X-Ray Diffraction (XRD) – XRD Principle, XRD Analysis and Applications

X-ray diffraction (XRD) is a powerful non-destructive analytical technique used to evaluate crystalline materials and determine their structural properties. As one of the most widely used characterization techniques in scientific research and industrial applications, XRD provides unparalleled insights into their atomic and molecular structure.

“X-ray diffraction” broadly refers to the physical phenomenon of X-ray beams changing direction as a result of interactions with the electrons around atoms. However, the term has become synonymous with the XRD spectroscopic technique that takes advantage of this phenomenon to study the atomic and molecular structure of crystalline materials.¹ When X-rays interact with a crystal lattice, they create a unique diffraction pattern that serves as a "fingerprint" for material identification and structural analysis. This phenomenon occurs due to the wave nature of X-rays, which are electromagnetic radiation with wavelengths comparable to the spacing between atoms in crystal structures (approximately 0.1–10 nm).² This similarity allows X-rays to interact constructively with the periodic arrangement of atoms, producing measurable diffraction patterns that reveal detailed structural information about the material under investigation.

XRD is particularly valuable because it provides both qualitative and quantitative information about crystalline materials. The technique can identify different phases present in a sample, determine their relative concentrations, measure lattice parameters, assess crystal quality and evaluate preferred orientation effects. Unlike many other analytical techniques, XRD is non-destructive, meaning the sample remains intact after analysis.

XRD analysis provides crucial information about:

• Crystal structure and phase identification with high precision
• Lattice parameters and unit cell dimensions for structural characterization
• Crystallite size and strain analysis for quality assessment
• Preferred orientation (texture) in polycrystalline materials
• Quantitative phase analysis in multi-component systems
• Residual stress measurement in manufactured components
• Degree of crystallinity in semi-crystalline materials

The versatility of XRD extends from routine quality control in manufacturing to cutting-edge research in materials development. Industries ranging from pharmaceuticals to aerospace rely on XRD for ensuring product quality, developing new materials and understanding structure–property relationships.

The XRD principle is based on the elastic scattering of X-rays by atoms in a crystal lattice.³ When monochromatic X-rays strike a crystalline sample, they interact with electrons around atoms, causing the X-rays to scatter in all directions. However, constructive interference occurs only at specific angles where scattered waves are in phase, creating the characteristic diffraction pattern.

The scattering process involves the interaction between X-ray photons and the electron density distribution around atoms. When X-rays encounter an atom, they cause the electrons to oscillate, which generates secondary X-rays with the same frequency as the incident beam. These secondary X-rays propagate in all directions, but only specific directions result in constructive interference that produce detectable diffraction peaks (Figure 1a).

Figure 1: a) Diagram of constructive vs. destructive interference. b) Simplified layout of the XRD analysis experiment. Credit: Technology Networks.

The key requirements (Figure 1b) for XRD analysis include:

X-ray source: The most common sources use copper (Cu Kα, λ = 1.54 Å) or molybdenum (Mo Kα, λ = 0.71 Å) targets to produce characteristic X-rays suitable for most materials.⁴ Copper radiation is ideal for most routine analyses, while molybdenum radiation is preferred for samples containing heavy elements or when higher resolution is needed.

Crystalline material: The material must have long-range periodic atomic arrangement to produce sharp diffraction peaks. Amorphous materials produce broad, diffuse scattering patterns rather than sharp diffraction peaks.

Geometric arrangement: The incident angle of the X-ray beam on the sample, sample orientation and detector position must be precisely controlled to measure diffraction angles accurately. Modern diffractometers use sophisticated goniometers and alignment systems to ensure precise angular positioning.

Monochromatic radiation: The X-ray beam must be monochromatic (single wavelength) to enable accurate d-spacing calculations through crystal monochromators, filters or wavelength-dispersive optics.

The diffraction process occurs when the path difference between X-rays scattered from parallel crystal planes equals an integer multiple of the X-ray wavelength. This condition ensures that scattered waves interfere constructively, creating detectable diffraction peaks.

XRD pattern characteristics

An XRD pattern displays diffraction intensity versus diffraction angle (2θ), where θ is the Bragg angle.⁷ Each peak corresponds to a specific set of parallel crystal planes characterized by Miller indices (hkl). The diffraction pattern serves as a unique fingerprint for each crystalline phase, enabling identification and quantitative analysis.

