Anharmonic effects in the specific heat of aluminum

Abstract

The specific heat at constant pressure, C p , of aluminum has been measured by Leadbetter between 300 and 772 K and by Brooks and Bingham between 330 and 893 K. Both sets of data are converted to the specific heat at constant 0 K volume, C v0, by the Slater-Overton method, based on the equation of state and not the Debye type of theory. Corrections to the work of Overton are given. Our analysis shows that the C v0 obtained from Leadbetter's data remains below 3R up to 750 K, whereas it becomes >3R for the Brooks and Bingham data in the temperature range 650–850 K. Calculations of C v0 (harmonic + anharmonic) from three pseudopotentials are reported for (a) Harrison modified point ion potential with Hubbard exchange and correlation factor in the dielectric function, e(q); (b) Ashcroft pseudopotential with the same e(q) as in (a); and (c) Dagens-Rasolt-Taylor (DRT) M2 pseudopotential with Geldart-Taylor e(q). The shape of the C v0 curve is found to be similar for all three potentials. For DRT potential, C v0 reaches 3R at 700 K, whereas the other two barely approach 3R about 900 K. The anharmonic contribution to C v0 is a factor of two larger for the Dagens et al. compared to the other two potentials. There is a marked difference between the C v0 curve from the analysis of the Brooks and Bingham data and the theoretical curves. It appears that the experimental points are too high from about 500 K up. The C v0 curve from Leadbetter's data is very similar to the three theoretical curves, but the results appear to be too low. A remeasurement of the specific heat from 500 K to the melting point is needed.