P–V–T equation of state of synthetic mirabilite (Na₂SO₄·10D₂O) determined by powder neutron diffraction

Neutron powder diffraction data have been collected from Na₂SO₄·10D₂O (the deuterated analogue of mirabilite), a highly hydrated sulfate salt that is thought to be a candidate rock-forming mineral in some icy satellites of the outer solar system. These measurements, made using the OSIRIS instrument on the ISIS neutron spallation source, covered the range 0.1 < P < 545 MPa and 150 < T < 270 K. The refined unit-cell volumes as a function of pressure and temperature are parameterized in the form of a Birch–Murnaghan third-order equation of state, and the anisotropic linear incompressibilities are represented in terms of the elastic strain tensor. At 270 K, the bulk modulus K_0,270 = 19.6 (1) GPa, its first pressure derivative ∂K/∂P = 5.8 (5) and its temperature dependence ∂K/∂T = −0.0175 (6) GPa K⁻¹. The stiffest direction at 270 K, with a linear bulk modulus of ∼82 GPa, is coincident with the twofold axis of this monoclinic crystal. Of the remaining two principal directions, the most compressible (K ≃ 44 GPa) is roughly aligned with the c axis, and the intermediate value (K ≃ 59 GPa) is therefore approximately collinear with a*. With the aid of additional published data, a number of other important thermodynamic quantities have been derived, including the Grüneisen and Anderson–Grüneisen parameters, and the volume and enthalpy of melting along the high-pressure melting curve. Additional data obtained during this work, concerning the elastic properties of deuterated ice IV, are also presented.