Thermodynamic Phase Diagram Calculations Research Articles

MODELLING OF PHASE EQUILIBRIA IN AlCu5Mg1 ALLOYS

Al-based alloys were one of the first material types to which thermodynamic phase diagram calculations were applied. Since then improvements in modelling and the increase in computing power has enabled very accurate predictions to be made for phase equilibria in real multicomponent alloys.

Study of non-equilibrium dendrite growth in an undercooled alloy

ABSTRACT Nonequilibrium thermodynamics and transportation kinetics near the propagating solid–liquid interface dominates the rapid solidification process, which is far from a thermodynamically stable state. Rapid solidification process can be described more precisely using quantitative thermodynamic calculation of phase diagram with nonlinear liquidus and solidus and evaluating the nonequilibrium effect in diffusion kinetics. Based on these basic principles, we have used a current nonequilibrium dendrite growth model to describe the rapid solidification process and the recalescence temperature of deeply undercooled alloys. Evolution of the key fundamental solidification parameters was also evaluated. The experimental data agree well with the model prediction.

Thermodynamics and Magnetism of YCo5 Compound Doped with Fe and Ni: An Ab Initio Study

YCo5 permanent magnet exhibits high uniaxial magnetocrystalline anisotropy energy and has a high Curie temperature. These are good properties for a permanent magnet, but YCo5 has a low energy product, which is notably insufficient for a permanent magnet. In order to improve the energy product in YCo5, we suggest replacing cobalt with iron, which has a much bigger magnetic moment. With a combination of density-functional-theory calculations and thermodynamic CALculation of PHAse Diagrams (CALPHAD) modeling, we show that a new magnet, YFe3(Ni1-xCox)2, is thermodynamically stable and exhibits an improved energy product without significant detrimental effects on the magnetocrystalline anisotropy energy or the Curie temperature.

Synthesis, structure, stability and phase diagrams of selected bimetallic silver- and nickel-based nanoparticles

An overview of the research on silver-based (Ag-Sn, Ag-Cu, Ag-Ni) and nickel-based (Cu-Ni, Au-Ni, Ni-Pt) bimetallic nanoparticles is presented. The investigated nanoparticles in this review are formed by elements that represent an important group of metals revealing fcc lattice under macro-sized conditions (with the exception of Sn). The effects of surface stabilizing layer of the alloy nanoparticles are also described. Our experience with synthesis, characterization and stabilization of alloy nanoparticles is summarized. The development of the nanoparticle synthesis represents an important and mandatory part of the experimental nanoalloy research. Main synthetic routes under focus are the low temperature borohydride reduction method, the high temperature oleylamine synthesis, and the high pressure method in autoclave. The subsequent structural studies are focused on both nanoparticle core and outer stabilizing layer. The cores of the nanoparticles are studied mainly by electron microscopy techniques. The phase stability of the nanoparticle core is investigated by thermal analysis. The Knudsen effusion mass spectrometry was applied for studies of stabilizing organic molecules that can be found on the surface of the nanoparticles. The presented overview of the experimental results is complemented by thermodynamic calculations of phase diagrams by the CALPHAD method.

Thermodynamics of fluoride-based molten fluxes for extraction of magnesium through the low temperature solid oxide membrane (LT-SOM) process

The melt quenching experiments and thermodynamic calculations of phase diagrams were carried out to investigate potential additives for the low temperature solid oxide membrane (LT-SOM) magnesium extraction process. The solubility of MgO, which is a major source of magnesium extraction, was also measured in the molten fluoride fluxes. The solubility of MgO in the 46.5MgF2-46.5CaF2-7LiF and 45MgF2-45CaF2-10NaF (wt%) systems reached 3.4 and 1.9 wt% at 1473 K, respectively, and 1.5 wt% MgO in both fluxes at 1223 K. In addition, the 45MgF2-55CaF2 binary eutectic flux, which has been widely used in SOM process, could dissolve up to 2.3 wt% MgO at 1473 K. This value is significantly lower than the literature value, i.e. 10 wt% MgO. From the evaluation of the activity coefficient of MgO in the 46.5MgF2-46.5CaF2-7LiF and 45MgF2-45CaF2-10NaF fluxes under MgO saturation, it was confirmed that the stability of MgO in the 7LiF flux is greater than that in the 10NaF flux. Hence, the driving force of MgO dissolution into the 7LiF flux is higher than that into the 10NaF flux. The newly developed molten flux for magnesium extraction using the LT-SOM process with an operating temperature lower than 1273 K is the 46.5MgF2-46.5CaF2-7LiF system.

