13.2 X-Ray Diffraction and Fluorescence

X-ray diffraction and fluorescence are powerful tools for mineral identification. XRD reveals crystal structures by analyzing how X-rays scatter off atomic planes, while XRF measures elemental composition through characteristic X-ray emissions.

These techniques provide complementary information about minerals. XRD identifies specific mineral phases and polymorphs, while XRF quantifies elemental content. Together, they offer a comprehensive approach to mineral characterization in various geological settings.

X-ray Diffraction for Mineral Identification

Principles of X-ray Diffraction

• X-ray diffraction results from X-rays interacting with periodic atomic structures in crystalline materials, producing constructive interference patterns
• Bragg's Law ($nλ = 2d sinθ$) describes diffraction conditions, relating X-ray wavelength to interplanar spacing and diffraction angle
• XRD employs monochromatic X-rays generated by sources (copper or molybdenum) to probe mineral crystal structures
• Diffraction patterns serve as unique "fingerprints" for mineral identification
• XRD provides information on crystal symmetry, unit cell parameters, and atomic positions within crystal lattices
• Powder XRD analyzes finely ground samples, identifying multiple mineral phases in mixtures

Applications in Mineralogy

• Phase identification determines specific minerals present in a sample
• Quantitative analysis measures relative abundances of minerals in mixtures
• Crystal structure refinements reveal detailed atomic arrangements
• Unit cell parameter determination calculates dimensions of crystal lattices
• Crystallinity assessment evaluates the degree of structural order in minerals
• Strain analysis measures deformation in crystal structures
• Texture analysis examines preferred orientation of crystallites in samples

Interpreting XRD Patterns

XRD Pattern Components

• Diffraction peaks represent X-rays plotted against diffraction angle (2θ)
• Peak positions correspond to specific lattice planes in crystal structures
• Peak intensities relate to atomic scattering factors and unit cell atom arrangements
• Background signal results from factors (sample holder, amorphous content)
• Peak width influenced by crystallite size and instrumental factors
• d-spacings calculated from peak positions using Bragg's Law
  • Example: A peak at 2θ = 26.6° for Cu Kα radiation corresponds to d = 3.34 Å (characteristic of quartz)
• International Centre for Diffraction Data (ICDD) maintains comprehensive XRD pattern database for minerals and materials

Pattern Analysis Techniques

• Indexing assigns Miller indices (hkl) to peaks, relating them to crystal planes
  • Example: For cubic crystals, (100), (110), and (111) are common low-index planes
• Determines crystal system and lattice parameters from peak positions and intensities
• Rietveld refinement extracts detailed structural information from XRD patterns
  • Refines atomic positions, occupancies, and thermal parameters
  • Accounts for factors (preferred orientation, absorption effects)
• Considers factors influencing patterns during interpretation
  • Preferred orientation affects relative peak intensities
  • Particle size effects broaden diffraction peaks
  • Strain in crystal lattices causes peak shifting and broadening

X-ray Fluorescence for Elemental Analysis

Principles of X-ray Fluorescence

• X-ray fluorescence occurs when atoms excited by high-energy X-rays emit characteristic X-rays
• Inner-shell electrons ejected, outer-shell electrons fill vacancies, emitting element-specific X-rays
• Emitted X-ray energies enable qualitative identification of elements in samples
• XRF performs qualitative and quantitative elemental analysis
• Detection limits typically in parts per million (ppm) range for many elements
• Energy-dispersive XRF (ED-XRF) uses semiconductor detectors to measure X-ray energies directly
• Wavelength-dispersive XRF (WD-XRF) employs crystal diffraction to separate X-rays by wavelength
  • WD-XRF offers higher spectral resolution but lower sensitivity than ED-XRF

XRF Analysis Considerations

• Matrix effects influence XRF measurements
  • Absorption reduces intensity of characteristic X-rays
  • Enhancement occurs when one element's fluorescence excites another
• XRF provides non-destructive analysis with minimal sample preparation
• Rapid elemental analysis ideal for minerals and rocks
• Limitations include difficulty detecting light elements (atomic number < 11)
• Potential interferences from overlapping spectral lines require careful interpretation
• Quantitative analysis requires calibration using standard reference materials
• Sample homogeneity crucial for accurate results in bulk analysis

Characterizing Minerals with XRD and XRF

Sample Preparation Techniques

• Proper sample preparation crucial for accurate XRD and XRF analysis
• XRD sample preparation methods
  • Powder preparation involves grinding samples to fine, uniform particle size
  • Oriented mounts used for clay mineral analysis
  • Single-crystal XRD requires selection of high-quality crystals
• XRF sample preparation techniques
  • Pressed pellets for analyzing major and trace elements in rocks
  • Fused beads eliminate particle size effects and reduce matrix effects
  • Loose powder analysis for non-destructive testing of small samples

Integrated Analysis Approaches

• Combining XRD and XRF provides complementary structural and compositional information
• XRD identifies mineral phases and polymorphs
  • Example: Distinguishing calcite (CaCO3) from aragonite (CaCO3) based on crystal structure
• XRF quantifies elemental data for chemical formulae and compositional variations
  • Example: Determining Fe/Mg ratio in olivine ((Mg,Fe)2SiO4) solid solution series
• Trace element analysis by XRF fingerprints mineral deposits
  • Example: Using rare earth element patterns to identify specific pegmatite sources
• Advanced XRD techniques provide insights into mineral behavior
  • In-situ high-temperature studies examine phase transitions
  • High-pressure experiments simulate deep Earth conditions
• Micro-XRF and micro-XRD enable spatially resolved analysis of heterogeneous samples
  • Study mineral zoning in metamorphic rocks
  • Analyze complex intergrowths in ore deposits
• Data integration requires specialized software and mineralogical databases
  • Example: Rietveld analysis software for quantitative phase analysis
  • Mineral identification databases (e.g., RRUFF project) for pattern matching