International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 9.1, p. 748

Table 9.1.1.2 

E. Kocha and W. Fischera

aInstitut für Mineralogie, Petrologie und Kristallographie, Universität Marburg, Hans-Meerwein-Strasse, D-35032 Marburg, Germany

Table 9.1.1.2| top | pdf |
Examples for sphere packings with high contact numbers and high densities and with low contact numbers and low densities

TypekSymmetryParametersDistance dNetStackingDensity
1 12 P63/mmc 2(c) [{1\over3},{2\over3},{1\over4}] [c/a={2\over3}\sqrt6] a (001) 36 3, 3 2 0.7405
2 12 [Fm\bar3m] 4(a) 0, 0, 0 [{1\over2}\sqrt2a] {111} 36 3, 3 3
{001} 44 4, 4 2
3 11 Cmca 8(f) 0, y, z [y = {1\over6}, z = {3\over2} \sqrt2 - 2]
[b/a=\sqrt3, c/a={2\over3}\sqrt6+\sqrt3]
a (001) 36 3, 2 4 0.7187
4 11 P3121 6(c) x, y, z [x={1\over2}, y={5\over6}, z=\sqrt2-{4\over3}]
[c/a=\sqrt6+{3\over2}\sqrt 3]
a (001) 36 3, 2 6
5 11 Fdd2 16(b) x, y, z [x={1\over6}, y={3\over4}\sqrt2 - 1, z=0]
[b/a={4\over 3}\sqrt2+2, c/a={1\over3}\sqrt 3]
c (010) 36 3, 2 8
6 11 P6522 12(c) x, y, z [x={1\over6}, y={1\over3}, z={1\over2}\sqrt2-{2\over3}]
[c/a=2\sqrt6+ 3\sqrt3]
a (001) 36 3, 2 12
7 11 C2/m 4(i) x, 0, z [x={1\over2}\sqrt2-{1\over2}, z=3\sqrt2 - 4]
[b/a = {1\over3}\sqrt3, c/a={1\over 6}\sqrt6+{1\over3}\sqrt3]
[\cos\beta={1\over6}\sqrt6-{1\over3}\sqrt 3]
b (001) 36 3, 2 12
8 11 P42/mnm 4(f) x, x, 0 [x={1\over2}\sqrt2-{1\over2}, c/a=2-\sqrt2] c 0.7187
9 10 I4/mmm 2(a) 0, 0, 0 [c/a={1\over3}\sqrt6] c {110} 36 2, 2 2 0.6981
10 10 P6222 3(c) [{1\over2},0,0] [c/a={3\over2}\sqrt3] a (001) 36 2, 2 3
11 10 Fddd 8(a) 0, 0, 0 [b/a=\sqrt3, c/a=2\sqrt 3] a (001) 36 2, 2 4
12 10 Fddd 16(g) [{1\over8},{1\over8},z] [z={5\over16}, b/a=\sqrt3, c/a=4\sqrt3] a (001) 36 2, 2 8
13 10 Cmcm 4(c) [0,y,{1\over4}] [y={3\over10},b/a={1\over3}\sqrt{15}, c/a={2\over5}\sqrt{10}] [{1\over3}\sqrt6a] (001) 44 3, 3 2 0.6981
14 10 Pnma 4(c) [x,{1\over4},z] [x={7\over20},z-{7\over8}, b/a={4\over5}, c/a={2\over15}\sqrt{15}] c (010) 44 3, 3 2
15 10 P63/mmc 4(f) [{1\over3},{2\over 3}, z] [z={3\over4}-{1\over4}\sqrt6,c/a={2\over3}\sqrt6+2] a (001) 36 3, 1 4 0.6657
16 10 [R\bar 3m] 6(c) 0, 0, z [z={1\over2}-{1\over6}\sqrt6, c/a=\sqrt6+3] a (001) 36 3, 1 6
17 10 Cmcm 4(c) [0,y,{1\over4}] [y={3\over 4}-{1\over4}\sqrt 6,]
[c/a=1, b/a=\sqrt3+\sqrt 2]
a (010) 44 4, 2 4 0.6657
18 10 I41/amd 8(e) 0, 0, z [z={1\over2}-{1\over8}\sqrt6, c/a=2\sqrt3 + 2\sqrt2] a (001) 44 4, 2 8
19 10 I4/m 8(h) x, y, 0 [x={6\over17}-{1\over17}\sqrt2, y={7\over 17}-{4\over17}\sqrt2]
[c/a=({14\over17} - {8\over17}\sqrt2)^{1/2}]
c 0.6619
20 10 [R\bar3] 18(f) x, y, z [x={3\over7}, y={1\over7},z=0,c/a={1\over7}\sqrt{42}] [{1\over7}\sqrt7a] (001) 346 3, 2 3 0.6347
 
21 4 [Fd\bar 3m] 32(e) x, x, x [x={3\over8}-{1\over8}\sqrt6] [({3\over4}\sqrt2-{1\over2}\sqrt3)a] 0.1235
22 4 [Im\bar3m] 48(j) 0, y, z [y={4\over7}-{3\over28}\sqrt2, z={5\over14}-{1\over 28}\sqrt2] [({3\over14}\sqrt2-{1\over7})a] 0.1033
23 4 I4132 48(i) x, y, z [x=y={1\over8}\sqrt2, z=0] [({1\over2}-{1\over4}\sqrt2)a] 0.0789
24 3 I4132 24(h) [{1\over8},y,{1\over4}-y] [y={1\over4}\sqrt3-{3\over8}] [({1\over2}\sqrt6-{3\over4}\sqrt2)a] 0.0555