xtdb-v014.tex

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%\date{June 2023}

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\begin{document}

\begin{center}

  {\Large \bf Proposal 0.1.4 of an XML format to replace TDB files}


  Bo Sundman, Tachi Abe, Qing Chen, Shuanglin Chen, Nathalie Dupin,
  Bengt Hallstedt, Aur{\'e}lie Jacob, Ursula R. Kattner, Lina Kjellquist,
  Reza Naraghi, Richard Otis, Alexander Pisch, Erwin
  Povoden-Karadeniz, Malin Selleby, Axel van de Walle, Fan Zhang and
  Fabio Miani


. \today

\end{center}

I put my name first to take the blames and Fabio at the end as the
project manager.

{\bf Recent changes in Appendix~\ref{sec:changes}.  The Examples are
  not updated.}

For minor changes enclose new text with {\color{green} with your own
  color} and delete text using \sout{deleted text}

\section{Background}

Within the Calphad community the databases with model parameters are
important and can often be used by several different software as well
as edited manually.  The most frequent format for such database is
called TDB and was created by the Scientific Group Thermodata Europe
(SGTE) while working on the unary databse for 78 elements which was
published 1991~\cite{91Din}.  It has been used for more than 40 years
but it has limitations, in particular when adding new new models and
features.

It is high time to change from this format and to adopt an accepted
Markup Language as XML or JSON.  The XML has been selected for a new
XTDB format as it has been around for a long time and is slightly more
explicit.  There are many Markup Languages but it is easy to convert
between any of them and thus the choice of XML is not very critical
except to avoid spending several years to discuss the choice.

XML is flexible and extendable and each software may add their own
flavour in a controlled way.  It will be simpler to use an XTDB file
by different softwares as one can easily indicate what is software
specific rather than try to modify or extend the TDB format.

To avoid the confusing use of {\bf element} both for chemical element
and the XML element the word {\bf tag} will be used for the XML
element.

\subsection{Objectives}

The TDB format is well established and used by students assessing
model parameters as well as database managers and researches trying to
develop new materials based on thermodynamic calculations.  This
proposal proposes a minimal change from the current TDB format but
will simplify future extensions.  The new format, called XTDB, will be
used for:
\begin{itemize}
  \item manually editing of an XTDB file should be as easy as the
    current TDB format also for non-experts.
  \item minimize problems when using software A to read a database
    file written by software B.
  \item simplify adding features and new models for different phase
    dependent physical properties in the thermodynamic database.
  \item provide users of a database with information about the models
    and bibliographic references, even for encrypted databases.
  \item improve collaboration between users and researchers dealing
    with Calphad databases.
  \item simplify for software developers to add tags and attributes in
    software and databases.  Such modifications should be discussed
    between developers and users and eventually integrated in the XTDB
    format.
\end{itemize}

Some software has already introduced features in the TDB file which
may not bee fully implemented in other software.  Some of these are
discussed in section~\ref{sec:wildcard}.

This XTDB definition may require minor modifications in the XML format
already adoped in some software.  Commercial companies providing
encrypted databases to customers can use whatever format they prefer
for such databases.  But they should provide a facility to read and
write unencrypted databases in the XTDB format.

\subsection{The XTDB file and some more}

The characters used in an XTDB file are restricted to the classical
ASCII character set.

The XTDB file is divided into lines (terminated by LF (Line Feed or
newline as preferred by UNIX dialects) or CRLF (Carriage Return and
Line Feed as preferred by Windows)).  For the XTDB file a line should
not exceed 2000 characters.

If you are not familiar with XML there are plenty of information
online.  A brief summary here:

XML has 3 reserved charaters, ``$<'', ``>$'' and ``\&''.  These must
not be used anywhere except for XML itself.

An XML file consists of ``tags'' with ``attributes'' where the
attributes contains the specific data for the tag.  An example makes
it easier to explain:

\begin{verbatim}
<Element Id="AL" Refstate="FCC_A1" Mass="26.982" H298="4577.3" S298="28.322" />
\end{verbatim}

Each tag has a name preceded by the reserved character ``$<$'' followd
by a ``tagname'' and the tag ends with ``$\eoxml$'' unless the tag
contains other tags.  Such nested tags are each on a new line and the
enclosing tag must be ended by ``$<$/tagname$>$'' on a separate
line.  For examples see Appendix~\ref{sec:phaseexample}.

An attribute is followed by an equal sign and the the data is enclosed
by double quotes, ".  {\bf If the data consists of several values they
  are separated by one or more spaces}, see
Appendix~\ref{sec:phaseexample}, do not use a comma or anything else.
An attribute can occur only once within a tag but the a tag be
repeated any number of times.

All tags and their attributes proposed for XTDB are listed in
section~\ref{sec:tags} and explained for each tag.  Several examples
are provided in later seactions and the Appendix~\ref{sec:complete}
has two complete XTDB files.

In this document a tag is usually written in {\bf bold} when refereced
in the text and an attribute in {\em italics}.  Many tags have an {\em
  Id} attribute which can be referenced to in other tags.  All values
of the {\em Id} attributes are case insensitive as they are in the TDB
file.  The value of an {\em Id} cannot be abbreviated when used in
other tags except for phase {\em Id}.  But such an abbreviation must
be unique.

All attributes of an XTDB tag should fit within a line and only one
XML tag per line in order to be easily readable by humans.  A tag with
nested tags has its attributes on the same line as the tag and each
nested tag begins on a new line.  The end of a tag including nested
tags should appear on a line by itself, see for example
Appendix~\ref{sec:phaseexample}.

The attribute {\em List} of the {\bf Constituent} tag for a gas phase
in a big system may exceed 2000 characters but several {\bf
  Constituent} tags can be used for a phase.

In the examples some long tags have been separated into several lines
in order to be readable.

A software reading the XTBD file should ignore XML tags and attributes
it does not support, preferably with a warning to the user.

The XML tagname and its attributes cannot be abbreviated and are case
sensitive.

Database users may be interested to add more or less temporary
comments inside the database and comments, starting with ``$<$!---''
and ending with ``---$>$'', can be added anywhere between tags in the
XML file.  There must not be any "--" or forbidden characters inside
the comment.

An XML parser is convenient for reading XML files but to simplify the
life for all the the humans reading and editing the XTDB file it is
strongly recommended that the attributes to an XML tag are provided in
the order listed for each tag below.  Software specific attributes can
be added to a tag but should come at the end.

\subsection{How this document can be read}

The following proposal is for a common definition of an XTDB file
format based on XML.  It can hopefully become an SGTE standard
acceptable by all software groups which develop or use Calphad
databases.

In section~\ref{sec:tags} all proposed tags are listed with a short
explanation.  In section~\ref{sec:attributes} a more detailed
explation are given of some tags and attributes and
section~\ref{sec:points} has a list of things to consider.

In the Appendix~\ref{sec:examples} there are several examples of tags
and attributes, in Appendix~\ref{sec:modelapp} an extensive list of
model tags and their attributes.  In Appendix~\ref{sec:partags} there
aee explanations how some thermodynamic models, such as
EBEF~\ref{sec:ebef}, have been integrated in the XTDB format using
wildcard feature.

In Appendix~\ref{sec:complete} the complete XTDB file for the binary
Al-C and Al-Li are listed and finally in Appendix~\ref{sec:changes} an
attempt to document recent changes in this proposal from earlier
versions together with some unresolved issues.

A software can easily extract randomly arranged tags from an XTDB
files but for a a human reader and for manual editing the XTDB file
the recommended order is {\bf DatabaseInfo, Defaults} and any {\bf
  AppendXTDB} tags followed by {\bf Element, Species} and {\bf Phases}
(with many nested tags).

The main part of the XTDB databas are the {\bf Parameter} and {\bf
  TPfun} and tags, which can be ordered by the phases or by the
systems.  For maintaing a database it may be convenient to keep
parameters inside {\bf BinarySystem} or {\bf TernarySystem} tags.  The
{\bf TernaryXpol} tags should be together binary parameters.

The {\bf Model} tag should appear before any {\bf Phase} or {\bf
  Parameter} tags and the {\bf Bibliography} at the end or both in a
separate{\bf AppendXTBD} file.  The {\bf AppendXTDB} tag, which
specifices additional files of an XTDB database, allows the database to
be split on several files.  The {\bf Defaults, DatabaseInfo} and {\bf
  AppendXTDB} tags and all {\bf Element, Species} and {\bf Phase} tags
must be present in the primary XTDB file.

With a few exceptions a tag or attribute starts with a capital letter
and if it consists of two or more parts, such as {\em NumberOf}, the
second part is joined without hyphen or underscore but starts with a
capital letter. 

\newpage

\section{The XTDB-v0.1.4 tags and attributes with short explanations}\label{sec:tags}

All proposed tags for the XTDB file are listed here. Further
explanations of the attributes can be found in
section~\ref{sec:attributes}.

Some tags are optional and many of them will appear several times in
the XTDB file to provide the data.

An exclamation marek ``!'' is indicated for the mandatory attributes of a tag.

