Noncentrosymmetry

The strain tensor 5 can be written for noncentrosymmetry point group crystals as ... 

Any symmetry operation is required to leave the sign and magnitude of physical properties unchanged and therefore y xxx = 0. The same line of reasoning can be used to show that all tensor components will vanish under inversion. Hence, second-order nonlinear optical properties are not allowed in centrosymmetric media using the electric dipole approximation. The presence of noncentrosymmetry is one of the most stringent requirements in... 

Non-cellulosic synthetic membranes, in hemodialysis, 26 825—828 Noncentrosymmetry point group crystals, 11 93-94... 

Strain hardening effect, 20 224 Straining efficiency, 77 340 Strain rate, 73 473 Strain recovery rate (Rr), in testing shape-memory polymers, 22 361 Strain sensors, 77 150, 151-152 Strain tensor, for noncentrosymmetry pont group crystals, 77 93-94 Strain versus time curve factors affecting, 73 473 material and microstructure effect on, 73 473-474... 

The use of salt formation to expand the number of crystals which contain a single molecular type was first applied by Meredith (26), and more recently by Marder et. al. (22). In the latter work, ionic interactions are used to offset dipolar interactions among achiral molecules, which enhances the probability that the resulting crystal will be noncentrosymmetric. In our case, of course, noncentrosymmetry is ensured by the chirality of the molecules involved. It is important to note that, within the picture we have presented, neither the assurance of noncentrosymmetry, nor the enhanced hyperpolarizability of the chiral molecule guarantees that the nonlinearity of any particular chiral organic salt crystal will be large. These properties simply ensure that each crystal so formed has an equal opportunity to express the molecular hyperpolarizability in an optimized way. 

Fiorini, C., Charra, F., Nunzi, J.-M., and Raimond, P. (1997). Quasi-permament all-optical encoding of noncentrosymmetry in azo-dye polymers./. Opt. Soc. Am. B 14, 1984-2003. Fiorini, C., Charra, E, Etile, A.-C., Raimond, R, and Nunzi, J.-M. (2000). Photoinduced non-centrosymmetry in azo-polymers using dual frequency interferences. In Advanced functional molecules and polymers (H. S. Nalwa, ed.), pp. 167-216, Gordon and Breach Science Publishers, Amsterdam. 

While, in principle, the second-order response should have a higher strength than the third-order response, a strong geometrical condition (noncentrosymmetry at the atomic/molecular and at the bulk levels) limits the availability of second-order nonlinear materials. Experimentally, one has to ensure that a noncentrosymmetric configuration is used if one desires to measure the strength of the second-order nonlinear response, characterized by... 

Figure 34. Two possible ways a tripodal molecule can crystallize trigonal noncentrosymmetry (a) and hexagonal centrosymmetry (b).

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