The following are the Special Quasirandom Structures [S.-H. Wei, L. G. Ferreira, J. E. Bernard, and A. Zunger Phys. Rev. B 42, 9622 (1990).] used in our SST group for A_1-xB_x alloys at x=1/4 and x=1/2. A atom is denoted as type 1 and B atom is denoted as type 2. I will give the lattice vector and atomic type and coordinates for these SQSs. I give here only the atomic positions (before relaxation) of the mixed atoms in the fcc sublattice. To get the coordinates of the C atoms in the zinc-blende alloy, just add (0.25,0.25,0.25) to each of the atomic position of the A and B atoms. For rock-salt alloy you need to add (0.50,0.50,0.50). ___________________________________________________________________________________________ Table I. Atomic correlation functions of the SQSs ___________________________________________________________________________________________ Superlattice J0 J1 J2 J3 J4 K2 L2 M2 N2 O2 P2 Direction SQS8(x=1/4)-I 1 -1/2 1/4 -1/4 1/2 1/3 1/12 1/6 5/12 1/8 7/24 (-3, 3, 1) SQS8(x=1/4)-II 1 -1/2 1/4 -1/4 1/2 1/3 1/4 0 1/6 0 1/3 ( 0,-1, 2) SQS16(x=1/4) 1 -1/2 1/4 -1/16 1/4 1/4 1/4 5/24 11/48 1/8 19/96 (-3,-1, 7) Random(x=1/4) 1 -1/2 1/4 -1/8 1/16 1/4 1/4 1/4 1/4 1/4 1/4 -------- SQS8(x=1/2)-a 1 0 0 -1/4 0 0 1/24 -1/12 1/12 0 -1/8 (-1, 1, 3) SQS8(x=1/2)-b 1 0 0 1/4 0 0 1/24 -1/12 1/12 0 -1/8 (-1, 1, 3) SQS16(x=1/2)-I 1 0 0 0 0 0 0 0 0 0 0 -------- SQS16(x=1/2)-II 1 0 0 0 0 0 0 0 0 0 0 -------- SQS16(x=1/2)-III 1 0 0 0 0 0 0 0 0 0 0 -------- Random(x=1/2) 1 0 0 0 0 0 0 0 0 0 0 -------- ___________________________________________________________________________________________ When you permutate A to B and vise versa (i.e. change x to 1-x) the odd correlation functions (J1 and J3 in Table I) change signs The following is the lattice vectors and atomic positions (in Cartesian coordinates) of these SQSs. _________________________________________________ SQS8(x=1/4)-I 0.50000 0.50000 0.00000 # a 0.50000 0.00000 1.50000 # a 1.00000 -1.50000 -0.50000 # a 2 0.0000 0.0000 0.0000 1 0.5000 0.0000 0.5000 1 1.0000 0.0000 1.0000 2 0.5000 -0.5000 0.0000 1 1.0000 -0.5000 0.5000 1 1.5000 -0.5000 1.0000 1 1.0000 -1.0000 0.0000 1 1.5000 -1.0000 0.5000 _________________________________________________ SQS8(x=1/4)-II 1.00000 0.00000 0.00000 # a 0.50000 1.00000 0.50000 # a -0.50000 -1.00000 1.50000 # a 2 0.0000 0.0000 0.0000 2 0.0000 -0.5000 1.5000 1 0.5000 0.0000 1.5000 1 0.5000 -0.5000 1.0000 1 0.0000 0.0000 1.0000 1 0.5000 0.5000 1.0000 1 0.5000 0.0000 0.5000 1 1.0000 0.5000 0.5000 _________________________________________________ SQS16(x=1/4) 1.00000 0.50000 