FactSage thermochemical software and databases, 2010 – 2016

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 s one can perform a wide variety of thermochemical calculations and generate tables, graphs and ﬁ gures of interest to chemical and physical metallurgists, chemical engineers, corrosion engineers, inorganic chemists, geochemists, ceramists, electrochemists, environmentalists, etc. This paper presents a summary of the developments in the FactSage thermo-chemical software and databases during the last six years. Particular emphasis is placed on the new databases and developments in calculating and manipulating phase diagrams.


Introduction
FactSage began in 1976 as F*A*C*T -Facility for the Analysis of Chemical Thermodynamicsa joint research project between McGill University and École Polytechnique de Montréal (Université de Montréal Campus). In 1984 the CRCT -Centre for Research in Computational Thermochemistry/Centre de Recherche en Calcul Thermochimiquewas founded at École Polytechnique de Montréal. A principal activity of the CRCT was, and still remains, the promotion and development of the F*A*C*T thermochemical databases and software.
During the 1990s F*A*C*T migrated to personal computers running in a Windows environment. In 2001 there was a fusion between F*A*C*T / FACT-Win and ChemSage (formerly SOLGASMIX [1])r e s u l ting in FactSage s . Since then FactSage has expanded into a fully integrated thermochemical software and database package that is used worldwide at over 800 sites in universities, governmental and nongovernmental research laboratories and industry.
The original F*A*C*T package was designed to simulate the thermochemistry of pyrometallurgical processing and plot classical binary and ternary phase diagrams. Today FactSage applications include hydrometallurgy, electrometallurgy, corrosion, glass technology, combustion, ceramics, geology, environmental studies, etc. and it can calculate and plot binary, ternary and multicomponent phase diagrams with a wide variety of axes. Forty years ago the turnaround time using a mainframe computer to calculate and print thermochemical tables was measured in hours. Using today'sp e r s o n a lc o mputers one can calculate and plot phase diagrams within seconds.
While an understanding of chemical thermodynamics is useful in order to run the modules, it is not essential for a user to be an expert in the field. With practice and the assistance of extensive documentation, one can acquire a practical understanding of the principles of thermochemistry, especially as these relate to complex phase equilibria. Articles on FactSage Thermochemical Software and Databases (2002) and FactSage Thermochemical Software and Databases -Recent Developments (2009) have been published in the Calphad Journal [2,3]. The reader who is unfamiliar with FactSage is encouraged to consult these original publications. The present article outlines the new databases and developments in calculating and manipulating phase diagrams that have been introduced since the last publication (2009) and briefly describes developments in the programs.

Info
The general option gives the user access to the latest slide shows, documentation on FactSage, Macro Processing, FactSage-Teach, What is New in FactSage 7.0, FAQ -Frequently Asked Questions, Information, List of references, FactSage family of products and services, etc. All topics are updated with each release of FactSage.

