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Bo Sundman, Fabio Miani, Axel van de Walle, Bengt Hallstedt, Ursula R. Kattner, Florian Tang, [Taichi Abe](https://orcid.org/0000-0002-5065-0939), Reza Naraghi, Erwin Povoden-Karadeniz, Aurelie Jacob, Shuanglin Chen, Richard Otis, Kazuhisa Shobu, Malin Selleby, Alexander Pisch
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[XTDB, an XML based format for Calphad databases](https://mdr.nims.go.jp/datasets/d4ef432e-488f-4bff-8f07-4314873b23f5)
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XTDB, an XML based format for Calphad databasesBo Sundmana, Fabio Mianib, Axel van de Wallec, Bengt Hallstedtd, UrsulaR Kattnere, Florian Tangf, Taichi Abeg, Reza Naraghih, ErwinPovoden-Karadenizi, Aurelie Jacobi, Shuanglin Chenj, Richard Otisk,Kazuhisa Shobul, Malin Sellebym, Alexander PischnaOpenCalphad, 9 Allée de l'Acerma, 91190 Gif sur Yvette, FrancebDPIA, University of Udine, Via delle Scienze 208, 33100 Udine, ItalycSchool of Engineering, Brown University, Providence, RI 02912, USAdIWM, RWTH Aachen University, Augustinerbach 4, 52062 Aachen, GermanyeMSE, NIST, 100 Bureau Drive, Stop 8555, Gaithersburg, MD 20899, USAfGTT-Technologies, 52134 Herzogenrath, GermanygNIMS, Sengen, Tsukuba, JapanhThermo-Calc Software AB, Råsundavägen 18, 169 67 Solna, SwedeniTU Wien, Getreidemarkt 9, 1060 Vienna, AustriajCompuTherm, Yellowstone Dr., Madison, WI 53719, USAkCalifornia Institute of Technology, Pasadena, CA 91109 USAlRICT, Inc. 674-18, Tashiro-hoka, Tosu, Saga, 841-0016, Japan.mMSE, KTH Royal Institute of Technology, Brinellvägen 23, 100 44 Stockholm, SwedennSIMAP, 1130, Rue de la Piscine, 38402 Saint-Martin d'Hères, FranceAbstractThe Calphad method uses models which depend on assessed parameters todescribe the thermodynamic properties of materials. These model parame-ters are assessed by researchers and students using experimental and theoret-ical data on binary and ternary systems which can be merged to multicom-ponent databases and used to calculate properties and simulate processes fora wide range of materials.There are several di�erent software using the Calphad method for calcu-lations and they can use slightly di�erent models and database formats. ThisEmail address: bo.sundman@gmail.com (Bo Sundman)Preprint submitted to Calphad March 30, 2025paper will give a short background to the current state of database develop-ment and proposes a new format based on the eXtensive Markup Language(XML) as a uni�ed database format. This change is particularly importantas several new models for the pure elements are currently introduced in theCalphad databases.Keywords:Computational Thermodynamics, Calphad, Models, Model parameters,Databases, XML1. IntroductionThe development of software to calculate thermodynamic properties ofalloys and other materials has been centered around the Calphad organizationformed in 1973 [1] and the use of the lattice stabilities for the pure elementsproposed by Kaufman [2]. These lattice stabilites made it possible to shareand combine assessment of binary and ternary systems made by researchersall over the world.The SGTE unary database published 1991 [3] represented a major im-provement as this database including heat capacity data and a separate mag-netic model[4, 5] using the Curie temperature and Bohr magneton numberwhich can be the composition dependent. This unary database transformedCalphad to a general tool for computational thermodynamics and togetherwith kinetic models and data, it could be applied to all kinds of simulations ofphase transformation and processes. The SGTE database proposed a simpledatabase format, called TDB (short for Thermodynamic DataBase) whichwith slight variations has been adopted by several software. During the last245 years several 1000 binary and ternary systems have been assessed basedon experimental and theoretical data using the Calphad models. These as-sessments have been integrated in several large databases, both commercialand freely available. With these databases reliable calculations can be madefor multicomponent alloys, nuclear materials and other systems, simplifyingthe development of new materials and better processes.The introduction of more complex models, integration of DFT data andadditional materials properties have increased the interest in thermodynamiccalculations [6, 7, 8, 9, 10, 11, 12, 13] and the TDB format is now past its�best before� date. In this paper a new XTDB format is proposed usingthe eXtended Markup Language (XML). It keeps the simplicity of manualediting of the TDB format and provides a consistent way to include newfeatures, models and complex properties as discussed in [14, 15, 16].2. The Gibbs energy and the organization of this paperWhen there are references in this text to the XTDB format a tag nameis written in bold and an attribute is written in italics and a short summaryof the XTDB format is in Appendix A. In Appendix B there are examplesof XTDB tags including the whole Al-C database and in Appendix C, anexample of the ModelDescriptions tag with a number of physical modelstogether their composition dependent parameter identi�ers. For those notfamiliar with XML an introduction can be found at [17].An XTDB database can be written and used by di�erent software and theModelDescriptions tag speci�es the models that are used in a particulardatabase. This tag is provided by the software generating the database and3if another software is reading the database it can check if a model extractedfrom the XTDB �le is actually implemented.2.1. The Gibbs energy expressionThe reason to put e�orts into creating databases with models for theGibbs energy of materials is that during a process or transformation a systemalways tries to reach its equilibrium state and the equilibrium is at a minimumof the Gibbs energy at constant T, P and overall composition, Ni:G = G(T, P,Ni) (1)where T is the absolute temperature, P the pressure and Ni the number ofmoles of component i.An essential feature of the Calphad method is that each phase in a systemis modeled independently and its Gibbs energy depends on T, P and thefractions of the constituents of the phase. Depending on the software