WHY DO CRYSTALS TWIN THE WAY THEY DO?

R.A. Sparks¹ and M. Ruf²

¹ Bruker-AXS Inc., 6300 Enterprise Lane, Madison, WI 53719, Email: rsparks@bruker-axs.com
² Bruker-AXS GmbH, Rheinbrückenstr, 76181 Karlsruhe, Email: michael.ruf@bruker-axs.de

For most twinned samples the relationship between the twin components is a rotation about a vector normal to a crystal face. Usually the rotation angle is 180o (60, 90 and 120o rotations are rare but possible). At the twin interface the unit cell faces are parallelograms. A rotation of 180o produces unit-cell faces which match across the twin interface. In general, no other rotation angle will have this effect. The bonding energy across this twin interface is slightly larger than the bonding energy for the corresponding layers in the single crystal.

For a small percentage of twinned samples the relationship between the components is a rotation about a vector parallel to a crystal edge. For these samples the unit cell faces do not match across the twin interface.

For non-merohedral twins it is possible to determine the centres of each twin component and the rotation vector relating one twin to the other. For structures with heavy atoms it is possible to determine the chirality of each component. From these quantities and the refined crystal structure it is possible to determine the atomic and molecular environment at the twin interface. Conclusions about the reasons for twinning can be postulated.

Examples of each type of twinning are shown.