Facet Model in MICRESS
Posted: Thu Jan 08, 2009 8:08 pm
Hi all,
MICRESS gives the possibility to use a facet model for the anisotropy. In the phase data input, the user has to specify all individual Normal vectors of the facets in the local coordinate system, which can consist of different types and thus have different properties, and which can be further optionally mirrored using cubic or hexagonal symmetry. Furthermore one has to specify the parameter kappa, which defines the broadness of the anisotropy factor. Up to MICRESS version 5.4 only one value of kappa is allowed for all phases, an improved beta-version is already available.
...
# Is phase 01 anisotrop?
# Options: isotropic anisotropic faceted antifaceted
faceted
# Crystal symmetry of the phase?
# Options: none xyz_axis cubic hexagonal
none
# Number of type of facets in phase 01
1
# kin. anisotropy parameter Kappa?
# only one value for all facets/phases
# 0 < kappa <= 1
0.5000000
# Number of possible orientations of a facet 1
4
# 1 -th normal vector facet 1 ? 3*
1.000000
1.000000
1.000000
# 2 -th normal vector facet 1 ? 3*
1.000000
1.000000
-1.000000
# 3 -th normal vector facet 1 ? 3*
1.000000
-1.000000
1.000000
# 4 -th normal vector facet 1 ? 3*
-1.000000
1.000000
1.000000
...
In the phase interaction input, a static and kinetic anisotropy coefficient has to be specified for each facet type, if one of the two interacting phases is faceted:
...
# Is interaction isotropic?
# Options: isotropic anisotropic
anisotropic
# static anisotropy coefficient of facet 1 (< 1. <0.1>)
0.10000
# kinetic anisotropy coefficient of facet 1 (< 1. <0.1>)
0.10000
...
the static anisotropy function is defined as
sigma = sigma0 * kSt ^2 * ( kSt^2 * cos(theta)^2 + sin(theta)^2) ^(-1.5)
where kSt is the static anisotropy coefficient of the facet and theta is the misorientation of the normal vector of the interface to the normal vector of the nearest facet and sigma is the surface stiffness. A value of 1 for kSt means no anisotropy, 0 means maximal anisotropy. Kappa has no influence on the static anisotropy.
The kinetic anisotropy is calculated as
mue = mue0 * (kKin + (1-kKin) * tanh(kappa/tan(theta)) * tan(theta)/kappa)
where kKin is the kinetic anisotropy coefficient of the facet and theta as stated above. Effectively, kappa determines the sharpness of the facet (in theta) and kKin gives the factor by which the mobility is reduced in direction of the facet. This is illustrated in the attached figure. Again, a value of 1 for kKin means no anisotropy and 0 maximal anisotropy.
MICRESS gives the possibility to use a facet model for the anisotropy. In the phase data input, the user has to specify all individual Normal vectors of the facets in the local coordinate system, which can consist of different types and thus have different properties, and which can be further optionally mirrored using cubic or hexagonal symmetry. Furthermore one has to specify the parameter kappa, which defines the broadness of the anisotropy factor. Up to MICRESS version 5.4 only one value of kappa is allowed for all phases, an improved beta-version is already available.
...
# Is phase 01 anisotrop?
# Options: isotropic anisotropic faceted antifaceted
faceted
# Crystal symmetry of the phase?
# Options: none xyz_axis cubic hexagonal
none
# Number of type of facets in phase 01
1
# kin. anisotropy parameter Kappa?
# only one value for all facets/phases
# 0 < kappa <= 1
0.5000000
# Number of possible orientations of a facet 1
4
# 1 -th normal vector facet 1 ? 3*
1.000000
1.000000
1.000000
# 2 -th normal vector facet 1 ? 3*
1.000000
1.000000
-1.000000
# 3 -th normal vector facet 1 ? 3*
1.000000
-1.000000
1.000000
# 4 -th normal vector facet 1 ? 3*
-1.000000
1.000000
1.000000
...
In the phase interaction input, a static and kinetic anisotropy coefficient has to be specified for each facet type, if one of the two interacting phases is faceted:
...
# Is interaction isotropic?
# Options: isotropic anisotropic
anisotropic
# static anisotropy coefficient of facet 1 (< 1. <0.1>)
0.10000
# kinetic anisotropy coefficient of facet 1 (< 1. <0.1>)
0.10000
...
the static anisotropy function is defined as
sigma = sigma0 * kSt ^2 * ( kSt^2 * cos(theta)^2 + sin(theta)^2) ^(-1.5)
where kSt is the static anisotropy coefficient of the facet and theta is the misorientation of the normal vector of the interface to the normal vector of the nearest facet and sigma is the surface stiffness. A value of 1 for kSt means no anisotropy, 0 means maximal anisotropy. Kappa has no influence on the static anisotropy.
The kinetic anisotropy is calculated as
mue = mue0 * (kKin + (1-kKin) * tanh(kappa/tan(theta)) * tan(theta)/kappa)
where kKin is the kinetic anisotropy coefficient of the facet and theta as stated above. Effectively, kappa determines the sharpness of the facet (in theta) and kKin gives the factor by which the mobility is reduced in direction of the facet. This is illustrated in the attached figure. Again, a value of 1 for kKin means no anisotropy and 0 maximal anisotropy.