Figure 3: An example of a powder XRD pattern simulated with Mercury software using pure Cu. Inset: Cu simulated packing with (111) plane visualized. Credit: Technology Networks.

The XRD pattern (example above, Figure 3) provides comprehensive structural information through various peak characteristics:

Peak position: The angular position directly relates to the d-spacing (interplanar spacing) through Bragg's law. Peak positions determine lattice parameters, identify phase and detect structural changes due to composition, temperature or pressure variations.

Peak intensity: The height or integrated area indicates the atomic arrangement within the crystal structure and the relative abundance of different phases. Intensity ratios provide information about preferred orientation effects and enable quantitative phase analysis.

Peak width: The breadth reveals crystal quality, including crystallite size and microstrain effects. Narrow peaks indicate large, well-formed crystals with minimal strain, while broad peaks suggest small crystallites or high levels of structural disorder.

Peak shape: The detailed shape provides insights into crystal defects, stacking faults and other structural imperfections. Asymmetric peak shapes often indicate compositional gradients or structural distortions.

X-ray diffractometer components

A modern X-ray diffractometer consists of several essential components working in coordination (Figure 4):⁸

Figure 4: Diagram of a common XRD instrumental layout. Credit: Technology Networks.

X-ray source: Generates monochromatic X-rays through electron bombardment of a metal target. The most common source uses copper with characteristic Kα radiation (λ = 1.5418 Å). The X-ray tube operates at high voltage (typically 30–60 kV) and current (10–50 mA) to produce sufficient intensity.

Incident beam optics: Various optical elements condition the X-ray beam including Soller slits for controlling beam divergence, monochromators for wavelength selection and focusing mirrors for beam concentration.

Sample stage: Holds the specimen and allows precise positioning and rotation during measurement. Powder samples are typically mounted on glass slides or in capillaries. The sample stage provides accurate angular positioning and may include environmental controls.

Detector system: Modern diffractometers employ position-sensitive detectors (PSDs) or area detectors that simultaneously collect data over a range of angles, significantly reducing measurement time while maintaining high resolution.

Goniometer: The precision mechanical system controlling angular relationships between X-ray source, sample and detector. Modern goniometers achieve angular accuracy better than 0.001°.

The instrument operates by directing X-rays at the sample while rotating both sample and detector according to θ-2θ geometry, ensuring the detector captures diffracted beams at the correct angle for constructive interference.

Single crystal XRD

When performing XRD on a single crystal, the pattern that is measured on the detector typically presents as a set of very defined isolated peaks (Figure 5). Each peak’s location on the detector plane and how intense those peaks are in relation to each other is how the full atomic arrangement is calculated.

Figure 5: Single crystal XRD data versus powder XRD data. Credit: Technology Networks.

Powder XRD

When there is not a single crystal, but a collection of microcrystals in a nice pile (a powder), the detector still sees the diffraction peaks, but they are in all directions as the material itself is oriented randomly in all directions (Figure 5). The symmetrical rings this produces are known as Debye rings. It is as if the single crystal peaks on the detector’s plane were perfectly rotated on the axis on the original, non-diffracted X-ray beam and “smeared” across the diffraction space. In the case of powder diffraction, these Debye rings only hold useful information on how intense the rings are and how far apart they are from each other. That is why the detector itself only scans in one direction, perpendicular to the Debye rings to gather the peak intensities in the space of interest (Figure 6), which takes minutes. In contrast, the detector in the single crystal experiment must scan the whole space taking a much longer time to complete and much more sophisticated equipment to accomplish.

Figure 6: Powder diffraction data acquisition in the diffraction space (black arrow) and where the typical powder diffraction peaks originate. Credit: Technology Networks.

Peak identification and phase analysis

XRD analysis begins with peak identification, requiring systematic examination of peak positions, intensities and shapes. Each crystalline phase produces a unique set of d-spacings and relative intensities that serve as its structural fingerprint.⁹

For example, using the diffraction pattern from Figure 2 one could complete the following sets of analyses:

Peak detection: Modern software automatically identifies peaks above a specified intensity threshold, though manual verification ensures accuracy. False peaks from noise or instrumental artifacts must be distinguished from genuine diffraction peaks.

Peak indexing: Determining Miller indices (hkl) for each diffraction peak requires knowledge of the crystal system and space group, assigning each peak to specific parallel crystal planes.

Database comparison: Matching observed patterns with reference databases like ICDD (International Centre for Diffraction Data) provides phase identification. The database contains over 900,000 reference patterns for known crystalline phases.

