Use of a Standard Reference Material for Precision Determination of Lattice Constants of Tetragonal Crystals PDF

Keywords

X-ray, diffractometry, lattice

Abstract

In X-ray diffractometry, precision lattice constant determination requires corrections to the measured 2θ- angles for instrumental, sample-dependent and random errors. The external standard method could correct for instrumental errors while the analytical least squares method could eliminate other sources of errors. It was, therefore, suggested that to obtain higher accuracy the externally calibrated 2θ-values should be refined by the analytical method. When applied to X-ray diffractometric data from Cu Al2 powder material (θ-phase) which has a tetragonal crystal structure, the lattice constants a0 and c0 were obtained as 0.60675 ± 0.00011 and 0.48775 ± 0.00006 nm, respectively. The internal standard method could correct for systematic errors. To minimize random errors, least squares formulae were developed for the tetragonal system. When applied to the internally calibrated 2θ-values of Cu Al2, the lattice constants a0 and c0 were obtained as 0.60695 ± 0.00010 and 0.48725 ± 0.00009 nm, respectively. The weighted average values of the lattice constants of CuAl2, at 298 K, corrected for most aberrations to peak positions were estimated as 0.60686 ± 0.00007 and 0.48760 ± 0.00005 nm. These values were considered as refinements of earlier published data.