Modulated phases in the Ba2SiO4-Ca2SiO4 system of A2BX4, K2SO4-related structures
Abstract The A2BX4 family of K2SO4-related structures have long been of interest to crystal chemists, largely due to the numerous different polymorphs and complicated sequences of phase transitions they sometimes exhibit as a function of temperature. For most such A2BX4 compounds, there are essentially only two distinct structure types or parent structures — a high-temperature, ‚hexagonal‘ form isomorphous to α-K2SO4 and a lower-temperature, orthorhombic form isomorphous to β-K2SO4. In addition to these two prototype structures, however, there often exist weakly distorted, or modulated, variants. In the case of the Ba2-xCaxSiO4 system, five such modulated variants have been found via an electron diffraction study and characterized. The characteristic satellite extinction conditions associated with the weak satellite reflections have been used to determine displacement eigenvectors and atomic displacement patterns associated with each of the observed modulation wave-vectors. The widespread occurrence of mo...