Dislocation Theory Of Melting Research Articles

Melting of short-chain polymers

The melting of paraffin layers is investigated in terms of the two-dimensional dislocation theory of melting. The theory is strictly applicable to short paraffin chains. For longer chains the melting criterion is modified to include the reduction of melting point due to chain flexibility (kinking). The results are found to be in satisfactory agreement with experiment.

Pressure dependence of melting temperature in alkali halides

We present an estimate of the pressure dependence of melting temperature in 16 alkali halides. We use the formulations due to Gilvarry and Lindemann, and due to Stacey and Davis for calculating the pressure derivative of melting temperature. The data for thermal expansivity, bulk modulus and the Grüneisen parameter used in calculations have been determined corresponding to melting temperature of alkali halides. The results obtained from the two models are compared with the available experimental data. It has been discussed that both of the quoted theories rely on the dislocation theory of melting, which gives a satisfactory description of the process of melting for alkali halides.

Dislocation melting of iron and the temperature of the inner core boundary, revisited

Summary The melting point Tm of iron at conditions of the Earth's inner core boundary (ICB) has been calculated from the dislocation theory of melting in metals. These calculations take into account the effects of pressure at ICB conditions and of possible freezing point depression resulting from dilution of pure iron in the outer core. Monte Carlo calculations have been used to estimate the uncertainties introduced by uncertainty in the geophysical parameters that are used in the calculations. With this approach Tm of pure e-Fe at a pressure of 330 GPa and without freezing point depression is 6160 ± 250 K, and 6110 K for a 1000 K freezing-point depression, Tm of pure y-Fe is not significantly different; these values agree well with shock-wave determinations of Tm. The estimated temperature of the ICB is lower by the freezing point depression, perhaps by 500-1000 K.

Spatial structure of solid-liquid interface near melting temperature

In this paper we discuss the solid-liquid interface which emerges from our dislocation theory of melting. We analyse how the dislocation order parameter varies across this interface and study the stability o the obtained solutions. We calculate the correlation radius and discuss physical characteristics of the system as functions of the coupling parameter.

Dislocation field fluctuations in the theory of melting

Abstract We determine dislocation field fluctuation effects in the free energy for a gas of planar dislocations embedded in an elastic medium. Our one-loop calculation confirms the two-phase character of the dislocation theory of melting.

Melting curve of iron under pressure

Abstract The dislocation theory of melting is generalized by considering the effect of pressure. The Kraut-Kennedy law is derived by using this generalized approach and applied to iron. The theoretical result is in good agreement with experiment

A dislocation model for the viscosity of water

A dislocation model for the shear viscosity of water is proposed, based upon the dislocation theory of melting and liquid state. This model, studied extensively within the last years in relation to phase transitions in two-dimensional systems, makes rigorous use of the similarity between the structure of a liquid and that of a crystalline solid. Viscous flow in water due to slip of dislocation loops is proposed as an alternative point of view to the hole theories and the cluster models of hydrogen bonded molecules. The model correctly yields the temperature dependence of the viscosity at normal pressure between melting and boiling point.

The physics of melting

The dislocation theory of melting, according to which the transition is supposed to proceed through a sudden proliferation of dislocations, is discussed, and recent supporting evidence is reviewed. An attempt is made to relate the dislocation-generation process to the nature of the energy barriers involved in the fundamental modes of motion in an assembly of atoms. This leads to an atomic-level picture of the transition which links it to a bifurcation instability.

Cooperativity in the dislocation theory of melting

THE interesting behaviour of the shear moduli of alkali halides in the vicinity of the melting transition was recently noted by Tallon, Robinson and Smedley1. These parameters do not fall to zero at the crystal melting temperature, Tm, as proposed by Born2, but a zero value is attained on extrapolating to the dilation corresponding to the liquid at Tm. It is suggested that ‘melting occurs when a solid can transform isothermally to a state of zero shear modulus’, and that a two-phase melting model follows. Although they do not deal with the microscopic processes occurring along the melting isotherm their discussion does have a bearing on the important role of cooperative effects. We comment here both on the specific points raised by their analysis and the question of cooperativity in the dislocation theory of melting.

Melting of the two-dimensional Wigner lattice

It is shown that the dislocation theory of melting gives a value for the melting temperature of a two-dimensional electron solid that is in good agreement with the value obtained in the molecular dynamics calculations of Hockney and Brown (1975).

A theory of melting in liquid crystals

A dislocation theory of melting is proposed to explain the smectic B to smectic A phase transition observed in liquid crystals. Besides providing a good description of the quasi-two-dimensional smectic phases, it establishes a new theoretical connection between the transition temperature and the elastic constants, as well as predicting the latent heat. We suggest that the finite shear viscosity of the smectic A phase may be understood in terms of the existence of thermodynamically stable isolated dislocations in the layer periodicity.

