Phonon density of states from the experimental heat capacity: an improved distribution function for solid aluminium using an inverse framework.

In this study it is reported the retrieval of the phonon density of states for solid aluminium from the temperature dependent heat capacity, the inverse heat capacity problem. The singularity in this ill posed problem was removed by the Tikhonov approach with the regularization parameter calculated as the L curve maximum curvature. A sensitivity analysis was also coupled to the numerical inversion. For temperatures ranging from 15 K to 300 K the heat capacity results, calculated from the inverted phonon density of states, yields an average error of about 0.3%, within the experimental errors that ranged from 2% to 3%. The predicted entropy, enthalpy and Gibbs free energy are also within experimental errors.