usingthe database a user may calculate the set of stable phases and other propertiesof a system for a very wide range of external conditions.2.2. The external variablesSometimes one is more interested in the activity of a component or theheat that is added or removed. All of these properties are available in theCalphad modeling as partial derivatives of the Gibbs energy:dG =(∂G∂T)P,NidT +(∂G∂P)T,NidP +∑i(∂G∂Ni)T,P,Nj ̸=idNi (2)where the variables that must be kept constant for each partial derivative areindicated. With simple mathematical transformations, see for example [18],4it is possible to use eq. 2 to calculate how the local equilibria in a systemrespond to changes in the external conditions of a process. In particular theheat capacity, CP , and the chemical potential, µi, of each component i:CP = −T(∂2G∂T 2)P,Ni(3)µi =(∂G∂Ni)T,P,Nj ̸=i(4)are essential for equilibrium calculations and kinetic simulations.2.3. The internal variablesIn Calphad the Gibbs energy of a system uses Gibbs energy models foreach phase, α, with di�erent sets of constituents, which can be elements orchemical species or ions, and each with its own set of model parameters:G =∑αℵα GαM(T, P, yαs,i) (5)GαM =∑IΠIs(yαs,i)◦GαI (T, P )− T cfgSαM(yαs,i) +EGαM(T, P, yαs,i) +phyGαM(T, P, yαs,i) (6)where ℵα is the number of moles formula unit of α and GαM is the Gibbsenergy of α per mole formula unit as a function of T, P and yαs,i which denotethe fraction of constituent i on sublattice s. The number of constituents ina phase can be much larger than the number of components of the system.In the term ΠI(yαs,i)◦GαI the I indicates an endmember of α representinga possible �compound� with �xed composition and ΠI(yαs,i) is the probabil-ity of the compound I and ◦GαI its Gibbs energy. In a solution it is thecontribution from this endmember to the total Gibbs energy of the phase.5cfgSαM(yαs,i) is the con�gurational entropy and EGαM(T, P, yαs,i) the contribu-tions from interactions of the constituents mixing on the same sublattice ofthe phase. If a single endmember represents the constitution of the α phasethen cfgSαM = EGαM = 0.The term phyGαM(T, P, yαs,i) is the contribution from various physical mod-els, for example magnetism. This contribution can also be split into a sumof the contributions to each endmember and excess terms. Most physicalmodels have parameters which depend on the constitution and sometimesalso T and P . They are discussed in section 4.6. If the phase has chargedconstituents there is an extra condition for equilibrium that the phase is elec-trically neutral. From now on we will only deal with expressions for a singlephase and the phase superscript is omitted.Already in the 1991 unary database a separate contribution from mag-netic properties was introduced, phyGM , which has been essential to calculatefor steels and other magnetic materials. The introduction of model param-eters for physical properties such as the Curie temperature and the Bohrmagneton number has greatly improved simulations of such materials.The mixing depends on the model of the phase which in the simplest caseassumes that all constituents mix on a single sublattice. Alternatively, therecan be two or more sublattices each with a speci�c set of constituents, forexample interstitial solutions. This a�ects the con�gurational entropy as wellas all the model parameters used to describe the Gibbs energy and its contri-butions from various physical models. The sublattices describe Long RangeOrdering (LRO) where the constituents mix randomly in each sublattice butsome models take Short Range Ordering (SRO) into account by adding con-6stituents representing clusters to modify the con�gurational entropy.2.4. The con�gurational entropyThe random mixing of constituents ys,i on one or more sublattices s is;cfgSM =∑sas∑iys,i ln(ys,i) (7)∑iys,i = 1 (8)M =∑sas (9)where as is the number of sites on sublattice s and ys,i is the fraction ofconstituent i on sublattice s. The sum of the sites is equal to the formulaunit, M , of the phase.There are many di�erent ways to include SRO in the con�gurationalentropy, see for example [19, 20, 21, 22]. There are no parameters in thedatabase for the con�gurational entropy model, the database only providesthe set of clusters in the phase and possibly a Gibbs energy of formation ofthe clusters. A method to approximate SRO in crystalline phases by usingreciprocal excess parameters was derived in [23] and is discussed in [24].3. The content of a Calphad databaseSelecting data for a system from the database a user normally speci�esthe elements in the system and all phases that can exist with these elementsare extracted by the software from the database together with their modelparameters. But this can be software and application dependent.7The major part of the current TDB as well as an XTDB database aremodel parameters and their representation in the database as discussed insection 4.6.3.1. Elements, species, vacancies and electronsThe elements are the basic part of the XTDB format and they are de�nedas shown in Appendix A.2. The vacancy, denoted VA, is included amongthe chemical elements because the vacancy is needed to model interstitialsolutions and defects in di�erent phases use the vacancy. This may seem toviolate the Gibbs phase rule:f = n+ 2− p (10)where f is the degrees of freedom in a system with n real elements (or com-ponents) and p is the number of stable phases. But the vacancy must haveits chemical potential equal to zero at equilibrium and thus it will not changethis rule.Several models for the liquid [20, 25] also include vacancies, with or with-out a charge, as an essential model constituent. The electron is never treatedas a constituent by itself but a charged vacancy can be used as a free electronor hole to model semiconductors. As each phase must be electrically neutralthere is no degree of freedom added by the ions.In the TDB �le the chemical species, including the vacancy and chargedspecies as cations and anions are introduced directly after the elements asshown in Appendix A.2. It would be possible eliminate the Species tagin the XTDB �le and instead de�ne the constituents separately for eachphase. However, the