Table 9.1.1.2

Koch, E.; Fischer, W.

doi:10.1107/97809553602060000617

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

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

Table 9.1.1.2

E. Koch^a and W. Fischer^a

^a Institut 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

Type	k	Symmetry			Parameters	Distance d	Net	Stacking	Density
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
2	12	$[Fm\bar3m]$	4(a)	0, 0, 0	–	$[{1\over2}\sqrt2a]$	{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	0.6981
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	0.6657
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	0.6657
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