Melting and superheating of crystalline solids: From bulk to nanocrystals

The microstructure of the Sn-Ag-Cu solder is examined by optical microscopy and scanning electron microscopy (SEM) for various compositions near the ternary eutectic for different cooling rates from the solder melt. Focus is on the size and orientation of Sn grains as indicated by cross-polarized, light optical microscopy, and pole figures from x-ray diffraction. We find that both composition and cooling rate have strong influences on Sn grain size, with Sn grain size increasing an order of magnitude as Cu concentration increases from 0% to 1.1%. Cyclic growth twinning, with twinning angles near 60°, is observed in Sn-Ag-Cu alloys near the composition Sn-3.9Ag-0.6Cu.

Growth of Sn and intermetallic compounds in Sn-Ag-Cu solder

Heterogeneous nucleation of solidification in melt spun Al-Si and Al-Si-P has been studied using differential scanning calorimetry, and transmission, scanning transmission and high resolution electron microscopies. The microstructures of the heat treated melt spun alloys all consist of an Al matrix, Al-Si eutectic distributed along the Al grain boundaries, and Si embedded in the Al matrix. The Si microstructure depends on the level of P: coarse faceted Si particles are nucleated by AlP particles in Al-Si containing 2 ppm P and Al-Si-P containing 35 ppm P whereas eutectic droplets of fine Si particles are nucleated by the surrounding Al matrix at a high undercooling in Al-Si containing 0.25 ppm P. The Si nucleation onset temperature remains approximately constant while the peak and end temperatures both decrease with increasing cooling rate, in agreement with classical nucleation theory. Kinetic analysis, using the spherical cap model gives contact angles of 10°, 43° and 10° for Si nucleation in low and high purity Al-Si and Al-Si-P respectively.

Heterogeneous nucleation of solidification of Si IN Al-Si and Al-Si-P alloys

Existing methods to rapidly compute interface-energy minimizing shapes with anisotropy are collected and clarified, and new methods are introduced. A description of freely available, platform-independent software for the computation and display of equilibrium geometries is provided. The software relies on a new computational method to rapidly find equilibrium geometries. It also features a graphical user interface and includes the 32 crystallographic point groups to simplify inputting interfacial energies and their associated orientations. When a particle is completely enclosed within a single interface (isolated), the software computes and provides visualization for Wulff shapes. When a particle is enclosed by two interfaces, such as a particle at a grain boundary, the software minimizes their collective interfacial energy; if one of the interfaces is planar, the computation reproduces the Winterbottom construction. When both interfaces are deformable, the software provides a new tool for calculating the particle shape and the distortions of boundaries that are attached to it, even for highly anisotropic interfaces. The properties of particles bounded by two deformable interfaces are discussed, and applications of the software are illustrated. In some cases, the software can be used as a method to infer values of relative interfacial energies from a microscopic observation.

New software tools for the calculation and display of isolated and attached interfacial-energy minimizing particle shapes

Melting and superheating of metals and alloys

Hypermonotectic alloys of Al-5 wt% Pb and Al-5 wt% Pb-0.5 wt% X where X = Mn, Cu, Zn, Fe and Si have been manufactured by chill-casting and melt-spinning. The resulting microstructures have been examined by a combination of optical microscopy, scanning and transmission electron microscopy, and electron probe microanalysis. The as-solidified hypermonotectic alloys exhibit a homogeneous bimodal distribution of faceted Pb particles embedded in a matrix of Al, with chill-cast Pb particle sizes of 1–2 μm and 5–50 μm, and melt-spun Pb particle sizes of 5–10 nm and 50–100 nm. The larger Pb particles are formed during cooling through the region of liquid immiscibility while the smaller Pb particles are formed during monotectic solidification of the Al matrix. The Pb particles exhibit a cube-cube orientation relationship with the Al matrix, and a truncated octahedral shape with {111} and {100} facets. The as-solidified Pb particle distributions are resistant to coarsening during post-solidification heat treatment. The equilibrium Pb particle shape and therefore the anisotropy of solid Al-solid Pb and solid Al-liquid Pb surface energies have been monitored by in situ heating in the transmission electron microscope over the temperature range between room temperature and 550°C. The anisotropy of solid Al-solid Pb surface energy is constant between room temperature and the Pb melting point, with the {100} surface energy 14% greater than the {111} surface energy, in good agreement with geometric near-neighbour bond energy calculations. The {100} facets disappear when the Pb particles melt, and the anisotropy of solid Al-liquid Pb surface energy decreases gradually with increasing temperature above the Pb melting point, until the Pb particles become spherical at about 550°C. The kinetics of Pb particle solidification have been examined by heating and cooling experiments in a differential scanning calorimeter. Pb particle solidification is nucleated catalytically by the Al matrix on the {111} facet surfaces, with an undercooling of 22K and a contact angle of 21°C. Ternary additions of Mn, Cu, Zn and Fe do not influence the Pb particle solidification behaviour, but Si is a potent catalyst and stimulates the Pb particles to solidify close to the equilibrium Pb melting point.

K.I. Moore

Papers

Solidification of Pb particles embedded in Al