Sidewall effects in the smoothing of an initial discontinuity of concentration

The velocity field of a binary mixture of incompressible miscible liquids is non-solenoidal when the densities of the two liquids are different. If the mixture density is linear in the volume fraction, as in the case of simple (ideal) mixtures or very nearly for glycerin and water, then the velocity can be decomposed into a solenoidal and an expansion part. In the context of this theory, we derive a new solution which describes the smoothing of an initial plane discontinuity in concentration across a channel bounded by sidewalls. The requirement that the velocity vanishes on the sidewall introduces a different initial discontinuity not present in the solenoidal theory. The problem may be reduced to a partial differential equation in two similarity variables, one for the smoothing of a concentration discontinuity without sidewalls and the other for the smoothing the velocity discontinuity at the sidewall. The similarity equations are solved explicitly in a special case.

Observation of pseudo 10-fold symmetry in the ordered iron-zinc delta phase

The δ phase is a Zn-rich intermetallic, having a composition range of ∼ 86.5 - 92.0 atomic percent Zn, and is stable up to 665°C. The stoichiometry of the δ phase has been reported as FeZn7 and FeZn10 The deviation in stoichiometry can be attributed to variations in alloy composition used by each investigator. The structure of the δ phase, as determined by powder x-ray diffraction, is hexagonal (P63mc or P63/mmc) with cell dimensions a = 1.28 nm, c = 5.76 nm, and 555±8 atoms per unit cell. Later work suggested that the layer produced by hot-dip galvanizing should be considered as two distinct phases which are characterized by their morphological differences, namely: the iron-rich region with a compact appearance (δk) and the zinc-rich region with a columnar or palisade microstructure (δp). The sub-division of the δ phase was also based on differences in diffusion behavior, and a concentration discontinuity across the δp/δk boundary. However, work utilizing Weisenberg photographs on δ single crystals reported that the variation in lattice parameters with composition was small and hence, structurally, the δk phase and the δp phase were the same and should be thought of as a single phase, δ. Bastin et al. determined the average cell dimensions to be a = 1.28 nm and c = 5.71 nm, and suggested that perhaps some kind of ordering process, which would not be observed by x-ray diffraction, may be responsible for the morphological differences within the δ phase.