Databases
FactSage provides access to both solution databases and compound databases. The former contain optimized model parameters for the Gibbs energy of solution phases as functions of composition and temperature. The latter contain the properties of stoichiometric compounds (pure substances), either obtained from published experimental data and phase diagram optimizations or taken from standard compilations.
During the past six years most of the databases have been revised and updated and some new ones have been added. The modifications to databases are outlined in the following sections. FactPS -(formerly FACT53) now contains pure substances data for 4777 compounds (was 4538 in 2009). It contains data from standard compilations as well as most of the data for those compounds that have been evaluated/optimized to be thermodynamically consistent with the FACT FToxid, FTsalt,… etc. solution databases.
FToxidis the FACT oxide database for slags, glasses, minerals, ceramics, refractories, etc. It has been extensively updated and now contains data for 374 stoichiometric oxides (was 264) and 87 oxide solutions (was 46 For systems containing Ca, Mn, Fe, Mg, Al and Si, FToxid-Slag covers the entire oxysulfide phase from pure oxide to pure sulfide. One such oxysulfide system is CaO-Al 2 O 3 -CaS(-Al 2 S 3 ), which is a core inclusion system of Al-killed steel followed by Ca injection. Fig. 2 shows the liquidus projection of the CaO-Al 2 O 3 -CaS system, calculated by the Phase Diagram module. Inclusions found in the  steel are generally a mixture of liquid oxysulfide and solid CaS as shown by an inset [4] in the same figure. FTOxid-Slag now allows for the calculation not only of the sulfide capacity (dilute S content in liquid oxide slag) but also of the evolution of such oxysulfide inclusions (high S content up to solid sulfide saturation or pure sulfide).
Oxyfluoride systems Ca, Mg, Na, Al, Si//O, F are new additions. The database is reliable for compositions up to 50 mol% fluoride. The database is particularly useful for calculations involving mold fluxes of the continuous steel casting processes and refining slags. For example, the phase diagram of the CaO-SiO 2 -Na 2 O-CaF 2 system is shown in Fig. 3.
Solid and liquid phases of unary, binary and many ternary P 2 O 5 -containing systems in the P 2 O 5 -CaO-MgO-Al 2 O 3 -SiO 2 -BaO-FeO -Fe 2 O 3 -MnO-Na 2 O system have been recently updated. The thermodynamic behavior of P in a slag is important for the refining of molten metals and also recycling phosphorus. For example, FactSage can be employed to calculate the equilibrium phosphorus distribution between molten slag and liquid Fe as depicted in Fig. 4. The calculations are in good agreement with experimental data.
FTmiscis the FACT miscellaneous database for sulfides, alloys, etc. All compounds and solutions of the former Light Metals subsection of FTmisc have been removed and some minor changes have been carried out. The database includes the following systems: the S-Cu-Fe-Mn-Ni-Co-Cr system; the matte smelting system S-Cu-Fe-Ni-Co-Pb-Zn-As; liquid Fe with dilute solutes Al, FTOxCNis a new FACT database for oxycarbonitride systems and contains data for performing equilibrium calculations in the Al-(Si-Ca-Mg-Fe-Na)-C-O-N-S system at very high temperatures. Carbonates, cyanides, nitrates, oxidized states of sulfur (e.g. SO 4 2À ,S 2 O 7 2À ,e t c . ) and polysulfides (e.g. S 2 2À ,S 3 2À ,S 4 2À ,e t c . )a r ea s s u m e dn o tt ob e stable under high-temperature relatively reducing conditions and are neglected. When Fe is present the database is only valid for reducing conditions. The FTOxCN solution database contains oxycarbonitride solutions and a compatible liquid metallic solution. In particular, the liquid "Slag" phase is treated as a single solution phase containing all 10 elements, valid at all temperatures and over all composition ranges of interest. This phase thus incorporates the high-temperature oxycarbide slag, sulfide-rich liquid and oxide slags which might appear at lower temperatures, oxynitride liquids, etc., all in one solution (with possible miscibility gaps, of course). The FTOxCN compound database contains all stoichiometric solid and liquid oxycarbonitride, sulfide and oxysulfide compounds evaluated/optimized to be thermodynamically consistent with the FTOxCN solution database.
FTfrtzis a new FACT database used for the production of nitratebased fertilizers, from hydrous to anhydrous conditions. It can also be used for calculating the thermodynamic properties and phase equilibria in the fertilizer products, and for some explosives. The FTfrtz compound and solution databases contain data for 26 pure salts and 14 salt solutions based on the family of ammonium nitrate (NH 4 NO 3 ), ammonium di-hydrogen phosphate (NH 4 H 2 PO 4 ), ammonium chloride (NH 4 Cl) and ammonium sulfate ((NH 4 ) 2 SO 4 ), fertilizers with additions of their corresponding potassium salts (and in some cases sodium salts). The model covers the addition of up to roughly 50 wt% water.   Nb, Nd, Ni, O, P, Pb, Pr, S, Sb, Sc, Si, Sm, Sn, Sr, Ta, Tb, Ti, Tm, V, W, Y, Yb, Zn and Zr. Mg Alloys: Ag, Al, B, Ba, Be, Bi, C, Ca, Ce, Cr, Cu, Dy, Er, Eu, Fe, Gd, Ge, H, Ho, In, K, La, Li, Lu, Mg, Mn, Na, Nd, Ni, Pb, Pr, Sb, Sc, Si, Sm, Sn, Sr, Tb, Ti, Tm, V, Y, Yb, Zn and Zr.
A total of 622 binary systems have been evaluated, for most of them over the entire range of composition and for all stable phases. For around 120 of these binary systems only the liquid phase mixing parameters are stored. Several dozen ternary systems have been assessed, and important quaternary systems have also been evaluated. The database contains 200 solution phases and over 1400 pure compounds (with more than 1700 stoichiometric phases counting allotropic forms).
FTnuclis a new FACT database that has been developed for the nuclear industry. It contains data for pure substances and solutions containing the following elements:( Th, U, Np, Pu, Am)þ (Zr, Fe, Ru, Ba) þ(Li, Na, K, Rb, Cs) þ(C, N, O, I)þ(He, Ne, Ar, Kr, Xe, Rn). The database can be used for the development of advanced nuclear fuels based on: Th, U, Np, Pu and Am; oxides; carbides, nitrides and carbo-nitrides; metals. It can also be used for estimating the thermodynamic behavior and phase relationships involving fission products based on Cs. I, Zr, Ru, Ba and Rb, and including noble gases and metallic claddings (Fe, Zr, C).
FThall -FACT Hall-Héroult aluminum database remains essentially unchanged. However, a density model, taking into account excess volume upon mixing [6], and a viscosity model [7] are now available for the NaF-AlF 3 -CaF 2 -Al 2 O 3 -LiF-MgF 2 electrolyte as a function of temperature and composition. Shortly, an electrical (ionic) conductivity model for the same electrolyte will be implemented in the database.
FThelg, FTpulp remain essentially unchanged since 2009. These FACT databases contain, respectively, the Helgeson [8] aqueous database (including solid precipitates and gases) and systems of interest primarily to the pulp and paper industry.

