Abstract A simple Born model involving a few adjustable parameters has been seen to explain very well the experimental data available for the Tl-based Tl1(2)Ba2an−1CunO2n + 3(4), n = 1 to 3 high — Tc oxide superconductors. In particular, for Tl2Ba2GaCu2O8 system the calculated phonon density of states is in very good agreement with the neutron data. The phonon bands show highly two-dimensional behaviour. Planar dispersions are significant only for the Gu-O2 layers. The lattice specific heat in the low temperature region shows a non-Debye behaviour i.e., a variation different from a T3 — one. This questions the reliability of the magnitude and the temperature dependence of the non — lattice contributions determined in an analysis of the observed total specific heat after assuming a T3 — dependent lattice contribution.
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