Phonon Instabilities in fcc and bcc Tungsten

The lattice dynamics of bcc and fcc W is studied as a function of pressure using the density-functional linear-response theory. At high pressures and $T=0$ K, bcc W has a higher enthalpy than the fcc and hcp phases and it develops phonon softening anomalies related to this thermodynamic instability; however, it remains dynamically stable. In contrast, the widely unstable shear modes of fcc W at zero pressure (when $H_W^{\mathrm{fcc}}>H_W^{\mathrm{bcc}}$) stabilize with increasing pressure before $H_W^{\mathrm{fcc}}<H_W^{\mathrm{bcc}}$. Hence the thermodynamic and dynamic instabilities are uncorrelated.