FactSage alloy databases-FScopp, FSlead, FSstel, FSupsi
FactSage (FS) databases for metallic alloys are the result of evaluations/optimizations by the FactSage groups (FACT, Montreal; GTT Technologies, Aachen; The Spencer Group, Trumansburg NY). For each group of systems there is a corresponding pair of databasesa solution database and a compound databasecontaining data for solutions and compounds which have been evaluated and optimized together.
FScoppcopper alloy database is directed primarily to the liquid state of Cu-rich alloys and includes the elements: Ag, Al, As, Au, Ba, Be, Bi, C, Ca, Cd, Ce, Co, Cr, Fe, Ga, Ge, In, Li, Mg, Mn, Nb, Nd, Ni, O, P, Pb, Pd, Pt, Pr, S, Sb, Se, Si, Sm, Sn, Sr, Te, Ti, Tl, V, Y, Zn, Zr and also includes data for Cu-rich solid phases. The database is generally valid for the temperature range of approximately 400-1600°C. Minor revisions have been performed and modifications have been carried out that simplify solution phase selection.
FSleadlead alloy database is directed primarily to the liquid state of Pb-rich alloys and includes the elements: Ag, Al, As, Au, Bi, C, Ca, Cd, Cu, Fe, Ga, Ge, Hg, In, Mn, Ni, O, Pd, S, Sb, Se, Si, Sn, Sr, Te, Tl, Zn, and Zr. It also includes data for Pb-rich solid phases. It permits the calculation of the complete Pb binary systems with all the above elements with the exception of the Pb-Fe, -Mn, -S, -Se and -Sr binary systems. It is intended to provide a sound basis for calculations relating to lead production and refining. Minor revisions have been performed (Cd-Pb system) and modifications have been carried out that simplify solution phase selection.
FSstelsteel database has been extensively updated and now contains data for 140 (was 115) completely assessed binary alloy systems, 100 (was 85) ternary and 17 quaternary systems that include the elements: Al, B, Bi, C, Ca, Ce, Co, Cr, Cu, Fe, La, Mg, Mn, Mo, N, O, Nb, Ni, P, Pb, S, Sb, Si, Sn, Ti, V, W and Zr. It is intended to provide a sound basis for calculations covering a wide range of steelmaking processes, e.g. reduction of oxygen and sulfur concentration levels through deoxidation and desulphurization of the melt; constitution of a wide range of steels, including austenitic, ferritic and duplex stainless steels and including carbide and nitride formation; conditions for heat treatment operations to produce a desired constitution; conditions for scrap remelting to maintain as low concentrations as possible of undesirable "tramp elements"; melt-crucible interactions, etc.
FSupsi database for ultrapure silicon remains essentially unchanged. From among these elements, there are some 577 completely assessed binary alloy systems, of which over 32 are newly assessed systems and many others have been revised or amended on the basis of newly published experimental information. The database also includes about 141 ternary and 15 higher-order systems for which assessed parameters are available for phases of practical relevance. The systems now incorporate approximately 317 different solution phases and 1166 stoichiometric intermetallic compound phases. The database is intended to provide a sound basis for calculations relating to the production, heat treatment, constitution, and application of a wide range of alloy types.

