Gypsum under pressure: A first-principles study

We investigate by means of first-principles methods the structural response of gypsum $\left({\text{CaSO}}_4\cdot 2{\text{H}}_2\text{O}\right)$ to pressures within and above the stability range of gypsum-I $\left(P\le 4\text{GPa}\right)$. Structural and vibrational properties calculated for gypsum-I are in excellent agreement with experimental data. Compression within gypsum-I takes place predominantly through a reduction in the volume of the ${\text{CaO}}_8$ polyhedra and through a distortion of the hydrogen bonds. The distance between ${\text{CaSO}}_4$ layers becomes increasingly incompressible, indicating a mechanical limit to the packing of water molecules between the layers. We find that a structure with collapsed interlayer distances becomes more stable than gypsum-I above about 5 GPa. The collapse is concomitant with a rearrangement of the hydrogen-bond network of the water molecules. Comparison of the vibrational spectra calculated for this structure with experimental data taken above 5 GPa supports the validity of our model for the high-pressure phase of gypsum.

Figure 1

(Color online) (a) Gypsum primitive unit cell. Hydrogen bonds $\text{O}\left(\text{w}\right)\text{-H}\left(1\right)\cdots \text{O}\left(1\right)$ and $\text{O}\left(\text{w}\right)\text{-H}\left(2\right)\cdots \text{O}\left(2\right)$ are shown. ${\pi }_1$ and ${\pi }_2$ are the oxygen planes defining the interlayer region and the polyhedral layer. (b) Extended view of the gypsum structure at ambient conditions. The size of the balls is in the order: Ca (largest), S, O, and H.

Figure 2

Gypsum cell parameters $a$, $b$, $c$, and $\beta$ vs applied pressure as calculated from first principles (filled squares) and as measured in experiment (open symbols, Ref. 16). Also reported the cell parameters (diamonds) above 4 GPa, that have been assigned to a new high-pressure phase (Ref. 16).

Figure 3

(a) Hydrogen-bond lengths $\text{O}\left(\text{w}\right)\text{-H}\left(1\right)\cdots \text{O}\left(1\right)$ (filled squares) and $\text{O}\left(\text{w}\right)\text{-H}\left(2\right)\cdots \text{O}\left(2\right)$ (disks) as a function of pressure. Experimental data (open symbols) are taken from Ref. 16. (b) Hydrogen-bond angles as a function of pressure.

Figure 4

(a) S-O bond distances $\left(\text{Å}\right)$ of the shortest (circles) and longest (squares) pairs of bonds in ${\text{SO}}_4$ as a function of pressure as calculated in this work (filled symbols) and as derived from experiment (Ref. 16, open symbols). (b) Volume of the ${\text{SO}}_4$ sulfate tetrahedron and (c) of the ${\text{CaO}}_8$ polyhedra, as a function of pressure, as calculated in this work (filled squares) and as derived from experiments (Ref. 16, open squares).

Figure 5

(a) Interlayer and (b) polyhedral layer thicknesses as calculated in this work (filled squares) and as derived from experiment (Ref. 16, open symbols).

Figure 6

Zone-center vibrational density of states of gypsum at 0 GPa and decompositions in terms of projections on H, O, S, Ca atoms. The contribution of the water molecules to the total oxygen density of states is also shown (dotted). A Gaussian broadening of $19{\text{cm}}^{-1}$ was applied.

Figure 7

(Color online) Raman spectrum of gypsum calculated at $P=0\text{GPa}$ (solid/black) compared to experimental data taken from Ref. 51. (a) Vibrational modes up to $1700{\text{cm}}^{-1}$. The theoretical scale is shown. Experimental data (dotted/red), originally in arbitrary units have been rescaled to match the height of the theoretical ${\text{SO}}_4$ symmetric stretching mode. (b) O-H stretching region. Experimental data (circles/red) are taken from Ref. 47.

Figure 8

(Color online) Ball and stick model of the high-pressure structure of gypsum at 5 GPa. Ca atoms (green), S atoms (yellow), O atoms (pink), H atoms (gray), and hydrogen bonds (dotted lines) are shown. The size of the balls is in the order: Ca (largest), S, O, and H.

Figure 9

(a) Energy as a function of volume for the high-pressure model structure (circles) and for gypsum-I (empty squares). Data are fitted with a Murnaghan equation of state (solid and dotted lines). (b) Enthalpy as a function of pressure for gypsum-I (solid) and for the high-pressure model structure (dotted).

Figure 10

Volume of the unit cell of the HP structure (filled circles) and of phase I (filled squares), as a function of pressure. Experimental data are from Ref. 16 (empty squares refer to gypsum-I, diamonds to the HP structure) and Ref. 32 (empty circles).

Figure 11

Zone-center vibrational density of states of the HP structure (dotted) and phase I (solid) of gypsum at 5 GPa. A Gaussian broadening of $19{\text{cm}}^{-1}$ was applied.

Figure 12

Theoretical infrared absorption spectrum of the HP gypsum structure at 5 GPa. A Gaussian broadening of $19{\text{cm}}^{-1}$ was applied (Ref. 55). The experimental spectrum (arb. units, Ref. 15) at 6 GPa is also reported for comparison.

Figure 13

(a) Theoretical Raman spectrum of the high-pressure gypsum structure at 5 GPa. (b) Comparison in the O-H stretching region with experimental spectra at 5.5 (dotted) and 8 GPa (disks) from Ref. 14.