Lattice Structure‐Based Model to Calculate Grüneisen Parameter for Metallic Nanomaterials

Abstract

In the present study, a model was derived for the first time to calculate the nanosize/shape‐dependence of the Grüneisen parameter for freestanding metallic nanomaterials of Cu, Ag, and Au based on thermodynamic‐related parameters, thermal expansion α, bulk modulus B, molar volume V, and specific heat C. Two types of nanomaterial shapes are taken into consideration: spherical and wire. Calculations were performed for the size and shape dependence of α, B, and C by using equations based on the effect of the surface‐to‐volume atomic ratio (N/n), whereas the nanosize dependence of V was calculated according to an equation derived based on the bond length variation for the first time. The calculation results of the related parameters were compared with the available experimental data. The outcomes demonstrated that the suggested models significantly impacted the size down to 15 nm. A strong agreement between theory and experiments demonstrated the suitableness of the proposed model. Accordingly, the Grüneisen parameter was calculated, and outcomes indicate that the Grüneisen parameter decreases as the size decreases. Reducing the lattice structure‐dependent Grüneisen parameter was explained and discussed.