Calculation of phase diagrams of the iron-copper and cobalt-copper systems

Synthesis of phase diagrams has been made on Fe-Cu and Co-Cu systems using thermodynamic parameters obtained by analysis of data on phase boundaries and thermodynamic properties. An anomaly in solubility of copper due to the magnetic transition was confirmed to occur in αFe as well as γCo. It was also detected that the solidus curves in both the systems exhibit remarkable retrograde solubility.     

Coupled phase diagrams and thermochemical data for transition metal binary systems — I

A data base covering the transition metals has been developed which permits coupling of thermochemical and phase diagram data and can readily be employed to compute ternary and higher order systems. The current paper which will be the first in a series of contributions, details the following ten binary systems: iron-titanium, iron-cobalt, iron-niobium, iron-molybdenum, iron-tungsten, chromium-cobalt, chromium-niobium, chromium-molybdenum and chromium-tungsten. Subsequent contributions will cover other binary members permitting calculation of a wide range of ternary systems.     

Coupled phase diagrams and thermochemical data for transition metal binary systems — II

A data base covering the transition metals has been developed which permits coupling of thermochemical and phase diagram data and can readily be employed to compute ternary and higher order systems. The current paper, which is part of a series, details the following twelve binary systems: nickel-titanium, nickel-cobalt, nickel-niobium, nickel-molybdenum, nickel-tungsten, titanium-cobalt, titanium-niobium, titanium-molybdenum, titanium-tungsten, cobalt-niobium, cobalt-molybdenum and cobalt-tungsten. This brings the total of such systems covered to twenty five. This paper together with the past and projected contributions will cover other sufficient binary members in order to permit calculation of a wide range of ternary systems.     

A modified electrolyte-Uniquac model for computing the activity coefficient and phase diagrams of electrolytes systems

A modified electrolyte-Uniquac model describing the behaviour of single and multicomponent electrolyte systems was developed. The thermodynamic properties of electrolyte solutions are considered to be the sum of two contributions: the long-range represented by Debye–Hückel contributions and the local-composition expression (modified Uniquac type) that have been applied to account for short-range contributions. The local mole fractions are calculated based on the assumptions proposed by Chen and coworkers. The model has been tested on 86 aqueous electrolyte solutions at 298.15 K and results have been compared with those obtained from the Pitzer and electrolyte-NRTL models. The modified electrolyte-Uniquac model led to the accurate calculation of individual activity coefficient of ion. This new model can also be used to predict the excess properties and the salt solubility in aqueous multielectrolyte solutions with the interaction parameters obtained from binary data.     

Calculated phase diagrams of Cu-W, Ag-W and Au-W binary systems

Phase diagrams for Cu-W, Au-W systems have been calculated based on available thermodynamic data. It was assumed that there is no mutual solid solubility in all the cases. Liquid phase equilibria were calculated on the basis of sub-regular solution model using Miedema's interaction parameters. Vapour phase boundaries have also been determined.     

Thermodynamic assessments of binary phase diagrams in organic and polymeric systems

The Sanchez–Lacombe (SL) model and the Flory–Huggins model were used for the calculation of binary phase diagrams in organic and polymer systems, respectively. The thermodynamic parameters of the liquid and gas phases in acetone–carbon disulfide (CS₂), butane–heptane, cyclohexane–aniline systems, and liquid phases in polystyrene–polybutadiene and polystyrene–bisphenol A poly-carbonate systems were optimized, based on the experimental data. The calculated results with various pressures are in good agreement with the experimental data. It is hoped that this method will be widely applied in the prediction of binary phase diagrams in organic and polymer systems.     

Action diagrams for systems analysts

Action diagrams are a powerful new technique for systems analysts. They help in describing both overall structures and detailed tests and conditions. Usually two separate techniques are required for these tasks. Action diagrams can also be used by end users and should be useful in conjunction with fourth-generation languages and computer-aided design techniques. One available action diagramming product runs on an IBM PC.     

Coupled phase diagrams and thermochemical descriptions of the titanium-beryllium,zirconium-beryllium and hafnium-beryllium systems

A data base covering the transition metals has been developed which permits coupling of thermochemical and phase diagram data and can readily be employed to compute ternary and higher order systems. Previous papers in the series of CALPHAD publications have illustrated development of the base through utilization of experimental phase diagram and thermochemical data. The present work examines the usefulness of Miedema's computed heats of solution for liquid phases in considering the development of coupled data for three simple transition metalberyllium systems. The final results are then employed to recalculate the titanium-beryllium-zirconium-ternary system in order to define the composition with the greatest liquid stability. Such information can be of particular value in synthesis of metallic glasses.     

Coupled phase diagrams and thermochemical data for transition metal binary systems — V

A data base covering the transition metals has been developed which permits coupling of thermochemical and phase diagram data and can readily be employed to compute ternary and higher order systems. The current paper, which is part of a series, details the following ten binary systems: aluminum-titanium, chromium-aluminum, aluminum-manganese, iron-aluminum, cobalt-aluminum, aluminum-nickel, aluminum-copper, niobium-aluminum, molybdenum-aluminum and tungsten-aluminum, thus bringing the total of such systems covered to fifty seven. This paper together with past and projected contributions will cover other binary members in order to permit calculation of a sufficiently wide range of ternary systems.     

