JP3570643B2 - Method for removing multiple reflection effect in X-ray diffraction measurement of single crystal sample - Google Patents

Description

[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to an X-ray diffraction measuring method for measuring the reflection intensity of diffracted X-rays reflected by a single crystal sample using a four-axis type X-ray diffractometer, in which a measurement error which may occur as a result of a so-called multiple reflection effect is eliminated. The present invention relates to a method for removing a multiple reflection effect for removing.
[0002]
[Prior art]
As a crystal structure analysis of a crystalline material, X-ray diffraction measurement using an X-ray diffraction phenomenon is known. That is, when X-rays are applied to the crystal material, the scattered X-rays reflected by each atom in the crystal are added. When the X-rays are monochromatic, the X-rays scattered by the respective atoms interfere with each other and generate strong diffracted X-rays in a specific direction. X-ray diffraction measurement of a single-crystal material involves irradiating a single-crystal sample with X-rays and changing the orientation of the single-crystal sample with respect to the incident X-ray little by little to accurately measure the intensity of successively generated diffracted X-rays. The measurement is performed, and the obtained diffraction X-ray intensity data is subjected to Fourier transform to clarify the arrangement of atoms, that is, the crystal structure.
[0003]
The concept of a reciprocal lattice and a reflecting sphere has been introduced as a theoretical explanation of the X-ray diffraction phenomenon of a crystalline material.
The reciprocal lattice refers to another spatial lattice in which a reciprocal system b1, b2, b3 is used as a basic vector with respect to a spatial lattice whose basic vector is given by a1, a2, a3. Here, between a1, a2, a3 and b1, b2, b3, (ai, ak) = δik (i = 1, 2, 3), δik = 1 (i = k), δik = 0 ( i ≠ k).
[0004]
The position vector r = h ・ b1 + k ・ b2 + 1ｌb3 (h, k, l is an integer) of the reciprocal lattice corresponds to the lattice plane of the Miller index (h k l) in the original spatial lattice and is perpendicular to the lattice plane. It is. If the lattice spacing is d, there is a relation of d = 1 / | r * |. r * is the position vector of the reciprocal lattice point closest to the origin in the same direction as r, and is obtained by dividing r by the common divisor n of h, k, l. r may be represented by (h, k, l). (See Iwanami Shoten Publishing, RIKEN Dictionary, "Reciprocal lattice".)
[0005]
The reflecting sphere is a sphere defined by a reciprocal lattice space of the spatial lattice of the crystal, and can indicate a direction in which diffracted X-rays appear by the reflecting sphere.
FIG. 1 shows the relationship between the reflecting sphere and the X-ray diffraction conditions. That is, assuming that X-rays are incident on the origin O of the reciprocal lattice space (reciprocal lattice origin), a point located at a distance of a wave number 1 / λ (λ is a wavelength) in a direction opposite to the incident direction of the X-rays is denoted by A. A sphere having a radius of 1 / λ centered on A is a reflection sphere.
[0006]
The X-ray diffraction condition is given in such a manner that when there is a reciprocal lattice point H (h, k, l) on the reflecting sphere, the diffraction X-ray is reflected in the AH direction. If the unit vectors of the X-ray incident direction AO and the diffracted X-ray reflection direction AH with respect to the single crystal sample are s0, s, and OH vectors, respectively, r (h, k, l), then r = s / λ− In s0 / λ, hi (i = 1, 2, 3) is an integer, which matches the Laue condition. On the other hand, assuming that the angle between s and s0 is 2θ, if the reciprocal of the magnitude of the OH vector r is d, then the Bragg condition of 2d sin θ = λ is derived. (See Iwanami Shoten Publishing, RIKEN Dictionary, "Reflection Sphere".)
[0007]
In other words, the relationship between the reflecting sphere and the X-ray diffraction condition is as follows: when the reciprocal lattice origin O on the reflecting sphere is the X-ray irradiation point of the single crystal sample, and X-rays are irradiated from point A toward the reciprocal lattice origin O , X-rays are reflected in a direction from point A to reciprocal lattice point H on the reflecting sphere. Then, from the nature of the reciprocal lattice, the lattice plane of (h, k, l) in the original spatial lattice becomes the reflection surface P in this case.
