Unsupervised Calculation of Free Energy Barriers in Large Crystalline Systems

Abstract

The calculation of free energy differences for thermally activated mechanisms in the solid state are routinely hindered by the inability to define a set of collective variable functions that accurately describe the mechanism under study. Even when possible, the requirement of descriptors for each mechanism under study prevents implementation of free energy calculations in the growing range of automated material simulation schemes. We provide a solution, deriving a path-based, exact expression for free energy differences in the solid state which does not require a converged reaction pathway, collective variable functions, Gram matrix evaluations, or probability flux-based estimators. The generality and efficiency of our method is demonstrated on a complex transformation of C15 interstitial defects in iron and double kink nucleation on a screw dislocation in tungsten, the latter system consisting of more than 120 000 atoms. Both cases exhibit significant anharmonicity under experimentally relevant temperatures.

Kink-limited Orowan strengthening explains the brittle to ductile transition of irradiated and unirradiated bcc metals

“…Accommodation of these features is known to be essential to accurately model high-temperature screw dislocation motion and thus capture experimental data. Recent calculations of the zero-stress double-kink-formation free energy in tungsten confirms the large contribution of vibrational entropic terms, which are not predicted in harmonic approximations using static curvatures [43]. Following previous studies, a general approximate form of the kink-formation free energy reads [8,24,26,27,29]…”

“…Whilst our Frenkel-Kontorova simulations can capture the statistics of the kink nucleation rate as a function of segment length and kink-formation energy over a wide parameter range, the intrinsic simplicity of the model clearly cannot reproduce the complex stress and temperature dependence found in fully atomistic simulations [25,[41][42][43]. In particular, the kink-formation free energy and flow stress are known to vanish at both the so-called "athermal" temperature T ath [24,29] and a temperature-dependent flow stress [8,24,26,27].…”

Reinforcing materials modelling by encoding the structures of defects in crystalline solids into distortion scores

“…As a consequence, QM/MM methods cannot have access neither to local nor to total energies. Without direct access to the energy of the system, the migration and transformation energy barriers can be fully recovered from the atomic forces using the mean force concept 8,9 both for the 0 K 53 and finite temperature calculations 10 . Here we consider an example of P images from a migration trajectory obtained using a standard pathway method, e.g., nudged elastic band (NEB) 54 .…”

Thermal fluctuations of dislocations reveal the interplay between their core energy and long-range elasticity

“…[1][2][3][4], their behavior at finite temperatures remains only partially explored. While recent progress was obtained on the free energy barrier against dislocation motion [5,6], dislocation thermal vibrations remain poorly understood despite their importance in setting the attempt frequency of thermally activated dislocation processes such as dislocation movement in solution-strengthened alloys, kink-pair nucleation, and cross slip [7,8].…”