Experimental Study of Phase Composition of B-Fe-Mn-V Alloys and Thermodynamic Calculations of Phase Equilibria in the B-Mn-V and B-Fe-Mn-V Systems

Phase compositions of B-Fe-Mn-V alloys were studied by several experimental methods (DTA measurement, X-ray diffractions, and scanning electron microscopy). Besides the experimental study of the quaternary system, thermodynamic modelling of the ternary B-Mn-V system by the Calphad method and thermodynamic calculations for the quaternary B-Fe-Mn-V system were performed. Calculations for the quaternary system are based on the ternary subsystems (B-Mn-V, B-Fe-V, B-Fe-Mn, and Fe-Mn-V). Boron is modelled as an interstitial element in all solid solutions of vanadium, manganese, and iron. Very good agreement between experimental results and thermodynamic calculations was achieved. The created thermodynamic database is suitable for thermodynamic calculations of phase diagrams for all the ternary subsystems and also for the B-Fe-Mn-V quaternary system.

Refinement of As-cast Austenite Microstructure in S45C Steel by Titanium Addition

The effect of Ti addition on as-cast austenite (y) structure of S45C steel has been investigated. The as-cast y structure without the Ti addition consists of coarse columnar grains. The Ti addition leads to formation of equiaxed γ-grains and also grain refinement of the y structure. Fully equiaxed and very fine γ-grain structure forms in a limited range of Ti addition of 0.13 to 0.17wt%. The thermodynamic calculation of phase diagram showed that Ti carbonitride crystallizes as a primary phase in this composition range. The formation of the very fine equiaxed γ-grain structure originates from the columnar-to-equiaxed transition (CET) in δ-dendrite solidification induced by the primary Ti carbonitride particles. These particles act as the nucleation sites of the equiaxed δ-dendrite. The experimental results are suggestive of existence of finer Ti carbonitride particles retarding the grain growth of γ-phase after the peritectic transformation, which leads to the refinement of the as-cast y structure.

Monotectic four-phase reaction in Al–Bi–Zn alloys

Thermodynamic phase diagram calculations were used for the systematic search for a monotectic four-phase reaction in ternary Al-alloys. Systems with intermetallic phases and also the elements Cd and Hg were excluded in the present search. The ternary Al–Bi–Zn is a rare occasion where such a reaction, L′ = L″ + (Al)′ + (Zn), actually occurs. Experimental work could be focused on key samples in that system and involved DSC for thermal analysis and calorimetry, and also metallographic analysis using SEM/EDX. Experimental results verify the existence of the monotectic reaction and were also used for a quantitative thermodynamic modeling of Al–Bi–Zn. Solidification paths and microstructures of Al–Bi–Zn alloys are shown to be rather complex. Using thermodynamic calculations, these rich details involving up to three invariant reactions and unexpected monovariant reaction types can be clearly revealed and understood.

Effects of Boron, Niobium and Titanium on Grain Growth in Ultra High Purity 18% Cr Ferritic Stainless Steel

