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

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°K. The data were obtained from single crystals, using a precision x-ray diffraction technique in the range 4.2 to 300°K and an interferometric dilatometer in the range 300 to 1130°K. Polynomial expressions, based on least-squares fitting of the data, are presented. Some of the parameters in Å are: at 4.2°K, $a=3.2294\mathrm{}$, $c=5.1414\mathrm{}$ ($\frac{c}{a}=1.5921\mathrm{}$); at 300°K, $a=3.2331\mathrm{}$, $c=5.1491\mathrm{}$ ($\frac{c}{a}=1.5926\mathrm{}$); at 1125°K, $a=3.2468\mathrm{}$, $c=5.1964\mathrm{}$ ($\frac{c}{a}=1.6004\mathrm{}$). Expansion coefficients ×${10}^6$ are: at 300°K, ${\alpha }_a=4.99\mathrm{}$, ${\alpha }_c=7.36\mathrm{}$, $\beta =17.35\mathrm{}$; at 1125°K, ${\alpha }_a=4.91\mathrm{}$, ${\alpha }_c=15.14\mathrm{}$, $\beta =24.94\mathrm{}$. The Grüneisen coefficient is found to be essentially constant from 100 to 1130°K; the directional Grüneisen coefficients are also computed.