X-ray diffraction (XRD) knowledge summary(1)

1. What is the purpose of XRD, to show its purity? Or can it show that it contains some kind of functional group?

X-rays are scattered when they strike a substance. Coherent scattering of X-rays by a crystalline substance is a diffraction phenomenon, i.e., the incident beam does not diverge but its direction is changed while its wavelength remains constant, which is a phenomenon unique to crystalline substances.

Most solid substances are crystalline, microcrystalline or quasi-crystalline and are capable of X-ray diffraction. The microstructure of crystals is characterized by a periodic long-range ordered structure. The X-ray diffraction pattern of a crystal is a physical transformation of the three-dimensional scene of the crystal microstructure and contains all the information about the crystal structure. X-ray diffractograms can be obtained from a small amount of solid powder or a small sample.

XRD (X-ray diffraction) is currently the most powerful method for studying the crystal structure (e.g. the distribution of the types and positions of atoms or ions and their groups, the shape and size of the crystal cells, etc.).

XRD is particularly suitable for phase analysis of crystalline substances. If the constituent elements or groups of a crystalline substance are not the same or their structures are different, their diffraction spectra show differences in the number of diffraction peaks, angular position, relative intensity order, and even in the shape of the diffraction peaks. Therefore, the qualitative identification of the composition and structure of the sample phase can be accomplished by comparing and analyzing the X-ray diffraction pattern of the sample with the X-ray diffraction pattern of the known crystalline material, and the quantitative analysis of the composition of the sample phase can be accomplished by analyzing and calculating the diffraction intensity data of the sample;

XRD can also be used to determine the size of the grains in the material or their arrangement orientation (the structure of the material)... XRD can also be used to determine the size of the grains or the orientation of their arrangement in the material (material texture).

At present, XRD is mainly applied to inorganic materials, but less to organic materials. 2.

2. How to determine if the sample is quasi-crystalline from the XRD spectra, and how to distinguish amorphous, quasi-crystalline and crystalline structures in the XRD spectra?

There is no clear-cut distinction between the three.

In the XRD spectra obtained by a diffractometer, if the sample is a good “crystalline” material, the spectra are characterized by a few or more narrow “sharp peaks”, generally independent of each other (with a 2θ width of 0.1°~0.2° at half height, which can be regarded as the “minimum width” of the diffraction peaks of a crystal as determined by the experimental conditions). If these “peaks” are significantly wider, it can be determined that the crystal in the sample has a particle size of less than 300 nm, and can be called a “microcrystal”. The theory of X-ray diffraction of crystals has a Scherrer formula.

The thickness of a grain in the direction of diffraction can be estimated from the amount of broadening of the spectral lines.

The amorphous diffractogram is characterized by the fact that over the entire range of scanning angles (starting from 2θ 1° to 2° to a few tens of degrees) only gentle variations in the intensity of the scattered X-rays are observed, with one or several maxima in between; the intensity is higher at the beginning because of the proximity to the direct beam, and then decreases rapidly as the angle is increased, and then slowly converges to the instrumental background value at higher angles.

From the point of view of Scherrer's formula, this phenomenon can be regarded as a result of the crystal's diffraction peaks greatly broadening, overlapping and blurring due to the limit of grain miniaturization. The limit of grain miniaturization is the “near-range order” between particles such as atoms or ions, which is the scenario we envision for the “amorphous” microstructure. A maximum value on an amorphous diffractogram corresponds to one of the commonly occurring interparticle distances in the amorphous mass.

The transition between these two types of amorphous states, with some “amorphous” transition, is the “quasi-crystalline” state. 3.

##3. When doing X-ray diffraction, if you use a different target, such as a Cu target or a Cr target, will the spectra of the two be the same? If they are different, what are the changes in the peak positions and intensities? Is there a pattern?

Different targets have different characteristic wavelengths. The angle of diffraction (often called the Bragg angle or 2θ angle) is determined by the wavelength used in the experiment (Bragg equation). Using different targets, i.e., different wavelengths of X-rays, the diffraction angle will be different for a certain group of planes with a spacing of d according to the Bragg equation, and the diffraction angle of the group of planes with each value of the spacing will show a regular change. Therefore, the positions of the diffraction peaks on the diffractograms obtained from X-ray tubes with different target materials are not the same, and the changes in the positions of the diffraction peaks are regular.

