Patrice Chartrand

• PhD
• Professor at Polytechnique Montréal

Contrary to the solid state, the understanding of thermal transport within molten salts remains limited. This study aims at establishing a robust theoretical framework for describing and predicting thermal transport in complex and dissociated multicomponent molten salt mixtures, considering both the composition and temperature variables. The propos...

This study outlines an extensive investigation of crystallographic data and thermodynamic properties (including solid-solid transition and fusion) for sodium dichromate, potassium dichromate, sodium dimolybdate, potassium dimolybdate, sodium ditungstate, and potassium ditungstate. A thorough literature review was conducted to obtain a good understa...

This paper evaluates crystallographic data and thermodynamic properties for sodium chromate, potassium chromate, sodium molybdate, potassium molybdate (K2MoO4), sodium tungstate, and potassium tungstate collected from the literature. A thorough literature review was carried out to obtain a good understanding of the available data, and a critical ev...

This study presents a theoretical model, based on kinetic theory, for accurately predicting thermal conductivity in molten salt mixtures, a vital factor in designing advanced energy systems such as concentrating solar power, thermal energy storage, and advanced nuclear reactors. Applicable to non-complex, non-reciprocal systems, the model represent...

In this work, a critical evaluation of all available phase diagrams and thermodynamic data for the As–Cd, As–Zn and As–Cd–Zn systems has been performed and thermodynamic assessments over the whole composition ranges are presented using the CALPHAD method. To predict thermodynamic properties and phase equilibria for these systems, the Modified Quasi...

A critical evaluation of all available phase diagram and thermodynamic data has been performed for Ag-As, Ag-S, As-S and Ag-As-S systems, including a detailed review of the gaseous species involved in the As-S system. Thermodynamic assessments over the whole composition range for these four systems are presented using the CALPHAD method. To predict...

In Hall–Héroult cells the uninvolved alumina precipitates on the top of the cathode to form resistive deposits which could significantly impact the energy consumption. A dynamic energy conservation (DEC) approach has been developed to quantify the flux of undissolved alumina piercing the interface between the electrolyte and the liquid metal in Hal...

A theoretical model for predicting the temperature-dependent thermal conductivity of pure molten salts, both simple and complex, is presented. The model is based on kinetic theory and incorporates Einstein’s concept of minimum thermal conductivity. The proposed formulation can consider the magnitude of thermal conductivity for separate salts, inclu...

In Hall-Héroult cells the uninvolved alumina precipitates on the top of the cathode tp form resistive deposit which could significantly impact the energy consumption. A dynamic energy conservation (DEC) approach has been developed to quantify the flux of undissolved alumina piercing the interface between the electrolyte and the liquid metal in Hall...

The properties of the carbon materials obtained as the final product of coal tar pitch carbonization process are a consequence of the type of chemical and physical phenomena occurring through the process. A new simplified approach for modeling of the primary carbonization is presented to provide the semi-quantitative knowledge about the process use...

An accurate knowledge of the interfacial tension between liquid aluminium and cryolitic melts is critical to better understand the process parameters influencing the current efficiency in electrolysis cells. In principle, the interfacial tension can be predicted from the surface tension of liquid aluminium, cryolitic melts and their adhesion energy...

An original theoretical model that can predict the temperature-dependent thermal conductivity for pure molten salts that are both simple and complex is proposed. The model is derived from kinetic theory and implements the Einstein's concept of minimum thermal conductivity. The proposed formulation can separately consider the magnitude of thermal di...

This research work falls under the generic theme of modeling high-temperature processes, during energy conversion, flaking, and corrosion phenomenon, for systems converting mainly organic matter into energy. Energy conversion facilities are made of a metal alloy of the type Fe–Cr–Ni–V–Mo–W and are exposed to gaseous species from combustion, or from...

The Modified Quasichemcial Model in the Distinguishable-Pair Approximation (MQMDPA) for manifold short-range orders in liquids has been successfully extended to multicomponent solutions. The extension is conducted by means of the geometrical interpolation method. Three types of interpolation models, namely Kohler, Toop and Chou, are introduced to i...

Among all the properties required for the design of the next generation of phase change materials (PCMs) (density, heat capacity, thermal expansion, latent energy, volume change upon melting, corrosion rate, etc.) the thermal transport properties are by far the least known, especially for molten salt mixtures and solid solutions. We present in this...

