Quantum mechanics

Crystal (programming language)

Statistics

Materials science

Computer science

Linearity

Physics

Mathematics

Optics

Burgers vector

Condensed matter physics

Mathematical analysis

Geometry

Programming language

Plot (graphics)

Diffraction

Fourier transform

Line (geometry)

Dislocation

Scripta Materialia

Diffraction peak profiles were calculated numerically for dislocation ensembles with different spatial arrangements and correlations between the Burgers vector signs. The latter property determines the stored elastic energy in the crystal and the width of the diffraction peaks. It is shown that within the approximation of the asymptotic line-profile theory the relationship between peak breadth and the magnitude of the diffraction vector in the modified Williamson-Hall (mWH) plot is linear. The slope of the line is proportional to the arrangement parameter M0.3 and to the square root of the dislocation density. The only rigorous way for determining M is the asymptotic Fourier method. Therefore, the evaluation of the dislocation density from the mWH-plot alone is impossible and should be avoided. The mWH plot however, is very useful in practice. Its linearity indicates a consistent asymptotic line-profile analysis.

The modified Williamson-Hall plot and dislocation density evaluation from diffraction peaks