Modulated phase ofK2MoxW1−xO4mixed compounds using orthorhombic symmetry: A powder diffraction study

Abstract

High-resolution x-ray powder diffraction data have been used to study the modulated phase of the ${\text{K}}_{2}{\text{WO}}_{4}$, ${\text{K}}_{2}{\text{Mo}}_{0.5}{\text{W}}_{0.5}{\text{O}}_{4}$, and ${\text{K}}_{2}{\text{MoO}}_{4}$ compounds. Literature considers ${\text{K}}_{2}{\text{WO}}_{4}$ and ${\text{K}}_{2}{\text{MoO}}_{4}$ as exceptions among the members of ${A}^{\ensuremath{'}}{A}^{\ensuremath{''}}B{X}_{4}$ family because their thermotropic phase transitions do not follow the commonly observed sequence and because their modulation wave vector, unusually, lies on the pseudohexagonal plane. Until now, the modulated phases of these compounds have been interpreted using hexagonal symmetry. The present work indicates, however, that a model consisting of threefold twinned orthorhombic modulated domains better describes the satellites observed in the temperature range of 620--740 K. The $Ccmm$ space group is proposed for the average structure of the whole family ${\text{K}}_{2}{\text{Mo}}_{x}{\text{W}}_{1\ensuremath{-}x}{\text{O}}_{4}$, whereas the $Ccmm(\ensuremath{\alpha}00)000$ with the wave vector $\mathbit{q}=(0.5+\ensuremath{\delta}){\mathbit{a}}^{\ensuremath{\ast}}$ is the appropriate superspace group for the description of the modulated structures. The coexistence of three orthorhombic domains, each of which is rotated by $120\ifmmode^\circ\else\textdegree\fi{}$ from each other, indeed reproduces a pseudohexagonal basis, which is a common feature in the ${A}^{\ensuremath{'}}{A}^{\ensuremath{''}}B{X}_{4}$ family. The usage of the twinning model allows a much simpler interpretation of the diffraction pattern and provides a more consistent way to describe the phase-transition sequence shown by the mixed ${\text{K}}_{2}{\text{Mo}}_{x}{\text{W}}_{1\ensuremath{-}x}{\text{O}}_{4}$ crystals.