Lattice instabilities in metallic elements

Abstract

Most metallic elements have a crystal structure that is either body-centered cubic (bcc), facecentered close packed, or hexagonal close packed. If the bcc lattice is the thermodynamically most stable structure, the close-packed structures usually are dynamically unstable, i.e., have elastic constants violating the Born stability conditions or, more generally, have phonons with imaginary frequencies. Conversely, the bcc lattice tends to be dynamically unstable if the equilibrium structure is close packed. This striking regularity essentially went unnoticed until ab initio total-energy calculations in the 1990s became accurate enough to model dynamical properties of solids in hypothetical lattice structures. After a review of stability criteria, thermodynamic functions in the vicinity of an instability, Bain paths, and how instabilities may arise or disappear when pressure, temperature, and/or chemical composition is varied are discussed. The role of dynamical instabilities in the ideal strength of solids and in metallurgical phase diagrams is then considered, and comments are made on amorphization, melting, and low-dimensional systems. The review concludes with extensive references to theoretical work on the stability properties of metallic elements.

Random phase approximation up to the melting point: Impact of anharmonicity and nonlocal many-body effects on the thermodynamics of Au

“…This is a limitation in two respects: (a) First, materials development and application takes place at finite temperatures at which entropic contributions become important. In particular, anharmonic phonon-phonon excitations have been revealed to strongly modify materials properties, e.g., for dynamically unstable systems [2] or for defect formation [3]. (b) Second, standard functionals are known to have intrinsic deficiencies, e.g., for elements with nearly full electron shells.…”

Multiporous carbon allotropes transformed from symmetry-matched carbon nanotubes

“…Mathematically, it requires all principal minors of the determinant with elastic constants must be positive. 64 From this condition, we can derive the mechanical stability criteria c 11 > 0, c 33 > 0, c 44 > 0, c 66 > 0, c 11 -|c 12 | > 0 and (c 11 + c 12 )c 33 − 2c 2 13 > 0 for hexagonal crystals and tetragonal crystals. Since the c i j of the 3060-Carbon and 4080-Carbon satisfy the above mentioned stability criteria, the two carbon allotropes are mechanical stable.…”

Order-parameter-aided temperature-accelerated sampling for the exploration of crystal polymorphism and solid-liquid phase transitions

“…65,66 Relying on MD simulations to observe the equilibrium melting of a solid is not optimal because, near the melting point, the melting transition is a rare event with a mean first passage time many orders of magnitude greater than characteristic lattice vibrational periods. Enhanced sampling methods, such as umbrella sampling and metadynamics, have been used to calculate free energy changes in solid-liquid transitions of ductile metals 67 and of ice/water.…”