Revision as of 14:41, 18 April 2006

Twins

Other languages

Macles (Fr). Geminati (It)

Oriented association and twinning

Crystals (also called individuals) belonging to the same phase form an oriented association if they can be brought to the same crystallographic orientation by translation, rotation or reflection. Individuals related by a translation form a parallel association; strictly speaking these individuals have the same orientation even without applying a translation. Individuals related either by a reflection (mirror plane or centre of symmetry) or a rotation form a twin.

symmetry of a twin

An element of symmetry crystallographically relating differently oriented crystals cannot belong to the individual. The element of symmetry that relates the indivduals of a twin is called twinning element of symmetry and the connected operation is a twinning operation of symmetry. The Mallard law states that the twin element (i.e. the geometrical element relative to which the twining operation is defined) is restricted to a direct lattice element: lattice nodes (twin centres), lattice rows (twin axes) and lattice planes (twin planes).

In most twins the symmetry of a twin (twin point group) is that of the individual point group augmented by the symmetry of the twinning operation; however, a symmetry element that is oblique to the twinning element of symmetry is absent in the twin (e.g., spinel twins).

twin law

The twin law is indicated by the symbol of the twinning element of symmetry: [math] \bar 1[/math], [uvw] and (hkl) for the centre of symmetry, direction of the rotation axis and Miller indeces of the mirror plane, in the order. Usually, instead of the single (hkl) plane, the symbol {hkl} is used to indicate all the planes equivalent for symmetry.

Classification of twins

Twins are classified following Friedel reticular (i.e. lattice) theory of twinning which indicates the presence, either in the lattice or a sublattice of a crystal, of (pseudo)symmetry elements as necessary, even if not sufficient, condition for the formation of twins. In presence of the reticular necessary conditions, the formation of a twing finally depends on the matching of the crystal structures at the contact surface between the individuals.

twinning by merohedry

twinning by pseudomerohedry

twinning by reticular merohedry

twinning by reticular pseudomerohedry

twin lattice

twin index

twin obliquity

Other categories of twins

Endemic conditions for twinning

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 The ''twin law'' is indicated by the symbol of the twinning element of symmetry: <math> \bar 1</math>, [uvw] and (''hkl'') for the centre of symmetry, direction of the rotation axis and [[Miller indeces]] of the mirror plane, in the order. Usually, instead of the single (''hkl'') plane, the symbol {''hkl''} is used to indicate all the planes equivalent for symmetry.
+= Classification of twins =
+Twins are classified following Friedel ''reticular'' (i.e. lattice) ''theory of twinning'' which indicates the presence, either in the lattice or a sublattice of a crystal, of (pseudo)symmetry elements as necessary, even if not sufficient, condition for the formation of twins. In presence of the reticular necessary conditions, the formation of a twing finally depends on the matching of the crystal structures at the contact surface between the individuals.
+* '''twinning by merohedry'''
+* '''twinning by pseudomerohedry'''
+* '''twinning by reticular merohedry'''
+* '''twinning by reticular pseudomerohedry'''
+* '''twin lattice'''
+* '''twin index'''
+* '''twin obliquity'''
+= Other categories of twins =
+= Endemic conditions for twinning =
 [[Category:Fundamental crystallography]]

Difference between revisions of "Twinning"

From Online Dictionary of Crystallography