Ultra-high purity 18% Cr ferritic stainless steel exhibits superior corrosion resistance. But, grain enlargement is likely to occur during their production and heat treatment, and this causes practical drawbacks in terms of surface qualities and mechanical properties. This study examines the effect of boron (B) addition on the grain growth of the ferritic stainless steel subjected to annealing after cold rolling. Since high Cr ferritic stainless steels often contain Nb or Ti, the effect of simultaneous addition of B with Nb or Ti is also examined as well as B single addition. It was found that B single addition retains grain growth after the recrystallization of the cold-rolled steel. The simultaneous addition of B and Nb leads to finer grain structure than Nb single addition, while the simultaneous addition of B and Ti leads to coarser grain structure than Ti single addition. When B is added with Nb, simultaneous precipitation of niobium carbide (Nb(C, B)) and boron nitride (BN) was found, where NbC is refined by the B addition and the total density of the precipitates along with BN is increased as compared with that in only Nb added steel. When B is added with Ti, on the other hand, coarse M 2 3 (C,B) 6 was found to precipitate primarily on titanium nitride (TiN), and hence, the total density of the precipitates in Ti+B steel becomes lower than that in only Ti added steel which contains both TiN and titanium carbide (TiC). These grain structure development observed in the present study is explained primarily by the pinning effect of precipitates, and the precipitation behavior observed is found to be supported by thermodynamic calculation of phase diagrams using Thermo Calc.

Thermodynamic Calculation of Phase Diagram in the Bi-In-Sb Ternary System

A thermodynamic description of the Bi–In–Sb ternary system of lead-free solder alloys using the CALPHAD (Calculation of Phase Diagram) method is presented. Phase equilibria information such as vertical sections, liquidus projection and thermochemical quantities were calculated and compared with the experimental data. The calculated and experimental data are in excellent agreement in most cases.

A set of phase-equilibrium equations in covariant form and its use for developing a general method of calculation of two-phase conodes in multicomponent systems

In the last 25–30 years, thermodynamic calculations of phase diagrams for both binary and multicomponent systems received wide application. The computer programs [1–7] developed in various research centers of the world are of wide use. The numerical methods involved in these programs can be divided into two classes. In studies of the first class [2], the Gibbsenergy minimum is sought for a heterogeneous system. In studies of the second class, the set of phase-equilibrium equations (establishing the equality of chemical potentials for the components of various phases) is solved [1, 3–7]. In this case, either the Newton–Raphson iterative method [1] or the Nelder–Mead modified simplex method is used to minimize the objective function representing the sum of residuals of the phaseequilibrium equations [7]. An essential constraint of the former methods is the impossibility of guaranteeing attainment of the global minimum of the Gibbs energy for a heterogeneous system. This means that the calculated phase diagram can be both stable and metastable. An essential disadvantage of the latter methods is the necessity of selecting a successful initial approximation for starting the iterative process, for which there is no assurance that the iterations will converge to the desired solution. Thus, the calculating methods of both the first and second class render it principally impossible to create autonomous computer programs for calculating phase diagrams and thermodynamic properties of multicomponent alloys of systems with three or more components.

Thermodynamic Phase Diagram Calculations and Cryoscopic Measurements in the NaCl-CaCl<SUB>2</SUB>-MgCl<SUB>2</SUB>-CaF<SUB>2</SUB> System

Thermodynamic Phase Diagram Calculations and Cryoscopic Measurements in the NaCl-CaCl<SUB>2</SUB>-MgCl<SUB>2</SUB>-CaF<SUB>2</SUB> System

Thermodynamic Phase Diagram Calculations and Cryoscopic Measurements in the NaCl-CaCl2-MgCl2-CaF2 System