XTDB tags needed for entering a phase, as explained in8section 3.2 and Appendix A.3, is already quite complex and in this proposalall constituents of a phase have separate Species tags independent of thePhase tag.A species has �xed stoichiometry and in some models additional proper-ties which must be provided as attributes in the Species tag.3.2. The phase, its constituents and modelsThe XTDB tags de�ning a phase are in Appendix A.3. The phase tagitself has only 3 attributes, Id is the name of the phase, Con�guration speci�eshow the con�gurational entropy should be calculated and the State which isneeded if the EEC model, see section 4.5, is used for the database.There are 3 standard values for the Con�guration:� CEF, the abbreviation for Compound Energy Formalism, covers allmodels with random mixing on one or more sublattices [26],� MQMQA is used for liquid with the Modi�ed Quasichemical model inthe Quadruplet Approximation [20],� I2SL is used for liquids with the Ionic 2-sublattice liquid model [25]with variable site ratios.At present there are no other established models for the con�gurational en-tropy for using XTDB databases.Nested inside the phase tag one must have a Sublattices tag even if thereis only one (or no) sublattices. In this tag the attributes NumberOf speci�esthe number of sublattices and Multiplicities the number of sites on each, i.e.9the value of as in eq. 9, which de�nes the formula unit of the phase. Thevalues of the model parameters must be for one formula unit of the phase.Within the Sublattices tag, there must be a Constituents tag for eachsublattice. It has two attributes, Sublattice which can be omitted if there isonly one, and List with a list of all constituents (already entered as Species),which can be present in the sublattice and separated by a space.If the phase has some physical contributions, see eq. 6, those must bespeci�ed using the AmendPhase tag. The Ids of several models can beincluded in its Models attribute, separated by a space. There can also be aDisorderedPart tag if the phase has two separate sets of fraction variables.See section 3.6.A solid phase can optionally have a CrystalStructure tag but usingCalphad models the crystallographic designation of the phase may changewith its constitution. Pure Fe as austenite can have the attribute Struc-turBericht A1 but the thermodynamic model for the same phase may bestable as ordered with StructurBericht L12 in Fe-Pt system or as a carbidewith the StructurBericht B1 in the Fe-Ti-C system. The software may usethe constitution of the phase to indicate this after an equilibrium calculation.3.3. Contribution from the physical modelsIn the TDB �les the way to specify physical contributions was varied.The XTDB format has a ModelDescriptions tag, where all models usedin the database are de�ned. The current models are listed with very shortexplanations in Appendix C. Each model has an Id attribute and possibly oneor more model parameter identi�ers (MPID) for parameters describing thecomposition dependence of the contribution. All models are not implemented10in all software. In for example:...the Models attribute speci�es that the FCC_4SL phase has the magneticmodel IHJQX, the Einstein low T heat capacity model, explained in sec-tion 3.4, and a permutation of the parameters on the 4 sublattices for or-dering explained in section 3.8. The DisorderedPart tag is explained insection 3.6 with examples in Appendix B.3.4. The Einstein low T extrapolation modelThe Einstein model is used to extrapolate the Gibbs energy of a solidphase of an element down to T = 0 K. The integrated Einstein heat capacityequation per mole atoms is:EinGm(θ) = 1.5Rθ + 3RT ln(1− exp(−θ/T )) (11)EinGαM = ℵα EinGm(θ) (12)where θ is the assessed Einstein temperature. Eq. 12, including the numberof moles of atoms per formula unit, ℵα of the α phase, is used in eq. 6. Thevalue of ln(θ) (called LNTH below) is used as composition dependent variablein the Einstein MPID parameter because it is considered more appropriatephysically.11Sometimes the heat capacity of an element is �tted using several Einsteinθ, each with a di�erent weight factor (the sum of which is unity), but only oneof them can be composition dependent using the LNTH parameter. Thusthe software must implement eq. 11 as a function called GEIN with θ asargument, for use in the Expr attribute, see section 4.7. The contributionsfrom all θ are included in the Gibbs energy parameter for the endmemberusing GEIN functions with their assessed weight factors as shown below forthe GRAPHITE phase in the assessment of Al-C by [27].where the TPfun tag with the Id attribute GEGRACC together with theLNTH parameter is the contribution from the Einstein model using 5 di�erentθ. The TPfuns GTSERCC and GHSERCC are the contribution at high Tand the enthalpy at T = 0 K respectively. One of the θ is selected to varywith the composition using the LNTH parameter and its GEIN function isincluded in GEGRACC multiplied with the factor (weight factor -1.0). Thewhole Al-C assessment is in Appendix B.1.123.5. The liquid 2-state modelThe Gibbs energy of the liquid phase for an element is extrapolated belowits melting T using the liquid 2 state model, proposed by [28, 29]. The Gibbsenergy expression for the liquid is:GLiqM = GamM −RT ln(1 + exp(−∆GMRT))(13)where GamM describes the metastable amorphous state at low T using an Ein-stein model together with the Gibbs energy parameter, �G�, as a polynomialin T with no heat capacity contribution at T = 0 K. The ∆GM parameter,divided by RT in eq. 13, describes the transition to the stable liquid and thestable liquid above the melting T .The MPID1 attribute GD in the Liquid2State tag is the ∆GM expres-sion, see Appendix C, and the �G� parameter describes the low T amorphousstate. The ∆GM polynomial, as included in to the ln(1 − exp(f(T ))) term,must not have any heat capacity contribution at T = 0 K, see [27, 29].3.6. Using two Gibbs energy functions for a phaseFor phases with many sublattices it is possible to use two separate sets ofparameters for the Gibbs energy. This may signi�cantly reduce the numberof model parameters, see section 3.7 and 3.9. It can be used for phases suchas