Lindemann Melting Criterion Research Articles

An extension of atomic mean square displacement method for calculating melting temperatures in II-VI compounds

Understanding how solids melt and determining their melting temperatures is of great significance for studying the properties of materials. Based on the main idea of Lindemann's melting criterion and the first-principles calculation of density functional theory, we proposed the atomic mean square displacement method to predict the melting temperature of the material. In this paper, the application range of this method for calculating melting temperature is extended. 8 kinds of Ⅱ-Ⅵ compounds were selected as verification objects. The results show the accuracy of our method in predicting the melting temperature of Ⅱ-Ⅵ compounds.

A Method for Predicting the Melting Temperature of Ionic Compounds.

Predicting the melting temperature of materials has always been a topic of great concern. This article proposes an alternative model for determining the melting temperature of materials based on the main idea of the Lindemann melting criterion combined with the first-principles calculations of density functional theory. To verify the accuracy of the melting model, this article selected typical ionic crystals of MgO and 10 alkali metal halides as the validation objects. The calculation results indicate that the melting temperature of the MgO crystals and I-VII compounds is in good agreement with the experimental results.

Investigation of some thermal properties of iron and chromium-based core-shell nanowires

Fe and Cr based core–shell nanowires (CSNWs) are modeled as cylindrical structures in which the atoms are arranged in a bcc crystal structure. Two different sizes with diameters of 2.5 nm and 4.5 nm for nanowires (NWs) are created and their lengths are set as four times their diameters. Their structural and thermodynamic properties are investigated through the molecular dynamics (MD) simulation technique in the canonical (NVT) statistical ensemble implemented in the open-source Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software package. Atomic interactions between the atoms are described by using the many-body potentials based on the Embedded Atom Model (EAM). The melting temperatures of the NWs have been determined by investigating the behavior of the potential energy, specific heat capacity, radial distribution function, Lindemann melting criterion, the mean square displacement, and diffusion coefficients as a variation of temperature. The same melting temperatures are acquired from all these temperature-dependent physical properties for all NWs considered in this study. To the best of our knowledge, our simulation results are presented for the first time in this work and have the potential to guide experimental studies.

The influence of boundary scattering phase shift on melting behavior of nanoparticles

Based on the Lindemann melting criterion and the lattice dynamical approach, we analytically estimated the melting temperature of nanoparticles with emphasis on the influence of the boundary scattering phase shift parameter α . With the decrease of size, the estimated relation shows that the melting temperature of free standing like nanoparticles will decrease, and the melting temperature of embedded nanoparticles will increase. The increase or decrease of the melting temperature depends on the boundary scattering phase shift parameter. The gradual change of parameter α from − 1 to 1 corresponds to the transition of the surface or environment of nanoparticles from the free boundary condition to the fixed boundary condition. Our analytical estimation qualitatively explains the experimental data, and its predictive capability will help the design of nanoparticles. • Based on the Lindemann criterion, An analytical estimation for size-dependent melting temperature of nanoparticles by lattice dynamical method will be given. • Our theoretical result can fit experimental data of nanoparticles in different environments qualitatively. • A simple boundary scattering phase shift is used to characterize the environment of nanoparticles.

Theoretical prediction of melting curves of gold and silver up to pressure 150 GPa

We investigate melting curves of gold and silver thanks to the statistical moment method in quantum statistical mechanics and the modified Lindemann melting criterion. Numerical calculations have been performed for face-centered cubic (fcc) gold and silver metals up to pressure 150 GPa. Our results are compared with available experimental data and ab initio molecular dynamics simulations where possible. We show that theoretical melting line of gold goes along with recent X-ray diffraction measurements reported by Weck et al. up to pressure more than 110GPa. For silver, our work virtually coincides with the quantum molecular dynamics melting curve which is a combination of fcc and body-centered cubic (bcc) segments freshly implemented by Baty et al. At the pressure 94.2 GPa of the predicted fcc–bcc-liquid triple point of silver, our calculated melting temperature is 4302 K that is only about 2% difference from the prediction of Baty et al. This research proposes a relatively simple approach made from the modified Lindemann criterion and the moment method for predicting melting points of materials at high pressure.

The melting curves of tin, uranium, cadmium, thallium and indium metals under pressure

The pressure effects on melting lines of tin, uranium, cadmium, thallium and indium metals have been studied by using the Lindemann melting criterion, the recent well-established Grüneisen parameter, and the third order Birch-Murnaghan equation-of-state up to pressure of 140 GPa. The analytic expression of volume-dependent melting temperature has been derived. Our results are in good agreement with laser-heating diamond-anvil cell measurement but lower than recent shock compression work. This method provides a quick approach to estimate the melting point of tin metal under pressure. Our reported melting temperatures increase the database of high-pressure melting, and could be used to analyze and verify the future high-pressure dynamic shock compression as well as diamond-anvil cell static compression experiments.

Role of Static Displacements in Stabilizing Body Centered Cubic High Entropy Alloys.

