A statistical evaluation of the free energy of Fe-base ternary ordering alloys

The free energy of the Fe-base ternary ordering alloys whereB2 andD0₃ ordered structures are formed is evaluated. The statistical theory is employed using a pairwise interaction approximation taking into account not only the atomic interaction but also the magnetic interaction, based upon the Bragg-Williams-Gorsky model. The application of this model on Fe-Si-Co ordering alloys are demonstrated. The propriety of the calculation results are performed by comparing the experimental results. The influences of the magnetic energy to the stability of ordered structures are also demonstrated.     

Experimental and theoretical phase diagrams of the iron-rich Fe-Si-Ge ordering system

The phase separation in iron-rich Fe-Si-Ge ternary alloys was investigated by means of transmission electron microscopy. The phase separations into A2 and D0₃ were recognized in several alloys in addition to the phase separation into B2 and D0₃ which has already been found in Fe-Si and Fe-Ge binary systems. On the basis of TEM observations, isothermal section diagrams are proposed for the iron-rich corner at 823, 873, 923 and 973 K. The A2 + D0₃ two-phase field exists in a band-shaped region at 823 K. With increase in temperature,the A2 + D0₃ field gradually shrinks and is eventually replaced at 973 Kwith the B2 + D0₃ field, which extends from both the Fe-Si and Fe-Ge binary sides. The phase diagrams were well reproduced by the calculations based on the so-called Bragg-Williams-Gorsky approximation, taking account of the chemical and magnetic pair interactions up to the second nearest neighbour. The effects of the magnetism on the equilibria are discussed.     

Investigation of ordering phenomenon in Me–Pt (Me=Fe,Ni) liquid alloys

Abstract

The phase diagrams of Fe–Pt and Ni–Pt liquid alloy systems show the existence of FePt and NiPt intermetallic compounds, respectively, in their solid intermediate states, and the associative tendency between unlike atoms in these liquid alloys has been analysed using the self-association model. The concentration dependences of mixing properties such as the free energy of mixing, G_M; the concentration fluctuations, S_cc(0), in the long-wavelength limits; the chemical short-range order (CSRO) parameter, α₁; as well as the chemical diffusion, enthalpy and entropy of the mixing of Fe–Pt and Ni–Pt liquid alloys have been investigated to determine the nature of ordering in the liquid alloys. The results show that heterocoordination occurs in the alloys at all concentrations. The effect of CSRO on S_cc(0), chemical diffusion, D, and the order parameter, α₁, has been considered. The ordering phenomenon in the liquid alloys is also related to the effect of the atomic size mismatch volume on S_cc(0).     

Investigation of ordering phenomenon in Me–Pt (Me=Fe,Ni) liquid alloys

The phase diagrams of Fe–Pt and Ni–Pt liquid alloy systems show the existence of FePt and NiPt intermetallic compounds, respectively, in their solid intermediate states, and the associative tendency between unlike atoms in these liquid alloys has been analysed using the self-association model. The concentration dependences of mixing properties such as the free energy of mixing, G_M; the concentration fluctuations, S_cc(0), in the long-wavelength limits; the chemical short-range order (CSRO) parameter, α₁; as well as the chemical diffusion, enthalpy and entropy of the mixing of Fe–Pt and Ni–Pt liquid alloys have been investigated to determine the nature of ordering in the liquid alloys. The results show that heterocoordination occurs in the alloys at all concentrations. The effect of CSRO on S_cc(0), chemical diffusion, D, and the order parameter, α₁, has been considered. The ordering phenomenon in the liquid alloys is also related to the effect of the atomic size mismatch volume on S_cc(0).     

Influence of temperature on phase separation in the ternary systems [Th(NO3)4(TBP)2]-decane-third organic component

The phase diagrams of ternary systems [Th(NO₃)₄(TBP)₂]-decane-third organic component (n-butanol, n-octanol, isobutanol, dimethylhexanol, chloroform, carbon tetrachloride, o-dichlorobenzene, tri-n-butyl phosphate, o-xylene, toluene, and linear carboxylic acids) were studied in the temperature range 288.15–333.15 K. These diagrams contain the fields of homogeneous solutions and the field of separation into two liquid phases (I, II). Phase I is enriched in Th(NO₃)₄(TBP)₂ and third component and phase II is enriched in decane. The phase separation is not appreciably influenced by temperature. In phase separation, the third component is predominantly concentrated in phase I, in spite of the fact that the third component and decane have infinite mutual solubility at all the temperatures. The composition of the ternary systems in the critical point is dependent on the kind of the third component.     

