, M: memory, C: data processing device.

Claims (1)

[Claims] In an X-ray diffractometer, the above coefficients are calculated by substituting the integral width of multiple diffraction line peaks actually measured using a standard sample into the relational expression that includes multiple coefficients between the diffraction angle θ and the integral width of the diffraction line peak. is determined, and the integral width of an arbitrary diffraction line peak in the sample to be measured is compared with the calculated integral width for the same diffraction line peak calculated by the formula in which the coefficient is determined. Data processing method for X-ray diffraction measurements.