Application of the embedded atom model to liquid metals: Liquid mercury

The procedure is suggested for the calculation of the embedded atom potential for a liquid metal, which involves the use of diffraction data on the structure of material in the vicinity of the melting point. The procedure is used for mercury at temperatures from 293 to 1803 K. The data on the structure of mercury at 293 K and the thermodynamic properties of mercury at 293 and 1673 K are used in selecting the parameters of embedded atom potential. The calculated critical temperature for mercury is close to the actual value of ～1750 K. The self-diffusion coefficients increase with temperature by the power law. The variation of the structure characteristics of liquid metal with the temperature increasing by several hundred degrees is described correctly. However, at temperatures above 1000 K, the predicted structure of models differs appreciably from the actual structure. These differences are explained by the dependence of the real potential of interparticle interaction of mercury on density during the metal-nonmetal transition occurring in the case of heating.     

Application of the embedded atom model to liquid metals: Liquid sodium

The procedure for the calculation of the embedded atom model (EAM) potential for liquid metal, which involves the use of diffraction data on the structure of material in the vicinity of the melting point, is applied to sodium. In fitting the parameters of EAM potential, use is made of the data on the structure of sodium at 378, 473, and 723 K, as well as on the thermodynamic properties of sodium at pressures up to 96 GPa. The use of the method of molecular dynamics (MD) and of the EAM potential produces good agreement with experiment as regards the structure, density, and potential energy of liquid metal along the p ? 0 isobar at temperatures up to 2300 K, as well as along the shock adiabat up to pressures of ～100 GPa and temperature of ～30 000 K. The melting temperature of bcc model of sodium with EAM potential is equal to 358 ± 1 K and close to real. The predicted value of bulk modulus at 378 K is close to the actual value. The self-diffusion coefficients under isobaric heating increase with temperature by the power law with exponent of 1.6546. The values of pressure, energy, heat capacity, and the temperature coefficient of pressure are calculated in a wide range of densities. The compression to 45–50% of normal volume causes a variation of the structure of liquid; this results in the emergence of atoms with a small radius of the first coordination sphere (～2.1 Å) and low coordination number, which form connected groups (clusters). Their concentration increases with decreasing volume and increasing temperature. The pre-peak of pair correlation functions, the height of which increases with heating, corresponds to these atoms. In the region of variation of the structure, the pressure decrease under isochoric heating follows the pattern of water anomaly.     

Optimal algorithm for constructing the embedded atom method potential for liquid metals

An optimal algorithm has been developed for calculating the embedding potential in the embedded atom method (EAM) with the aim of describing not only the temperature-dependent density of a liquid metal but also its energy up to its critical temperature. The algorithm is based on the unification of the form of the potential and calculation of its parameters from known density and energy data for the liquid metal. The basis of the algorithm is the use of least squares fitting of the pressure and energy in molecular dynamics simulations to data for a series of states of the liquid along an isobar. To describe liquid potassium, the pair contribution to the potential is represented by a power series in interparticle distance. Data on the properties of potassium at 343, 473, 723, 1000, 1500, 2000, and 2200 K were used. The embedding potential was expanded in terms of 1 − ρ, where ρ is the effective electron density in the EAM. In least squares fitting, fifteen equations were included: eight for the energy and seven for the pressure. The number of unknown coefficients was seven. Iterative calculations allow one to find optimal expansion coefficients and construct equilibrium models through molecular dynamics simulations. It is shown that the discrepancy in energy between simulations and the real metal at high temperatures can be eliminated by taking the electron excitation energy into consideration. The difference between the actual energy of a metal and the energy obtained in EAM simulations is very close to the contribution of the electron heat capacity.     

Electron contribution to energy of alkali metals in the scheme of an embedded atom model

The behavior of the energy of molecular dynamics models of alkali metals constructed using the embedded atom potential at high temperatures is discussed. Pair potentials and embedding potentials for lithium, sodium, potassium, rubidium, and cesium are presented as uniform analytical expressions. If the parameters of the potential of the embedded atom model (EAM) are selected based on the known dependence of the density of liquid metal on temperature, then, as temperature approaches the critical one, the actual energy increases faster than the energy of the models in all cases. The thermal contribution of electron gas to the energy of metal is considered as the cause of the discrepancy. It is shown that it is possible to eliminate the discrepancy between energies of models and the actual metal at high temperatures, if the energy of thermal excitation of electrons is taken into consideration. The difference between the actual energy of metal and the energies of EAM for liquid Li, K, and Cs is almost equal to the contribution of the thermal energy of electrons. The thermal energy of electrons is taken into account in analysis of data obtained using shock compression.     

