The P–V–T equation of state of D₂O ice VI determined by neutron powder diffraction in the range 0 < P < 2.6 GPa and 120 < T < 330 K, and the isothermal equation of state of D₂O ice VII from 2 to 7 GPa at room temperature

Neutron powder diffraction data have been collected from deuterated ice VI (space group P4₂/nmc, Z = 10) at 76 state points in its field of thermodynamic stability above 150 K (approximately 0.6 < P < 2.1 GPa) and in a region of metastable persistence below 150 K (0 < P < 2.6 GPa). The refined unit-cell parameters and unit-cell volume have been fitted with six-parameter functions based upon a Murnaghan equation of state (EoS), with simple polynomial expressions to describe the temperature dependence of the volume (or axis length) and the bulk modulus (or axial incompressibility). This P–V–T EoS is compared with earlier empirically derived and computationally obtained equations of state, and with the elastic properties determined by ultrasonic or Brillouin scattering methods. It is found that D₂O ice VI is ∼5% stiffer (i.e. it has a larger bulk modulus, K, at a given P and T) than H₂O ice VI, in agreement with unpublished c_ij/ρ data for D₂O ice VI provided by the Shimizu Laboratory, Gifu University, Japan (S. Sasaki, personal communication). This difference is due entirely to a greater incompressibility parallel to the a axis than for the protonated isotopologue; the incompressibilities of the c axis for both H₂O and D₂O ice VI are very similar. The P–V–T EoS is used to estimate the volume change and enthalpy of melting. Additional data on the isothermal compression of ices II and V at 240 K (0.2–0.4 and 0.4–0.7 GPa, respectively), and of ice VII at 295–300 K (2–7 GPa), are also reported and compared with earlier literature data.