Turnbull Equation Research Articles

Kinetics of the coesite to quartz transformation

The survival of coesite in ultrahigh-pressure (UHP) rocks has important implications for the exhumation of subducted crustal rocks. We have conducted experiments to study the mechanism and rate of the coesite→quartz transformation using polycrystalline coesite aggregates, fabricated by devitrifying silica glass cylinders containing 2850 H/10 6 Si at 1000°C and 3.6 GPa for 24 h. Conditions were adjusted following synthesis to transform the samples at 700–1000°C at pressures 190–410 MPa below the quartz–coesite equilibrium boundary. Reaction proceeds via grain-boundary nucleation and interface-controlled growth, with characteristic reaction textures remarkably similar to those seen in natural UHP rocks. We infer that the experimental reaction mechanism is identical to that in nature, a prerequisite for reliable extrapolation of the rate data. Growth rates obtained by direct measurement differ by up to two orders of magnitude from those estimated by fitting a rate equation to the transformation–time data. Fitting the rates to Turnbull's equation for growth therefore yields two distinct sets of parameters with similar activation energies (242 or 269 kJ/mol) but significantly different pre-exponential constants. Extrapolation based on either set of growth rates suggests that coesite should not be preserved on geologic time scales if it reaches the quartz stability field at temperatures above 375–400°C. The survival of coesite has previously been linked to its inclusion in strong phases, such as garnet, that can sustain a high internal pressure during decompression. Other factors that may play a crucial role in preservation are low fluid availability — possibly even less than that of our nominally “dry” experiments — and the development of transformation stress, which inhibits nucleation and growth. These issues are discussed in the context of our experiments as well as recent observations from natural rocks.

On the growth of dendritic needles from a supercooled melt

A model of dendrite growth in deeply undercooled pure substances is developed. The dendrite growth velocities and the tip radii are determined theoretically using the analytical solution of the heat diffusion equation, the recently developed theory of the thermally activated phase transition processes, based on the classical Turnbull equation, and the maximal growth velocity principle. The application of the model developed here to a concrete pure substance provides a correct description of the experimental evidence.

Studies on physicochemical properties of the eutectic and monotectic in the urea—p. chloronitrobenzene system

The phase diagram of an organic analog of a nonmetal—nonmetal-type system involving urea and p. chloronitrobenzene shows the formation of a eutectic (0.982 mole fraction of p. chloronitrobenzene) and a monotectic (0.020 mole fraction of p. chloronitrobenzene) with a liquid miscibility gap in the system. The linear velocity of crystallization ( v) data determined at different undercoolings ( ΔT) by measuring the rate of advance of an interface in a capillary obey the Hillig—Turnbull equation, v = u( ΔT) n , where u and n are constants depending on the solidification behaviour of the materials involved. From the enthalpy of fusion of the pure components, the eutectic and the monotectic, enthalpy of mixing, excess thermodynamic functions, entropy of fusion and interfacial energy were calculated. Optical microphotographs of the eutectic and monotectic give their characteristic features.

A contribution to the kinetics of γ → αm transformation in Fe

The kinetics of γ → α m transformation in pure Fe have been determined in relation to the transformation interface velocity V and the driving force P (i.e. the difference in Gibbs free energy between parent and product phases) associated with the structural transformation. An experimental device for the implementation of the unidirectional transformation technique was constructed to measure V as a function of the interface temperature T. Velocities calculated with the Turnbull equation and an estimated value for the diffusion coefficient at the migrating interface are in good agreement with the measured velocity values.

On the solute redistribution at thermally activated phase transition processes I. Theory

The main problem of the paper is the nature of the thermally activated phase transitions processes. A set of equations, based on the classical Turnbull equation for the migration of the phase boundary interface and the assumption that the system undergoes phase transition with minimal loss of energy, are obtained. The derived equations link together the processes of solute redistribution between the growing and the initial phases with the new phase growth rate. It can be shown that the equations so obtained are consistent with the ones obtained until now. In some cases the already existing equations are particular cases of the one derived in the present paper. The equations so obtained solved together with the heat and mass transport equations determine explicitly the process of the new phase growth.

Chemistry of Organic Eutectics: p-Phenylenediamine–m-Nitrobenzoic Acid System Involving the 1:2 Addition Compound

Abstract The phase diagram of p-phenylenediamine–m-nitrobenzoic acid system, determined by the thaw-melt method, show the formation of two eutectics and a 1:2 addition compound. The linear velocity of crystallization of pure components, eutectics and addition compound, measured by determining the rate of movement of growth front in a capillary, suggests that crystallization data obey the Hillig–Turnbull equation. Using experimental values of heats of fusion, determined by the DTA method, entropy of fusion, heat of mixing and excess thermodynamic functions were calculated and the results are explained on the basis of cluster formation in the melts. Microscopic studies reveal that the eutectics have different characteristics microstructures as compared to those of parent components. X-Ray diffraction data suggest that there is preferential ordering of atomic planes in the formation of the eutectics.

Some physicochemical studies on organic eutectics and 1:1 addition compound; p-phenylenediamine – benzoic acid system

The phase diagram of p-phenylenediamine – benzoic acid system, determined by the thaw–melt method, shows the formation of two eutectics and a 1:1 addition compound. The linear velocity of crystallization of pure components, eutectics and addition compound, determined by measuring the movement of growth front in a capillary, suggests that crystallization data obey the Hillig–Turnbull equation. Using experimental values of heats of fusion, entropy of fusion and excess thermodynamic functions were calculated and the results are explained on the basis of cluster formation in the melts. X-ray diffraction data infer that these eutectics are not simply the mechanical mixture of the two components and there is preferential ordering of atomic planes during their formation. The infrared spectral studies suggest the formation of intermolecular hydrogen bonding between the components forming the molecular complex. Keywords: organic eutectics, growth kinetics, phase diagram, thermochemistry, X-ray diffraction studies.

Thermal, mechanical and spectral studies of some organic charge-transfer complexes

The thermal, mechanical and spectral properties of complex formed by picric acid with naphthalene and anthracene respectively have been studied using phase-diagram, linear velocity of solidification, degree of undercooling, fracture value, modulii of elasticity and IR, UV-visible spectral measurements. The phase-diagrams show that the 1:1 molecular complexes which are formed in these systems are stable in the solid state and remain intact in the molten state. The kinetics of solidification in both follows the Hilling and Turnbull equation and the observed kinetic data suggest the Winegard et al, mechanism for the solidification phenomena in the two complexes. The experimental and the theoretically calculated values of heats of fusion were compared. These properties of the pure components and the complexes were studied in the light of molecular interactions which play an important role in deciding the crystal structure of binary organic systems with the formation of congruent melting compounds having structures consisting of infinite stacks of alternate donor and acceptor molecules.