Molecular dynamics studies of melting: III. Spontaneous dislocation generation and the dynamics of melting

Abstract The dislocation theory of melting has been further investigated by means of dynamical computer experiments. An f.c.c. Lennard-Jones solid was taken through the melting transition, and it was found that the process is initiated by thermal generation of tiny dislocation loops of the Shockley type. The dislocation density was found to increase steadily during the transition, producing ultimately a system consisting of dislocation cores preferentially arranged as dipole loops, and predominantly in the screw orientation. A simple geometrical interpretation of Lindemann's rule emerges from the model.

Molecular dynamics studies of melting: II. Dislocation density and thermodynamic functions

Abstract The dislocation theory of melting has been investigated by means of a pseudostatic computational model, employed previously to demonstrate the connection between dislocation density and the pair distribution function. The model has been used to investigate the changes in certain thermodynamic functions across the melting transition. Random dislocations were generated in an otherwise perfect f.c.c. model, according to the elastic equations, and the atoms in the core regions were subsequently permitted to relax. From atomic configurations representing crystals saturated with perfect dislocations, values for the latent heat of fusion, the entropy of fusion, and the melting temperature were obtained and found to be in reasonable agreement with experimental results for the noble gases. It is found that this agreement could be even better if the saturation was caused by partial dislocations of the Shockley type.

Thermodynamic study of theHe4monolayer adsorbed on Grafoil

A calorimetric and vapor-pressure study of the behavior of $^{4}\mathrm{He}$ adsorbed on Grafoil in the temperature range 4 to 15 K is reported. These results have been combined with preexisting low-temperature heat-capacity data to form a complete thermodynamic description of the film. The Grafoil substrate evidently consists almost entirely of basal-plane graphite, with only a small fraction of energetically distinct adsorption sites. Techniques of semiempirical modelling are introduced which make it possible to eliminate the effects both of these inhomogeneities and of the formation of second and higher layers, so that a detailed picture may be formed of the behavior of the $^{4}\mathrm{He}$ first layer on an ideal graphite substrate. The binding energy of a $^{4}\mathrm{He}$ atom on the graphite substrate is reported to be 143 \ifmmode\pm\else\textpm\fi{} 2 K, with a first excited state at 89 \ifmmode\pm\else\textpm\fi{} 3 K. A lattice-gas ordering transition occurs near 3 K at a coverage corresponding to one $^{4}\mathrm{He}$ atom for every three carbon hexagons in the graphite surface, and is used as a fiducial for calibrating our system relative to those of previous investigators. At both higher and lower densities the film seems little influenced by the crystal structure of the substrate. Particular attention is given to the high-coverage low-temperature region, which has been identified as a two-dimensional (2D) solid bounded by a melting-phase transition. The available data are combined with two-dimensional elastic theory to establish the presence of low-lying transverse sound modes, thus confirming the solidlike character of this medium. The behavior of the thermodynamic variables of state through the observed transition is also presented. The theoretical implications of the existence of a 2D solid are discussed, together with a dislocation theory of melting which gives rise to the well-known three-dimensional Lindemann empirical melting formula without an adjustable parameter. It is shown that at very low coverage the film does not form a low-density solid as previously suggested, but is rather dominated by substrate inhomogeneities. At intermediate temperatures and coverages the film is a fluid which is accurately described if a leading-order quantum virial correction is made to the 2D ideal-gas equation of state.

Molecular dynamics studies of melting : I. dislocation density and the pair distribution function

Abstract The dislocation theory of melting has been investigated by means of a pseudostatic computational model, in which random dislocations were generated according to the elastic equations, allowance being made for relaxations in the core regions. It is found that when the dislocation density reaches a certain value, a liquid-like pair distribution function is obtained. The model also gives an estimate of the formation volume of an ‘average dislocation’. Furthermore, the model gives a reasonable value for the volume expansion of melting, at a saturation density of dislocations corresponding to the beginning of core overlap.

Radial correlation functions of metallic melts calculated from structural models of the liquid state

Abstract Two models for the possible structure of metallic melts are proposed which were suggested by a dislocation theory of melting and connect the atomic structure of the liquid to that of the solid phase. One of the models is based on planar order such that the preferred plane has the order of the most prominent slip plane of the corresponding crystal. In the other model, linear order is assumed with the order of atomic rows parallel to the preferred direction taken to be the order of the atomic rows parallel to the preferred slip direction in the solid. Radial correlation functions are computed from both of the models for molten lead, sodium, thallium, mercury, indium and tin, and are compared with the corresponding experimental radial distribution functions. In each case, excepting tin, good agreement is found for at least one of the models.