\subsection{The system XTDB tags}\label{sec:first}

The {\bf AppendXTDB} tag makes it possible to separate a large XTDB
database on several files.  There are some restrictions which types of
tags can be used in such files, for example the tags for {\bf Element,
  Species, Phase} are not allowed in AppendXTDB files.

\begin{tabular}{|p{0.06\textwidth} p{0.15\textwidth} p{0.8\textwidth}|}\hline
  Tagname & Attributes & Explanation\\\hline

  XTDB    &         & Containing XML tags for an XTDB database.\\
!          & Version & Version of XTDB for this file.\\
           &Software & Name of software generating the database.\\
!          &Date     & Year/month/day the database was written or last edited\\
!          &Signature & Name/email of person or organisation generating the database.\\\hline
  
  Defaults & & Optional tag to provide default values of attributes in
  different XML tags and some other things.  Some software, as
  specified XTDB tag,  may have some ``mandatory'' defaults.\\
           & LowT & Default value of low $T$ limit.\\
           & HighT & Default value of high $T$ limit.\\
           & Bibref & Default bibliographic reference for parameters. \\
           & Elements & For example ``VA'' and/or ``/-'' (the electron).\\
           & RKorder & see section~\ref{sec:rkorder} \\
           & TernaryXpol & see section~\ref{sec:toop} \\
           & GlobalModel & Any model applicable to the whole database,
                 for example EEC~\cite{21Sun}\\\hline

  DatabaseInfo & & Optional tag with information about the database\\
           & Info & Free text (excluding the characters $< >$ \& ).\\
           & Date & Last update of the database information.\\\hline

  AppendXTDB & & Optional tag with additional file for the XTDB database.  
              It should contain XTBD tags but some tags are forbidden,
              see above.\\
         & Models & The {\bf Model} tag with MPID specifications, read first.\\
         & Parameters & With mainly {\bf Parameter} tags.\\
         & TPfuns & With all {\bf TPfun} tags which may have to be rewinded and
                    read several times.\\
         & Bibliography & With bibliographic tags.\\
         & Miscellaneous & Whatever the database manager wishes.\\\hline
\end{tabular}

Note that in this and later tables the exclamation mark at the far
left side of some attributes means they are mandatory.

\subsection{The element and species tags}\label{sec:elements}

All constituents of the phases must be specified as {\bf Species} and
the species are aggregates of one or more {\bf Element} with fixed
stoichiometric ratios.  The vacancy, denoted ``VA'', is considered an
element which must have activity 1 at equilibrium but cannot have a
fixed amount.  The electron ``/-'' is considered as an element and can
be used as a fixed charge on a {\bf Species}.  A phase with charged
species must have an extra internal software condition that the phase
is electrically neutral at equilibrium.

There are strong feelinga about upper and lower case for elements and
sometimes phases.  But in fact the elements are only used to specify
the stoichiometry of species and that is not a very big thing.  The name
of species, i.e. their {\em Id} , is case insensitive and the species
are the constituents of the phases.

Species names are important not only for listing and plotting results
because constituents, i.e. the species, can be used when setting
conditions for a equilibrium calculation.  The elements are
automatically entered as species with a case insensitive {\em Id}.

An ion, for example an iron species with positive charge can have the
stoichiometry ``FE/+2''.  One can create a species for an electron
using the stoichiometry ``VA/--1'', or a species for a ``hole'' with
stochiometry ``VA/+1''

\begin{tabular}{|p{0.06\textwidth} p{0.15\textwidth} p{0.8\textwidth}|}\hline
  Tagname & Attributes & Explanation\\\hline

  Element & & Specifies a chemical element in the database.  In addition
              the vacancy, denoted ``VA'', and the electron, `denoted `/-'',
              are included to handle defects and ions.\\
!          & Id        &  Chemical element symbol, one or two latters, 
                         for example FE, H.  The symbol is case insensitive,
                         see section~\ref{sec:lettercase}.
                         Fictitious element names can be used. \\
          & Refstate  &  Name of the reference  phase, for example GAS.  The
                         database may not have any data for this phase. \\
!          & Mass      &  Mass in g/mol\\
          & H298      &  Enthalpy difference between 0 and 298.15~K 
                         in the reference state.  Not used in equilibrium
                         calculations. \\
          & S298      &  Entropy difference between 0 and 298.15~K in 
                         the reference state.  Not used in equilibrium
                         calculations\\\hline

  Species & & Specifies a chemical species used as a constituent of phases.  
                        The elements, except the electron, are also species.\\
!          & Id        & Species name max 24 letters and some special
                         characters, see section~\ref{sec:speciesID}.\\
!          & Stoichiometry & One or more element {\em Id} each followed by 
                        an unsigned real or two integers separated by a ``/'' 
                        representing the stoichiometric ratio,
                        see section~\ref{sec:speciesSS}.  See also
                        Appendix~\ref{sec:elementexample}.\\
          & MQMQA     & For a constituent in the MQMQA model.  See 
                        section~\ref{sec:mqmqa}.\\
          & UNIQUAC   & For a constituent in the UNIQUAC model. See 
                        section~\ref{sec:uniquac}.\\\hline

\end{tabular}

\subsection{The function and temperature range tags}\label{sec:tpfun}

The thermodynamic model parameters are usually simple mathematical
expressions but many of them contain common parts refering to the same
element.  In order to reduce this complexity one can enter a
mathematical expression with the {\bf TPfun} tag and use the {\em Id}
of this {\bf TPfun} inside the {\em Expr} attribute of several {\bf
  Parameter}, {\bf Parameter2} tags or other {\bf Tpfun} tags,.  

\begin{tabular}{|p{0.06\textwidth} p{0.15\textwidth} p{0.8\textwidth}|}\hline
  Tagname & Attributes & Explanation\\\hline

  TPfun & & Defines a $T, P$ expression to be used in parameters or other functions.\\
!        & Id & Function name, max 16 characters, see 
           section~\ref{sec:lettercase}.  The name is used in the
         ``Expr'' attribute of other functions or parameters, 
           see section~\ref{sec:tpfunattr}.\\
        & LowT & Can be omitted if the default low $T$ limit applies.\\
!       & Expr &  Simple mathematical expression terminated by ;.   Use the {\bf Trange} tag if several ranges.  See section~\ref{sec:expr}\\
        & HighT & Omitted the default high $T$ limit applies.\\\hline

  Trange & & Only inside a {\bf TPfun} or {\bf Parameter} tag for an expression with several $T$ ranges.\\ 
!         & Expr & Simple mathematical expression terminated by ;.  See section~\ref{sec:expr}.\\
         & HighT & Omitted if the default high $T$ limit applies.\\\hline
\end{tabular}

See section~\ref{sec:expr} for the restrictions of the mathenatical
expresson in the {\em Expr} attribute and Appendix~\ref{sec:tpfuns}
and others for examples.  There is no way at present to handle several
pressure ranges in the XTDB file.  For high $P$ a separate model for
the volume should be used.

The value of a function, as well as its first and second derivatives
with respect to $T$ and $P$, must be continuous across an interval of
$T$ range.  Breakpoints will normally occur only for {\bf TPfun} of
pure element data and those in the unary 1991~\cite{91Din} have been
checked.  Using the {\em Id} of a {\bf TPfun} tag inside another {\bf
  TPfun} may create infinite loops by circular calls but is left for
the software to detect this.

%\newpage 

\subsection{The phase tag and its nested tags}\label{sec:phase}\label{sec:dispart}

The phase tag has two ``compulsory subtags'' i.e. {\bf Sublattices}
and {\bf Constituents}.

\begin{tabular}{|p{0.06\textwidth} p{0.15\textwidth} p{0.8\textwidth}|}\hline
  Tagname& Attributes & Explanation\\\hline

  Phase & & All thermodynamic data is part of a phase.\\
!       & Id & Phase name, see sections~\ref{sec:lettercase} and 
               \ref{sec:phaseid}. \\

!       & Configuration &  Model for the configurational entropy, 
                see section~\ref{sec:cfg}.\\

         & State & G for gas phase, L for liquid phase.  
                Only needed for the liquid if EEC is used.\\\hline

  CrystalStructure & & Optional tag inside a {\bf Phase} tag.\\
        & Prototype & Prototype phase \\
        & StructurBericht & For example A3, B2, C14, D0\_3 etc.\\
        & PearsonSymbol & Specification.\\
        & SpaceGroup & Specification.\\\hline

  Sublattices & & Only once inside a {\bf Phase} tag.\\
!        & NumberOf &  Number of sublattices, an integer value 1 - ?. \\
!        & Multiplicities & Sites on each sublattice, as many reals as
               sublattices separated by a space.  For an example 
               see Appendix~\ref{sec:phaseexample}\\\hline

  Constituents & & One for each sublattice inside the {\bf Sublattices} tag.\\
             & Sublattice & Omitted if only one sublattice.\\
!           & List &  Species {\em Id} in the sublattice,
             separated by a space, see Appendix~\ref{sec:phaseexample}.\\\hline

  AmendPhase & & Optional tag inside a {\bf Phase} tag to specify
               for example a contribution due to a magnetic model.\\
     & Model & One or more models {\em Id}s, separated by a space, for this
         phase.  See section~\ref{sec:models}, Appendix~\ref{sec:modelapp}
         and \ref{sec:phaseexample}.\\\hline

  DisorderedPart & & Optional tag inside the {\bf Phase} tag of an 
              ordered phase with or without order/disorder transions.
              The Gibbs energies of the ordered and disordered parts
              of a phase are added according to eq.~\ref{eq:nosub} or
              \ref{eq:sub} below.

              In order to use eq.~\ref{eq:sub} the the constituents on
              the ordering sublattices must be identical and the
              attribute {\em Subtract} must be included.  See also
              section~\ref{sec:dispart}.  (with identical constituents
              but different number of sublattices)

              The configurational Gibbs energy is calculated for
              the ordered part only.  \\

   & Disordered & Optional attribute with the name of the disordered phase, 
            see section~\ref{sec:nodis}.  Some software have the parameters
            for the ordered and disordered part with the same phase name.\\

!  & Sum & Number of sublattices, starting from the first sublattice in the
              ordered phase to be summed for the disordered phase
              constitution.  Optionally an extra interstitial
              sublattice can be present.\\

   & Subtract & Must be specified if eq.~\ref{eq:sub} should be used.
                It can be assigned any value but must be present.\\\hline
\end{tabular}

\bigskip
For a phase with the {\bf DisorderedPart} tag the Gibbs energy
(excluding the configurational entropy) is calculated by one of these
equations:
\begin{eqnarray}
G_M &=& ~^{\rm dis}G_M(x) + ~^{\rm ord}G_M(y) \label{eq:nosub}\\
G_M &=& ~^{\rm dis}G_M(x) + ~^{\rm ord}G_M(y) - ~^{\rm ord}G_M(y=x) \label{eq:sub}
\end{eqnarray}
where $x$ is averaged values of $y$ for some (or all) sublattices in
the ordered phase.  Eq.~\ref{eq:nosub} is mainly used for phaes with
many sublattices which never disorder for example intermetallic
phases.

