Tetragonal symmetry

There is also another quite different reason for dismissing such arrangements they would be unstable. For instance, the forces between the ions in Fig, 180 a (assuming the orientations of the ions were maintained) would make the a and c axes equal and the symmetry tetragonal with b as the fourfold axis.)... 

Tl2Ba2Cu06 phase exists in two crystal symmetries, tetragonal and orthorhombic. All the other phases are found to exist mostly in tetragonal symmetries. 

Some insight into the mechanism by which Pc is changed is provided by the frequency of the soft mode responsible for the phase transition. In the stability field of the high symmetry (tetragonal) phase, the inverse order parameter susceptibility, x of the order parameter varies as... 

For K2[PdCl4] the situation was complicated by the lower symmetry, tetragonal rather than cubic. Also, all of the intensity outside the lattice mode region is quantitatively accounted for by the known modes. Careful analysis of the lattice mode region showed that the inactive Vs mode was at 136 cm . This was the first time this mode had been observed in any homoleptic square planar complex. 

The reciprocal lattices of merohedral twins superimpose exactly and the presence of twinning is not immediately obvious from the diffraction pattern. The twin law is a symmetry operator of the Lane group but not of the point group of the crystal structure. Merohedral twins are possible in the low-symmetry tetragonal, trigonal, hexagonal, and cubic systems. Also see twinning by inversion. 

Fig. 2. Structures for the solid (a) fee Cco, (b) fee MCco, (c) fee M2C60 (d) fee MsCeo, (e) hypothetical bee Ceo, (0 bet M4C60, and two structures for MeCeo (g) bee MeCeo for (M= K, Rb, Cs), and (h) fee MeCeo which is appropriate for M = Na, using the notation of Ref [42]. The notation fee, bee, and bet refer, respectively, to face centered cubic, body centered cubic, and body centered tetragonal structures. The large spheres denote Ceo molecules and the small spheres denote alkali metal ions. For fee M3C60, which has four Ceo molecules per cubic unit cell, the M atoms can either be on octahedral or tetrahedral symmetry sites. Undoped solid Ceo also exhibits the fee crystal structure, but in this case all tetrahedral and octahedral sites are unoccupied. For (g) bcc MeCeo all the M atoms are on distorted tetrahedral sites. For (f) bet M4Ceo, the dopant is also found on distorted tetrahedral sites. For (c) pertaining to small alkali metal ions such as Na, only the tetrahedral sites are occupied. For (h) we see that four Na ions can occupy an octahedral site of this fee lattice.

For the alkali metal doped Cgo compounds, charge transfer of one electron per M atom to the Cgo molecule occurs, resulting in M+ ions at the tetrahedral and/or octahedral symmetry interstices of the cubic Cgo host structure. For the composition MaCgg, the resulting metallic crystal has basically the fee structure (see Fig. 2). Within this structure the alkali metal ions can sit on either tetragonal symmetry (1/4,1/4,1/4) sites, which are twice as numerous as the octahedral (l/2,0,0) sites (referenced to a simple cubic coordinate system). The electron-poor alkali metal ions tend to lie adjacent to a C=C double... 

Inspired by experimental observations on bundles of carbon nanotubes, calculations of the electronic structure have also been carried out on arrays of (6,6) armchair nanotubes to determine the crystalline structure of the arrays, the relative orientation of adjacent nanotubes, and the optimal spacing between them. Figure 5 shows one tetragonal and two hexagonal arrays that were considered, with space group symmetries P42/mmc P6/mmni Dh,), and P6/mcc... 

Fig. 5. Schematic representation of arrays of carbon nanotubes with a common tubule axial direction in the (a) tetragonal, (b) hexagonal I, and (c) hexagonal II arrangements. The reference nanotube is generated using a planar ring of twelve carbon atoms arranged in six pairs with the symmetry [16,17,30].

The magnetic FeaNi system was modeled in a tetragonal symmetry with 4 atoms per unit cell (see Fig. la). The CuZn alloy was also considered to have a tetragonal unit cell, in this case c/a = 1 leads to a CsCl structure, which was shown in Fig. lb. 

Figure 1. Representation of unit cells for (a) FeaNi and (b) CuZn. Corresponding to a tetragonal symmetry in the case of FeaNi (Ni atoms are marked black) and to the LI2 (CuaAu) structure in the case of c/a = 1. CuZn shows also tetragonal symmetry, whereby c/a = 1 corresponds to the B2 structure (black circles represent Cu atoms). In (b) a frozen phonon in [001] direction is indicated for the Zn atom.

Some of the above discussed precursor phenomena are also observed prior to diffusion driven phase transformations. A typical example are the conventional EM tweed images obtained in the tetragonal parent phase in high Tc superconductors and other ceramics. In a recent survey by Putnis St e of such observations it was concluded that in these cases the tweed contrast resulted from underlying microstructures fomied by symmetry changes driven by cation ordering. These symmetry changes yield a fine patchwork of twin related domains which coarsen when the transfomiation proceeds. However, in view of the diffusion driven character of the latter examples, these cases should be clearly separated from those in the field of the martensites. 

---