Mixing-segregation equilibrium

The physical picture is as follows a batch of A and B particles have been mixed until equilibrium has been reached. There are no segregating or clustering tendencies therefore, A is considered to be randomly distributed throughout the mixture. If this is true, then the probability of finding a particle of type A at any point in the mixture is a constant equal to the proportion of that kind of particle in the whole mixture. This key statement immediately identifies the distribution of spot sample compositions (expressed in terms of number of A particles or particle... 

This possibility is due to the non-equivalence of Mg and Fe which segregate into corrensite and chlorite respectively. This effect is discussed in the chlorite chapter. Thus four major phyllosilicate phases could be present in an equilibrium situation. It should be noted that the expanding trioctahedral phase is or can be more aluminous than chlorite. This might lead one to think that some of the layers might in fact be dioctahedral such as those in sudoite. The importance of the differentiation of the two types of mixed layered minerals lies in the segregation of alumina and potassium in one (the dioctahedral mixed layered mineral)... 

Fig. Ell.la The in-phase G and out-of-phase G" moduli of the PET/TGIC samples, one molecularly mixed (solution) and the other made of compressed and initially segregated PET. As expected, the homogeneous sample, after the required time for thermal equilibrium, shows the expected response of first-order kinetics. [Reprinted by permission from R. Dhavalkikar and M. Xanthos, Monitoring the Evolution of PET Branching Through Chemorheology, Polym. Eng. Sci., 44, 474 (2004).]...

This finding demonstrated that the presence of segregated stacks is a necessary condition for electrical conductivity. Reflecting the relative stabilities for the two stacking modes noted above, crystals of the red semiconductor form are obtained from a thermodynamic or equilibrium crystallization equimolar solutions of the donor and acceptor in accetonitrile are mixed and allowed to evaporate slowly. On the other hand, crystals of the black form are obtained from a kinetic or non-equilibrium crystallization hot equimolar solutions of the donor and acceptor in (the same) acetonitrile solvent are mixed and cooled rapidly. Some microcrystals of the resulting black powder are then used as seeds to obtain larger crystals of the segregated stack black form. 

Shinbrot, T. Muzzio, F.J. Non-equilibrium patterns in granular mixing and segregation. Physics Today, March, 2000 25-30. 

If a surface is sputtered at sufficiently low temperature to avoid bulk diffusion, atoms of the species preferentially sputtered can reach the surface by displacement mixing and radiation-induced segregation. This leads to a so-called altered layer, which has a composition different from that of the bulk and a thickness close to the penetration depth of the projectiles. Since surface diffusion has a much lower activation barrier than bulk diffusion, annealing a sputtered alloy surface first leads to a local equilibrium between the surface and the immediate subsurface layers, which still belong to the altered layer. Only after the onset of bulk diffusion is reached, usually around 60 - 70% of the melting temperature, the altered layer equilibrates with the bulk and true equilibrium segregation is observed [45]. For alloys of atoms with different size the existence and dissolution of an altered layer can be studied by STM because of the development of a misfit dislocation network between the altered layer and the bulk [46] (Fig. 7). 

A fundamental study of solids mixing is given, with experimental data for a rotating horizontal cylinder containing salt and sand. Theoretical random equilibrium mixture, chi-square test, and sampling considerations are discussed. Also rate equations and segregating effects are covered. 

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