SGTE databases
SGnoblnoble metal database has been extensively updated and n o wc o n t a i n s1 2 4s o l u t i o n s( w a s5 3 )a n d3 6 2c o m p o u n d s( w a s1 0 5 ) . The database contains evaluated thermodynamic parameters for 223 b i n a r ya n d1 3 0t e r n a r ya l l o y so fA g ,A u ,I r ,O s ,P d ,P t ,R h ,R ua l l o y e d amongst themselves and also in alloys with the metals Al, As, B, Ba, Be, Bi,C,Ca,Cd,Ce,Co,Cr ,Cu,Dy ,Fe,Ge,Hf,In,Mg,Mo,Nb,Ni,Pb,Re,Sb, S i ,S n ,T a ,T c ,T e ,T i ,T l ,V ,W ,Z na n dZ r .N o b l em e t a l sa n dt h e i ra l l o y s have a wide variety of applications, and calculations of relevant phase equilibria in a particular case are important e.g. for optimizing suitable alloy compositions or predicting reaction products in chemically aggressive environments.
BINARY 2014 -free alloy database is the new SGTE free binary alloy database and comprises some 115 of the binary systems taken from the SGTE 2014 alloy databases.
SGPS, the SGTE pure substance database, SGnucl, the database for applications in the nuclear industry, and SGsold, the solder database, remain essentially unchanged since 2009. Reactions of the carbide, nitride, boride and silicide systems with such refractory oxides and with oxygen-containing gas atmospheres can be calculated using FactSage by selecting the SpMCBN database together with appropriate combinations of the FToxid, FactPS and SGPS databases for the materials in question. Some application examples are in furnace construction, high-temperature coatings, cutting tools, abrasives, aircraft brake linings, rockets, jets, turbines, and nuclear power plants.
TDmephthe MEPHISTA database for a new generation of nuclear fuels from IRSN in Cadarache, France. MEPHISTA-Multiphase Equilibria in Fuels via Standard Thermodynamic Analysisis a self-consistent database designed for thermochemical equilibria calculation codes. It contains 14 þ2 elements: Ba-C-Ce-Cs-Fe-La-Mo-O-Pu-Ru-Si-Sr-U-Zr þAr-H (Ar and H are only taken into account in the gas phase). This database covers the entire field from metal to oxide domains, and the temperature range up to 3500 K. 78 binary, 34 quasi-binary, 18 ternary, 2 quasi-ternary systems, 219 condensed stoichiometric compounds and 151 gaseous species are included in the database.
TDNuclanother database for the nuclear industry remains essentially unchanged.

Documentation
The Documentation opens the FactSage Browser and enables one to manipulate the database help files and display the phase diagram previews. The List of stored phase diagrams posted in the FactSage Browser has been updated to 4967. For example, Fig. 5 lists the calculated phase diagrams in the SGTE 2014 database and shows the calculated Al-Ca-Si liquidus polythermal projection.

