Anisotropy coefficient for Mg

[yichen]

Dear Bernd,
I am doing a simulation of the solidification process of Mg alloy. Could you please tell me how to set the value of the static anisotropy coefficient and kinetic anisotropy coefficient for the hexagonal crystal? Which value is sutiable?
Thank you very much!

[Bernd]

Hi yichen,

welcome to the MICRESS forum!

I currently have not been involved so much in the simulation of Mg alloys, but Janin has a lot of experience with that as she developed and implemented the hexagonal anisotropy formulation in MICRESS. She currently is on a conference, but I think she can answer you when she is back!

Janin also published several papers on that topic (see MICRESS references), maybe you find some information.

Bernd

[janin]

Hi,

Standard 2D model

In my 2D simulations I used the following values:
kinetic coefficient (moblity): 0.0496
static coefficent (interfacial stiffness): 0.0712
(which corresponds to a coeffiecient of 0.002033 for the interfacial energy, due to a factor of35)

There is no direct source for these values, but I calibrated these values in comparison with MD data for Mg, which you can find in:
[1] Z. G. Xia, D. Y. Sun, M. Asta and J. J.Hoyt, “Molecular Dynamics Calculations of the Crystal-melt Interfacial Mobility for Hexagonal Close-Packed Mg” Physical Review B, 75 (2007), 012103
[2] D. Y. Sun, M. I. Mendelev, C. A. Becker, K. Kudin, T. Haxhimali, M.Asta, J. Hoyt, A. Karma and D. J. Srolovitz “Crystal-melt Interfacial Free Energies in Hcp Metals: A Molecular Dynamics Study of Mg” Physical Review B, 73 (2006), 024116

Standard 3D model

In my early papers I published a 3D anistropy function showing 6 maxima in <11-20>maxima in two additional maxima in <0001> (c- direction), but soon found out that this is not correct! If you want to use the standard 3D model in MIcress, take care to get rid of the unphysical <0001> directions by chosing a small z/x coefficents.

Special 3D model based on spherical harmonics

For most of my own 3D phase-field simulations on Mg-based alloys I have used a special ansitropy formulation based on spherical harmonics which allows direct imput of the MD data. It will become part of the next release in Mai 2013. It has the major advantage that one can directly use the coefficents derived by molecular dynamics studies. The given MD data by Sun et al. reveals 6 arms in <11-20> directions, but does not yet reproduce the experimentally obsereved aditional arms in <22-45> dircetion. In my publication you will find an improved 3D-anisotropy formulation which reproduces both <11-20> and <22-45> arms.

My work is published in:
J.Eiken, Phase-field simulation of microstructure formation in technical magnesium alloys
International Journal of Materials Research 2010/04, Page 503-509
(I'm not allowed to put it online, but if someone wants a copy, I may send it by email.)

Janin

[yichen]

Dear Professor Janin,
Thank you for your reply. I have tried the anisotropy coefficient you gived in the simulation (kinetic coefficient (moblity): 0.0496; static coefficent (interfacial stiffness): 0.0712). I followed with the example "AlCu_Equiaxed_dri" and changed the parameters for Mg-9Al alloy. But the result reveals a four-fold anisotropy, while the morphology of α-Mg should be anisotropy. Are there any other parameters should be set in the input file? Could you please give me some suggestion?

[janin]

You still have to define Crystal symmetry of the phase as 'hexagonal':

# Data for phase 1:
# -----------------
# Simulation of recrystallisation in phase 1 ?
# Options: recrystall no_recrystall
no_recrystall
# Is phase 1 anisotrop?
# Options: isotropic anisotropic faceted
anisotropic
# Crystal symmetry of the phase?
# Options: none xyz_axis cubic hexagonal
hexagonal


Regards,
Janin