Models for mean bonding length, melting point and lattice thermal expansion of nanoparticle materials

A model, based on the ratio number of surface atoms to that of its internal, is derived to calculate the size dependence of lattice volume of nanoscaled materials. The model is applied to Si, Sn and Au nanoparticles. For Si, that the lattice volume is increases from 20 Å3 for bulk to 57 Å3 for a 2 nm size nanocrystals. A model, for calculating melting point of nanoscaled materials, is modified by considering the effect of lattice volume. A good approach of calculating size-dependent melting point begins from the bulk state down to about 2 nm diameter nanoparticle. Both values of lattice volume and melting point obtained for nanosized materials are used to calculate lattice thermal expansion by using a formula applicable for tetrahedral semiconductors. Results for Si, change from 3.7 × 10−6 K−1 for a bulk crystal down to a minimum value of 0.1 × 10−6 K−1 for a 6 nm diameter nanoparticle.

Three models are derived to explain the nanoparticles size dependence of mean bonding length, melting temperature and lattice thermal expansion applied on Sn, Si and Au. The following figures are shown as an example for Sn nanoparticles indicates hilly applicable models for nanoparticles radius larger than 3 nm.Figure optionsDownload as PowerPoint slideHighlights
► A model for a size dependent mean bonding length is derived.
► The size dependent melting point of nanoparticles is modified.
► The bulk model for lattice thermal expansion is successfully used on nanoparticles.