The next generations of Concentrated Solar Thermal Power (CSTP) systems use anhydrous salts as the heat transfer fluid and thermal storage medium. Unfortunately, a severe lack of experimental data is observed for the thermal transport properties of molten salt mixtures, generating constraints in exploring new potential materials for CSTP systems. T...

Among all the properties required for the design of the next generation of PCM (density, heat capacity, thermal expansion, latent energy, volume change upon melting, corrosion rate, etc.) the thermal transport properties are by far the least known, especially for molten salt mixtures and solid solutions. We present in this paper a theoretical frame...

Ever-increasing interests for more accurate thermodynamic predictions of phase diagrams motivate the development of more reliable thermodynamic models. The Modified Quasichemical Model within the two-sublattice Quadruplet Approximation (MQMQA) was thus established in well response to these interests and motivations. However, the model still needs t...

Because of the importance of thermodynamic behavior of Polycyclic Aromatic Hydrocarbon (PAH) compounds in coal tar pitch carbonization process, a thermodynamic model for the prediction of thermodynamic properties of PAH compounds is developed. Heat capacity functions as well as standard thermodynamic properties of PAHs in solid, liquid, and gas sta...

Ever-increasing interests for more accurate thermodynamic predictions of phase diagrams motivate the development of more reliable thermodynamic models. The Modified Quasichemical Model within the two-sublattice Quadruplet Approximation (MQMQA) was thus established in well response to these interests and motivations. However, the model still needs t...

Contrary to the ionic conductivity, the electronic conductivity of cryolitic melts, which can be up to 30 pct of the total conductivity in industrial electrolysis cells, remains largely unknown as very few experimental data are reported in the literature. The aim of this work is to fill this gap by providing reliable estimations of the electronic c...

Carbonaceous mesophase appears as an intermediate product in production of electrical and mechanical carbon materials, needle coke for graphite electrodes used in electric-arc furnaces, pitch-based fibers and aluminum-smelting prebaked electrodes through carbonization process. A thermodynamic approach for phase behavior estimation of carbonaceous m...

An accurate knowledge of the electrical properties of molten salts and slags is important for the design, optimization and control of several electrochemical processes. The electrical conductivity of molten salts and slags is in principle of ionic nature, however when metals are dissolved in electrolyte electrons may also contribute to the electric...

The charge and electron transport properties of molten ionic systems are among the most relevant properties to consider in the control of several electrochemical processes. First-principles\revadd{-based} equilibrium molecular dynamics (EMD) can provide reliable predictions of both the total and partial charge transport properties. \revadd{In this...

Due to the important similarities between olivine-LiFePO4 and olivine-LiMnPO4, manganese doping has drawn a lot of attention since it can improve the electronic and ionic conductivity of LiFePO4, hence enhance the electrochemical properties. The thermodynamic behavior of Mn-doped-LiFePO4 cathodes has been examined through the thermodynamic investig...

In aluminium reduction cells, an electrochemical reaction occurs between the molten electrolyte film below the aluminium pad and the carbon cathode blocks, leading to the formation of an Al4C3 layer on the cathode blocks. The properties and role of this Al4C3 layer are therefore important for the aluminium production industry, as they could help in...

Glass forming ability (GFA) of Mg-Zn alloys with Sr addition has been experimentally studied coupled with CALPHAD method. Two series of metallic glasses (MGs), Mg98−xZnxSr2 (x = 38, 36, 33, 30, 28) and Mg95−xZnxSr5 (x = 37, 33, 30, 27, 23), were designed and prepared successfully for the first time. The crystallization characteristics of these MGs...

Reciprocal molten halides are a distinctive class of high-temperature ionic liquids used as thermal and electrolytic media in the respective fields of MSR (molten salt nuclear reactor) and metallurgy. Strong Short-Range Ordering (SRO) from both the first-nearest (cation-anion) and second-nearest (cation-cation and anion-anion) neighbors defy accura...

Experimental surface tension data for many binary, ternary and higher order metallic systems is unfortunately currently unavailable in the literature. This could be detrimental in several practical and industrial applications. Consequently, having a theoretical model with a good predictive capability is highly desirable. In general, the surface ten...

