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This paper reports the experimentally measured thermal and electrical conductivities from which the Lorenz numbers as functions of temperature were derived for the solids and melts of elemental Te and samples of Hg1-xCdxTe of x = 0, 0.1 and 0.2. The structural changes in the vicinity of the solid-liquid phase transition of elemental Te and various Hg1-xCdxTe solid solutions were assessed by closely examining these experimental properties and the derived Lorenz numbers. The values of Lorenz numbers for the solids of these samples were higher than the value of L0, i.e., the Lorenz number for the free electron gas derived by Sommerfeld, implying the characteristics of non-degenerate semiconductor. With the increasing value of x, or the larger bandgap, the materials become more non-degenerate with larger deviation from L0. As the solids started to melt, the measured values of Lorenz number for all samples started to decrease and eventually reached and maintained at values close to L0 at higher temperatures. The trend of the Lorenz number indicates that the transition from non-degenerate semiconductor of the solid samples to metal or degenerate semiconductor when the samples temperature reached above their liquidus temperatures.