X-ray diffraction analysis

Technology of material structure analysis using X-ray diffraction effect in crystal material

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Phase analysis of x-ray diffraction is a technology that uses the diffraction effect of X-ray in crystal materials to analyze the structure of materials.

Chinese name: X-ray diffraction analysis
Foreign name: phase analysisof xray diffraction

Abbreviation: XRD(X-ray Diffraction)
Category: Structural analysis method

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brief introduction

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X-ray diffraction analysis

X-ray diffraction phase analysis and utilization X-ray The technique of analyzing the structure of a crystal material by its diffraction effect. Each kind of crystalline material has its specific crystal structure, including lattice type, crystal plane spacing and other parameters. When the sample is irradiated with X-ray with sufficient energy, the material in the sample will be excited to produce secondary fluorescent X-ray (identification X-ray), and the crystal plane reflection of the crystal follows Bragg's law. Qualitative analysis of compounds can be carried out by measuring the position of diffraction angle (peak position), quantitative analysis can be carried out by measuring the integral intensity (peak intensity) of spectral lines, and the size and shape of grains can be measured by measuring the relationship between the intensity of spectral lines and the angle.

theoretical development

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Discover diffraction phenomenon

Generation of X-ray diffraction

In 1912, Laue et al. predicted according to theory and confirmed by experiments X-ray Can occur when meeting with crystal Diffraction phenomenon , which proves that X-ray has electromagnetic wave The first milestone of X - ray diffraction is the property of X - ray diffraction. When a beam of monochromatic X-ray is incident on a crystal, the crystal is regularly arranged by atoms Unit cell Composition, the distance between these regularly arranged atoms and the incident X-ray wavelength yes

Same order of magnitude, so different atom Scattered X-rays interfere with each other and produce strong X-ray diffraction in some special directions. The orientation and intensity of diffraction rays in space are closely related to the crystal structure. This is the basic principle of X-ray diffraction. The relationship between spatial orientation of diffracted rays and crystal structure is available Bragg The equation represents:

2dsinθ=nλ

Where: λ is X ray wavelength ； θ is the Bragg angle; D Yes Crystalline surface Interval; N is an integer. The wavelength λ can be measured by the known X-ray diffraction angle, and then the plane spacing, that is, the regular arrangement of atoms or ions in the crystal, can be obtained. The material structure of the sample crystal can be determined by comparing the calculated diffraction X-ray intensity and plane spacing with the known table, which is called qualitative analysis. Quantitative analysis can be carried out from the comparison of diffracted X-ray intensity.

Kinematic diffraction theory

Darwin's theory is called X-ray diffraction kinematics theory. This theory Diffraction phenomenon As a three-dimensional Fraunhofer diffraction problem, it is considered that the scattering of each volume element of the crystal is independent of the scattering of other volume elements, and the scattered rays will not be scattered when passing through the crystal. Although this treatment can yield sufficiently accurate Diffraction direction The diffraction intensity can also be obtained, but the fundamental assumption of kinematics theory is not completely reasonable. Because the scattered lines must be scattered again in the crystal, in addition to combining with the original rays, the scattered rays can also combine with each other. Darwin soon realized this and made multiple scattering corrections in his theory.

Dynamic diffraction theory

Ewald's theory is called kinetic theory. This theory takes into account the interaction of all waves in the crystal, and believes that Incoming ray Coherent combination with diffraction rays in the crystal, and can exchange back and forth energy 。 Two theories apply to small Crystalline powder Strength obtained formula The same, but for large and complete crystals, we must use the kinetic theory to get the correct results.

development direction

With the new development of X-ray analysis, metal X-ray analysis has gradually become a conventional method for metal research, organic materials and nano materials testing due to the popularization of equipment and technology. It is also used for dynamic measurement. In the early days, photographic method was often used, which took a long time, and the accuracy of intensity measurement was low. The counter diffractometer method, which came out in the early 1950s, has been widely used because of its advantages of fast speed, accurate intensity measurement, and computer control. However, the photographic method using monochromator still has its own characteristics in the analysis of micro samples and the exploration of unknown new phases. Since the 1970s, with the emergence of high-intensity X-ray sources (including ultra-high intensity rotating anode X-ray generators, electron synchrotron radiation, high-voltage pulsed X-ray sources) and high-sensitivity detectors, as well as the application of electronic computer analysis, metal X-ray has gained new impetus. The combination of these new technologies not only greatly speeds up the analysis speed and improves the accuracy, but also enables instantaneous dynamic observation and research on more subtle or subtle effects.

