On the Lindemann law of melting of solids

The Lindemann law of melting has been investigated by lattice dynamics. It is found that the law is not universal so far as the Lindemann parameter is concerned, and is structure and interaction dependent. This holds separately for each class of solids having similar structure and inter-particle interaction; i.e. the parameter has one value for all solids possessing the same structure as well as interparticle interaction.     

Structure and melting of Morse solids

Isothermal-isobaric ensemble Monte Carlo simulations are used to study the melting of Morse solids. At a given pressure, the temperature at which the solid ceases to be metastable and also the fractional changes in density and potential energy increase with decreasing range of the Morse pair potential. The structural properties of the liquid and solid phases vary significantly with the range. The longer range, softer potentials are associated with increased densities and cohesive energies in both the solid and liquid phases. The extent of local disorder associated with lattice sites in the solid phase, as measured by the Lindemann and bond orientational order parameters, increases with increasing range of the pair potential.     

Pressure dependence of the melting temperature of rare-gas solids

According to Lindemann's law and the Debye model and with the assumption that the volume derivative [Formula: see text] of the Grüineisen parameter [Formula: see text] is a constant depending on the material, we present a new expression for the analysis of the experimental data for the melting temperature of solids under a high pressure. The test on rare-gas solids (Ne, Ar, Kr and Xe) shows that the calculated results are in good agreement with the corresponding experimental data.     

Effect of intensity modulation on radiation-induced melting and vaporization of solids

Linear response of steady-state melting and of evaporation processes to the modulation of radiation intensity is considered in the framework of a Stephan-like approach. It is shown that resonance behaviour of the surface temperature pertinent to the evaporation process persists in the case where the evaporation front is preceded by a melting transition.     

The melting line for ethylene on graphite

Using the minimum in the nuclear magnetic spin-lattice relaxation time versus temperature as an indicator of melting we have mapped out the solid-fluid phase boundary for ethylene adsorbed on graphite. At low coverages the ethylene forms a self-bound monolayer solid with a melting temperature of about 68 K. The molecules in the solid retain orientational mobility down to 55 K, the lowest temperatures explored.     

Analog of the Lindemann melting criterion for softening of vitreous solids

A condition for the glass-liquid transition that is similar to the Lindemann melting criterion is suggested.     

Relationship between crystalline order and melting mechanisms of solids

The mechanism for homogeneous nucleation of the liquid phase in Lennard-Jones solids is studied by combining the Landau free energy approach with some of the methodology developed to characterise transition path ensembles. The second-order bond orientational order parameter, Q ₆ which indexes the overall degree of crystalline order, is shown to provide a dynamically significant collective coordinate describing the melting process. Trajectories generated from configurations sampled in the vicinity of the maximum in the Landau free energy curve, F(Q ₆), are shown to have equal likelihood of teminating in either the solid or liquid-like free energy minima. It is also demonstrated that Q ₆ is necessary but not sufficient as a dynamical coordinate to describe melting and it is necessary to explore possiblities for additional coordinates which are critical for initiating melting. Our sudy suggests that the additional coordinates for describing the melting process would be some type of localised defect, much smaller in spatial extent than the size of the critical nucleus predicted by classical nucleation theory.      

First-principles simulations on the nature of the melting line of sodium

We report a first-principles molecular dynamics study of the reentering behavior that has been recently observed experimentally in the melting line of bcc sodium [Gregoryanz et al., Phys. Rev. Lett. 94, 185502 (2005)10.1103/PhysRevLett.94.185502]. Our results show the liquid phase to be more compressible than the solid phase, and to remain so at high pressures, eventually becoming denser than the solid phase and hence causing the change of slope in the melting line from positive to negative. The maximum of the melting line thus occurs without any accompanying first-order liquid-liquid phase transition.     

Hard-core bosons on the kagome lattice: valence-bond solids and their quantum melting

Using large scale quantum Monte Carlo simulations and dual vortex theory, we analyze the ground state phase diagram of hard-core bosons on the kagome lattice with nearest-neighbor repulsion. In contrast with the case of a triangular lattice, no supersolid emerges for strong interactions. While a uniform superfluid prevails at half filling, two novel solid phases emerge at densities rho=1/3 and rho=2/3. These solids exhibit an only partial ordering of the bosonic density, allowing for local resonances on a subset of hexagons of the kagome lattice. We provide evidence for a weakly first-order phase transition at the quantum melting point between these solid phases and the superfluid.     

Unifying the criteria of elastic stability of solids

The elastic stability criterion formulated by Born is based on the convexity requirement of the equilibrium free energy F of a stress-free crystal under small strain fluctuation, that demands the elastic constant tensor C to be positive definite, |C| > 0. For a crystal subject to an external stress, Hill specifies that for the crystal to be stable, the difference between its internal energy change δE and the work done to the system δW must be positive, i.e. δE - δW > 0. Polanyi, Frenkel, and Orowan proposed a different stability criterion based on stress increment for a loaded system, τ(ε + Δε) - τ(ε) > 0 until the limit is reached at dτ/dε = 0. Although known empirically, the formal connection between the different criteria has not been established rigorously. Using finite deformation theory, we show quite simply that the different formulations of the stability criteria originate from the same necessary condition for the convexity of the free energy of the system subject to external loading, f = F - W. However, in practice caution must be taken in implementation of the different criteria; they may lead to quite different results, especially when stability bifurcation occurs.     

Excitonic line shapes of disordered solids

The optical absorption for a disordered one-dimensional excitonic solid has been studied by numerical methods. We have considered both Gaussian and binary energy fluctuations. Our results indicate that the physical properties associated with the spectra are selfaveraging. Results obtained on a single realization of random variables are consistent with recent ensemble averaged results obtained numerically on smaller samples. We also show that for binary disordered solids in the band splitting limit, spectra are dominated by cluster effects and can not be described through analytical treatments.     

Disorder driven melting of the vortex line lattice

The 3D XY model with random in-plane couplings is simulated to model the phase diagram of a disordered type II superconductor as a function of temperature T and randomness strength p for fixed applied magnetic field. As p increases to a critical p(c), the first order vortex lattice melting line turns parallel to the T axis, continuing down to low temperatures, rather than ending at a critical point. Above p(c) preliminary results suggest the absence of a phase coherent vortex glass.     

Dynamic loading of solids with a negative slope of the melting curve

The results of experiments on shock-wave loading of materials distinguished by a negative slope of the melting curve are reported. An anomalous situation is possible, when the material is melted by a shock wave and then a fast transition to the solid phase takes place in the expansion wave. The newly formed phase should be a nanostructural formation of the given element. Experiments confirmed the existence of the transition from the liquid to the solid phase of the nanostructural modification.     

Theoretical melting curves for cubic solids at high pressure

The Lindemann law, the fourth-order anharmonic equation of state and a model for the volume dependence of the Grüneisen coefficient in cubic crystals are used to derive temperature-strain-pressure relations at melting. The relations depend for their application on knowing the values of fourth-order elastic parameters which are not measured experimentally. It is shown that these values can be estimated from melting data at low pressure. A comparative study of the results with previous determinations obtained from shock-wave data is given for copper, silver and gold. Finally, the theoretical fourth-order melting curves of the three selected metals are calculated using both the Lagrangian and Eulerian strain measures.