Compound and Solution Modules
Thermodynamic data can be stored in private compound and solution databases via the Compound and Solution modules.
In FactSage 7.0 the solution file structures have been completely reformatted. The old solution files (*.dat, *.sdb, *.sda)have been replaced by two new files (*.sln, *.sdc). The Solution module has been completely rewritten and replaces the old module that was programmed over a decade ago.
With the new Solution module, data can be entered and stored using the following solution models: One-sublattice polynomial model (simple, Redlich-Kister or Legendre polynomials with interpolations to multicomponent systems using Muggianu, Kohler or Toop methods), Compound Energy Formalism with up to 5 sublattices [9],T w o -s u blattice polynomial model with or without short-range-ordering [10], One-sublattice Modified Quasichemical Model [11,12],T w o -s u b l a t t i c e Modified Quasichemical Model including coupling between first-and second-nearest-neighbor short-range-ordering [13], Ionic Liquid Model [14],U n i fied Interaction Parameter Formalism (corrected Wagner formalism) [15], and the Pitzer model. Data can also be entered for magnetic and volumetric (density, expansivity, compressibility) properties.
Data are entered by via a highly flexible user interface that offers extensive editing capabilities. For example Fig. 6 displays the expanded tree-views of a private solution database with access to the Functions and solution phase Sublattices, End Members and Interactions. Fig. 7 shows the entry of a ternary Redlich-Kister parameter in the Al-Sn-Zn system.
The Solution module has other new features which include: expressions of Gibbs energy for solution end-members can be imported from a compound database and stored as functions within the new solution database. The required expressions are selected using the Compound module then imported by drag and drop into the Solution module.
stored functions in the database are accessible to all solution phases within that database.

View Data Module
The View Data module displays a summary of the thermochemical data stored in the solution and compound databases. The data may be sorted and displayed in a variety of formats.
Previously it was not possible to list all the phases in a solution database. In   the solution data (interactions and expressions) that have been stored in a private database.

Calculate
This group of modules is at the heart of FactSage. One can interact withthesoftwareanddatabasesinavarietyofwaysandcalculateand display thermochemical equilibria and phase diagrams in a multitude of formats. Major modifications have been carried out on the Equilib and Phase Diagram modules.

Equilib Module
The Equilib m o d u l ei st h eG i b b se n e r g ym i n i m i z a t i o nw o r k h o r s e of FactSage. The Equilib module calculates the conditions for multiphase, multicomponent equilibria, with a wide variety of tabular and graphical output modes, under a large range of possible constraints through Gibbs energy minimization based on the ChemApp algorithm [16]. There are many different types of Equilib calculations, for example: -Equilibrium using thermochemical data from single or multiple databases -Scheil-Gulliver and Equilibrium Cooling -Casting algorithms -Open calculations -Simulation of processes -Macro Processing -Streams and recycling -Fact-XML customized outputtables, spreadsheets, graphs -Fact-Function-Buildercustomized functions -FactOptimalidentifying the optimal conditions for alloy and process design using thermodynamic and property databases

Equilibrium cooling and Scheil-Gulliver cooling
Equilib performs both Equilibrium cooling and Gulliver-Scheil cooling calculations. In Equilibrium cooling the total mass balance remains constant. In Gulliver-Scheil cooling, as phases precipitate from the Scheil target phase, they are dropped from the total mass balance.
Generally a value for T (the initial temperature) and a cooling step size must be specified in the Final Conditions frame. In Gulliver-Scheil cooling the Scheil calculation is repeated until the Scheil Target Phase disappears. However, it is possible to stop the calculation by either specifying a second temperature in the Final Conditions frame, or by specifying a target mass. The Scheil target phase must be the gas phase or a real solution. Fig. 9 shows the Equilib setup for a Scheil cooling calculation of a AZ91 þ 0.25 wt% Mn alloy (FTlite-Liqu). All possible 26 solution phases as well as 42 solid compounds (pure substances) are included in the phase selection as possible products. The 'coolingstep' is 5 K. The results (Fig. 10) give a Summary of all the constituents and phases at the final disappearance of the liquid (340.89°C) as well as a list of the Transitions during cooling. A more detailed list of Microstructure constituents is given in Fig. 11.

FactOptimal Module
The FactOptimal module [17] is accessed through the Equilib module. FactOptimal is a new program that computes optimal conditions for material and process design by coupling FactSage with the Mesh Adaptive Direct Search (MADS) [18] algorithm for nonlinear optimization developed by the GERAD research group at the Ecole Polytechnique de Montréal. FactOptimal was developed in part to assist industry in optimizing alloy and process design.   are calculated by Equilib the functions may be non-smooth (e.g. liquidus temperature) the estimation of derivatives may be problematic the evaluations of f may be time-consuming the function calculation may fail unexpectedly at some points the constraints may be non-linear, non-smooth or Boolean Fig. 12 shows the FactOptimal Results Window for the calculation of the minimum liquidus temperature of the LiCl-NaCl-KCl-LiF-NaF-KF system using data from the FTsalt database. During the calculation various constraints on composition, density, Cp and cost were imposed. After 895 calculations FactOptimal determined the minimum liquidus temperature of 577.39°Ca t 0.037 wt% LiCl þ41.909 wt% NaCl þ28.505 wt% KCl þ9.963 wt% LiFþ 14.156 wt% NaF þ5.430 wt% KF.

