The stability of the shape of a moving planar liquid‐solid interface during the unidirectional freezing of a dilute binary alloy is theoretically investigated by calculating the time dependence of the amplitude of a sinusoidal perturbation of infinitesimal amplitude introduced into the planar shape. The calculation is accomplished by using gradients of the steady‐state thermal and diffusion fields satisfying the perturbed boundary conditions (capillarity included) to determine the velocity of each element of interface, a procedure justified in some detail. Instability occurs if any Fourier component of an arbitrary perturbation grows; stability occurs if all components decay. A stability criterion expressed in terms of growth parameters and system characteristics is thereby deduced and is compared with the currently used stability criterion of constitutional supercooling; some very marked differences are discussed.

Stability of a Planar Interface During Solidification of a Dilute Binary Alloy

A theory is presented which describes the development of surface grooves at the grain boundaries of a heated polycrystal. The mechanisms of evaporation‐condensation and surface diffusion are discussed with the use of the Gibbs‐Thompson formula and the assumption that the properties of an interface do not depend on its orientation. For the idealized case in which only one of the mechanisms is operative, the groove profile is shown to have a time‐independent shape whose linear dimensions are proportional to t½ for evaporation‐condensation, and to t½ for surface diffusion. The proportionality constants are evaluated, and criteria are developed which permit one to estimate which process predominates in practice. Order of magnitude agreement is obtained with estimates of actual grooving speeds and profiles.

Theory of Thermal Grooving

According to a suggestion of Nabarro, any crystal can change its shape by self‐diffusion in such way as to yield to an applied shearing stress, and this can cause the macroscopic behavior of a polycrystalline solid to be like that of a viscous fluid. It is possible that this phenomenon is the predominant cause of creep at very high temperatures and very low stresses, though not under more usual conditions. The theory underlying it is developed quantitatively, and calculations of rate of creep, or equivalently of effective viscosity, are given for aggregates of quasi‐spherical grains and for wires composed of cylindrical grains. Allowance is made for the effect of tangential stress relaxation at the grain boundaries. It is suggested that mosaic boundaries and boundaries between grains of nearly the same orientation may be unable to serve as sources or sinks of the diffusion currents, in which case the creep rate will depend only on the configuration of grain boundaries having a sizable orientation differen...

Diffusional Viscosity of a Polycrystalline Solid

Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications

The redistribution of solute atoms during the solidification of metals

Solidification, in the sense used in this context, is the process by which a liquid is transformed into a crystalline solid. In crystal growth the solid that forms first is solvent rich as distinct from crystallisation, in which the crystals that are formed are solute rich. It is not always possible to make a clear distinction. Solidification is important as the process employed in the widely used process of casting, in all its forms from large ingots of steel to small crystals of silicon. While in principle it would seem simple to convert a homogeneous liquid into an equally homogeneous perfect crystal, this is extremely difficult, if not impossible to achieve in practice. Thorough understanding requires that the process be studied at various levels, which can be conveniently described as the angstrom level, the micron level and the centimetre level.

Principles of Solidification

The interaction between particles and an advancing solid‐liquid interface has been investigated both experimentally and theoretically. For each particular type of particle, a ``critical velocity'' was observed, below which the particles are rejected by the interface, and above which they are trapped in the solid. The dependence of the critical velocity on various properties of matrix and particle was investigated. A theory has been developed, based on the assumption that a very short‐range repulsion exists between the particle and the solid. This repulsion occurs when the particle‐solid interfacial free energy is greater than the sum of the particle‐liquid and liquid‐solid interfacial free energies. The particle is pushed along ahead of the advancing interface and becomes incorporated into the solid if liquid cannot diffuse sufficiently rapidly to the growing solid behind the particle. Reasonable agreement was obtained between the calculated and experimentally observed critical velocities.

Bruce Chalmers

Papers

The redistribution of solute atoms during the solidification of metals

Principles of Solidification

Interaction Between Particles and a Solid‐Liquid Interface

Multiple slip in bicrystal deformation

A coincidence — Ledge — Dislocation description of grain boundaries