Knowing the charge-transport properties of molten oxides is essential for industrial applications, particularly when attempting to control the energy required to separate a metal from its ore concentrate. Nowadays, in the context of a drastic increase of computational resources, research in industrial process simulation and their optimization is ga...

LiFePO4 (LFP) is a safe and low cost cathode material for Li‐ion batteries. Its solid‐state synthesis requires micron‐sized reactants yielding high production costs. Here, we melt‐synthesized up to 5 kg batches of LFP from low‐cost coarse Fe2O3 (509 µm) in an induction furnace. Graphite from the crucible was an effective reducing agent. Adding meta...

An accurate knowledge of the surface tension of liquid metals is critical for many theoretical and practical applications, especially in the current context of emerging growth of nanotechnology. The surface tension and its temperature dependence are drastically influenced by the level of impurities in the metal such as oxygen, sulphur or carbon. Fo...

In many metallurgical applications, an accurate knowledge of miscibility gaps and spinodal decompositions is highly desirable. Some binary systems where the main constituents of the same crystal structures have similar lattice parameters (less than 15 % difference) reveal a composition, temperature shift of the miscibility gap due to lattice cohere...

Not all carbons graphitize in equal measure. Some will develop a structure which approaches the one of perfect graphite (graphitizable carbons)upon heat treatment, while others will not (non-graphitizable carbons). The present work develops a phenomenological model for the conceptual understanding of graphitizability (capacity to graphitize). To su...

Since Goodenough's team laid the foundation to apply LiFePO4 as an alternative to lithium cobalt oxide for Li‐ion positive electrodes,[1,2] Web of Science (WoS)[3] has indexed over 6000 articles related to lithium iron phosphate| LFP. Manufacturers synthesize‐LFP with both solid state and solvent assisted hydrothermal technology. Both have their ad...

The surface tension of liquid metals depends strongly on atmosphere conditions, in particular on the partial pressure of oxygen, on top of temperature. Predicting the surface tension of metals in different atmosphere conditions is highly desirable for many fundamental and practical applications. Currently, none of the theoretical and semi-empirical...

LiFePO4 (LFP) as a promising cathode material has been extensively studied. However, the high cost of current batch production technology limits its application, especially in automotive industries. To develop the new melting synthesis of LFP, the process conditions have to be strictly controlled, such as temperature, composition, and the partial p...

A thermodynamic model for the FePO4‐LiFePO4 olivine join has been developed in order to provide support for the understanding of the charge transport behaviour within the cathode material during the battery operation. The Gibbs energy model for the olivine solution is based on the compound energy formalism with long‐range‐order and has been calibra...

The effect of coherent strains which is involved during the fast charge/discharge processes and the influence of particle size reduction which improves the electrochemical performance of the cathode material are modelled in this study. An extension of the linear isotropic approximation for elastic energy stored in the coherent boundaries of an orth...

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the (LiCl + NaCl + KCl + MgCl2 + CaCl2 + CeCl3) system, and optimized model parameters have been found. The (LiCl + NaCl + KCl + MgCl2 + CaCl2) subsystem has been critically evaluated in a previous article. The model p...

Compared with large‐scale processes, the LiFePO4 (LFP) melt‐synthesis is a low‐cost method with short dwell times and rapid reaction rates. However, secondary phases and impurities remaining in the olivine structure lower the cathode's electrochemical properties. Starting from a low‐cost Fe³⁺ precursor, we evaluated tin and silver charged metallic...

A new thermodynamic model has been developed for molten salt-water solutions. The model applies particularly to salt-rich solutions but may be applied over the entire composition range from anhydrous salts to pure H2O. The model is an extension of the two-sublattice Modified Quasichemical Model for molten anhydrous salt solutions with first-nearest...

Molten cryolite mixed with some additives is used as solvent of alumina by aluminium producers. Cryolite represents the dominating compounds in the wall protecting side-ledge and at the bottom part of the frozen crust on the top of the cells. As the heat, generated in the cell, is lost mainly through the top and the lateral sides of the pot, the th...

This paper presents a quantitative thermodynamic description for water, hydrogen fluoride and hydrogen dissolutions in cryolite-base molten salts, which is of technological importance to the Hall–He´roult electrolytic aluminum extraction cell. The Modified Quasichemical Model in the Quadruplet Approximation (MQMQA), as used to treat a large variety...

