Robert W. Hopper

Plane Stokes flow driven by capillarity on a free surface

The free creeping viscous incompressible plane flow of a finite region, bounded by a simple smooth closed curve and driven solely by surface tension, is analysed. The shape evolution is described in terms of a time-dependent mapping function z = Ω (ζ, t ) of the unit circle, conformal on |ζ| [les ] 1. An equation giving the time evolution of the Ω (ζ, t ) is derived. In practice, it has been necessary to guess a parametric form, i.e. Ω (ζ, t ) = Ω[ζ; a 1 ( t ), a 2 ( t ), …], whose validity must be verified using the shape-evolution equation. Polynomial and proper rational mappings with no repeated factors are apparently always valid in principle. Solutions are given for (i) regions bounded initially by a regular epitrochoid, (ii) the limiting case of a half-plane bounded by a trochoid, and (iii) a class of rosettes whose mapping is rational. The two-lobed rosette gives the exact solution of the coalescence of equal cylinders. All these mappings involve limiting initial shapes having inward-pointing cusps. Useful parameterizations providing regions whose limiting shapes possess corners or outward-pointing cusps have not been found.

Explosive fabrication of rapidly quenched materials

Research into methods for explosive fabrication of alloy glasses--one class of rapidly quenched materials--is described. Recent developments have resulted in two major breakthroughs for the processing of metallic alloy glasses. The first was the successful demonstration that a Ni/sub 40/Fe/sub 40/B/sub 20/ alloy glass ribbon can be explosively welded or cladded to A516-70 steel. To accomplish this, the alloy glass ribbon was driven downward onto the steel by a powdered explosive. The welded ribbon was bonded tightly to the steel. Large-angle x-ray scans revealed that the welded ribbon still was amorphous. A second series of tests demonstrated that the alloy glass ribbon could be explosively welded to a second ribbon, suggesting that three-dimensional structures can be fabricated from a stack of alloy glass ribbons. (GHT)

Low-density microcellular carbon foams

A method has been developed to produce vitreous carbon foams having both low densities (0.03 to 0.10gcm−3) and small cell sizes (∼ 20 μm). This process involves the replication of a porous sacrificial substrate, i.e. sodium chloride. The salt is pressed initially into bars and sintered to give a structure with continuous porosity. The pores are infused with a phenolic solution, the solvent is evaporated, and the resin is pyrolysed within the salt substrate. Extraction of the salt and freeze drying lead to the final carbon foam. The substrate serves two purposes in this process: (1) it prevents shrinkage of the foam during pyrolysis, and (2) it dictates the cell size of the foam.

A kinetic treatment of glass formation: IV. Crystallization on reheating a glass

Abstract An analysis, based on the approach of crystallization statistics, is presented to describe crystallization on reheating a glass. The analysis treats heating carried out at the same or different rate relative to the cooling rate used to form the glass. The analysis takes account of the finite size of the critical nucleus and provides a description of the state of crystallinity in a body for both short and long times. The temperature of crystallization on reheating a glass is shown to depend strongly on the heating rate and on the barrier to crystal nucleation and less strongly on the cooling rate used to form the glass. For glasses with volume fractions crystallized greater than 10−9, the stability on subsequent heating increases with decreasing fraction crystallized at the glass transition.

Plane Stokes flow driven by capillarity on a free surface. Part 2. Further developments

For the free creeping viscous incompressible plane flow of a finite region, bounded by a simple smooth closed curve and driven solely by surface tension, analyzed previously, the shape evolution was described in terms of a time-dependent mapping function z = Ω(ζ, t ) of the unit circle, conformal on |ζ| [les ] 1. An equation giving the time evolution of the map, typically in parametric form, was derived. In this article, the flow of the infinite region exterior to a hypotrochoid is given. This includes the elliptic hole, which shrinks at a constant rate with a constant aspect ratio. The theory is extended to a class of semi-infinite regions, mapped from Im ζ [les ] 0, and used to solve the flow in a half-space bounded by a certain groove. The depth of the groove ultimately decays inversely with time.