The configurational entropy of high entropy alloys (HEAs) plays little role in the stabilization of one particular crystal structure over another. We show that disorder-induced atomic displacements help stabilize body centered cubic (bcc) structure HEAs with average valences <4.7. These disorder-induced atomic displacements mimic the temperature-induced vibrations that stabilize the bcc structure of group IV elemental metals at high temperatures. The static displacements are significantly larger than for face centered cubic HEAs, approaching values associated with the Lindemann criterion for melting. Chemical disorder in high entropy alloys have a previously unidentified, nonentropic energy contribution that stabilizes a particular crystalline ground state.

Investigation of pressure effects on melting temperature and shear modulus of B1-LiF

The pressure effects on melting temperature and shear modulus of the B1 phase of LiF are investigated based on a semi-empirical approach. We derived analytical expressions of these quantities as functions of pressure. Numerical calculations are performed for LiF up to pressure of 100 GPa. Our work reveals that the melting curve derived from the Simon-Glatzel equation shows a high gradient at pressure below 30 GPa and rather quickly flattens with the increasing of pressure in accord with experiments, much more precise than the calculations based on the Lindemann melting criterion and the power-law of Grüneisen parameter. Meanwhile, the pressure-dependent shear modulus derived from Burakovsky’s model and the power-law of Grüneisen parameter shows a good agreement with ab initio calculations. Our results provide a further supplement to the database of high-pressure melting temperature and shear modulus of LiF. The present work could be used to verify as well as analyze the future high-pressure experiments.

The generalized Lindemann melting coefficient

Lindemann developed the melting temperature theory over 100 years ago, known as the Lindemann criterion. Its main assumption is that melting occurs when the root-mean-square vibration amplitude of ions and atoms in crystals exceeds a critical fraction, η of the inter-atomic spacing in crystals. The Lindemann coefficient η is undefined and scientific papers report different η values for different elements. Here we present previously unobserved data trends pointing to the fact that the Lindemann coefficient could be linked to the periodic groups of the periodic table, having an exact value for each element belonging to a given periodic group. We report 12 distinctive Lindemann coefficient values corresponding to 12 groups of the periodic table containing solid elements with identifiable melting temperature. Using these vales, the recalculation of the melting temperatures indicates a good match to the experimental values for 39 elements, corresponding to 12 out of 15 periodic groups. This newly observed result opens up the possibility of further refining the Lindemann melting criterion by stimulating analytical studies of the Lindemann coefficient in the light of this newly discovered result.

Lindemann melting criterion in two dimensions

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 three and two dimensions. Moreover, in two dimensions the Lindemann's melting criterion essentially coincides with the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young melting condition of dislocation unbinding.

High-pressure Melting Curves of and Phases of Iron

Statistical moment method (SMM) has been applied in combination with Lindemann melting criterion to investigate pressure effects on melting temperature of iron. Melting curves of phase with body-centered cubic structure and phase with face-centered cubic structure of iron have been derived up to pressure 13 GPa and 90 GPa, respectively. This work shows that melting curves of these two phases of iron are increasing functions of pressure, and the higher the pressure is the lower the slopes of melting curves are. Our results are compared with those of available experimental data to verify the developed theory. The efficiency of the SMM on the investigation of melting temperatures of and phases of iron allows us to believe that the present SMM scheme can be developed extensively to determine melting temperatures of other phases of iron as well as other materials.

Size-dependent melting behavior of nanowires in lattice dynamical approach

Abstract An analytical estimation is presented for the melting point of nanowires by acoustic phonon spectrum and phonon boundary scattering phase shift. The estimation is developed within the context of Lindemann melting criterion. The estimation coincides with previous researches in the melting temperature satisfying a reciprocal linear relation with the diameter of wires, but it provides a new logarithmic term in numerator. We verified this estimation against experimental results, and show it as a simple and valuable means for design of nanowires.

On the Calculation of the Debye Temperature and Crystal–Liquid Phase Transition Temperature of a Binary Substitution Alloy

A method of estimating the interatomic pair interaction potential parameters for a binary substitution alloy with consideration for the deviation of its lattice parameter from the Vegard law is proposed. This method is used as a basis to calculate the Debye temperature and Gruneisen parameters of a SiGe alloy. It is shown that all these function nonlinearly variate with a change in the germanium concentration. Based on this technique and Lindemann's melting criterion, a method for calculating the liquidus and solidus temperatures of a disordered substitution alloy is proposed. The method is tested on the SiGe alloy and demonstrates good agreement with experimental data. It is shown that when the size of a nanocrystal of a solid substitution solution decreases, the difference between the liquidus and solidus temperatures decreases the more, the more noticeably the nanocrystal shape is deflected from the most energetically optimal shape.