FCC, BCC and HCP, which can be both ordered and disordered, andfor phases which are always ordered such as σ, µ etc. It is indicated by aDisorderedPart tag inside the AmendPhase tag of the ordered Phasetag.The DisorderedPart tag has 3 attributes, the Sum which speci�es thenumber of sublattices, n, in the ordered phase to be summed to obtain the13fractions of the disordered phase as:xdisi =∑ns=1 as∑i ys,i∑ns=1 as(14)where s represent the sublattices to be summed and ys,i are the site frac-tion of i on the sublattice s. All ordered sublattices should have the sameconstituents but there can be a �nal interstitial sublattice in both the or-dered and disordered part. It is not necessary that the sublattices which aresummed are crystallographically identical, a σ phase can also have a disor-dered part, in particular when using EBEF discussed in section 3.9. Thesoftware is responsible to ensure the number of atoms in the ordered anddisordered parts are the same.In the disordered part the Gibbs energies of the endmembers, ◦Gi, providea surface of reference relative to the stable state of the elements i. Thusall parameters in the ordered part become a kind of excess Gibbs energyparameters relative to this surface. For a phase with the DisorderedParttag the Gibbs energy is calculated by one of these 2 equations:GM = disGM(x) + ordGM(y) (15)GM = disGM(x) + ordGM(y)− ordGM(y = x) (16)where x are averaged values of y according to eq. 14. The con�gurationalGibbs energy is calculated for the ordered part only. Eq. 15 is mainly used forphases with many sublattices which never disorder for example TCP phases.In order to use eq. 16 one must specify the attribute Subtract="Y" in theDisorderedPart tag and it is used for phases with order/disorder transitionssuch as FCC, BCC and HCP when the model parameters for the disordered14phase, including disordered excess parameters, have been assessed separately.Subtracting ordGM(y = x) means that the model parameters of the orderedphase will not a�ect the disordered state. But there are many relationsbetween the parameters to be considered using this, for details see [14, 30].The third attribute is Disordered which can indicate the Id of the dis-ordered phase if those parameters are entered in a separate phase. Theparameters for the disordered phase can also be part of the ordered one,using parameters with fewer sublattices, see Appendix B.4.3.7. The use of wildcards as constituentsIt is possible to use parameters that does not specify the constituentin one or more of the sublattices. An extreme case is to use a parameterG(C14_Laves,*) which will add the value of the parameter to the Gibbsenergy of the C14_Laves phase at all compositions. In a simulation a positivevalue of such a parameter can be considered as a nucleation threshold.In some compounds which are stable in a limited composition range butmay dissolve many elements an excess parameter G(C14_Laves,A,B:*) canbe a useful approximation of the interaction between A and B independentof the constituent in the second sublattice.The implementation of the wildcard parameter has sometimes been mis-understood. It is wrong if the software replaces the wildcard in the parameterwith the actual constituents in the sublattice with the wildcard. Instead anyparameter with an explicit constituent in the sublattice with the wildcard.should be added to the wildcard parameter. For example:15should have their contribution to the Gibbs energy calculated as:∆G = y1,Ay1,BLA,B:∗ + y1,Ay1,By2,CLA,B:C (17)where the two parameters are totally independent and can be modi�ed sepa-rately. Even if C is the only constituent in the 2nd sublattice both parametersshould be extracted from the database.3.8. Permutations of parameters in some ordered phasesWhen modeling ordering in phases with crystallographically identical sub-lattices such as L12 and L10 ordering in FCC, the endmember G(FCC,A:B:B:B)has 4 permutations of the constituent A on the 4 sublattices which must haveidentical Gibbs energy. Using theDisorderedPart tag and the endmembersin the disordered part to represent the Gibbs energy relative to the stablestate of the constituents, the endmembers in the ordered part are related justto the bonds between the constituents. If the AB bond, uAB is independentof composition one has:G(FCC,A : A : A : B) = 3uABG(FCC,A : A : B : B) = 4uAB (18)G(FCC,A : B : B : B) = 3uABBy specifying FCC4PERM in the Models attribute of the AmendPhasetag the permutations of a parameter G(FCC,A:A:A:B) need to be included16only once in the XTDB �le. It is the software which must take care ofcalculating these parameters with the 3 or 4 di�erent sets of fractions, eitherby an internal loop or by storing the parameter at the 4 appropriate positionsin its data structure. See also Appendix B.4An excess parameters, such as G(FCC,A,B:*:*:*) must also be permutedby the software for all identical sublattices when read from the database.Such a parameter assumes that the interaction between A and B in a sub-lattice is independent of the constituents on the other 3 sublattices which isreasonable even if the wildcard represents a third element. The reciprocal pa-rameter, G(FCC,A,B:A,B:*:*), with 6 permutations is of particular interestbecause it can approximate the SRO contribution to the phase, see [24].How the permutations are implemented in the software is not discussedhere. Either the software stores the parameter explicitly for all possible per-mutations or stores the parameter only once and uses an internal loop tomultiply the parameter with all relevant constituent fractions in the sublat-tices. The latter is recommended as it makes it easier to change the expressionof the parameter. The BCC4PERM permutation is more complicated for thesoftware as the tetrahedron is not symmetrical.3.9. The EBEF modelThe wildcard feature has been further explored by Dupin [15] improvingthe modeling of intermetallic phases with many sublattices. Again com-bining the DisorderedPart feature described in section 3.6, the Gibbsenergy of the ordered part of such phases is independent of the referencestates of the elements. In a σ phase with 5 sublattices an endmemberparameter G(SIGMA,A:B:*:*:*) thus