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principle

X-ray diffraction analysis It is a structural analysis method for the spatial distribution of atoms in the material by using the X-ray diffraction formed by crystals. Will have certain wavelength When X ray of, X-ray scattering occurs when it encounters regularly arranged atoms or ions in the crystal, and the phase of the scattered X-ray is strengthened in some directions, thus showing the unique diffraction phenomenon corresponding to the crystal structure. Diffraction X-ray meets Bragg （W.L.Bragg） equation : 2dsin θ=n λ where λ is X-ray wavelength ； θ is Diffraction angle ； D is the spacing of crystal planes; N is an integer. wavelength λ Available with known X-ray Diffraction angle Measure, and then obtain the plane spacing, that is, within the crystal atom Or the regular arrangement of ions. The material structure of the sample crystal can be determined by comparing the calculated diffraction X-ray intensity and plane spacing with the known table, which is called qualitative analysis. From the comparison of diffracted X-ray intensity quantitative analysis 。 The feature of this method is that it can obtain the chemical state of elements and the way of combining atoms, so that it can be used for valence analysis and environmental protection Solid pollutants Phase identification, such as wind sand and soil composition in atmospheric particles, metals and their compounds discharged from industry（ dust ）, in the exhaust Halogenation Lead composition, water sediment or Suspended solids The state in which metals exist.

Single crystal diffraction

single crystal The basic methods of X-ray diffraction analysis are Laue method and revolving crystal method.

Laue Fa

Lauer method sends out continuous X-ray irradiation with light source sample Single crystal samples at rest on the platform shall be recorded with plate negative to generate diffracted rays. According to the position of the negative film, Laue method can be divided into transmissive Laue method and back reflection Laue method. The back reflection Laue method is not limited by the sample thickness and absorption, and is a commonly used method. The diffraction pattern of Laue method consists of several Laue spots, each Laue spot corresponds to the 1-n level reflection of the crystal plane, and the distribution of each Laue spot forms a Crystal band curve 。

Turnover crystal method

Diffraction pattern

Rotating by monochromatic X-ray irradiation single crystal Sample Rotating shaft Cylindrical with axis negative Record the generated diffracted rays and form discrete diffracted spots on the negative. Such diffraction pattern can easily and accurately determine the Diffraction direction And diffraction intensity, suitable for structural analysis of unknown crystals. It is easy to analyze crystals with low symmetry (such as orthogonality monoclinic And triclinic equicrystalline system), but its application is less.

Polycrystalline diffraction method

Polycrystalline X-ray diffraction Methods include photographic method and diffractometer method.

Photographic method

Radiography - Exposure to characteristic X-rays from light sources Polycrystalline Sample and record the diffraction pattern with negative film. according to sample In relation to the position of the negative film, photography can be divided into Debye method, focusing method and pinhole method, of which Debye method is the most widely used.

Debye method irradiates a small powder sample with a beam of collimated characteristic X-ray, and records the diffraction information with a narrow strip negative rolled into a cylinder and installed coaxially with the sample. The diffraction patterns obtained are some diffraction arcs. The advantages of this method are: ⑴ The amount of sample used is small (0.1 mg); ⑵ Including all reflection lines generated by the sample; ⑶ The device and technology are relatively simple.

Focus method film and sample In the same circumference The larger area on the sample is irradiated by monochromatic X-ray with greater divergence. Because of the same circumference Same arc on Circumferential angle Equal, so that Polycrystalline Diffraction ray of equivalent crystal plane in the sample negative To focus into a point or line. Focusing method time of exposure Short, the resolution is twice that of Debye method, but the diffraction lines in the small θ range are few and wide, which is not suitable for analyzing unknown samples.

The pinhole method uses three pinhole collimated monochromatic X-ray as the light source to illuminate the flat sample. according to negative The needle hole method at different positions can be divided into the penetration needle hole method and the back injection needle hole method. The diffraction pattern obtained by the pinhole method is the entire ring of the diffraction line, which is suitable for studying the grain size, crystal integrity, macro residual stress and Polycrystalline Preferred orientation in the sample, etc. However, this method can only record a few diffraction rings and is not suitable for other applications.

Diffractometer method

X-ray diffractometer with Bragg The experimental device is a prototype, integrating mechanical and electronic technologies and other achievements. The diffractometer consists of an X-ray generator X-ray goniometer 、 Radiation detector It is a diffraction experimental device that irradiates polycrystalline samples with characteristic X-ray and records diffraction information with radiation detector. Modern X-ray diffractometer is also equipped with control operation and operation Software Computer system. The imaging principle of the X-ray diffractometer is the same as the aggregation method, but the recording method and the corresponding diffraction patterns are different. The diffractometer adopts the incoming ray with a certain divergence, and also uses "the same arc on the same circumference Circumferential angle The difference is that the radius of the focusing circle changes with the change of 2 θ. The diffractometer method has replaced the photographic method in many fields because of its convenience, rapidity, accuracy and automatic data processing. Now it has become the main method for crystal structure analysis.

