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 Ba_2-xCa_xSiO₄ 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 modulated phases within the A₂BX₄ family of K₂SO₄-related structures suggests an almost chronic instability to displacive modulation.