Development of Microstructure in Rapidly Solidified Intermetallics
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the ordered phase, or to more rapid coarsening of the domains near grain boundaries due to higher aluminium content [3]. The microstructure of rapidly solidified alloys can, in principle, be predicted based on the modelling of solidification and post-solidification transitions. So far, such analyses have been carried out separately for the two stages. An example of the modelling of solidification of intermetallics is given in detail in [4] and will be reviewed briefly in this paper. The work of Chen and Khachaturyan [1] on the kinetics of ordering in the solid state is an example of the modelling which can be applied to the post-solidification stage. Their simulations are based on the microscopic kinetic equations which describe all the diffusion processes, ordering, the formation and movement of anti-phase domain boundaries, and phase separation. The microstructure is described by a single-site occupation probability n(r,t), which is a function of the position of the lattice site r and time t, and varies from 0 to 1. The microscopic kinetic equations are presented in terms of the relation between the evolution rate dn(r,t)/dt and the thermodynamic driving force. The separate modelling of solidification and then solid-state ordering excludes some microstructural features, in particular columnar APDs. The focus of the present work is therefore to combine the simulations (as in [1]) of solid-state ordering with solidification modelling. The combined modelling can include the development of different patterns of APDBs observed in rapidly solidified intermetallics and is useful in determining the solidification history. 75 Mat. Res. Soc. Symp. Proc. Vol. 398 ©1996 Materials Research Society
EXPERIMENT AND MODELLING Droplets of stoichiometric and Ni-rich Ni 3 Al were processed in a drop-tube or by electromagnetic levitation, offering different thermal and solidification histories. The microstructure of the as-processed samples, in particular the patterns of APDBs, was studied using transmission electron microscopy (TEM). Details of the processing techniques and sample preparation for TEM are given in [5, 6]. The formation of APDB patterns is interpreted using the models, described below, for solidification and for solid-state ordering. Modelling of Solidification According to the competitive growth criterion, the primary solid phase growing in a positive temperature gradient, i.e. where the heat flow and the growth directions are opposite, would be the one with the highest interface temperature. However, the droplet solidification methods in the present study give growth into an undercooled melt; the temperature gradient ahead of the interface is negative, and the primary phase is that with the highest growth velocity. The interface temperature or the growth velocity of a solid phase for given imposed solidification conditions can be calculated. A key point in the modelling is knowledge of the conditions at the solid/liquid interface, expressed as a set of relations between the interface variables (i.e., the growth ve
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