Double crystal diffraction method

The double crystal diffractometer irradiates the surface of a reference crystal with a beam of X-ray (usually Ka1 is used as the ray source) to make Prague condition One of wavelength The X ray of Reflection ray , and then use an appropriate aperture as a limit to obtain an X-ray beam of near standard value. Take this X-ray as the incoming ray of the second crystal, and the second crystal and Counter tube Swing at the angle of Δθ and Δ (2 θ) near the diffraction position to form the common Bicrystal Diffractometer.

In near complete crystals, defects, distortion, etc. are reflected in the X-ray spectrum, which is only tens of arc seconds, while semiconductor materials epitaxial growth requirement lattice Mismatch should be 10-4 or less. Such fine requirements make Bicrystal X-ray diffraction technology has become a necessary measuring instrument for the development of modern optoelectronic materials and devices. The four crystal and five crystal diffraction technology (also known as double crystal diffraction) developed on the basis of double crystal diffraction technology has become a sign of outstanding achievements in modern X-ray diffraction technology. but Bicrystal The second crystal of the diffractometer should be the same as the first crystal, otherwise dispersion 。 So when measuring, Bicrystal The reference crystal of the diffractometer should be the same as the measured crystal, which limits the use of the twin crystal diffractometer.

Application examples

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Sample requirements

1. Metal samples, such as block, plate and cylinder, shall be ground into a plane with an area of no less than 10X10mm. If the area is too small, several pieces can be pasted together.

2. For the flaky and cylindrical samples, there will be serious preferential orientation and abnormal diffraction intensity. Therefore, it is required to reasonably select the response direction plane during the test.

3. For measuring the microstructure of metal samples stress （ Lattice distortion ）The residual austenite shall be measured. It is required that the sample shall not be simply rough ground. It is required to prepare a metallographic sample, and carry out ordinary polishing or electrolytic polishing to eliminate the surface strain layer.

4. The powder sample is required to be ground to 320 mesh size, about 40 microns. The coarse particle size has low diffraction intensity, bad peak shape and low resolution. Understand the physical and chemical properties of the sample, such as whether it is flammable, easily deliquescent, corrosive, toxic and volatile.

5. The powder sample is required to be about 3 grams, or 5 milligrams if it is too small.

6. The sample can be metal Nonmetal Organic and inorganic material powder.

Scope of application

Phase analysis

The X-ray diffraction image of a crystal is essentially a fine and complex transformation of the crystal microstructure. There is a one-to-one correspondence between the structure of each crystal and its X-ray diffraction image. Its characteristic X-ray diffraction pattern will not change because other substances are mixed together, which is the basis of the X-ray diffraction phase analysis method. Prepare diffraction patterns of various standard single-phase materials and make them Normalization The diffraction pattern of the substance to be analyzed is compared with it to determine the composition phase of the substance, which becomes the basic method of qualitative analysis of the substance phase. After each phase is identified, it is proportional to the strength of each phase pattern Components The existing amount (except for those requiring absorption correction) can be used for various components quantitative analysis 。 At present, diffractometer method is commonly used to obtain diffraction patterns, and the "Powder Diffraction Card (PDF Card)" edited and published by the "Powder Diffraction Standards Association (JCPDS)" Phase analysis 。

At present, Phase analysis The main problems are as follows: ⑴ The strongest line in the object pattern to be measured may not be the strongest line of a single phase, but the result of the superposition of some sub strong or three strong lines of two or more phases. At this time, if this line is used as the strongest line of a phase, no corresponding card will be found. ⑵ It is very complicated and complicated to find the cards that meet the conditions among many cards. Although computer-assisted retrieval can be used, it is still unsatisfactory. ⑶ Prepare samples and draw calibration during quantitative analysis curve Or K value measurement and calculation are complex and arduous work. For this reason, some people proposed a possible solution, thinking that from the opposite point of view, the preliminary results of qualitative analysis should be polyphasic according to the standard data (PDF card) fitting Display Diffraction angle Simulated diffraction with diffraction intensity curve 。 By adjusting the proportion of each phase and comparing it with the diffraction pattern obtained by the diffractometer scanning, the results of qualitative and quantitative analysis can be obtained more accurately, thus eliminating some qualitative analysis and the entire quantitative analysis of the experiment and calculation process.

