Effects of cluster size and shapes of nanomaterials on Debye temperature and depression of melting temperature

In this work the variation of melting temperature, Debye temperature of solids with different shapes and sizes of nanoclusture (NS) are discussed. The depression of melting temperature NS solids from its bulk counterpart occurs due to large surface volume ratio. It also depends on shapes of NS because different shaped NS have different surface area in spite of same volume. Depression of melting point of a NS over bulk solid have least value for spherical cluster with respect to any other shape. The model proposed here is an extension of Debye – Lindeman criterion with incorporation of surface Debye temperature which simulates the finite size effect of nanocluster solids. Melting temperature of solids are directly related to the atomic bond strength of materials. For pure bulk material the melting point occurs at a particular temperature but in case of nanoparticle it occurs over a broad range of temperature. In this model we have considered extra modes of vibration due to surface phonons. Extra surface modes of vibration are accounted separately. It has been found that experimental results accounts the depression of melting point increase with decrease in cluster size. This present calculation uses the experimental data on Pb, Sn, Fe metallic nanocluster with of size 0.28nm, 0.35nm, 0.252nm respectively. Our theoretical prediction gives a good account of the experimental results. (author)