International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. D. ch. 1.9, p. 233

Table 1.9.3.3 

W. F. Kuhsa*

a GZG Abt. Kristallographie, Goldschmidtstrasse 1, 37077 Göttingen, Germany
Correspondence e-mail: wkuhs1@gwdg.de

Table 1.9.3.3 | top | pdf |
Symmetry restrictions on coefficients in third-rank symmetric polar tensors

Cross-reference No. of independent variables Symbols and coefficient indices
A B C D E F G H I J
(1) (2) (3) (1) (1) (1) (1) (2) (2) (1)
(1) (2) (3) (1) (2) (1) (3) (2) (3) (2)
(1) (2) (3) (2) (2) (3) (3) (3) (3) (3)
C0 0 0 0 0 0 0 0 0 0 0 0
C1 1 0 0 0 0 0 0 0 0 0 J
C2 1 0 0 0 0 0 F 0 −F 0 0
C3 1 0 0 0 D 0 0 0 0 −D 0
C4 1 0 0 0 0 E 0 −E 0 0 0
C5 1 0 0 0 D −D −D D D −D 0
C6 1 0 0 0 D −D D D −D −D 0
C7 1 0 0 0 D D D −D −D −D 0
C8 1 0 0 0 D D −D −D D −D 0
C9 1 0 0 0 D D 0 0 0 0 0
C10 1 A −A 0 A/2 −A/2 0 0 0 0 0
C11 1 0 0 0 0 0 F 0 0 0 F
C12 1 0 0 0 0 0 0 0 H 0 H
C13 2 0 0 C 0 0 F 0 F 0 0
C14 2 0 B 0 D 0 0 0 0 D 0
C15 2 A 0 0 0 E 0 E 0 0 0
C16 2 0 0 0 0 0 F 0 −F 0 J
C17 2 0 0 0 D 0 0 0 0 −D J
C18 2 0 0 0 0 E 0 −E 0 0 J
C19 2 0 0 C 0 0 F 0 F 0 F/2
C20 2 A −A 0 D D − A 0 0 0 0 0
C21 3 0 0 C 0 0 F 0 H 0 0
C22 3 0 0 C 0 0 F 0 F 0 J
C23 3 0 B 0 D 0 0 0 0 I 0
C24 3 0 B 0 D 0 0 0 0 D J
C25 3 A 0 0 0 E 0 G 0 0 0
C26 3 A 0 0 0 E 0 E 0 0 J
C27 3 A A 0 D D 0 G 0 G 0
C28 3 A −A 0 D −D 0 G 0 −G 0
C29 3 A 0 A 0 E F F E 0 0
C30 3 A 0 −A 0 E F −F −E 0 0
C31 3 0 B B D 0 D 0 H H 0
C32 3 0 B −B D 0 −D 0 H −H 0
C33 3 A A A D D D D D D J
C34 3 A A −A D D −D D −D D J
C35 3 A −A A D −D −D −D −D D J
C36 3 A −A −A D −D D −D D D J
C37 3 A −A C A/2 −A/2 F 0 F 0 F/2
C38 3 0 0 C D D F 0 F 0 F/2
C39 3 0 0 C 0 0 F 0 H 0 F/2
C40 3 0 0 C 0 0 F 0 H 0 H/2
C41 3 A 0 0 D D 0 G 0 0 0
C42 3 A B 0 A/2 A/6 + 2B/3 0 G 0 G/2 0
C43 3 A B 0 B/6 + 2A/3 B/2 0 G 0 2G 0
C44 3 0 B 0 D D 0 0 0 I 0
C45 4 0 0 C 0 0 F 0 H 0 J
C46 4 0 B 0 D 0 0 0 0 I J
C47 4 A 0 0 0 E 0 G 0 0 J
C48 4 A A 0 D D F G −F G 0
C49 4 A −A 0 D −D F G −F −G 0
C50 4 A 0 A D E F F E −D 0
C51 4 A 0 −A D E F −F −E −D 0
C52 4 0 B B D E D −E H H 0
C53 4 0 B −B D E −D −E H −H 0
C54 4 A A A D E E D D E J
C55 4 A A −A D E −E D −D E J
C56 4 A −A A D E E −D −D −E J
C57 4 A −A −A D E −E −D D −E J
C58 4 A −A C D D − A F 0 F 0 F/2
C59 4 A 0 0 D D F G 0 0 F
C60 4 A B 0 A/2 A/6 + 2B/3 0 G H G/2 H
C61 4 A B 0 B/6 + 2A/3 B/2 F G 0 2G F
C62 4 0 B 0 D D 0 0 H I H
C63 6 A B 0 D E 0 G 0 I 0
C64 6 A 0 C 0 E F G H 0 0
C65 6 0 B C D 0 F 0 H I 0
C66 6 A −A C D −D F G F −G J
C67 6 A A C D D F G F G J
C68 6 A B −A D E F −F −E D J
C69 6 A B A D E F F E D J
C70 6 A B −B D E −D E H −H J
C71 6 A B B D E D E H H J
C72 6 A B C B/6 + 2A/3 B/2 F G H 2G H/2
C73 6 0 B C D D F 0 H I F/2
C74 6 A 0 C D D F G H 0 H/2
C75 6 A B C A/2 A/6 + 2B/3 F G H G/2 F/2
C76 10 A B C D E F G H I J