Specific Heat of Lutetium Metal Between 0.38 and 4°K

The specific heat of lutetium metal has been measured in a ${\mathrm{He}}^3$ cryostat. Between 0.38 and 4°K (in mJ/mole °K) $C_p=0.210\mathrm{}{T}^3+11.27T+0.094\mathrm{}{T}^{-2\mathrm{}}$. Scatter of individual points from this curve is, except in a few isolated cases, less than 0.5%. The lattice specific heat corresponds to a Debye characteristic temperature $\theta =210\mathrm{}°$K, which is considerably higher than $\theta \text{'}\mathrm{s}$ previously assigned to rare earths. The discrepancy is probably due to difficulties in determining $\theta$ accurately for those lanthanides which have large magnetic contributions to $C_p$. On the basis of this and other researches it is suggested that for all trivalent rare earths, $\theta$ can be calculated by linear interpolation, as a function of the atomic number, between $\theta =210\mathrm{}°$K for Lu and $\theta =142\mathrm{}°$K for La. An accuracy of ±5°K may be expected. The present value for the coefficient in the electronic specific heat $C_E$ for Lu and previous measurements on La, Sc, and Y suggest that within ±7% accuracy we may write for all trivalent lanthanides $C_E=10.5T$. The small $T^{-2\mathrm{}}$ term in $C_p$ could be caused by interaction of the nuclear quadrupole moment with the crystalline field gradient or it may be due to long-range exchange-type coupling between the electronic moments of rare-earth impurities in our Lu sample. If the former interpretation is accepted, the electric field gradient, along the symmetry axis, becomes 2.2×${10}^{24}$ ${\mathrm{cm}}^{-3\mathrm{}}$.