lattice Accurate determination of constants

lattice constant It is the basis of crystal material Structural parameters , measuring the lattice constant in the study of solid state phase transition , Confirm Solid solution Type, determination of solid solution solubility curve , Measurement Coefficient of thermal expansion And other aspects have been applied. lattice The constant is measured by measuring the position (θ) of the X-ray diffraction line. A lattice constant can be obtained by measuring the position of each diffraction line in the diffraction pattern.

lattice Constant determination accuracy It involves two independent issues, namely wavelength Of accuracy and Bragg Angular measurement accuracy 。 wavelength It is mainly the responsibility of the X-ray spectrometer. The task of the diffraction workers is to establish a one-to-one correspondence between the wavelength distribution and the diffraction ray distribution. Know each Reflection ray Of Miller index Then the corresponding formula can be used to calculate according to different crystal systems lattice Constant. Interplanar spacing The measurement accuracy increases with the increase of θ angle, The greater the θ, the greater the lattice The more accurate the constant value is, the higher angle diffraction ray should be selected for the determination of lattice constant. error Diagrams are generally used Extrapolation and least square method To eliminate, lattice The accuracy limit of constant measurement is around 1 × 10-5.

Determination of stress

X-ray measurement stress The variation of diffraction pattern characteristics is taken as the measurement of strain. macroscopic stress Evenly distributed in a large range of objects, the uniform strain produced is shown as grain Middle Same Name Interplanar spacing The same changes lead to the displacement of diffracted rays in a certain direction, which is the basis of X-ray measurement of macro stress; The micro stress is different between grains and even between parts of a grain. The uneven strain produced is shown by the increase in the spacing of crystal planes in some areas and the decrease in the spacing of crystal planes in some areas. As a result, the diffraction rays move in different directions, making their diffraction rays diffuse and widen, which is the basis of X-ray measurement of micro stress. Ultramicro Stress deflects atoms in the strain zone Balance position The intensity of diffraction rays is weakened, so the ultramicro stress can be measured by the change of X-ray intensity. The stress is generally measured by diffractometer.

X-ray measurement stress It is non-destructive and can be measured in a small range Local stress , measurable Surface stress It can distinguish the stress type, and it is not necessary to make the material at zero during measurement Stress state But its measurement accuracy is greatly affected by the organizational structure, It is also difficult to measure the dynamic transient stress by X-ray.

Grain size and Lattice distortion Determination of

if Polycrystalline Material grain There is no distortion and it is large enough. Theoretically, the spectral line of its powder diffraction pattern should be particularly sharp, but in actual experiments, this spectral line cannot be seen. This is due to the comprehensive influence of instrument factors and physical factors, which makes the pure diffraction spectrum line widened. The shape and width of pure spectral lines are determined by the average grain size, size distribution and Crystal lattice In principle, information about the nature and scale of the above influencing factors can be obtained by properly analyzing the alignment.

In grain size and Lattice distortion In the process of determination, there are two tasks to be done: ⑴ The pure diffraction line shape is obtained from the experimental line shape, and the most common methods are Fourier transform method and repeated continuous convolution method. ⑵ The information of grain size and defects can be obtained from the appropriate spectral lines of the diffraction pattern. This step is mainly to find out various Line broadening And separate the influence of these factors on the width, so as to calculate the required results. The main methods are Fourier method, linear variance method and integral width method.

single crystal Orientation and Polycrystalline Texture measurement

single crystal The determination of orientation is to find out the relationship between the crystallographic orientation in the crystal sample and the orientation in the external coordinate system of the sample. Although it can be determined by physical methods such as optical methods single crystal Orientation, but X Diffraction method It can not only accurately orient the single crystal, but also obtain the information of the internal microstructure of the crystal. Generally, Laue method is used single crystal The orientation is based on the position relationship between the polar stereographic projection of Laue spot conversion on the negative film and the polar stereographic projection of the external coordinate axis of the sample. Transmission Laue method is only applicable to samples with small thickness and absorption coefficient; The back reflection Laue method does not need to prepare samples specially, and the thickness of samples is not limited, so this method is often used.

Polycrystalline The phenomenon of grain orientation segregation along a certain direction in materials is called texture The common textures are silk texture and plate texture. In order to reflect the general picture of texture and determine the texture index, there are three methods to describe texture: Polar graph 、 Antipolar diagram And three-dimensional orientation function. For silk texture, it is necessary to know Polar graph Only the index of the filament axis is required to be calculated, and the photographic method and diffractometer method are available. The pole distribution of the texture of the plate is relatively complex, which needs two indexes to express, and is usually measured by a diffractometer.^[1]

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