Expansivity and heat capacity data for Lu and Sc crystals from 1 to 300 K: Spin-fluctuation and electron-phonon effects

Linear thermal expansivity (α) measurements from 1 to 300 K and heat capacity (Cₚ) measurements from 1 to 110 K are reported for single crystals of the hexagonal scandium and lutetium metals; the Cₚ data were combined with previous data to obtain smooth representations to 305 K for Lu and 350 K for Sc. The Θ₀'s (352 and 190 K, respectively, for Sc and Lu) and γ's (10.38 and 8.30 mJ/mol K², respectively for Sc and Lu) are in reasonable agreement with previous data of various kinds. Electronic contributions are much larger for the α's than for the Cₚ's, with the large anisotropies of the α's primarily electronic in origin. The equivalent Debye Θ's for the lattice Cₚ's and the Gr\"uneisen parameters Γ for the lattice α's both show an unexpected T dependence at "high" T(TΘ₀2) which can be associated with the disappearance of spin-fluctuation and electron-phonon enhancements to the electronic properties; this effect has been reported previously for Sc C_ν's by Pleschiutschnig et al. [Phys. Rev. B 44, 6794 (1991)]. While the resulting high-temperature "bare" or "density of states" γ for Sc, γb=5.75(25) mJ/mol K², is slightly larger than that calculated recently by G\"otz and Winter [J. Phys. Condens. Matter 5, 1721 (1993)], the magnitude of the sum (γₛₚᵢₙ+γₑₚ) agrees well. For Lu, for which no recent calculations exist, γb=5.50(25) mJ/mol K². The various Γ's (a and c axis, lattice, and electronic) generally are quite anisotropic, with no obvious correlation between high- and low-T behavior. The anisotropy in Γ which is associated with the enhancement (spin plus e-p) contribution is very large, with similar magnitudes for the c-axis values ({~}17), but + for Lu and - for Sc. A 186-at. ppm Fe impurity in the scandium crystals makes a significant contribution to all of the data below 3.5 K. The resulting impurity Γ's are very large and very anisotropic (ΓₐFe=-40, ΓcFe=30).