[Pw_forum] Query regarding real space interatomic force constant

[Sandeep Kumar]

Dear PWSCF users,
I have carried out linear response phonon calculations for Al over a 4 * 4 * 4 grid of q-points. This corresponds to a calculation in a supercell comprised of 4 * 4* 4 unit cells (primitive).
 We recall that the lattice vectors in fractional coordinate system of a fcc primitive cell are-
 a=(0.5, 0.5, 0.0)
 b=(0.0, 0.5, 0.5)
 c=(0.5, 0.0, 0.5)

>From the force-constant file (Al44.fc)  I obtained the force constant matrix Phi(i1,i2, na, nb) for pairs of atoms in the super-cell with the relative positions given  by
 R = (i-1)*a + (j-1)*b +(k-1)*c
 where i j and k are read from Al444.fc file.
 However, such a supercell does not include the pair of atoms located along the cube axis direction i.e R = (a,0,0) or (0,a,0) or (0,0,a), and hence the calculation CAN NOT give us the force-constant matrices along those pair of atoms.
 How do we obtain the force-constant matrices for pair of atoms located along the cube axes direction.
 I will be VERY VERY GRATEFUL to any help in this regard.

Sandeep K. Lahiri
Department of Mechanical Engineering
Massachusetts Institute of Technology
Cambridge, MA