143 research outputs found
Phase-field-crystal model for fcc ordering
We develop and analyze a two-mode phase-field-crystal model to describe fcc
ordering. The model is formulated by coupling two different sets of crystal
density waves corresponding to and reciprocal lattice vectors,
which are chosen to form triads so as to produce a simple free- energy
landscape with coexistence of crystal and liquid phases. The feasibility of the
approach is demonstrated with numerical examples of polycrystalline and (111)
twin growth. We use a two-mode amplitude expansion to characterize analytically
the free-energy landscape of the model, identifying parameter ranges where fcc
is stable or metastable with respect to bcc. In addition, we derive analytical
expressions for the elastic constants for both fcc and bcc. Those expressions
show that a non-vanishing amplitude of [200] density waves is essential to
obtain mechanically stable fcc crystals with a non-vanishing tetragonal shear
modulus (C11 - C12)/2. We determine the model parameters for specific materials
by fitting the peak liquid structure factor properties and solid density wave
amplitudes following the approach developed for bcc [K.-A. Wu and A. Karma,
Phys. Rev. B 76, 184107 (2007)]. This procedure yields reasonable predictions
of elastic constants for both bcc Fe and fcc Ni using input parameters from
molecular dynamics simulations. The application of the model to two-dimensional
square lattices is also briefly examined.Comment: 14 figure
Quantitative Phase Field Model of Alloy Solidification
We present a detailed derivation and thin interface analysis of a phase-field
model that can accurately simulate microstructural pattern formation for
low-speed directional solidification of a dilute binary alloy. This advance
with respect to previous phase-field models is achieved by the addition of a
phenomenological "antitrapping" solute current in the mass conservation
relation [A. Karma, Phys. Rev. Lett 87, 115701 (2001)]. This antitrapping
current counterbalances the physical, albeit artificially large, solute
trapping effect generated when a mesoscopic interface thickness is used to
simulate the interface evolution on experimental length and time scales.
Furthermore, it provides additional freedom in the model to suppress other
spurious effects that scale with this thickness when the diffusivity is unequal
in solid and liquid [R. F. Almgren, SIAM J. Appl. Math 59, 2086 (1999)], which
include surface diffusion and a curvature correction to the Stefan condition.
This freedom can also be exploited to make the kinetic undercooling of the
interface arbitrarily small even for mesoscopic values of both the interface
thickness and the phase-field relaxation time, as for the solidification of
pure melts [A. Karma and W.-J. Rappel, Phys. Rev. E 53, R3017 (1996)]. The
performance of the model is demonstrated by calculating accurately for the
first time within a phase-field approach the Mullins-Sekerka stability spectrum
of a planar interface and nonlinear cellular shapes for realistic alloy
parameters and growth conditions.Comment: 51 pages RevTeX, 5 figures; expanded introduction and discussion; one
table and one reference added; various small correction
- …