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

International Tables for Crystallography (2006). Vol. D, ch. 1.9, pp. 230-231

Table 1.9.3.1 

W. F. Kuhsa*

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

Table 1.9.3.1| top | pdf |
Site-symmetry table giving key to Tables 1.9.3.2[link] to 1.9.3.6[link][link][link][link] for restrictions on the symmetry of various thermal-motion tensors

Hex denotes hexagonal axes.

Point symmetry at special positionPosition [x,y,z]Cross-reference for tensor tables
Symmetry axesPoint-group generators1B1C1D1E1F
[m3m]   [4[0,0,1]] [3[1,1,1]] [\bar 1] [0,0,0] B1 C0 D1 E0 F1
[\bar 43m]   [\bar 4[0,0,1]] [3[1,1,1]]   [0,0,0] B1 C1 D1 E1 F1
[432]   [4[0,0,1]] [3[1,1,1]]   [0,0,0] B1 C0 D1 E0 F1
[m3]   [3[1,1,1]] [2[0,0,1]] [\bar 1] [0,0,0] B1 C0 D1 E0 F2
[23]   [3[1,1,1]] [2[0,0,1]]   [0,0,0] B1 C1 D1 E1 F2
[6/mmm] Hex [6[0,0,1]] [2[1,0,0]] [\bar 1] [0,0,0] B9 C0 D2 E0 F3
[\bar 6m2] Hex [\bar 6[0,0,1]] [2[1,0,0]]   [0,0,0] B9 C9 D2 E5 F3
[\bar 6m2] Hex [\bar 6[0,0,1]] [2[1,2,0]]   [0,0,0] B9 C10 D2 E6 F3
[6mm] Hex [6[0,0,1]] [\bar 2[1,0,0]]   [0,0,z] B9 C19 D2 E17 F3
[622] Hex [6[0,0,1]] [2[1,0,0]]   [0,0,0] B9 C0 D2 E0 F4
[6/m] Hex [6[0,0,1]] [\bar 1]   [0,0,0] B9 C0 D2 E0 F4
[\bar 6] Hex [\bar 6[0,0,1]]     [0,0,0] B9 C20 D2 E24 F4
[6] Hex [6[0,0,1]]     [0,0,z] B9 C19 D2 E17 F4
[4/mmm]   [4[0,0,1]] [2[1,0,0]] [\bar 1] [0,0,0] B2 C0 D3 E0 F5
[4/mmm]   [4[0,1,0]] [2[0,0,1]] [\bar 1] [0,0,0] B3 C0 D4 E0 F6
[4/mmm]   [4[1,0,0]] [2[0,1,0]] [\bar 1] [0,0,0] B4 C0 D5 E0 F7
[\bar 42m]   [\bar 4[0,0,1]] [2[1,0,0]]   [0,0,0] B2 C1 D3 E7 F5
[\bar 42m]   [\bar 4[0,0,1]] [2[1,1,0]]   [0,0,0] B2 C2 D3 E8 F5
[\bar 42m]   [\bar 4[0,1,0]] [2[0,0,1]]   [0,0,0] B3 C1 D4 E9 F6
[\bar 42m]   [\bar 4[0,1,0]] [2[1,0,1]]   [0,0,0] B3 C3 D4 E10 F6
[\bar 42m]   [\bar 4[1,0,0]] [2[0,1,0]]   [0,0,0] B4 C1 D5 E11 F7
[\bar 42m]   [\bar 4[1,0,0]] [2[0,1,1]]   [0,0,0] B4 C4 D5 E12 F7
[4mm]   [4[0,0,1]] [\bar 2[1,0,0]]   [0,0,z] B2 C13 D3 E25 F5
[4mm]   [4[0,1,0]] [\bar 2[0,0,1]]   [0,y,0] B3 C14 D4 E26 F6
[4mm]   [4[1,0,0]] [\bar 2[0,1,0]]   [x,0,0] B4 C15 D5 E27 F7
[422]   [4[0,0,1]] [2[1,0,0]]   [0,0,0] B2 C0 D3 E2 F5
[422]   [4[0,1,0]] [2[0,0,1]]   [0,0,0] B3 C0 D4 E3 F6
[422]   [4[1,0,0]] [2[0,1,0]]   [0,0,0] B4 C0 D5 E4 F7
[4/m]   [4[0,0,1]] [\bar 1]   [0,0,0] B2 C0 D12 E0 F14
[4/m]   [4[0,1,0]] [\bar 1]   [0,0,0] B3 C0 D13 E0 F15