Activities and ternary phase diagrams

A set of theoretical formulae for calculating activities along the liquid surface in ternary phase diagrams has been presented. These formulae are rigorous since no assumption is made in the derivation. The expressions are generalized and can be simplified to the forms presented by Pelton, Chou, Elliott and Gokcen under certain conditions. In practice, the activity of the components are desired at a fixed temperature instead of a variable temperature like that along a liquid surface. Under this situation, with reasonable assumptions the equations can be further simplified such that they do not contain any partial thermodynamic properties. Activities can then be readily calculated from phase diagrams. The method presented in this paper is for a ternary system and can be extended to multicomponent systems.     

Computerized prediction of phase diagrams of the eutectic binary systems of nontransition-nontransition metals

The relationship between the interaction parameters of liquid alloys and the atomic parameters of constituent elements has been investigated by artificial neural network method. The relationship found can be used for the computerized prediction of phase diagrams of the eutectic binary systems between non-transition elements.     

Models for the determination of kinetic phase diagrams and kinetic phase separation domains

Several theoretical models for the determination of kinetic phase diagrams for solid solution growth from the liquid phase are presented and compared to each other. These models include a Monte Carlo simulation model, used as a reference model, a previously defined analytical model, based on linear non-equilibrium thermodynamics, and a new model, rooted in the kinetics at kink sites.All models have in common that the composition of the growing solid phase tends to the liquid phase composition for increasing undercooling, enhancing mixing even for systems with a strong tendency to phase separation. However, depending on the system parameters considerable quantitative differences can occur between the results from the model based on non-equilibrium thermodynamics and the MC model. Instead, the new model follows very well the trends of the MC simulations, both for well-mixing systems and for phase separating systems.For phase separating systems the analytical models predict kinetic phase separation domains, zones in the kinetic phase diagram yielding steady state growth of more than one solid phase with different compositions. According to MC simulations such domains in phase space correspond to domain formation in real space. Also in this case the new model is consistent with the MC results.     

Predicate diagrams for the verification of real-time systems

This article discusses a new format of predicate diagrams for the verification of real-time systems. We consider systems that are defined as extended timed graphs, a format that combines timed automata and constructs for modelling data, possibly over infinite domains. Predicate diagrams are succinct and intuitive representations of Boolean abstractions. They also represent an interface between deductive tools used to establish the correctness of an abstraction, and model checking tools that can verify behavioral properties of finite-state models. The contribution of this article is to extend the format of predicate diagrams to timed systems. We establish a set of verification conditions that are sufficient to prove that a given predicate diagram is a correct abstraction of an extended timed graph; these verification conditions can often be discharged with SMT solvers such as CVC-lite. Additionally, we describe how this approach extends naturally to the verification of parameterized systems. The formalism is supported by a toolkit, and we demonstrate its use at the hand of Fischer’s real-time mutual-exclusion protocol.     

Coupled phase diagrams and thermochemical descriptions of the iron-beryllium,cobalt-beryllium,nickel-beryllium and copper-beryllium systems

A data base covering the transition metals has been developed which permits coupling of thermochemical and phase diagram data and can readily be employed to compute ternary and higher-order systems. Previous papers in the series of CALPHAD publications have illustrated development of the base through utilization of experimental phase diagram and thermochemical data. The present work examines the phase diagrams and thermochemical properties of the iron-beryllium, cobalt-beryllium, nickel-beryllium and copper-beryllium systems in order to evaluate the characteristics of the $\text{A2}\text{B2}$ (bcc/CsC1) ordering reactions and their dependence on composition.     

Algorithms useful for calculating multi-component equilibria,phase diagrams and other kinds of diagrams

Phase diagrams are important in materials science. They consist of lines separating regions with different sets of stable phases and different kind of axes can be used. Many available phase diagrams are drawn directly from experimental information. However, they are closely related to the thermodynamic properties of the phases and can be calculated from thermodynamic models of the phases using the Calphad technique. This paper presents a set of algorithms to calculate equilibria and several kinds of diagrams using a very flexible set of conditions and axes. The algorithms can be applied to multi-component systems using model parameters in thermodynamic databases.     

Program for the calculation and construction of isothermal phase stability diagrams

For the calculation and graphic construction of isothermal phase stability diagrams a procedure is proposed and described. In the calculations, coordinates of invariant points are determined first. Then phase boundaries connecting either two invariant points or an invariant point and a boundary point of a diagram are constructed. The algorithm described is limited to systems formed by three chemical elements, where besides the ideal gaseous mixture only single condensed phases are considered. Partial pressures of two gaseous species are used as coordinates of a diagram.     

Computerized prediction of interaction parameters and phase diagrams of the immiscible binary systems of nontransition-nontransition metals

The relationship between the interaction parameters of liquid alloys and the atomic parameters of constituent elements has been investigated by artificial neural network method. The relationship found can be used for the computerized prediction of phase diagrams of liquid-liquid immiscible binary systems between non-transition elements.     

Data decision diagrams for Promela systems analysis

In this paper, we show how to verify computation tree logic (CTL) properties, using symbolic methods, on systems described in Promela. Symbolic representation is based on data decision diagrams (DDDs) which are n-valued Shared Decision Trees designed to represent dynamic systems with integer domain variables. We describe principal components used for the verification of Promela systems (DDD, representation of Promela programs with DDD, the transposition of the execution of Promela instructions into DDD). Then we compare and contrast our method with the model checker SPIN or classical binary decision diagram (BDD) techniques to highlight as to which system classes SPIN or our tool is more relevant.