Mean-field nucleation theory

Miich effort in recent years has been aimed at modelling nucleation at surfaces and several excellent reviews exist [20, 21 and 22]. Mean-field nucleation theory is one of these models and has a simple picture at its core. 

The validity of mean field theory for N —y oo has striking consequences for the initial stages of phase separation. " In a metastable state slightly inside the coexistence curve, the nucleation free energy barrier is due to spherical droplets with a radius R The free energy excess of a droplet is written in terms of bulk and surface terms " "... 

Martensitic traasfonnation Master ec[uations Mean field crossover to Ising Mechanical properties Metallic alloys Metallic glasses Metastable alloys Microhardness test Microscopic theory of nucleation... 

Many other efforts were made to test the validity of the nucleation theories using computer simulations [68,69], and droplet formation was studied utihzing mean-field theory or density fimctional analysis [70-72]. 

Another popular concept has been the idea that the hysteresis is caused at the single pore level by the existence of metastable states analogous to the supercooled liquid and superheated vapor states which can be encoimtered in bulk systems when nucleation of condensation or evaporation is delayed. Hysteresis loops of this type will emerge from any theory of the van der Waals or mean field t3q)e. This idea dates back to... 

Demixing, Fig. 2 (a) Characteristic lengths (a) and (b) nucleation barrier AF plotted versus concentration cb. Full curves show the predictions of the Cahn-Hillard mean-field theory of nucleation and spinodal decomposition for the critical wavelength and the correlation length of concentration fluctuations in a metastable... 

RMD Simulation of Chemical Nucleation (22). A series of microscopic computer experiments was performed using the cooperative isomerization model (Eq. 2). This system was selected for the trial simulations for several reasons First, only two chemical species are involved, so that a minimal number of particles is needed. Second, the absence of buffered chemicals (e.g., A and B in the Trimolecular reaction of the next section) eliminates the need for creation or destruction of particles in order to maintain constant populations (19., 22j. Third, the dynamical model of the cooperative mean-field interaction can be examined as a convenient means of introducing cubic or higher nonlinearity into molecular models based on binary collisions. Finally, the need for a microscopic simulation is most apparent for transitions between multi -pie macroscopic states. Indeed, the characterization of spatially localized fluctuations is of obvious importance to the understanding of nucleation phenomena. As for the equilibrium vapor-liquid and liquid-solid transitions, detailed simulations at the molecular level should provide deep physical insight into chemical nucleation processes whkh is unattainable from theory, higher-level simulation, or experiment. 

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