Equation of state and pressure-induced structural changes in mirabilite (Na2SO4·10H2O) determined from ab initio density functional theory calculations

Abstract

We have carried out ab initio calculations using density functional theory to determine the bulk elastic properties of mirabilite, Na2SO4·10H2O, and to obtain information on structural trends caused by the application of high pressure up to ~60 GPa. We have found that there are substantial isosymmetric discontinuous structural re-organisations at ~7.7 and ~20 GPa caused by changes in the manner in which the sodium cations are coordinated by water molecules. The low-pressure and intermediate-pressure phases both have sodium in sixfold coordination but in the high-pressure phase the coordination changes from sixfold to sevenfold. These coordination changes force a re-arrangement of the hydrogen-bond network in the crystal. The trend is towards a reduction in the number of hydrogen bonds donated to the sulphate group (from twelve down to six over the range 0–60 GPa) and an increase in hydrogen bonding amongst the Na-coordinated water molecules and the two interstitial water molecules. Ultimately, we observe proton transfers from the interstitial waters (forming OH− ions) to two of the Na-coordinated waters (forming a pair of H3O+ ions). The equation of state in the athermal limit of the low-pressure phase of mirabilite, parameterised by fitting an integrated form of the third-order Birch-Murnaghan expression to the calculated energy as a function of unit-cell volume, yields the zero-pressure unit-cell volume, V0 = 1468.6(9) A3, the incompressibility, K0 = 22.21(9) GPa, and the first pressure derivative K0′ = (∂K/∂P)0 = 5.6(1).