# Journal of Applied Crystallography

### Volume 46, Part 2 (April 2013)

## research papers

*J. Appl. Cryst.* (2013). **46**, 448-460 [ doi:10.1107/S0021889813001362 ]

*P*-*V*-*T* equation of state of synthetic mirabilite (Na_{2}SO_{4}·10D_{2}O) determined by powder neutron diffraction

**Abstract:** Neutron powder diffraction data have been collected from Na_{2}SO_{4}·10D_{2}O (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.

**Keywords: mirabilite; equations of state; neutron diffraction; ice IV.**

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