Theory of the bcc-to-9R structural phase transformation of Li

Between Harmonic Crystal and Glass: Solids with Dimpled Potential-Energy Surfaces Having Multiple Local Energy Minima

Solids with dimpled potential-energy surfaces are ubiquitous in nature and, typically, exhibit structural (elastic or phonon) instabilities. Dimpled potentials are not harmonic; thus, the conventional quasiharmonic approximation at finite temperatures fails to describe anharmonic vibrations in such solids. At sufficiently high temperatures, their crystal structure is stabilized by entropy; in this phase, a diffraction pattern of a periodic crystal is combined with vibrational properties of a phonon glass. As temperature is lowered, the solid undergoes a symmetry-breaking transition and transforms into a lower-symmetry phase with lower lattice entropy. Here, we identify specific features in the potential-energy surface that lead to such polymorphic behavior; we establish reliable estimates for the relative energies and temperatures associated with the anharmonic vibrations and the solid–solid symmetry-breaking phase transitions. We show that computational phonon methods can be applied to address anharmonic vibrations in a polymorphic solid at fixed temperature. To illustrate the ubiquity of this class of materials, we present a range of examples (elemental metals, a shape-memory alloy, and a layered charge-density-wave system); we show that our theoretical predictions compare well with known experimental data.

Quantum and isotope effects in lithium metal

The crystal structure of elements at zero pressure and temperature is the most fundamental information in condensed matter physics. For decades it has been believed that lithium, the simplest metallic element, has a complicated ground-state crystal structure. Using synchrotron x-ray diffraction in diamond anvil cells and multiscale simulations with density functional theory and molecular dynamics, we show that the previously accepted martensitic ground state is metastable. The actual ground state is face-centered cubic (fcc). We find that isotopes of lithium, under similar thermal paths, exhibit a considerable difference in martensitic transition temperature. Lithium exhibits nuclear quantum mechanical effects, serving as a metallic intermediate between helium, with its quantum effect-dominated structures, and the higher-mass elements. By disentangling the quantum kinetic complexities, we prove that fcc lithium is the ground state, and we synthesize it by decompression.

Total Energy Calculations for Structural Phase Transformations

The structural integrity and physical properties of crys talline solids are frequently limited or enhanced by the occurrence of phase transformations. Martensitic trans formations involve the collective displacement of atoms from one ordered state to another. Modern methods to determine the microscopic electronic changes as the atoms move are now accurate enough to evaluate the very small energy differences involved. Extensive first principles calculations for the prototypical Martensitic transformation from body-centered cubic (bcc) to close- packed 9R structure in sodium metal are described. The minimum energy coordinate or configuration path be tween the bcc and 9R structures is determined as well as paths to other competing close-packed structures. The energy barriers and important anharmonic interactions are identified and general conclusions drawn. The calcu lational methods used to solve the Schrödinger equa tion include pseudopotentials, fast Fourier transforms, efficient matrix diagonalization, and supercells with many atoms.

Strain induced incommensurate structures in vicinity of reconstructive phase transitions

General conditions controlling the formation of incommensurate phases in crystals undergoing reconstructive phase transitions are analyzed in the framework of a model-free phenomenological approach. A universal trend to stabilizing such intermediate phases in the vicinity of reconstructive phase transitions stems from the fact that certain high-order improper Lifshitz invariants reduce at such transformations to ones bi-linearly coupling critical displacement gradients and strains or even to the proper Lifshitz invariant. The approach developed here introduces a universal mechanism for the formation both of premartensite incommensurate phases and complex structures with giant unit cells, as found in some elemental crystals at high pressure.

Early-time particle dynamics and non-affine deformations during microstructure selection in solids

Solid-solid transitions are invariably associated with groups of particles whose deformations cannot be expressed as an affine strain about a reference configuration. The dynamics of these non-affine zones (NAZ) determine the subsequent microstructure, i.e. the mesoscale patterning resulting from the structural transition. Here, we focus on early-time dynamics of individual particles within an NAZ associated with a nucleation event. We show that the early-time behavior of these particles have distinctive characteristics depending on the transition temperature. The dynamics is heterogeneous, consisting of a few active particles exhibiting complex intermittent jamming and flow in response to internal stresses generated during the transformation. At low temperatures, the dynamics of these active particles is ballistic and the structural transformation proceeds via string-like correlated movement of active particles, along ridges in the potential energy topography set up by inactive particles. On increasing temperature, the dynamics of active particles show an abrupt transition from ballistic to diffusive behavior with a diffusion coefficient which appears to be independent of temperature. This dynamical transition in the nature of the trajectories of particles is coincident with a discontinuous transition in the microstructure of the solid. Finally, we characterize this transition in terms of a dynamical order parameter in the space of trajectories and discuss its connection with the glass transition and rheology of soft and granular matter.

Phonons at Martensitic Phase Transitions of bcc-Ti, bcc-Zr and bcc-Hf

Inelastic neutron scattering on in situ grown bcc single crystals of the group 4 metals Ti, Zr and Hf show a band of low energy and strongly damped phonons. Geometrical considerations show how these damped lattice vibrations achieve the displacements necessary for the two martensitic phase transitions from bcc to ω(under pressure) and from bcc to hcp (upon lowering the temperature). The low energy and temperature dependent phonons are precursor fluctuations of the hcp or ω phase within the bcc phase.

Coarse-graining microscopic strains in a harmonic, two-dimensional solid: elasticity, nonlocal susceptibilities, and nonaffine noise

In soft matter systems the local displacement field can be accessed directly by video microscopy enabling one to compute local strain fields and hence the elastic moduli in these systems using a coarse-graining procedure. We study this process in detail for a simple triangular, harmonic lattice in two dimensions. Coarse-graining local strains obtained from particle configurations in a Monte Carlo simulation generates nontrivial, nonlocal strain correlations (susceptibilities). These may be understood within a generalized, Landau-type elastic Hamiltonian containing up to quartic terms in strain gradients [K. Franzrahe, Phys. Rev. E 78, 026106 (2008)10.1103/PhysRevE.78.026106]. In order to demonstrate the versatility of the analysis of these correlations and to make our calculations directly relevant for experiments on colloidal solids, we systematically study various parameters such as the choice of statistical ensemble, presence of external pressure and boundary conditions. Crucially, we show that special care needs to be taken for an accurate application of our results to actual experiments, where the analyzed area is embedded within a larger system, to which it is mechanically coupled. Apart from the smooth, affine strain fields, the coarse-graining procedure also gives rise to a noise field (χ) made up of nonaffine displacements. Several properties of χ may be rationalized for the harmonic solid using a simple "cell model" calculation. Furthermore the scaling behavior of the probability distribution of the noise field (χ) is studied. We find that for any inverse temperature β, spring constant f, density ρ and coarse-graining length Λ the probability distribution can be obtained from a master curve of the scaling variable X=χβf/ρΛ(2).