Shapes and sizes of nanoscale Pb inclusions in Al

Al-Pb alloys are monotectic and characterized by a large miscibility gap in the liquid phase area and extremely limited mutual solubility in the solid phase. Due to the extent of the miscibility gap the alloys are difficult to make in conventional processing. However, alloys with relatively homogeneous microstructures of fine Pb inclusions in an Al matrix can he made hy metastable processing such as rapid solidification, ion implantation, ball milling and physical vapor deposition. The first two techniques have been employed to make alloys of Al with 0.5-3 at.% Pb. The alloys contain fine dispersions of nanoscale Pb : implantation and from about 10-500 nm after rapid solidification. Inclusions inclusions with sizes in the range from 1 to about 20 nm after ion embedded in the Al matrix are single crystalline, and they grow in parallel cube alignment with the matrix. They have cuboctahedral shape with atomically smooth {111} and {100} facets determined from a minimization of the interface energy. Using high resolution TEM, two types of deviations from the classical Wulff construction which alter the shape of the inclusions, have been studied. The smallest inclusions, less than about 20 nm in size, adopt a series of magic sizes that can be related to the occurrence of periodic minima in the residual strain energy. Likewise, in this size range, the energy contribution from the cuboctahedral edges becomes non-negligible leading to an increase in the aspect ratio of the inclusions with decreasing size. Inclusions located in grain boundaries in general adopt a single crystal morphology where one part is faceted and grows in parallel cube alignment with the matrix grain, while the other part has a shape approximating a spherical cap. In special cases such as twin boundaries and {111} twist boundaries, the inclusions are bicrystalline where each part is aligned with the respective grain and the two parts are separated by a boundary similar to that of the matrix. These shapes can be explained using the Cahn-Hoffman xi -vector construction, which generalizes the Wulff construction to determine equilibrium shapes at anisotropic interfaces and their junctions. (C) 2001 Elsevier Science B.V. All rights reserved.