I just calculated the stiffness tensor for a given material (a monoclinic molecular crystal) using molecular simulation. When trying to compare my results to published experimental results I found that the crystal structure I used for simulation, though essentially the same as the one used as reference system in experiment, has different base vectors/reference frame (P21/n vs P21/a) - therefore I can compare invariants and averages but not the individual components c_ij of the stiffness (as matrix in Voigt notation).
So my question is: given the, altogether six, lattice vectors of the two crystal structures, how can I use this information to generate a rotation matrix to transform the Voigt matrix from experiment (based on a crystal in the P21/a space group) so that I can compare it to my calculated numbers from simulation (based on a crystal with P21/n symmetry)?
What comes closest to an answer I found here: http://solidmechanics.org/text/Chapter3_2/Chapter3_2.htm but I am not sure what the two bases (e and m, in section 3.2.11 Basis change formulas for anisotropic elastic constants) are - are these the normalized lattice vectors of the two structures in Cartesian coordinates? if not what else?