Instead, a crystal has its own set of d-values that are intrinsic to its structure and can be used as a signature parameter for that crystalline substance. Therefore, regardless of the type of target X-ray tube used, the set of d-values of a sample obtained from the resulting diffractogram is independent of the target material. The relative intensities between the diffraction peaks on the diffractogram are mainly determined by the structure of the crystal, but since the absorption properties of the sample are also related to the wavelength of the incident ray. Therefore, the relative intensities of the diffraction peaks on the diffractograms of the same sample obtained with different targets may vary slightly, depending on the target material.

Review the Bragg formula and the intensity formula for diffraction and you will have all the answers to your questions. 4.

4. I want to know the crystal planes corresponding to different diffraction angles.

If you can find the corresponding powder diffraction data card for your diagram, then the problem is simple. Most of the powder diffraction data cards give the diffraction index of each diffraction line, so you can know the corresponding crystal planes.

If the crystal structure is unknown, the diffraction index of each diffraction line needs to be solved, which is called “indexing the diffraction map”. If you want to solve the problem by yourself, you need to have a basic knowledge of crystallography, and then learn one or two indexing tools (e.g. treaor90) to try it out.

5. For the cell parameters of an orthorhombic crystal system, where a, b, c represent the lengths of the three prongs of the cell. However, I am not sure how to define the orientation of a, b, c, i.e. on what basis the orientation of these three prongs is determined? Is there a clear definition or can it be customized arbitrarily?

In general you can use the orientation principle a < b < c. Actually, you can use any orientation, they can be converted by matrices.

The a, b, and c of a cell are the lengths of the unit translation vectors in the direction of the three crystallographic axes, called axial lengths, not the lengths of the “three prongs”. The symbols a0, b0, and c0 are also commonly used for the axial lengths. The unit of axial length is often Å (Angstrom) or nm (nanometer). There is no such thing as a “prism” in a crystal structure, there is only a crystal coordinate system, which is expressed in terms of six parameters: a, b, c, α, β, γ, with α, β and γ representing the angles between the three axes. The “prisms” are the edges of the crystal shape. Therefore, it is wrong to say that “a, b, c represent the lengths of the three prongs of the crystal cell”. 6.

6. How to calculate the volume of a crystal cell? For example, if I want to calculate the cell volume of a zirconium dioxide tetragonal phase, or even the individual cell parameters, how can I use the software to do this?

First of all, you need to have a good knowledge of crystallography. These software is for us to deal with some crystallographic problems, so you can not leave crystallography to use the software.

You can't use the software without crystallography, but you have to have the necessary crystallography knowledge to learn how to use the software, so that you can understand the contents of help. The problem of cell volume that you are talking about now is actually the problem of accurate determination of cell parameters, because after the cell parameters are determined accurately, the cell volume will be known naturally.

7. Is there any software that can draw the spatial structure of crystals based on fractional coordinates? It is the kind with octahedra or tetrahedra.

According to the structural data of the crystal, the space structure of the crystal can be drawn with a professional crystal structure drawing software such as diamond or atoms. 8.

8. Which is the intrinsic preferred growth direction of a hexagonal crystal?

Generally speaking, the crystal grows faster along the short-axis direction, and the density of the crystal faces perpendicular to the long-axis direction is higher, which is more stable from the energy point of view when the crystal grows.

9. How to know the coordinates of the atoms in a crystal?

The coordinates of atoms in a crystal can only be obtained by single crystal X-ray diffraction. In addition to four-circle, single crystal X-ray diffraction is also possible with CCD. 10.

10. How to calculate the grain size lattice constant and distortion from the X-ray diffraction data, what theory and formula are used?

Grain size lattice constants and distortions can be calculated from the peak shape data of the diffraction peaks. In the case where the broadening of the diffraction peaks is only due to the fineness of the grains, the thickness of the grains in the direction of diffraction can be estimated from the amount of broadening of the diffraction peaks using the Scherrer formula. If you need to do these calculations and need some additional knowledge, you can find some information on this topic on this public website.