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\ifmmode^\circ\else\textdegree\fi{}K using the ultrasonic pulse technique. Extrapolation of the data to absolute zero gives ${c}_{11}=2.431\ifmmode\pm\else\textpm\fi{}0.008$, ${c}_{12}=1.381\ifmmode\pm\else\textpm\fi{}0.004$, and ${c}_{44}=1.219\ifmmode\pm\else\textpm\fi{}0.004$, all expressed in units of ${10}^{12}$ dyne ${\mathrm{cm}}^{\ensuremath{-}2}$. The corresponding limiting value of the Debye temperature is ${\ensuremath{\theta}}_{0}=(477\ifmmode\pm\else\textpm\fi{}2)\ifmmode^\circ\else\textdegree\fi{}$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 $C=\ensuremath{\gamma}T+\ensuremath{\beta}{T}^{3}+\ensuremath{\alpha}{T}^{\frac{3}{2}}$. A least squares fit of $\frac{(C\ensuremath{-}\ensuremath{\beta}{T}^{3})}{T}$ versus ${T}^{\frac{1}{2}}$ gives $\ensuremath{\gamma}=(11.7\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ cal ${\mathrm{mole}}^{\ensuremath{-}1}$ ${\mathrm{deg}}^{\ensuremath{-}2}$, $\ensuremath{\alpha}=(2\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5} \mathrm{cal} {\mathrm{mole}}^{\ensuremath{-}} {\mathrm{deg}}^{\ensuremath{-}\frac{5}{2}}$. There is agreement, within experimental error, between the latter figure and the theoretical estimate of $\ensuremath{\alpha}=0.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5} \mathrm{cal} {\mathrm{mole}}^{\ensuremath{-}1} {\mathrm{deg}}^{\ensuremath{-}\frac{5}{2}}$ obtained from the low-temperature magnetization data of Fallot. From the room temperature elastic constants, the compressibility of iron is found to be $K=(5.95\ifmmode\pm\else\textpm\fi{}0.02)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ ${\mathrm{cm}}^{2}$ ${\mathrm{dyne}}^{\ensuremath{-}1}$, which agrees exactly with the static value obtained by Bridgman.