Properties of the Quartic Anharmonic Contribution to the Specific Heat of a Face-Centered Cubic Lattice

In this paper we study Maradudin's recent approximation to the complex many-body expression for the quartic anharmonic contribution F4 to the free energy of a face-centered cubic crystal. It turns out that one can calculate C4, the quartic anharmonic contribution to the specific heat corresponding to F4, almost exactly at any arbitrary temperature by use of the vibration spectrum, thus necessitating only a single summation over the Brillouin zone. The machine-calculated result is an accurately determined curve of C4/Char, where Char is the harmonic specific heat, for a lattice model chosen to represent copper. This curve shows structural features in the form of wiggles and in the discussion it is argued that the cubic anharmonic contribution C3/Char would not negate the structure of C4/Char in the total form of the anharmonic contribution to the specific heat (C3+C4)/Char. Consequently, the theoretical results are compared with the experimental specific heat of copper expressed in the form CL[T, V(0°K)]/Char, where CL denotes the experimental lattice specific heat remaining after the necessary thermodynamic corrections have been made. Certain features of the experimental curve agree with the structural features of C4/Char alone, despite the fact that C3/Char is not presently taken into account.