In order to use eq.~\ref{eq:sub} one must specify the attribute {\em
  Subtract} (with any value).  This equation can be used for phases
with order/disorder transitions such as FCC, BCC and HCP.  Such phases
are stable as disordered in many systems but sometimes exhitit
ordering.  Using eq.~\ref{eq:sub} the model parameters as ordered and
disordered phase can be assessed separately because calculating the
Gibbs energy of the ordered phase twice, the second time using the
disordered fractions, and then subtracting means the ordered
parameters will not affect the disorderd state.  For details
see~\cite{97Ans} and~\cite{07Hal}

A phase with very long list of constituents (for example the gas) can
have several {\bf Constituent} tags.

\subsection{The parameter tag}\label{sec:parametertag}

All thermodynamic data, and possibly kinetic and other physical phase
dependent properties, are defined by the parameter tags.  They should
be arranged after the {\bf Phase} tags or inside a {\bf BinarySystem}
tag, see~\ref{sec:subsys}.  They can have nested {\bf Trange} tags.
Examples in sections~\ref{sec:parameter2}, Appendix~\ref{sec:parameter
  examples}, \ref{sec:partags} and \ref{sec:complete}.

\bigskip
\begin{tabular}{|p{0.06\textwidth} p{0.15\textwidth} p{0.8\textwidth}|}\hline
  Tagname& Attributes & Explanation\\\hline

  Parameter & & Specifies the $T, P$ expression of a model parameter for a set of constituents.\\
!      & Id & As in a TDB files, for example G(LIQUID,A,B:VA;2).  See also the {\bf Parameter2} tag. \\
      & LowT & Can be omitted if the default low $T$ limit applies.\\
!      & Expr & Simple mathematical expression terminated by ;.  If several ranges use a {\bf Trange} tag.  See section~\ref{sec:tpfun} and \ref{sec:expr}.\\
      & HighT & Can be omitted if the default high $T$ limit applies.\\
!      & Bibref & Bibliographic reference, unless the default bibref is set.\\\hline
\end{tabular}

The attribute {\em Id} defines the parameter as in the current TDB
file.  It starts with a model parameter identifier (MPID), see
Appendix~\ref{sec:mpid}, followed within parenthesis by a phase name
(which can be abbreviated) and one or more constituents in each
sublattice of the phase in the order of the sublattices.

Constituents are given in the order of the sublattices defined by the
phase tag, separated by a colon, ``:''.  Constituents in the same
sublattice, i.e.  for interaction parameters, are separated by a
comma, ``,''.  The order of sublattices and their constituents are as
defined by the {\bf Phase} tag, see section~\ref{sec:phase}.

After the constituents in the last sublattice a semicolon, ``;''
followed by a single digit, 0-9, can be used to indicate a degree.
This degree can have different meanings in different models but is
normally used for the power in a Redlich-Kister series, see
section~\ref{sec:rkorder}.  If the digit is zero the semicolon and the
digit can be omitted.

An asterisk ``*'', also known as wildcard, see
section~\ref{sec:wildcard}. can be used as constituent in a sublattice
indicating that the parameter is independent of the constituents in
the sublattice.  The wildcard is an important feature of some models,
see section~\ref{sec:ebef}.

The parameters are the essential parts of the database and more
examples can be found in Appendix~\ref{sec:partags}.  They are
generated from separate assessment of experimental and theoretical
data for binary and higher order systems.  One aim of this XTDB format
is also to provide a simple and unified way to publish and report such
assessments.  Databases are collections of such assessment and
database managers integrate separate assessment and sometimes modify
some parameters for compatibility with other systems.  In addition to
the bibliographic reference the database managers are encouraged to
add comments of such actions within the {\bf Parameter} tag in order
to pass on information to the next manager of the database.

\subsection{The elaborate parameter tag}\label{sec:parameter2}

An alternative more elaborated XML tag can be used for parameters
which may be preferred by software.  It is straightforward to convert
from one to another.  It must have a subtag, {\bf Constarray} with one
or more tags {\bf SublConst} for each constituent in each sublattice.

\bigskip
\begin{tabular}{|p{0.06\textwidth} p{0.15\textwidth} p{0.8\textwidth}|}\hline
  Tagname& Attributes &  Explanation\\\hline

  Parameter2 & & A more detailed parameter tag preferred by software.\\
      & Id & As in TDB file, for example G(LIQUID,A,B:VA;2).  See also the {\bf Parameter} tag. \\
!      & MPID & Model parameter identifier, for example G or TC.\\
!      & Phase &  Can be omitted inside a phase tag, otherwise the phase name.\\
      & LowT & Can be omitted if the default low $T$ limit applies.\\
!      & Expr & Simple mathematical expression terminated by ;.  If several ranges use a {\bf Trange} tag.  See section~\ref{sec:tpfun} and \ref{sec:expr}.\\
      & HighT & Can be omitted if the default high $T$ limit applies.\\
!      & Bibref & Bibliographic reference.\\\hline

  ConstArray & & Only inside a {\bf Parameter2} tag.  Encloses the
                   SublConst tags.\\
      & Degree & Can be omitted if zero.  See section~\ref{sec:degree}\\\hline
  
  SublConst & & Only inside a {\bf ConstArray} tag. There must be at least
              one tag like this for each sublattice.\\
!      & Sublattice &  Sublattice of constituent.\\
!      & Species & A species {\em Id}.  Two or more species in the same 
             sublattice means an excess parameter.\\\hline  
\end{tabular}

\bigskip
The {\bf Parameter2} tag may be preferred by software but for
manual editing {\bf Parameter} is simpler, see the
Appendix~\ref{sec:parameter examples}.  Both tags can be used in
the XTDB file and software can easily convert between them.

If the {\em Id} attribute is present in a {\bf Parameter2} tag the
software should check that this {\em Id} is identical to the long form
and report an error if not.

\subsection{Bibliography for parameters and models.}\label{sec:biblio}

For each parameter there must be a bibliographic reference.  This can
be the same for all parameters from the same source.  The models also
have a reference which should indicate a paper where the model is
explained, see Appendix~\ref{sec:modelex}.

It is important to inform the users that thermodynamic databases are
not not created by computers or appear from thin air.

\bigskip
\begin{tabular}{|p{0.06\textwidth} p{0.15\textwidth} p{0.8\textwidth}|}\hline
  Tagname& Attributes &  Explanation\\\hline

  Bibliography & & Contains bibliographic references\\\hline

  Bibitem & & Only inside a {\bf Bibliography} tag.\\
!      & Id &   Used as value in the {\em bibref} attribute for a parameter
            or model, normally a paper or a comment by the database manager.\\
!      & Text & Reference to a paper or comment.\\
       & DOI & DOI of paper where the parameter was assesses.\\\hline
\end{tabular}

\subsection{The model tags}\label{sec:models}

The XML tags for generally accepted models can be on a separate file
and the model {\em Id} attribute is the important and used in the {\bf
  AmendPhase} tag for each phase which has the model.  Most models
have one or more model parameter identifiers (MPID) as attributes and
these are used in the {\bf Parameter} tag for the phases.  Models must
be explained in a model tag with an appropriate bibliographic
reference.  Typically the {\bf Model} tag is in an AppendXTDB file.
See Appendix~\ref{sec:modelapp}.  The Model tag and Some currently
used model tags are listed here.  The models normally specify one or
more model parameter identifiers (MPIDs) used in parameters needed for
the model.  Additional text outside the attributes can be added
describing the model.

\bigskip
\begin{tabular}{|p{0.06\textwidth} p{0.15\textwidth} p{0.8\textwidth}|}\hline
  Tagname& Attributes & Explanation\\\hline

  Models & & Contains model tags usually with an {\em Id} attribute
               used in {\bf AmendPhase} tags inside {\bf Phase} tahs.  
               The models usually specify one or more model parameter 
               identifiers (MPID) needed by the model.  Some models, 
               such as {\bf DisorderedPart}  must be included as tags 
               within the {\bf Phase} tag.\\\hline
%\end{tabular}
%
%\bigskip
%\begin{tabular}{|p{0.06\textwidth} p{0.15\textwidth} p{0.8\textwidth}|}\hline
%  Tagname& Attributes & Explanation\\\hline

  Magnetic & & There are several magnetic models.\\
!      & Id & This is used in {\em Model} attribute of the 
               {\bf AmendPhase} tag.  There are currently 3 variants:
               IHJBCC, IHJREST and IHJQX explained 
               in Appendix~\ref{sec:modelapp}. \\
      & Aff   & The antiferromagnetic factor (-1, -3 or 0).  It is
                 redundant but kept for compatibility with TDB file.\\
!      & MPID1 & Specifies a magnetic model parameter 
                    identifier (MPID) for parameters.\\
!      & MPID2 & Specifies a magnetic model parameter 
                    identifier (MPID) for parameters.\\
!      & MPID3 & Specifies a magnetic model parameter 
                    identifier (MPID) for parameters.\\
!      & Bibref & Where the model is described.\\\hline

 Permutations & & For FCC, HCP and BCC lattices a 4 sublattice tetrahedron
                model, identical permutations of a parameter will be included 
                only once in the XTDB file.  See section~\ref{sec:permut}.\\
!     & Id & This is used in the {\em Model} attribute of the
                {\bf AmendPhase} tag.  Its can be either FCC4PERM or BCC4PERM.
                There are no MPID. \\
!     & Bibref & Where the model is explained.\\\hline

\end{tabular}

The permutations means that a parameter which can have permutation of
its constituents on idetical sites is stored only once in the
database.  For example in an FCC ordered phase a parameter

G(FCC\_4SL,FE:AL:AL:AL:VA)

\noindent
has 3 identical permutations: G(FCC\_4SL,AL:FE:AL:AL:VA),
G(FCC\_4SL,AL:AL:FE:AL:VA) and G(FCC\_4SL,AL:AL:AL:FE:VA) which are
not included in the database but taken care of by the software.  This
reduce the size of the database and avoid human errors.  It requires
that the software calculates automatcally the contribution from all 4
permutations of the constituents of indentical sides.  There are other
excess parameters with up to 24 permutations.

