Band structure theory of the bcc to hcp Burgers distortion

The Burgers distortion is a two-stage transition between bcc and hcp structures. Refractory metal elements from the Sc and Ti columns of the periodic table (bcc/hcp elements) form bcc structures at high temperatures but transition to hcp at low temperatures via the Burgers distortion. Elements of the V and Cr columns, in contrast, remain bcc at all temperatures. The energy landscape of bcc/hcp elements exhibits an alternating slide instability, while the normal bcc elements remain stable as bcc structures. This instability is verified by the presence of unstable elastic constants and vibrational modes for bcc/hcp elements, while those elastic constants and modes are stable in bcc elements. We show that a pseudogap opening in the density of states at the Fermi level drives the Burgers distortion in bcc/hcp elements, suggesting the transition is of the Jahn-Teller-Peierls type. The pseudogap lies below the Fermi level for regular bcc elements in the V and Cr columns of the periodic table. The wave vector ${\mathbf{k}}_{S}$ when the gap opens relates to the reciprocal lattice vector $\mathbf{G}=(1\phantom{\rule{0.16em}{0ex}}\frac{1}{2}\phantom{\rule{0.16em}{0ex}}\frac{1}{2})$ of the distorted bcc structure as ${\mathbf{k}}_{S}=\frac{1}{2}\mathbf{G}$. The bcc binary alloys containing both bcc/hcp and bcc elements exhibit a similar instability but stabilize part way through the bcc to hcp transition.