Bruce Chalmers

Principles of Solidification

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.

The redistribution of solute atoms during the solidification of metals

Abstract A quantitative analysis is made of the redistribution of solute resulting from solidification in the absence of convection of a binary solution for transient and steady state conditions. Diffusion in the liquid is taken into account and shown to be of importance in determining the solute distribution in both the liquid and the solid. It is shown that the distribution for both normal freezing and zonemelting depends on the rate of solidification. When the speed of solidification is increased abruptly, a band of high solute concentration is formed in the solid; the reverse occurs when the speed is decreased abruptly. Values for the length of the constitutionally supercooled zone of liquid adjacent to a growing solid-liquid interface are calculated.

Multiple slip in bicrystal deformation

Abstract The tensile deformation of bicrystal specimens with longitudinal grain boundaries has been considered, both from the point of view of macroscopic plasticity and from that of dislocation theory. Emphasis has been on the multiple slip associated with the interaction between the two crystals at the boundary. It has been shown that macroscopic continuity at the boundary will in general require the crystals of a bicrystal to deform on at least four slip systems between them, distributed either with two in each crystal or with three in one crystal and one in the other. A model employing the pile-up of dislocations at a grain boundary has led to a method of predicting which additional slip systems will operate in a given bicrystal. Experimental observations of slip lines on twenty-four aluminum bicrystals deformed in tension have supported the predictions made by this method.

The direction of growth of the surface of a crystal in contact with its melt

Abstract A new experimental technique is described for studying the relationship between the direction of growth of a crystal surface and the meniscus at the solid-liquid-vapor junction. An important application of the technique is to determine the required conditions, as given by the angle O 0 between the meniscus and the growth axis, for crystal growth with a uniform cross-section. The experiment involves the analysis of radially frozen zones in thin wafers which are held in a horizontal plane. The method is applied to single crystal silicon wafers, and gives O 0 = 11 ± 1° for the melt growth of silicon; preliminary results for germanium give O 0 ⋍ 8°. Observations taken under conditions of decreasing or increasing crystal dimension in silicon are in conflict with the existing theories. The accuracy of the present experiments is deemed to exceed that of techniques for measuring O 0 by direct observation. Several modifications and improvements in the experimental and analytical procedures are proposed.

Computer Calculations of the Structure and Energy of High‐Angle Grain Boundaries

A method that has been developed to obtain the geometry of a grain boundary associated with a minimum internal energy is described in detail. A Morse potential is employed to represent the interatomic forces. The procedure was applied to a series of boundaries of the coincidence orientations. The resulting structures are consistent with experimental observations.

The plastic deformation of bicrystals of f.c.c. metals

Abstract An analysis is given of the conditions that govern the compatibility of the deformation of the two crystals of a bicrystal and the interaction of adjacent crystals is discussed in terms of macroscopic and microscopic effects. A technique is described for the production of bicrystals and for the preparation of a new type of bicrystal in which one crystal totally surrounds the other: also a technique for the preparation of specimens of silver consisting of a single crystal surrounded by a layer of polycrystalline metal. The results of tensile tests on such specimens are reported and discussed in terms of the conditions of microscopic and macroscopic compatibility.

Freezing of Liquids in Porous Media with Special Reference to Frost Heave in Soils

If the surface area of a liquid is large compared to its volume, the normal freezing temperature of the liquid will be altered. In a porous material a liquid can therefore exist in equilibrium, below its normal freezing temperature. However, such a liquid will be unstable with respect to bulk solid. This instability provides the driving force for frost heave in soils.

The Thermal Etching of Silver

The mechanism whereby grain boundaries are delineated and striations formed on polished surfaces of heated metal specimens has been examined. Experiments on electrolytically polished silver show that grooves form at grain boundaries at temperatures as low as 300° C and striations at 500° C in air. Striations only appear in the presence of oxygen and may be removed by heating in nitrogen. A furnace for high-temperature photomicrography, suitable for specimen temperatures up to about 950° C, is described. Previous theories are found inadequate to explain the effects observed in silver, and a theory which regards the surface etching as an approach to equilibrium by the reduction of surface free energy is suggested. Thus the equilibrium condition of the boundary is a groove whose shape is determined by the relative magnitudes of the free energy per unit area of the boundary and the surface energies of the crystalline faces meeting the boundary in the surface of the specimen. The striations are caused by the development of those crystalline planes having the lowest free energy; the relative surface energies of different planes being modified by the presence of oxygen. It is suggested that the chief means whereby the boundary grooves are formed is that of surface migration of ions: both surface migration of ions and evaporation of silver oxide molecules may be expected to play major parts in the formation of the striations.

The growth of shaped crystals from the melt

Abstract The growth of shaped crystals from the melt occurs by a process referred to as meniscus-controlles growth. In a meniscus-controlled process, the relationship of the crystal shape to that of the liquid-vapor interface is reflected by the observed constancy of the relative angle φ0 between the crystal and liquid free-surfaces at the crystal-liquid-vapor junction. An experimental technique is described for determining the characteristic values of φ0 for silicon and germanium. A general theory is presented for the time evolution and stability of the crystal shape in meniscus-controlled growth processes. A linear perturbation analysis of the dynamic crystal growth equation is carried out to derive the necessary and sufficient conditions for crystal shape stability. Application of the analysis is made to the more conventional shaped growth processes such as Czochralski and floating zone growth, and to techniques which utilize a die shaper such as the Stepanov and Edge-defined Film-fed Growth (EFG) methods. The advantages and disadvantages of using wetted and non-wetted dies in the shaping process are discussed. Specific numerical examples deal with the growth of silicon crystals by the various methods.

Edge-defined, film-fed crystal growth

Abstract Crystal formation from the melt by the edge-defined, film-fed growth process is discussed quantitative in relation to the range of conditions under which continuous growth is possible. It is showin that two distinct modes of growth can occur, in one of which the extraction of latent heat is by radiation into the growing crystal. This is relatively slow process, and because a planar interface is inherently stable in the thermal situation, it can produce crystals of high quality. Also, because of the thermal geometry, there is no upper limit to the cross section that can be grown in this way. The second mode is that in which heat extraction is largely by conduction into and through the liquid film. Crystals can be grown much faster by this process; the interface is inherently unstable, with the result that imperfections arise from cellular or dendritic growth. In the fast mode, the cross section for continuous growth is limited because the position of the interface is stabilized by edge effects, which become inoperative at large cross sections. The quantitative results of these analyses are in close accord with the results of experiments and with observations made in routine production of sapphire crystals.