It is the purpose of the present note to consider the application of theories of dendritic growth to the symmetrical precipitation reactions in β brass; that is, the precipitation of α and γ products from the parent β.
Two recent experimental investigations are relevant. Purdy (i) investigated the kinetics of growth of Widmanstatten α rods from ordered β brass and compared his results with the theoretical predictions of Trivedi (2). By taking account of the strongly non-ideal solution character of the parent phase, he obtained good agreement with a local equilibrium model. The kinetics of growth of γ dendrites from the β matrix were studied by Bainbridge and Doherty (3). They found their results to be in good accord with the Ivantsov (4) equation. This analysis neglects both the effect of capillarity and the possible influence of interface kinetics terms. They did not attempt to apply an optimization procedure in their analysis. Bainbridge and Doherty also carried out a preliminary study of the rates of growth of α from β brass, and noted that for similar undercoolings and temperatures α needles grow approximately 7 times as fast as γ dendrites.
This latter observation immediately raises the possibility of determining the influence of an interface kinetics term. It is well established that α-β interracial free energies for orientations corresponding to the rod tips are roughly five or ten times as large as γ-β interfacial free energies (5,6), and any kinetic analysis which includes the effect of capillarity, and supposes that local equilibrium obtains, must predict an inverse relationship between magnitude of interfacial free energy and the maximum rate of growth for a given supersaturation and temperature. The advantage of comparing growth rates of α and γ brass from the 'same' β matrix is that we are able to eliminate much of the experimental uncertainty surrounding diffusion data and thermodynamic parameters.
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