FactOptimal example-minimum liquidus temperature
The following steps show how FactOptimal arrives at this minimum liquidus temperature.
Step 1: Equilib module - Fig. 13 shows the Equilib Menu Window for a single equilibrium calculation at an arbitrary composition for the system LiCl-NaCl-KCl-LiF-NaF-KF. A precipitate (P) calculation on the liquid is specified (i.e. liquidus temperature calculation) and "include molar volumes" is checked (for the calculation of the density). The equilibrium results in Fig. 14 show the calculated precipitate (liquidus) temperature 658.73°C for this arbitrary composition. Although these particular results are unimportant, the Menu Window setup is essential for the next stage where FactOptimal is opened.
Step 2: in the FactOptimal Properties Window (Fig. 15) the following conditions are imposed: (1) one considers one property; (2) one wants to minimize this property; (3) the property is temperature; (4) the cost is included in the optimization.
Step 3: in the FactOptimal Variables Window (not shown) the permissible composition range and a set of initial estimates are defined.
Step 6: in the FactOptimal Parameters Window (not shown) are defined the maximum number of Equilib calculations (1000). The results were shown in the FactOptimal Results Window (Fig. 12).

FactOptimal example-characteristic points in a reciprocal system
FactOptimal is able to calculate the compositions of eutectics, temperature minima and congruent melting points of a multicomponent system. These are referred to as the characteristic points on the liquidus surface. This option is straightforward to apply and no initial parameters are required. The calculated characteristic points on the liquidus surface in the Li þ ,N a þ ,K þ , Mg þþ ,C a þþ /F À ,C l À reciprocal salt system (a system with 2 or more cations and 2 or more anions) are shown in Fig. 16. The complete details of equilibrium for any particular point can be obtained by selecting Open in Equilib.  Fig. 17 shows the results and a plot of solid fraction vs. liquidus temperature. When simultaneously optimizing two properties P1 (solid fraction) and P2 (liquidus temperature) there are an infinite number of solutions, that is there is no unique composition where both solid fraction and liquidus temperature are minimized. The calculated Pareto front consists of the points shown in Fig. 17. At any selected temperature a point on the Pareto front gives the minimum solid fraction and at any selected solid fraction a point on the Pareto front gives the minimum liquidus temperature. The user must select a value on the Pareto front that, in his judgment, is the "best" compromise.

FactOptimal example-double target optimization
With FactOptimal one can calculate the optimal composition to target two properties under constraints of compositions and/or properties. For example, one can calculate the composition of the MgO-Al 2 O 3 -CaO-PbO-ZnO-SiO 2 oxide system while fixing, within a given tolerance, the liquidus temperature and the solid mass fraction 200°C below the liquidus temperature. Fig. 18 shows the results and a plot of error in mass fraction vs. error in composition.
More FactOptimal examples of industrial applications are given in [19,20].

Viscosities of oxide melts
The viscosity of oxide melts can vary by orders of magnitude depending upon the composition and temperature and it is strongly related to the connectivity of the silica network. The connectivity of the network (which is related to the probability of Si-O-Si bridges) can be calculated from the Modified Quasichemical Model [11,12] parameters for FToxid, the FactSage thermodynamic database for molten oxides.
The parameters of the viscosity model are obtained by critical evaluation and optimization of data for pure oxides and selected     Fig. 19 shows a comparison between calculated and experimental viscosities in the Na 2 O-Al 2 O 3 -SiO 2 ternary system with the viscosities calculated using the molten slag database. Note the calculation of the important "charge compensation effect" [21,22]. During the last several years the accuracy of the database for the high iron oxide (FeO and Fe 2 O 3 ) slag systems has been greatly improved due to recent literature data and in-house data by academic and industrial collaborators. The database now gives reliable predictions of the viscosity of mold fluxes in the continuous casting process of steel and of slags in the electro-slag remelting (ESR) processes.

