Symmetry Relations at Phase Transitions. Twinned Crystals

The crystal data compared to expected values assuming no distortions are summarized in Table 18.1. Inspection of the atomic coordinates reveals that the distortions of the packing of spheres are only marginal. As expected, the greatest deviations are observed for the molecular compounds PI3 and NMe3. 

4 Symmetry Relations at Phase Transitions. Twinned Crystals 

The lattice parameters a and b become different during the transition from the tetragonal to the orthorhombic structure. Either a b or a b results, depending on the direction of the rotation of the octahedra strands. During the phase transition both directions of rotation occur at random domains appear, in which either a b or a b. The obtained crystal is a twinned crystal or twin, consisting of intergrown domains. The twin domains are 

Definition An intergrowth of two or more macroscopic individuals of the same crystal species is a twin, if the orientation relations between the individuals conform to crystallographic laws. The individuals are called twin partners, twin components or twin domains. 

Group-subgroup relation between the modifications of calcium chloride (cf Fig. 4.1, p. 33) 

Three structure types of composition MXj are mentioned in the left branch of Fig. 18.6. Hexagonal Til3 has strands of occupied face-sharing octahedra in the direction of c (gray boxes one on top of the other cf. also Fig. 16.10, p. 175). OAg, has edge-sharing octahedra joined to layers as in the Bilj type (gray boxes side-by-side cf. Fig. 16.8, p. 174). The occupied octahedra of NNi, share vertices. 

The structures of Tilj, OAg, and NNi, are followed by distorted variants with the same occupation patterns (lower part of the left branch). The symmetries are further reduced because in all three cases Are atoms are shifted away from the octahedron centers this is marked by the dots . The Ru atoms of RuBrj have shifted toward each other in pairs (Ru-Ru bonds). The P atoms of PI3 have lone electron pairs. Each P atoms has shifted toward an octahedron face parallel to -i-c in this way the P atoms obtain three short P-I bonds and tlrree long P -1 contacts. A similar situation arises in crystalline trimethylamine, whose methyl groups form a hexagonal closet-packing. Tlie N atoms are alternately shifted in Are directions -i-c and —c out of the midpoints of the octahedra. 

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