[0008]
[Problems to be solved by the invention]
In X-ray diffraction measurement of a single crystal sample using a four-axis X-ray diffractometer, the reflection intensity of diffracted X-rays reflected at a reciprocal lattice point (reflection surface) on a reflecting sphere is measured, and the measurement data is obtained. The crystal structure of a single crystal sample is analyzed based on the above. Now, if only one reciprocal lattice point is on the reflecting sphere, since the X-ray diffraction phenomenon occurs on only one reflecting surface in the single crystal sample, the reflection intensity of the obtained diffracted X-ray is obtained. Does not include the error.
[0009]
However, in the conventional X-ray diffraction measurement, depending on the orientation of the single crystal sample, reciprocal lattice points other than the measurement point may be placed on the reflecting sphere together with the reciprocal lattice point as the measurement point. In this case, the X-rays incident on the reciprocal lattice point (reflection surface), which is the original measurement point, are weakened by the amount reflected at the reciprocal lattice point (reflection surface) other than the measurement point on the reflection sphere. Then, the reflection intensity of the detected diffracted X-ray becomes smaller than the original value. Further, diffracted X-rays reflected at a reciprocal lattice point (reflective surface) other than the measurement point are superimposed on incident X-rays from the X-ray source and incident on the reciprocal lattice point (reflective surface) which is a measurement point. In some cases, the reflection intensity of diffracted X-rays at a lattice point (reflection surface) is increased.
[0010]
Generally, such a phenomenon is referred to as a multiple reflection effect in the X-ray diffraction measurement of a single crystal sample, and in the conventional X-ray diffraction measurement, data errors due to the multiple reflection effect could not be removed.
However, this multiple reflection effect is rarely remarkable, and generally satisfactory analysis results can be obtained in ordinary single crystal structure analysis even if errors due to the multiple reflection effect are ignored. .
[0011]
However, analysis of the absolute structure of a single crystal that does not contain heavy atoms, precise measurement of the electron density distribution in the single crystal, determination of the electron wave function, precise determination of the crystal lattice strain, or atomic deficiency and its occupancy in determining the crystal structure When the X-ray diffraction measurement belonging to the so-called precision measurement, such as the determination of the above, is performed, the error due to the multiple reflection effect cannot be ignored.
[0012]
Conventionally, in an X-ray diffraction measurement belonging to this kind of precision measurement, it is subjectively determined whether or not an error due to a multiple reflection effect is included based on the experience of a data analyzer, and it is considered that such an error is included. Analysis of the structure of the single crystal was performed by removing the measurement data.
[0013]
The present invention has been made in view of the above circumstances, and has as its object to eliminate errors due to the multiple reflection effect by an objective method and realize highly accurate X-ray diffraction measurement of a single crystal sample.
[0014]
[Means for Solving the Problems]
In order to achieve the above object, the present invention includes an intensity measuring step of irradiating a single crystal sample with X-rays using a four-axis X-ray diffractometer and measuring the reflection intensity of the diffracted X-rays reflected by the sample. In the X-ray diffraction measurement, the intensity measurement step is performed by rotating the single crystal sample by an arbitrary angle around an axis (ψ axis) passing through the X-ray irradiation point on the single crystal sample and orthogonal to the diffraction X-ray reflection surface. It is characterized by being repeated.
[0015]
The present invention will be described with reference to the relationship diagram between the reflecting sphere and the X-ray diffraction condition shown in FIG. 1. X-ray diffraction measurement is based on the reciprocal lattice origin O on the reflecting sphere (ie, the X-ray of the single crystal sample). Rotating a straight line (ψ axis) connecting the reciprocal lattice points in the single crystal sample around the (irradiation point), the reflection of the diffracted X-rays reflected at the reciprocal lattice points (reflection surface) on the reflecting sphere Measure the strength. In the measurement of the reflection intensity, even when a reciprocal lattice point other than the reciprocal lattice point H, which is the measurement point, is on the reflecting sphere, the single crystal sample is rotated by an arbitrary angle around the straight line (ψ axis). Thereby, since the reciprocal lattice points other than the measurement point on the reflecting sphere in the previous measurement are separated from the reflecting sphere, the reciprocal lattice point does not satisfy the diffraction condition, and as a result, other than the measuring point The reflection of diffracted X-rays at the reciprocal lattice point is eliminated, and the multiple reflection effect can be eliminated.