Phase Diagram and Figure Modules
In the Phase Diagram module two thermodynamic properties are plotted on the X-and Y-axes, while the other properties are held constant. The properties that may be selected as axes or constants are: T (or 1/TK)-temperature; P-total pressure; V-volume; Comp-Composition (mole fractions, molar ratios, weight fractions, weight ratios); Potl-Chemical potentials (RT ln(a i ), RT ln(P i ),

Manipulate
FactSage offers a variety of ways one can interact with the modules during the calculations (Macro Processing,), and after the calculations through post-processing of the tabular and graphical results of the complex equilibrium calculations in Equilib and Phase Diagram (Streams, Results module, Fact-XML).

Calculation of Phase Diagrams
In the following examples all the figures have been calculated by the Phase Diagram module and the domains have been automatically labeled (or tie-lines added) by simply pointing the mouse to the appropriate coordinate and clicking. In some cases text has been edited and symbols added by using the editing features of the Figure module. Some of the calculations also involve private databases only. Only the various types of phase diagrams that are new to FactSage during the period 2010-2016 are presented here. Fig. 20 is the isothermal section of the Zn-Hg-Cd system at 700°C, 1 bar and shows tie-lines for the two-phase gas-liquid equilibria (condensation-evaporation). Fig. 21 is the plot of the polythermal projections of condensation (horizontal isotherms of first liquid condensates, precipitate "P" target) and of evaporation (vertical isotherms of gas formation, format "F" target) in the Zn-Hg-Cd ternary system at 1 bar.

Enthalpy-Composition Diagrams
In an enthalpy-composition (H-X) phase diagram the vertical axis is the enthalpy relative to the enthalpy at a specified reference temperature (for example, 25°C) and the horizontal axis is the composition, either in a binary system or along a constant composition path (isopleth) in a multicomponent system. Fig. 22 is the calculated temperature vs. wt% Si phase diagram for Mg-Si-Al-Sr at 0.3 wt% Mg and  0.1 wt% Sr.I nt h ee n t h a l p y -composition diagram for the same system (Fig. 23)onecanreadataglancetheheatchangeassociatedwitheach stage of cooling a Mg-Si-Al-Sr alloy down to 25°C. The heat change includes the sensible heat during cooling, as well as heat changes during eutectic reactions, etc.
The components are Ca, Al, O and N. In a Reciprocal Diagram the Y-axis is the "equivalent fraction" 2O/(2O þ3N) in the range 0-1 and the X-axis is the "equivalent fraction" 2Ca/(2Ca þ3Al) in the range 0-1 where (2Ca þ3Al) ¼(2O þ3N). Note the corners are not This is necessary to ensure the tie-lines are straight lines. A new feature in Phase Diagram permits the user to select the reciprocal phase diagram option and then enter the cationic and anionic components (Fig. 24). This results in the calculation of a polythermal projection (Fig. 25) which is labeled with the pertinent information associated with the reciprocal system.

Volume Diagrams
Volume or log volume may be specified as an X-o rY-axis. Typical volume diagrams include V (or log V) vs. T and V(or log V) vs. X. Fig. 26 shows a Volume Diagram of log(V)vs.T(K)intheSi-C-Osystem when Si/(SiþCþO) ¼0.1 and C/(SiþCþO) ¼0.3 (mol/mol).

