Tetragonal system

Authier, A.

doi:10.1107/97809553602060000628

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

pdf | chapter contents | chapter index | related articles

International Tables for Crystallography (2006). Vol. D. ch. 1.1, pp. 18-19

Section 1.1.4.8.5. Tetragonal system

A. Authier^a ^*

^a Institut de Minéralogie et de la Physique des Milieux Condensés, Bâtiment 7, 140 rue de Lourmel, 75015 Paris, France
Correspondence e-mail: aauthier@wanadoo.fr

1.1.4.8.5. Tetragonal system

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1.1.4.8.5.1. Group

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The method of direct inspection can be applied for a fourfold axis. One finds [Scheme scheme22]

There are 7 independent components.

1.1.4.8.5.2. Group

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One combines the reductions for groups 4 and 222: [Scheme scheme23]

There are 3 independent components.

1.1.4.8.5.3. Group

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One combines the reductions for groups 4 and 2m: [Scheme scheme24]

There are 4 independent components.

1.1.4.8.5.4. Group

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All the components are equal to zero.

1.1.4.8.5.5. Group $[\bar{4}]$

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The matrix corresponding to axis $[\bar{4}]$ is $[\pmatrix{0 &\bar{1} &0\cr 1 &0 &0\cr 0 &0 &\bar{1}\cr}]$ and the form of the $[3 \times 9]$ matrix is [Scheme scheme25]

There are 6 independent components.

1.1.4.8.5.6. Group $[\bar{4}2m]$

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One combines either the reductions for groups $[\bar{4}]$ and 222, or the reductions for groups $[\bar{4}]$ and 2mm.

(i) Twofold axis parallel to $[Ox_{1}]$ :

There are 6 independent components.
(ii) Mirror perpendicular to $[Ox_{1}]$ (the twofold axis is at $[45 ^{\circ}]$ )