The nonlinear integral equations governing phase transition kinetics with homogeneous nucleation and growth site impingement are developed and solved to the first order for the two‐dimensional case. It is shown that the fractional transformed area at time t is given approximately by a(t) = Kt3/(1 + Kt3). The iteration method used to get the solution is applicable to certain other nonlinear differential and integral equations. It is shown that the theory predicts the total number of growth sites formed, and that the nucleation rate and growth constants can be deduced from this and the gross kinetic data. The extension of the method of three‐dimensional growth is indicated.
SynopsisThe kinetics of phase transformation are treated for heterogeneous nucleation, where all nuclei are simultaneously initiated, and where initiation follows first-order kinetcs. The phase transformation curves are sigmoid. For simultaneous initiation in two dimensions, a ( t ) / ( la ( t ) ) a t 2 .For first-order initiation, we have, approximately, a ( t ) / ( l -a ( t ) ) 0: t2.85, and u ( t ) / ( lu ( t ) ) a t3.74 I 2253
Satisfactory Raman spectra of crystalline lysozyme, pepsin, and alpha chymotrypsin were obtained with laser excitation. The spectra are very similar to each other, but show enough minor differences to make this a useful method of identification. The readily identified bands assignable to specific groupings are noted.
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