X-ray diffraction

X-ray diffraction (XRD) is a powerful analytical technique in the fields of chemistry, physics, and materials science. It is used primarily to analyze the structure of crystalline substances. Using XRD, researchers can determine the arrangement of atoms within a crystal, measure the dimensions of a crystal, and assess the purity and defects of a crystal. This analytical method uses the diffraction of electromagnetic radiation with wavelengths on the atomic scale—X-rays—by a crystal lattice.

Fundamentals of X-ray diffraction

X-rays are a form of electromagnetic radiation with wavelengths typically ranging from 0.01 to 10 nanometers. In the context of XRD, X-rays generated and focused on a crystal interact with the crystal lattice. According to Bragg's law, when these X-rays strike the crystal, they scatter in specific directions. Bragg's law is expressed mathematically as:

nλ = 2d sin θ

Where:

• n is the order of diffraction, an integer.
• λ is the wavelength of the incident X-ray beam.
• d is the distance between the crystal lattice planes.
• θ is the angle between the incident X-ray and the scattering planes.

The key to understanding X-ray diffraction lies in Bragg's law, which relates the scattering angle to the wavelength of the incident X-rays and the lattice spacing of the crystal. When these criteria are satisfied, constructive interference occurs, producing an observable diffraction peak at the detector.

Crystal structure analysis

A primary use of X-ray diffraction is to determine crystal structures. Understanding the structure of a substance at the atomic level provides in-depth information about its chemical and physical properties. For example, the crystalline structure of minerals, biological macromolecules such as proteins, and other compounds can be elucidated through XRD.

Powder X-ray diffraction (PXRD)

Powder XRD is a widely used form of X-ray diffraction involving polycrystalline or powdered samples. This method is simple and advantageous for investigating materials that do not form large single crystals or are available in powder form. Powdered samples usually contain a random array of microcrystals, which ensures that all possible crystal orientations are sampled when exposed to X-ray radiation. The diffracted intensity is measured as a function of the scattering angle and converted into a pattern that can be referenced against known standards.

PXRD pattern = Intensity vs. 2θ (where 2θ is the scattering angle)

This technique provides important information about the unit cell dimensions and can be used for qualitative phase identification by comparing experimental diffraction patterns with established databases.

Single-crystal X-ray diffraction

Single-crystal XRD is used to obtain more detailed information about the three-dimensional arrangement of atoms in a crystal. The sample is a single crystal, mounted on a goniometer, and systematically rotated under the X-ray beam to build up a complete data set. This method is more complex than PXRD, but provides extensive insight into the architecture of the crystal.

Equipment

The typical setup for an X-ray diffraction experiment includes several major components:

• X-ray source: This can be a sealed tube or a rotating anode that generates the X-rays. Mo Kα and Cu Kα are the most common wavelengths used.
• Sample holder: Holds the crystalline sample, this may involve spinning the sample to randomize the orientation in PXRD.
• Monochromator: Selects radiation of a single wavelength to improve the clarity and resolution of diffraction data.
• Detector: Measures the intensity of the diffracted X-rays. Modern detectors use charge-coupled devices (CCDs) for high sensitivity.

The sample and detector are aligned such that the detector can collect data over a range of angles (2θ) as the sample is irradiated by the X-rays.

Applications of X-ray diffraction

Phase detection

One of the most important applications of XRD is to identify phases in polycrystalline materials. Each compound has a unique XRD pattern (often called a "fingerprint"), which allows phase identification by comparing experimental data with reference patterns held in databases such as the International Diffraction Data Center (ICDD).

Determination of unit cell dimensions

XRD can accurately measure the dimensions of the unit cell, the smallest repeating unit in a crystal lattice. These dimensions are important in characterizing the crystal structure and predicting properties such as density and thermal expansion.

Texture analysis

The preferred orientation of crystallites, known as texture, can be investigated through XRD. Texture analysis helps to understand how crystallographic orientation affects material properties such as strength and ductility.

Strain measurements

XRD can be used to determine changes in the lattice spacing caused by stress in a material. By analyzing the changes in the diffraction fringes, scientists can quantify stress and strain, providing invaluable information in metallurgy and materials engineering.

Crystallite size and microstrain

The Scherrer equation relates the width of the diffraction peaks to the size of the crystallites:

D = (Kλ) / (βcosθ)

Where:

• K is the shape factor (typically ~0.9).
• λ is the wavelength of the X-ray.
• β is the full width at half maximum (FWHM) of the peak.
• θ is the Bragg angle.

This equation helps to predict the crystallite size and assess the uniformity of the material. It is particularly useful in understanding nanoparticles or thin films.

Visualization with examples

XRD is best understood visually. Consider a simple crystal structure such as sodium chloride (NaCl). The crystal is composed of alternating sodium and chloride ions in a cubic arrangement. If you want to look at its diffraction pattern:

Suppose a beam of X-rays interacts with this crystal. The diffraction pattern produced will have distinct peaks corresponding to planes of high electron density created by the alternation of Na ⁺ and Cl ^- ions.

Recent advances in X-ray diffraction

Over the past few years, advances in X-ray sources, detectors, and computational techniques have significantly increased the speed, accuracy, and range of XRD applications. High-resolution detectors and synchrotron radiation sources are among the improvements that have broadened XRD capabilities, allowing the investigation of smaller samples and faster data collection.

Additionally, integration with computational chemistry tools provides more accurate models for studying complex materials and biological systems. This synergy helps uncover information that was difficult to obtain using traditional methods of analysis.

Conclusion

X-ray diffraction is an indispensable tool in analytical chemistry and materials science. Its ability to provide crucial information about the atomic structure of substances makes it essential for research and development in a variety of fields. From the determination of complex biological macromolecules to phase identification in metallurgical engineering, XRD serves as a cornerstone for many scientific investigations. As the technique evolves, its applications will continue to expand, supporting further discoveries in a variety of disciplines.

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