Quantitative analysis: Using peak intensities to determine relative phase concentrations requires careful consideration of factors affecting intensity, including preferred orientation, absorption and microstructural effects.

Advanced analysis techniques

An X-ray diffractogram provides a wealth of data beyond quantifying the concentration of individual phases present. Each phase encompasses a range of geometric orientations, which can also be systematically measured.

Rietveld refinement: This sophisticated method fits calculated diffraction patterns to experimental data, providing accurate quantitative phase analysis and structural parameters.¹⁰ The technique simultaneously refines crystal structure parameters, preferred orientation and instrumental factors.

Pattern decomposition: Advanced peak fitting algorithms separate overlapping peaks and extract accurate position, intensity and width information for detailed structural analysis.

Texture analysis: Pole figure measurements and orientation distribution function (ODF) analysis quantify preferred orientation effects in polycrystalline materials.

Structural parameter determination

There can be minor variations in the overall structure of a single phase. Most indexed phases represent measured arrangements of atoms, although these arrangements may vary to some extent. Such variations may result from differences in the formation process or from specific conditions, such as differing pressures or temperatures during formation.

Lattice parameters: Unit cell dimensions calculated from peak positions using Bragg's law and crystal system geometry. High-precision measurements detect lattice parameter changes as small as 0.001%.

Crystallite size: Determined from peak broadening using the Scherrer equation, relating peak width to volume-weighted average crystallite size. Analysis requires careful separation of size and strain broadening effects.

Microstrain: Analyzed through peak width variations with diffraction angle using methods like Williamson-Hall analysis, reflecting lattice parameter variations within the sample.

Preferred orientation: Assessed by comparing observed and calculated peak intensities; preferred orientation effects significantly impact quantitative analysis.

While related, XRD and X-ray crystallography have distinct characteristics, summarized in Table 1:

Table 1: A comparison of XRD and X-ray crystallography.

	X-Ray Diffraction (XRD)	X-Ray Crystallography
Sample Types	Powders, polycrystalline materials, thin films, textured samples	High-quality single crystals (typically 0.1–1 mm in size and hand-picked by optical microscopy)
Information Provided	Phase identification, lattice parameters, crystallite size, microstrain, preferred orientation, quantitative phase analysis	Complete 3D atomic structure, including precise atomic positions, bond lengths, bond angles, thermal parameters
Data Collection	Rapid analysis           (minutes to hours)	Extensive measurements (hours to days)
Sample Requirements	Minimal preparation; small amounts needed	High-quality single crystals, extensive growth methods
Applications	Quality control, phase analysis, materials characterization, process monitoring	New material design, drug discovery, protein structure determination, fundamental research

Single crystal X-ray crystallography provides atomic positions with precision better than 0.01 Å and generally requires extensive crystal growth and preparation methods to provide large enough crystals for the analysis. ¹¹ However, powder XRD is more versatile and practical for routine analysis of polycrystalline materials. Typically, the sample preparation method for powder XRD only requires reducing the particle size of the powder below 50 microns with a simple mortar and pestle.

XRD, X-ray scattering (SAXS) and grazing incidence SAXS (GISAXS) are complementary techniques probing different length scales. A comparison is made in Table 2.

Table 2: A comparison of XRD, SAXS and GISAXS.

Technique	Angular Range (2θ)	Length Scale	Information Provided	Applications
XRD (Wide-Angle X-Ray Scattering)	5–90°	0.1–10 nm (atomic and molecular level)	Crystal structure, phase identification, lattice parameters, crystallite size, microstrain	Phase identification, structural characterization, quality control
SAXS (Small-Angle X-Ray Scattering)	0.1–5°	1–100 nm (nanostructure level)	Particle size and shape, surface area, pore structure, domain organization, interface characteristics	Nanoparticle characterization, polymer science, biological macromolecules, porous materials
GISAXS (Grazing Incidence SAXS)	Below 0.1°	Surface and nanostructure level from 100 nm to microns	Combines surface sensitivity with nanostructure characterization for thin films and surface structures	Analysis of thin films and surface structures

The complementary nature of XRD and SAXS makes them powerful tools for comprehensive structural characterization spanning atomic to nanoscale levels. ¹²

XRD spectroscopy is a versatile analytical technique that has found widespread applications across various scientific disciplines. Its ability to provide detailed information about the crystallographic structure, chemical composition and physical properties of materials makes it an indispensable tool in both research and industry. The following sections will delve into the diverse applications of XRD spectroscopy, highlighting its significance in advancing our understanding of materials at the atomic and molecular levels.