[4/m]   [4[1,0,0]] [\bar 1]   [0,0,0] B4 C0 D14 E0 F16
[\bar 4]   [\bar 4[0,0,1]]     [0,0,0] B2 C16 D12 E28 F14
[\bar 4]   [\bar 4[0,1,0]]     [0,0,0] B3 C17 D13 E29 F15
[\bar 4]   [\bar 4[1,0,0]]     [0,0,0] B4 C18 D14 E30 F16
[4]   [4[0,0,1]]     [0,0,z] B2 C13 D12 E31 F14
[4]   [4[0,1,0]]     [0,y,0] B3 C14 D13 E32 F15
[4]   [4[1,0,0]]     [x,0,0] B4 C15 D14 E33 F16
[\bar 3m]   [3[1,1,1]] [2[1,\bar 1,0]] [\bar 1] [0,0,0] B5 C0 D6 E0 F8
[\bar 3m]   [3[1,1,\bar 1]] [2[1,\bar 1,0]] [\bar 1] [0,0,0] B6 C0 D7 E0 F9
[\bar 3m]   [3[1,\bar 1,1]] [2[1,1,0]] [\bar 1] [0,0,0] B7 C0 D8 E0 F10
[\bar 3m]   [3[\bar 1,1,1]] [2[1,1,0]] [\bar 1] [0,0,0] B8 C0 D9 E0 F11
[\bar 3m] Hex [3[0,0,1]] [2[1,0,0]] [\bar 1] [0,0,0] B9 C0 D10 E0 F12
[\bar 3m] Hex [3[0,0,1]] [2[1,2,0]] [\bar 1] [0,0,0] B9 C0 D11 E0 F13
[3m]   [3[1,1,1]] [\bar 2[1,\bar 1,0]]   [x,x,x] B5 C33 D6 E34 F8
[3m]   [3[1,1,\bar 1]] [\bar 2[1,\bar 1,0]]   [x,x,\bar x] B6 C34 D7 E35 F9
[3m]   [3[1,\bar 1,1]] [\bar 2[1,1,0]]   [x,\bar x,x] B7 C35 D8 E36 F10
[3m]   [3[\bar 1,1,1]] [\bar 2[1,1,0]]   [\bar x,x,x] B8 C36 D9 D37 F11
[3m] Hex [3[0,0,1]] [\bar 2[1,0,0]]   [0,0,z] B9 C37 D10 E38 F12
[3m] Hex [3[0,0,1]] [\bar 2[1,2,0]]   [0,0,z] B9 C38 D11 E39 F13
[32]   [3[1,1,1]] [2[1,\bar 1,0]]   [0,0,0] B5 C5 D6 E13 F8
[32]   [3[1,1,\bar 1]] [2[1,\bar 1,0]]   [0,0,0] B6 C6 D7 E14 F9
[32]   [3[1,\bar 1,1]] [2[1,1,0]]   [0,0,0] B7 C7 D8 E15 F10
[32]   [3[\bar 1,1,1]] [2[1,1,0]]   [0,0,0] B8 C8 D9 E16 F11
[32] Hex [3[0,0,1]] [2[1,0,0]]   [0,0,0] B9 C9 D10 E5 F12
[32] Hex [3[0,0,1]] [2[1,2,0]]   [0,0,0] B9 C10 D11 E6 F13
[\bar 3]   [\bar 3[1,1,1]]     [0,0,0] B5 C0 D15 E0 F17
[\bar 3]   [\bar 3[1,1,\bar 1]]     [0,0,0] B6 C0 D16 E0 F18
[\bar 3]   [\bar 3[1,\bar 1,1]]     [0,0,0] B7 C0 D17 E0 F19
[\bar 3]   [\bar 3[\bar 1,1,1]]     [0,0,0] B8 C0 D18 E0 F20
[\bar 3] Hex [\bar 3[0,0,1]]     [0,0,0] B9 C0 D19 E0 F21
[3]   [3[1,1,1]]     [x,x,x] B5 C54 D15 E58 F17
[3]   [3[1,1,\bar 1]]     [x,x,\bar x] B6 C55 D16 E59 F18
[3]   [3[1,\bar 1,1]]     [x,\bar x,x] B7 C56 D17 E60 F19
[3] Hex [3[\bar 1,1,1]]     [\bar x,x,x] B8 C57 D18 E61 F20
[3]   [3[0,0,1]]     [0,0,z] B9 C58 D19 E62 F21
[mmm]   [2[0,0,1]] [2[1,0,0]] [\bar 1] [0,0,0] B10 C0 D20 E0 F22
[mmm]   [2[0,0,1]] [2[1,1,0]] [\bar 1] [0,0,0] B11 C0 D21 E0 F23
[mmm]   [2[0,1,0]] [2[1,0,1]] [\bar 1] [0,0,0] B12 C0 D22 E0 F24
[mmm]   [2[1,0,0]] [2[0,1,1]] [\bar 1] [0,0,0] B13 C0 D23 E0 F25
