Reactive Diffusion - Competition of Stable and Metastable Phases
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subcritical and vanish. For example, in the case of two intermediate phases 1,2 growing between initial materials A,B (with negligibly small mutual solubility) the velocities of layers' boundaries are given by following equations.
c
dA.41
di
DIAC1 ( Ax 1+' cAx
A ,2
DIACI
D2AC2
dx2, 2) di 2±)"x+-+
D2AC2
Ax2+
(
Here DAC, = bf(C)dC, where integration is made over the homogenity range AC, of the i-th phase. The variation of flux from left phase boundary to right one can be neglected as it was rigorously shown earlier. The constants 2, correspond to the finite reaction rates on the interfaces. In the first variant of naive theory the magnitudes of A, were supposed to be less than the critical sizes of the nuclei. In this case the velocities of layer growth are
diX. di -
d
2
I
' DjAUj X #
C2
- - C, j=°=C (2I.2) I,a#=
-
l-C, AC,«l< I-
(1.2)
11 1 -C2
If one considers critical nuclei sizes as the initial values of Ax, than the velocities in eq.2 can be 2cr negative as well as positive depending on the ratio D1 AC 1. - . One can easily show that only D2 AC2 I-"
three possibilities exist: If r < C1 / C 2, the velocity is positive for phase 2 and negative for phase 1, e.g. in the initial period only phase 2 ("vampire") grows suppressing the nuclei of phase 1. If CJC 2 L,_ the dependence AG(R) becomes nonmonotonous and the nucleation becomes thermodynamically possible with Ii < R < R2 , / 2 growing to infinity together with L. Of course, this model of homogeneous nucleation of spherical particle is too simplified. We must consider the form variation, and the possibility of heterogeneous nucleation. Rigorous approach will be described elsewhere. For this case also the critical value L exists. The main difference is as follows: if L > L, the nucleus begins to grow preferentially in transversal direction until it meets another nucleus or external boundary . Therefore precipitates must have a flattened form.
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Roughly speaking nucleation of the intermediate phase on the base of amorphous one becomes possible from the thermodynamic point of view when the width of amorphous layer
exceeds the value of the order
'Cr AC' where AC is the concentration range within which intermediate phase is more favorable than parent one.
3. Amorphizing in the process of reactive diffusion in diffusion couple During the growth of the amorphous layer the intermetallic compounds with the concentration ranges neighboring to or overlapping with that of the amorphous metastable phase are absent for rather a long time. Three questions arise: 3.1. Why do intermetallic phases not grow between amorphous layer and one of initial materials? Shortly speaking, their critical nuclei are sucked out by vampire amorphous phase: Gibbs' free energy dependence on concentration for amorphous, intermetallic and initial phases. Let the nucleus of intermetallic compound 1 appear between the amorphous layer and the parent material B (C = 1). Let us consider the case when the phase I is in the state of metastable quasiequilibrium with the amorpho
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