Prediction of the equilibrium,paraequilibrium and no-partition local equilibrium phase diagrams for multicomponent Fe-C base alloys

A method is described for the accurate prediction of Fe-C base multicomponent phasediagrams in the α-γ-cem range for both equilibrium and no-partitioning transformation states (paraequilibrium or no-partition local equilibrium) and applicable for total alloy contents (Mn + Si + Ni + Cr + Mo + Cu) less than 5 wt% and Si less than 1 wt%. The equilibrium predictions based on independent thermodynamic data collated by Uhrenius are in excellent agreement with Ae₃ temperatures given in the U.S.S. Atlas and published by Grange in Metal Progress. Calculations of the A₁ (eutectoid) temperatures indicate that Fe-C-Cr alloys transform in the equilibrium partition mode whereas Fe-C-Mn and Fe-C-Ni alloys tend to favour the paraequilibrium mode. This latter inference is in broad agreement with the pearlite partitioning experiments of Ridley and coworkers.     

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.     

基于LabVIEWTM7 Express绘制二元金属相图的虚拟仪器

设计开发了基于LabVIEWTM7 Express自动绘制二元金属相图的虚拟仪器系统.实验表明利用LabVIEW开发绘制相图的虚拟仪器,编程直观高效,仪器面板友好、易操作、功能易扩展;避免了人工数据记录、处理、绘图的烦琐和人为误差,还可利用LabVIEW强大的数据处理功能对实验数据做深层次处理,大大提高实验结果的准确性和重现性.用该虚拟仪器自动绘制的Pb-Sn金属相图,其低共熔点与文献值比较相对误差为-0.219%,结果令人满意.     

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.     

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.     

An algorithm and computer program for calculating composition phase diagrams

An algorithm has been developed to determine the minimum Gibbs energy surfaces and composition phase diagrams of chemical systems. In order to apply the algorithm, phases are represented by points in the parametric space of a system. This requires that the compositional variation of solutions be described by a series of “pseudo-compounds” of differing compositions. All phase regions of an approximated c component system are thus linear as they are defined by the coordinates of c point phases (i.e., phases of fixed composition), which may correspond in part or entirely to a single solution phase. These regions form c-1 dimensional simplicial facets on the Gibbs energy-composition surface of the system and are identified by an abbreviated combinatorial method. This method is feasible because the chemical potentials of the components are constant in any region and can be rapidly determined from linear algebraic techniques. The true phase rule variance of phase regions is found by counting the number homogeneous phases, which may be represented by one or more point phases, in each region as identified by the algorithm. The algorithm can be generalized to other thermodynamic state functions for systems with additional extensive independent variables, such as volume and entropy. The procedure has been coded as a FORTRAN computer program, Bounds, which is capable of treating five component systems with up to eight hundred point phases. Because the calculation of stable phase equilibria is assured by the algorithm, Bounds can be used to calculate composition phase diagrams for systems with complex phase relations, e.g., multinodal solvi. Bounds also provides the basis for a simple method of calculating phase diagrams as a function of both composition and variables like pressure, temperature, and chemical potentials.     

Thermodynamically calculated phase diagrams for the Co-Cr-Ta and Co-Cr-Nb systems

Phase diagrams for the Co-Cr-Ta and Co-Cr-Nb systems have been calculated from thermodynamic data for the binary systems involved. Eleven isothermal sections for temperatures between 2200 and 1500 K are given. The calculations are in good agreement with the limited available experimental phase diagram data for these systems.     

An interactive computer program for calculating ternary phase diagrams

A computer program is described which calculates ternary phase diagrams from the thermodynamic properties of the phases. Sample calculations are given for the molten salt system KClCaCl₂NaCI, the alloy system 7nSnBi, the super-alloy system CrNlFe, and the organic system acetone-chloroform-methyl isobutyl ketone. A computational strategy known as the base phase method is used. This results in a simplification of the algorithms and a large Increase in efficiency. The program, which is highly Interactive with very flexible input and graphical output, is available on-line to North American and European users.     

Undulate phase boundaries on binary diagrams

Usually, an inflection point on a phase boundary is considered as an unambiguous indication that one of phases participating in the equilibrium is internally unstable, i.e. that it is prone to separation. Subsequently, it is habitually deemed that the inflection point may appear only if a thermodynamic model of this phase contains an excess term.

It is shown that in contrast to this belief, inflection points on a phase boundary may appear when a pure solid component or a stoichiometric binary phase is in equilibrium with the ideal binary solution, which is internally stable, indeed.     

Coupled phase diagrams and thermochemical data for transition metal binary systems-III

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: titanium-manganese, chromium-manganese, iron-manganese, cobalt-manganese, manganese-nickel, copper-manganese, titanium-copper, cobalt-copper, copper-chromium, iron-copper, nickel-copper and niobium-copper. This brings the total of such systems covered to thirty-seven. This paper together with the past and projected contributions will cover other binary members in order to permit calculation of a sufficiently wide range of ternary systems.     

Calculation of phase diagrams using partial phase diagram data

The interaction parameters for various phases were calculated using binary phase diagram data. Since two equilibrium compositions of a binary tie line have some errors in their measurements, a particular attention was paid to the effect of a small variation of the equilibrium compositions on the fluctuation in the calculated free energy curves. From this investigation, it was recommended that the widest possible tie line or tie lines located in the central region of a phase diagram be used to calculate the interaction parameters. Based on these facts, the interaction parameters for various phases in the Ti-W, Pd-W, Zr-W and Hf-W systems were estimated, which were subsequently used to calculate the phase diagrams of the above systems.     

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.     

Coupled phase diagrams and thermochemical data for transition metal binary systems-IV

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-carbon, titanium-carbon, manganese-carbon, chromium-carbon, iron-carbon, cobalt-carbon, nickel-carbon, niobiumcarbon, molybdenum-carbon and tungsten-carbon. This brings the total of such systems covered to forty 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.     

基于LabVIEWTM7 Express绘制二元金属相图的虚拟仪器

设计开发了基于LabVIEW^TM7 Express自动绘制二元金属相图的虚拟仪器系统。实验表明：利用LabVIEW开发绘制相图的虚拟仪器,编程直观高效,仪器面板友好、易操作、功能易扩展;避免了人工数据记录、处理、绘图的烦琐和人为误差,还可利用LabVIEW强大的数据处理功能对实验数据做深层次处理,大大提高实验结果的准确性和重现性。用该虚拟仪器自动绘制的Pb—Sn金属相图,其低共熔点与文献值比较相对误差为-0．219％,结果令人满意。     

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.