## A question about the faceted model in 3-D

### A question about the faceted model in 3-D

Hi,

I have been simulating the primary silicon by using MICRESS. As we know, primary silicon grains grow from the melt in a faceted behavior. I had saw the faceted model in the MICRESS forum, but it is used for 2-D simulation. So, i have a question, what is the anisotropy equations about faceted model in 3-D simulation ?

Thank you

seaworld

I have been simulating the primary silicon by using MICRESS. As we know, primary silicon grains grow from the melt in a faceted behavior. I had saw the faceted model in the MICRESS forum, but it is used for 2-D simulation. So, i have a question, what is the anisotropy equations about faceted model in 3-D simulation ?

Thank you

seaworld

### Re: A question about the faceted model in 3-D

Hi seaworld,

Welcome to the MICRESS forum.

Janin, our expert on the facet model, is on travel now. Meanwhile, I can give you the link of her most recent paper about eutectic morphology evolution in the Al-Si-Sr-P system:

http://iopscience.iop.org/1757-899X/84/ ... 012084.pdf

Best wishes

Bernd

Welcome to the MICRESS forum.

Janin, our expert on the facet model, is on travel now. Meanwhile, I can give you the link of her most recent paper about eutectic morphology evolution in the Al-Si-Sr-P system:

http://iopscience.iop.org/1757-899X/84/ ... 012084.pdf

Best wishes

Bernd

### Re: A question about the faceted model in 3-D

Hi

I have found a problem about facet model about theta(θ). In Micress users forum, theta is the misorientation of the normal vector of the interface to the normal vector of the nearest facet. but theta denotes the angle between the interfacial normal vector and the nearest {111}-facet vector fn by J Eiken . Are they the same?

Lilly

I have found a problem about facet model about theta(θ). In Micress users forum, theta is the misorientation of the normal vector of the interface to the normal vector of the nearest facet. but theta denotes the angle between the interfacial normal vector and the nearest {111}-facet vector fn by J Eiken . Are they the same?

Lilly

### Re: A question about the faceted model in 3-D

Yes, this is the same definition. In the Micress facet model theta(θ) gennerally denotes the angle between the normal interface vector to the nearest normal facet vector that you have defined. I my publication on AlSi I model the ansiotropy of Silicon by defining a set of 111-facets, hence in this case theta denotes the angle between the normal vector of the interface to the normal vector of the nearest defined 111-facet.

Janin

Janin

### Re: A question about the faceted model in 3-D

Dear janin，

Is the definition with σ*(interfacial stiffness) in your article (Eutectic morphology evolution and Sr-modification in Al-Si based alloys studied by 3D phase-field simulation coupled to Calphad data) the same as σ+σ'' ( σ''is the second derivative of σ with respect to θ). If not, can you give me a specific definition with σ*?

Lilly

Is the definition with σ*(interfacial stiffness) in your article (Eutectic morphology evolution and Sr-modification in Al-Si based alloys studied by 3D phase-field simulation coupled to Calphad data) the same as σ+σ'' ( σ''is the second derivative of σ with respect to θ). If not, can you give me a specific definition with σ*?

Lilly

### Re: A question about the faceted model in 3-D

The general definition of the interfacial stiffness is always σ*=σ+σ''.

And indeed, in model ‘facet_a’ (which works fine if you have only one type of facets) you have an explicit formulation of the interfacial energy σ. Here you can evaluate the interfacial stiffness by adding the second derivative. This is illustrated in the attached figure. In the case of model facet_b we don’t have an explicit formulation of the interfacial energy σ, but directly start with definition of a stiffness function similar to the one used for the kinetic attachment.

The amplitudes, i.e. the stiffness value in direction of the facet-vectors are identical in both model a and model b.

Anyware, you should be aware that the present facet model in Micress is rather pragmatic and the choice of the function is more or less arbitrary. The fundamental problem of modelling facetted growth is that there exist forbidden regions with negative stiffness which cannot not be handled numerically. For this reason we use regularized functions which model facet-like morphologies with rounded corners.

Regards,

Janin

And indeed, in model ‘facet_a’ (which works fine if you have only one type of facets) you have an explicit formulation of the interfacial energy σ. Here you can evaluate the interfacial stiffness by adding the second derivative. This is illustrated in the attached figure. In the case of model facet_b we don’t have an explicit formulation of the interfacial energy σ, but directly start with definition of a stiffness function similar to the one used for the kinetic attachment.

The amplitudes, i.e. the stiffness value in direction of the facet-vectors are identical in both model a and model b.

Anyware, you should be aware that the present facet model in Micress is rather pragmatic and the choice of the function is more or less arbitrary. The fundamental problem of modelling facetted growth is that there exist forbidden regions with negative stiffness which cannot not be handled numerically. For this reason we use regularized functions which model facet-like morphologies with rounded corners.

Regards,

Janin

### Re: A question about the faceted model in 3-D

Hi janin

I have a problem in your literature(Eutectic morphology evolution and Sr-modification in Al-Si based alloys studied by 3D phase-field simulation coupled to Calphad data) that additional {111}-facet of potential twin crystals is {511} instead of {211}.

Best wishes

Lilly

I have a problem in your literature(Eutectic morphology evolution and Sr-modification in Al-Si based alloys studied by 3D phase-field simulation coupled to Calphad data) that additional {111}-facet of potential twin crystals is {511} instead of {211}.

Best wishes

Lilly

### Re: A question about the faceted model in 3-D

You get the addtional (1,1,5) vectors by 60° rotations of your original (1,1,1) facet vectors around the 111-axes.

For example the matrix for a 60° rotation around 111 is:

2/3 2/3 -1/2

-1/3 2/3 2/3

2/3 -1/3 2/3

If you multiply this rotation matrix e.g with the (1,1,-1) vector you will get a (5, -1, -1) vector.

Ypu can do the same for all combinations of 111-twins and 111-vectors, i.e (1,1,1), (1,1,-1), (1,-1,1) and (-1,1,1).

Regards,

Janin

For example the matrix for a 60° rotation around 111 is:

2/3 2/3 -1/2

-1/3 2/3 2/3

2/3 -1/3 2/3

If you multiply this rotation matrix e.g with the (1,1,-1) vector you will get a (5, -1, -1) vector.

Ypu can do the same for all combinations of 111-twins and 111-vectors, i.e (1,1,1), (1,1,-1), (1,-1,1) and (-1,1,1).

Regards,

Janin