0.50000 # a -0.50000 1.50000 0.00000 # a -0.50000 -0.50000 2.00000 # a 2 0.0000 0.0000 0.0000 1 0.0000 0.0000 2.0000 1 -0.5000 0.0000 1.5000 1 0.0000 0.5000 1.5000 1 -0.5000 0.5000 1.0000 2 0.0000 1.0000 1.0000 2 -0.5000 1.0000 0.5000 1 0.0000 1.5000 0.5000 2 0.0000 0.5000 0.5000 1 0.5000 1.0000 0.5000 1 -0.5000 0.5000 2.0000 1 0.0000 1.0000 2.0000 1 -0.5000 1.0000 1.5000 1 0.0000 1.5000 1.5000 1 0.0000 0.0000 1.0000 1 0.5000 0.5000 1.0000 _________________________________________________ _________________________________________________ SQS8(x=1/2)-a 0.50000 0.50000 0.00000 # a 1.00000 -0.50000 0.50000 # a 1.00000 -1.00000 -2.00000 # a 2 0.0000 0.0000 0.0000 2 1.5000 -1.0000 -1.5000 1 1.0000 -0.5000 -1.5000 2 1.5000 -0.5000 -1.0000 2 0.5000 -0.5000 -1.0000 1 1.0000 -0.5000 -0.5000 1 0.5000 0.0000 -0.5000 1 1.0000 0.0000 0.0000 _________________________________________________ SQS8(x=1/2)-b Same as SQS8(x=1/2)-a but switch type 1 with type 2 _________________________________________________ SQS16(x=1/2)-I 1.00000 0.50000 0.50000 # a 0.00000 1.00000 -1.00000 # a -1.00000 1.50000 1.50000 # a 2 0.0000 0.0000 0.0000 1 0.5000 0.5000 0.0000 2 0.0000 0.5000 -0.5000 2 0.5000 1.0000 -0.5000 1 0.0000 0.5000 0.5000 2 0.5000 1.0000 0.5000 2 0.0000 1.0000 0.0000 2 0.5000 1.5000 0.0000 1 0.0000 1.0000 1.0000 2 -0.5000 1.0000 0.5000 1 0.0000 1.5000 0.5000 1 -0.5000 1.5000 0.0000 2 0.0000 1.5000 1.5000 1 -0.5000 1.5000 1.0000 1 0.0000 2.0000 1.0000 1 -0.5000 2.0000 0.5000 _________________________________________________ SQS16(x=1/2)-II 1.00000 1.00000 0.00000 # a 1.00000 0.00000 1.00000 # a 2.00000 -1.00000 -1.00000 # a 2 0.0000 0.0000 0.0000 1 0.5000 0.5000 0.0000 2 0.5000 0.0000 0.5000 2 1.0000 0.5000 0.5000 1 2.0000 -0.5000 -0.5000 2 2.5000 0.0000 -0.5000 2 2.5000 -0.5000 0.0000 2 3.0000 0.0000 0.0000 1 2.0000 0.0000 0.0000 2 1.5000 -0.5000 0.0000 1 1.5000 0.0000 -0.5000 1 1.0000 -0.5000 -0.5000 2 2.0000 0.5000 0.5000 1 1.5000 0.0000 0.5000 1 1.5000 0.5000 0.0000 1 1.0000 0.0000 0.0000 _________________________________________________ SQS16(x=1/2)-III 0.50000 0.50000 0.00000 # a 1.00000 -1.00000 2.00000 # a 1.00000 -1.00000 -2.00000 # a 2 0.0000 0.0000 0.0000 1 0.5000 0.0000 0.5000 2 0.5000 -0.5000 1.0000 1 1.0000 -0.5000 1.5000 2 1.0000 -0.5000 -1.5000 2 1.0000 -1.0000 -1.0000 1 1.5000 -1.0000 -0.5000 2 1.5000 -1.5000 0.0000 1 0.5000 -0.5000 -1.0000 2 1.0000 -0.5000 -0.5000 1 1.0000 -1.0000 0.0000 2 1.5000 -1.0000 0.5000 2 0.5000 0.0000 -0.5000 1 0.5000 -0.5000 0.0000 1 1.0000 -0.5000 0.5000 1 1.0000 -1.0000 1.0000 _________________________________________________