Structural Relaxation Coefficient

The extent of the mismatch between average and local bond distances at the perovskite octahedral site can be parameterized by means of the structural relaxation coefficient (e)  

Going back to the YAli Cr 03 perovskite solid solution [52], it was foimd that the octahedral mean bond distances (i.e., those observed from structural refinements) increased linearly from 1.911(3) to 1.984(3) A (for 

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Figure 12.7 Structural relaxation coefficient e spinel-Mg-chromite [59], Pyr-Knr for the...

By this empirical relationship, structural relaxation coefficients f = 0.11(5) and 0.15(5) for La(Gai cCrJ03 and Nd(Gai Cr c)03 perovskite solid solutions, respectively, have been calculated (Figure 12.12). In conclusion, both methods lead to the same structural relaxation coefficient values. 

Figure 12.12 Structural relaxation coefficient [e] as a function of tan - see text for details. Labels refer to LaGa-LaCr and NdGa-NdCr (this work), YAl-YCr for the perovskite (52), Crn-Esk for the corundum-eskolaite (65), Gah-ZnChr for the gahnite-Zn-chromite and Spn-MgChr for the spinel-Mg-chromite [59],...

Determination of V3 and V6 Fourier coefficients have been made for several other molecules possessing methyl groups. Selected examples are displayed in Table 2. In all but the notable case of m-fluorotoluene65, the V6 term comes out comparatively small, usually less than 5% of V3. Mostly, it is found to be positive. Determination of structure relaxation has been attempted in CH3OH66, ... 

Figure 4.4 shows a dilatometric or calorimetric experiment to show structural relaxation (physical aging) and glass transition hysteresis. The sample is cooled from T0 to T it is kept at Tj for a certain time and heated again to T0. During the cooling step, the material vitrifies at B, resulting in an abrupt decrease in both the expansion coefficient and the specific heat. 

The hydrogen diffusion coefficient is not constant, but decreases with time (Street et al. 1987b). The data in Fig. 2.22 show a power law decrease in p-type a-Si H of the form r , with a 0.2 at the measurement temperature of 2(X) C. The time dependence is associated with a distribution of traps originating from the disorder. A similar effect is found in the trap-limited motion of electrons and holes and is analyzed in Section 3.2.1. The time dependence of is reflected in the kinetics of structural relaxation discussed in Section 6.3.1. 

The main feature of the nonequilibrium behavior of solutions dnring cryocrystallization is the appearance of amorphous solids. Generally vitrification of the liquid system depends on the rate of structural relaxation processes, which are substantially determined by the viscosity of the solution. At higher cooling rates and reduced temperatures, the cluster structure of the solution cannot follow the changes, predetermined by the equilibrium behavior of the system, so that even after solidification, the structure of the amorphous solid is very similar to the structure of the solution at low temperatnres. According to modem concepts, the amorphous state can be considered as a kind of snpercooled liqnid with an extremely high viscosity coefficient. 

As discussed in Sect. 4, in the fluid, MCT-ITT flnds a linear or Newtonian regime in the limit y 0, where it recovers the standard MCT approximation for Newtonian viscosity rio of a viscoelastic fluid [2, 38]. Hence a yrio holds for Pe 1, as shown in Fig. 13, where Pe calculated with the structural relaxation time T is included. As discussed, the growth of T (asymptotically) dominates all transport coefficients of the colloidal suspension and causes a proportional increase in the viscosity j]. For Pe > 1, the non-linear viscosity shear thins, and a increases sublin-early with y. The stress vs strain rate plot in Fig. 13 clearly exhibits a broad crossover between the linear Newtonian and a much weaker (asymptotically) y-independent variation of the stress. In the fluid, the flow curve takes a S-shape in double logarithmic representation, while in the glass it is bent upward only. 

The Nernst-Planck model is based on limiting laws for ideal systems. It accounts only for diffusion and electric transference of ions, not for electroosmotic solvent transfer in the ion-exchanger phase, swelling or shrinking of the ion-exchange material, variations of activity coefficients and diffu-sivities, and possible slow structural relaxation of the exchanger matrix. It also postulates the existence of individual diffusion coefficients for ions. 

Since structural relaxation arises from the decay of density fluctuations, one might expect, from simple hydrodynamics, that the relaxation time at a given self-diffusion coefficient, would show dependence where k is the smallest wave vector allowed by the primary box dimension. A system size dependence for the relaxation time also is predicted by generalized hydrodynamics in which the transport coefficients are dependent on both k and w ... 

Einstein-Simha coefficient (Ch. 1), Poisson s ratio (Ch. 3), deuterium quadrupolar splitting (Ch. 7), frequency of a structural relaxation process (Ch. 11)... 

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