The wildcard, see section~\ref{sec:parametertag} is frequently used
for parameters of ordered phases, see Appendix~\ref{sec:wildcard},
\ref{sec:OD} and the following sections.

\subsubsection{Models tags for new unary models}

After long discussions the unary group has decided to use a single
composition dependent Einstein parameter for each phase and element in
the new unary database.  An element with its heat capacity fitted
using several Einstein $\theta$ will have the additional $\theta$
described by the GEIN function in the {\em Expr} attribute in the {\bf
  Parameter} or {\bf TPfun} tag, the GEIN function is defined in
eq.~\ref{eq:gein} in section~\ref{sec:expr}.  For multiple $\theta$
see the Al-C example in Appendix~\ref{sec:alc}.

New {\bf Model} tags may be developed and included in the XTDB file in
order to specify new MPIDs for parameters.

\bigskip
\begin{tabular}{|p{0.06\textwidth} p{0.15\textwidth} p{0.8\textwidth}|}\hline
  Tagname& Attributes & Explanation\\\hline

    Volume & & Specifies the model for volume of a phase.\\
!      & Id & This is used in the {\bf AmendPhase} tag.\\
!      & MPID1 & Specifies a volume model parameter identifier
                    (MPID) for parameters.\\
!      & MPID2 & Specifies volume model parameter identifier
                    (MPID) for parameters.\\
!      & MPID3 & Specifies volume model parameter identifier
                    (MPID) for parameters.\\
!      & Bibref & Where the model is described.\\\hline

  Einstein & & The low $T$ vibrational model.\\
!      & Id & This Id is used in {\bf AmendPhase} tag.\\
!      & MPID1 & Specifies the Einstein model parameter identifier (MPID)
          for parameters.\\
!      & Bibref & Where the model is described.\\\hline

  Liquid2state & & The liquid 2-state model.\\
!      & Id & This Id is used in {\bf AmendPhase} tag.\\
!      & MPID1 & Specifies liquid model parameter identifier (MPID)
         for parameters.\\
!      & MPID2 & Specifies Einstein model parameter identifier (MPID)
         for parameters.\\
!      & Bibref & Where the model is described.\\\hline

  EEC & & Specifies that the Equi-entropy model applies to the database.
          This must be implemented in the software.  The liquid 
         {\bf Phase} tag must also have the {\em State} attribute equal to L. \\
!      & Id     & has the value EEC.\\
!      & Bibref & Where the model is described.\\\hline

\end{tabular}

\subsubsection{Ternary extrapolation methods}\label{sec:toop}

Some models are concern a subset of the constituents of a phase and
they must be specified explicitly and cannot be included in the {\bf
  AmendPhase} tag for the phase because they include additional
information.  The {\bf DisorderedPart} 
models are explained together with the {\bf Phase} tag.

The Toop, Kohler and Muggianu ternary extrapolation methods are most
likely specified together with the parameters for a specific ternary.
The Muggianu method is often the default ternary extrapolation model
but there are other extrapolation methods to be considered and they
must be integrated in the XTDB format.

\begin{tabular}{|p{0.06\textwidth} p{0.15\textwidth} p{0.8\textwidth}|}\hline
  Tagname& Attributes & Explanation\\\hline

  TernaryXpol & & A subset of 3 constituents for which do not use the default
              extrapolation method of the binary compositions inside
              a ternary subsystem.\\
!       & Phase & Can be omitted if used inside a {\bf Phase} tag.  Normally  
              this tag will appear close to the {\bf Parameter} for which the
              extrapolation should be used.\\
!      & Constituents & Specifies 3 constituents of the phase sepated by
          spaces.\\
!      & Xmode & See below.\\\hline
\end{tabular}

Examples:

\begin{verbatim}
<TernaryXpol Phase="Liquid" Constituents="Fe Mn Mo" Xmode="KKK" />
<TernaryXpol Phase="Liquid" Constituents="Si Fe Mn" Xmode="T1T1M" />
\end{verbatim}

Where the first ternary extrapolates use the Kohler extrapolation for
all binaries.  In the second the first binary, Si-Fe, use Toop
extrapolation with Si (the first constituent) as Toop element.  The
second binary, Si-Mn, has also Si (still the first constituent) as
Toop elemet and the third binary, Fe-Mn, use the Muggianu
extrapolation method.  The {\em Cmode} attribute is a bit particular
and explained further in Appendix~\ref{sec:ternaryxpol}.

\subsection{Organizing the data and software specific attributes}\label{sec:subsys}\label{sec:soft}\label{sec:last}

Each parameter in the database has a bibliography attribute and
normally a software reading the database lists the relevant
bibliographic data after extracting the data from the database or it
can be listed from inside the software for calculations.  The
references is an important feature to assure the user the database is
reliable and to inform the users that thermodynamic databases are not
not created by AI or appear from thin air.  The number of references
for a multicomponent system with 1000 or more parameters from many
assessments is very impressive.

Additionally, the database manager often arranges the model parameter
per system to simplify updates and this habit has resulted in
introducing a new tag in the XTDB format.  This arrangement in the
XTDB file has no influence on the way the software handles the
parameters.

\bigskip
\begin{tabular}{|p{0.06\textwidth} p{0.15\textwidth} p{0.8\textwidth}|}\hline
  Tagname& Attributes &  Explanation\\\hline

  UnarySystem  && Encloses a set of {\bf Parameter} tags for the unary data.
          There can be parameters for the unary also outside this tag.\\
!          & Elements & Constituent for the parameters in the system.\\
!          & Bibref & Main bibliographic references.\\\hline

  BinarySystem  && Encloses a set of {\bf Parameter} tags for different
          phases of a binary system.
          There can be parameters for the binary outside this tag.  It may
          have a software dependent attribute to calculate the binary.\\
!          & Species & Two constituents for the parameters 
                       separated by spaces.  \\
!          & Bibref & Main bibliographic references.\\
          & CalcDia & Software specific commands to calculate the binary
                       phase diagram.  The software is specified in the
                       {\bf XTDB} tag.\\\hline

  TernarySystem  && Encloses a set of {\bf Parameters} tags for different
           phases for a ternary system.
          There can be parameters for the system outside this tag.\\
!          & Species & Constituents for the parameters in the system 
                       separated by spaces.\\
!          & Bibref & Main bibliographic references.\\
          & CalcDia & Software specific commands to calculate some particular
                     ternary diagram for the system.\\\hline
\end{tabular}

\bigskip
Inside a {\bf BinarySystem} tag the {\bf Parameter} tags for all
phases assessed for the constituents in the {\em Species} attribute
can be included.  The parameters should have their own bibliographic
reference.  The {\em Bibref} for the {\bf BinarySystem} and {\bf
  TernarySystem} can be listed when reading the database informing the
user which assessed systems that are in the database.

{\begin{verbatim}
  <BinarySystem Species="C Co" Bibref="88FER1 97KUS 06MAR" >
    <Parameter Id="G(LIQUID,C,CO;0)"  Expr=" -107940.6+24.956*T;"  Bibref="87FER1" />
    <Parameter Id="G(LIQUID,C,CO;1)"  Expr=" -9805.5;"  Bibref="87FER1" />
    <Parameter Id="G2(B2_BCC,CO:C;0)"  Expr=" +GHSERCO+3*GHSERCC+247373.5-33.574*T;"  Bibref="88FER1" />
    <Parameter Id="G(BCC_A2,CO:C;0)"  Expr=" +GHSERCO+3*GHSERCC+247373.5-33.574*T;"  Bibref="88FER1" />
    <Parameter Id="G(CBCC_A12,CO:C;0)"  Expr=" +UN_ASS;"  Bibref="Default" />
    <Parameter Id="G(CEMENTITE_D011,CO:C;0)"  Expr=" +3*GHSERCO+GHSERCC-1567+3.963*T;"  Bibref="88FER1" />
    <Parameter Id="G(CR3C2_D510,CO:C;0)"  Expr=" +63920+794.135*T-132.57*T*LN(+T)-2.35E-05*T**2
               +1296100*T**(-1);"  Bibref="14KAP" />
    <Parameter Id="G(CUB_A13,CO:C;0)"  Expr=" +UN_ASS;"  Bibref="Default" />
    <Parameter Id="G2(FCC_4SL,CO:C;0)"  Expr=" +GHSERCO+GHSERCC+50463.8-6.849*T;"  Bibref="89FER1" />
    <Parameter Id="G(FCC_A1,CO:C;0)"  Expr=" +GHSERCO+GHSERCC+50463.8-6.849*T;"  Bibref="89FER1" />
    <Parameter Id="G(HCP_A3,CO:C;0)"  Expr=" +GHSERCO+0.5*GHSERCC+22916.5-2.855*T;"  Bibref="87FER1" />
    <Parameter Id="G(M23C6_D84,CO:CO:C;0)"  Expr=" +GCO23C6;"  Bibref="97KUS" />
    <Parameter Id="G(M7C3_D101,CO:C;0)"  Expr=" -5706.9+1408.9*T-249.28*T*LN(+T)+956820*T**(-1);"
               Bibref="06MAR" />
  </BinarySystem>
\end{verbatim}
}

In the {\em CalcDia} attribute there can be software specific
instructions how to calculate a phase diagram or some other diagram.
This tag can be used also in an encrypted database for the systems
that are assessed in the database.

