# Table 2 Total number of possible atom combinations for different substitution levels x and different supercell sizes of the $$\hbox {A}_\mathrm{x} \hbox {Pb}_\mathrm{1-x}\hbox {Te}$$ system
 N 8 16 24 32 64 Cell, $$a\times b \times c$$ $$1\times 1 \times 1$$ $$1\times 1 \times 2$$ $$1\times 1 \times 3$$ $$1\times 2 \times 2$$ $$2\times 2 \times 2$$ Symmetry operations 192 128 192 256 1536 $$x=\frac{1}{16}$$ N/A N/A N/A 16 (1) 496 (5) $$x=\frac{1}{8}$$ N/A 8 (1) N/A 120 (5) 35,960 (71) $$x=\frac{1}{4}$$ 4 (1) 28 (4) 220 (9) 1820 (33) 10,518,300 (8043) $$x=\frac{1}{2}$$ 6 (1) 70 (8) 924 (34) 12,870 (153) 601,080,390 (404,582)
1. N is the total number of atoms in the supercell. The number of unique (non-symmetric) combinations are given in parenthesis. The total number of combinations depends only on N, whereas the number of unique combinations can depend on the supercell formula $$a\times b \times c$$. The number of combinations for substitutions $$1-x$$ is equal to the number of combinations for $$x$$ and are consequently not shown 