Monovariant Reactions Research Articles

About the Alkemade Theorem and the Limits of its Applicability for the Construction of Ternary Liquidus Surfaces

The Alkemade theorem goes back to a very fundamental paper on the graphical description of thermodynamic equilibrium problems from 1893 (van Rijn van Alkemade in Z Phys Chem 11: 289-327, 1893). It is one of the most helpful implements for the construction of the liquidus surface of ternary phase diagrams. In its original form, it allows to find the direction of falling or increasing temperature along the monovariant reaction lines forming the boundaries of the primary crystallization fields. The theorem is valid for systems with any number of phases; however, its geometrical construction rule is only defined for the case of stoichiometric phases and it is not clear how to apply the theorem in the case of phases with extended homogeneity ranges. Some examples from a ternary, transition-metal-based system containing phases with large homogeneity ranges are presented, and the usefulness and limits of applicability of the theorem are discussed.

Experimental Study of the Cr-Hf-Nb System: Liquidus Projection and 1200 °C Isothermal Section

Phase equilibria data from ternary Cr-Nb-X (X = Hf, Ta, Ti, Zr) systems are relevant to the development of Niobium-silicide based composites for use in jet engines. Such systems present at several temperatures a pseudo-binary of Cr2Nb-Cr2X Laves phases. This work presents the experimentally determined liquidus projection and the 1200 °C isothermal section for the Cr-Hf-Nb system based on microstructural characterization of as-cast and heat-treated alloys. The microstructural characterization using x-ray diffractometry, scanning electron microscopy and electron probe microanalysis showed four eutectic-type monovariant reactions and two class II invariant reactions in the liquidus projection. The 1200 °C isothermal section showed complete solubility between Nb and Hf in (C15) phase and one three phase equilibria field.

Using DTA/DSC data for assessment of the Toop and Muggianu predictive models for the Ag–Au–In ternary

The relative performance of the Muggianu and Toop methods of preliminary prediction of thermodynamic properties of solution phases is tested using Ag–Au–In ternary as a model system, which was recently studied by the present authors. The temperatures of solids, monovariant reaction (where appropriate) and liquids, as well as the heat of melting of solid solutions, were measured by DTA/DSC for five ternary samples. Different extrapolation models generate very different descriptions of phase equilibria. However, accounting for ternary interactions brings all the results into moderately close agreement. In both methods, the values of ternary parameters for liquid phase are more negative than for solid phases (about twice in modulo in Muggianu one and up to ten times in Toop case). This implies the stabilization of liquid in central concentration region. Neither predictive model captures this without accounting for ternary interactions.

The Cu-Li-Sb system: A thermodynamic investigation on a materials system promising for lithium ion batteries

Lithium containing intermetallic alloys have recently become the focus of many investigations regarding their potential application as electrode materials for lithium ion batteries. However the overwhelming increase in volume during lithiation prohibits a general use of these materials in state of the art batteries. The Cu-Li-Sb system has gained much attention in this respect, as the intermetallic compound η-Cu2Sb showed remarkable cycling stabilities combined with a high charge capacity. To fully understand the reactions taking place upon charging/discharging of this material, a reliable phase diagram of the system is a prerequisite. Nevertheless almost no such data is available for the Cu-Li-Sb system. Especially reactions taking place at elevated temperatures become relevant regarding system malfunctions like e.g., thermal runaways of the battery cells.Therefore a substantial experimental investigation was conducted to enable the construction of three isothermal sections at 573 K, 673 K and 873 K. 83 alloy samples were thus metallurgically prepared and annealed at different temperatures. Analysis was done by powder X-ray diffraction. To validate the phase descriptions obtained from this data, electrochemical measurements were conducted. Coulometric titrations with four different Cu-Sb alloys (Cu concentrations = 80 at.%, 67 at.%, 50 at.%, 33 at.%) showed a good agreement with the phase fields expected from the powder X-ray diffraction data.48 of the 83 samples were in addition analyzed by differential thermal analysis, which enabled the construction of two vertical sections (isopleths). These followed the lines connecting the binary alloy compositions Cu66Sb34 and Cu50Sb50 with Li. In addition a liquidus projection showing in- and mono-variant reactions, together with liquidus isopleths could be outlined.Finally a reaction scheme including all invariant reactions found within the system was developed.

On the structure of the melting diagrams of quaternary systems

Topological and geometric images of invariant and monovariant reactions with the participation of melt in quaternary systems were presented. A network of invariant points and monovariant lines characterizes the structure of the liquidus hypersurface. Each invariant reaction produces an association of four solid phases, which is an element of the solidus hypersurface. Its topology is conveniently described by a graph of adjacency of tetrahedra that partition the composition tetrahedron of a system with a given set of binary, ternary, and quaternary compounds. It was demonstrated that it is possible to construct a spatial network of invariant points and monovariant lines on the liquidus hypersurface using the tetrahedron incidence graph with consideration for the phase reactions occurring in the system.

