Lattice dynamics, thermal expansion, and bulk modulus of ruthenium

Abstract

The lattice dynamics, third-order elastic (TOE) constants, and the temperature variation of the volume Gruneisen function of ruthenium have been calculated using the nearest neighbor central interaction model for hexagonal metals proposed by Srinivasan and Ramji Rao. The TOE constants have been employed to calculate the low-temperature limit $$\bar \gamma _L $$ of the lattice thermal expansion, the Anderson-Gruneisen (AG) parameter δ, and the second Gruneisen constantq of ruthenium. $$\bar \gamma _L $$ has the value 2.79 for ruthenium. The high-temperature limit $$\bar \gamma _H $$ has the value 3.31, which agrees well with the experimental value 3.25 obtained from thermal expansion and specific heat data of ruthenium. Anderson's theory has been used to explain the temperature dependence of the bulk modulus of ruthenium up to 923 K and has been compared with the experimental values obtained from the elastic constant data of Fisher and Dever. The variation of the lattice parameters of ruthenium with hydrostatic pressure up to 400 kbar has been calculated from its TOE constant data using the extrapolation formula of Thurston and has been compared with the experimental results of Clendenen and Drickamer. The fit is remarkably good.