| Large ({dollar}sim{dollar}0.3 cm{dollar}sp3){dollar} high quality single crystal samples of H{dollar}sb2{dollar}O ice III, Ice V, and Ice VI have been produced in a high pressure cell. The cell was pressurized by means of hydraulic fluid and specifically designed so that the samples could be rotated about the vertical without having to reduce the pressure. Liquid water was initially placed inside the sample containment cell and the pressure increased at room temperature. The temperature was then reduced to approximately {dollar}{lcub}-{rcub}35spcirc{dollar}C. After several hours the supercooled water sample froze directly into the desired phase, depending on the pressure. The frozen sample was then partially melted until only a small seed comprised of a few grains remained. After a controlled refreeze large grained polycrystals were produced; successive iterations of this process eventually yielded small single crystal seeds, from which large high quality single crystals were grown. Once produced, samples were kept under pressure at constant temperature and acoustic data collected using Brillouin spectroscopy at several crystallographic orientations. In all, measurements were collected from three single crystals of ice III (tetragonal), three single crystals of Ice V (monoclinic) and four single crystals of Ice VI (tetragonal).; The elastic constants were fitted to the acoustic data by making use of the Christofell determinant and the Brillouin equation. Six independent elastic constants of ice III were determined between 2.2 and 3.0 Kbar. At {dollar}{lcub}-{rcub}20spcirc{dollar}C, and 2.2 Kbar the values were found to be {dollar}rm Csb{lcub}11{rcub}=15.37, Csb{lcub}12{rcub}=9.95, Csb{lcub}13{rcub}=6.51, Csb{lcub}33{rcub}=11.55, Csb{lcub}44{rcub}=4.46, Csb{lcub}55{rcub}=5.68 (times10sp4{dollar} bar). Thirteen independant elastic constants of ice V were determined at 3.0 kbar and {dollar}{lcub}-{rcub}35spcirc{dollar}C, and were found to be {dollar}rm Csb{lcub}11{rcub}=21.4, Csb{lcub}22{rcub}=19.3, Csb{lcub}33{rcub}=21.1, Csb{lcub}44{rcub}=7.5, Csb{lcub}55{rcub}=3.7, Csb{lcub}66{rcub}=7.5, Csb{lcub}12{rcub}=12.2, Csb{lcub}13{rcub}=9.5, Csb{lcub}15{rcub}=0.17, Csb{lcub}23{rcub}=11.8, Csb{lcub}25{rcub}={lcub}-{rcub}0.1, Csb{lcub}35{rcub}={lcub}-{rcub}0.3, Csb{lcub}46{rcub}={lcub}-{rcub}2.1 (times 10sp4{dollar} bar). Six independent elastic constants of ice VI were determined between 6.2 and 8.2 kbar at {dollar}{lcub}-{rcub}2spcirc{dollar}C, the values at 7.2 kbar were found to be {dollar}rm Csb{lcub}11{rcub}=26.84, Csb{lcub}12{rcub}=14.52, Csb{lcub}13{rcub}=12.82, Csb{lcub}33{rcub}=26.21, Csb{lcub}44{rcub}=6.31, Csb{lcub}55{rcub}=10.38 (times10sp4{dollar} bar).; The isotropic elastic properties of polycrystalline aggregates of ice III, V and VI were also calculated. The elastic constants were used to calculate the acoustic velocity in many crystallographic directions covering 4{dollar}pi{dollar} steradians, the average longitudinal acoustic velocity was then found by performing a weighted average over all crystallographic directions. The bulk modulus was calculated using either elastic constant values or the compliance constant values. The average longitudinal acoustic velocity and the bulk Modulus enabled the calculation of Young's modulus, Lame constants, average transverse acoustic velocity and Poisson's ratio. These are easily compared with similar values calculated from the acoustic velocity and bulk modulus as measured directly from polycrystalline samples. In all cases the agreement is excellent. |