First-Melting Projection Diagram
The first-melting projection of the phase diagram of a ternary or higher-order system shows the temperature at which a liquid phase first appears upon heating at any given composition in a    system at thermodynamic equilibrium. In most systems, firstmelting projections are identical to solidus projections and they obey the same well-known topological rules as isothermal sections of phase diagrams. Hence, their interpretation is straightforward. Only in systems with catatectic invariants or retrograde solid solubility do exceptions to these rules occur, and then only over limited composition regions. For more details on the algorithm and explanations refer to [23]. For example, Fig. 27 shows a polythermal first-melting (solidus) projection in the ternary Zn-Mg-Al system; Fig. 28 shows a polythermal first-melting (solidus) projection in the quaternary system Zn-Mg-Al-Y.
6.6. Paraequilibrium phase diagram [24] Paraequilibrium refers to the concept that diffusion of interstitial solutes is much faster than that of substitutional atoms. For example, in the Fe-Cr-C-N system carbon and nitrogen diffuse much more rapidly than Fe and Cr. That is, the diffusion of Fe and Cr during relatively rapid cooling can be ignored.
For example, Fig. 29 is the T(K) vs. Cr/(FeþCr) (mol/mol) phase diagram of the Fe-Cr-C-N system at C/(Fe þCr) (mol/mol) ¼0.02 and N/(Feþ Cr) (mol/mol) ¼0.02 calculated under normal     equilibrium conditions (orthoequilibrium). Data are taken from the SGTE alloy databases. Fig. 30 is the paraequilibrium diagram for the same system with only C and N diffusing. Fig. 31 is a special case when C is the only diffusing component. For more details on paraequilibrium phase diagrams refer to [24].
It is also possible to calculate phase diagrams in which the phase fields show the single phase with the minimum Gibbs energy at any given point on the diagram as shown in Fig. 32. Such calculations may be of practical interest in physical vapour deposition where deposition from the vapour phase is so rapid that phase separation cannot occur, resulting in a single-phase solid deposit.

Isobars and iso-activity lines
On a calculated phase diagram it is now possible to plot isobars of a gaseous species or gas phase and iso-activity lines of a compound (pure liquid or solid). For compound species, isobars and     iso-activity lines are defined in the Compound Selection Window as shown in Fig. 33. The resulting diagram (Fig. 34) shows the calculated O 2 (g) isobars in the Cu-O binary system using data from the FScopp database. Fig. 35 shows calculated O 2 (g) isobars in the FeO-Fe 2 O 3 -Cr 2 O 3 ternary system at 1300°C using data from the FToxid database. Fig. 35 shows calculated C(s) iso-activity lines in the Fe-Cr-C ternary system (Fig. 36).
The basic principles behind the calculation of isobars and isoactivity lines have been discussed by [25]. It involves the introduction of an auxiliary phase, and its Gibbs energy function is manipulated in order to plot a specific iso-line as if it were a pseudo-phase boundary (as a zero-phase-fraction-line) of this auxiliary phase. This approach can be extended to calculate other iso-lines for other properties (activity coefficients, sulfide capacities, surface tension, etc.) For example, Fig. 37 [26] shows calculated iso-sulfide capacity (C S ) lines of CaO-SiO 2 -Al 2 O 3 slags at 1400°C and the calculated liquidus (thin lines).

Miscellaneous
It is should be noted that the Phase Diagram module requires no starting values or initial estimates. All phase diagrams shown here were calculated and plotted by simply selecting "Calculate 44". In some cases text and labels were manually added for clarity.

Current developments
With the release of FactSage 7.1 it will be possible to calculate Scheil-Gulliver phase diagrams showing the phases which result when a system is cooled under Scheil-Gulliver conditions (see Section 3.2).
Classical Eh-pH (Pourbaix) diagrams are not true phase diagrams inasmuch as (a) the aqueous phase fields show the regions where one aqueous species is predominant, whereas this is actually only one continuous aqueous phase field, (b) they are calculated only at infinite dilution. In Fig. 38 is shown a phase diagram calculated by Phase Diagram for the system H 2 O-Cu-NaOH-HCl-H 2 in which the X-axis is the molar ratio NaOH/(NaOH þHCl), which is related to the pH, and    Fig. 40. At present, the conversion involves a good deal of manipulation by the user. In FactSage 7.1 it is planned to render the conversion automatic.

Internet
All the calculated phase diagrams and associated database documentation in the FactSage package are accessible on the internet through www.factsage.com. In addition, it is possible to display and interact with calculated phase diagrams through the Fact-Web suite of interactive programs 〈www.crct.polymtl.ca/fact web.php〉. Fact-Web provides limited access to some of the Fact-Sage modules (View Compound, Reaction, EpH, Predom, Equilib, Phase Diagram) and access to all the compounds in FactPSthe FACT pure substances database.

Summary and conclusions
This article has presented a summary of the most recent developments (2010-2016) in the FactSage thermochemical software and database package with emphasis on the optimization, calculation and manipulation of phase diagrams.
FactSage software and database development is ongoing. Information on the status of FactSage as well as sample phase diagrams of hundreds of alloy, salt, oxide etc. systems is available through the Internet at www.factsage.com.