О вычислении температуры Дебая и температуры фазового перехода кристалл-жидкость для бинарного сплава замещения

AbstractA method of estimating the interatomic pair interaction potential parameters for a binary substitution alloy with consideration for the deviation of its lattice parameter from the Vegard law is proposed. This method is used as a basis to calculate the Debye temperature and Grüneisen parameters of a SiGe alloy. It is shown that all these function nonlinearly variate with a change in the germanium concentration. Based on this technique and Lindemann's melting criterion, a method for calculating the liquidus and solidus temperatures of a disordered substitution alloy is proposed. The method is tested on the SiGe alloy and demonstrates good agreement with experimental data. It is shown that when the size of a nanocrystal of a solid substitution solution decreases, the difference between the liquidus and solidus temperatures decreases the more, the more noticeably the nanocrystal shape is deflected from the most energetically optimal shape.

Volume and pressure-dependent thermodynamic properties of sodium

In this work, the volume and pressure effects on thermodynamic quantities including Grüneisen parameter and melting temperature of sodium have been studied of to 65 GPa. The volume dependence of Grüneisen parameter of sodium has been firstly analyzed. Based on this result and the Lindemann criterion of melting we derived the analytical expression of volume-dependent melting temperature. Combining with Vinet equation-of-state, the melting curve of sodium at high pressure has been proposed. Numerical calculations were performed for solid sodium up to pressure 65 GPa. Theoretical calculations are compared with available experimental data showing the good and reasonable agreements in the pressure range 0–30 GPa. This research proposes the good volume- and pressure-dependent Grüneisen parameter as well as the potential of Lindemann criterion approach on predicting high-pressure melting of materials.

Logarithmic Size-Dependent Melting Temperature of Nanoparticles

This work describes the logarithmic term in the size-dependent melting temperature of nanoparticles. The Lindemann melting criterion and the thermal phonon contribution are intended primarily as a clear approach for our study of melting temperature. The ratio of the melting temperature (Tmn) of a nanoparticle to the bulk melting temperature (Tmb) is numerically evaluated up to the order of the inverse of the size L of a nanoparticle: Tmn/Tmb = 1 – A/L. We show that the coefficient A is not a constant but has a logarithmic part. The logarithmic term is the dominate term in the factor A(L). Our investigation suggests the behavior of the size-dependent melting is Tmn/Tmb = 1 – (B + C ln L)/(L – 2ls) where B and C are constant factors and ls is the number dimension of the surface layers reconstructed or premelted. The results present a challenge to reach a higher resolution in future thermal experiments in order to distinguish ln L/L behavior from the previously accepted pure 1/L behavior.

Structural evolution of proteinlike heteropolymers.

The biological function of a protein often depends on the formation of an ordered structure in order to support a smaller, chemically active configuration of amino acids against thermal fluctuations. Here we explore the development of proteins evolving to satisfy this requirement using an off-lattice polymer model in which monomers interact as low resolution amino acids. To evolve the model, we construct a Markov process in which sequences are subjected to random replacements, insertions, and deletions and are selected to recover a predefined minimum number of solid-ordered monomers using the Lindemann melting criterion. We show that polymers generated by this process consistently fold into soluble, ordered globules of similar length and complexity to small protein motifs. To compare the evolution of the globules with proteins, we analyze the statistics of amino acid replacements, the dependence of site mutation rates on solvent exposure, and the dependence of structural distance on sequence distance for homologous alignments. Despite the simplicity of the model, the results display a surprisingly close correspondence with protein data.

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.

Amorphization of oxides under irradiation with fast neutrons

A variant of the solid-state radiation amorphization as a result of accumulation of the critical concentration of defects in the crystal has been considered using the example of oxides with the garnet and perovskite structures irradiated by fast neutrons. It has been shown that such defects can be antisite defects, the formation of which leads to considerable static displacements from the equilibrium sites of nearest ions and, consequently, to the loss of stability of the crystalline structure. The dependences of the root-mean-square displacements of oxygen ions on the concentration of the antisite defects are constructed based on the analysis of the experimental data. It has been established that the so-called critical concentrations of antisite defects, at which the spontaneous amorphization occurs, differ for oxides with the garnet and perovskite structures. As the criterion of the spontaneous radiation amorphization, it is proposed to consider the critical static displacement of the ions, which is identical for studied oxides and equal to ∼0.28 A, or ∼0.14 in fractions of interatomic distances, which is close to the well-known Lindemann melting criterion.

Short range order in anomalous liquid metals

Liquid metals with anomalous physical properties such as increasing sound velocity with temperature or density anomalies, exhibit a complex structure in their one dimensional experimental diffraction patterns. Typically, their radial distribution functions are characterized by an asymmetric first peak and a subsidiary peak or shoulder on the right hand side of the first main peak. It has been hypothesized that the complex structure is associated with short range ordering the liquid. Specifically in the liquid pnictides, it has been proposed that such order may be associated with the underlying solid A7 structure. We present an analysis of the short range order in liquids using a modified quasi-crystalline model of liquid structure. This model is shown to fit the experimental radial distribution function very well and to reproduce the experimentally observed structure factor. Using this model we find that the short range order in the liquid pnictides is dominated by an A7-like structure with two types of bonds, in close agreement with the underlying solid phase. The existence of two bond lengths is necessary within this model to explain the asymmetry in the first peak as well as the change in coordination number along the pnictide series. The quasi-crystalline model is discussed and shown to correlate with the Lindemann melting criterion.