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

This chapter provides a discussion of temperature-composition phase diagrams of ternary systems. Isothermal and isoplethal sections as well as polythermal liquidus and solidus projections are treated. Liquidus and solidus projections in quaternary and higher-order systems are also presented.

Ternary Temperature-Composition Phase Diagrams

A complete review, critical evaluation, and thermodynamic optimization of phase equilibrium and thermodynamic properties of the CaO-MnO-SiO 2 and CaO-MnO-Al 2 O 3 systems at 1 bar pressure are presented. The molten oxide phase was described by the Modified Quasichemical Model, the Gibbs energy of the olivine solid solution was modeled with the Compound Energy Formalism, and the wollastonite s.s., rhodonite s.s., and α- and α'-Ca 2 SiO 4 solutions were modeled by polynomial expansions of the excess Gibbs energy. Sets of optimized model parameters for all phases were obtained which reproduce all available reliable thermodynamic and phase equilibrium data within experimental error limits from 25°C to above the liquidus temperatures over the entire ranges of composition. The liquidus surface of the CaO-MnO-Al 2 O 3 system, which has not been measured, has been predicted. Complex phase relationships in these systems have been elucidated, and discrepancies among the data have been resolved. Phase equilibria between liquid slag and manganese alloys have been calculated. The database of model parameters can be used along with software for Gibbs energy minimization in order to calculate any phase diagram section or thermodynamic property.

Critical Thermodynamic Evaluation and Optimization of the CaO—MnO—SiO2 and CaO—MnO—Al2O3 Systems

The Co-Na (Cobalt-Sodium) system

The Ca−K (Calcium-Potassium) system

The phase diagrams of the MCl 3 -MF 3 -MgCl 2 -MgF 2 (where M = La, Nd, Ce) reciprocal ternary systems have been calculated thermodynamically from available data on the common-ion binary sub-systems and from available data on the MCl 3 -MgF 2 joins. These joins are quasi-binary and divide each system into two quasi-ternary systems: the MCl 3 -MgF 2 -MF 3 system with a ternary eutectic and the MCl 3 -MgF 2 -MgCl 2 system also with a ternary eutectic.

Arthur D. Pelton

Papers

Ternary Temperature-Composition Phase Diagrams

Critical Thermodynamic Evaluation and Optimization of the CaO—MnO—SiO2 and CaO—MnO—Al2O3 Systems

The Co-Na (Cobalt-Sodium) system

The Ca−K (Calcium-Potassium) system

Thermodynamic evaluation of phase equilibria in MCl3-MF3-MgCl2-MgF2 systems where M = La, Nd, Ce