Effective Lennard–Jones potential for cubic metals in the frame of embedded atom model

Generalized Lennard–Jones potentials are proposed in the frame of the embedded-atom method (EAM) of Daw and Baskes for homonuclear cubic metals. The basic functions of the model (the pair interaction potential, electron density function and embedding energy function) are presented in analytical forms. It is shown that N-body Finnis–Sinclair potentials and Daw–Baskes embedded atom potentials are mathematically equivalent. The developed potentials suit very well most of the fcc metals and alkali metals, and they are convenient for computer simulations.     

An embedded atom hyperelastic constitutive model and multiscale cohesive finite element method

Based on embedded atom method (EAM), an embedded atom hyperelastic (EAH) constitutive model is developed. The proposed EAH constitutive model provides a multiscale formalism to determine mesoscale or macroscale material behavior by atomistic information. By combining the EAH with cohesive zone model (CZM), a multiscale embedded atom cohesive finite element model (EA-cohesive FEM) is developed for simulating failure of materials at mesoscale and macroscale, e.g. fracture and crack propagation etc. Based on EAH, the EA-cohesive FEM applies the Cauchy-Born rule to calculate mesoscale or macroscale material response for bulk elements. Within the cohesive zone, a generalized Cauchy-Born rule is applied to find the effective normal and tangential traction-separation cohesive laws of EAH material. Since the EAM is a realistic semi-empirical interatomic potential formalism, the EAH constitutive model and the EA-cohesive FEM are physically meaningful when it is compared with experimental data. The proposed EA-cohesive FEM is validated by comparing the simulation results with the results of large scale molecular dynamics simulation. Simulation result of dynamic crack propagation is presented to demonstrate the capacity of EA-cohesive FEM in capturing the dynamic fracture.     

Corrosion of refractory metals and alloys in liquid lithium (a review)

Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 26, No. 6, pp. 3–16, November–December, 1990.     

The reaction of liquid metals to form intermetallics

The formation of intermetallic compounds of high melting point, by reaction between liquid metals at low temperatures, was studied for a number of binary systems, in particular Al-Sb, Mg-Sb, Mg-Bi and Na-Bi.Two regimes of behaviour on mixing were found:

Application of vibrational parameters to locate the solid/liquid interface during solidification and melting of metals

A method to locate the solid/liquid interface with vibrational parameters during solidification is proposed for the first time. The sufficient difference in resistance to shear stresses between liquid and solid phases of metals and alloys permits the application of vibrational parameters to locate the interface in real time and in a situation during solidification. Based on the solidification theory, continuum mechanics, vibrational modal analysis and sensitivity analysis, the mechanical model and the dynamic equations of a typical Bridgman solidifying system have been established, the sensitivity of eigenvalues of the Bridgman system to the location of the solid/liquid interface has been derived, and the formulae concerned calculated. The experimental results are in good agreement with the computed ones.     

Wetting and mechanical properties, a case study: Liquid metal embrittlement of a martensitic steel by liquid lead and other liquid metals

We present experimental results of tensile and fatigue properties of the T91 (a 9% Cr martensitic steel) in a stagnant molten metallic bath (Pb, Pb-Bi or Sn for instance). Under particular experimental conditions, the tensile tests revealed an instantaneous embrittlement of the material, more pronounced at low temperature, that disappears as the temperature is raised above 450°C. This behavior is explained by the reduction of the surface energy of the bare metal induced by the adsorption of the liquid metal. When the steel is submitted to low cycle fatigue tests in presence of the liquid Pb-Bi eutectic at 300°C, its lifetime is significantly reduced compared to tests performed in air. In this case, given the complexity of the mechanisms leading to a fatigue fracture, it is more difficult to ascribe the observed embrittlement to the sole surface-energy reduction effect, but and adsorption-induced localization of the plastic deformation at the very crack tip is an appealing hypothesis.     