\subsection{Adding new XML tags or attributes}

The XTDB tags listed above is intended to cover all the basic modeling
of thermodynamic data needed for calculations.  But this set of basic
XTDB tags must not prevent the development of new models and there
will be new tags and attributes added in the future.  But such
additions can, with some care, be integrated in XTDB files without
corrupting the data and information already established.

There may be a need for conditional tag in the XTDB file.  Maybe this
can be implemented in a software independent way, but temporarily this
can be handled by software specific tags, for example if certain
actions should be taken depending on the user selection of elements ot
species.

\bigskip
\begin{tabular}{|p{0.06\textwidth} p{0.15\textwidth} p{0.8\textwidth}|}\hline
  Tagname& Attributes &  Explanation\\\hline

  IfSpecies & & Depending on the species selected by user\\
!      & Species & If one (or more enclosed by parenthesis) species
                  in this attribute have been selected\\
      & AndSpecies & And one (or more) species in this attribute have
                     been selected\\
      & OrSpecies & Or one (or more) species in this attribute have
                     been selected\\
!      & Do & software specific way to act if this clause is true.\\\hline
  
\end{tabular}

This is an tentative tag which has to be elaborated.

An example of the use of this clause consider that if Fe and Ti and C
have been selected then the software should automatically create two
composition sets for the FCC phase to describe the cubic carbide
(maybe with a slightly modified name).  The same may be useful to
provide for an ordered L1$_2$ phase when reading data for the Al-Ni
system from an XTDB file.

\section{Further explanation of XTDB tags and attributes}\label{sec:attributes}

Note that the XML tags and attributes are case sensitive whereas the
names i.e. {\em Id} of species, functions, phases and other identifiers
are {\bf case insensitive} as in the TDB file.  For example a chemical
species written FE, Fe, fe and fE is the same element.  Thus CO is
Cobalt and to specify the stoichiometry of carbonmonoxide one must use
C1O.

Presenting information and results for a user still have limitation
imposed by the size of th computer screen or peper width and it is
difficult to format nice output with very long names of functions or
species or phases.  For a human it is also complicated to handle long
names, even if they may be abbreviated.

\subsection{About UPPER and lower characters, abbreviations and forbidden characters}\label{sec:lettercase}

In an TDB file UPPER and lower case letters are treated as identical.
In XML the tags and attributes are case sensitive.  In this proposal
all letters A-Z of the attributes, for example the name of elements,
species and phases, the UPPER and lower case letters will be
considered as identical.

In particular the characters ``(`` and ``)'' are not allowed in the
{\em Id} attribute of {\bf Species, Phase} or {\bf TPfun} tags.  This
is necessary to simplify the parsing the {\em Id} attribute of the
{\bf Parameter} tag and to simplify interpreting commands in the user
interface of the software.  The allowed characters are explained the
the sections~\ref{sec:elements} and \ref{sec:phase}.

In some software using a command line user i/f one can use a command:

\vspace{-3mm}
\begin{verbatim}
set condition y(gas,co2)=0.1
\end{verbatim}
\noindent
in order to specify that the gas phase should have the constituent
fraction of CO$_2$ equal to 0.1.  It could be complicated if both the
phase name and species name can contain parenthesis and be
abbreviated.

It is not allowed to abbreviate {\bf Species} {\em Id} and {\bf TPfun}
{\em Id}.  Note that the species {\em Id} is normally not its
stoichiometric formula and rather short names are recommended for
complex molecules.  In general ``(`` and ``)'' are not allowed in any
{\em Id} attribute except for {\bf Parameter}.

Abbreviation of {\bf Phase} {\em Id} is allowed because there may be
many variants of almost the same phase..  Phase identification can be
very complex with the attributes {\em StructurBerict,
  PearsonSymbol} or {\em SpaceGroup} can be provided in separate
attributes such in the {\bf CrystalStructure} tag.  But to identify
the phase in a parameter in the XTDB file the {\em Id} is used.

The rule for abbreviation of the {\em Id} is that any part of a phase
name starting with an underscore can be abbreviated separately, thus
two phases MONOCLINIC\_A and MONOCLINIC\_B can be abbreviated as M\_A
and M\_B.

\subsection{The Species and its attributes}\label{sec:speciesID}

The species are the constituents of phases.  A species name (i.e. the
{\em Id} attribute) is {\bf case insensitive} and must start with
letter A-Z and can contain letters, digits and the special characters
``\_'', ``/'', ``-'' and ``+''.  It must not be abbreviated when used
as constituent in tags and attributes such as {\bf Phase, Parameter}
etc. 

In some software the constituents are defined for each phase
separately and have no separate identification but in other software
the species name, i.e. {\em Id} can be used for setting conditions and
used when listing and plotting.  The XTDB format must not limit this
facility.

\subsubsection{Species stoichiometry}\label{sec:speciesSS}

The species stoichiometry is a sequence of one or more chemical
element names, each followed by a real number specifying its
stoichiometric ratio.  Following the TDB standard a chemical element
with a two letter name does not need a stoichiometric ratio equal to
unity, for example MGO for MG1O1.  A stoichiometry of unity at the end
can also be omitted.  Stoichiometric fractions can be specified as
AlO3/2 or by real numbers such as AlO1.5 but avoid numbers such as
0.333333, use 1/3.

No grouping using parenthesis are allowed when specifying the
stoichiometry, for example use AL2S3O12, not Al2(S1O4)3.  It may not
be very elegant but computers do not bother about nice formatting.

\subsubsection{MQMQA attribute}\label{sec:mqmqa}
The {\em MQMQA} attribute should contain two or more chemical element
names separated a comma or a sublattice separator ``:'' and followed
by equal number of unsigned reals representing the bond fractions, For
example:

  $<$Species Id="LA/F"    MQMQA="LA:F     6.0 2.0 2.4" $\eoxml$
  $<$Species Id="CSLA/F"  MQMQA="CS,LA:F  9.0 6.0 4.0" $\eoxml$

According to the MQMQA model the cluster stoichometry is calculated as
2.0 divided by the bond fractions.  The MQMQA species (or cluster) is
always electrically neutral.  For MQMQA species that are endmembers
(with one cation and one anion) a real representing the SNN/FNN ratio,
usually 2.4, must be supplied.  See also
Appendix~\ref{sec:elementexample}.  For MQMQA clusters the
stoichiometry can maybe be omitted?


\subsubsection{UNIQUAC attribute}\label{sec:uniquac}

For species in the UNIQUAC model.  Contains two reals representing
area and volume of the species in that order but in unspecified units.

\subsection{The Expr attribute of TPfun and Parameter}\label{sec:tpfunattr}\label{sec:expr}

The {\em Id} attribute of a {\bf TPfun} must start with a letter A-Z
and may contain letters, digits and the special character ``\_''.  It
must not be longer than 16 characters.  It must not be abbreviated
when used in other tags.

When used in an {\em Expr} attribute it does not have to be terminated
by the hash character "\#" as in current TDB files.

The mathematical expressions for $T$ and $P$ used in the {\em Expr}
attribute in {\bf TPfun, Trange} and {\bf Parameter} are the same as
in TDB files.  It is very restricted because some software must
calculate first and and second derivatives with respect to $T, P$ (and
constitution).  A more extended mathematical expression could be
allowed for expressions which are not used for database parameters.
In OC it is allowed to enter more complex expressions for post
processing in batch/macro files but they are not included in the
database.

In the 1990 definition of the TDB file the type of expression allowed
consists of ``simple terms'' such as:

[signed real number] * [{\bf TPfun Id} ] ** [power] *T** [power] *P**[power]

where [power] is an integer (a negative power must be within
parenthesis, a positive must not).  No spaces allowed in a simple
term.  A ``complex term'' is a simple term multiplied with a math
function (EXP, LN or GEIN) of a simple term, such as:

[simple term] *LN( [simple term] )

An {\em Expr} attribute in {\bf TPfun, Trange} or {\bf Parameter}
consists one or more complex terms.  A positive sign of the first term
can be omitted.
  
It is not allowed to group several terms together using parenthesis,
for example ``exp(5.7-3*T+2*T*LN(T))''.  The complex expression after
``exp'' must be entered as a separate {\bf TPfun} and then used as the
agrument of the exponential function.  For example a square root of
$T$ is entered as two {\bf TPfun}://
\begin{verbatim}
<TPfun Id="HALFT" Expr="0.5*LN(T);" />
<TPfun Id="SQRT"  Expr="EXP(HALFT);" />
\end{verbatim}

For thermodynamic parameters the expressions are usually quite simple
but for other physical properties it may be interesting to allow more
elaborate expressions.  However, separating a complex expression into
several parts may be useful for tracing its origin and can simplify
updating and calculations.
  
The following general math functions are allowed in OC:\\ $\exp(),
\ln(), \log(),$ erf().  Note that $\log()$ and $\ln()$ is the same and
erf() is the error function.  The number of math functions can be
extended as discussed in the nect section.