[0016]
The operation of rotating the single crystal sample by an arbitrary angle around the straight line (直線 axis) connecting the reciprocal lattice points, in other words, the X-ray irradiation point O on the single crystal sample passes through the reflection plane P of the diffracted X-ray. Is to rotate the single crystal sample by an arbitrary angle about an axis (ψ-axis) orthogonal to.
[0017]
When this invention is applied to X-ray diffraction measurement, a plurality of measurement data will be obtained at each measurement point. Therefore, a method is required for discriminating, among these measurement data, data including an error due to the multiple reflection effect and data not including the error.
[0018]
Therefore, in the invention of claim 2, the intensity measurement step is performed at least two times by rotating the single crystal sample by an arbitrary angle about an axis passing through the X-ray irradiation point on the single crystal sample and orthogonal to the diffraction X-ray reflection surface. Iteratively, at least three measurement data obtained in the intensity measurement process are compared, and at least measurement data showing a value clearly different from the other two measurement data is removed as measurement data including a multiple reflection effect. It is.
[0019]
Further, according to the third aspect of the invention, the average value of the measurement data other than the measurement data removed as including the multiple reflection effect is used as the appropriate measurement data to improve the measurement accuracy.
[0020]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
A four-axis X-ray diffractometer used for X-ray diffraction measurement is used to automatically set the orientation of a single crystal sample with respect to incident X-rays, move a reciprocal lattice point as a measurement point, and move a counter tube. It has a goniometer called an axial goniometer.
[0021]
FIG. 2 is a schematic diagram showing the configuration of the rotating shaft of the four-axis goniometer.
As shown in the figure, the four-axis goniometer has an Ω axis that determines the direction of the crystal, and a Θ-φ assembly and a 2Θ axis that detects the diffracted X-rays thereon.
The crystal sample is attached to the center C of each axis. Further, the X-ray counter tube rotates about the 2 ° axis to detect diffracted X-rays. Here, the zero point of each of the four axes is determined as follows.
[0022]
2Θ = X-ray incident beam direction (2θ = 0)
Ω = Χ Circle is perpendicular to X-ray incident beam (ω = 0)
Χ = Position where Φ axis coincides with Ω axis (χ = 0)
Φ = arbitrarily determined (φ = 0)
Here, 2Ω, Ω, Φ, and Φ are the names of the respective circles of the goniometer, and 2θ, ω, χ, and φ represent angles.
[0023]
The four-axis goniometer is automatically operated by computer control. The coordinate system serving as a reference for initial settings and data analysis in the computer control is an X-axis, a Y-axis, and a Z-axis as shown in FIG. The orthogonal coordinate system is set. Here, the Y axis is set in the X-ray incident direction, the Z axis is set in the Ω axis direction, and the X axis is set in a direction orthogonal to these Y axis and Z axis.
X-ray diffraction measurement on a single crystal sample is automatically performed using a four-axis X-ray diffractometer equipped with such a four-axis goniometer.
[0024]
FIG. 4 is a block diagram showing general steps in the case where the structure of a single crystal sample is automatically analyzed by a four-axis X-ray diffractometer.
First, a single crystal sample is mounted on a sample stage of a four-axis X-ray diffractometer, and a peak point of the reflection intensity is searched (S1). The search for the peak point of the reflection intensity is performed by fixing each axis of 2Θ, Ω, and た shown in FIG. 2 and rotating the single crystal sample around the Φ axis. Further, the Χ axis is rotated by one step, and similarly, the peak point of the reflection intensity is searched for by rotation around the Φ axis. In this way, 20 to 25 reflection intensity peak points are searched.
[0025]
Next, the simple unit cell of the single crystal sample is determined based on the peak point of the reflection intensity obtained by the search, and the Miller index (h, k, l) of the sample is further determined (S2). Subsequently, a Delaunay lattice transformation is performed, and a Bravais lattice is further determined from the determined simple unit lattice, and a lattice constant is determined by the least square method (S3).
