Entropic effect on the rate of dislocation nucleation

Abstract

Dislocation nucleation is essential to our understanding of plastic deformation, ductility, and mechanical strength of crystalline materials. Molecular dynamics simulation has played an important role in uncovering the fundamental mechanisms of dislocation nucleation, but its limited timescale remains a significant challenge for studying nucleation at experimentally relevant conditions. Here we show that dislocation nucleation rates can be accurately predicted over a wide range of conditions by determining the activation free energy from umbrella sampling. Our data reveal very large activation entropies, which contribute a multiplicative factor of many orders of magnitude to the nucleation rate. The activation entropy at constant strain is caused by thermal expansion, with negligible contribution from the vibrational entropy. The activation entropy at constant stress is significantly larger than that at constant strain, as a result of thermal softening. The large activation entropies are caused by anharmonic effects, showing the limitations of the harmonic approximation widely used for rate estimation in solids. Similar behaviors are expected to occur in other nucleation processes in solids. N ucleation plays an important role in a wide range of physical, chemical, and biological processes (1-6). In the last two decades, the nucleation of dislocations in crystalline solids has attracted significant attention, not only for the reliability of microelectronic devices (7), but also as a responsible mechanism for incipient plasticity in nanomaterials (8-10) and nanoindentation (11-13). However, predicting the nucleation rate as a function of temperature and stress from fundamental physics is extremely difficult. Because the critical nucleus can be as small as a few lattice spacings, the applicability of continuum theory (14) becomes questionable. At the same time, the timescale of molecular dynamics (MD) simulations is about ten orders of magnitude smaller than the experimental timescale. Hence MD simulations of dislocation nucleation are limited to conditions at which the nucleation rate is extremely high (15,16).One way to predict the dislocation nucleation rate under common experimental loading rates (17) is to combine the transition state theory (TST) (5, 18) and the nudged elastic band (NEB) method (19). TST predicts that the nucleation rate per nucleation site in a crystal subjected to constant strain γ can be written aswhere F c is the activation free energy, T is temperature, and k B is Boltzmann's constant. The frequency prefactor is ν 0 ¼ k B T∕h, where h is Planck's constant. Note that F c ðT;γÞ ¼ E c ðγÞ − TS c ðγÞ, where E c and S c are the activation energy and activation entropy, respectively. Here we assume the dependence of E c and S c on T is weak, which is later confirmed numerically for T ≤ 400 K. For a crystal subjected to constant stress σ, F c ðT;γÞ in Eq. 1 should be replaced by the activation Gibbs free energy G c ðT;σÞ ¼ H c ðσÞ− TS c ðσÞ, where H c is the activation enthalpy. Because the NE...

Peierls Barrier of Screw Dislocation in bcc Iron at Finite Temperature

“…Ryu et al 12) have shown that the entropic effect of dislocation nucleation primarily arises from thermal expansion at temperatures below 400 K. The anharmonic thermal vibration increases the equilibrium distances between each pair of atoms, and the mutual interactions become weak. It is then easier for the atomic configuration to change to a configuration that is more stable at finite temperature.…”

“…This is a typical entropic effect similar to those of thermal expansion and softening. Recently, it has been shown that, for this entropic effect, the activation free energy for dislocation nucleation decreases significantly with increasing temperature, 12) which indicates that the atomic positions and motion are temperature dependent. In other words, the atomic positions and motion follow the free energy surface (FES), rather than the PES, at finite temperature.…”

Growth of deformation twins in tantalum via coherent twin boundary migration

“…Adoption of an accelerated molecular dynamics scheme would be advantageous 7,8 in order to extend the range of of nucleation rates by orders of magnitude. This would allow to study the validity of the Eq.…”

“…A direct fit to this data gives a large exponential prefactor of 2.7 × 10 66 m −2 s −1 , counterbalanced by a high activation energy of 12.83 eV in the exponential function. The dramatic difference from the constant strain case is to be expected; it has already been established that the entropic contribution in a constant stress ensemble is significantly higher than the corresponding entropic contribution in the constant strain ensemble 8,9 . In Fig.…”

“…Another possible mechanism of twin growth is the 2d-nucleation and growth of (possibly multiple) closed twinning dislocation loops on the coherent twin boundary. (A related atomistic and continuum theory study of the homogeneous nucleation of isolated, perfect dislocation loops has been recently been published [7][8][9] .) This second mechanism can operate in the absence of additional defects to act as a pole, e.g., in nearly perfect crystals.…”