Symmetry changes

At this stage, we would like to mention that the model, without the vector potential, is constructed in such a way that it obeys certain selection rules, namely, only the even —> even and the odd —> odd transitions are allowed. Thus any deviation in the results from these selection rules will be interpreted as a symmetry change due to non-adiabatic effects from upper electronic states. 

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. 

The thermal strain measurements described above have the common feature of anisotropic behaviour in a supposed isotropic state (cubic structure). These observations go well beyond the short-range, static strain fields associated with the lattice impurities responsible for Huang scattering. This then raises the question of the temperature at which the lattice symmetry changes and the implications of this for the central mode scattering. 

Type Adsorbate Adsorbent Possible symmetry change X-> Y Predicted coincidences1 X Y Changes observed Ref. 

Creation operator, 505 representation of, 507 Critical value, 338 Crystallographic point groups irreducible representations, 726 Crystallographic symmetry groups construction of mixed groups, 728 Crystal, eigenstates of, 725 Crystal symmetry, changes in, 758 Crystals... 

The mean-field phase diagram in the WSL calculated by Matsen et al. [138] predicts a transition from C to the disordered state via the bcc and the fee array with decreasing /N. This was not followed here. Transitions from the C to S (at 115.7 °C), to the lattice-disordered sphere - where the bcc lattice was distorted by thermal fluctuations - and finally to the disordered state (estimation > 180 °C but not attained in the study) were observed. It was reasoned to consider the lattice-disordered spheres as a fluctuation-induced lattice disordered phase. This enlarges the window for the disordered one and causes the fee phase to disappear. Even if the latter should exist, its observation will be aggravated by its narrow temperature width of about 8 K and its slow formation due to the symmetry changes between fee and bcc spheres. 

Other features in the absorption spectrum are due to local site symmetry about the absorber that dictates the intensity of the various molecular transitions. Figure 2 compares two compounds, VgO and V naphthenate. The considerable differences in peak intensities, particularly in the pre-edge absorption at "5465 eV, are due to symmetry changes resulting from different local geometries. 

Another important contribution by Landau is related to symmetry changes accompanying phase transitions. In second-order or structural transitions, the symmetry of the crystal changes discontinuously, causing the appearance (or disappearance) of certain symmetry elements, unlike first-order transitions, where there is no relation between the symmetries of the high- and low-temperature phases. If p(x, y, z) describes the probability distribution of atom positions in a crystal, then p would reflect the symmetry group of the crystal. This means that for T> T p must be consistent with... 

The symmetry changes of the vortex lattice in borocarbide superconductors affect their pinning properties as was shown for YNi2B2C (Silhanek et al. 2001). For the field orientation // c, the reorientation transition of the vortex lattice mentioned above was found to be associated with a significant kink in the volume pinning force Fp, whereas in the basal plane (for H c) the signature of nonlocal effects is a fourfold periodicity of Fp. 

The crystal symmetry changes that accompany order-disorder transitions, discussed in Section 17.1.2, give rise to diffraction phenomena that allow the transitions to be studied quantitatively. In particular, the loss of symmetry is accompanied by the appearance of additional Bragg peaks, called superlattice reflections, and their intensities can be used to measure the evolution of order parameters. 

The rhombohedral structure, obtained via the optimization of crystal energy [equation (1)] without the JT term inclusion or setting IVj = 0, is stable with respect to deformations of the crystal. The experimental and calculated structure parameters are listed in Table 2. As the temperature decreases down to about 400 K [5,8] the crystal symmetry changes to monoclinic phase. The major difference between the monoclinic and rhombohedral phases is the presence of JT distortions and a doubled primitive cell. The local values of JT distortions on different Mn3+ ions could be obtained via the projection of oxygen ions coordinates onto the normal local Eg modes of each [Mn06] octahedra (the numbering of Mn3+ is carried out according to Fig. 1). 

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