Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

Energy production and storage technologies have attracted a great deal of attention for day-to-day applications. In recent decades, advances in lithium-ion battery (LIB) technology have improved living conditions around the globe. LIBs are used in most mobile electronic devices as well as in zero-emission electronic vehicles. However, there are increasing concerns regarding load leveling of renewable energy sources and the smart grid as well as the sustainability of lithium sources due to their limited availability and consequent expected price increase. Therefore, whether LIBs alone can satisfy the rising demand for small- and/or mid-to-large-format energy storage applications remains unclear. To mitigate these issues, recent research has focused on alternative energy storage systems. Sodium-ion batteries (SIBs) are considered as the best candidate power sources because sodium is widely available and exhibits similar chemistry to that of LIBs; therefore, SIBs are promising next-generation alternatives. Recently, sodiated layer transition metal oxides, phosphates and organic compounds have been introduced as cathode materials for SIBs. Simultaneously, recent developments have been facilitated by the use of select carbonaceous materials, transition metal oxides (or sulfides), and intermetallic and organic compounds as anodes for SIBs. Apart from electrode materials, suitable electrolytes, additives, and binders are equally important for the development of practical SIBs. Despite developments in electrode materials and other components, there remain several challenges, including cell design and electrode balancing, in the application of sodium ion cells. In this article, we summarize and discuss current research on materials and propose future directions for SIBs. This will provide important insights into scientific and practical issues in the development of SIBs.

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Sodium-ion batteries: present and future

This paper presents a summary of the FactSage thermochemical software and databases. FactSage was introduced in 2001 and is the fusion of the FACT-Win/F∗A∗C∗T and ChemSage/SOLGASMIX thermochemical packages that were founded over 25 years ago. The FactSage package runs on a PC operating under Microsoft Windows® and consists of a series of information, database, calculation and manipulation modules that enable one to access and manipulate pure substances and solution databases. With the various modules one can perform a wide variety of thermochemical calculations and generate tables, graphs and figures of interest to chemical and physical metallurgists, chemical engineers, corrosion engineers, inorganic chemists, geochemists, ceramists, electrochemists, environmentalists, etc. In this article emphasis is placed on the calculation and manipulation of phase diagrams. However the reputation of FactSage has been established mainly in the field of complex chemical equilibria and process simulation where the software has unique capabilities. Some of these capabilities are also shown in this paper.

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FactSage thermochemical software and databases

FactSage® was introduced in 2001 as the fusion of the F*A*C*T/FACT-Win and ChemSage thermochemical packages. The FactSage package runs on a PC operating under Microsoft Windows® and consists of a series of information, database, calculation and manipulation modules that enable one to access and manipulate pure substances and solution databases. With the various modules one can perform a wide variety of thermochemical calculations and generate tables, graphs and figures of interest to chemical and physical metallurgists, chemical engineers, corrosion engineers, inorganic chemists, geochemists, ceramists, electrochemists, environmentalists, etc. This paper presents a summary of the recent developments in the FactSage thermochemical software and databases. In the article, emphasis is placed on the new databases and the calculation and manipulation of phase diagrams and complex phase equilibria.

FactSage thermochemical software and databases - recent developments

The FactSage computer package consists of a series of information, calculation and manipulation modules that enable one to access and manipulate compound and solution databases. With the various modules running under Microsoft Windows® one can perform a wide variety of thermochemical calculations and generate tables, graphs and figures of interest to chemical and physical metallurgists, chemical engineers, corrosion engineers, inorganic chemists, geochemists, ceramists, electrochemists, environmentalists, etc. This paper presents a summary of the developments in the FactSage thermochemical software and databases during the last six years. Particular emphasis is placed on the new databases and developments in calculating and manipulating phase diagrams.

FactSage thermochemical software and databases, 2010–2016

Thermodynamic analysis of binary liquid silicates and prediction of ternary solution properties by modified quasichemical equations

For relattively dilute solutions of oxygen and a deoxidizer M (M=Al, Cr, Ca, Mg, ...) in molten Fe, a thermodynamic model is proposed wherein the dissolved species are M*O associates as well as unassociated M and O atoms. At higher metal concentrations, a small amount of M
 2*O associates also form. Experimental deoxidation equilibria for 15 deoxidizers M are quantitatively reproduced at all temperatures, with only a constant, temperature-independent and composition-independent empirical parameter for the Gibbs energy of formation of each associate. The deoxidation behavior of Mg, Ca, and Ba is elucidated for the first time. The parameters are stored in a database, which can be used to predict complex deoxidation equilibria in multicomponent steels.

A thermodynamic model for deoxidation equilibria in steel

A thorough review and critical evaluation of phase equilibria and thermodynamic data for all phases in the iron-sulfur (Fe-S) binary system at 1 bar pressure has been made over the entire composition range for temperatures from 25 °C to above the liquidus. The Gibbs energies of ten phases have been modeled, and optimized model parameters have been obtained that reproduce all data simultaneously within experimental error limits. For the liquid phase, the recently extended modified quasi-chemical model is applied for the first time to a liquid metal-sulfur phase. A two-sublattice model within the framework of the compound energy formalism is used for the high-temperature monosulfide pyrrhotite solution. A substitutional model is used for the dissolution of S in solid iron. The Gibbs energies of six stoichiometric compounds are also modeled.

Thermodynamic modeling of the Fe-S system

The Li-Mg (Lithium-Magnesium) system

Molten silicates are ordered solutions whose excess Gibbs energies cannot be well represented by the usual polynomial representation of deviations from ideal solution behavior. An adaptation of quasichemical theory has been proposed which is capable of describing the properties of ordered solutions and of representing the measured properties of binary silicates over broad ranges of composition and temperatures. For simple silicates such as the MgO-FeO-SiO2 ternary system in which silica is the only acid component, a combining rule generally leads to good predictions of the thermodynamic properties of ternary (and probably higher order) solutions from those of the binaries. In basic solutions, these predictions are consistent with those of the Conformal Ionic Solution Theory. Our results indicate that our approach could provide a potentially powerful tool for representing and predicting the thermodynamic properties of multicomponent molten silicates. A complete critical evaluation of the thermodynamic properties and phase diagrams of the FeO-MgO, FeO-SiO2, MgO-SiO2 and FeO-MgO-SiO2 systems is presented in which the modified quasichemical model is used for the liquid phase. Optimized equations for the thermodynamic properties of all phases are obtained which reproduce all thermodynamic and phase diagram data to within experimental error limits from 25°C to liquidus temperatures at all compositions. The optimized thermodynamic properties and phase diagrams are the best estimates presently available.

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Arthur D. Pelton

Papers

Thermodynamic analysis of binary liquid silicates and prediction of ternary solution properties by modified quasichemical equations

A thermodynamic model for deoxidation equilibria in steel

Thermodynamic modeling of the Fe-S system

The Li-Mg (Lithium-Magnesium) system

Prediction of the thermodynamic properties and phase diagrams of silicate systems : evaluation of the feo-mgo-sio2 system