Domain growth

In both cases the late stages of kinetics show power law domain growth, the nature of which does not depend on the mitial state it depends on the nature of the fluctuating variable(s) which is (are) driving the phase separation process. Such a fluctuating variable is called the order parameter for a binary mixture, tlie order parameter o(r,0 is tlie relative concentration of one of the two species and its fluctuation around the mean value is 5e(/,t) = c(r,t) - c. In the disordered phase, the system s concentration is homogeneous and the order... 

Considerable amount of research effort has been devoted, especially over the last tln-ee decades, on various issues in domain growth and dynamical scaling. See the reviews [13,14, H, 16 and 17],... 

For a conserved order parameter, the interface dynamics and late-stage domain growth involve the evapomtion-diffusion-condensation mechanism whereby large droplets (small curvature) grow at tlie expense of small droplets (large curvature). This is also the basis for the Lifshitz-Slyozov analysis which is discussed in section A3.3.4. 

Milchev A, Binder K and Heermann D W 1986 Fluctuations and lack of self-averaging in the kinetics of domain growth Z. Phys. B. Condens. Matter. 63 521 -35... 

M. Porta, C. Frontera, F. Vives, T. Castan. Effect of the vacancy interaction on antiphase domain growth in a two-dimensional binary alloy. Phys Rev B 56 5261, 1997. 

Comparison of Ordering After Quenching from above T, with Order-Order Relaxations The Influence of Antiphase Domain Growth... 

The requirement I > 2 can be understood from the symmetry considerations. The case of no restoring force, 1=1, corresponds to a domain translation. Within our picture, this mode corresponds to the tunneling transition itself. The translation of the defects center of mass violates momentum conservation and thus must be accompanied by absorbing a phonon. Such resonant processes couple linearly to the lattice strain and contribute the most to the phonon absorption at the low temperatures, dominated by one-phonon processes. On the other hand, I = 0 corresponds to a uniform dilation of the shell. This mode is formally related to the domain growth at T>Tg and is described by the theory in Xia and Wolynes [ 1 ]. It is thus possible, in principle, to interpret our formalism as a multipole expansion of the interaction of the domain with the rest of the sample. Harmonics with I > 2 correspond to pure shape modulations of the membrane. 

Lateral structures were observed after 40 min of annealing, when typical spinodally decomposed structures were apparent. After 315 min the mean diameter of the dPS particles has reached the film thickness, and for larger times, two-dimensional domain growth takes place. 

Figure 31. The domain growth during the phase separation process reflected by the shift of the first zero in the pair correlation function (a) and by the surface area reduction (b). Although the surface area and first zero of the pair-correlation functions are equivalent lengthscales, the time dependence of the surface area is less affected by the finite lattice size affects.

Abstract. We review the recent development of quantum dynamics for nonequilibrium phase transitions. To describe the detailed dynamical processes of nonequilibrium phase transitions, the Liouville-von Neumann method is applied to quenched second order phase transitions. Domain growth and topological defect formation is discussed in the second order phase transitions. Thermofield dynamics is extended to nonequilibrium phase transitions. Finally, we discuss the physical implications of nonequilibrium processes such as decoherence of order parameter and thermalization. 

Keywords Nonequilibrium phase transitions, Liouville-von Neumann approach, domain growth, topological defect formation. 

Now we study the effects of the dynamical processes of nonequilibrium phase transitions on domain growth and topological defects. The quench models describe such nonequilibrium processes, which can be... 

Finally, we discuss the effect of nonlinear coupling on domain growth, decoherence, and thermalization. As the wave functionals l/o of Ho are easily found, Eq. (16) leads to the wave functional beyond the Hartree approximation. Putting the perturbation terms (19) into Eq. (16), we first find the wave functional of the form... 

We review Monte Carlo calculations of phase transitions and ordering behavior in lattice gas models of adsorbed layers on surfaces. The technical aspects of Monte Carlo methods are briefly summarized and results for a wide variety of models are described. Included are calculations of internal energies and order parameters for these models as a function of temperature and coverage along with adsorption isotherms and dynamic quantities such as self-diffusion constants. We also show results which are applicable to the interpretation of experimental data on physical systems such as H on Pd(lOO) and H on Fe(110). Other studies which are presented address fundamental theoretical questions about the nature of phase transitions in a two-dimensional geometry such as the existence of Kosterlitz-Thouless transitions or the nature of dynamic critical exponents. Lastly, we briefly mention multilayer adsorption and wetting phenomena and touch on the kinetics of domain growth at surfaces. 

Figure 10.16 The figure clearly shows that the total external electric field, induced by the whole tip array, decreases to less then 103 V/cm at a distance of 1 pm from the sample surface, due to the fast decay of the electric field caused by the shape and size of the tip. Thus, although the tip array creates almost a uniform electric field at distances > 1 pm from the surface, this does not change the domain growth relative to the single tip case.

If one assumes that domain growth proceeds below dc in conformity with the Lifschitz-Slyozov process (Eq. 40), then, one can associate dc with the period of time tc in which the periodic structure exists after initiation of the phase separation. This may be slightly generalized to d ta. It follows that... 

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