Materials science applications

XRD serves as a cornerstone technique in materials science.¹³ Through phase identification, scientists can quickly discern crystalline phases present in complex materials, which is crucial for understanding how these materials behave and for predicting their properties. In the domain of alloy development, XRD is indispensable for tracking phase formation during heat treatment, identifying precipitates and monitoring solid solution formation – all vital for guiding the design of advanced alloys.

For ceramics and composites, XRD allows for precise characterization of ceramic phases, tracking of sintering processes and identification of reaction products within composite structures. When it comes to thin film analysis, specialized XRD methods are used to characterize epitaxial relationships, measure film thickness and analyze strain states in multilayer assemblies. Additionally, stress analysis via XRD offers non-destructive measurement of residual stresses in manufactured components, which is essential for understanding and predicting fatigue behavior.

Pharmaceutical applications

The pharmaceutical industry also relies heavily on XRD. For polymorph screening, the technique helps identify and quantify different crystalline forms of drug compounds, which can greatly impact a drug’s dissolution rate and bioavailability.¹⁴ XRD is essential for solid-state characterization, providing detailed information on the crystal structure, particle size and degree of crystallinity in active pharmaceutical ingredients (APIs).

In formulation development, an understanding of solid-state behavior leads to more rational design of formulations and optimization of manufacturing processes. Stability studies use XRD to monitor phase changes during storage, which helps in predicting shelf life and optimizing storage conditions. Finally, regulatory compliance demands comprehensive solid-state characterization data, including XRD results, as a requirement for drug approval by regulatory agencies.

Geological and environmental applications

In geological and environmental applications, XRD is widely used for mineral identification, enabling the definitive identification of minerals in rocks, soils and sediments – an essential step for geological mapping and resource exploration. The analysis of clay minerals often requires specialized XRD techniques, such as glycolation and heating treatments, to distinguish between subtle mineralogical differences.¹⁵

XRD is also pivotal in environmental monitoring, where it is employed to identify hazardous crystalline phases like asbestos, quartz and heavy metal compounds in environmental samples. In the petroleum industry, the analysis of drilling mud, reservoir rocks and completion fluids through XRD yields information crucial for optimizing drilling operations.

Advanced applications

Advanced applications of XRD are rapidly expanding. In battery technology, XRD is used to characterize electrode materials and to monitor structural changes during charge and discharge cycles, which is vital for the development of next-generation batteries. In additive manufacturing, XRD reveals phase composition, residual stresses and microstructural features that influence the mechanical properties of 3D-printed materials.

Nanotechnology also benefits from XRD, as it enables the characterization of nanoparticles, quantum dots and nanocomposites to provide essential insights into their size-dependent properties. With the advent of synchrotron XRD, high-intensity synchrotron radiation now allows for rapid data collection, enhanced resolution and specialized techniques previously unattainable in laboratory settings. Finally, in-situ XRD empowers researchers to monitor structural changes in real time during heating, cooling or chemical reactions, offering valuable insights into transformation kinetics.

XRD stands as one of the most powerful and versatile analytical techniques in modern science and technology. From its fundamental principles rooted in Bragg's law to its sophisticated applications across diverse fields, XRD continues to provide unparalleled insights into the structure and properties of crystalline materials.

Modern XRD instruments combine high-precision mechanics, advanced optics and sophisticated data analysis software to deliver structural information with unprecedented accuracy and speed.

The non-destructive nature of XRD, combined with its ability to analyze samples ranging from single crystals to complex polycrystalline mixtures, makes it indispensable for quality control, research and development. Whether identifying unknown phases, optimizing manufacturing processes or developing new materials, XRD provides essential quantitative structural information.

As technology advances, new frontiers in XRD analysis are emerging. Machine learning algorithms automate pattern analysis and phase identification, while improved detector technologies enable faster data collection. Portable XRD instruments bring laboratory-quality analysis to field applications, while synchrotron sources push the boundaries of resolution and sensitivity.

Understanding XRD principles, capabilities and limitations remains crucial for scientists and engineers working with crystalline materials. The technique's unique combination of structural sensitivity, quantitative accuracy and practical applicability ensures its continued importance in advancing materials understanding and enabling technological innovation.