Principle of X-ray diffraction study of a crystalline mineral.

Fundamentals of Crystallography and X-rays

Before delving into XRD, it’s essential to understand the concept of crystallinity. Minerals are often crystalline, meaning their atoms are arranged in a highly ordered, repeating three-dimensional pattern. This pattern is described by a crystal lattice. Amorphous materials, in contrast, lack this long-range order.

X-rays are electromagnetic radiation with wavelengths comparable to the interatomic spacing in crystals (typically 0.1 to 10 nanometers). This makes them ideal for probing the structure of crystalline materials. When an X-ray beam interacts with a crystalline material, several phenomena can occur: transmission, absorption, and diffraction.

Bragg's Law: The Core Principle

The foundation of X-ray diffraction is Bragg's Law, formulated by William Henry Bragg and William Lawrence Bragg in 1913. This law describes the conditions for constructive interference of X-rays diffracted by a crystal lattice.

Bragg's Law is mathematically expressed as: nλ = 2dsinθ

• n: An integer representing the order of diffraction (usually 1).
• λ: The wavelength of the X-rays used.
• d: The interplanar spacing – the distance between parallel planes of atoms in the crystal lattice.
• θ: The angle of incidence (and reflection) of the X-ray beam, also known as the Bragg angle.

Constructive interference occurs only when the path difference between X-rays reflected from adjacent planes is equal to an integer multiple of the wavelength. This results in strong diffracted beams at specific angles.

The X-ray Diffraction Process

A typical XRD setup involves:

• X-ray source: Generates a beam of monochromatic X-rays (usually copper or molybdenum Kα radiation).
• Sample holder: Holds the crystalline mineral in a specific orientation.
• Detector: Measures the intensity of the diffracted X-rays as a function of the diffraction angle (2θ).

The sample is irradiated with the X-ray beam, and the detector scans through a range of 2θ angles. The intensity of the diffracted X-rays is recorded at each angle, creating a diffraction pattern. This pattern is a series of peaks, each corresponding to constructive interference from a specific set of crystal planes.

Interpreting Diffraction Patterns

The diffraction pattern is unique to each crystalline mineral and can be used for identification. The position (2θ) of the peaks is related to the d-spacing of the crystal planes via Bragg's Law. By measuring the peak positions and using known X-ray wavelengths, the d-spacings can be calculated.

These d-spacings are then compared to a database of known mineral diffraction patterns (e.g., the Powder Diffraction File (PDF) maintained by the International Centre for Diffraction Data (ICDD)). The matching pattern confirms the mineral's identity.

The intensity of the peaks is related to the abundance and arrangement of atoms in the crystal planes. This information can be used to determine the mineral's crystal structure and refine its atomic positions.

Applications in Mineralogy

• Mineral Identification: The primary application, allowing for rapid and accurate identification of unknown minerals.
• Phase Analysis: Determining the different crystalline phases present in a rock or soil sample.
• Quantitative Analysis: Determining the relative amounts of different minerals in a mixture.
• Structural Refinement: Determining the precise atomic arrangement within a crystal structure.
• Strain Analysis: Measuring the stress and strain within a mineral crystal.