86 research outputs found
The influence of short range forces on melting along grain boundaries
We investigate a model which couples diffusional melting and nanoscale
structural forces via a combined nano-mesoscale description. Specifically, we
obtain analytic and numerical solutions for melting processes at grain
boundaries influenced by structural disjoining forces in the experimentally
relevant regime of small deviations from the melting temperature. Though
spatially limited to the close vicinity of the tip of the propagating melt
finger, the influence of the disjoining forces is remarkable and leads to a
strong modification of the penetration velocity. The problem is represented in
terms of a sharp interface model to capture the wide range of relevant length
scales, predicting the growth velocity and the length scale describing the
pattern, depending on temperature, grain boundary energy, strength and length
scale of the exponential decay of the disjoining potential. Close to
equilibrium the short-range effects near the triple junctions can be expressed
through a contact angle renormalisation in a mesoscale formulation. For higher
driving forces strong deviations are found, leading to a significantly higher
melting velocity than predicted from a purely mesoscopic description.Comment: 10 page
Non-linear elastic effects in phase field crystal and amplitude equations: Comparison to ab initio simulations of bcc metals and graphene
We investigate non-linear elastic deformations in the phase field crystal
model and derived amplitude equations formulations. Two sources of
non-linearity are found, one of them based on geometric non-linearity expressed
through a finite strain tensor. It reflects the Eulerian structure of the
continuum models and correctly describes the strain dependence of the
stiffness. In general, the relevant strain tensor is related to the left
Cauchy-Green deformation tensor. In isotropic one- and two-dimensional
situations the elastic energy can be expressed equivalently through the right
deformation tensor. The predicted isotropic low temperature non-linear elastic
effects are directly related to the Birch-Murnaghan equation of state with bulk
modulus derivative for bcc. A two-dimensional generalization suggests
. These predictions are in agreement with ab initio results for
large strain bulk deformations of various bcc elements and graphene. Physical
non-linearity arises if the strain dependence of the density wave amplitudes is
taken into account and leads to elastic weakening. For anisotropic deformations
the magnitudes of the amplitudes depend on their relative orientation to the
applied strain.Comment: 16 page
Phase field modelling of grain boundary premelting using obstacle potentials
We investigate the multi-order parameter phase field model of Steinbach and
Pezzolla [I. Steinbach, F. Pezzolla, A generalized field method for multiphase
transformations using interface fields, Physica D 134 (1999) 385-393]
concerning its ability to describe grain boundary premelting. For a single
order parameter situation solid-melt interfaces are always attractive, which
allows to have (unstable) equilibrium solid-melt-solid coexistence above the
bulk melting point. The temperature dependent melt layer thickness and the
disjoining potential, which describe the interface interaction, are affected by
the choice of the thermal coupling function and the measure to define the
amount of the liquid phase. Due to the strictly finite interface thickness also
the interaction range is finite. For a multi-order parameter model we find
either purely attractive or purely repulsive finite-ranged interactions. The
premelting transition is then directly linked to the ratio of the grain
boundary and solid-melt interfacial energy.Comment: 12 page
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