Investigations of the phase diagram of the NaCl-CaCl2-MgCl2-CaF2 reciprocal quaternary system have been performed by thermodynamic phase diagram calculations and cryoscopy. A limited concentration region of the system is used as a flux medium for liquid magnesium metal in connection with the casting process. In this connection the knowledge of liquidus temperatures is important to avoid precipitation from the liquid flux resulting in composition and property changes. Cryoscopic measurements were performed in the composition range of 40-60 wt% NaCl, 40-60 wt% CaCl2, 0-15 wt% MgCl2 and 0-10 wt% CaF2. A thermodynamic model has been developed for multicomponent reciprocal molten salt solutions. The parameters of the model were obtained by critical evaluation and optimization of available thermodynamic data of the pure components and of 9 binary and 5 ternary subsystems. This thermodynamic model makes it possible to calculate crystallization temperatures in this quaternary reciprocal system. These calculated crystallization temperatures agree reasonably well with measured temperatures. An average deviation of 8 °C was observed between calculated and measured data while the uncertainty in the calculated data was estimated to be ±15 °C. This shows that it is possible to obtain reliable calculated crystallization temperatures in multicomponent molten salt systems. This result is very promising in view of the large amount of experimental work needed to measure such data in the whole composition volume of the multicomponent system.Le système réciproque quaternaire NaCl-CaCl2-MgCl2-CaF2 a été étudié expérimentalement par cryoscopie, et un modèle thermodynamique a été développé pour reproduire les propriétés thermodynamiques et l'équilibre des phases dans ce système. Une petite région de composition de ce système est utilisée comme flux métallurgique pour la coulée et le moulage du magnésium liquide. La connaissance des températures du liquidus est donc importante pour éviter la précipitation du flux qui impliquerait un changement de sa composition et de ses propriétés. Des mesures cryoscopiques ont été faites pour une région de composition de 40% à 60% poids NaCl, de 40% à 60% poids CaCl2, de 0% à 15% poids MgCl2 et de 0% à 10% poids CaF2. Un modèle thermodynamique a été développé pour les solutions de sels fondus multicomposantes réciproques. Les paramètres du modèle ont été obtenus par une analyse critique et l'évaluation des données thermodynamiques expérimentales pour les composants purs, les 9 sous-systèmes binaires et les 5 sous-systèmes ternaires. Ce modèle thermodynamique permet le calcul des températures de cristallisation dans ce système quaternaire réciproque. Les températures de cristallisation données par le modèle sont en accord avec les températures mesurées. Une déviation moyenne de 8 °C est observée entre les données calculées et les données expérimentales. L'incertitude sur les températures calculées à d'autres compositions que celles mesurées est estimée à ±15 °C, ce qui montre qu'il est possible d'obtenir des calculs fiables de températures de cristallisation d'un mélange multicomposant réciproque de sels fondus. Face à la quantité d'expériences nécessaires à la caractérisation de l'équilibre des phases pour la totalité du champ de composition d'un système multicomposant, cette approche est très prometteuse.

Entropy of bcc → L, fcc → L, and fcc → bcc phase transitions of elemental substances as function of transition temperature

In the last two-three decades, the thermodynamic calculations of phase diagrams for both binary and multicomponent systems have been in general use (see, e.g., [1–3]). For most systems, a thermodynamic description of virtual phase transitions for pure components entering a system is necessary for performing these calculations. Thus, e.g., for calculating the Ni–Cr phase diagram, it is necessary to know the enthalpies and entropies of phase transitions for Ni and Cr both in the case of the actual phase transitions [fcc liquid melt (L) for Ni and bcc L for Cr] and virtual phase transitions of metastable phases of pure Ni (bcc phase) and Cr (fcc phase) to the liquid phase.

Bulk diffusion studies of metallizations on titanium- based contacts at 600°C

The reactions occurring at the interface metal/Ti–Si–C, where metal=gold, aluminum or palladium and Ti–Si–C=Ti 3SiC 2, TiSi 2 or TiC, have been investigated on bulk diffusion couples. Prior to experimental work thermodynamic phase diagram calculations were performed to gain information about reactions likely to take place. After annealing cross sections of the metal/Ti–Si–C samples for 1.5 (metal+TiSi 2), 8 (metal+Ti 3SiC 2) and 23 h (metal+TiC) of samples were analyzed using SEM/EDX. The reactivity between the metals and the Ti–Si–C phases decreases in the sequence TiSi 2–Ti 3SiC 2–TiC and Au–Al–Pd. Using gold as metallization a liquid eutectic AuSi formed at the interface to TiSi 2 and Ti 3SiC 2, aluminum on both TiC and TiSi 2 results in formation of TiAl 3 and palladium on TiSi 2 reacts to an undetermined phase. In case a reaction occurred the layer thickness varied from over 100 μm for gold/TiSi 2 and 1.5 μm for palladium/TiSi 2.

