Martin E. Glicksman

Bio: Martin E. Glicksman is an academic researcher from Florida Institute of Technology. The author has contributed to research in topics: Dendrite (crystal) & Succinonitrile. The author has an hindex of 40, co-authored 299 publications receiving 7708 citations. Previous affiliations of Martin E. Glicksman include United States Naval Research Laboratory & University of Florida.

Dendritic growth-A test of theory

Abstract: Steady-state theories of dendritic solidification are reviewed, and three nonisothermal theories, expressed as simple power laws, are chosen for experimental verification. Specifically, the axial growth rate,V, of a freely growing dendrite can be expressed asV =βGΔθn, wheren andβ are the exponent and prefactor derived from each theory,G is a lumped material parameter, andΔθ is the supercooling. Succinonitrile, a low entropy-of-fusion plastic crystal, was prepared in several states of purity as the test system, and dendritic growth was studied both in the usual manner in long tubes, and in a novel apparatus in which the conditions for “free” dendritic growth were attained. Kinetic measurements show that only when “free” growth conditions obtain are the data reconcilable with current theory in the form discussed above. In particular, we show thatn = 2.6, in agreement with the theories of Nash and Glicksman and that of Trivedi; however, the prefactorsβ of those theories do not agree with the value determined for succinonitrile, which is the only substance for whichG is known accurately. Tip radius measurements, taken over a relatively narrow range of supercooling, when combined with the growth rate data prove that the Peclet number-supercooling relationship derived for each of the three nonisothermal steady-state theoriesall agree with experiment. This curious agreement, along with the inability to “decompose” the Peclet numbers into acceptable velocity-supercooling and tip radius-supercooling relationships is explained on the basis of the limitations imposed by the steady-state assumption itself. Directions for future theoretical and experimental investigation are discussed in the light of the findings presented.

Principles of Solidification

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Pattern formation outside of equilibrium

Abstract: A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

Theory of phase-ordering kinetics

Abstract: The theory of phase-ordering dynamics that is the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken-symmetry phase, is reviewed, with the emphasis on recent developments. Interest will focus on the scaling regime that develops at long times after the quench. How can one determine the growth laws that describe the time dependence of characteristic length scales, and what can be said about the form of the associated scaling functions? Particular attention will be paid to systems described by more complicated order parameters than the simple scalars usually considered, for example vector and tensor fields. The latter are needed, for example, to describe phase ordering in nematic liquid crystals, on which there have been a number of recent experiments. The study of topological defects (domain walls, vortices, strings and monopoles) provides a unifying framework for discussing coarsening in these different systems.

Under what conditions can a glass be formed

Abstract: Summary Generally substances are more stable in a crystalline than in a glassy state. Therefore, to form a glass, crystallization must be bypassed. Under certain conditions, the melts of many substances can be cooled to the glass state. Whether or not the melt of a given material forms a glass is determined principally by a set of factors which can be specified to some extent in the laboratory, namely, the cooling rate, - T, the liquid volume, v], and the seed density, ps and upon a set of materials constants: the reduced crystal–liquid interfacial tension, α the fraction, f, of acceptor sites in the crystal surface, and the reduced glass temperature, Trg . The glass-forming tendency will be greater the larger are - T and Trg and the smaller are v]. ps, and f. The number and variety of substances which have been prepared in a glassy or ‘amorphous solid’ form have been greatly increased with techniques in which the material is condensed from solution on to a surface held well below its glass temperature. T...