Transforming matrix so that the unit cell's angles are changed.

[letshin]

Dear All,

I would like to transform a unit cell triclinic unit cell that is angled (Angle =/= Pi/2) into a cubic form (all angles == Pi/2) for better visualisation and analysis. As a sample a trigonal cell has been used, with parameters (a = 3, b = 3, c = 3, Alpha = Pi/2, Beta = Pi/2, Gamma = Pi/2). The resulting cell should have an angle of Alpha = Pi/3, e.g. (a = 3, b = 3, c = 3, Alpha = Pi/3, Beta = Pi/2, Gamma = Pi/2)

I have tried using the G-matrix relationship where:

G[new] = S G[old] S[t]

where G[new] is the G matrix of the new cell, S is the transformation matrix, G[old] is the G matrix of the old cell, and S[t] is the transpose of the old transformation matrix. G is given as:

g:= 

{a^2, a*b*Cos[Gamma], a*c*Cos[Beta]}, 

{a*b*Cos[Gamma], b^2, b*c*Cos[Alpha]}, 

{a*c*Cos[Beta], b*c*Cos[Alpha], c^2}

The resultant transformation matrix to skew Alpha to Pi/3 is then:

S = {1, 0, 0}, {0, 1, 0.5}, {0, 0.5, 1}

Although if I use this transformation matrix into Vesta I get these parameters in the unit cell where b and c have changed and Alpha =/= Pi/3:

(a = 3, b = 3.35, c = 3.35, Alpha = 36.86 Degrees, Beta = Pi/2, Gamma = Pi/2).

I am not able to figure out what I am doing wrong. Is it a problem with constraints that I am not considering - I have tried picking b and c to be fed into G[new] so that the volume of G[old] and G[new] is constant, and also trying so that the resolved magnitude along b-c is constant but neither are working.

Many thanks,

Zhao