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)