Computer calculations of phase diagrams

The thermodynamic route of establishing phase diagrams is a relatively recent activity, considering that till about the fifties most phase diagrams were determined by the measurement of certain physical property or quantitative microscopy using light optics or x-ray diffraction. The thermodynamic formalism used by Kaufman and Bernstein is explained and illustrated with examples of the development of hypothetical binary phase diagrams. The calculation of ternary phase diagrams can begin with the binary phase diagram data as a first approximation. However, to calculate a reasonably accurate ternary phase diagram a certain amount of ternary solution data is necessary. Various empirical equations have been proposed in the literature to express ternary thermodynamic data. Calculation of simple ternary isothermal sections is illustrated with the examples of Mo-V-W and Cd-Sn-Pb systems. The numerical techniques which involve the differentiation of thermodynamic parameters with respect to composition get more involved with the number of components becoming 3 or more. A simpler approach has been applied recently to find the minimum position on the Gibbs free energy surface.     

Existence domains for invariant reactions in binary regular solution phase diagrams exhibiting two phases

The thermodynamic origin of various types of phase diagrams in simple binary systems exhibiting two phases (e.g. a liquid and a solid phase) has been examined using the regular solution model. The necessary conditions for the occurrence of each of these types are identified in terms of the appropriate intersections of the miscibility gap boundaries (in solid/liquid phases) and the liquidus/solidus/iso-G curves. Thus, the regions of occurrence of the different types of possible phase diagrams in the space of the regular solution interchange energy parameters (W ^α,W ^β) are clearly delineated. This analysis makes it easier to make intelligent initial selections of model (energy) parameters for their optimization in the calculation of phase diagrams using thermodynamic models such as CALPHAD/CVM.     

低温区间的Fe-N二元相图理论分析

采用亚点阵的化合物能模型计算低温区间Fe-N二元相图。计算结果表明,25～350℃低温区,分别存在着α-Fe(N)和γ＇-Fe4N,γ＇-Fe4N和ε-Fe₂N_1-x二相平衡。α-Fe(N),γ＇-Fe₄N,ε-Fe₂N_1-x均为热力学稳定相。依据Guillermet和Du的热力学性质参数计算的低温区间Fe-N二元相图与现有实验数据相符。     

Phase Stability, Kinetic Diagrams and Diffusion Path in High Temperature Oxidation of Binary Solid-Solution Alloys

The phase diagrams of ternary systems involving two metal components and one oxidant are considered first, the limitations to their use is discussed in relation to the high temperature oxidation of binary alloys. Kinetic diagrams,which are useful to predict the conditions for the stability of the two mutually insoluble oxides as the external scale, are then calculated on the basis of thermodynamic and kinetic data concerning both the alloys and the oxides, assuming the validity of the parabolic rate law. A combination of the two types of diagrams provides a more detail information about the oxidation behavior of binary alloys. The calculation of the diffusion paths, which relate the oxidant pressure to the composition of the system in terms of the alloy components both in the alloy and in the scale during an initial stage of the reaction in the presence of the parabolic rate law, is finally developed.     

Experimental investigation and thermodynamic modeling of the U-Nb system

The phase equilibria and thermodynamic properties of the U-Nb system were investigated through experiments and thermodynamic modeling.In the experiments,a series of samples with different con-tent of Nb were prepared by arc melting.The Nb content covers the entire composition range of the U-Nb binary system.After solidification,the samples were annealed and then analyzed by X-ray diffraction,scanning electron microscopy,energy dispersive X-ray spectroscopy,differential scanning calorime-ter and neutron diffraction.The equilibrium phases,including γ1 (U-rich bcc),αU,and γ2 (U-depleted bcc),were determined in detail from the experimental characterization.The occurrence of the invariant reaction γ1 → αU + γ2 was confirmed,and the reaction temperature and composition were accurately identified.Moreover,the experimental findings clarify the dispute between the Dwight and Terekhov theories regarding the phase region (i.e.,whether the phase region is αU + γ1 or βU + γ'2).Furthermore,the U-Nb phase diagram was reassessed by incorporating the present experimental data and previously published reliable experimental data from the literature.A set of self-consistent thermodynamic param-eters were developed using CALPHAD (Calculation of phase diagrams),and the calculations reasonably agree with the experimental observations.     