Physicochemical model for the crystallization of rocks of the calc-alkaline series

The Al-rich region of the CaO-MgO-Al2O3-SiO2 system was experimentally studied at pressures of 1.0–2.8 GPa and temperatures of 1300–1535°C. The slopes of the lines of the monovariant reactions An + Sp = Cpx + Cor + (Ga) and L = Cpx + Ga + Cor + Sp and the compositions of the phases involved in these reactions are determined. The results are utilized in the topological analysis of the aluminous region of the CaO-MgO-Al2O3-SiO2 system. On this basis, the principal structure of the phase diagram is analyzed, and a phase diagram is constructed for the junction region of the quaternary system and the CaO-Al2O3-SiO2 ternary system. A continuous series of the monovariant eutectic: L = Cpx + Opx + Fo + An, L = Cpx + Opx + An + Sp, L = Cpx + (Ga) + An + Sp, L = Cpx + Cor + (Ga) + An, L = An + Ga + Cpx + Ky and L = Ga + Cpx + Ky + Qz is examined within the pressure range from atmospheric to 3.0 GPa and higher. Analogous “telescoped” eutectic series are of fundamental character for interpreting the evolution of magmatic melts. A physicochemical model is suggested for the evolution of magmatic melts that produce rocks of the calc-alkaline series, with this model underlain by the fact that a change in the composition of magmatic melt at a pressure decrease should correspond to the minimum melting temperatures, i.e., to melts in the fundamental series of eutectic reactions. The comparison of our physicochemical model and rocks of the calc-alkaline series shows that the compositions of rocks of the calc-alkaline series are close to the compositions determined for the eutectic equilibria, and the mineralogical composition of xenoliths and megacrysts in volcanic and dike varieties of the rocks are similar to the subsolidus phases of the established fundamental eutectic system.

Modeling of deep-seated high-alumina parageneses on the basis of the stability fields of corundum- and spinel-normative assemblages of the system CaO–MgO–Al 2O 3–SiO 2

To elaborate physicochemical models for the origin of crystalline rocks, experimental studies of the field of high-alumina assemblages of the system CaO–MgO–Al 2O 3–SiO 2 were carried out at 10–30 kbar and 1250–1535 °C. We have determined the phase relations between the melt (L) and An, Sp, Cpx, Cor, and Ga, the slope of the rays of the monovariant reactions An + Sp = Cpx + Cor + (Ga) and L = Cpx +Ga + Cor + Sp, the position of the nonvariant point (An, Sp, Cpx, Cor, Ga, L), and the compositions of phases participating in these reactions. Based on a topological analysis of the studied segment of the system CaO–MgO–Al 2O 3–SiO 2, we have substantiated that “eclogitization” must follow the reaction Opx + An + Sp = Cpx + Ga. A fundamental continuous series of eutectic monovariant equilibria was observed: L = Cpx + Opx + Fo + An, L = Cpx + Opx + An + Sp, L = Cpx (+ Ga) + An + Sp, and L = Cpx + Cor (+ Ga) + An. A change in the melt composition in this series of eutectic reactions depending on pressure must reflect the most likely magma genesis trend in nature. Comparision of the composition fields in which the above series of reactions is observed with the composition fields of the rocks of magmatic formations showed that this series is most similar to the alkali-earth series of rocks. The mineralogical compositions of cumulates and phenocrysts found in the effusive and dike varieties of these rocks correspond to unique sets of subsolidus phase associations and individual subsolidus phases crystallizing in this fundamental eutectic series.

Study on the performance of hybrid adsorption–compression type II heat pumps based on ammonia salt adsorption

Sorption heat pumps based on monovariant reactions, such as ammonia-salt systems, can operate at low driving temperatures and achieve high power densities in comparison with multi-variant sorption systems. The disadvantage of monovariant systems, however, is the inflexibility towards required temperature levels. Where multivariant systems scale over a large range of temperatures, for the monovariant system, the temperature range is limited by the discrete transition from (fully) adsorbed to desorbed state. To increase flexibility towards changes in operating temperatures of the monovariant sorption systems, the extension of such systems with a compressor has been studied. Focus of this research is on the use of ammonia salts for type II heat pump for upgrading low temperature industrial waste heat to low-medium pressure steam. At ECN, a system based on LiCl-MgCl2 ammonia reactions has proved to achieve sufficient temperature lift (.508C) and cyclic stability (.100 cycles) but requires a minimum temperature of 1208C for proper operation. To add flexibility to this system, i.e. to be able to use waste heat below 1208C, the performance of a hybrid variant containing both thermally driven sorption reactors and a compressor has been evaluated. This evaluation focuses on extension in temperature range, and exergy efficiency and economic consequences of such a hybrid system. In addition, the possibility to use other ammonia-salt combinations has been investigated. The conclusions are that hybrid systems can reduce primary energy consumption and be economically feasible. It also shows that salt combinations other than LiCl-MgCl2 could be more suitable for a hybrid thermo-chemical adsorption-compression system.

