Negative elastic constant

In fig. 77 we exploit the possibilities of a negative elastic constant. Boppart et al. (1980a) have glued strain gauges on the faces of a (100) cleaved crystal of IV TmSe... 

Another commonly used elastic constant is the Poisson s ratio V, which relates the lateral contraction to longitudinal extension in uniaxial tension. Typical Poisson s ratios are also given in Table 1. Other less commonly used elastic moduH include the shear modulus G, which describes the amount of strain induced by a shear stress, and the bulk modulus K, which is a proportionaHty constant between hydrostatic pressure and the negative of the volume... 

One final point. We earlier defined Poisson s ratio as the negative of the lateral shrinkage strain to the tensile strain. This quantity, Poisson s ratio, is also an elastic constant, so we have four elastic constants E, G, K and v. In a moment when we give data for the elastic constants we list data only for . For many materials it is useful to know that... 

The application of an electric field above the threshold value results in a reorientation of the nematic liquid crystal mixture, if the nematic phase is of negative dielectric anisotropy. The optically active dopant then applies a torque to the nematic phase and causes a helical structure to be formed in the plane of the display. The guest dye molecules are also reoriented and, therefore, the display appears coloured in the activated pixels. Thus, a positive contrast display is produced of coloured information against a white background. The threshold voltage is dependent upon the elastic constants, the magnitude of the dielectric anisotropy, and the ratio of the cell gap to the chiral nematic pitch ... 

Nematic liquid crystals of negative dielectric anisotropy with a low rotational viscosity and a high value of the twist elastic constant k22 are required, see Equations 38-40. Furthermore, a high value for the resistivity and short... 

In the uniaxial tension test (Fig. 2.8), there is usually a transverse strain, i.e., a strain perpendicular to the applied stress. This can be used to define a second elastic constant, Poisson s ratio (v), as the negative ratio of the transverse strain (e.j.) to the longitudinal strain (s ), i.e., v= -Sj/cl- For isotropic materials, it can be shown from thermodynamic arguments, that -1< u <0.5. For many ceramics and glasses, v is usually in the range 0.18-0.30. 

If an accurate equation for the interatomic potential is known, the elastic constants can be calculated from first principles. This analysis is straightforward for cubic ionic crystals. The potential for a pair of positive and negative ions is often written in the form... 

The result, Eq. (43), can also be used to calculate the elastic constants of interfaces in ternary diblock-copolymer systems [100]. The saddle-splay modulus is found to be always positive, which favors the formation of ordered bicontinuous structures, as observed experimentally [9] and theoretically [77,80] in diblock-copolymer systems. In contrast, molecular models for diblock-copolymer monolayers [68,69], which are applicable to the strong-segregation limit, always give a negative value of k. This result can be understood intuitively [68], as the volume of a saddle-shaped film of constant thickness is smaller than... 

Elastic anomalies in actinide-based heavy-fermion systems are most pronounced for UPt3. The temperature dependences of two representative elastic modes are shown in flg. 36 (Yoshizawa et al. 1985). Unlike the case of UPdj, CF effects as a possible source do not seem very likely. The phonon dispersions of UBOjj, as measured by neutron scattering (Robinson et al. 1986), do not show strong anomalies. The elastic constant Cj2, however, is negative at low temperatures, similar to some IV compounds. Remarkably, UBejj possesses a low Debye... 

For an isotropic, elastic material two elastic constants are sufficient to describe the material response, the elastic modulus E (eq. 7) and the Poisson s Ratio (v), defined as the ratio of the axial to the (negative) transverse strain (- 11/622). 

Anomalies in the phonon spectra of UTe have also been found (Buyers and Holden 1985) and attempts were made by the authors to use the same theories described above, which essentially relate to an intermediate-valence picture. Unfortunately, as Buyers and Holden describe (see their p. 304) this does not lead to a convincing conclusion. There is, of course, no direct electronic evidence (e.g., from photoemission) that materials such as UTe exhibit valence fluctuations. We must conclude that the electron-phonon interaction is different in detail between the 4f intermediate-valence matmals and tiie actinide compounds. In both cases, however, the result is a negative Poisson ratio (which is directly related to the elastic constant C12). 

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