JPH0868702A - X-ray stress measuring method - Google Patents

Abstract

PURPOSE: To realize highly accurate measurement of stress by increasing the number of set inclination angles depending on the required accuracy of measurement, employing the angle at the center of gravity of each diffraction line profile as a diffraction angle, and weighting the interplanar spacing with the integration intensity of diffraction line profile for each inclination angle. CONSTITUTION: A sample 1 is irradiated with an incident X-ray 2 having wavelength λ and the X-ray is diffracted on the crystal lattice plane F having interplanar spacing of (a) to produce a diffracted X-ray 3. The number of set inclination angle ϕ of the lattice plane F is increased as the accuracy required for the measurement of stress increases and then the diffraction line profile is measured for each inclination angle ϕ. Subsequently, the center of gravity is determined for the profile thus measured and the corresponding angle is set at the diffraction angle θ for the inclination angle ϕ. The distance (d) is then determined according to a formula; 2dsinθ=nλ (n: integer) and weighted with the integration intensity I of each profile thus describing a graph d-sin<2> θ. The processing is repeated for all measuring points thus determining the stress from the d-sin<2> ϕ graph with high accuracy.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an X-ray stress measuring method suitable for measuring stress on a coarse grain sample or a minute portion.

[0002]

2. Description of the Related Art FIG. 2 shows a relationship between a sample for stress measurement and X-rays applied to the sample. In FIG. 2, 1 is a sample to be measured, 2 is an incident X-ray that is irradiated on the sample 1 for stress measurement, 3 is a diffracted X-ray, and F is a crystal lattice plane F that contributes to the diffraction of the incident X-ray 2. , H is the sample 1
, Mo is a sample surface normal M perpendicular to the sample surface H.
o and M are crystal lattice plane normals perpendicular to the crystal lattice plane F, and d
Is the inter-lattice plane distance, which is the distance between the crystal lattice planes F, and ψ is the angle between the sample surface normal Mo and the crystal lattice plane normal M (that is, the inclination of the crystal lattice plane F, hereinafter referred to as the tilt angle). ).

Conventionally, when measuring the stress σ acting on the crystal lattice plane F, first, a diffraction line profile at the tilt angle ψ is measured, and the diffraction angle θ (incident X-ray 2 And half of the angle formed by the diffracted X-ray 3), and based on the diffraction angle θ, the following formula (1)
The inter-lattice plane distance d is obtained from the Bragg equation shown in.

2dsin θ = nλ (1) In the above formula (1), λ is the wavelength of the incident X-ray 2, and
n is a positive integer (usually n = 1).

Next, the calculated inter-lattice distance d is substituted into the following equation (2) to obtain the stress σ d = σ · const-sin ² ψ (2) In the above equation (2), const Is a constant determined by the crystal lattice plane to be measured and the elastic coefficient of the sample.

FIG. 3 shows an example of a diffraction line profile (diffraction X-ray intensity profile) measured at a certain tilt angle ψ. The example shown here is for the case where the number of crystal grains contributing to diffraction in the measurement sample is sufficiently large and the diffracted X-ray intensity is sufficiently high, and a smooth profile having one peak value in the center Has become.

As a typical method of determining the diffraction angle θ from such a profile, a half-value width method, a parabolic approximation method, a center of gravity method, etc. are known.

In the full width at half maximum method, a center line parallel to the background is drawn at a height of 1/2 of the peak value Ip of the diffraction line profile, and the angle .theta. It is what In the parabolic approximation method, several points are selected near the apex of the diffraction line profile, a parabola passing through these points is obtained by the least squares method, and the angle θ at the apex position of the parabola is taken as the diffraction angle. The centroid method is an angle θ of the centroid position w of a diffraction line profile (diffraction intensity curve) in an appropriate angle range including the peak position.
Is the diffraction angle.

When one peak value is significant as shown in FIG. 3, it is possible to simply use the angle of the peak position as the diffraction angle, and the half width method, parabola approximation method, and center of gravity method described above can be used. Any of the above can be used, and the diffraction angle can be set relatively easily and with a small error by any method.

Theoretically, two points are set as the tilt angle ψ, a diffraction line profile is obtained for each of the tilt angles ψ ₁ and ψ ₂ , and a diffraction angle θ is determined for each diffraction line profile to determine the above-mentioned. If the inter-lattice surface distance d is calculated by the equation (1), the solution can be obtained by the equation (2). However, generally, in consideration of the measurement error, four points are set as the inclination angle ψ and the processing is performed. Then, when two or more points are set as the inclination angle ψ, a statistical process such as the least square method is used.