Monovariant eutectic reaction in the Fe-Ni-S system as studied by directional solidification

The reaction of binary eutectic formation from (Fe1 − yNiy)S1 − z and γ-(FeyNi1 − y) solid solutions was studied using directional solidification of a three-component melt in a quasi-equilibrium mode. An experiment was carried out to obtain a sample comprising a single-phase region and a two-phase region. Component distribution curves for this sample were constructed; a change in the melt composition was calculated. These data were used to determine the change in phase compositions during solidification, construct the relevant dependences on the triangular diagram, and determine the transformation of tie-lines along monovariant curves on liquidus and solidus surfaces.

Topological classification of ternary phase diagrams with stoichiometric compounds

The topology of a three-component phase diagram can be described by a graph with tervalent nodes that correspond to invariant reactions. The graph edges correspond to monovariant reactions. For a structural description of the diagram, it is sufficient to indexing the graph nodes and edges so that they represent the sequences of invariant phase reactions. Therefore, a topological classification of phase diagrams is reduced to a classification of their graphs. We propose a set of classification features for systems with stoichiometric compounds and without phase transitions. We show a hierarchic relationship between these features and develop principles of a topological classification for the class of diagrams in question.

Mathematical modeling of solidification paths in ternary alloys: Limiting cases of solute redistribution

A simple mathematical framework is provided for calculating solidification paths of ternary alloys for equilibrium, paraequilibrium, and nonequilibrium conditions. The results are useful for estimating the possible range of primary solidification paths, the type of monovariant reaction expected to occur, and the relative amount of primary, monovariant eutectic and ternary eutectic constituents that form during solidification. Example calculations show that, for solidification of a ternary eutectic alloy under equilibrium conditions, the monovariant eutectic reaction will only occur when the nominal alloy concentration is above the maximum solid solubility. This result is similar to the binary case. For paraequilibrium conditions, a monovariant eutectic reaction is always expected to occur, but solidification can terminate before the invariant ternary eutectic reaction is reached. Finally, for nonequilibrium conditions, both the monovariant and invariant ternary eutectic reactions are always expected to occur, which is similar to the binary nonequilibrium case. The direction of liquid enrichment on the monovariant eutectic line can also be determined from the results.

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.

Intermetallic compound formation in Fe–Al–Si ternary system: Part II

The phase equilibria in the Fe–Al–Si ternary system have been studied in the temperature range 600–900 °C using ternary diffusion couple experiments with pure Fe and high purity Al–Si eutectic alloy. A number of binary and ternary intermetallic compounds have been observed. Except for the FeAl 3 binary phase, the remaining intermetallics of the system, namely, Fe 2Al 5, FeAl and Fe 3Al, are observed to form as solid layers next to pure iron. The FeAl 3 phase was observed in association with the liquid which solidified into secondary and tertiary crystallization products. A number of ternary phases, namely, τ 1, τ 2, τ 4, τ 5 and τ 6 have been observed. These phases have crystallized either directly from the liquid or through the invariant or monovariant reactions. The composition of the phases and associated microstructure of each phase has been presented.

A contribution to the ternary copper-magnesium-nickel phase diagram

The ternary CuMgNi phase diagram has been studied by differential thermal analyses, X-ray powder diffraction and isopiestic vapour pressure measurements. Three different isopleths with constant x Cu x Ni ratios of 2.0, 1.0 and 0.5, and one with a constant magnesium content of 71 at.% were constructed from these measurements. Together with literature information it was possible to define the four invariant four-phase equilibria in the system with respect to the temperature and compositions of the participating phases, and to derive the monovariant reaction lines on the liquidus surface. Furthermore, it was confirmed that Mg 2Ni dissolves up to about 25 at.% Cu at 450°C.

Calculated Al–Ti–Be phase diagram and interpretation of grain refinement results

The Al corner of the Al–Ti–Be is calculated using the FACT* EQUILIB computer program and applied in interpreting grain refinement and precipitation behaviour results for AI–0·2Ti–0·2Be (wt-%) alloy. Isothermal sections calculated for the temperature interval 527–727°C show that small additions of Be transform the isothermal peritectic reaction for the Al–Ti binary to a monovariant reaction in which secondary Al crystals are formed over a temperature range, and that Be and Ti restrict severely their mutual solubility in solid Al, precipitating as TiBe12. The effects of Be on the Al–Ti system are consistent with the grain refinement and precipitation enhancement for the Be containing alloys.MST/1223

