Fig. 12. Dependence of the elastic constant C22 in chain direction on the conversion in partly polymerized PTS crystals. The black square is the theoretically expected value for the pure polymer. The curves marked (V) and (R) are calculated according to Eq. (3) and (4), respectively |

In recent years there has been increased interest in the theoretical calculation of the elastic constants for ideal and fully oriented polymers based on knowledge of their crystal structures. This increased interest arises from the major developments in computational methods and from the success achieved in producing very highly oriented polymers with reasonably high stiffness. [Pg.139]

Spectra and Certran). There has therefore been an increased interest in theoretical calculations of the elastic constants, of oriented polymers. This has been given added impetus by the development of more sophisticated computational techniques, some of which are available as commercial software packages (e.g. Accelrys, [57]). [Pg.193]

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 [Pg.79]

The elastic constants of iron have been studied experimentally and theoretically at low temperature and high pressure (Mao et al. 1998 Soderlind et al. 1996 Steinle-Neumann et al. 1999 Stixrude and Cohen 1995), but there has not yet been a first principles calculation of the full elastic constant tensor at inner core conditions (see Nye 1985 for a review of elastic constants). Laio et al. (2000) developed a clever hybrid method that combines first principles total energy and force calculations for a limited number of time steps with a semi-empirical potential fit to the first principles results. These authors investigated a number of properties with their ab initio method including [Pg.336]

Table I. Experimental and calculated lattice constants a (in A), elastic constants, bulk and shear moduli (in units of 10 ) for the M3X (X = Mn, Al, Ga, Ge, Si) intermetallic series. Also listed are values of the anisotropy factor A and Poisson s ratio V. The experimental data for a are from Ref. . The experimental data for B, the elastic constants, A and v are taken from Ref. . The theoretical values for NiaSi are from Ref.. Also listed in the table are values of the polycrystalline elastic quantities-shear moduli G, Yoimg moduli (in units of and the ratio The experimental data for these quantities are from Ref. |

Pd4oCu4oP2o Pd5oCu3oP2o, and PdgoCu2oP2o alloys were measured by resonant ultrasound spectroscopy (RUS). In this technique, the spectrum of mechanical resonances for a parallelepiped sample is measured and compared with a theoretical spectrum calculated for a given set of elastic constants. The true set of elastic constants is calculated by a recursive regression method that matches the two spectra [28,29]. [Pg.295]

In Figure 1 the solid lines correspond to the above theory. The fitted parameters are Pth (O) and Uth- The agreement between the experimental curve and the theoretical one is satisfactory for both material. From Pth (O) and Uth two separate values of the effective elastic constants can be calculated. The measurements provide for OCB A" = 0.63 X 10 N and AT = 0.53 X 10 N for MBBA AT = 0.62 X 10 N and K = 0.54 10 N resp. (for the refractive index data see Refs. [2,5]). The consistency of these data and their agreement with independently measured values of elastic constants can be regarded satisfactory tak- [Pg.146]

The two Lame constants occurring in Equations (22) through (26) are one possible choiee of elastic constants which can be used in the case of isotropie materials. Depending on the application in question, other elastic constants can be more advantageous, e.g. the tensile modulus (Yoimg s modulus) E (imits [GPa]), the shear modulus G (imits [GPa]), the bulk modulus K (imits [GPa]) and the Poisson ratio V (dimensionless). Some of these constants are preferable from the practical point of view, since they can be relatively easily determined by standard test procedures E and G ), while others are preferable from the theoretical point of view, e.g. for micromechanical calculations (G and K). Note, however, that even in the case of isotropic materials always two of these elastic constants are needed to determine the elastic behavior completely. [Pg.42]

The shear and compressional acoustic wave velocities for the inner core are the direct output parameters from seismological observations. In order to make a direct comparison between the seismic data and measured physical properties, measurements of the acoustic velocities for iron at core pressures are required. Only very recently has it become possible to measure the elastic constants of s-Fe at high pressures and room temperature (Mao etal., 1999 Lubbers etal., 2000 Fiquet et al., 2001 Anderson et at, 2001). Recent advances in theory and computational methods have also provided new tools for computing the elastic constants of s-Fe at core pressures (Stixrude and Cohen, 1995 Soderhnd et al., 1996 Cohen et al., 1997 Steinle-Neumann and Stixrude, 1999) and core conditions (Laio et al., 2000 Steinle-Neumann et al, 2001 Alfe et al., 2001). There is considerable disagreement on the elastic constants of s-Fe between experimental results and theoretical calculations. The dilferences in the aggregate shear (FJ and compressional (Vp) wave velocities are smaller (Hemley and Mao, 2001 Steinle-Neumann et ai, 2001). Further improvement of theory and experiment is required to resolve the discrepancies. [Pg.1225]

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