MICRESS Forum

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!

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