6.2 Powder X-ray diffraction
4 min read•august 16, 2024
Powder X-ray diffraction (PXRD) is a powerful technique for analyzing crystalline materials. It uses X-rays to create unique diffraction patterns, revealing crucial information about crystal structures, phases, and material properties.
PXRD offers advantages over single-crystal methods, including faster data collection and simpler sample preparation. It's ideal for , quantitative analysis, and studying materials with preferred orientation or strain.
Principles and Instrumentation of Powder X-ray Diffraction
Fundamental Concepts and Equations
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- Powder X-ray diffraction (PXRD) utilizes X-ray interaction with crystalline materials to produce characteristic diffraction patterns
- Bragg equation governs constructive interference in PXRD
- Relates X-ray wavelength (λ) to (d) and diffraction angle (θ)
- Random orientation of crystallites in powdered samples ensures uniform X-ray exposure
- PXRD patterns display intensity versus 2θ (twice the Bragg angle)
- Peak positions reveal crystal structure information
- Peak intensities indicate atomic positions and thermal motion
Instrumentation and Sample Preparation
- PXRD instruments comprise several key components
- X-ray source (typically Cu Kα radiation)
- Sample holder (flat plate or capillary)
- Goniometer for precise angle measurements
- (scintillation counter or position-sensitive detector)
- Sample preparation involves grinding crystalline material into fine powder (particle size ~10 μm)
- Debye-Scherrer method employs cylindrical camera to collect diffraction patterns on film strip
- Modern diffractometers use electronic detectors for rapid data collection
- Sample mounting techniques include:
- Flat plate for reflection geometry
- Capillary for transmission geometry (air-sensitive samples)
Analyzing Powder X-ray Diffraction Patterns
Pattern Interpretation and Phase Identification
- PXRD patterns consist of peaks representing different crystal planes
- Phase identification compares experimental patterns with reference data
- Utilizes databases like Powder Diffraction File (PDF) from International Centre for Diffraction Data (ICDD)
- D-spacing and relative intensities serve as "fingerprints" for unknown crystalline phases
- Indexing assigns Miller indices (hkl) to diffraction peaks
- Crucial for determining crystal system and lattice parameters
- Qualitative phase analysis identifies characteristic peaks of different phases in mixtures
- Semi-quantitative analysis estimates relative abundances based on peak intensities
Peak Analysis and Structural Information
- Peak positions determined by parameters
- Peak intensities influenced by atomic positions, thermal motion, and multiplicity
- Peak broadening provides information on crystallite size and strain
- Scherrer equation relates peak width to crystallite size:
- D represents crystallite size
- K denotes shape factor (typically 0.9)
- β signifies peak broadening (FWHM)
- Williamson-Hall plot separates size and strain contributions to peak broadening
- ε represents microstrain
Applications of Powder X-ray Diffraction
Quantitative Phase Analysis
- Quantitative analysis based on proportionality between peak intensities and phase volume fractions
- Reference Intensity Ratio (RIR) method compares sample peak intensities to standard (corundum)
- Enables quantification of multi-phase mixtures
- Direct comparison method utilizes pure phase standards for calibration
- Matrix flushing technique incorporates internal standard for improved accuracy
Structure Refinement Techniques
- extracts detailed structural information from PXRD data
- Fits calculated pattern to observed data through least-squares refinement
- Simultaneously refines crystal structure, sample characteristics, and instrumental factors
- Whole-pattern fitting techniques extract accurate lattice parameters and peak intensities
- Pawley method refines unit cell and peak profile parameters
- Le Bail method additionally refines peak intensities
- Pair Distribution Function (PDF) analysis probes local structure in crystalline and amorphous materials
- Fourier transform of total scattering data yields real-space atomic correlations
Powder vs Single Crystal X-ray Diffraction
Data Collection and Information Content
- PXRD compresses three-dimensional diffraction data into one-dimensional pattern
- SCXRD provides full three-dimensional diffraction data
- PXRD yields less precise structural information compared to SCXRD
- Better suited for phase identification and quantitative analysis
- SCXRD offers more detailed atomic positions and thermal parameters
- Superior for solving unknown crystal structures
Sample Requirements and Preparation
- PXRD requires polycrystalline powders or bulk materials
- Non-destructive and uses minimal sample material
- SCXRD demands high-quality single crystals
- Challenging to obtain for some materials
- PXRD accommodates materials with preferred orientation, texture, or strain
- Provides valuable information on these properties
- SCXRD analysis complicated by crystal imperfections or twinning
Experimental Considerations
- PXRD enables faster data collection compared to SCXRD
- Time-resolved and in-situ studies more feasible with PXRD
- Simpler sample environments and quicker measurements
- PXRD better suited for studying phase transitions and reaction kinetics
- SCXRD provides higher resolution and more accurate bond lengths and angles
- PXRD advantageous for materials prone to radiation damage
- Distributes X-ray exposure over larger sample volume
Key Terms to Review (18)
Bragg's Law: Bragg's Law is a fundamental principle in crystallography that relates the angle at which X-rays are diffracted by a crystal lattice to the distance between the crystal planes. This law, expressed mathematically as $$n\lambda = 2d\sin\theta$$, is essential for understanding how the arrangement of atoms in a crystal can be determined through diffraction techniques.
