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Topic reserved by: Yutong Song

X-ray diffraction (XRD) is an effective method for studying crystalline materials. Because of its advantages of being nondestructive, rapid, and only requiring a very small amount of sample, XRD is widely used for phase identification, single crystal analysis, residual stress measurement, etc. Currently, XRD is mainly applied for inorganic materials and less for organic materials. There are two main XRD methods, single crystal XRD and powder XRD (i.e., polycrystalline XRD). This wiki page focuses on powder XRD.

Principles

When a monochromatic X-ray is incident on a crystalline sample, the X-rays will scatter from the electrons of an atom. And if Bragg's condition (nλ = 2dsinθ, where n = positive integer,  λ = wavelength and d = d-spacings, i.e., the interplanar spacing of the crystal, shown in Figure 1

) is met, the interaction of the incident light with the sample will produce a diffracted wave. Due to the random orientation of the powder material, all possible diffraction directions of the lattice could be obtained by scanning the sample through the range of 2θ angle. These diffracted X-rays are then detected, processed and counted. Since each mineral has a unique set of d-spacings, converting the diffraction peaks to d-spacings makes it possible to identify each mineral. Typically, this is done by comparing the d-spacing with a standard reference pattern

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Figure 1. Bragg’s representation of the diffraction condition as the scattering of X-rays by lattice planes (h k l)

. (License: © Mineralogical Society of America)

It is worth mentioning that organic materials typically have lower electron densities and crystallinity than inorganic materials, which can make their XRD patterns less intense and more difficult to interpret than those obtained for inorganic materials (based on the principle of XRD: the more the electrons, the better the scattering). Additionally, organic materials may be more prone to damage from X-ray radiation, which can affect the accuracy of the measurements

. Overall, while XRD is not typically the first choice for the analysis of organic materials, with careful sample preparation and data analysis, it can still be a useful tool in certain applications where the structural information provided by XRD is necessary, such as the study of polymers and pharmaceuticals.

Instrumentation

The geometry of an X-ray diffractometer is shown in Figure 2, which consists of four basic elements: an X-ray source (usually an X-ray tube), a sample holder, an X-ray detector, and a goniometer that can change angle θ.

Figure 2. Schematic diagram of an X-ray diffractometer.

(License: © CC BY-NC-SA 4.0)

X-rays are generated in a cathode ray tube by heating a filament to produce electrons, accelerating the electrons toward a target by applying a voltage, and bombarding the target material with electrons. When electrons have sufficient energy to dislodge the inner shell electrons of the target material, characteristic X-ray spectra are produced

. The monochromatic X-rays needed for diffraction can be obtained by a foil or crystal monochromator. These X-rays are collimated and directed onto the sample at some angle θ, while the detector opposite the source reads the intensity of the X-rays it receives at 2θ away from the source path. As the sample and detector are rotated, the detector angle always remains 2θ above the source path. For typical inorganic samples, the scan range is set at 5–70°

. When the geometry of the incident X-rays impinging the sample satisfies the Bragg Equation, constructive interference occurs and a peak in intensity occurs. The intensity of the reflected X-rays is processed and converted to a count rate which is then output to a device such as a computer monitor. 

Sample Preparation

To obtain high-quality XRD patterns, the sample is required to be ground into powder form. The particle size of the ground sample is at most 44 microns, which means that if you rub the sample with your finger, you cannot feel the individual particles. The intensity of the diffraction peaks is related to the number of crystal planes that are oriented at the correct angle to the incident X-rays. If the sample is not ground enough, the powder particles may be too large and only a small number of planes will be detected, resulting in a weaker signal even some of the small peaks that can be detected in well-ground samples disappear. In addition, the ratios of the peaks may shift due to the insufficiently random orientation of the crystallites

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On the other hand, due to the texture or other physical properties of the sample material, such as materials that have been processed or shaped in a particular way, non-random orientation of crystallites may also occur. For example, samples that are fibrous, bladed, or plate-shaped would like to orient themselves in the preferred direction due to their shape, causing that some lattice planes will be detected more than others. This also leads to changes in the intensity and shape of XRD diffraction peaks, which can complicate the interpretation of the diffraction pattern.. Non-random orientation is difficult to avoid in this case, but can be mitigated by proper grinding and rotating the analyzed face while mounting the sample

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Analysis

The result obtained by XRD is called diffractogram. The XRD pattern consists of peaks at different angles (2θ) and intensities. Each peak corresponds to a particular set of crystallographic planes in the sample. So each crystalline phase has a characteristic powder XRD pattern which can be used as a fingerprint for identification purposes

. By matching the observed peak positions and intensities to those in the database of known XRD patterns, it is possible to identify the different phases present in the sample. There are several databases available for PDFs (Powder Diffraction Files): the commercial (ICDD, International Centre for Diffraction Data) and open sources, such as COD (Crystallography open database). This can be done by manually inspecting the data, or using software that compares the observed and known patterns, such as QualX and MDI Jade. Here is an example of using MDI JADE software for phase identification (shown in Figure 3) : 

(1) Input experimental data: Click "File" → "Read", select the file containing the experimental data of a series of 2θ and relative intensity, usually in TXT or RAW format.

(2) Click "S/M" (Select/Match) button.

(3) Choose "All Subfiles" and "Use Chemistry Filter" and then Click “OK”.

Figure 3. Example of using MDI JADE software for phase identification (Reference: open database; Data and permission from Mengqi Sun; Figure: Yutong Song)

The matching result indicates the presence of calcium ferrite compound Ca₂Fe₉O₁₃ since the XRD pattern of the sample fits well with that of Ca₂Fe₉O₁₃ (space group: C2) in the standard PDF card, and other impurity peaks are not quite obvious.

Powder XRD patterns can also be simulated if the crystal structure is known. VESTA has built-in tools to run simulation of powder XRD patterns based on the crystal structures visualization. The information needed in determining the crystal structure is the lattice constant, and the space group adopted. Both of these information can be used to determine the position of an atom in a unit cell of a crystalline material. The X-ray diffraction patterns can be obtained after visualization of the crystal structure is performed

. Here is an example of using VESTA to simulate the XRD pattern of a known crystal structure(shown in Figure 4) : 

(1) Open a CIF file (Crystallographic Information File, the standard format for storing crystallographic structural data, which can be downloaded from databases such as ICSD, COD, CSD, etc.) / create a new crystal structure. 

(2) Click "Utilities" → Choose "Powder Diffraction Pattern" → Open "Conditions" tab and set only one x-ray wavelength (Here Cu-Kα: wavelength=1.5406 Å) .

(3) Click "Calculate" to simulate the pattern → Open "Plot" tab to see the pattern, open "Reflections" tab to see a peak listing.

Figure 4. Example of using VESTA to simulate the XRD pattern of a known crystal structure. (Data: CaF₂ (Fm-3m)

from ICSD; Figure: Yutong Song)

In the above two examples, high-intensity sharp peaks were obtained in the XRD patterns due to the fact that the materials are crystalline. However, if the XRD sample is amorphous, the XRD pattern will show a very low and broad humped peak (like (a) in Figure 5

) or a diffuse background (like sample B in Figure 6

). This is because X-rays will be scattered in many directions (i.e., diffuse scattering)

. For partly amorphous or partly crystallized samples, the XRD pattern may show a relatively broad and low-intensity peaks (like sample A in Figure 6

). Analyzing such XRD patterns can be more challenging than for fully crystalline samples, as the peaks may be broadened or overlapped by the diffuse background thus making it difficult to identify. In such cases, additional techniques may be needed to fully characterize the sample.

Reference