represent the bond energy between17constituent A in sublattice 1 and constituent B in sublattice 2, indepen-dent of the constituents in the other sublattices. As the sublattices are notcrystallographically identical (as in an ordered FCC phase) an endmemberG(SIGMA,B:A:*:*;*) will not have the same value. Using the notation EstA:Bfor a parameter with constituent A in sublattice s and constituent B in sub-lattice t, we can describe the energy to exchange of A and B in any pair ofsublattices as:∆GσA,B =4∑s=15∑t=s+1ys,Ayt,BEs,tA,B + ys,Byt,AEs,tB,A (19)where the Es,tA,B can be �tted to DFT calculations for all combinations ofendmembers in all 5 sublattices. This set of EstA,B is similar to an excessparameter LA,B in a phase with a single sublattice and very good resultshave been found when extrapolating such parameters, evaluated in binarysystems, to higher order systems. An example can be found in Appendix B.2.Using model parameters such as G(SIGMA,A:B*:*:*) it is essential thatthe software treats them as eq. 17, i.e. independent of the fractions in thesublattices with wildcards.3.10. Composition dependence of excess parametersThis section applies to all kinds of excess parameters for the di�erentphysical models, not just the Gibbs energy parameters. In a binary systemthe composition dependence of the constituent fractions can be expressed indi�erent ways. Most frequently used is the so called Redlich-Kister model,which for a substitutional model is:binGAB = xAxBn∑ν=0(xA − xB)ν · νLAB (20)18where νLAB can be a function of T . There are also other series expansionsbut they can always be transformed to a RK polynomial. Thus the XTDB�le will only support the RK binary excess expression. However, some soft-ware calculate the di�erence xA − xB in the alphabetical order, some in theorder the constituents are listed in the parameter. This may require thesoftware to change the sign of the parameters with odd powers. The compo-sition dependent Redlich-Kister parameters have the degree speci�ed after asemicolon in the Id attribute in the Parameter tag, see section 4.6.3.10.1. Ternary excess parametersParameters for ternary extrapolations can be composition dependent ac-cording to the suggestion in [31]. The ternary composition dependence for aparameter L1,2,3:∗ implemented in TDB �les as:terG1,2,3 = y1y2y3(v1 · 0L1,2,3:∗ + v2 · 1L1,2,3:∗ + v3 · 2L1,2,3:∗) (21)where 1, 2, 3 are constituents in alphabetical order. The values of vi are:v1 = (1 + 2y1 − y2 − y3)/3v2 = (1 + 2y2 − y3 − y1)/3 (22)v3 = (1 + 2y3 − y1 − y2)/3v1 + v2 + v3 = 1 (23)where eq. 23 ensures the contribution is symmetrical in higher order systems.When implemented in the TDB format 40 years ago there was an inconsis-tency with the degrees of the parameter. A single 0L1,2,3:∗ was assumed tobe composition independent and in order to have a composition dependent19ternary parameter one must specify all 3 parameters with indices 0, 1 and 2even if one of the parameters is zero.This will be modi�ed in the XTDB by including an 0L1,2,3:∗ which iscomposition independent and use 1, 2, 3 for the composition dependent pa-rameters, i.e.:terG1,2,3 = y1y2y3(0L1,2,3:∗ +v1 · 1L1,2,3:∗ + v2 · 2L1,2,3:∗ + v3 · 3L1,2,3:∗) (24)It is not possible to make such a change reading a TDB �les becausethere are so many old TDB �les that cannot be changed consistently. Butin the XTDB �les this change can be made automatically by any softwareconverting a TDB �le to XTDB. There is no need for any special informationin the XTDB �le.3.10.2. Reciprocal excess parametersThe reciprocal parameters with simultaneous interaction in two sublat-tices are important for an approximate SRO contribution as shown in [23]but they rarely have a higher order composition dependence. For a reciprocalparameter there is a composition dependence using the degree 0, 1 and 2:∆G = y1,Ay1,By2,Cy2,D(0LA,B:C,D +(y1,A − y1B) · 1LA,B:C,D + (y2,C − y2,D) · 2LA,B:C,D) (25)with the constituents in alphabetical order.3.11. Ternary extrapolation methodsIn ternary systems the composition dependence of the binary excess pa-rameters can be extrapolated in di�erent ways. Three methods are used and20explained in [31, 32] and there is a TernaryXpol tag that can specify theextrapolation method for each case. For example:the Xpol attribute has one letter for the extrapolation method for each binary,K and M mean Kohler or Mugganu, T means Toop and one must indicatealso indicate the Toop constituent: 1, 2 or 3. The binaries are in the orderof the element listed in the Constituent attribute. In the example abovethis means that the binaries Fe-Cr is Kohler, Fe-Si is Toop with Si as Toopelement and Cr-Si is Toop also with Si as Toop element.4. Some explanations related to Appendix AThe summary of XTDB in Appendix A is short and some additionalinformation is provided here.4.1. Names, texts and Upper and lower caseThe XML itself is case sensitive. The tags and attributes in XTDB mustbe written exactly as de�ned in Appendix A. New tags and attributes canbe added when needed to handle new features.For the data provided in the attributes the thermodynamic software isfree to handle names and other texts. In the TDB format upper and lowercase was treated as equivalent and XTDB will follow the same rule. Exceptfor the cases listed below, any Id must start with a letter A-Z and containonly letters, numbers 0-9 and the underscore character, �_�.21The length of Ids for species, phases, functions, etc. in the TDB �leshave been quite restricted. In XTDB there will be no restriction but arecommendation not to exceed 24 characters for any Id. But a softwarereading an XTDB �le is allowed to modify any Id according to its own rulesand such changes of the Id relative to the XTDB �le should be displayed tothe user while reading the database. Such changes should be saved in a waythat the user can at any time obtain the original and modi�ed Ids.4.2. The MQMQA and UNIQUAC constituentsThe constituents needed to calculate the con�gurational entropy andGibbs energy for the MQMQA model are provided as in the FactSage DAT�le and must be speci�ed in the MQMQA attribute of the Species tag.Also for the UNIQUAC model [33] for orgainic liquids each Species has