Phase diagrams of light metals and thermodynamic calculations of phase diagrams

Phase diagrams of light metals and thermodynamic calculations of phase diagrams

Phase diagram calculations for high-temperature structural materials

Materials in use at high temperatures can reach states which are close to equilibrium and knowledge of the stable phase structure at fabrication and working temperatures can therefore be very important. The field of high-temperature structural materials provided one of the areas where thermodynamic phase diagram calculations were first used some two to three decades ago. However, although some general features of phase equilibria were predicted reasonably well, the early attempts were not able to provide sufficient accuracy for more general, practical use. Recent work has now shown that it is possible to make very accurate predictions for phase equilibria in a number of high-temperature structural materials and it is possible to demonstrate that predictions for phase equilibria in ‘real’ multicomponent alloys provide results close to those which are measured experimentally. This paper will present typical results which can now be obtained for γ-TiAl-based intermetallics and Ni-based superalloys and some specific examples of usage will be shown. A further advantage of the CALPHAD (calculation of phase diagrams) route is that other properties can be predicted using input data from the calculations, for example non-equilibrium solidification phenomena, time-temperature-transformation diagrams, antiphase domain boundary and stacking fault energies. This extension of the CALPHAD method will be briefly discussed.

Thermodynamic calculation of phase diagrams of the 60 common-ion ternary systems containing cations Li, Na, K, Rb, Cs and anions F, Cl, Br, I

The phase diagrams of all 60 possible common-ion ternary alkali halide systems were calculated thermodynamically. The thermodynamic properties of the ternary phases were calculated from the optimized properties of the binary subsystems, which were obtained from previously reported critical evaluations of binary data. Calculated ternary phase diagrams are compared with experimental diagrams in those 47 systems for which the latter are available. In most cases, agreement is within experimental error limits. For five systems, a small empirical correction term was added to the Gibbs energy expression in order to bring the calculated and reported diagrams into coincidence. The calculated ternary diagrams are considered to be the best evaluated diagrams that can be deduced from currently available data. A probable maximum inaccuracy was estimated for each system.

Bonding properties and vibrational entropy of transition metal MeB 2(AlB 2) diborides

The transition metal diborides MeB 2 were chosen as an example to illustrate an approach introduced by us, by which existing thermodynamic information can be systematized and new information generated. We consider trends in the melting temperature, the enthalpy of formation and lattice vibration properties as the metal Me varies along the 3d, 4d and 5d transition metal series. The trends show a consistent picture which can be explained from the electronic density of states by a rigid-band like argument. This fact gives us confidence to apply the regularities and obtain new information by interpolation and extrapolation procedures. In particular, we estimate the standard entropy S⊖ at 298.15 K for stable AlB 2 structure compounds where there are no previous measurements and for some metastable compounds ( Me ≡ Sc, V, Cr, Mn, Y, Mo, Tc, W and Re). The results are compared with estimates based on various empirical methods. In the Me-B systems, the MeB 2 phase may be stable at all temperatures, or be a high-temperature phase or a metastable phase. We explain the observed trend. Through the use of thermodynamic phase diagram calculations (the so-called CALPHAD method), we study the thermodynamic properties of the metastable AlB 2 structure phase FeB 2.

Evaluation of glass forming ability in binary and ternary metallic alloy systems – an application of thermodynamic phase diagram calculations

AbstractThe glass forming ability (GFA) of a wide range of binary and ternary alloy systems (Au–Si, Pd–Si, Ti–Be, Zr–Be, Hf–Be, Cu–Ti, Co–Zr, Ni–Zr, Cu–Zr, Ni–P, Pd–P, Ni–Pd–P, Cu–Pd–P, Co–Ti–Zr, Zr–Be–Hf, Ti–Be–Hf, Ti–Be–Zr) was calculated using a combined thermodynamic and kinetic approach. There is good agreement between the predicted glass forming ranges and those experimentally observed. By using this combined approach it has also proved possible to estimate critical cooling rates for phases not observed in the equilibrium phase diagram. A significant advantage of the approach is that, for multicomponent alloys, the melting temperatures and thermodynamic input parameters for the kinetic equations are derived using the constituent binary thermodynamic phase diagram calculations and, therefore, it has the potential to predict GFA in multicomponent systems using information from mainly binary systems.MST/788