FIG. 4 shows the above equation (2), d
It is called a −sin ² ψ diagram, and λ can be obtained from the slope of the d-sin ² ψ line. In order to improve the accuracy of the stress value σ to be obtained, it is necessary to obtain d with higher accuracy.

[0012]

By the way, the above-mentioned formula (2) used in the conventional stress measuring method for obtaining the stress σ from the value of the inter-lattice distance d is large in the number of crystal grains and completely non-oriented. It is not suitable for the case where a crystalline polycrystal is used as a measurement sample and the measurement target is limited to a coarse grain material having a small number of crystal grains or a minute region.

There are two reasons for this.

One is diffraction X for coarse-grained materials and minute areas.
In the measurement of the X-ray, few crystal grains contribute to the X-ray diffraction, and the variation in the directionality of the crystal grains also greatly affects the measured diffraction line profile, as shown in FIG. Diffraction lines from are shown in a separated state, and a smooth profile cannot be obtained. Therefore, it is considered that it is difficult to determine the diffraction angle θ, and the measurement error of the value of the inter-lattice surface distance d obtained from the diffraction angle θ tends to increase.

The other one is an even greater factor. For example, when the diffraction line profile is measured at the tilt angle ψ ₁ , all the crystals within the irradiation range of the incident X-ray diffract. It means that only the crystal grains having the crystal lattice plane inclination of ψ ₁ are diffracted. Therefore, if the number of such crystal grains is small and the volume thereof is also small, the value of the inter-lattice plane distance d obtained from the diffraction line profile cannot be said to be representative of the entire sample, and it is as it is. When used in the equation (2), it results in an extremely large error.

Conventionally, as a remedy for the problem at the time of measuring the X-ray stress for such a coarse-grained material or a minute area,
To increase the number of crystal grains that contribute to diffraction as much as possible,
It has been considered to deal with widening the divergence angle of the incident X-ray or rocking the sample. However, since such a measure causes a change in the tilt angle ψ, it is necessary to limit the expansion of the divergence angle of the incident X-ray and the swing width to a small value, and in the end, such an effect cannot be expected.

The present invention has been made in view of the above circumstances. Even when the sample to be measured is limited to a coarse-grained material having a small number of crystal grains or a minute region, it is possible to measure the diffraction X-rays. An object of the present invention is to provide an X-ray stress measurement method capable of obtaining stress with high accuracy.

[0018]

In the X-ray stress measurement method according to the present invention, the tilt angle of the crystal lattice plane, which is the angle formed by the sample surface normal Mo and the crystal lattice plane normal M of the sample to be measured, is defined as ψ. _{In the case of i} , the sample is irradiated with a characteristic X-ray having a wavelength λ, and the stress σ acting on the sample is calculated from the obtained diffraction line profile. increase the set number of the inclination angle [psi _i higher, the inclination angle [psi _i
The diffraction line profile is measured at.

Then, the inter-lattice surface distance d _{i at} each tilt angle ψ _i is calculated based on the Bragg equation with the angle of the center of gravity of each diffraction line profile as the diffraction angle θ _i .

When the d-sin ² ψ diagram showing the correlation between the inter-lattice face distance d and sin ² ψ is obtained, the volume of crystal grains contributing to diffraction is taken into consideration as the inter-lattice face distance d. In order to do so, the calculated value d _i at each ψ _i is weighted by the integrated intensity I _i of each diffraction line profile, and d _i · F (I
_i ) is used to determine the stress σ in the sample.

[0021]

In the X-ray stress measuring method according to the present invention, the number of tilt angles ψ _i is increased according to the required accuracy of the stress to be measured, and more measurement data is obtained, so that the number of crystal grains can be reduced. This prevents an increase in measurement error caused by the existence of the error.

Further, by using the angle of the barycentric position of each measured diffraction line profile as the diffraction angle θ _i , the influence of the individual crystal grains contributing to the diffraction is averaged to identify a part of the diffraction line profile. Prevent the stress state of the crystal grains from being overestimated.

Further, by attaching a weight to the lattice plane spacing d in the integrated intensity of the diffraction line profile for each of the inclination angle [psi _i, also variations due to differences in crystal grains to contribute to the diffraction of each inclination angle [psi _i Make it smaller.