Calculated Al–Ti–Be phase diagram and interpretation of grain refinement results

The Al corner of the Al–Ti–Be is calculated using the FACT* EQUILIB computer program and applied in interpreting grain refinement and precipitation behaviour results for AI–0·2Ti–0·2Be (wt-%) alloy. Isothermal sections calculated for the temperature interval 527–727°C show that small additions of Be transform the isothermal peritectic reaction for the Al–Ti binary to a monovariant reaction in which secondary Al crystals are formed over a temperature range, and that Be and Ti restrict severely their mutual solubility in solid Al, precipitating as TiBe12. The effects of Be on the Al–Ti system are consistent with the grain refinement and precipitation enhancement for the Be containing alloys.MST/1223

The assemblage orthopyroxene+cummingtonite+quartz. The low-temperature stability limit

The monovariant reaction Opx+H2O⇄ Cum+Ol+Q and the Cum+Opx+Q stability field were studied under hydrothermal conditions at Ptotal=2940, 4900 bar and the oxygen fugacity of the QFM buffer. Under these conditions, the Opx lower stability brackets were 730°±10° and 740°±5° C, respectively. The kinetics of the reactions in the Cum+ Opx+Q mixture showed that there were only minor differences in the equilibrium compositions of the coexisting Opx and Cum over the 740°–780° C range. At T=780°, 760° and 740° C, the FeO/FeO+MgO ratio, in mol% was: Opx52.5−Cum49.5, Opx62−Cum57, Opx72−Cum66 (P=2940 bar) and Opx62−Cum58.5 Opx71.5−Cum66.5, Opx80−Cum75 (P= 4900 bar). The results are in good agreement with earlier studies in the Opx+Ol+Q and Cum+Ol+Q assemblages.

The constitution of the system Al-Ti-B with reference to aluminum-base alloys

Direct and differential thermal analyses have been used to determine the liquidus temperatures and isothermals in the aluminum-base corner of the Al-Ti-B system, and with microscopical information and electron microprobe analyses provide results on which is based a provisional phase diagram. The TiB2 liquidus rises very steeply from the aluminum corner of the diagram and is bounded on either side by monovariant reactions which almost coincide with the binary Al-B and Al-Ti liquidus curves. If the Ti:B ratio exceeds 7∶3 wt pct (1∶2 at. pct), TiB2 precipitates on cooling until there occurs a monovariant reaction involving Al3Ti, while at lower Ti:B ratios there occurs a monovariant reaction which involves AlB2. The grain refining action of ternary alloys is discussed with reference to the form of the phase diagram.

Liquidus Surfaces of Ternary Nickel-Boron-Silicon Alloy for Infiltrant

In order to determine the liquidus surfaces, the ternary system Ni-B(<30 at %)-Si(<30 at %) was studied by thermal analysis, X-ray diffraction and the observation of microstructures. The results obtained are summarized as follows:(1) The phases appeared in this region were Ni(solid solution), Ni3B, Ni2B, Ni3Si, Ni5Si2 and Ni6Si2B.(2) Quasi-binary eutectic reactions took place at the boundaries of liquidus surfaces of Ni(solid solution) and Ni3B; Ni3B and Ni2B; Ni(solid solution) and Ni3Si; Ni3Si and Ni3B; Ni3B and Ni6Si2B; and Ni2B and Ni6Si2B. Monovariant-peritectie reactions took place at the boundaries of liquidus surfaces of Ni5Si2 and Ni3Si, and Ni5Si2 and Ni6Si2B.(3) Following four invariant reactions with melt were observed at the intersections of the above i monovariant reaction lines;L(11 at %B, 13 at %Si)+Ni5Si2=Ni6Si2B+Ni3Si at 1012°CL(12.3 at %B, 12.0 at %Si)+Ni6Si2B = Ni3B+Ni3Si at 1002°CL(9.8 at %B, 12.9 at %Si)=(Ni)+Ni3B+Ni3Si at 993°CL(20.3 at %B, 9.8 at %Si)=Ni3B+Ni2B+Ni6Si2B at 991°CThus, the liquidus surfaces have been experimentally determined.

Influence of water on melting of silicates at high pressure

The conditions of solidus in water-silicate systems are analysed from thermodynamic considerations. In the region of low H 2O pressures a molar volume of water is considerably greater than that of silicates. It is shown that this fact must determine the inevitable temperature decrease of silicate melting in the presence of water. A substantial decrease of the water molar volume with pressure increase leads to the fact that thermodynamic conditions are created under which the melting temperature of water-silicate systems will augment, i.e. with respect to pressure the water-silicate systems will behave similarly to dry systems. This fact is of considerable petrological interest for the solution of problems of Earth material transitions to the molten state. When passing from low pressures to high ones the change of the d T/d P sign from negative to positive may occur either in the point of extremum for temperature or in the invariant point which lies on the intersection of the T- P curve of the monovariant reaction of melting with the line of solid phase transformations.