[0026]
Thereafter, the process shifts to reflection intensity data collection through processes such as confirmation of Laue pattern symmetry (S4), determination of reflection intensity data collection conditions (S5), and refinement of lattice constant (S6) (S7). ). The conditions for collecting the reflection intensity data include, for example, the scanning range (Δω), the standard reflection intensity, and the size of the light receiving slit. Then, a structural analysis of the single crystal sample is performed based on the collected reflection intensity data (S8).
[0027]
FIG. 5 is a flowchart specifically showing a process of collecting the reflection intensity data shown in FIG. The method for removing the multiple reflection effect according to the embodiment of the present invention is incorporated in the step of collecting the reflection intensity data. Note that the processing of each step shown in the figure is automatically executed by a computer.
[0028]
As shown in the figure, first, the Miller indices (h, k, l) are initialized based on the Miller indices (h, k, l) determined in the step S2 shown in FIG. 4 (S10). Subsequently, a so-called symmetric setting method for setting ω to θ (U.W. Arndt and BTM Willis: Single Crystal Diffractometry (Cambridge) (1966)) is used to set the angle 2θ of the four-axis goniometer. ωs, χs, φs are calculated, and the orientation of the single crystal sample is set (S11). Here, the value of the counter N for counting the number of times of measurement of the integrated intensity is set to 0, and the rotation angle around the ψ axis is also set to 0.
[0029]
From this state, the integrated intensity (reflection intensity) is measured (S12). When the integrated intensity is measured such that a plurality of reciprocal lattice points ride on the reflective sphere shown in FIG. 1, the multiple reflection effect occurs as described above, and the obtained integral is obtained. The intensity data will contain errors.
Therefore, in the present embodiment, after the first measurement of the integrated intensity is completed, the counter N is increased by one to N + 1 (S13), and the state in which the single crystal sample is rotated by Δψ around the ψ axis is formed. (S15).
[0030]
Even if a plurality of reciprocal lattice points are on the reflecting sphere in the previous measurement of the integrated intensity, the rotation around this ψ axis causes the reciprocal lattice points other than the measurement point to be separated from the reflecting sphere. And an error due to the multiple reflection effect can be removed. However, rotating by Δψ around the ψ axis may cause multiple reflections in the current measurement. Therefore, in this embodiment, at least three times of the integrated intensity measurement are performed by changing the angle ψ, and the measured data is compared, and the measured data which clearly shows a value different from the other two is converted into an error due to the multiple reflection effect. Is removed as measurement data containing
[0031]
As described above, when the single crystal sample is rotated by Δψ around the ψ axis, the angles 2θ, ω, χ, and φ of the four-axis goniometer also shift accordingly. Therefore, 2θ, ωs + Δω (ψ ), Χs + Δχ (ψ), φs + Δφ (ψ), and adjust the rotation angle of the four-axis goniometer. (S16).
[0032]
In this way, the integrated intensity is measured again (S12). Steps S12 to S17 are repeated until the number of the counter N reaches a preset maximum count number. As described above, in this embodiment, since the integrated intensity measurement is performed at least three times while changing the angle ψ, the maximum count number is set to an arbitrary number of 3 or more. Then, when the number of the counter N reaches the maximum count number (S14), the setting of the Miller index (h, k, l) is changed (S20), and the steps of S11 to S17 are executed again to obtain the integrated intensity data. collect.
[0033]
If each angle value calculated in step S16 exceeds the rotatable range of the four-axis goniometer, the step of S15 is executed again by shifting the reference angle of ψ (ψ0) (S18). If the reference angle (ψ0) of ψ exceeds the maximum angle (ψmax) (S19), the integrated intensity measurement at the Miller index (h, k, l) is terminated, and the next Miller index (h, k) is stopped. , L) (S20).
[0034]
As described above, after collecting the integrated intensity at each Miller index (h, k, l), the integrated intensity data including the error due to the multiple reflection effect is removed, and the average of the other appropriate integrated intensity data is removed. Is performed. This step is inserted between steps S7 and S8 shown in FIG.