\subsection{The GEIN function used of TPfun and Parameters}\label{sec:gein}

In the 3rd generation unary project the Einsten function for the low
$T$ vibrational heat capacity has been introduced:
\begin{eqnarray}
{\rm GEIN}(\theta) &=& 1.5R\theta+3RT\ln(1-\exp(-\theta/T)) \label{eq:gein}
\end{eqnarray}
where the argument of GEIN function should be a fitted Einstein
temparature, $\theta$ in Kelvin.  This $\theta$ must be allowed to
vary with the composition of the phase and thus the $\theta$ was
introduced as a model parameter identifier (MPID) called LNTH in OC.
For physical reasons it was decided that the logarithm of $\theta$ was
a more appropriate value to vary with the composition.  In
Appendix~\ref{sec:alc} the whole assessment of Al-C is listed and
below just the G and LNTH parameter for the diamond phase:

\begin{verbatim}
  <Parameter Id="G(DIAMOND,C;0)"  Expr=" +G0DIACC+GEDIACC;"  Bibref="20HE" />
  <Parameter Id="LNTH(DIAMOND,C;0)"  Expr=" +LN(1601.4467);"  Bibref="20HE" />
\end{verbatim}

However, during the assessment it was found that using several
$\theta$ together with weighting factors (that summed up to unity) a
better fit could be obtained.  The fitted $\theta_i$ and factors $f_i$
are in the table below:

\begin{tabular}{lrrrrrr}
State  & $f_1$   & $\theta_1$ & $f_2$   & $\theta_2$ & $f_3$  & $\theta_3$ \\
Fitted &  0.2318 & 813.637 & 0.01148 & 345.35 & 0.763257 & 1601.4467\\
in {\bf TPfun} &  0.2318 & 813.637 & 0.01148 & 345.35 & -0.236743 & 1601.4467\\
\end{tabular}

Multiple $\theta$ is no big surprise as the Einstein function is a
simple but rather crude approximation of the low $T$ heat capacity.
But for several reasons one cannot have several LNTH parameters and
thus one must select one $\theta$ to vary with the composition and the
other are included in the {\em Expr} attribute in the {\bf Parameter}
tag for the Gibbs energy of C in the diamond phase above.  In the {\bf
  TPfun} GEDIACC the factor for the GEIN function of $\theta_3$ is
negative to compensate for the contribution from the LNTH parameter.

\begin{verbatim}
  <TPfun Id="GEDIACC" Expr=" +0.2318*GEIN(813.637)+.01148*GEIN(345.35)-0.236743*GEIN(1601.4467);" /> 
\end{verbatim}

It is recommended to use LN($\theta$) in the {\em Expr} of the LNTH
parameter rather than its the numeric value to visualize the
correspondance with the arguments of the GEIN function.

\subsection{The phase tag and attributes}\label{sec:phasetag}

All data in the XTDB database is part of a phase.  The model of a
phase is a simplification of the reality.

\subsubsection{The phase Id}\label{sec:phaseid}

A phase name must start with a letter A-Z and have no more than 24
characters.  It can contain letters, numbers and the special character
``\_''.  {\bf The characters ``(`` and ``)'' must not be used in phase
  names.}   

Some phases which appear in different systems with different names for
example CaO (lime) and MgO (periclase) are modeled as the same phase
in the database because they can form (at least theoretically) a
continuous solution.  Thus a more structure related phase {\rm Id} is
preferred in the database, for example ``halite''.  More specific
information about the phase can be provided using the {\bf
  CrystalStructure} tag but it will not cover all cases for which a
phase may be stable.

A phase name may be abbreviated in parameters and some other cases and
thus each phase name must be unique and not an abbreviation of another
phase.  One must not have a phase Al2O3 and another Al2O3\_BIS.  Phase
names has to be considered carefully when adding new assessments to a
database.

\subsubsection{The configurational entropy model}\label{sec:cfg}

For the configurational entropy model we have CEF, I2SL, MQMQA,
UNIQUAC and maybe some more.  Maybe also ``IDEAL'' could be used when
there are ideal mixing and no interactions (as in ideal gas) and maybe
``REGULAR'' for a phase with ideal mixing in a single lattice with one
site and some excess parameters.

\subsubsection{Using several fraction variables}\label{sec:nodis}

A phase with a {\bf DisorderedPart} tag tag can have an optional
attribute specifying a phase with the parameters for the disordered
phase (with a different number of sublattices). The constituents of
this phase on its first sublattice must be the same as in the ordered
phase with this tag.  The disordered phase many has an extra
sublattice interstitals, corresponding to the last sublattice in the
ordered phase.  This means the software must calculate a separate set
of fraction variables from the ordered phase by summing the first {\em
  Sum} sublattices of the ordered phase.
\begin{eqnarray}
y^{1,\rm dis}_i &=& \sum^{Sum}_{s=1} a_s y^{(s),\rm ord}_i
\end{eqnarray}
where $y^{(s)\rm ord}_i$ is the constituent fraction of $i$ on
sublattice $s$ in the ordered phase and $y^{\rm dis,1}_i$ the fraction
of $i$ in the first sublattice of the disordered phase.  $a_s$ is the
number of sites on sublattice $s$ in the ordered phase.

If the attribute {\em Disordered} is specified in the {\bf
  DisorderedPart} tag, this phase should be hidden by the software
from the list of phases as its parameters are actually a part of the
ordered phase.  In some software the disordered parameters have the
same phase name as the ordered phase, just a reduced number of
sublattices as indicated by the attribute {\em Sum}.

Calculating a {\bf DisorderedPart} model with the attribute {\em
  Subtract} works the same way.  The reason to subtract the
``ordered'' part calculated with the disordered set of fractions was
to allow separate assessments of the ordered and disordered phases.

For phases which never disorder, for example the sigma phase, one can
also have a ``disordered'' part with a single sublattice containing
the species representing elements as endmembers (and possibly some
long range interaction parameters).  In Thermo-Calc terminology this
is the ``NEVER'' model.  See also the section for EBEF~\ref{sec:ebef}.

If the attribute {\em Disordered} is not set the parameters for the
disordered part will have the same phase as those for the ordered part
in the {\bf Parameter} tag but a reduced number of sublattices.

Parameters in the ordered part of a phase with {\bf DisorderedPart}
have constituents in as many sublattices as defined for the phase.  In
the disordered part the number of sublattices is given by the
attributes {\em NumberOf} for the phase subtracted by ({\em Sum}+1) in
the {\bf DisorderedPart} tag.  Thus for a BCC phase with 5 sublattice
a parameter tag:
\begin{verbatim}
<Parameter Id="G(BCC_4SL,FE:FE:AL:AL:VA)" Expr="-3*UBCCFEAL" Bibitem="09Sun" />
\end{verbatim}
indicates a parameter in the ordered BCC phase with 4 sublattices for
ordering whereas a parameter for the same phase but only 2 sublattices:
\begin{verbatim}
<Parameter Id="G(BCC_4SL,FE:VA)" Expr="GHSERFE" Bibitem="91Din" />
\end{verbatim}
indicares a parameter in the disordered BCC phase because the value of
{\em Sum} is 4 in this case.  Alternatively all parameters in the
disordered part can be entered as a separate phase specified by the
{\em Disordered} attribute.

See also the Appendix on wildcards~\ref{sec:wildcard} when dealing
with phases witn many sublattices.

It is unfortunate we did not start to use XML 20 years ago, we could
have avoided some complications.

\subsection{The use of the Parameter tag}

An XTDB database will consist mainly of {\bf Parameter} tags, defined
in~\ref{sec:parametertag}, and expanations of its use depend very much
on the models used.  Some further explainations can be found in
Appendix~\ref{sec:partags}

\section{A few more points}\label{sec:points}

A summary of things done and to be considered

\begin{enumerate}
\item One of the reasons developing a new format for thermodynamic
  databases was that TDB files generated by one software could not be
  read by another software without some sophistacated editing.  
  This XTDB definition will make it easier to collaborate and
  develop Calphad databases.

\item The ternary extrapolation method is a bew feature.  An attribute
  {\em TernaryXpol} can be added to the {\bf Defaults}.

\item The {\bf Elements} should automatically by considered as species but
  there is no error to include them also in the list of species.

\item All phase constituents must have a defined {\em Id} in a {\bf
  Species} tag in order to make ot possible to use these for setting
  conditions, listing results and plotting.

\item The model parameter identifier ``L'' can be used for interaction
  Gibbs energies.

\item If a {\bf TPfun} or {\bf Parameter} is calculated outside its
  defined $T$ range the value calculated should use the
  expression in the range closest below or above the actual $T$. 

\item The use of wildcards have not been defined outside users of
  Thermo-Calc and OpenCalphad.  An explication is found
  section~\ref{sec:wildcard}.

\item The GEIN function can be used in the attribute {\em Expr} of a
  {\bf Parameter} or a {\bf TPfun}.  If a pure element modeled with
  several Einstein $\theta$ only with different weight factors (the
  sum of which is unity), one of these, normally that with the highest
  weight, is selected to vary with composition, see
  section~\ref{sec:gein}.

\item Based on the XTDB format one may create additional facilities
  for example a program to list the parameters in a nice format for
  publishing using LaTeX or Word.  Papers publishing assessments
  should provide them in the XTDB format as supplementary material.

\item We should agree on a list of MPID and how to handle software
  specific MPIDs.  However, with the {\bf Model} tag one may
  substitute the default software MPID by those used in the XTDB file
  for the same model.

  There will be many MPID for kinetic and other properties which does
  not concern the thermodynamic data but they should anyway have
  welldefined MPIDs.

\item The schema for XTDB and a formal XTDB definition written as XML
  should be written.  Who can do that?
  
\end{enumerate}

\section{Summary}

There are certainly many more things to take care of but I think it is
more important to agree very soon on a minimum common XTDB format
which can make the thermodynamic databases more useful both for
experimentalists, assessments, database maintenance and thermodynamic
software, in particular for the development of new models and
applications.

