Table 9.2.5.2

Wolff, P. M. de

doi:10.1107/97809553602060000518

International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by Th. Hahn

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International Tables for Crystallography (2006). Vol. A. ch. 9.2, p. 754

Table 9.2.5.2

P. M. de Wolff^a ^‡

^a Laboratorium voor Technische Natuurkunde, Technische Hogeschool, Delft, The Netherlands

Table 9.2.5.2 | top | pdf |
Lattice characters described by relations between conventional cell parameters

Under each of the roman numerals below `Lattice characters in', numbers of characters (cf. Table 9.2.5.1, first column) are listed for which the key parameter p lies in the interval defined by the same roman numeral below `Intervals of p'. For instance, a lattice with character No. 15 under IV has [p = c/a] ; so it falls in the interval IV with $[\surd 2 \lt c/a\ (\lt \infty)]$ ; No. 33 under II has [p = b] ; therefore the interval [a - c] for II yields the relation $[a \lt b \lt c]$ .

Lattice symmetry		Bravais type^†	p = key parameter	Lattice characters in					Intervals of p									Conventions^‡‡
Lattice symmetry		Bravais type^†	p = key parameter	I	II	III	IV			I		II		III		IV		Conventions^‡‡
Tetragonal		tP		21	11	–	–		0		1		∞		–		–
Tetragonal		tI		18	6	7	15		0		$[\surd (2/3)]$		1		$[\surd 2]$		∞
Hexagonal		hP		22	12	–	–		0		1		∞		–		–
Rhombohedral		hR		24	4	2	9		0		$[\surd (3/8)]$		$[\surd (3/2)]$		$[\surd 6]$		∞	Hexagonal axes
Orthorhombic		oP	–	32 no relations					–		–		–		–		–	$[a \lt b \lt c]$
Orthorhombic		oS
$[\quad b \lt a/\surd 3]$			c	23	13	–	–		0		d ^‡		∞		–		–	$[a \lt b]$
$[\quad b \gt a/\surd 3]$			c	40	36	38	–		0		a		d ^‡		∞		–
Orthorhombic		oI	r ^§	8	19	42	–		0		a		b		∞		–	$[a \lt b \lt c]$
Orthorhombic		oF		16	26	–	–		1		$[\surd 3]$		∞		–		–	$[a \lt b \lt c]$
Monoclinic		mP	b	35	33	34	–		0		a		c		∞		–	$[a \lt c]$ ^††
Monoclinic		mS
Centred net $[\Bigg\{]$	^¶			–	–	–	$[\cases{28\cr 29\cr}]$	$[\Bigg\}]$	0		$[\surd(1/3)]$		1		$[\surd 3]$		∞	C centred^††
				–	–	–	30
				$[\cases{37\cr 41\cr}]$	20	25	–
				$[\cases{27\cr 39\cr}]$	$[\cases{10\cr 17\cr}]$	14	–
				43	–	–	–		1		∞		–		–		–	I centred^††
Triclinic		aP	$[\alpha, \beta, \gamma]$	31	44	–	–		60°		90°		120°		–		–	$[a \lt b \lt c]$
Cubic		cP	–	$[\left.\matrix{3\cr 5\cr 1\cr}\right\}\hbox{ no relations}]$					–		–		–		–		–
		cI	–						–		–		–		–		–
		cF	–						–		–		–		–		–

^†The symbols for Bravais lattices were adopted by the International Union of Crystallography in 1985; cf. de Wolff et al. (1985)

.
^‡ $[d = {1 \over 2} \surd (a^{2} + b^{2})]$ .
^§ $[r = {1 \over 2} \surd (a^{2} + b^{2} + c^{2})]$ .
^¶This number specifies the centred net among the three orthogonal nets parallel to the twofold axis and passing through (1) the shortest, (2) the second shortest, and (3) the third shortest lattice vector perpendicular to the axis. For example, `2, 3' means that either net (2) or net (3) is the centred one.
^††Setting with unique axis b; $[\beta \gt 90^{\circ}]$ ; $[a \lt c]$ for both P and I cells, $[a \lt c]$ or $[a \gt c]$ for C cells.
^‡‡These conventions refer to the cells obtained by the transformations of Table 9.2.5.1

. They have been chosen for convenience in this table.