That is, when comparing at least three pieces of measurement data obtained by changing the angle ψ at each Miller index (h, k, l), the integrated intensity data including an error due to the multiple reflection effect is clearly different from other measurement data. Shows different values. By removing the integrated intensity data having a value clearly different from the other measured data from the measured data, it is possible to obtain a measurement result that does not include an error due to the multiple reflection effect.
[0035]
Any of the remaining measurement data does not include an error due to the multiple reflection effect, and any of them may be selected. In this embodiment, the average value of the measurement data is used as the integrated intensity data.
When there is no measurement data showing clearly different values, it is considered that multiple reflection did not occur in the measurement. In this case, all the integrated intensity measurement data at the Miller index (h, k, l) may be averaged, or any measurement data among them may be selected.
[0036]
The removal of the integrated intensity data including the error due to the multiple reflection effect and the averaging of the other appropriate integrated intensity data are sequentially performed during the process shown in S7 of FIG. 4, that is, in the flowchart of FIG. You can also. For example, after the collection of the integrated intensity data at the set Miller index is completed (S14), these processes may be inserted before the process proceeds to the collection of the integrated intensity data at the next Miller index (S20).
Further, the method of the present invention can be carried out using various types of four-axis goniometers such as a κ-type goniometer using a κ-axis instead of the χ-axis.
[0037]
【The invention's effect】
As described above, according to the present invention, the intensity measurement step is performed by rotating the single crystal sample by an arbitrary angle about the axis passing through the X-ray irradiation point on the single crystal sample and orthogonal to the reflection surface of the diffracted X-ray. By repeating, an error due to the multiple reflection effect can be eliminated by an objective method, and highly accurate X-ray diffraction measurement of a single crystal sample can be realized.
[Brief description of the drawings]
FIG. 1 is a schematic diagram showing the relationship between a reflecting sphere and X-ray diffraction conditions.
FIG. 2 is a schematic diagram illustrating a configuration of a rotating shaft of a four-axis goniometer.
FIG. 3 is a diagram showing an orthogonal coordinate system corresponding to a rotation axis of a four-axis goniometer.
FIG. 4 is a block diagram showing an example of steps up to analyzing the structure of a single crystal sample by X-ray diffraction measurement.
FIG. 5 is a flowchart illustrating a method of removing a multiple reflection effect according to the embodiment of the present invention.
[Explanation of symbols]
H: reciprocal lattice point O: reciprocal lattice origin P: reflective surface

Claims (3)

In an X-ray diffraction measurement including an intensity measurement step of irradiating a single crystal sample with X-rays using a four-axis X-ray diffractometer and measuring the reflection intensity of diffracted X-rays reflected by the sample,
Each intensity measurement is performed by rotating the single crystal sample by an arbitrary angle around an axis passing through the X-ray irradiation point on the single crystal sample and orthogonal to the reflection surface of the diffracted X-rays and repeating the intensity measurement step. method of determining multiple reflection effects in X-ray diffraction measurement of a single crystal sample, characterized in that from the measurement data obtained in step to determine the measurement data including the error due to the multiple reflection effect. In an X-ray diffraction measurement including an intensity measurement step of irradiating a single crystal sample with X-rays using a four-axis X-ray diffractometer and measuring the reflection intensity of diffracted X-rays reflected by the sample ,
The intensity measurement step is performed at least three times by rotating the single crystal sample by an arbitrary angle about an axis passing through the X-ray irradiation point on the single crystal sample and orthogonal to the reflection surface of the diffracted X-rays, At least three measurement data obtained in the measurement process are compared, and measurement data showing a value clearly different from at least the other two measurement data is removed as measurement data including an error due to a multiple reflection effect. A method for removing a multiple reflection effect in X-ray diffraction measurement of a single crystal sample. The method for removing a multiple reflection effect in X-ray diffraction measurement of a single crystal sample according to claim 2,
A method for removing a multiple reflection effect in X-ray diffraction measurement of a single crystal sample, wherein an average value of measurement data other than the removed measurement data is used as appropriate measurement data.

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