S. Hagège

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

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.

Observations of interface premelting at grain-boundary precipitates of Pb in Al

This work reports direct observations showing the effect of size and interface structure on premelting behaviour of nanoscale inclusions. Using in-situ transmission electron microscopy it was possible to observe premelting of individual Pb inclusions in Al, each bounded by two distinctly different topotaxial interfaces. Such particles were generated by precipitating single-crystal Pb inclusions a few tens of nanometres in size at grain boundaries in Al. At equilibrium these particles adopt compound shapes, made from two segments whose shape and interface structure is characteristic of their misorientation with the matrix crystal. Only one of these interfaces premelts. In close agreement with a simple model, the width of the liquid layer depends reversibly on undercooling and interface curvature, and hence on particle size. The observed behaviour confirms previous reports on interface-dependent melting. By observing the selective melting of different interfaces for the first time on individual particles, it was possible to rule out experimental uncertainties and to show unambiguously that inclusion melting depends strongly on interface structure.

Internal reduction of (Mg,Cu)O

Abstract (Mg, Cu)O single crystals are internally reduced at temperatures ranging from 1273 to 1673 K in the presence of either a C/CO buffer or a CO/CO2 gas flow. As a result, a reduction scale containing discrete precipitates develops. At low reaction temperature, this scale is divided in an outer part where discrete copper precipitates are present in the MgO matrix, and an inner part where both metallic copper and cuprite Cu2O precipitates coexist in the MgO matrix. At high temperatures, the inner scale is very narrow. Transmission electron microscopy (TEM) investigations of the reduction scale reveal special orientation relationships between the MgO lattice (m) and that of the precipitates (p):

Structural analysis of phases and heterophase interfaces in the zirconium–boron system

The αZr–ZrB2 eutectic, a model system for metal–boride interfaces, was prepared by r.f. induction melting from high-purity zirconium ingots and zirconium diboride powders. At the eutectic composition and depending on the cooling rate, the formation of either the ZrB phase or a Zr(B) solid solution has been observed in addition to the expected compound αZr and ZrB2. For slow cooling rates, the formation of the compound ZrB by a peritectoid reaction and most likely stabilized by light elements (carbon, nitrogen, oxygen) has been observed. After rapid quenching, TEM investigations revealed the formation of a zirconium-based metastable phase; this new phase, with a nearly fcc structure, has been found in thin foils and is directly related to hexagonal αZr by a Shoji–Nishiyama orientation relationship. The structure at interfaces with habit planes featured by trigonal symmetry ({0 0 0 1} for hexagonal and {1 1 1} for fcc), has been investigated using weak-beam diffraction contrast and high-resolution transmission electron microscopy. The interfaces with a small difference in lattice parameter are accommodated by a misfit dislocation network, whilst those with a large difference in lattice parameter exhibit a more complex structure with ledges and facets.

On the structure of faulted interfaces in aluminium nitride ceramics

Abstract An unusual two-dimensional structure in hot-pressed wurtzite A1N, composed of a mixture of both curved and flat elements, is analysed by weak-beam and high-resolution electron microscopy. It is demonstrated that the structure, in its elementary form, is a ‘dome’-like faulted defect. This defect is characterized by a Frank-type dislocation loop containing a metal-vacancy-induced stacking fault in the basal plane with displacement Rp = (1/3) [1100] + 0·15[0001] and a curved faulted interface with displacement vector Rc = (1/3)[1100] + (1/2)[0001]. The elementary dome is found always pointing in the same direction, reflecting the lack of symmetry in the tetrahedral unit structure of A1N with respect to the basal plane. Condensation of supersaturated metal vacancies on both interfaces, combined with the segregation of impurities, mainly oxygen, only on the planar interface, is considered to be the driving force for the nucleation and growth of the structure.