The aim of this work is a formulation of a thermodynamic model for the development of new aluminum machining alloys. The three additives Bi, Pb and Sn have proven to help machining. Hence, a review of the literature showed that the liquid phase equilibria and thermodynamic data for the three binary systems Al-Bi, Al-Pb and Al-Sn is very thorough bu...

Individual transport numbers provide a measure of the charge ratio which is carried by each ionic species of an electrolyte. However, unlike the electrical conductivity or diffusion coefficients, this quantity lacks a clear definition from the statistical mechanics point of view. In practice, it is measured via complex experimental setups, and most...

The present paper develops a thermodynamic model for the calculation of the Gibbs energy of graphitizable carbons near the graphitization temperature threshold of 2550K. The graphitization threshold is the minimal heat treatment temperature for the establishment of true graphitic ordering in a graphitizable carbon. The present model represents the...

A thermodynamic evaluation and optimization of the CALPHAD type of the Cu-O-F system, together with phase diagram measurements, are considered in the present work as the first step towards a complete evaluation of Cu in the multicomponent system Cu-Fe-Ni-Na-Al-Ca-O-F. Differential Scanning Calorimetry experiments were conducted using a closed cruci...

An electrothermodynamic model is proposed for the carbon anode consumption of the aluminium electrolysis process. Anode consumption produces a primary anode gas composed of CO and CO2. Experimentally, higher electrolysis potentials at the bath/anode interface promotes the formation of CO2 over CO, reducing the carbon consumption at the cost of grea...

This paper presents a database for the temperature-dependent thermal conductivity of compounds potentially present in the side ledge formed in aluminium electrolysis cells, between the molten electrolyte used to dissolve the alumina and the side wall. The database is given in the form of an analytical model with sets of parameters for each compound...

In aluminum electrolysis cells, a ledge of frozen electrolyte is formed on the sides. Controlling the side ledge thickness (a few centimeters) is essential to maintain a reasonable life span of the electrolysis cell, as the ledge acts as a protective layer against chemical attacks from the electrolyte bath used to dissolve alumina. The numerical mo...

During aluminiumelectrolysis, a ledge of frozen electrolytes is generally formed, attached to the sides of the cells. This ledge acts as a protective layer, preventing erosion and chemical attacks of both the electrolyte melt and the liquid aluminium on the side wall materials. The control of the sideledge thickness is thus essential in ensuring a...

CALculation of PHAseDiagram-type (CALPHAD-type) thermodynamic databases for Mg alloy systems have been developed over the last two decades. In the present study, recent updates of the thermodynamic data related to the Mg-RE and Mg-Sn based systems to the FactSage FTlite database are reviewed. Several examples of applications of the new database to...

Numerical modeling of heat transport in the side ledge of a cryolite bath as a function of its thickness requires an accurate knowledge of the thermal transport properties of the cryolite bath as well as the solid phases constituting the side ledge. Unfortunately, due to experimental limitations, there is a lack of experimental data on this subject...

In aluminium electrolysis cells, a ledge of frozen electrolyte is formed, attached to the sides of the cell. The control of the side ledge thickness is essential in ensuring a reasonable lifetime for the cells. Numerical modelling of the side ledge thickness requires an accurate knowledge of the thermal transport properties as a function of tempera...

A new thermodynamically self-consistent (TSC) method, based on the quasi-harmonic approximation (QHA), is used to obtain the Debye temperatures of LiFePO4 (LFP) and FePO4 (FP) from available experimental specific heat capacities for a wide temperature range. The calculated Debye temperatures show an interesting critical and peculiar behavior so tha...

The FactSage computer package consists of a series of information, calculation and manipulation modules that enable one to access and manipulate compound and solution databases. With the various modules running under Microsoft Windows® one can perform a wide variety of thermochemical calculations and generate tables, graphs and figures of interest...

With its good thermal stability, abundance in nature and benign environmental impact, LiFePO4 (LFP) cathode material is seen as one of the most promising candidate for the next generation of Li-ion batteries. Many synthetic routes have already been used for preparing LFP material, best known being solid state, sol-gel, hydrothermal, co-precipitatio...

How graphitic structures evolve from non-graphitic carbons, during heat treatment, is conceptually understood through the graphitization mechanisms of the turbostratic model. However, inadequacies exist, most notably concerning the temperature behaviour of the intercrystalline carbon material located between turbostratic crystallites. Previous ther...

