134 Regular intergrowth of crystals

Figure 7.6. Morphological variation expected in twins of real crystals. The symbols

indicate dislocations. Only similar forms or unidirectional growth are expected.

such a case, the mechanism proposed to continue preferential growth by twinning is alternately repeating the re-entrant corner effect and rough interface growth [9]. Figure 7.7 shows the situation in which a stacking fault is introduced and a twin relation is generated in an fcc structure. It is seen that through the twinning operation, re-entrant corners and rough {100} faces appear alternately at an angle of 60° to the interface edge. As a result of preferential growth at re-entrant corners, rough {100} faces appear, and, in the following step, re-entrant corners appear as a result of growth on rough {100} faces. Since this alternation continues forever and is self-perpetuating, a thin platy twinned crystal appears in this type of crystal, even if the crystals do not have dislocations.

7.2.4Penetration twins and contact twins

Penetration twins have an irregular composition plane, and the twin plane and the composition plane are not the same. As a representative example, the {111} twin of fluorite, CaF2, is shown in Fig. 7.8.

On the {100} faces of individual A, the 111 corner bounded by three {100}

7.2 Twinning 135

Figure 7.7. Morphological evolution due to growth by the alternating re-entrant corner effect and rough interface growth [8].

Figure 7.8. Penetration twin of fluorite. Note the origin of growth layers on the {100}

face.

136 Regular intergrowth of crystals

high

supersaturation

low

Figure 7.9. Process of formation of a penetration twin, starting from a contact twin,

followed by Tracht change associated with growth (as supersaturation decreases).

faces of individual B protrudes. All growth layers on the {100} faces of both A and B individuals originate from the points of contact of the two individuals, indicating that the twin relation acts to promote the growth. As a result, twins grow larger than the coexisting single crystals. However, no change is observed in their morphology, because there are six directions along which to accelerate growth.

The origin of penetration twins of this type observed in fluorite and galena may be analyzed as follows [10]. They start out as contact twins by the joining together of two octahedral crystals, with the (111) face as the composition plane, and, as growth proceeds, their Tracht changes from {111} octahedral to {100} cubic, resulting in the appearance of a penetration twin. This is shown in Fig. 7.9. For two individuals to join together in a twin relation, it is necessary that the crystal is already bounded by well developed flat faces. Examples such as these, where twins formed first as contact twins and changed to apparent penetration twins due to Tracht change, may be expected in crystals other than fluorite and galena. The characteristic V-shape or fan-shape morphology of quartz crystals following the Japan law was previously explained as representing the upper half of an X-shape twin (penetration twin), but may now be accounted for as representing the upper half of a Y- shape twin (contact twin), which started out as a contact twin on well developed {1011} faces that appeared at the nucleation stage, followed by a Tracht change (see Chapter 10). There must be many examples of penetration twins formed by this process.

7.2.5Transformation twin

In general, a low-temperature polymorph has lower symmetry than a high-temperature polymorph. So, in the phase transformation from highto lowtemperature polymorph, the low-temperature polymorph can have two orientations, which leads to twin formation. This is called the transformation twin. To minimize the interface energy between twinned individuals through transfor-