Effects of instrument function, crystallite size, and strain on reflection profiles

Abstract

Abstract Abstract A new approach to the analysis of reflection profiles is introduced. The basic idea is to calculate the instrument function by ray-tracing and include in the whole-pattern fitting a background function of the correct dependence on the scattering vector. In this way, only the effects of crystallite size and strain remain to be modeled. The instrument function is presented in general form, which can be adapted to energy-dispersive or angle-dispersive powder diffraction. The effects of the source size and wavelength distribution, equatorial and axial divergences, beam penetration in the sample, and different slits are included. Most of these aberrations are independent and can be cast in analytical forms, and the total instrument function is found by successive convolutions. The background arising from inelastic and resonant scattering is calculated from theory, while disorder scattering is modeled by a pair-correlation function and thermal diffuse scattering (TDS) by the Debye model for acoustic phonons and by the Einstein model for optical phonons. The total TDS is calculated as the part of the Bragg reflections lost due to thermal motion. The effects of crystallite size are treated in a general formalism where the reflection profile is the Fourier transform of the common volume of the crystallite and its ‘ghost’ shifted a distance tin the direction of the scattering vector k.The effects of strain are included in a distribution function of unit-cell displacements. Long-distance strain is described by a characteristic function, and the local strain by a correction term to the structure factor. Formulae that cover transition from local strain to long-distance strain are given. Anisotropic crystallite size and strain are described in terms of spherical harmonics which obey the crystal symmetry. The diffraction pattern of PbBr2 measured using CuKa1radiation is resolved using the procedure described above. The model parameters include only the thermal motion amplitudes and coefficients of the spherical harmonics that give the anisotropic crystallite size and strain.