\textit{Ab initio} calculations of the phonon spectra and thermal expansion coefficients of the 4$d$ metals
P. Souvatzis and O. Eriksson

We have performed first principles calculations of the phonon spectra of the 4d transition metals with the so called supercell method, and found good agreement with observations. Furthermore, the electron and phonon contributions to the free energy for the 4d metals have been calculated from a first principles method. From the free energy the thermal expansion of the metals are calculated. The calculated thermal expansion coefficients for the cubic elements are in overall good agreement with experiment when the LDA approximation is employed, while the GGA calculations yields a discrepancy as big as $\sim$30\%. For the hexagonal elements reasonable agreement is found between calculations and experiment for the volume thermal expansion at temperatures $200 K\lesssim T \lesssim 300 K$. PACS number(s): 62.50.+p

© 2008 The American Physical Society.