We can take one step at a time but be careful to to set limits for
future extensions.  Many different kinds of physical data for
materials will probably be added to this XTDB format.

\begin{thebibliography}{00Zzzz}
\bibitem{80Hil} Mats Hillert,  Caphad, {\bf 4}, (1980), pp 1--12
\bibitem{91Din} A Dindsdale, Calphad, {\bf 15}, (1991), 317--425
\bibitem{97Ans} Ibrahim. Ansara, Nathalie Dupin, Hans Leo Lukas and Bo Sundman,
  J All and Comp, {\bf 247} (1997) pp 20--30
\bibitem{98Sun} B Sundman, S G Fries and A Oates, (1998) Calphad
\bibitem{07Hal} Bengt Hallstedt, Nathalie Dupin, Mats Hillert, Lars
  H{\"o}glund, Hans Leo Lukas, Julius C. Shuster and Nuri Solak,
  Calphad, {\bf 31} (2007) pp 28--37.
\bibitem{01Pel} Arthur D Pelton, Calphad {\bf 25} (2001) pp 319--328
\bibitem{18Dup} Nathalie Dupin, Ursula R Kattner, Bo Sundman, Mauro
  Palumbo and Suzana G Fries, J Res NIST, {\bf 123}, (2018)
  doi:10.6028/jres.123.020
\bibitem{21Sun} Bo Sundman, Ursula R. Kattner, Mats Hillert, Malin
  Selleby, John Ågren, Sedigheh Bigdeli, Qing Chen, Alan Dinsdale,
  Bengt Hallstedt, Alexandra Khvan, Huahai Mao, Richard Otis, Calphad,
  {\bf 68} (2020) 101737
\end{thebibliography}


\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Appendices
\begin{appendices}
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Some features listed above have not been implemented in the examples.

\section{Some examples}\label{sec:examples}

In the OC software I have now implemented a command to write an XTDB
file (maybe not exactly identical to this definition as I am modifying
details).  In this Appendix I enclude som exmples.

Developing routines to read an XTDB file is more complicated and I
prefer to wait until there is a general agreement on the XTB format.

\subsection{Chemical elements and species.}\label{sec:elementexample}

The way to define MQMQA constituents and stoichiometry is tentative.

{\small
\begin{verbatim}
  <Element Id="/-" Refstate="ELECTRON_GAS" Mass="  0.000000E+00" />
  <Element Id="VA" Refstate="VACUUM" Mass="  0.000000E+00" />
  <Element Id="AL" Refstate="FCC_A1" Mass="  2.698200E+01" H298="  4.577300E+03" S298="  2.832200E+01" />
  <Element Id="FE" Refstate="BCC_A2" Mass="  5.584700E+01" H298="  4.489000E+03" S298="  2.728000E+01" />
...
  <Species Id="VA" Stoichiometry="VA" />
  <Species Id="AL" Stoichiometry="AL" />
  <Species Id="FE" Stoichiometry="FE" />
  <Species Id="AL2FE" Stoichiometry="AL2/3FE1/3" />
  ...
  <Species Id="LA/F" Stoichiometry="LA1/3F1" MQMQA="LA:F 6.0 2.0 2.4" />
  <Species Id="LACS/F" MQMQA="LA,CS:F 9.0 6.0 4.0" />
\end{verbatim}
}

The stoichiometry of the MQMQA species is calculated from the bond
ratios according to the model.  The {\em MQMQA} attribute for an
``endmember'' also include a factor, SNN/FNN, needed in the
configurational entropy expression.

Note that {\bf species names must not be abbreviated as constituents
  in phases or parameters} because one can have a species name which
is an abbreviations of another species name, for example ``C1O'' and
``C1O2''.

\subsection{Defaults, TPfun and Trange}\label{sec:tpfuns}

Using default $T$ limits the function are not much more complex than
in the TDB file.

{\small
\begin{verbatim}
  <Defaults LowT="298.15" HighT="6000" Bibref="U.N.Known" Elements="VA /-" />
...
  <TPfun Id="GHSERAL"  >
    <Trange HighT="700" Expr=" -7976.15+137.093038*T-24.3671976*T*LN(T)-.001884662*T**2-8.77664E-07*T**3+
74092*T**(-1);" />
    <Trange HighT="933.47" Expr=" -11276.24+223.048446*T-38.5844296*T*LN(T)+.018531982*T**2
-5.764227E-06*T**3+74092*T**(-1);" />
    <Trange HighT="2900" Expr=" -11278.378+188.684153*T-31.748192*T*LN(T)-1.230524E+28*T**(-9);" />
  </TPfun>
...
  <TPfun Id="LFALFE0"  Expr="-104700+30.65*T;" />
  <TPfun Id="LFALFE1"  Expr="+30000-7*T;" />
  <TPfun Id="LFALFE2"  Expr="+32200-17*T;" />
  <TPfun Id="UFALFE"  Expr="-4000+T;" />
  <TPfun Id="GAL3FE"  Expr="+3*UFALFE+9000;" />
  <TPfun Id="GAL2FE2"  Expr="+4*UFALFE;" />
...
  <TPfun Id="G0SERCC"  Expr=" -17752.213+GTSERCC;" /> 
  <TPfun Id="GEINGRACC"  Expr=" -0.5159523*GEIN(+7.57725)+0.121519*GEIN(+6.10479)+0.3496843*GEIN(+6.8533)
        +.0388463*GEIN(+5.26269)+.005840323*GEIN(+4.166667);" /> 
\end{verbatim}
}

\subsection{Phase}\label{sec:phaseexample}

Entering phases in the XTDB file is a bit more complex but we have get
rid of the TYPE\_DEFINITION.  It is not so nice to use CEF for the
liquid, that is why I think RKM might be a nice option for a liquid
model without sublattices and maybe {\bf Sublattices} can be omitted?

{\small
\begin{verbatim}
 <Phase Id="LIQUID" Configuration="RKM" state="L" >
    <Sites NumberOf="1"  Multiplicities="1" >
      <Constituents List="AL C" />
    </Sites>
    <AmendPhase Model="LIQ2STATE" />
  </Phase>
...
  <Phase Id="A2_BCC" Configuration="CEF" state="S" >
    <Sites NumberOf="2"  Multiplicities="1  3" >
      <Constituents Sublattice="1" List="AL FE" />
      <Constituents Sublattice="2" List="VA" />
    </Sites>
    <AmendPhase Model="IHJBCC" />
  </Phase>
...
  <Phase Id="AL8FE5_D82" Configuration="CEF" state="S" >
    <Sites NumberOf="2"  Multiplicities="8  5" >
      <Constituents Sublattice="1" List="AL FE" />
      <Constituents Sublattice="2" List="AL FE" />
    </Sites>
  </Phase>
...
  <Phase Id="BCC_4SL" Configuration="CEF" state="S" >
    <Sites NumberOf="5"  Multiplicities="0.25  0.25  0.25  0.25  3" >
      <Constituents Sublattice="1" List="AL FE" />
      <Constituents Sublattice="2" List="AL FE" />
      <Constituents Sublattice="3" List="AL FE" />
      <Constituents Sublattice="4" List="AL FE" />
      <Constituents Sublattice="5" List="VA" />
    </Sites>
    <Disordered_3Part Disordered="A2_BCC" Sum="4" Bibref="09Sun" />
    <AmendPhase Model="IHJBCC BCC4Perm" />
  </Phase>
...
  <Phase Id="SIGMA" Configuration="CEF" State="S" >
    <Sites NumberOf="5" Multiplicities="2 4 8 8 8" >
      <Constituents Sublattice="1" List="MO RE" />
      <Constituents Sublattice="2" List="MO RE" />
      <Constituents Sublattice="3" List="MO RE" />
      <Constituents Sublattice="4" List="MO RE" />
      <Constituents Sublattice="5" List="MO RE" />
    </Sites>
    <Disordered_2Part Sum="5" />
  </Phase>
\end{verbatim}
}

Abbreviation of phase names is allowed and thus one cannot have a phase
with a name which is an abbreviation of another phase name.  Phase
names can be abbreviated for each part separated by an underscore,
``\_''.  A phase name ``AL\_X'' is thus an abbreviation of ``AL2\_X''.

\subsection{The Parameter tag}\label{sec:parameter examples}

{\small
\begin{verbatim}
    <Parameter Id="G(A2_BCC,FE:VA;0)"   Expr="+GHSERFE;" Bibref="91Din" />
    <Parameter Id="TC(A2_BCC,FE:VA;0)"   Expr="1043;" Bibref="91Din" />
    <Parameter Id="BMAGN(A2_BCC,FE:VA;0)"   Expr="2.22;" Bibref="91Din" />
    <Parameter Id="G(AL8FE5_D82,AL:AL;0)"   Expr="+13*GALBCC;" Bibref="08Sun" />
...
    <Parameter Id="G(BCC_4SL,AL:AL:FE:FE:VA;0)"   Expr="+GB2ALFE;" Bibref="08Sun" />
    <Parameter id="G(BCC_4SL,AL,FE:*:*:*:VA;1)"   Expr="-634+0.68*T;" Bibref="08Sun" />
\end{verbatim}
}

In the last parameter above the ``wildcard'' or asterisk, ``*'', is
used for species in three of the sublattices and it means that the
parameter is independent of the constituents in these sublattices.
See the discussion in section~\ref{sec:wildcard} how this is treated.


\subsection{The Parameter2 tag}

Using the {\bf Parameter2} tag the last two parameters above are:

{\small
\begin{verbatim}
    <Parameter2 Id="G(BCC_4SL,AL:AL:FE:FE:VA;0)" Expr="+GB2ALFE;" Bibref="08Sun" MPID="G" Phase="BCC_4SL" >
       <ConstArray Degree="0">
           <SublConst Sublattice=="1" Species="AL" />
           <SublConst Sublattice=="2" Species="AL" />
           <SublConst Sublattice=="3" Species="FE" />
           <SublConst Sublattice=="4" Species="FE" />
           <SublConst Sublattice=="5" Species="VA" />
       </ConstArray>
    </Parameter2>
...
    <Parameter2 id="G(BCC_4SL,AL,FE:*:*:*:VA;1)" Expr="-634+0.68*T;" Bibref="08Sun" MPID="G" Phase="BCC_4SL" >
       <ConstArray Degree="1">
           <SublConst Sublattice=="1" Species="AL" />
           <SublConst Sublattice=="1" Species="FE" />
           <SublConst Sublattice=="2" Species="*" />
           <SublConst Sublattice=="3" Species="*" />
           <SublConst Sublattice=="4" Species="*" />
           <SublConst Sublattice=="5" Species="VA" />
       </ConstArray>
    </Parameter2>
\end{verbatim}
}

TCSAB worry that the XTDB format will increase the size of their
databases which are already very big.  This kind of parameter record
will make them much bigger.

