Dendritic solidification

Chapter I contains a summary of solidification theory, including theories of the interface processes in pure materials and alloys and applications of analytical diffusion treatments to complex solidification problems. Chapter II contains more detailed literature surveys related to the present work. Section (a) gives a summary of work on dendritic growth, spacing and segregation, including a collation of spacing data, to complement an earlier, more discursive review.(1) Section (b) gives an extensive discussion of theoretical and experimental studies of temperature gradient zone melting and similar migration phenomena. Section (c) is a summary of experimental studies using transparent organic analogues for metallic solidification as in the present work, while section (d) covers previous work(1) by the author. Literature surveys also appear in chapter IV(a) (dendrite tip shapes, effects of convection and the container surface), Chapter V(a) (interdendritic solidification models), chapter VIII(c) (theory of fibre coarsening) and chapter VIII(d) (temperature gradient zone melting during crystal growth.) Chapter III describes the temperature gradient stages for the optical microscope used in the experimental work of chapters IV and VII. A new type of stage was designed for fixed-area studies during solidification, in which the hot and cold plates were together driven across the stage while the specimen cell was held stationary in the microscope viewfield. Horizontal and vertical thermal gradients in specimen cells, with and without the plates moving, were measured with thermocouples and by observing temperature gradient zone melting. As a result, the apparatus was modified to reduce local convective heat losses, to control the heating plate temperatures and reduce heat transfer problems in order to make the thermal field reproducible, and to minimize vertical thermal gradients in cells. Some observations on optical perfection and image contrast are also presented. Chapter IV describes experimental studies on dendritic growth of succinonitrile and CBr4 alloys in thin specimen cells using the above apparatus. The effects of constraint by the cell walls on growth direction were studied, partly to test the effectiveness of the technique in reproducing bulk dendritic growth features but also to investigate the crystallography of preferred dendritic growth direction. For a given material, dendritic growth form depended largely on grain orientation, and some orientations produced growth forms reasonably similar to bulk growth. There were, however, distinct differences between different alloys although all were cubic, non-faceting, with preferred growth direction [100]. Dendrite spacings and tip temperatures were also measured. There was clear evidence of the influence of convection on primary spacing. Growth temperature measurements were in reasonable agreement with theory. (51) Chapter V covers theoretical developments of established models of interdendritic solidification. Liquid-state diffusion is discussed in order to correct errors in earlier work and integrate the diffusion analysis with the more intuitive "complete mixing"(49) treatment of dendritic solidification. An analytical treatment(49) of solid-state diffusion is marginally improved and included in the analysis but found to remain quite inaccurate. Previous calculations on microsegregation in aluminium-copper alloys(103) are re-assessed, using self-consistency of the results to obtain a reliable estimate of the solid-state diffusion coefficient, and it is concluded that only one-quarter of the observed(104) homogenization during solidification can be explained by the solid-state diffusion model. Chapter VI describes theoretical work on temperature gradient zone melting. In previous work, the concentration gradient across a migrating region has generally been assumed, e.g. as linear. Such an assumption is not adequate to discuss TGZM during solidification. In this chapter, exact TGZM diffusion solutions are presented for special cases. These are then used to derive approximate solutions of wider validity. Besides describing TGZM during solidification, these solutions show serious faults in previous treatments of fibre coarsening by differential migration(124) (see also chap. VTII(c)), droplet shape distorsions,(144) and interface stability during TGZM.(129) Solid-state diffusion outside migrating zones and droplets is also analyzed: "forces" on migrating droplets and droplet shape distorsions and retardations during TGZM are discussed. An expression is given for the distance migrated during solidification by an interdendritic liquid pool. Chapter VII covers experimental studies of TGZM in organics. Migration of interdendritic liquid pools during solidification was shown experimentally to be similar to droplet migration in a static thermal gradient. Detailed observations of migration velocities as a function of droplet size in succinonitrile showed considerable variations at low temperatures. Possible explanations in terms of interface kinetics affected by adsorption, or dislocation dragging by migrating drops, are presented and discussed. Much smaller size dependences of migration velocity were obtained at higher temperature and these were satisfactorily explained in terms of the curvature effect alone. Grain boundaries in succinonitrile were sometimes observed to migrate up the temperature gradient like liquid drops, suggesting that they (and perhaps also dislocations) can behave as microscopic liquid zones. Some observations on gas bubbles and diffusion coefficient measurements in TGZM are also presented. Chapter VIII includes various applications of TGZM theory. The simplicity of the theory is used to advantage in calculating the purity required of a "pure" material in which phase transformations can be said to be "controlled" by heat flow rather than solute diffusion: a purity ≳ 99-99% is obtained. It is shown that despite their very different thermal properties, organic materials remain good analogues for metals in this respect. The theory of chapter VI is shown not to invalidate theories(18) of interface kinetics in TGZM, but some special features of the melting kinetics are discussed. The theory(124) of fibre coarsening by differential migration is extensively amended but shown not to account for experimental observations satisfactorily. Using insights gained from the introduction of a dimensionless parameter unifying the theories of various solidification phenomena in a thermal gradient (chap. IV(e)), it is shown that droplets inside a crystal growing with a planar interface often migrate as fast as the crystal grows. Implications for high-quality crystal growth are discussed. Finally, some amendments and extensions to earlier work(1) on homogenization and coarsening by TGZM during dendritic solidification are presented.