[mmm] Hex [2[0,0,1]] [2[1,0,0]] [\bar 1] [0,0,0] B14 C0 D24 E0 F26
[mmm] Hex [2[0,0,1]] [2[1,1,0]] [\bar 1] [0,0,0] B11 C0 D21 E0 F23
[mmm] Hex [2[0,0,1]] [2[0,1,0]] [\bar 1] [0,0,0] B15 C0 D25 E0 F27
[mm]   [2[0,0,1]] [\bar 2[1,0,0]]   [0,0,z] B10 C21 D20 E40 F22
[mm]   [2[0,0,1]] [\bar 2[1,1,0]]   [0,0,z] B11 C22 D21 E41 F23
[mm]   [2[0,1,0]] [\bar 2[0,0,1]]   [0,y,0] B10 C23 D20 E42 F22
[mm]   [2[0,1,0]] [\bar 2[1,0,1]]   [0,y,0] B12 C24 D22 E43 F24
[mm]   [2[1,0,0]] [\bar 2[0,0,1]]   [x,0,0] B10 C25 D20 E44 F22
[mm]   [2[1,0,0]] [\bar 2[0,1,1]]   [x,0,0] B13 C26 D23 E45 F25
[mm]   [2[1,1,0]] [\bar 2[0,0,1]]   [x,x,0] B11 C27 D21 E46 F23
[mm]   [2[1,\bar 1,0]] [\bar 2[0,0,1]]   [x,\bar x,0] B11 C28 D21 E47 F23
[mm]   [2[1,0,1]] [\bar 2[0,1,0]]   [x,0,x] B12 C29 D22 E48 F24
[mm]   [2[1,0,\bar 1]] [\bar 2[0,1,0]]   [x,0,\bar x] B12 C30 D22 E49 F24
[mm]   [2[0,1,1]] [\bar 2[1,0,0]]   [0,y,y] B13 C31 D23 E50 F25
[mm]   [2[0,1,\bar 1]] [\bar 2[1,0,0]]   [0,y,\bar y] B13 C32 D23 E51 F25
[mm] Hex [2[0,0,1]] [\bar 2[1,0,0]]   [0,0,z] B14 C40 D24 E52 F26
[mm] Hex [2[0,0,1]] [\bar 2[1,1,0]]   [0,0,z] B11 C22 D21 E41 F23
[mm] Hex [2[0,0,1]] [\bar 2[0,1,0]]   [0,0,z] B15 C39 D25 E53 F27
[mm] Hex [2[1,0,0]] [\bar 2[0,0,1]]   [x,0,0] B14 C41 D24 E54 F26
[mm] Hex [2[2,1,0]] [\bar 2[0,0,1]]   [2x,x,0] B15 C42 D25 E55 F27
[mm] Hex [2[1,1,0]] [\bar 2[0,0,1]]   [x,x,0] B11 C27 D21 E46 F23
[mm] Hex [2[1,2,0]] [\bar 2[0,0,1]]   [x,2x,0] B14 C43 D24 E56 F26
[mm] Hex [2[0,1,0]] [\bar 2[0,0,1]]   [0,y,0] B15 C44 D25 E57 F27
[mm] Hex [2[1,\bar 1,0]] [\bar 2[0,0,1]]   [x,\bar x,0] B11 C28 D21 E47 F23
[222]   [2[0,0,1]] [2[1,0,0]]   [0,0,0] B10 C1 D20 E18 F22
[222]   [2[0,0,1]] [2[1,1,0]]   [0,0,0] B11 C2 D21 E19 F23
[222]   [2[0,1,0]] [2[1,0,1]]   [0,0,0] B12 C3 D22 E20 F24
[222]   [2[1,0,0]] [2[0,1,1]]   [0,0,0] B13 C4 D23 E21 F25
[222] Hex [2[0,0,1]] [2[1,0,0]]   [0,0,0] B14 C11 D24 E22 F26
[222] Hex [2[0,0,1]] [2[1,1,0]]   [0,0,0] B11 C2 D21 E19 F23
[222] Hex [2[0,0,1]] [2[0,1,0]]   [0,0,0] B15 C12 D25 E23 F27
[2/m]   [2[0,0,1]] [\bar 1]   [0,0,0] B16 C0 D26 E0 F28
[2/m]   [2[0,1,0]] [\bar 1]   [0,0,0] B17 C0 D27 E0 F29
[2/m]   [2[1,0,0]] [\bar 1]   [0,0,0] B18 C0 D28 E0 F30
[2/m]   [2[1,1,0]] [\bar 1]   [0,0,0] B19 C0 D29 E0 F31
[2/m]   [2[1,\bar 1,0]] [\bar 1]   [0,0,0] B20 C0 D30 E0 F32
[2/m]   [2[1,0,1]] [\bar 1]   [0,0,0] B21 C0 D31 E0 F33
[2/m]   [2[1,0,\bar 1]] [\bar 1]   [0,0,0] B22 C0 D32 E0 F34
