Nucleation surface energy

This effect assumes importance only at very small radii, but it has some applications in the treatment of nucleation theory where the excess surface energy of small clusters is involved (see Section IX-2). An intrinsic difficulty with equations such as 111-20 is that the treatment, if not modelistic and hence partly empirical, assumes a continuous medium, yet the effect does not become important until curvature comparable to molecular dimensions is reached. Fisher and Israelachvili [24] measured the force due to the Laplace pressure for a pendular ring of liquid between crossed mica cylinders and concluded that for several organic liquids the effective surface tension remained unchanged... 

The resistance to nucleation is associated with the surface energy of forming small clusters. Once beyond a critical size, the growth proceeds with the considerable driving force due to the supersaturation or subcooling. It is the definition of this critical nucleus size that has consumed much theoretical and experimental research. We present a brief description of the classic nucleation theory along with some examples of crystal nucleation and growth studies. 

Figure 1.9 The balance of endothermic surface energy and the exothermic formation of the stable condensed phase during nucleation from the vapour phase. The critical radius, above which the nuclei become stable, is where the resultant Gibbs energy change has zero slope...

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 " "... 

The MD simulations provided the necessary thermodynamic information to obtain the equilibrium configurations of the films. Often the deposition process will produce films which are not in the equilibrium configuration, and then the problem is to determine the stablity of these films against changes in morphology. Here simulations can also be helpful, since data on the surface energies and chemical potentials of strained films can be used to calculate the probability of cluster nucleation, using classical nucleation theory. 

In addition to the role of the physical characteristics of the amorphous state on nucleation and growth, as indicated by Eq. 11, surface energies also play a role. The role of these properties on film orientation and microstruc-... 

The "classical" theory of nucleation concentrates primarily on calculating the nucleation free energy barrier, AG. Chemical interactions are included under the form of thermodynamic quantities, such as the surface tension. A link with chemistry is made by relating the surface tension to the solubility which provides a kinetic explanation of the Ostwald Step Rule and the often observed disequilibrium conditions in natural systems. Can the chemical model be complemented and expanded by considering specific chemical interactions (surface complex formation) of the components of the cluster with the surface ... 

A very accurate measurement of Ccrjt would allow back-calculation of the surface energy for a given crystal. Because Ccrjt is dependent on the square of Y, such a measurement could be a very sensitive method of measuring interfacial energy at dislocation outcrops. The calculated interfacial energy from our experiments is 280+ 90 mJm- for the rhombohedral face of quartz at 300°C. Parks (10) estimated 25°C value of 360 + 30 mJm is well within the experimental error of our measurement. The best way to determine the value of Ccrjt would be to measure etch pit nucleation rate on... 

Several refinements of our experiments could test these theories further. By measuring etch pit densities as well as pit dimensions on sequentially-etched crystals, nucleation rate data and pit growth data could be collected, yielding information about the rate-limiting steps and mechanisms of dissolution. In addition, since the critical concentration is extremely dependent on surface energy of the crystal-water interface (Equation 4), careful measurement of Ccrit yields a precise measurement of Y. Our data indicates an interfacial energy of 280 + 90 mjm- for Arkansas quartz at 300°C, which compares well with Parks value of 360 mJm for 25°C (10). Similar experiments on other minerals could provide essential surface energy data. 

Properties of nanoparticles (nuclei) are different from those of the bulk counterparts. Metastable phases may nucleate first because nanoparticles of these phases are more stable (e.g., due to low surface energy) than the nanoparticles of phases that are more stable in bulk (Ranade et al., 2002). 

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