VARIATION OF ELASTIC CONSTANTS OF SODIUM WITH TEMPERATURE AND PRESSURE

The variation with temperature and pressure of the velocities of 10-MHz elastic waves propagating in monocrystalline bcc sodium was measured by the phase-comparison technique. At atmospheric pressure, the elastic constants C11, C′=12(C11-C12), and C44 appear to decrease linearly with temperature between 150 and 299 °K, while their second temperature derivatives are all negative between 78 and 150 °K. At P=0 and T=195 °K, the following values of the adiabatic elastic constants were obtained: C11=81.3 kbar, C′=6.65 kbar, C44=51.0 kbar. At T=78 °K, 195 °K,273 °K, and 299 °K, the first two pressure derivatives of the effective elastic constants C11, C′, and C44 were computed by Cook's method from measurements of the pressure dependence of the transit times extending up to 9 kbar. The pressure derivatives dC11dp=4.17±0.20 and dC′dp=0.258±0.015 are independent of temperature for 78 °K≤T≤299 °K, while dC44dp equals 1.74±0.08 for 195 °K≤T≤299 °K, decreasing to 1.17±0.07 at 78 °K. The following bounds on the second pressure derivatives of all the elastic constants were established: -5×10-4≤C-1d2Cdp2≤-2×10-4 kbar-2. To within experiment alerror, the fractional pressure derivatives of the adiabatic elastic constants decrease linearly with temperature in such a way that at 273 °K, C11-1dC11dp=0.054 kbar-1, C′-1dC′dp=0.042 kbar-1, and C44-1dC44dp=0.039 kbar-1, while at 78 °K these quantities are equal to 0.049, 0.037, and 0.025 kbar-1, respectively. Although the absolute values of the isothermal elastic constants BT=13(C11+2C12), C′, and C44 as well as dBTdp and dC44dp at T=78 °K are in good agreement with simple theory, dC′dp is much larger than expected. © 1969 The American Physical Society.