The FactSage computer package consists of a series of information, calculation and manipulation modules that enable one to access and manipulate compound and solution databases. With the various modules running under Microsoft Windows® one can perform a wide variety of thermochemical calculations and generate tables, graphs and figures of interest...

LiFePO 4 (LFP) has attracted much attention as a promising candidate for cathode materials in new generation of Li-ion batteries due to its good thermal stability, being environmentally friendly and abundance in nature. Many synthetic routes, such as solid state, sol-gel, hydrothermal, co-precipitation, and microwave preparations, have been used fo...

An approach to calculate various properties of solution is presented using CALPHAD phase diagram software. The properties include iso-bar, iso-activity, iso-activity coefficient, iso-sulfide capacity, iso-surface tension of various types of solutions such as liquid oxide or liquid alloy. Auxiliary phase(s) is introduced in order to set an equilibri...

The present work has been performed with the aim to optimize the existing process for the production of high purity bismuth (99.999 pct). A thermo-chemical database including most of the probable impurities of bismuth (Bi-X, X = Ag, Au, Al, Ca, Cu, Fe, Mg, Mn, Na, Ni, Pb, S, Sb, Sn, Si, Te, Zn) has been constructed to perform different thermodynami...

Introduction LiFePO 4 (LFP) was proposed by Padhi et al. ¹ in 1997 as a promising cathode material for Li-ion batteries and very soon became the center of attention for researchers and industries in energy fields. Nowadays, it is commercialized and available in mass production through different methods. A lot of improvements in terms of material an...

This work describes the application of a direct search method to the optimization of problems of real industrial interest, namely three new material science applications designed with the FactSage software. The search method is BiMADS, the biobjective version of the mesh adaptive direct search (MADS) algorithm, designed for blackbox optimization. W...

In this study, density functional theory (DFT) with a thermodynamically self-consistent (TSC) method are used to predict the thermophysical properties of metallic compounds. The TSC method used in this work is, in summary, an extension of the classical quasi-harmonic approximation satisfying the Maxwell relations and thus ensuring thermodynamic con...

A careful evaluation and optimization of all available phase equilibrium and thermodynamic data for the (KF + YF3), (KCl + YCl3) and (YF3 + YbF3) binary systems was performed to obtain optimized model parameters for all solid and liquid phases. After the discussion of four different optimization strategies, the Modified Quasichemical Model in the p...

A theoretical model for the description of thermal conductivity of molten salt mixtures as a function of composition and temperature is presented. The model is derived by considering the classical kinetic theory and requires, for its parametrization, only information on thermal conductivity of pure compounds. In this sense, the model is predictive....

A size-dependant thermodynamical model for the carbon-hydrogen previously developed by Ouzilleau et al. [1] has been expanded here to include chemisorption of methyl groups. Gibbsenergy minimalisation calculations using FACTSAGE software on this model indicates that hydrogen bonding through methyl groups is energetically favoured as an intermediate...

Current efficiency is an important indicator used in the aluminum reduction technology. Values for this indicator are usually determined among potlines and they are not representative of the fluctuations that may occur in a single electrolysis cell. To measure or calculate an accurate value on a monthly basis would be a very interesting tool for pr...

The corrosion of the cathode refractory lining in electrolysis cells, partly due to the cryolite bath, can shorten the lifespan of the cell. This corrosion is usually studied with laboratory tests and cathode autopsies of shutdown cells, but the results might not correspond to the reactions taking place in service. The simplified corrosion problem...

A method for the prediction of the thermal transport properties of macroscopic and isotropic oxides systems, above the standard temperature of T = 298.15 K , is presented. This method combines: (i) the kinetic theory, (ii) a thermodynamically self consistent method for the density of the lattice vibration energy, and (iii) the three-phonon umkl...

Rear face flash experiments were performed in order to determine the thermal conductivity of sintered tungsten at room temperature. Ten different samples were synthesized with the spark plasma sintering technique. The microstructure obtained from the sintering is porous and consists of angular grains with medium sphericity. The average grain size (...

