Experimental thermal expansivities for single-crystal gadolinium metal near the Curie temperature

Linear thermal-expansivity results are presented for the critical region for both an $a$-axis and a $c$-axis single crystal of high-purity gadolinium metal. These results show agreement with the three-dimensional Heisenberg model for high temperatures, with a crossover to a new state occurring for $\epsilon =\frac{(T-T_c)}{T_c<{10}^{-3\mathrm{}}}$ and an enhanced increase in ordering on cooling below this temperature. Similar, although less marked, changes in behavior appear for temperatures below $T_c$. The results are highly asymmetric about $T_c$ for both crystals, in agreement with heat-capacity results, the temperature dependence of the expansivity being much smaller for $T<\mathrm{}{T}_c$. The present results are combined with other elastic-constant and heat-capacity data to obtain total, magnetic, and lattice Grüneisen parameters for the two crystallographic directions. These reflect the anisotropy of the magnetic properties, with the $a$- and $c$-axis magnetic Grüneisen parameters being approximately -1.0 and -4.0, respectively, at $T_c$. These magnetic Grüneisen parameters each are roughly temperature independent above and below $T_c$, but with the ratio of their extrapolated values to $T_c$ being 1.3 for each crystallographic direction. This result is consistent with the conclusion that the critical thermodynamic properties of gadolinium cannot be represented by a common reduced equation of state through the critical temperature.