Using Zwanzig's projection technique to understand the stochastic dynamics of crystal defects

The mechanical response and microstructural evolution of a crystal is in large part dictated by the motion of the crystal defects (vacancies, dislocations, impurities) it contains. At finite temperature defect motion is stochastic and viscous due to a strong coupling with thermal phonons, but existing theories based on phonon scattering often show large disagreements with the results from classical atomistic simulations, failing completely for nanoscale defects such as self-interstitial clusters.

We have shown that these failures stem from treating defects and phonons as canonical particles in a harmonic system. In our approach [1], defect motion is a general structural transformation described by an affine parameter isomorphic to the defect position. We have used Zwanzig's projection technique[2] to derive a stochastic equation of motion for the defect with the defect-phonon coupling emerging as a Green-Kubo relation to the defect force, which can be evaluated statically or dynamically. The form of the friction kernel is closely related to previous microscopic heat bath models.

In my talk I will discuss some properties of this new stochastic equation of motion and explain why phonon scattering theories fail to predict the defect-phonon coupling.