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The general Tarasov function is fitted to the skeletal heat capacities of materials with widely different crystal structures. Examples are chosen from flexible macromolecules (polyethylene, polypropylene, poly(ethylene terephthalate), selenium, rigid macromolecules (diamond and graphite), and a small molecule (fullerene, C60). A new optimization approach using the Mathematica software is developed. It results in one-, two-, and three-dimensional Debye temperatures, Q1, Q2 and Q3 the fitting parameters of the Tarasov function. In addition to the Tarasov function, the evaluation of the heat capacities makes use of approximate group-vibrational spectra. The results support the earlier assumption that Q2=Q3 for simple, solid, linear macromolecules. In more complicated bonding situations, Q1, Q2 and Q3 are used as averaging fitting parameters. This general approach provides an improvement in the quantitative thermal analyses of polymers and other substances included in the ATHAS Data Bank. Sufficient programming information is provided to enable anyone the computation with a copy of the popular Mathematica software. The programming file is also downloadable from the WWW.
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