## Harmonic_Expansion model

dendritic solidification, eutectics, peritectics,....
g.azizi
Posts: 3
Joined: Sun Apr 19, 2020 7:30 pm
anti_bot: 333

### Harmonic_Expansion model

Hi
i'm trying to model solidification of a Al alloy in 3D and I want to use harmonic expansion model. this is the part of my driving file:
# Is interaction isotropic?
# Optionen: isotropic anisotropic [harmonic_expansion]
[harmonic_expansion]

but I receive an input error considering [harmonic_expansion]. I tried "harmonic_expansion" without [] but still I have the same problem. what is the correct way to use harmonic_expansion model?
should I input epsilon-1 and epsilon-2 in one line or two successive lines?

Thanks

Bernd
Posts: 1221
Joined: Mon Jun 23, 2008 9:29 pm

### Re: Harmonic_Expansion model

Hi g.azizi,

Welcome to the MICRESS Forum!

"harmonic_expansion" is an optional parameter (hence written with [] in the options list) and has to be put into the same line with "anisotropic". In the next two lines, the anisotropic coefficients eps1 and eps2 have to be in one line, each:

# Is interaction isotropic?
# Options: isotropic anisotropic [junction_force] [harmonic_expansion]
anisotropic harmonic_expansion
# Anisotropy of interfacial energy? (cubic)
# 1 + eps1*Y1 + eps2*Y2
# Y1= 4*(nx^4 +ny^4 +nz^4) - 3
# Y2= nx^6 +ny^6 +nz^6 +30*nx^2*ny^2*nz^2
# Coefficients eps1, eps2? (2 REALS in one line)
0.2 0.1
# Anisotropy of interfacial mobility? (cubic)
# 1 + eps1*Y1 + eps2*Y2
# Y1= 4*(nx^4 +ny^4 +nz^4) - 3
# Y2= nx^6 +ny^6 +nz^6 +30*nx^2*ny^2*nz^2
# Coefficients eps1, eps2? (2 REALS in one line)
0.2 0.1

Best wishes
Bernd

g.azizi
Posts: 3
Joined: Sun Apr 19, 2020 7:30 pm
anti_bot: 333

### Re: Harmonic_Expansion model

Thanks a lot Brend
one more question, I got interfacial energy and its anisotropy coefficients from molecular dynamic simulation. But i'm not sure what is anistropy of interfacial mobility. there is not much about it in MICRESS manuals. would you pleases explain what is exactly interfacial mobility anisotropy and its role? how do you calculate it? where can I read about it?
Thank you in advance

Bernd
Posts: 1221
Joined: Mon Jun 23, 2008 9:29 pm

### Re: Harmonic_Expansion model

Hi g.azizi,

The interface mobility is defined as the velocity per driving force, i.e.

v = μ x ΔG

The interface mobility μ typically depends on the lattice directions, which is expressed as the kinetic anisotropy coefficient. It relates the mobility in direction φ with respect to the reference value μ0:

μ(φ) = μ0 * k(φ)

This k is the coefficient which you specify by the harmonic expansion model. I cannot advice you any standard literature, and I am also not an expert how to do MD simulations or experiments for determination.

Physically, the interface mobility is determined by reordering of atoms during the phase transformation. For that reason, the mobility typically is high if phases have a simple structure like liquid or solid solutions, while phases with complex lattice structures have much lower mobilities (e.g. tcp phases). The value of the interface mobility is also strongly linked with the diffusion mobilities in the involved phases.

What makes things a bit more complicated for simulation is that for diffusion limited growth (with very high interface mobility) the anisotropy of mobility is physically not so relevant. However, as we often simulate with coarse resolution, we use lower (numerical) interface mobilities in order to avoid artificial solute trapping. Then, the anisotropy of the interface mobility gains importance and compensates for the loss of the numerical effect of the static anisotropy...

Bernd