Three-dimensional chemical imaging of embedded nanoparticles using atom probe tomography

Analysis of nanoparticles is often challenging especially when they are embedded in a matrix. Hence, we have used laser-assisted atom probe tomography (APT) to analyze the Au nanoclusters synthesized in situ using ion-beam implantation in a single crystal MgO matrix. APT analysis along with scanning transmission electron microscopy and energy dispersive spectroscopy (STEM-EDX) indicated that the nanoparticles have an average size ~8-12 nm. While it is difficult to analyze the composition of individual nanoparticles using STEM, APT analysis can give three-dimensional compositions of the same. It was shown that the maximum Au concentration in the nanoparticles increases with increasing particle size, with a maximum Au concentration of up to 50%.     

Thermodynamic superheating of low-dimensional metals embedded in matrix

A simple model for size-dependent melting temperature and melting entropy of nanocrystals embedded in a matrix is introduced to interpret the superheating phenomenon. The model predicts not only melting temperature and the melting entropy increase for embedded nanocrystals as the size of the nanocrystals decreases, but also melting temperature and the melting entropy depression for free-standing nanocrystals with reducing size. The model is supported by available experimental results of nanoparticles and thin films.     

On the fracture pressure of liquid metals

Fracture pressure of six liquid metals, Pb, Al, Cu, Ni, Ti and Fe have been calculated at their melting points in three different ways; (i) by extrapolating molecular dynamic (MD) data reported in the literature for various temperatures to their melting points, (ii) by using the fracture pressure equation developed by Fisher and (iii) by using the work of nucleation suggested by Fletcher. Results have shown that the Fisher equation and MDs estimates agree closely, whereas the ones based on the work of nucleation are systematically lower than the other two. In all cases, calculated fracture pressures are several orders of magnitude different from those assumed in the literature, emphasizing the extent of weakening by extrinsic factors in liquid metals.     

Centrifugation of liquid low-melting metals

Special purity grade metallic gallium in the melted state was centrifuged for the first time at various accelerations in the range from 1000g to 12000g. The crystallized metal exhibits a small change in the lattice period and a significant increase in the microhardness with increasing acceleration. The previously observed effects of the centrifugal acceleration upon the structure, composition, and properties of multicomponent systems are confirmed for the first time in a one-component liquid metal system (with point defects probably playing the role of the second component).     

Density of liquid alkali metals

With the aid of the thermodynamic similarity method generalized equations for the density of liquid alkali metals are obtained. Values of the density of liquid rubidium and cesium are calculated up to 600°C.     

Emerging application of 3D-printing techniques in lithium batteries: From liquid to solid

There is rapid progress in the field of 3D printing technology for the production of electrodes, electrolytes, and packages of batteries due to the technique’s low cost, a wide range of geometries printable, and rapid prototyping speed by combining computer-aided design with advanced manufacturing procedures. The most important part of 3D printing applied in batteries is the printing of electrodes, electrolytes, and packages. These will affect the battery energy/power density. However, there are still several challenges that need to be overcome to print active and stable electrodes/electrolytes for energy storage systems that can rival that of the state-of-the-art. In this review, the printing materials, and methods for batteries from liquid to solid-state batteries are discussed and recent examples of this technique applied in high power/energy batteries are highlighted. This review for batteries will cover 3D printing technologies, printed cathode, and anode in conventional batteries, and printed solid-state electrolytes in solid-state batteries. The working principles, advantages, and limitations for solid-state batteries via the 3D printing method will be discussed before highlighting the printing materials for electrodes and electrolytes. We will then discuss how to modify the electrode and solid-state electrolyte to raise the electrochemical performance of solid-state batteries using 3D printing. Finally, we will give our insights into the future perspectives of this printing technique for fabricating batteries.     

Application of the double slip plane crack model to temperature and strain rate sensitive BCC metals

The double slip plane crack model proposed by Weertman, Lin and Thomson (1982) has been applied to model the effect of temperature and strain rate on the stress intensity factor at a crack tip in temperature and strain rate sensitive materials. Increase in temperature or decrease in strain rate (as well as a decrease in slip plane spacing) are shown to increase the shielding of the crack tip by dislocation distributions on the slip planes. Furthermore, the effect of temperature on the fracture toughness, K_llc, at various strain rates was shown to exhibit the same sigmoidal shaped curve seen for K_lc data in typical alloy steels.