Thermodynamic characterization of Al–Cr,Al–Zr,and Al–Cr–Zr alloy systems

Abstract

The equilibrium phase diagrams of Al–Cr, Al–Zr, and Al–Cr-Zr, with particular reference to aluminium-rich alloys, have been critically reviewed. On the basis of these, and consistent with measured thermodynamic values, the binary systems have been thermodynamically characterized. Using these characterizations, phase equilibria have been extrapolated in the ternary, with the intention of augmenting the sparse experimental information concerning the equilibrium liquidus (0–10 at.%Cr, Zr) and solid solution range of aluminium in Al–Cr–Zr. Using the same parameters that define the equilibrium phase relationships, metastable phase relationships can also be extrapolated into the ternary.

MST/418     

Prediction of the Occurrence of a Phase in Austenitic Matrix of Ni-base Superalloys Using Thermodynamic Equilibria Calculation

Using the calculation of thermodynamicequilibria in multicomponent systems,two ternaryphase diagrams,Ni-Cr-Mo and Ni-Cr-Co,havebeen calculated by optimizing the Gibbs free ener-gies with respect to phase diagrams andthermodynamic data.On the basis of this calcula-tion,the occurrence of σ-phase in the residual solidsolution of commercial Ni-base superalloys,IN-713C and U-700,has been predicted.The re-sults show that the calculation of phase equilibria issuccessful in the prediction of the occurrence of theσ-phase.     

SUMMARY AND PREDICTION OF PHASE DIAGRAMS FOR BINARY PHOSPHATE SYSTEMS

本文对磷酸盐二元系的相图进行概括和预测。以离子场强和离子键成分为参数的线性函数关系是微观粒子结构要素相互作用的反映。本研究支持Pauling 的混合键理论。     

Origin of pre-peak in structure factors of liquid Cu-Al-Ni alloys

Hägg carbide (χ) is, during the tempering of carbon-rich martensite, referred to as a transition carbide which eventually gives way to cementite. However, there are Fe–C binary phase diagrams estimated using thermodynamic data, that define a low-temperature phase field where a mixture of Hägg carbide and ferrite is more stable than that of cementite and ferrite. In this scenario, it may be cementite which is the transition carbide. Evidence is presented here that the predominance of Hägg carbide over cementite in the circumstances described is unlikely to be correct based on historical and new observations. Literature data are also interpreted to show that η and ?-carbides are best regarded as transition-phases relative to mixtures of cementite and ferrite.     

C-H-N体系生长金刚石薄膜

通过热力学分析从理论计算上给出了C－H－N体系中低压生长金刚石的三元相图．该相图中存在金刚石生长区．不同温度和压强下金刚石生长区几乎都位于CH₄－N连线以下,并且随衬底温度的改变而有显著的变化．随着氮含量的增加,金刚石生长区向碳含量减少的方向移动．使用该相图对优化添加含氮气源生长金刚石的实验条件提供了理论依据．     

Equilibrium phase diagrams of isolated nano-phases

 Materials processing and fabrication shows a strong trend toward manipulation of materials at ever decreasing sizes. This is especially true in microelectronics. Once the size of a material extends below the sub-micrometer level significant changes in the properties and behavior of materials emerges. It is sometimes difficult to determine if the changes observed at this nano-scale are a result of the process variables or are inherent to material because of its small size. In order to address this difficulty with regard to crystal structure and composition, phase diagrams as a function of size would be particularly useful. In the present paper experimental data on phase equilibria are presented as well as a thermodynamical analysis based on capillarity effects from surface curvature. The analysis and experimental data for binary phase diagrams agree with one another and show that isolated particles of less than 100 nm exhibit substantial decreases in liquidus temperature, factors of more than 10 increase in solubility, and narrowing of the two-phase fields. The details of the thermodynamic model and its predictive powers are presented along with a three-dimensional phase diagram which has temperature-composition-size as its axes. Received: 10 August 1998 / Reviewed and accepted: 27 September 1998     

Thermophysical Properties of Liquid In–Sn Alloys

The surface tension of liquid In–Sn alloys was measured with three experimental techniques carried out in a protective atmosphere of a mixture of argon and hydrogen: tensiometric (in Chemnitz), and maximum bubble pressure and sessile drop (in Kraków). Attempts were undertaken to confirm the correlation of surface tension with electrical conductivity and viscosity and to compare them with literature data. The lack of such correlation or a weak one was observed, probably due to a slight negative departure of thermodynamic properties of liquid In–Sn alloys from ideal behavior. Both resistivity and viscosity correlated with the existence of In-rich β and Sn-rich γ phases of the In–Sn phase diagram. The mutual correlations of thermodynamic and physical properties, structure, and the type of phase diagram were confirmed previously for Li–Sn and Mg–Sn systems with evident negative thermodynamic departures from ideal behavior and with the occurrence of intermetallic compounds (IMCs) in the phase diagrams. Due to nearly the same values of surface tension and density of pure In and Sn, the concentration dependence on the surface tension and density was practically unchanged within an extensive range of temperatures in studies on Pb-free solders of binary and multicomponent alloys containing both metals. Thus, the beneficial influence of In on the wettability of In–Sn alloys was observed solely by the lowering of the contact angle.     

