Ginzburg-Landau theory of the bcc-liquid interface kinetic coefficient

Wu, Kuo-An; Wang, Ching-Hao; Hoyt, Jeffrey J.; Karma, Alain

doi:10.1103/physrevb.91.014107

Ginzburg-Landau theory of the bcc-liquid interface kinetic coefficient

Journal Article · Mon Jan 19 23:00:00 EST 2015 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/physrevb.91.014107· OSTI ID:1906114

Wu, Kuo-An ^[1]; Wang, Ching-Hao ^[2]; Hoyt, Jeffrey J. ^[3]; Karma, Alain ^[4]

National Tsing-Hua Univ., Hsinchu (Taiwan); Northeastern University
National Tsing-Hua Univ., Hsinchu (Taiwan)
McMaster Univ., Hamilton, ON (Canada)
Northeastern Univ., Boston, MA (United States)

We extend the Ginzburg-Landau (GL) theory of atomically rough bcc-liquid interfaces outside of equilibrium. We use this extension to derive an analytical expression for the kinetic coefficient, which is the proportionality constant μ(nˆ) between the interface velocity along a direction nˆ normal to the interface and the interface undercooling. The kinetic coefficient is expressed as a spatial integral along the normal direction of a sum of gradient square terms corresponding to different nonlinear density wave profiles. Anisotropy arises naturally from the dependence of those profiles on the angles between the principal reciprocal lattice vectors K^→i and nˆ. Values of the kinetic coefficient for the (100), (110), and (111) interfaces are compared quantitatively to the prediction of linear Mikheev-Chernov (MC) theory and previous molecular dynamics (MD) simulation studies of crystallization kinetics for a classical model of Fe. Additional MD simulations are carried out here to compute the relaxation time of density waves in the liquid in order to make this comparison free of fit parameters. The GL theory predicts an expression for μ similar to the MC theory but yields a better agreement with MD simulations for both its magnitude and anisotropy due to a fully nonlinear description of density wave profiles across the solid-liquid interface. In particular, the overall magnitude of μ predicted by GL theory is an order of magnitude larger than predicted by the MC theory. GL theory is also used to derive an inverse relation between μ and the solid-liquid interfacial free energy. Here, the general methodology used here to derive an expression for μ(nˆ) also applies to amplitude equations derived from the phase-field-crystal model, which only differ from GL theory by the choice of cubic and higher order nonlinearities in the free-energy density.

View Accepted Manuscript (DOE)

Research Organization:: Northeastern Univ., Boston, MA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG02-07ER46400; FG02-92ER45471

OSTI ID:: 1906114

Alternate ID(s):: OSTI ID: 1181507

Journal Information:: Physical Review. B, Condensed Matter and Materials Physics, Journal Name: Physical Review. B, Condensed Matter and Materials Physics Journal Issue: 1 Vol. 91; ISSN 1098-0121

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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