[0024]

EXAMPLE FIG. 6 is a diagram showing the relationship between a sample whose stress is measured by the X-ray stress measuring method according to an embodiment of the present invention and the X-rays irradiated on the sample. In FIG. 6, 1 is a sample to be measured, 2 is an incident X-ray of wavelength λ with which the sample 1 is irradiated for stress measurement, 3 is a diffracted X-ray, and F is the incident X-ray 2.
Crystal lattice planes that contribute to diffraction of H, H is the surface of the sample 1,
Mo is a sample surface normal line perpendicular to the sample surface H, M is a crystal lattice plane normal line perpendicular to the crystal lattice plane F, d is a lattice plane distance which is a distance between crystal lattice planes F, and ψ _i is the above The angle between the sample surface normal Mo and the crystal lattice plane normal M (that is,
The tilt angle of the crystal lattice plane F).

FIG. 1 shows a processing procedure by an X-ray stress measuring method according to an embodiment of the present invention.

In the conventional X-ray stress measurement method, generally,
The number of set points of the tilt angle ψ is kept constant (for example, 4 points) regardless of the required accuracy of the stress to be measured, and in order to improve the accuracy of the stress, the accuracy of measuring the inter-lattice surface distance d is improved. However, the X-ray stress measurement method of this embodiment is premised on the measurement of stress on a coarse-grained material or a minute area, and the number of set points of the tilt angle ψ _i is increased as compared with the conventional method, and the measurement is performed. The higher the required accuracy of the power stress is, the larger the number of inclination angles ψ _i is set, and the diffraction line profile is measured at each inclination angle ψ _i .

According to statistics, the mean value of M values with statistical variation has an error that is inversely proportional to the square root of M with respect to the true value. This is also clear from the fact that the diffraction line profile becomes smoother as the number of crystal grains contributing to diffraction increases, and the diffraction angle θ with less error can be calculated. Therefore, the incident X-ray irradiation position on the sample is adjusted so that the number of crystal grains contributing to the diffraction is increased, but such measures are limited, and a large improvement cannot be expected. Can not. However, as in this embodiment, the measure to increase the ψ point to be measured can relatively easily and surely increase the number of crystal grains to be measured.

A series of processes for one tilt angle ψ _i will be described below with reference to FIG.

First, a diffraction line profile is obtained for the first ψ _i preset as a measurement point (for example, ψ ₁ when i = ₁ ) (step 101). When the sample 1 is a coarse-grained material or the like and there are few crystal grains that contribute to diffraction, as shown in FIG. 5, the diffraction line profile has a shape with many undulations due to the separation of diffraction lines from individual crystal grains. Becomes

Next, the barycentric position of the measured diffraction line profile is determined, and the angle with respect to the barycentric position is determined as the diffraction angle θ ₁ at the tilt angle ψ ₁ (step 102). Even if the diffraction line profile is not smooth, the center of gravity can be obtained relatively easily and with high accuracy.

At the time of measuring the diffracted X-ray at the tilt angle ψ ₁ , the number of crystal grains contributing to the diffraction is m ₁ . If the volume of the j-th crystal grain is v _1j , the integrated intensity I _i of the diffraction line with respect to the ψ _i point is the total volume V _{i of} the crystal grains contributing to the diffraction.
= Proportional to Σv _1j . The diffraction angle θ ₁ which is the angle of the center of gravity means the average diffraction angle of the crystal grains of the volume V _i .

[0032] Then, by using the diffraction angle theta _1, to calculate the lattice plane spacing d ₁ at the inclination angle [psi ₁ from the Bragg equation (step 103).

[0033] Next, draw a d-sin ² [psi diagram showing a correlation between interstitial plane distance d and sin ² [psi, in this case, in advance, the integrated intensity in the diffraction line profile of inclination [psi ₁ (i.e., the diffraction The area I ₁ surrounding the line profile is calculated. Then, the distance d ₁ between the lattice planes is weighted by the integrated intensity I ₁ of each diffraction line profile, d ₁ · F (I ₁ )
Is used as the inter-lattice plane distance d in the d-sin ² ψ diagram (step 104). The weight F (I _i ) is set when the number of crystal grains actually contributing to diffraction is small and the volume thereof is small, and the calculated inter-lattice distance d _i is unsuitable to be treated as a representative value of the entire sample. This is for reducing the influence of the inter-lattice surface distance d _i and is determined by statistical processing.

[0034] Then, when there remains [psi _i to be measured other repeats the steps 101 to 104 for the value of the [psi _i. In this embodiment, ψ ₁ , ψ
₂ , ψ ₃ , ... ψ _k, and the above steps 101 to 104 are repeated for the number of the planned measurement points (step 1
05, 106).

