Session U4: Phase Transitions IV: Modeling

Introduction to the Phase Transition Kinetics Program at LLNL

At Lawrence Livermore National Laboratory (LLNL) a new theoretical program has been launched with the objective of developing predictive theories and simulation codes for the description of non-equilibrium phase transitions that occur under shock and/or ramp compresion. The approach taken by our program is to formulate the precise nature of the problem at the atomistic, meso and continuum scales and to pursue a number of lines of inquiry that enable us to overcome several key theoretical barriers -- this has taken the form of five cross-cutting research strands. In this talk, we will provide an overview of our program, present recent advances that our program has made on several fronts, and highlight the series of talks that members of the kinetics team will present at this conference. We will then focus on our hydrodynamically coupled multi-phase field and inline equation of state methodology that is embodied in the new LLNL code ``Samsa.'' Lawrence Livermore National Laboratory is operated by Lawrence Livermore National Security, LLC, for the U.S. Department of Energy, National Nuclear Security Administration under Contract DE-AC52-07NA2   

Time-dependent Ginzburg-Landau type Multiphase Field for description of shock-induced Phase Transition

Phase-field models have become popular in last two decades to describe a host of free-boundary problems. The strength of the method relies on implicitly describing the dynamics of surfaces and interfaces by continuous scalar field that enter in the global grand free energy functional of the system. We adapt this method in order to describe shock-induced phase transition. To this end we make use of the Multiphase Field Theory (MFT)\footnote{I. Steinbach et al., Physica 94D, 135 (1996)} to account for the existence of multiple phases during the transition. In this talk I will initially describe the constitutive equations that couple the dynamic of the phase field with that of the thermodynamic fields like T, P, c etc. I will then give details on developing a thermodynamically consistent phase-field interpolation function for multiple-phase system in the context of shock-induced phase-transition. At the end I will briefly comment on relating the dynamics of the interfaces in the shock/ramp compression to the Kardar-Parisi-Zhang\footnote{M. Kardar et al., Phys. Rev. Let 56, 889 (1986)} equation.   

Nanosecond Timescale Homogeneous Nucleation and Crystal Growth in Shock-Compressed SiO$_{2}$

Understanding the kinetics of shock compressed SiO2 is of great importance for mitigating optical damage for high intensity lasers and understanding meteoroid impacts. Experimental work has placed some thermodynamic bounds on the formation of high pressure crystal phases, but the kinetics and microscopic mechanisms are yet to be elucidated. The latter are particularly relevant for this material which has long-lived metastable states. Enabled by million atom multiscale shock technique (MSST) molecular dynamics studies of shock compressed fused silica and quartz using variations on the BKS analytical potential, we discover here that crystallization occurs within as little as a few nanoseconds. In surprising contrast to shock induced solid-solid phase transformations in metals, we find that the transition from quartz obeys a diffusion mediated homogeneous nucleation and growth model due to formation of an intermediate disordered phase. We construct a quantitative model of diffusion mediated nucleation and growth kinetics and compare to stishovite grain sizes observed in laser damage events and near the Barringer Crater. We also study the effect of quantum nuclear effects using the quantum bath MSST and find that shock temperatures are shifted up to 500 K from classical values.   

Towards a kinetics model for dynamically driven liquid-solid transitions built from atomistic simulations

We discuss the development of a kinetics model for the liquid-to-solid transition in Cu as modeled by the Mishin et al. EAM Cu potential [1]. Starting from a determination of the multiphase EOS of this system, and a series of MD simulations in which solidification was observed by quenching and pressurizing at various rates, we describe our initial attempts to fit a kinetics model to be used in continuum simulations. The phenomena of nucleation and growth of the fcc phase, as well as the appearance and effects of bcc wetting layers, are discussed. This work is performed under the auspices of the U. S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. \\[4pt] [1] Y. Mishin et al., Phys. Rev. B vol.63, 224106 (2001).