Time-Dependent Nucleation in Partitioning Systems
- PDF / 400,635 Bytes
- 6 Pages / 414.72 x 648 pts Page_size
- 64 Downloads / 175 Views
solution, such as oxygen precipitation in single crystal silicon [4], suggest the need for a new model of nucleation linking diffusion in the parent phase with the stochastic process of interfacial attachment [4,5]. These points are examined briefly here. TIME-DEPENDENT NUCLEATION IN Na 2O-CaO-SiO 2 GLASSES DEPENDENT INTERFACIAL FREE ENERGY
- COMPOSITION
A few studies of the time-dependent nucleation rates as a function of composition have been made in silicate glasses. Typically, nuclei are produced by annealing in a temperature range where the nucleation rate is significant; these are grown to visible size by annealing at a higher temperature (the growth temperature, TG), where the growth rate is high, but the nucleation rate is low [6]. The number of nuclei produced as a function of time, X(t), is directly related to the nucleation rate (I(t) = dX/dt). For long annealing times, X increases linearly with time, consistent with a constant, steady-state nucleation rate, Is. The induction time for nucleation, 0, is defined by the intercept of the extrapolated linear region of X(t) to the time axis. It provides a measure of the relaxation rate of the cluster distribution to the steady-state one (see ref. 7). Figure 1 shows the steady-state nucleation rates, Ir and induction times, 0, for as-quenched glasses of Na 2O.2CaO.3SiO 2 made with varying Si0 2 concentrations. To most easily indicate the 107 Mat. Res. Soc. Symp. Proc. Vol. 481 ©1998 Materials Research Society
amount of silica used to prepare the glass, the glass compositions are written as (Na 2O.2CaO)1 . x(3SiO 2)x. In this notation, Na2 O.2CaO and Si0 2 are treated as separate units; x = 0.5 represents the stoichiometric glass. The induction time for nucleation is defined by the intercept of the extrapolated linear region to the time axis. It provides a measure of the relaxation rate of the cluster distribution to the steady-state one. The magnitude of the steady-state nucleation rates decreases with increasing [Si0 21; the temperatures of the peak nucleation rates are approximately independent of the SiO 2 concentration. The induction times increase with decreasing nucleation rates. Within the classical theory of nucleation, the steady state nucleation rate in a binary mixture is expected to have the form [7], 15 =
A;, exp-
(-alAGjk'
(1)
where Aa,b is a dynamical pre-factor that is linear in the atomic mobility, nab is the critical cluster size for nucleation (containing both a and b components), AG'
is the volume free energy on
solidification of the crystalline phase, Ga,b is the interfacial free energy, a is a constant, k] is Boltzmann's constant and T is the annealing temperature. The exact form of the induction time is less certain, but it should be inversely proportional to the atomic mobility and only weakly dependent on the driving free energy and the interfacial free energy [7].
"103 . 102 .
-AA A V
10' 10 120
I
'
I
I
.2• 90 ' 60
30
585
600
615
Temperature (C)
630
Fig. 1. Crystal steady-state nucleation rates (top) and induct
Data Loading...
