Crystallites surface free energy

Equation (6) shows that if the interaction energy Ucsbetween the two materials is greater than twice the surface free energy acg of the crystallite, then the crystallite will spread over the surface of the substrate. Since ocg is large for... 

AHu is the heat associated with the melting of one mole of monomer units, T0 is the melting temperature of the pure isotactic polymer 6m is the value of 6 when T = Tm and Tm is the melting temperature of partially isotactic polymer D is a function of the surface free energy per unit surface associated with the end surfaces of the crystallite. 

Here AFu is the standard free energy change per repeat unit on melting, and ae is the surface free energy change per chain at the ends of the crystallite. It can be shown that the surface free energy associated with lateral surfaces may be ignored in the present case. 

Here the first term is the surface free energy, proportional to the surface area of the crystallite, while the second is the bulk free energy, proportional to its volume. The first term is always positive because of the work that must be done to create an interface, while the second is negative in the supercooled liquid, because the solid has the lower free energy under these circumstances. It is clear from the form of this equation that the free energy of the crystallites increases up to a size i, which is called the critical nucleus and represents a barrier that must be surmounted on the path from pure liquid to pure crystal. 

The mechanistic implications of the GPLE have been only partially discussed. Standard models cannot be used to justify the use of a steady-state distribution because they were developed using only aggregation kernels. However, there is no fundamental reason why steady-state configurations do not exist as shown by Puentes and Gamas [6] based on an analysis of the surface free energy corresponding to a crystallite distribution. 

Pt/Si02,Al203 H2, N2, CO I Crystallite shape and surface free energy depend on 850-1200°C 1 atm high temp, annealing produces spherical particles SAM, SEM, 1 with (100) and (111) facets. N2 has little effect in H2 theoretical calcns. 1 (100) facets grow in CO Pt (210) facets grow. 37... 

Surface adsorbates and adatoms serve to restmcture surfaces, especially at high temperatures. At sufficiently high temperature, equilibrium crystallite shape and surface free energy vary with atmosphere. Metal clusters and crystallites are observed to form epitaxial layers on supports this epitaxy can contribute to a stronger metal-support interaction. 

For polymers manifesting the most common type of crystalline morphology (folded chain lamellae), the "equilibrium" values (asymptotic limits at infinite lamellar thickness) of Tm, of the heat of fusion per unit volume, and of the surface free energy of the lamellar folds, are all lowered relative to the homopolymer with increasing defect incorporation in the crystallites. By contrast, if chain defects are excluded completely from the lamellae, the equilibrium limits remain unchanged since the lamellae remain those of the homopolymer, but the values of these properties still decrease for actual specimens since the average lamella becomes thinner because of the interruption of crystallization by non-crystallizable defects along the chains. 

Sintering is essentially a process in which fine particles, which are in contact with each other, agglomerate when heated to a suitable temperature roughly one-half to two-thirds of the melting temperature. At this temperature, the crystallite faces display disorder, which enables rapid surface diffusion. The body of the powder remains solid while the surfaces become slippery. This agglomeration is accompanied by a decrease in the porosity and an increase in the bulk density of the mass. Simultaneously, there is a reduction in surface area and surface free energy, and hence a reduction in the total free energy of the system itself. 

Assuming that the surface free energy of the fold surfaces is 93 mJ that the density of the crystallites p,. = 1-00 x 10 kg m and that the increase in enthalpy per unit mass, Ah, on melting is 2.55 x 10 J kg for an infinitely thick crystal, determine the equilibrium melting temperature. 

During their initial growth stages, the clusters are likely to have structures that are more disordered than that of the bulk solid (Garten and Head, 1970). This idea has been incorporated into models that posit the formation of a disordered cluster as an initial step followed by the formation of a crystallite in a second step (Erdemir et al, 2009). These models are more complicated conceptually and quantitatively than the classical model presented here. Alternatively, Sohnel and Garside (1988) deal with this possibility by making the surface free energy of the clusters a fimction of their size. 

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