Related papers: The generalized Lindemann melting coefficient
It is commonly believed that melting occurs when mean square displacement (MSD) of a particle of crystalline solid exceeds a threshold value. This is known as the Lindemann criterion, first introduced in the year of 1910 by Lindemann.…
Melting is analyzed dynamically as a problem of localization at a liquid-solid interface. A Lindemann-like criterion of melting is derived in terms of particular vibrational amplitudes, which turn out to equal a universal quotient (about…
Melting is well understood in terms of the Lindemann criterion, essentially stating that crystalline materials melt when the thermal vibrations of their atoms become such vigorous that they shake themselves free of the binding forces.…
It is demonstrated that the Lindemann's criterion of melting can be formulated for two-dimensional classical solids using statistical mechanics arguments. With this formulation the expressions for the melting temperature are equivalent in…
Since more than 100 years, melting is thought to be governed by the Lindemann criterion. It assumes that a crystal melts when, upon heating, the growing atomic vibration amplitudes become sufficiently large to destabilize its crystalline…
We propose a general formula for the melting temperature of metals in terms of electronic mass, electronic number, and nearest-neighbor lattice distance. We derive it from the instability of the transverse phonon in the solid phase, using…
The Lindemann criterion is reformulated in terms of the average shear modulus $G_c$ of the melting crystal, indicating a critical melting shear strain which is necessary to form the many different inherent states of the liquid. In glass…
Iron represents the principal constituent of the Earth's core, but its high-pressure melting diagram remains ambiguous. Here we present a simple analytical approach to predict the melting properties of iron under deep-Earth conditions. In…
A revisiting of the Lindemann criterion under the recently established minimal viscosity formulation is proposed which uncovers intriguing insights into the melting process. The approach suggests that melting involves competition between…
The prediction of the melting curve of metals by extrapolation to high pressures and temperatures based on the Lindemann-Gilvarry criterion (LG) assuming harmonic Debye solid is presented. The LG formulation uses the bulk modulus B and its…
The effects of flexibility and chemical composition in the variation of the glass transition temperature are obtained by using the Lindemann criteria, that relates melting temperature with atomic vibrations. Using this criteria and that…
Recently, a universal relation between the thermal expansion coefficient of glasses $\alpha_g$, their glass-transition temperature Tg, and the so-called fragility index m of the corresponding supercooled liquid state was found to be valid…
A phenomenological criterion for the superfluid transition is proposed, which is similar to the Lindemann criterion for the crystal melting. Then we derive a new formula for the critical temperature, relating $T_{\lambda}$ to the mean…
Using the Lindemann criterion, we analyzed the quantum and thermal melting of electronic/excitonic crystals recently discovered in two-dimensional (2D) semiconductor moir\'e patterns. We show that the finite 2D screening of the atomically…
A microscopic picture of the ``preparation'' of a crystal to the transition to liquid state at the approach to melting temperature is proposed. Basing on simple crystallogeometric considerations and the analysis of the computational results…
In the framework of melting as a dislocation-mediated phase transition we derive an equation for the pressure dependence of the melting temperatures of the elements valid up to pressures of order their ambient bulk moduli. Melting curves…
Although usually considered as a technique for predicting electron states in dense plasmas, atom-in-jellium calculations can be used to predict the mean displacement of the ion from its equilibrium position in colder matter, as a function…
We set up simple harmonic lattice models for elastic fluctuations in bcc and fcc lattices and the excitation of dislocations and disclinations. From these we derive, in a lowest approximation, universal formulas which predict melting…
The ratio of the mean square amplitude root of thermal vibrations and the interatomic distance is a universal constant dls at the melting temperature Tm. The classical Gibbs free energy change completed by a volume energy saving els (or…
The exact Lifshitz theory is utilized for the systematic calculation of the retarded room temperature Hamaker coefficients between 26 identical isotropic elemental metals embedded in vacuum or pure water. The full spectral method,…