Crystal-field induced anisotropy

The crystal field does, however, have a dramatic effect on the magnetic anisotropy of lanthanide complexes. For complexes of less than cubic symmetry the three principal values of the susceptibility tensor are unequal. For uniaxial symmetry, Xx — Xy Xz and for biaxial symmetry Xx Xy Xz- Very extensive studies632-640 have been carried out on the single crystal susceptibilities of the D3d lanthanide hexakis(antipyrene) triiodides over the temperature range 80-300 K, and crystal field parameters were obtained. This crystal field-induced anisotropy is responsible for the effectiveness of lanthanide complexes as NMR shift reagents, and single crystal anisotropies of lanthanide complexes have been determined in this connection also.563... 

Estimated values of anisotropy fields in RjCoj B compound are 0.6 T for R = La and 7.5 T for R = Pr (Buschow et al. 1985c). The cobalt sublattice anisotropy favours an easy magnetization direction perpendicular to c-axis, whereas the crystal field induced anisotropy of the 4f sublattice corresponds to the second order Stevens factor Uj of R component. 

The first observation of natural optical anisotropy was made in 1669 by Bartolinius in calcite crystals, in which light travels at different velocities depending on the direction of propagation relative to the crystal structure. The electrooptic effect, electric-field-induced anisotropy, was first observed in glass in 1875 by J. Kerr. Kerr found a nonlinear dependence of refractive index on applied electric field. The term Kerr effect is used to describe the quadratic electrooptic effect observed in isotropic materials. The linear electrooptic effect was first observed in quartz crystals in 1883 by W. Rontgen and A. Kundt. Pockels broadened the analysis of this relationship in quartz and other crystals, which led to the term Pockels effect to describe linear behavior. In the 1960s several developments... 

Thus, when acted on by an electric (or indeed any) external field, naturally isotropic bodies become endowed with anisotropic properties like those possessed by naturally anisotropic ones, such as crystals. The electric permittivity tensor e(Ep) describing this induced anisotropy can be represented in matrix form, as follows, in a Cartesian system of co-ordinate axes X, y, z ... 

In 2-17 compounds, the atoms located in the dumb-bell sites make a strong contribution to the anisotropy. These sites are preferentially occupied by the substituents when Co is partially replaced by other TM atoms, and this can even change the sign of 7C1, inducing EA behavior (Deportes et al. 1976). This effect has also been described in terms of a single-ion, local crystal-field model but certain results seem to require that band-structure changes also be considered (Perkins and Strassler 1977) i.e., that 3d-electrons be treated as collectivized. 

Abstract A systematic overview of various electric-field induced pattern forming instabilities in nematic liquid crystals is given. Particular emphasis is laid on the characterization of the threshold voltage and the critical wavenumber of the resulting patterns. The standard hydrodynamic description of nematics predicts the occurrence of striped patterns (rolls) in five different wavenumber ranges, which depend on the anisotropies of the dielectric permittivity and of the electrical conductivity as well as on the initial director orientation (planar or homeotropic). Experiments have revealed two additional pattern types which are not captured by the standard model of electroconvection and which still need a theoretical explanation. 

The basic mechanism for the electric-field-induced instabilities is now quite well understood. The current carriers in the nematic phase are ions whose mobility is greater along the preferred axis of the molecules than perpendicular to it. The ratio of the conductivities is usually about. Because of this anisotropy, space charge can be formed by ion segregation in the liquid crystal itself, as was first pointed out by Carr. The manner in which the space charge can build up due to a bend fluctuation is shown... 

Second, we consider the optical anisotropy of the blue phases. Generally speaking, the refractive indices of a crystal form an ellipsoid, as discussed in Chapter 2. Now the blue phases have cubic symmetries. On a macroscopic scale, the refractive index ellipsoid must have the same cubic symmetries. Cubic symmetries contain four-fold rotational symmetry around three orthogonal axes. Therefore the refractive index ellipsoid must be a sphere, that is, the refractive index in any direction is the same at macroscopic scale. Due to this optical isotropy, when a blue phase sample is sandwiched between two crossed polarizers, the transmittance is zero. This is the dark state of the blue phase display based on field induced birefringence. 

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