Crystal symmetry: Crystal symmetry refers to the orderly arrangement of atoms in a crystal structure that is characterized by repeating patterns and specific geometric relationships. This property is crucial for understanding the physical properties of materials, as it influences aspects such as stability, mechanical strength, and optical behavior. The symmetrical arrangement of particles allows for predictable interactions between them, which can be examined through techniques like X-ray diffraction.
Crystalline solids: Crystalline solids are materials whose constituent atoms, ions, or molecules are arranged in an ordered and repeating three-dimensional pattern. This regular structure results in distinct physical properties, such as sharp melting points and anisotropic behavior, which are essential for various applications in material science and solid-state physics.
Detector: A detector is a device that captures and measures the intensity of radiation, converting it into an electronic signal that can be analyzed to provide information about the structure and properties of crystalline materials. In crystallography, detectors play a crucial role in interpreting the diffraction patterns generated when X-rays interact with a crystal, enabling researchers to determine the arrangement of atoms within the crystal lattice.
Full width at half maximum (fwhm): Full width at half maximum (FWHM) is a measurement used to describe the width of a peak in a distribution, particularly in spectroscopy and diffraction patterns. It indicates the range of values over which the intensity reaches half of its maximum value, helping to quantify the sharpness or broadness of a peak. In powder X-ray diffraction, FWHM is crucial as it relates to crystallite size, strain, and instrumental effects, playing a vital role in analyzing materials' structural properties.
Interplanar Spacing: Interplanar spacing refers to the distance between parallel planes of atoms in a crystalline material. This distance plays a crucial role in determining the diffraction patterns observed in X-ray crystallography, as it influences how waves interact with the crystal lattice and provides insights into the arrangement of atoms within the material.
Material Science: Material science is an interdisciplinary field that focuses on the properties, performance, and applications of materials, particularly in understanding how their structure at atomic or molecular levels affects their macroscopic behavior. This field bridges physics, chemistry, and engineering to develop new materials and improve existing ones for various uses in technology and industry.
Peak position: Peak position refers to the specific angle or location on a diffraction pattern where the intensity of scattered X-rays reaches a maximum. This position is crucial for identifying the crystal structure and determining the spacing between lattice planes in powdered samples, which is essential for analyzing materials through techniques like powder X-ray diffraction.
Pharmaceutical analysis: Pharmaceutical analysis is the process of evaluating the quality, safety, and efficacy of pharmaceutical substances and products through various scientific techniques. This critical field ensures that medications are formulated correctly, are free from contaminants, and have the intended therapeutic effects. It encompasses both qualitative and quantitative assessments, which can include identifying chemical compounds and determining their concentrations in drug formulations.
Phase identification: Phase identification is the process of determining the specific crystalline phases present in a material, which is crucial for understanding its structural and functional properties. This process typically involves analyzing diffraction patterns obtained from various techniques to match observed data with known reference patterns. Accurate phase identification allows researchers to gain insights into the material's composition, purity, and potential applications.
Polycrystalline materials: Polycrystalline materials are solids composed of many small crystals or grains, each with its own orientation. These materials have distinct physical properties resulting from their grain structure and can exhibit anisotropic behavior, meaning their properties can vary depending on the direction of measurement. The analysis of polycrystalline materials often involves various diffraction techniques to investigate their crystalline structure and phase composition.
Reciprocal Lattice: A reciprocal lattice is a mathematical construct used in crystallography to represent the periodicity of a crystal in momentum space rather than real space. It is essential for understanding diffraction patterns, as the points in the reciprocal lattice correspond to the conditions for constructive interference of scattered waves, which directly relate to crystal structures and properties.
Rietveld Refinement: Rietveld refinement is a mathematical technique used in crystallography to extract precise structural information from powder diffraction data. This method allows researchers to refine crystal structures by fitting a calculated diffraction pattern to observed data, making it essential for determining the atomic positions, thermal vibrations, and overall quality of the crystal model. Its significance is rooted in historical advancements and continues to play a crucial role in various diffraction techniques, enabling phase identification and quantification.
Texture Analysis: Texture analysis refers to the study of the preferred orientation of crystallites in a material, providing insight into the material's properties and behaviors. Understanding texture is essential as it influences mechanical, thermal, and optical characteristics, which are crucial for predicting how materials will perform in various applications.
Unit Cell: A unit cell is the smallest repeating unit of a crystal lattice that, when stacked together with identical units, forms the entire crystal structure. Understanding the unit cell is essential as it connects various concepts, such as atomic arrangement, symmetry, and the overall properties of materials.
William Henry Bragg: William Henry Bragg was a renowned British physicist and chemist, famous for his pioneering work in the field of crystallography, particularly for developing X-ray crystallography methods. His contributions significantly advanced the understanding of crystal structures, which laid the groundwork for modern crystallography and its applications in various scientific fields.
William Lawrence Bragg: William Lawrence Bragg was a prominent physicist known for his pioneering work in X-ray crystallography, which earned him the Nobel Prize in Physics in 1915. His groundbreaking contributions significantly advanced the understanding of crystal structures through the application of X-ray diffraction techniques, directly influencing various fields including chemistry and materials science.
X-ray diffractometer: An X-ray diffractometer is an advanced instrument used to analyze the structural properties of crystalline materials by measuring the angles and intensities of X-rays scattered off a sample. It operates by directing a beam of X-rays at the sample, causing the X-rays to be diffracted at specific angles that depend on the crystal structure. The resulting data allows researchers to determine lattice parameters, crystal orientation, and other crucial information about the material's internal arrangement.