After the processing of steps 101 to 104 is completed for all the planned number of measurement points, the stress σ is obtained from the drawn d-sin ² ψ diagram (step 1
07), a series of stress measurement processing ends.

In the X-ray stress measurement method as described above,
By increasing the number of set points of the tilt angle ψ _i , it is possible to prevent an increase in measurement error due to the small number of crystal grains. Moreover, by using the angle of the center of gravity position of each measured diffraction line profile as the diffraction angle θ _i , it is possible to reduce the risk of overestimating the stress state of some specific crystal grains shown in the diffraction line profile. You can Furthermore, when a d-sin ² ψ diagram is obtained from a plurality of measured diffraction line profiles, the inter-lattice plane distance d _{i obtained} for each diffraction line profile is weighted by the integrated intensity of each diffraction line profile. Therefore, each tilt angle ψ
Even if the crystal grains that contributed to the diffraction at _i are different, the variation caused by the difference can be reduced.

Due to the above synergistic effect, an increase in measurement error due to the small number of crystal grains contributing to diffraction is prevented, and the sample to be measured is a coarse-grained material having a small number of crystal grains or a minute region. Even in the case where the stress is limited to, the stress can be obtained with high accuracy by measuring the diffraction X-ray.

In the above embodiment, as shown in FIG. 1, the diffraction line profile is measured for one ψ point,
After the processes such as the calculation of the center of gravity position and the determination of the diffraction angle are performed, the same process is repeated for another ψ point, but the process order is not limited to that shown in FIG.

[0039]

As is apparent from the above description, in the X-ray stress measurement method according to the present invention, the number of set points of the tilt angle ψ _i is increased, so that the number of crystal grains is small. By preventing an increase in error and using the angle of the center of gravity position of each measured diffraction line profile as the diffraction angle θ _i , the stress state of some specific crystal grains shown in the diffraction line profile is overestimated. prevented by attaching a weight to the lattice plane spacing d in the integrated intensity of the diffraction line profile for each of the inclination angle [psi _i, each inclination angle [psi _i
The variation caused by the difference in crystal grains contributing to each diffraction is reduced.

Therefore, an increase in measurement error due to the small number of crystal grains contributing to diffraction is prevented, and the sample to be measured is limited to a coarse grain material having a small number of crystal grains or a minute region. Also in this case, the stress can be obtained with high accuracy by measuring the diffraction X-ray.

[Brief description of drawings]

FIG. 1 is an explanatory diagram of a processing procedure according to an embodiment of the present invention.

FIG. 2 is a schematic explanatory diagram of an X-ray stress measurement method.

FIG. 3 is an explanatory diagram of a diffraction line profile of a polycrystalline sample.

FIG. 4 is an explanatory diagram of a d-sin ² ψ diagram used in the X-ray stress measurement method.

FIG. 5 is an explanatory diagram of a diffraction line profile of a coarse grain material or the like.

FIG. 6 is a schematic explanatory diagram according to an embodiment of the present invention.

[Explanation of symbols]

1 ... Sample, 2 ... incident X-ray, d, d _i ... lattice plane spacing, M
o ... Sample surface normal, M ... Crystal lattice plane normal, ψ, ψ _i ... Inclination angle.

Claims (1)

[Claims] 1. When a tilt angle of a crystal lattice plane, which is an angle formed by a sample surface normal Mo and a crystal lattice plane normal M of a sample to be measured, is ψ _i , a characteristic X-ray having a wavelength λ is applied to the sample. An X-ray stress measurement method of irradiating and calculating the stress σ acting on the sample from the obtained diffraction line profile, wherein the higher the required accuracy of the stress to be measured, the greater the number of setting of the tilt angle ψ _i. Te, the diffraction line profile measured at each inclination angle [psi _i, lattice plane distance d _i for each inclination angle [psi _i is the angle of the center of gravity of each diffraction line profile as a diffraction angle theta _i, calculated on the basis of Bragg equation , And d− which indicates the correlation between the lattice plane distance d and sin ² ψ.
When obtaining the sin ² ψ diagram, in order to consider the volume of the crystal grains that contributed to diffraction as the inter-lattice distance d,
Use integrated intensity I _i d was weighted at _i · F _{(I i)} of each diffraction line profile calculated value d _i at each [psi _i, X-rays and obtains the stress σ in the sample Stress measurement method.