Phase equilibria in the Mg–Zn–Sr ternary system, in the composition range 0–35 at% Sr at 300 °C, were investigated using two diffusion couples and 23 alloy samples. Scanning electron microscopy equipped with an energy-dispersive spectroscope and electron probe micro-analysis were employed to analyze the constituted phases and their compositions in...

Critical evaluations and thermodynamic modeling of the Ag-(Ca, Li, and Zn) and Ca-(In, Li) binary systems are presented. Thermodynamic optimization of the Ag–Li binary system was carried out in the present work at first. Thermodynamic re-optimizations of the Ag–Ca, Ag–Zn, Ca–In and Ca–Li binary systems were carried out in the present work, which pr...

A new ternary compound, Mg15 − xZnxSr3 with extensive solid solubility in the Mg–Zn–Sr system was observed and studied using electron probe microanalysis (EPMA), scanning electron microscopy SEM, and X-ray techniques. The solid solubility limits of this compound were found to be Mg15 − xZnxSr3 (0.24 ≤ x ≤ 10.58, at.%) at 300 °C using a diffusion co...

The development is presented of a model of the thermodynamic functions of enthalpy, entropy and Gibbs energy for the elements carbon and hydrogen in coke crystallites. It is applicable to varying degrees of graphitization, described by the crystallite length La and the crystallite height Lc. The model parameters are derived from known properties su...

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the (NaNO3 + KNO3 + Na2SO4 + K2SO4) ternary reciprocal system, and optimised model parameters have been found. The model parameters obtained for the four binary common-ion subsystems (i.e. (NaNO3 + Na2SO4), (KNO3 + K2S...

The composition dependence of thermal transport properties of the (Na,K)Cl rocksalt solid solution is investigated through equilibrium molecular dynamics (EMD) simulations in the entire range of composition and the results are compared with experiments published in recent work [Gheribi et al., J. Chem. phys. 141, 104508 (2014)]. The thermal diffusi...

A size-dependant thermodynamical model for the carbon-hydrogen previously developed by Ouzilleau et al. [1] has been expanded here to include chemisorption of methyl groups. Gibbs-energy minimalisation calculations using FACTSAGE software on this model indicates that hydrogen bonding through methyl groups is energetically favoured as an intermediat...

Changes in the quality of green cokes available for the production of pre-baked carbon anodes used in the production of aluminum are stimulating the development of a better understanding of the thermodynamic behavior of cokes. Impurity content and crystallite sizes (over a wide range of temperature) are of particular concern. No thermodynamic model...

Changes in the quality of green cokes available for the production of pre-baked carbon anodes used in the production of aluminum are stimulating the development of a better understanding of the thermodynamic behavior of cokes. Impurity content and crystallite sizes (over a wide range of temperature) are of particular concern. No thermodynamic model...

We have developed a quantitative thermodynamic description of the NH4H2PO4-(NH4)2H2P2O7-KH2PO4-K2H2P2O7-NH4NO3-KNO3-NH4Cl-KCl-H2O system, which is of great importance for fertilizers applications. The liquid phase and all solid solutions were modeled using the Modified Quasichemical Model for short-range ordering. The liquid model includes the reac...

The critical re-optimization of the Li–Sn binary system and optimization of Mg–Sn–Li ternary system in the Mg-rich portion have been conducted using a coupled first-principles calculations and CALPHAD method. The enthalpies of formation of LiSn, Li7Sn3, Li5Sn2, Li13Sn5, Li7Sn2, Li2Sn5, Li17Sn4 and Li2MgSn phases at 0 K were obtained by first-princi...

We present two theoretical models to predict the lattice thermal conductivity degradation of insulating materials at high temperature (above one-third of the Debye temperature). This degradation is due to the presence of grains, with known sizes and shapes, inducing thermal resistance at their boundaries. The first model is derived directly from th...

The composition dependence of the lattice thermal conductivity in NaCl-KCl solid solutions has been measured as a function of composition and temperature. Samples with systematically varied compositions were prepared and the laser flash technique was used to determine the thermal diffusivity from 373 K to 823 K. A theoretical model, based on the De...

Bi-alkali metal (Li, Na, K, Rb) binary systems have been systematically assessed based on the available phase diagrams and thermodynamic data. The modified quasichemical model, which takes short-range ordering into account, is used to describe the liquid phase. All intermetallic phases are treated as stoichiometric compounds. A set of self-consiste...