Table 9.1.8.1

Burzlaff, H.; Zimmermann, H.

doi:10.1107/97809553602060000517

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. 9.1, p. 748

Table 9.1.8.1

H. Burzlaff^a and H. Zimmermann^b ^*

^a Universität Erlangen–Nürnberg, Robert-Koch-Strasse 4a, D-91080 Uttenreuth, Germany, and ^bInstitut für Angewandte Physik, Lehrstuhl für Kristallographie und Strukturphysik, Universität Erlangen–Nürnberg, Bismarckstrasse 10, D-91054 Erlangen, Germany
Correspondence e-mail: helmuth.zimmermann@knot.uni-erlangen.de

Table 9.1.8.1 | top | pdf |
The 24 `Symmetrische Sorten'

In the centred monoclinic lattices, the set $[\{{\bf a},{\bf c},{\bf a}+{\bf c}\}=\{{\bf p},{\bf q},{\bf r}\}]$ of the three shortest vectors in the ac plane is used to describe the metrical conditions. These vectors are renamed according to their relation to the projection of the centring point in the ac plane: p designates the vector that crosses the projection of the centring point, q is the shorter one of the two others and r labels the third one.

Delaunay symbol	Bravais type	Metrical conditions (parameters of conventional cells)	Voronoi type	Notation of the scalar products according to equation (9.1.8.1)						Transformation matrix $[\bi P]$
Delaunay symbol	Bravais type	Metrical conditions (parameters of conventional cells)	Voronoi type	12	13	14	23	24	34	Transformation matrix $[\bi P]$
K1	cI	–	I	12	12	12	12	12	12
K2	cF	–	III	0	13	13	13	13	0	$[1 \bar{1}1/111/002]$
K3	cP	–	V	0	0	14	14	14	0
K3	cP	–	V	0	0	14	0	14	14
H	hP	–	IV	12	0	12	0	12	34
R1	hR	$[2c^{2} \;\lt\; 3a^{2}]$	I	12	12	14	12	14	14	$[101/\bar{1}11/0\bar{1}1]$
R2	hR	$[2c^{2} \;\gt\; 3a^{2}]$	III	0	13	13	13	24	0
Q1	tI	$[c^{2} \;\lt\; 2a^{2}]$	I	12	13	13	13	13	12
Q2	tI	$[c^{2} \;\gt\; 2a^{2}]$	II	0	13	13	13	13	34
Q3	tP	–	V	0	0	14	0	14	34
				0	0	14	14	24	0
				0	0	14	23	0	23
O1	oF	–	I	12	13	13	13	13	34	$[1\bar{1}1/111/002]$
O2	oI	$[a^{2}+b^{2} \;\gt\; c^{2}]$	I	12	13	14	14	13	12
O3	oI	$[a^{2}+b^{2} \;\lt\; c^{2}]$	II	0	13	13	23	23	34
O4	oI	$[a^{2}+b^{2} = c^{2}]$	III	0	13	14	14	13	0
O4	oI	$[a^{2}+b^{2} = c^{2}]$	III	0	13	13	23	23	0
O5	o(AB)C	–	IV	12	0	14	0	12	34
O5	o(AB)C	–	IV	12	0	14	0	14	34	$[110/\bar{1}10/001]$
O6	oP	–	V	0	0	14	0	24	34
O6	oP	–	V	0	0	14	23	24	0
M1	m(AC)I	$[b^{2} \;\gt\; p^{2}]$	I	12	13	14	13	14	34	$[\bar{1}10/\bar{1}\bar{1}0/\bar{1}01]$
M2	m(AC)I	$[p^{2} \;\gt\; b^{2} \;\gt\; r^{2}-q^{2}]$	I	12	13	14	14	13	34	$[01\bar{1}/110/10\bar{1}]$
M3	m(AC)I	$[r^{2}-q^{2} \;\gt\; b^{2}]$	II	0	13	14	23	23	34	$[\bar{1}01/\bar{1}10/\bar{2}00]$
M4	m(AC)I	$[b^{2} = p^{2}]$	II	0	13	14	14	13	34	$[01\bar{1}/110/10\bar{1}]$
M4	m(AC)I	$[b^{2} = p^{2}]$	II	0	13	14	13	14	34	$[\bar{1}10/\bar{1}\bar{1}0/\bar{1}01]$
M5	m(AC)I	$[b^{2} = r^{2}-q^{2}]$	III	0	13	14	23	23	0	$[\bar{1}01/\bar{1}10/\bar{2}00]$
M5	m(AC)I	$[b^{2} = r^{2}-q^{2}]$	III	0	13	14	23	13	0	$[10\bar{1}/1\bar{1}0/0\bar{1}\bar{1}]$
M6	mP	–	IV	0	13	14	0	24	34
T1	aP	–	I	12	13	14	23	24	34
T2	aP	–	II	0	13	14	23	24	34
T3	aP	–	III	0	13	14	23	24	0