Lattice Parameters, Thermal Expansions, and Grüneisen Coefficients of Zirconium, 4.2 to 1130°K

Abstract

The lattice parameters, atomic volume, nearest-neighbor interatomic distance, axial ratio, and coefficients of thermal expansion of zirconium are reported over the temperature range 4.2 to 1130\ifmmode^\circ\else\textdegree\fi{}K. The data were obtained from single crystals, using a precision x-ray diffraction technique in the range 4.2 to 300\ifmmode^\circ\else\textdegree\fi{}K and an interferometric dilatometer in the range 300 to 1130\ifmmode^\circ\else\textdegree\fi{}K. Polynomial expressions, based on least-squares fitting of the data, are presented. Some of the parameters in \AA{} are: at 4.2\ifmmode^\circ\else\textdegree\fi{}K, $a=3.2294$, $c=5.1414$ ($\frac{c}{a}=1.5921$); at 300\ifmmode^\circ\else\textdegree\fi{}K, $a=3.2331$, $c=5.1491$ ($\frac{c}{a}=1.5926$); at 1125\ifmmode^\circ\else\textdegree\fi{}K, $a=3.2468$, $c=5.1964$ ($\frac{c}{a}=1.6004$). Expansion coefficients \ifmmode\times\else\texttimes\fi{}${10}^{6}$ are: at 300\ifmmode^\circ\else\textdegree\fi{}K, ${\ensuremath{\alpha}}_{a}=4.99$, ${\ensuremath{\alpha}}_{c}=7.36$, $\ensuremath{\beta}=17.35$; at 1125\ifmmode^\circ\else\textdegree\fi{}K, ${\ensuremath{\alpha}}_{a}=4.91$, ${\ensuremath{\alpha}}_{c}=15.14$, $\ensuremath{\beta}=24.94$. The Gr\"uneisen coefficient is found to be essentially constant from 100 to 1130\ifmmode^\circ\else\textdegree\fi{}K; the directional Gr\"uneisen coefficients are also computed.