[2/m]   [2[0,1,1]] [\bar 1]   [0,0,0] B23 C0 D33 E0 F35
[2/m]   [2[0,1,\bar 1]] [\bar 1]   [0,0,0] B24 C0 D34 E0 F36
[2/m] Hex [2[0,0,1]] [\bar 1]   [0,0,0] B16 C0 D26 E0 F28
[2/m] Hex [2[1,0,0]] [\bar 1]   [0,0,0] B25 C0 D35 E0 F37
[2/m] Hex [2[2,1,0]] [\bar 1]   [0,0,0] B26 C0 D36 E0 F38
[2/m] Hex [2[1,1,0]] [\bar 1]   [0,0,0] B19 C0 D29 E0 F31
[2/m] Hex [2[1,2,0]] [\bar 1]   [0,0,0] B27 C0 D37 E0 F39
[2/m] Hex [2[0,1,0]] [\bar 1]   [0,0,0] B28 C0 D38 E0 F40
[2/m] Hex [2[1,\bar 1,0]] [\bar 1]   [0,0,0] B20 C0 D30 E0 F32
m   [\bar 2[0,1,0]]     [x,0,z] B17 C64 D27 E77 F29
m   [\bar 2[1,0,0]]     [0,y,z] B18 C65 D28 E78 F30
m   [\bar 2[1,1,0]]     [x,\bar x,z] B19 C66 D29 E79 F31
m   [\bar 2[1,\bar 1,0]]     [x,x,z] B20 C67 D30 E80 F32
m   [\bar 2[1,0,1]]     [x,y,\bar x] B21 C68 D31 E81 F33
m   [\bar 2[1,0,\bar 1]]     [x,y,x] B22 C69 D32 E82 F34
m   [\bar 2[0,1,1]]     [x,y,\bar y] B23 C70 D33 E83 F35
m   [\bar 2[0,1,\bar 1]]     [x,y,y] B24 C71 D34 E84 F36
m Hex [\bar 2[0,0,1]]     [x,y,0] B16 C63 D26 E76 F28
m Hex [\bar 2[1,0,0]]     [x,2x,z] B25 C72 D35 E85 F37
m Hex [\bar 2[2,1,0]]     [0,y,z] B26 C73 D36 E86 F38
m Hex [\bar 2[1,1,0]]     [x,\bar x,z] B19 C66 D29 E79 F31
m Hex [\bar 2[1,2,0]]     [x,0,z] B27 C74 D37 E87 F39
m Hex [\bar 2[0,1,0]]     [2x,x,z] B28 C75 D38 E88 F40
m Hex [\bar 2[1,\bar 1,0]]     [x,x,z] B20 C67 D30 E80 F32
[2]   [2[0,0,1]]     [0,0,z] B16 C45 D26 E63 F28
[2]   [2[0,1,0]]     [0,y,0] B17 C46 D27 E64 F29
[2]   [2[1,0,0]]     [x,0,0] B18 C47 D28 E65 F30
[2]   [2[1,1,0]]     [x,x,0] B19 C48 D29 E66 F31
[2]   [2[1,\bar 1,0]]     [x,\bar x,0] B20 C49 D30 E67 F32
[2]   [2[1,0,1]]     [x,0,x] B21 C50 D31 E68 F33
[2]   [2[1,0,\bar 1]]     [x,0,\bar x] B22 C51 D32 E69 F34
[2]   [2[0,1,1]]     [0,y,y] B23 C52 D33 E70 F35
[2]   [2[0,1,\bar 1]]     [0,y,\bar y] B24 C53 D34 E71 F36
[2] Hex [2[0,0,1]]     [0,0,z] B16 C45 D26 E63 F28
[2] Hex [2[1,0,0]]     [x,0,0] B25 C59 D35 E72 F37
[2] Hex [2[2,1,0]]     [2x,x,0] B26 C60 D36 E73 F38
[2] Hex [2[1,1,0]]     [x,x,0] B19 C48 D29 E66 F31
[2] Hex [2[1,2,0]]     [x,2x,0] B27 C61 D37 E74 F39
[2] Hex [2[0,1,0]]     [0,y,0] B28 C62 D38 E75 F40
[2] Hex [2[1,\bar 1,0]]     [x,\bar x,0] B20 C49 D30 E67 F32
[\bar 1]   [\bar 1]     [0,0,0] B29 C0 D39 E0 F41
[\bar 1] Hex [\bar 1]     [0,0,0] B29 C0 D39 E0 F41
[1]   [1]     [x,y,z] B29 C76 D39 E89 F41
[1] Hex [1]     [x,y,z] B29 C76 D39 E89 F41