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

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

Section 1.1.4.8.5. Tetragonal system

A. Authiera*

aInstitut 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 [4]

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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 [422]

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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 [4mm]

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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 [4/m]

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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}]: [Scheme scheme26]

    There are 6 independent components.

  • (ii) Mirror perpendicular to [Ox_{1}] (the twofold axis is at [45 ^{\circ}]) [Scheme scheme27]

The number of independent components is of course the same, 6.

1.1.4.8.5.7. Group [4/mm]

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All the components are equal to zero.








































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