the angle between the interface normal and the x-axis

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shoney
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the angle between the interface normal and the x-axis

Post by shoney » Mon Jul 18, 2011 4:48 am

For phase-field method, we need to calculate the angle between the direction normal to the interface and the x-axis when anisotropy is considered.
In the published papers, the authors just gave the expression θ=atan(Φy/Φx), where Φ is the phase-field variable, Φy and Φx mean the derivative with respect to y and x.
For this expression, the results will be the same value for these two situations: (1)Φy>0, Φx>0; (2)Φy<0, Φx<0. In another word, this expression cannot represent all of the angles that exist.
So what's the exact expression that can calculate all of the angles? Thank you!

Bernd
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Re: the angle between the interface normal and the x-axis

Post by Bernd » Mon Jul 18, 2011 8:58 am

Hi shoney,

In MICRESS, the direction of the interface, e.g. for calculation of anisotropy, is expressed as a normal vector which has 2 or 3 components (depending on whether 2D or 3D orientations are used). This normal vector perfectly defines all possible orientations and enters into the corresponding anisotropy description.
Sometimes orientations can be reduced: if you specify cubic symmetry, e.g., your two cases are identical! I do not know from which of our papers you took the expression for for the angle which you gave in your post, but I guess it is valid only for the case of symmetry.

Bernd

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