Materials Science & Solid State

Crystallography, Stress-Strain & Failure Distribution Models

Specialized equations for X-ray diffraction (XRD) peak profile analysis, crystallite size and lattice microstrain estimation, Weibull mechanical reliability, and high-pressure equations of state.

Target Disciplines:Materials ScienceCrystallography (XRD)MetallurgySolid State PhysicsFailure Reliability

Common Fitting Challenges in Materials Science & Solid State

  • Accurate determination of integral breadth and Lorentzian fraction (η) for Scherrer and Williamson-Hall analysis
  • Reliable Weibull modulus (m) estimation in low-sample-size fracture strength testing
  • High non-linearity in third-order Birch-Murnaghan volumetric compression data

AltaiPlot High-Performance Fitting Engine

  • Pseudo-Voigt and Pearson VII profile fitting with direct FWHM and shape factor extraction
  • Batch matrix processing for multi-scan temperature or pressure dependent diffractograms
  • Automated Scherrer crystallite size calculation directly from fitted peak parameters

Materials Science & Solid State Models (1)

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materials-physics2 params

Weibull Distribution (Cumulative & Density)

The standard continuous probability distribution for brittle fracture strength and component failure lifetime analysis.

$P_f(\sigma) = 1 - \exp\left( -\left(\frac{\sigma}{\sigma_0}\right)^m \right)$
Materials ScienceFailure Engineering
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