Elastic Constants of Iron from 4.2 to 300°K

Abstract

The zero-field elastic constants of iron have been measured from 4.2 to 300°K using the ultrasonic pulse technique. Extrapolation of the data to absolute zero gives $c_{11}=2.431\mathrm{}\pm 0.008$, $c_{12}=1.381\mathrm{}\pm 0.004$, and $c_{44}=1.219\mathrm{}\pm 0.004$, all expressed in units of ${10}^{12}$ dyne ${\mathrm{cm}}^{-2\mathrm{}}$. The corresponding limiting value of the Debye temperature is ${\theta }_0=(477\mathrm{}\pm 2)°$K. Using this figure, the low-temperature heat capacity data for iron have been reanalyzed assuming the presence of a spin-wave contribution to the specific heat, i.e., the heat capacity is assumed to follow the relation $C=\gamma T+\beta T^3+\alpha T^{\frac{3}{2}}$. A least squares fit of $\frac{(C-\beta T^3)}{T}$ versus $T^{\frac{1}{2}}$ gives $\gamma =(11.7\mathrm{}\pm 0.1)\times {10}^{-4\mathrm{}}$ cal ${\mathrm{mole}}^{-1\mathrm{}}$ ${\mathrm{deg}}^{-2\mathrm{}}$, $\alpha =(2\mathrm{}\pm 1)\times {10}^{-5\mathrm{}} \mathrm{cal} {\mathrm{mole}}^{-} {\mathrm{deg}}^{-\frac{5}{2}}$. There is agreement, within experimental error, between the latter figure and the theoretical estimate of $\alpha =0.8\mathrm{}\times {10}^{-5\mathrm{}} \mathrm{cal} {\mathrm{mole}}^{-1\mathrm{}} {\mathrm{deg}}^{-\frac{5}{2}}$ obtained from the low-temperature magnetization data of Fallot. From the room temperature elastic constants, the compressibility of iron is found to be $K=(5.95\mathrm{}\pm 0.02)\times {10}^{-13\mathrm{}}$ ${\mathrm{cm}}^2$ ${\mathrm{dyne}}^{-1\mathrm{}}$, which agrees exactly with the static value obtained by Bridgman.