Dear All, I would appreciate if someone can help me to understand what crystal basis we deal with (composed from direct or reciprocal vectors) in the routines PH/trntnsc.f90 and PW/trntns.f90.
In the routine PH/trntnsc.f90 there is a comment that it does a transformation of a complex tensor (like the dynamical matrix) from crystal to cartesian axes or viceversa. I have a question: Which crystal axes we are dealing with, the crystal basis of direct vectors (at(i),i=1,2,3) or the crystal basis of reciprocal vectors (bg(i),i=1,2,3)? Crystal -> Cartesian : D_cart = B * D_cryst * B^T , Crystal <- Cartesian : D_cryst = A^T * D_cart * A , where D_cryst, D_cart are the tensors of the dynamical matrix in the crystal and cartesian basis respectively, A is the matrix composed from the direct lattice vectors (at(i),i=1,2,3), B is the matrix composed from the reciprocal lattice vectors (bg(i),i=1,2,3), the symbol * stands for the matrix multiplication, and "T" stands for the transposition of the matrix. It seems to me that in these routines (PH/trntnsc.f90 and PW/trntns.f90) we are dealing with the crystal basis of reciprocal vectors, not sure. And I think that if one wants to do a transformation from the cartesian basis to the crystal basis of direct vectors then the equations would read: Crystal(direct vectors) -> Cartesian : W_cart = A * W_cryst * A^T , Crystal(direct vectors) <- Cartesian : W_cryst = B^T * W_cart * B , here W is some tensor. Is it true? Yours faithfully, Iurii Timrov Iurii TIMROV Doctorant (PhD student) Laboratoire des Solides Irradies Ecole Polytechnique F-91128 Palaiseau +33 1 69 33 45 08 timrov at theory.polytechnique.fr
