Specific Heat of Lutetium Metal Between 0.38 and 4°K

The specific heat of lutetium metal has been measured in a He³ cryostat. Between 0.38 and 4^∘{}K (in mJ/mole ^∘{}K) Cₚ=0.210T³+11.27T+0.094T^-2. 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 θ=210^∘K, which is considerably higher than θ's previously assigned to rare earths. The discrepancy is probably due to difficulties in determining θ accurately for those lanthanides which have large magnetic contributions to Cₚ. On the basis of this and other researches it is suggested that for all trivalent rare earths, θ can be calculated by linear interpolation, as a function of the atomic number, between θ=210^∘K for Lu and θ=142^∘K for La. An accuracy of ±{}5^∘{}K may be expected. The present value for the coefficient in the electronic specific heat CE for Lu and previous measurements on La, Sc, and Y suggest that within ±{}7% accuracy we may write for all trivalent lanthanides CE=10.5T. The small T^-2 term in Cₚ 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×{}10²⁴ cm^-3.