Influence of temperature on phase separation in the binary system tetradecane-Nd(III) nitrate solvate with tri-n-butyl phosphate and ternary system tetradecane-tri-n-butyl phosphate-Nd(III) nitrate solvate with tri-n-butyl phosphate

The phase diagrams of the liquid binary system tetradecane-Nd(III) nitrate solvate with tri-n-butyl phosphate [Nd(NO₃)₃ (TBP)₃] and ternary liquid system tetradecane-tri-n-butyl phosphate-Nd(III) nitrate solvate with tri-n-butyl phosphate were studied in the temperature range 298.15–344.85 K. The phase diagrams of the binary and ternary systems contain an area of homogeneous solutions and an area of separation into two liquid phases (I, II). Phases I and II are enriched in tetradecane and Nd(NO₃)₃ (TBP)₃, respectively. With increasing temperature, the areas of separation into two liquid phases in the binary and ternary systems contract. The compositions of the binary and ternary systems in the critical points at different temperatures and their upper critical solution temperatures were determined.Translated from Radiokhimiya, Vol. 46, No. 5, 2004, pp. 433–435.Original Russian Text Copyright © 2004 by Pyartman, Kudrova, Keskinov.     

Properties of As–Te alloys and their reactions with Zn substrate

The equilibrium phase relationship, glass formation, glass transition temperature, microhardness and density of As–Te alloys are examined. It is found that the available As–Te equilibrium phase diagram might not be correct, and a possible phase diagram is proposed. As–Te glasses are formed in quenching processes, and the As–Te alloys in the compositional range near As_0.5Te_0.5 have the highest glass formation ability (GFA). Besides studies of the properties of As–Te alloys, their interfacial reactions with Zn substrate are also investigated. ZnTe phase is formed in the As_0.271Te_0.729 alloy/Zn reaction couple annealed at 380 and 395°C. Schematic isothermal sections of the As–Te–Zn ternary systems are proposed based on the limited ternary phase equilibria data and the equilibrium phase diagrams of its three constituent binary systems. The reaction paths of the As–Te/Zn couples in both temperatures are liquid/ZnTe/Zn, and are consistent with the proposed isothermal sections.     

Influence of temperature on phase separation in the ternary systems [Th(NO3)4(TBP)2]-isooctane-third organic component

The phase diagrams of ternary liquid systems (TLSs) [Th(NO₃)₄(TBP)₂]-isooctane-third organic component [n-butanol, isobutanol, n-octanol, n-decanol, cyclohexanol, toluene, o-xylene, CCl₄, CHCl₃, o-dichlorobenzene, TBP, and higher isomeric carboxylic acids (HICAs)] were studied in the temperature range 298.15–333.15 K. These diagrams contain the fields of homogeneous solutions and the field of separation into two liquid phases (I, II). Phases I is enriched in [Th(NO₃)₄(TBP)₂] and third component, and phase II is enriched in isooctane. With increasing temperature, the field of separation into two liquid phases contracts and the content of the third component in the critical points decreases. The compositions of ternary systems in the critical point depend on the kind of the third component. In phase separation, the third component is predominantly concentrated in phase I, in spite of the fact that the third component and isooctane have infinite mutual solubility at all the temperatures.     

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.     

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.     

In Situ Diffraction Experiments for the Investigation of Phase Fractions and Ordering Temperatures in Ti‐44 at% Al‐(3‐7) at% Mo Alloys

Being a strong β stabilizer, Mo has gained importance as an alloying element for so‐called β/γ‐TiAl alloys. Intermetallic TiAl‐based alloys which contain a significant volume fraction of the body‐centered cubic β‐phase at elevated temperatures have proven to exhibit good processing characteristics during hot‐working. Unfortunately, the effect of Mo on the appearing phases and their temperature dependence is not well known. In this work, sections of the Ti‐Al‐Mo ternary phase diagram derived from thermodynamic calculations as well as experimental data are presented. The phase transition temperatures stated in these phase diagrams are compared with the results of high‐temperature diffraction studies using high‐energy synchrotron radiation. Additionally, the disordering temperature of the β_o‐phase is determined.     

