  Application of isotropic pressure or uniaxial strain alters the elastic
properties of materials; sufficiently large strains can drive structural
transformations. Linear elasticity describes stability against infinitesimal
strains, while nonlinear elasticity describes the response to finite
deformations. It was previously shown that uniaxial strain along [100] drives
refractory metals and alloys towards mechanical instabilities. These include an
extensional instability, and a symmetry-breaking orthorhombic distortion caused
by a Jahn-Teller-Peierls instability that splays the cubic lattice vectors.
Here, we analyze these transitions in depth. Eigenvalues and eigenvectors of
the Wallace tensor identify and classify linear instabilities in the presence
of strain. We show that both instabilities are discontinuous, leading to
discrete jumps in the lattice parameters. We provide physical intuition for the
instabilities by analyzing the changes in first principles energy, stress, bond
lengths and angles upon application of strain. Electronic band structure
calculations show differential occupation of bonding and anti-bonding orbitals,
driven by the changing bond lengths and leading to the structural
transformations. Strain thresholds for these instabilities depend on the
valence electron count.
