Evolution of Ge Precipitate Morphology in Al
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on the nucleation of two-dimensional islands when the free energy of a step AG = AH — TAS is positive. At a critical temperature, Tc = AH/AS, the step energy disappears and the surface acquires random steps and long-range fluctuations. Growth above this roughening transition is no longer limited by two-dimensional nucleation. The equilibrium state, rough or faceted, of a surface or interface is thus directly related to the mechanism of growth. The roughening transition of a surface will be visible as the disappearance of its energy cusp in the y plot and can be observed as the rounding of its corresponding facet if that facet is represented on the equilibrium shape.2 Experimental observation of a roughening transition can be made on equilibrium shapes by measuring the disappearance of facets with temperature, or on growth shapes by measuring the rates and morphologies of crystal growth at different temperatures and at relatively low supersaturation.3 Surfaces or Crystal/Vapor Interfaces Although Burton et al1 originally estimated the critical temperature for surface roughening to be above the melting point for {111} and {100} faces of fee crystals, it has since been shown that a number of fee metals exhibit observable roughening transitions of these and other faces below the melting point. The macroscopic equilibrium shape of small crystals changes reversibly with temperature. On heating above the critical temperature, flat crystallographic facets may give way to rounded surfaces. Surface motion, and hence growth and dissolution, are then controlled by atomic transport to or from the surface whereas below the critical temperature the rate controlling step is the nucleation of ledges.
Crystal/Crystal Interfaces Although in principle the concepts developed for single-crystal particles and voids can be applied directly to crystals enclosed inside a crystalline matrix, several additional factors must be considered. Most notably, the interface structure and hence its behavior with temperature now depend on both adjoining crystals and so must obey the bicrystal symmetry, which is usually lower than that of each crystal alone.4"5 For example, two equivalent {111} faces of a cubic precipitate may behave differently if they are in contact with two different crystallographic planes of the matrix. Furthermore, with increasing temperature, precipitates often dissolve in the matrix before melting. Finally, the equilibrium shape will depend on elastic constraints from the solid matrix.6 Experimental An Al-2.2% Ge alloy was quenched from 450°C and aged at 250 and 300°C to produce well-faceted precipitates. Although several morphologies and orientation relationships are known to form/"11 here only the lath-shaped precipitates were investigated. Thin foils containing suitable precipitates that were entirely contained in the foil were observed during in situ temperature cycling in a high-voltage electron microscope at an operating voltage of 1,500 kV. The dynamic behavior of individual precipitates was videotaped and at appropr
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