Stokes flow of a cylinder and half-space driven by capillarity

The coalescence of a cylinder with half-space by creeping viscous flow driven solely by surface tension is analysed using methods developed previously. The evolution of the shape with time is described, exactly, in terms of a time-dependent mapping function z = ω(ζ, t ) of the upper half-plane, conformal on Im ζ [Gt ] 0. The results are in closed analytic form except for the time, which requires a quadrature. The height of the figure decays as t −1 as t → ∞, which is consistent with Kuikens analysis of an isolated disturbance. (Previously, the author reported an erroneous solution which behaved otherwise.) The results are compared with the coalescence of equal cylinders obtained previously. For a modest degree of coalescence, the shapes are rather alike. In the limit as t → 0. the time dependence of the minimum widths (necks) are the same. At the times when the minimum widths disappear, the heights of the two shapes are equal. Appended is a note providing a counter-example to earlier conjecture. A simply connected region undergoing this type of flow need not remain so.

Stochastic theory of scattering from idealized spinodal structures. II: Scattering in general and for the basic late stage model

Abstract Certain model late stage spinodal structures can be generated mathematically by the relation ΔCL(r) = G[ΔC09r], where ΔCL(r) is the composition deviation from the mean of the late stage structure and ΔC0(r) is a random superposition of waves. Then the autocorrelation function (ACF) of ΔCL(r) depends only on the ACF of ΔC0)r), and the latter is related simply to the distribution of wavelengths present. Coherent scattering (light, small-angle X-ray, etc.) can be computed from the ACF. The “basic late stage model” (BLSM) is defined by G(ΔC) = 2H(ΔC)−1, where H(x) is the Heaviside step function. This converts the smooth, wavy ΔC0(r) into a late stage structure having the same morphology but equilibrium compositions and sharp interfaces. The scattering theory formalism is developed generally and then applied to the BLSM using illustrative wavelength distributions. Scattering as a function of angle and wavelength is computed. It is also found that the BLSM turbidity ≌ Ck 4 w 3 , where w is the mean phase width and C depends only weakly upon the wavelength distribution of ΔC0(r).

Positron lifetime study of Fe40Ni40P14B6 glass

Positron lifetimes were measured in the as-received alloy after treatment to embrittle, crystallize, or deform the alloy thus changing its internal structure.

Stochastic theory of scattering from idealized spinodal structures, I: Structure and autocorrelation function

Abstract In the early stage (ES) of spinodal decomposition, composition fluctuations in a nominally homogeneous glass are selectively amplified over a narrow range of wavelengths. As their amplitude increases, nonlinear coupling slows further amplitude growth, coarsens the structure, sharpens the interfaces, and adjusts the phase compositions and volume fractions toward their equilibrium values; but the morphology of the late stage (LS) structure is dominated by the ES morphology. It is widely believed that the LS morphology can be modelled as the positive and negative composition deviations from the average, that are obtained from a superposition of waves of fixed wavelength Λ but of random orientation and phase. Here, Λ is not identified with the dominant ES wavelength. This LS model, and modifications of it, are analysed using stochastic theory. The autocorrelation function of the model is determined using methods developed for the analysis of electrical random noise signals that have passed through a nonlinear amplifier.

Search for the most stable PdSiCu metallic glass using the phase diagram approach

Abstract It is shown that slow cooling from the melt accompanied by intermittent annealing of alloys in the ternary system PdSiCu produces microstructures in which the “last freezing” areas of a ternary eutectic can be identified and subjected to electron microprobe analysis. In this way the composition of the ternary eutectic point was identified as Pd 80.1 Si 14.7 Cu 5.2 . The combination of the slow cooling and microprobe techniques also permitted us to establish the most probable projection contours of the surfaces of primary crystallization in the eutectic region, as well as to identify the principal primary phases involved. The eutectic composition alloy is an easy glass former with a reduced glass temperature T rg of 0.63. This high value of T rg is the result of the lowest liquidus temperature T 1 of 698 °C attained at the eutectic point. The approach described in this paper is expected to be useful in locating regions of the probable glass-forming alloys in multicomponent systems.