Structural change associated with the incommensurate-normal phase transition in akermanite, Ca₂MgSi₂O₇, at high pressure

Abstract

 The structural changes associated with the incommensurate (IC)-normal (N) phase transition in akermanite have been studied with high-pressure single-crystal X-ray diffraction up to 3.79 GPa. The IC phase, stable at room pressure, transforms to the N phase at ∼1.33 GPa. The structural transformation is marked by a small but discernable change in the slopes of all unit-cell parameters as a function of pressure. It is reversible with an apparent hysteresis and is classified as a tricritical phase transition. The linear compressibility of the a and c axes are 0.00280(10) and 0.00418(6) GPa⁻¹ for the IC phase, and 0.00299(11) and 0.00367(8) GPa⁻¹ for the N phase, respectively. Weighted volume and pressure data, fitted to a second-order Birch-Murnaghan equation of state (K′≡4.0), yield V₀=307.4(1) ų and K₀=100(3) GPa for the IC phase and V₀=307.6(2) ų and K₀=90(2) GPa for the N phase. No significant discontinuities in Si–O, Mg–O and Ca–O distances were observed across the transition, except for the Ca–O1 distance, which is more compressible in the IC phase than in the N phase. From room pressure to 3.79 GP the volume of the [SiO₄] tetrahedron is unchanged (2.16 ų), whereas the volumes of the [MgO₄] and [CaO₈] polyhedra decrease from 3.61 to 3.55(1) ų and 32.8 to 30.9(2) ų, respectively. Intensities of satellite reflections are found to vary linearly with the isotropic displacement parametr of Ca and the librational amplitude of the [SiO₄] tetrahedron. At room pressure, there is a mismatch between the size of the Ca cations and the configuration of tetrahedral sheets, which appears to be responsible for the formation of the modulated structure; as pressure increases, the misfit is diminished through the relative rotation and distortion of [MgO₄] and [SiO₄] tetrahedra and the differential compression of individual Ca–O distances, concurrent with a displacement of Ca along the (110) mirror plane toward the O1 atom. We regard the high-pressure normal structure as a result of the elimination of microdomains in the modulated structure.