Zero-temperature generalized phase diagram of the 4d transition metals under pressure

TL;DR

This study uses advanced density functional theory to map the zero-temperature phase diagram of 4d transition metals under pressure, revealing structural transitions and discrepancies with experimental data.

Contribution

It provides a detailed, pressure-dependent phase diagram for 4d transition metals using high-precision DFT calculations with the Wu-Cohen functional.

Findings

Agreement with experimental equations of state is excellent.

Major phase boundaries slope towards lower atomic numbers with increasing pressure.

Mo exhibits a bcc to fcc transition, not the expected bcc-hcp transition.

Abstract

We use an accurate implementation of density functional theory (DFT) to calculate the zero-temperature generalized phase diagram of the 4$d$ series of transition metals from Y to Pd as a function of pressure $P$ and atomic number $Z$. The implementation used is full-potential linearized augmented plane waves (FP-LAPW), and we employ the exchange-correlation functional recently developed by Wu and Cohen. For each element, we obtain the ground-state energy for several crystal structures over a range of volumes, the energy being converged with respect to all technical parameters to within $\sim 1$ meV/atom. The calculated transition pressures for all the elements and all transitions we have found are compared with experiment wherever possible, and we discuss the origin of the significant discrepancies. Agreement with experiment for the zero-temperature equation of state is generally excellent. The generalized phase diagram of the 4$d$ series shows that the major boundaries slope towards lower $Z$ with increasing $P$ for the early elements, as expected from the pressure induced transfer of electrons from $sp$ states to $d$ states, but are almost independent of $P$ for the later elements. Our results for Mo indicate a transition from bcc to fcc, rather than the bcc-hcp transition expected from $sp$-$d$ transfer.