anattribute UNIQUAC which de�nes the area and volume needed for its con-�gurational entropy expression. Information for this is provided in the fullXTDB documentation available at [34].4.3. AppendXTDB �lesThe XTDB �le for a large system can be very big. The set of modelparameters for a σ phase with 5 sublattices and 10 constituents in each is105. There are models such as the EBEF, explained in section 3.9, which canreduce this signi�cantly but a single �le for a database may still be di�cultto manage. A way to handle this is to use the AppendXTDB tag. Sucha tag is allowed only in the primary XTDB �le and the primary XTDB �leshould also include all Defaults, DatabaseInfo, AppendXTDB, Ele-ment, Species, Phase tags and their subtags. But all or parts of the Tp-22fun, Trange, Parameter, ModelDescriptions and Bibliography tagscan be on separate AppendXTDB �les.4.4. The phase and species IdAs explained in section 4.1 upper and lower case are the same in phaseId. In a species Id the characters �/�, �+� and �-� are also allowed.Any parenthesis �(� and �)�, comma �,� , colon �:� and semicolon �;�are forbidden as they are used to separate the various parts of the modelparameters as explained in section 4.6.4.5. The equi-entropy criterion, EECThe equi-entropy criterion [35] was proposed as a method to avoid artifactbreakpoints in the extrapolated Gibbs energy of solid phases. It means thesoftware, while calculating an equilibrium, should prevent any solid phasefrom becoming stable if it has higher entropy than a liquid phase at the sameT , irrespectively of the composition of the phases. When EEC is applicable,the database must indicate if a phase represent a liquid or a solid phase inthe State attribute.4.6. The model parametersThe major part of a Calphad database is the model parameters. In theXTDB �le they are written in the same compact way as in the TDB �le.The parameters use the Ids for model parameter identi�ers (MPID) in theModelDescriptions tag, see Appendix A.7, the Id of the Phase and theIds of the constituent Species. For example:� G(LIQUID,FE+2:VA;0) is the endmember of Fe in the I2SL model.23� TC(FCC_4SL,FE:AL:AL:AL:VA;0) is the endmember of the Curie Tin a 4 sublattice ordering model of the FCC phase with interstitials.� BMAGN(BCC_A2,CR,FE:VA;1) is a �rst order Redlich-Kister termfor the Bohr magneton in the BCC phase. The value after the semicolonindicates the power ν used for parameter in eq. 20 in section 3.10.� G(SIGMA,MO:CR:*:*:*) is an EBEF parameter representing one halfof the bond energy parameter for Cr-Mo in a 5 sublattice model of theσ phase, see Appendix B.2.� LNTH(AL4C3,AL:C) is the logarithm of the Einstein θ in the Al4C3phase, see Appendix B.1.The Parameter tag for XTDB has an Id attribute using the same simplenotation as in TDB to de�ne: 1) the MPID, 2) the phase, 3) the compositiondependence and 4) the degree of a parameter. The �rst part of the Id, beforethe parenthesis, is the MPID. For parameters in the Gibbs energy expression◦GI a simple G is used as MPID. For parameters used in the EGM one canuse G or L as MPID.In the other examples above TC is the Curie temperature and BMAGNis the Bohr magneton number in the IHJREST magnetic model, see Ap-pendix A.7. LNTH is the MPID for the logarithm of the Einstein θ, explanedin section 3.4.After the MPID, and within parenthesis, �rst the phase Id (which canbe abbreviated, see section 4.1), followed by the Ids of the constituents inthe sublattices in the order de�ned in the Phase tag. The constituentsin di�erent sublattices are separated by a colon, �:�. When two or more24constituents mix on the same sublattice they are separated by a comma �,�.For a binary Redlich-Kister parameters the order of the mixing constituentsmay be important, see section 3.10.Before the closing parenthesis of the Id in the Parameter tag there canbe a semicolon, �;�, followed by a digit. The meaning of this digit dependson the model.As the Id of a Parameter tag contains the phase Id these can be arrangedin the XTDB �le as the database manager prefers (but after the Phase tags).Some may prefer to have the parameters for all phases for a binary or ternarysystem together to simplify updates.4.7. The Expr attribute in TPfun and Parameter tagsMany endmember parameters include an expression depending on thedata for the pure elements and to avoid repeating this one can use the TPfuntag for an expression including the T and P as variables, and use the Id ofthese TPfuns in the Expr attribute of other TPfun or Parameter tags.The Expr attribute in TPfun, Trange and Parameters must be verysimple. Below are some rules:A �simple term� in Exp is a signed real or integer value possibly multipliedwith an integer power of T and P. A negative power must be enclosed byparenthesis. Examples:12000 -5*T**2 3.1416E12*T**(-9) 4*T*PA simple term can be used as argument of EXP, LN or LOG function(both LN and LOG are the natural logarithm) or it can be muliplied withthe Id of a TPfun. There is also the special GEIN function, de�ned byeq. 11 in section 4.6, which is needed when a phase has been �tted with25several Einstein θ, only one of which can be used as composition dependentin the LNTH parameter, see Appendix B.1.Multiplying several simple terms enclosed by parenthesis with anotherterm is not allowed in Expr and neither is division. To handle such cases andfor example√T , one can combine TPfuns:but Expr="EXP(0.5*LN(T));" is not allowed.If the Trange tag is used the expression as well as its �rst and secondderivatives with respect to T and P , must be continuous across the break-point. Otherwise the breakpoint represents a phase transition.5. SummaryThe XTDB format proposed here is very similar to the TDB formatwhich has been used for more then 30 years to develop large multicomponentdatabases for Calphad applications. It has also been su�ciently �exibleto handle many new models and may even have stimulated some of them.XTDB does not provide any facilities for internal veri�cation, such featuresrequire a much more complex splitting of the data. For maintaining largecommercial databases such veri�cation is important but not for studentsand scientists editing small databases and manipulate