聚醚砜四元制膜液体系的相图计算

以Ｆｌｏｒｙ－Ｈｕｇｇｉｎｓ理论为基础，对ＰＥＳ－ＰＧ－ＮＭＰ＿Ｈ２Ｏ＿）聚醚砜丙二醇－Ｎ－甲基－２－哟咯烷酮水）四元制液体系的相图进行了计算，利用三元相图考察Ｈ２Ｏ和ＰＧ对液－液相分离的影响，在三元的理论的基础上提出了低分子量添加剂的卤元改性Ｆｌｏｒｙ－Ｈｕｇｇｉｎｓ理论，并提出了一种获得四元相图的方法，利用四元相图能较争地描述四元体系，利用改性的四元理论，能了地理解该种体系的液－液相分离行为。     

Reliability of the diffusion-multiple approach for phase diagram mapping

The diffusion-multiple approach can be used to map phase diagrams at an efficiency orders of magnitude faster than the conventional equilibrated alloy method. This paper addresses a concern about the reliability of the results, especially whether the data obtained from diffusion multiples can produce reliable equilibrium phase diagrams. The following topics will be discussed: (a) establishment of local equilibrium at the phase interfaces, (b) X-ray interaction volume vs. thickness of the phases (microprobe related issues), (c) reliability of phase diagrams from equilibrated alloys, (d) usefulness of electron backscatter diffraction, (e) impurity-induced stabilization of metastable phases, and, (f) missing phase situations. A direct comparison of several ternary systems obtained from both diffusion multiples and equilibrated alloys was made. The good agreement between them clearly demonstrates the reliability of phase diagrams determined from diffusion multiples.     

Phase separation and ordering in the Fe-Co system

The Fe₅₀Co₅₀, Fe₆₅Co₃₅, and Fe₃₅Co₆₅ alloys heat-treated between 500 and 1300°C were characterized by x-ray diffraction and transmission electron microscopy. The surface layer of the alloys was found to phase-separate in the range 900–1300°C, leading to the formation of alternating α and γ zones on the order of 0.5 μm in thickness. Phase separation in the bulk of the alloys led to precipitation of an fcc phase, with a volume fraction no greater than 0.1. In the ordering region, the volume fraction of the B2 phase was also no greater than 0.1. The phase-separation region was shown to be divided from the ordering region by a solid-solution phase. Below 550°C, the alloys undergo a phase transformation accompanied by a slight increase in lattice parameter. Comparison with a similar transformation of the Fe₆₀Cr₃₀Co₁₀ alloy suggests that, under certain conditions, this transformation may lead to a significant rise in coercivity. The results are represented in a modified Fe-Co phase diagram.     

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.     

Thermodynamic properties of Mn-Y-Si(Ge,Sn, Pb,C) melts

The effect of Group IVA elements on the integral enthalpy of mixing of Mn-Y-Si(Ge, Sn, Pb, C) melts has been studied using the mixing enthalpies of Mn-Y-Si(Ge) melts determined earlier by calorimetry at 1770 ± 5 K. Since the thermochemical properties of Mn-Y-C(Sn, Pb) melts are unexplored, they have been calculated by the Bonnier-Caboz method using reliable data for the constituent binary systems. To this end, we have performed critical evaluation of the phase diagrams and thermochemical data for the constituent binary systems and have compared the enthalpies of formation of solid Δ_f H and liquid Δ_mix H binary alloys. The results indicate that, among liquid Mn-Y-IVA alloys, the formation of Mn-Y-Ge melts is the most exothermic. The thermochemical properties of all the ternary alloys examined are determined by the properties of the Y-Si(Ge, Sn, Pb, C) constituent binary systems, which have the highest exothermic mixing enthalpies.     

Alloy-oxide equilibria in the system Pt-Rh-O

The composition of Pt-Rh alloys that co-exist with Rh₂O₃ in air have been identified by experiment at 1273 K. The isothermal sections of the phase diagram for the ternary system Pt-Rh-O at 973 K and 1273 K have been computed based on experimentally determined phase relations and recent thermodynamic measurements on Pt_1−X Rh _X alloys and Rh₂O₃. The composition dependence of the oxygen partial pressure for the oxidation of Pt_1−X Rh _X alloys at different temperatures, and temperature for the oxidation of the alloys in air are computed. The diagrams provide quantitative information for optimization of the composition of Pt_1−X Rh _X alloys for high temperature application in oxidizing atmospheres.     

Interfacial energy determination of nano-scale precipitates by CALPHAD description of Gibbs–Thomson effect

A theory based on calculation of phase diagrams in the binary systems was developed that describes Gibbs–Thomson effect. In this model effect of both interfacial energy and interface confinement (Laplace–Young pressure) are included in energy shift of alloys and phases. By using the CALPHAD model, interfacial energy of Cu₄Ti precipitates in Cu–Ti system was obtained which shows better consistency with experimental results of Gibbs–Thomson effect of 10–20 nm radius precipitates.     

Ordering of Glassy Alloys

The short-range ordering and acoustic properties of Fe-base glassy and ordered alloys are studied. The role of ordering in crystallization processes is examined, and structural analogs are considered. The experimental data are compared with calculations in a dynamic model.