Wetting in Multiphase Systems with Complex Geometries

We address the shape and distribution of two-phase systems embedded within a third phase. To motivate this work, we begin by describing transmission electron microscopy observations of the configurations adopted by the solid and vapor phases of lead when these are confined together within a silicon cavity. We then perform analytical calculations of the stability of various possible configurations of two-phase systems confined in a cubic-shaped cavity. The most stable configurations are a function of the volume ratio of the two phases in the cavity, and of a parameter describing the wetting behavior in the three-phase system. The wealth of configurations obtained for embedded solid/fluid or condensed/fluid phases within a solid cavity is presented. Wetting anisotropy on the walls of the cavity, and the faceted or isotropic character of the interface between the two embedded phases, are shown to be physical parameters that determine the number of possible stable configurations.

Lead Inclusions in Silicon: Structure, Morphology, and Thermal Behavior

Small inclusions of lead have been embedded in pure silicon by rapid quenching. They are topotactic-truncated octahedra with a smaller aspect ratio than the ones found in aluminum. They appear also on single and multiple twins as a bicrystalline unit with a compound morphology. No overheating has been detected, while undercooling is size dependent and can reach 80 K. These results are compared to the structure, morphology and thermal behavior of lead inclusions in aluminum and other cubic matrices.

TEM and RBS/channelling of nanosized bicrystalline (Pb,Cd) inclusions in Al made by sequential ion implantation

Abstract Sequential ion implantation of Pb and Cd in Al at 425 K and 475 K respectively has been used to produce dense distributions of nanosized (Pb,Cd) inclusions with equiatomic composition. Pb and Cd form a simple eutectic system, but both elements are insoluble in solid Al, and the inclusions are Cd-rich in comparison with the eutectic composition. Inclusions in the size range from 1 to 20 nm were observed in as-implanted samples. Their overall shape was nearly cuboctahedral. Most of the inclusions were bicrystalline with an fcc Pb part forming a segment of a cuboctahedron and an hcp Cd slab attached to one of the {111}Pb facets. The orientation relationship had close-packed planes and directions parallel in the three structures. In situ melting/solidification experiments combining TEM and RBS/channelling showed that melting of the inclusion ensemble occurs within a narrow temperature interval of 10–15 K around the eutectic temperature of 521 K. Solidification takes place with undercoolings of about 50–65 K below the liquidus line in a two-stage process where Cd solidifies 15 to 20 K before Pb.

Copper clusters made by implantation in aluminium nitride

Abstract Copper has been implanted in AIN at 80 and 300 K with an average concentration around 14%. X-ray absorption spectroscopy performed at the K edge of Cu on as-implanted samples and on samples annealed at 800°C for 1 and 5 h show that Cu precipitated in the host matrix even for implantations performed at low temperature. Analysis of the spectra allows the average size of the clusters to be deduced. These crystalline entities grow with dense planes of each phase parallel to each other, as shown from previous transmission electron microscopy experiments. The initial implantation fluence together with the subsequent annealing times and temperatures appear to be easy tools to monitor the cluster size.

The shapes of two-phase particles: THE case of trapped voids in lead particles embedded in silicon

Abstract This paper examines the factors that determine the position occupied by a void associated with an embedded precipitate particle. Analytical expressions are developed for the energy changes associated with positioning the void and the precipitate at various possible locations within a cubic cavity bounded by interfaces of a single crystallographic type. The calculated energies include consideration of the void volume fraction as well as the wetting criteria to account for interfacial energetics. The results of the analysis are applied to the interpretation of previous experimental results obtained on voids associated with Pb precipitates in a Si matrix, where the precipitate and void are confined within a more complex cubo-octahedral cavity. By taking into account the volume fraction of the void and the wetting conditions for Pb on Si, it is verified that voids in Pb precipitates embedded in Si should be convex and occupy corner sites. A computer graphics analysis of three-dimensional voids and particles confined to a cubo-octahedral cavity is found to reproduce the four corner positions observed in the transmission electron microscopy images of the voids taken along a <110> direction. These are shown to be equivalent by a suitable set of symmetry operations.