models as part of anassessment. The XTDB format will make it easier to integrate Calphaddatabases with other types of materials databases and software.26Software for verifying the TDB database �les are used by the commercialproviders of thermodynamic databases and such software can also accomo-date the XTDB database format. A well cocumented and easily expandablethermodynamic database format will be greatly appreciated by all scientistsworking with thermodynamic assessments, modeling and applications. A fu-ture project is the development of an ML based format for experimental andDFT data for use in assessments for Calphad databases.AcknowledgmentsThe authors are grateful for creative discussion with Nathalie Dupin. Eco-nomic support from Stiftelsen för Tillämpad Termodynamik (STT) and theScienti�c Group Thermodata Europe (SGTE) are gratefully acknowledged.References[1] P. J. Spencer, A brief history of CALPHAD, Calphad, 32, (2008),doi.org:10.1016/j.calphad.2007.10.001[2] L. Kaufman and H. Bernstein Computer Calculation of Phase Dia-grams. With Special Reference to Refractory Metals (1970) AcademicPress NY[3] A. Dinsdale, SGTE Data for pure elements, Calphad, 15 (1991),doi:10.1016/0364-5916(91)90030-N[4] G. Inden, The role of magentism in the calculation of phase diagrams,Physica, 103B, doi:10.1016/0378-4363(81)91004-427[5] S. Hertzman and B. Sundman, A thermodynamic analysis of the Fe-Cr system, 6, 1982, doi:10.1016/0364-5916(82)90018-9[6] M. Hillert, Phase equilibria, Phase diagrams and Phasetransitions 2nd Ed. (2008) Cambridge Univ Pressdoi:10.1017/CBO9780511812781[7] H. L. Lukas, S. G. Fries and B. Sundman, Computational Ther-modynamics, the Calphad method, (2007) Cambridge Univ Pressdoi:10.1017/CBO9780511804137[8] P.E.A Turchi, I. Abrikosov, B. Burton, S.G. Fries, G. Grimvall,L. Kaufman, P. Korzhavyi, V. R. Manga, M. Ohno, A. Pisch, A.Scott. W Zhang, Interface between quantum-mechanical-based ap-proaches, experiments and Calphad methodology, Calphad, 31, 2007,doi.org:10.1016/j.calphad.2006.02.009[9] A. D. Pelton Phase Diagrams and Thermodynamic Modeling of So-lutions, Elsevier, (2019) doi.org:10.1016/C2013-0-19504-9[10] R. 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Selleby The third generation Calphaddescription of Al-C including revision of pure Al and C., Calphad 72(2021) doi:10.1016/j.calphad.2021.10225030[28] J. Ågren, Thermodynmaics of supercooled liquids and their glass tran-sition, Phys Chem Liq, 18 (1988), doi:10.1080/00319108808078586.[29] C. A. Becker, J. Agren, M. Baricco, Q Chen, S. A. Decterov,U. R. Kattner, J. H. Perepezko, G. R. Pottlacher and M. Sell-eby, Thermodynamic modelling of liquids, Phys Stat Sol B (2013),doi:10.1002/pssb.201350149[30] I. Ansara, T. G. Chart, A. Fernández Guillermet, P. C. Hayes, U. R.Kattner, D. G. Pettifor, N. Saunders, K.Zeng, Thermodynamic mod-elling of selected topologically close-packed intermetallic compounds,Calphad, 21, (1997), doi:10.1016/S0364-5916(97)00021-7[31] M. Hillert, Empirical methods of predicting and representing thermo-dynamic properties of ternary solution phases, Calphad 4 pp 1�12,doi:10.1016/0364-5916(80)90016-4[32] A. Pelton, A general �geometric� thermodynamic model for multicom-ponent solutions, Calphad 25 (2001) pp 319�328 doi:10.1016/S0364-5916(01)00052-9[33] J Li, B. Sundman, J. G. M. Winkelman, A. I. Vakis, F. Picchioni, Im-plementation of the UNIQUAC model in the OpenCalphad software,Fluid Phase Eq., 507, (2020), doi:10.1016/j.�uid.2019.112398[34] https://github.com/sundmanbo/XTDB/[35] B. Sundman, U. R. Kattner, M. Hillert,M. Selleby, J. Ågren, S.Bigdeli, Q. Chen, A. Dinsdale, B. Hallstedt, A. Khvan, H. Mao, and31R. Otis, A method for handling the extrapolation of solid crystallinephases to temperatures far above their melting point, Calphad, 68(2020), 101737 doi:10.1016/j.calphad.2020.10173732Appendix A. A summary of the XML tags and attributesA complete version is available at [34]. Attributes which are mandatoryare indicated by a !M to the left.Appendix A.1. Global tagsTag Attributes NoteXTDB Containing XML tags for an XTDB database.!M Version Version of XTDB used for this database.!M Software Name of software generating the database.!M Date Year/month/day the database was written or last edited!M Signature person or organisation generating the database.Defaults Optional tag to provide default values of attributes in di�erentXML tags and some other things.LowT Default value of low T limit.HighT Default value of high T limit.Elements For example �VA� (vacancy) and �/-� (the electron).GlobalModel Any model applicable to the whole database.DatabaseInfo Optional tag with information about the databaseInfo Free text (excluding the characters <> & ).Date Last update of the database information.AppendXTDB Optional tag with additional �les for the XTDB database. Itshould contain XTBD tags see section 4.3.Models The ModelDescriptions tag, see section 3.3.Parameters With mainly Parameter tags.TPfuns With some or all TPfun tags.Bibliography With bibliographic tags.Misc Whatever the database manager needs.33Appendix A.2. The Element and Species tagsTag Attributes ExplanationElement Speci�es a chemical element in the database. In addition the va-cancy, denoted �VA�, and the electron, `denoted `/-�, are includedto handle defects and ions.!M Id Chemical element symbol, one or two letters, for example FE, H.The Id is case insensitive, see section 4.1.Refstate Name of the reference phase for the element.!M Mass Mass in g/molH298 Enthalpy di�erence between 0 and 298.15 K in the reference state.S298 Entropy di�erence between 0 and 298.15 K in the reference state.Species Speci�es a chemical species used as a constituent of phases. Theelements, except the electron, are also species.!M Id Species name, see section 4.1.!M Stoichiometry One or more element Id each followed by an unsigned real or twointegers separated by a �/� representing the stoichiometric ratio.A �/-� or �/+� followed by a digit means a negative or positiveelectric charge. If no digit 1 is assumed. See section 4.1.MQMQA For a constituent in the MQMQA model. See section 4.2.UNIQUAC For a constituent in the UNIQUAC model. See section 4.2.34Appendix A.3. The phase