Concentration inhomogeneities and phase diagrams of eutectic systems

We show that it is possible to determine the regions of compositions with developed concentration inhomogeneities in the liquid phase by analysis of the phase diagrams of binary eutectic systems.     

卤素原子在化学气相淀积金刚石薄膜过程中的作用

根据非平衡热力学耦合模型计算得到了碳氢氟和碳氢氯体低压金刚石生长的非平衡定态相图，计算与大量实验事实符合良好。     

Ti-Si-C三元系组元化学位稳定性相图

收集并计算了Ti-SI-C三元系在1200度温度下各组元化合物的热力学数据,利用Ti-SI-C三元系在该温度下的平衡相图以及对碳化物未知热力学数据所做的估算,计算该三元系中各组元化学位并作出的相应的化学位稳定性相图。     

Calculation of the Quasiternary Systems:Si_3N_4-Y_2O_3-SiO_2,Y_2O_3-SiO_2-BeO and Y_2O_3-Al_2O_3-BeO

Based on the thermodynamic model of Kaufman for the calculation of quasibinary and quasiternary system, numerical method for the calculation of stable equilibrium is developed and thermodynamic data of undefined phases are discussed in this work for several ceramic systems.The calculated isothermal sections in Si3N4-Y2O3-SiO2 system meet well with other previous calculated phase diagrams and experimental results. The diagrams in Y2O3-SiO2-BeO and Y2O3-Al2O3-BeO systems are calculated for the approach of prediction.     

Thermodynamic analysis of NiTi formation by mechanical alloying

Disordered B2-NiTi intermetallic phase was produced from a mixture of Ni and Ti powders by mechanical alloying (MA). X-ray technique was used for phase analysis. The results indicated that Ni(Ti) solid solution can be formed earlier and changed to disordered B2-NiTi intermetallic phase after 60 h of MA. A thermodynamic analysis of the process was then carried out using Miedema model. The results showed that there is a thermodynamic driving force in Ni–Ti binary to form solid solution at all compositions and amorphous phase in the composition range X_Ni: 0.05–0.95 where X_Ni is mole fraction of Ni. However, the stable phase which has the minimal Gibbs free energy is solid solution compared to amorphous phase at all compositions. The results of MA were compared with thermodynamic analysis and it was indicated that the product of MA is the most stable phase in Ni–Ti binary system.     

The calculation and use of chemical vapor deposition phase diagrams with applications to the TiBClH system between 1200 and 800 K

A simple method for calculating multicomponent gas-solid equilibrium phase diagrams for chemical vapor deposition (CVD) systems is presented. The method proceeds in three steps: determination of stable solid assemblages, evaluation of gas-solid stability relations, and calculation of conventional phase diagrams using a free energy minimization technique. The phase diagrams can be used to determine (1) bulk compositions and phase fields accessible by CVD techniques, (2) expected condensed phases for various starting gas mixtures and (3) maximum equilibrium yields for specific CVD process variables. The three-step thermodynamic method is used to calculate phase diagrams for the example CVD system TiBClH at 1200 and 800 K. Examples of applications of the diagrams for yield optimization and experimental accessibility studies are presented and discussed. Experimental verification of phase field boundaries at 1200 K, H/Cl = 1 and H/Cl = 5, confirms the calculated boundaries and indicates that equilibrium is nearly and rapidly approached in this system under laboratory conditions.     

Computer generated phase diagrams for ethylene and propylene

A method which uses computer graphics to construct pictorial views of three-dimensional thermodynamic phase diagrams is demonstrated. Pressure-volume-temperature diagrams are presented for ethylene and propylene so that quantitative comparisons can be made between the phase surfaces representing the ideal gas law, the Redlich-Kwong equation and a highly accurate, 20-constant equation of state proposed by Bender. Pictorial views of enthalpy-entropy-pressure diagrams for ethylene based solely on P-V-T relations and ideal gas heat capacities are also shown along with their Mollier projections. Interesting comparisons that confirm our understanding of equations of state are made with H-S-P diagrams that represent the properties of an ideal gas in contrast to those of a Redlich-Kwong fluid. Reference is made to earlier papers that describe the computer graphics algorithms in detail.