tagsTag Attributes ExplanationPhase All thermodynamic data is part of a phase.!M Id Phase name, see sections 4.1 and 4.4.!M Con�guration Model for the con�gurational entropy, see section 2.4.State see section 4.5.CrystalStructure Optional inside a Phase tag.Prototype Prototype phaseStrukturBericht For example A3, B2, C14, D0_3 etc.PearsonSymbol For example hR21 cI2.SpaceGroup For example 127, 166.Sublattices Only once inside a Phase tag.!M NumberOf Number of sublattices, an integer value > 0.!M Multiplicities One real value> 0 for each sublattice, See Appendix B.1Constituents Only inside the Sublattices tag.Sublattice Can be omitted if only one sublattice.Wycko�Position Optinonal speci�cation.!M List Species Id separated by a space, see section 3.2.AmendPhase Optional tag inside a Phase tag to specify a contrinution from aphysical model, see section 3.3, Appendix C and Appendix B.1.Models One or more model Ids, separated by a space, for this phase.There can also be an DisorderedPart tag inside this tag.35Appendix A.4. The function tagTag Attributes ExplanationTPfun De�nes a T, P expression to be used in parameters or other func-tions.!M Id The Id can be used in the Expr attribute of other functions orparameters, see section 4.1.LowT Can be omitted if the default low T limit applies.!M Expr Simple mathematical expression terminated by ;. See section 4.7.Use the Trange tag if several ranges.HighT Can be omitted the default high T limit applies.Trange Only inside a TPfun or Parameter tag for an expression withseveral T ranges. The function and its �rst and second derivativemust be continous.!M Expr Simple mathematical expression terminated by ;. See section 4.7.HighT Can be omitted if the default high T limit applies.There is no provision for breakpoints in P . Separate models are neededfor pressure dependence above a few MPa.36Appendix A.5. The parameter tagThe model parameters are the central part of an XTDB database. In theexample here the very compact form used in TDB �les is retained.Tag Attributes ExplanationParameter Speci�es the T, P expression of a model parameter for a setof constituents.!M Id As in a TDB �le, See section 4.6LowT Can be omitted if the default low T limit applies.!M Expr Simple mathematical expression terminated by ;. If severalranges use a Trange tag. See section 4.7.HighT Can be omitted if the default high T limit applies.!M Bibref Bibliographic reference.Appendix A.6. The bibliography for parametersTag Attributes ExplanationBibliography Contains bibliographic references. There are no attributes.Bibitem Only inside a Bibliography tag.!M Id Used as value in the bibref attribute for a parameter or model,normally a paper or a comment by the database manager.!M Text Reference to a paper or comment.DOI DOI of paper where the parameter was assessed.37Appendix A.7. The tags for current modelsTag Attributes ExplanationModelDescriptions Contains model tags usually with an Id attribute used inAmendPhase tags inside a Phase tag. Most models haveone or more model parameter identi�ers (MPID).!M Software Name of software using these models.Magnetic There are several magnetic models. See section Appendix C.!M Id This is used in Models attribute of the AmendPhase tag.There are 3 variants: IHJBCC, IHJREST and IHJQX,A� The antiferromagnetic factor (-1, -3 or 0).!M MPID1 Speci�es the Bohr magneton number MPID!M MPID2 Speci�es a Curie or combined Curie/Neel temperature MPIDMPID3 Speci�es a Neel temperature MPID for IHJQX!M Bibref Where the model is described.Permutations For FCC, HCP and BCC lattices a 4 sublattice tetrahedronmodel, See section 3.8.!M Id This is used in the Models attribute of the AmendPhasetag. Its can be either FCC4PERM or BCC4PERM.!M Bibref Where the model is explained.DisorderedPart Optional tag inside the AmendPhase tag of an orderedphase with or without order/disorder. See section 3.6.Disordered Optional attribute with the Id of the disordered phase.!M Sum Number of sublattices in the ordered phase in eq. 14.Subtract Must be speci�ed if eq. 16 in section 3.6 should be used.!M Bibref Where the model is described.38Appendix A.8. The tags for the new unary databaseTag Attributes ExplanationEinstein The low T vibrational model, see section 3.4.!M Id This Id is used in AmendPhase tag.!M MPID1 Speci�es the MPID for the Einstein θ.!M Bibref Where the model is described.Liquid2state The liquid 2-state model, see section 3.5.!M Id This Id is used in AmendPhase tag.!M MPID1 Speci�es the MPID for the 2-state transition energy.!M MPID2 Speci�es the MPID for the Einstein θ for the low T extrapo-lation.!M Bibref Where the model is described.EEC Speci�es that the Equi-entropy model applies to the wholedatabase. See section 4.5. The liquid Phase tag must alsohave the State attribute equal to L.!M Id has the value EEC.!M Bibref Where the model is described.39Appendix A.9. Miscellaneous tagsTag Attributes ExplanationTernaryXpol The extrapolation method for a ternary. See section 3.11.!M Phase The Id of a phase.!M Constituents The Ids of 3 Species that are constituents of the phase.!M Xpol The type of extrapolations, for example KKK if the Kohlermethod is used for all 3 binaries.!M Bibref Where the model is described.BinarySystem Optional tag for a database manager to surround a set ofmodel parameters for a binary system. It can be used to listwhich assessed systems that are present in the database.!M System The Ids of the two elements inside the tag.CalcDia Software dependent way to calculate the binary system40Appendix B. Examples of XTDB �lesAppendix B.1. A complete Al-C database41424344Appendix B.2. A σ phase with EBEF and DisorderedPart 4546The TPfuns SIGMA_X_AsBt can be �tted to DFT calculated endmem-bers. In a ternary EBEF there are 63 parameters, without wildcards thereare 35 = 243 endmembers.Appendix B.3. A σ phase with EBEF and DisorderedPartBelow is a suggestion of a future possibility for a shorter notation. Models="EBEF" 47Appendix B.4. An FCC phase with wildcards and DisorderedPart484950Appendix C. A tentative ModelDescriptions tagThis de�nes the physical models and their model parameter identi�ers(MPID) used in the XTDB �le. Each software can have its own version.51 5354