\subsection{Models}\label{sec:modelex}

An extended form of the {\bf Models} tag including references should
be provided by SGTE as general {\bf AppendXTDB} file with the tags
for all generally accepted models including {\em Id} and all {\em
  MIPID} and detailed description.  But the models used in an XTDB
file can also appear in a short form as below.

{\small
\begin{verbatim}
  <Models>
    <Magnetic Id="IHJBCC"  MPID1="TC" MPID2="BMAGN" Bibref="82Her" />
    <Magnetic Id="IHJREST"  MPID1="TC" MPID2="BMAGN" Bibref="82Her" />
    <Einstein Id="GEIN" MPID1="LNTH" bibref="01Che" /> 
    <Liquid2state Id="LIQ2STATE" MPID1="G2"  MPID2="LNTH" bibref="14Becker" >
       <!-- Unified model for the liquid and the amorphous state treated as an Einstein solid -->
    </Liquid2state>
    <Volume Id="VOLOWP" MPID1="V0"  MPID2="VA" MPID3="VB" bibref="05Lu" />
  ...
  </Models>
  ...
  <TernaryXpol Phase="Liquid" Constituents"Si Fe Cr" Xmode=T1T1K" />
\end{verbatim}
}

The {\bf TernaryXpol} tag can appear anywhere in the XTDB file, even
within the {\bf Phase} tag but, most likely together with the {\bf
  Parameter} tags from the assessment of the ternary system in order
to simplify editing and reading a large XTDB file.

The {\bf DisorderedPart} section~\ref{sec:phaseexample} must be nested
within a {\bf Phase} tag for the ordered phase.

\newpage 

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\section{An attempt to summarize model tags and MPIDs.}\label{sec:modelapp}

The XTDB file should include an {\bf AppendXTDB} with a link to the
file defining the MPID used for models such as magnetism, low $T$ heat
capacity etc.  This Appendix is such a file.

For models that are not trivial an extended description of the model
and its model parameter identifiers (MPIDs) should be provided.

{\small
\begin{verbatim}
  <Models>
  <!-- This is a short explanation of XTDB model tags and their attributes, the models for except for
  the configurational entropy.
  The AmendPhase tag (nested inside a Phase tag) is used to specify some additional models for the phase
  by using the attribute "Id" specified for most of the models below.
  In these model tags there are model parameter identifiers (MPID) describing the dependence on composition, T and P.
  A DisorderedPart tag must be inside the Phase tag as it has additional information.
  The TenaryXpol tag will normally appear together with model parameters for the binaries and has thus a phase attribute.
  The EEC tag is global for the whole database if included.
  Some model tags and MPIDs are tentative and some attributes of the tags are optional. -->
  <Magnetic Id="IHJBCC" MPID1="TC" MPID2="BMAGN" Aff=" -1.00" Bibref="82Her" > 
    <!-- f_below_TC= +1-0.905299383*TAO**(-1)-0.153008346*TAO**3-.00680037095*TAO**9-.00153008346*TAO**15; and
    f_above_TC= -.0641731208*TAO**(-5)-.00203724193*TAO**(-15)-.000427820805*TAO**(-25); 
    in G=f(TAO)*LN(BMAGN+1) where TAO=T/TC.  Aff is the antiferromagnetic factor.
    TC is a combined Curie/Neel T and BMAGN the average Bohr magneton number. -->
  </Magnetic>
  <Magnetic Id="IHJREST"  MPID1="TC" MPID2="BMAGN" Aff=" -3.00" Bibref="82Her" > 
    <!-- f_below_TC= +1-0.860338755*TAO**(-1)-0.17449124*TAO**3-.00775516624*TAO**9-.0017449124*TAO**15; and 
    f_above_TC= -.0426902268*TAO**(-5)-.0013552453*TAO**(-15)-.000284601512*TAO**(-25); 
    in G=f(TAO)*LN(BMAGN+1) where TAO=T/TC.  Aff is the antiferromagnetic factor.
    TC is a combined Curie/Neel T and BMAGN the average Bohr magneton number. -->
  </Magnetic>
  <Magnetic Id="IHJQX" MPID1="CT" MPID2="NT" MPID3="BMAGN" Aff=" 0.00" Bibref="01Che 12Xio" > 
    <!-- f_below_TC= +1-0.842849633*TAO**(-1)-0.174242226*TAO**3-.00774409892*TAO**9-.00174242226*TAO**15
    -.000646538871*TAO**21;
    f_above_TC= -.0261039233*TAO**(-7)-.000870130777*TAO**(-21)-.000184262988*TAO**(-35)-6.65916411E-05*TAO**(-49);
    in G=f(TAO)*LN(BMAGN+1) where TAO=T/CT or T/NT.  Aff is a (redundant) antiferromagnetic factor.
    CT is the Curie T and NT the Neel T and BMAGN the average Bohr magneton number. -->
  </Magnetic>
  <Einstein Id="GEIN" MPID1="LNTH" Bibref="01Che" > 
    <-- The Gibbs energy due to the Einstein low T vibrational model, G=1.5*R*THETA+3*R*T*LN(1-EXP(-THETA/T)).
   The value used for LNTH should be ln(THETA)
    as this varies with composition in a more physically reasonable way. -->
  </Einstein>
  <Liquid2state Id="LIQ2STATE" MPID1="G2"  MPID2="LNTH" Bibref="88Agr 13Bec" > 
    <!-- Unified model for the liquid and the amorphous state which is treated as an Einstein solid.
    The G2 parameter describes the stable liquid and the transition to the amorphous state and
    LNTH is the logarithm of the Einstein THETA for the amorphous phase. -->
  </Liquid2state>
  <Volume Id="VOLOWP" MPID1="V0"  MPID2="VA" MPID3="VB" Bibref="05Lu" > 
    <!-- The volume of a phase as function of T, moderate P and constitution via the model parameters:
    V0 is the volume at the reference state, VA is the integrated thermal expansion and VB is the isothermal
    compressibilty at 1 bar. -->
    </Volume>
\end{verbatim}

\newpage

\begin{verbatim}
  <DisorderedPart Disordered=" " Sum=" " [Subtract=Y] Bibref="97Ans 07Hal" > 
    <!-- This tag is nested inside the ordered phase tag.  The disordered fractions are averaged over the number of
    ordered sublattices indicated by Sum.
    The Gibbs energy is calculated separately for the ordered and disordered model parameters and added 
    but the configurational Gibbs energy is calculated only for the ordered phase.
  If the attribute Subtract is included the Gibbs energy of the ordered phas is calculated a second time as
 disordered and subtracted -->
    Some software has no special disordered phase but all parameters are stored in the ordered one and
    the parameters for the disordered phase has and fewer number of sublattices. -->
  </DisorderedPart>
  <Permutations Id="FCC4Perm" Bibref="09Sun" > 
    <!-- An FCC phase with 4 sublattices for the ordered tetrahedron use this model to indicate that parameters 
    with permutations of the same set of constituents on identical sublattices are included only once. -->
  </Permutations>
  <Permutations Id="BCC4Perm" Bibref="09Sun" > 
    <!-- A BCC phase with 4 sublattices for the ordered asymmetric tetrahedron use this model to indicate that
    parameters with permutations of the same set of constituents on identical sublattices are included only once. -->
  </Permutations>
  <EEC Id="EEC" Bibref="20Sun" > 
    <!-- The Equi-Entropy Criterion means that the software must ensure that solid phases with higher entropy than
    the liquid phase must not be stable. -->
  </EEC>
  <TernaryXpol Phase=" " Constituents=" " Xmode=" "  Bibref="01Pel" > 
     <!-- The ternary extrapolation of the binary parameters is modified.
     The following Types are recognized: Muggianu, Kohler, Toop and ToopM -->
  </TernaryXpol>
  <EBEF Id="EBEF" Bibref="18Dup" > 
     <!-- The Effective Bond Energy Formalism for phases with multiple sublattices using wildcards, "*", in the
     parameters for sublattices with irrelevant constituents.
     The parameters may also use the short form "constituent@sublattice" in order to specify only the constituents
     in sublattices without wildcards.  It also requires the DisorderedPart model. -->
  </EBEF>
  </Models>
  <Bibliography> 
    <Bibitem Id="82Her" Text="S. Hertzman and B. Sundman, A Thermodynamic analysis of the Fe-Cr system,' Calphad, Vol 6 (1982) pp 67-80" />
    <Bibitem Id="88Agr" Text="J. Agren, Thermodynmaics of supercooled liquids and their glass transition, Phys Chem Liq, Vol 18 (1988) pp 123-139" />
    <Bibitem Id="97Ans" Text="I. Ansara, N. Dupin, H. L. Lukas and B. Sundman, Thermodynamic assessment of the Al-Ni system, J All and Comp, Vol 247 (1997) pp 20-30" />
    <Bibitem Id="01Che" Text="Q. Chen and B. Sundman, Modeling of Thermodynamic Properties for BCC, FCC, Liquid and Amorphous Iron, J Phase Eq, Vol 22 (2001) pp 631-644" />
    <Bibitem Id="01Pel" Text="A. D. Pelton, A General Geometric Thermodynamic Model for Multicomponent  solutions, Calphad, Vol 25 (2001) pp 319-328" />
    <Bibitem Id="05Lu" Text="X.-G. Lu, M. Selleby B. Sundman, Implementation of a new model for pressure dependence of condensed phases in Thermo-Calc, Calphad, Vol 29 (2005) pp 49-55" />
    <Bibitem Id="07Hal" Text="B. Hallstedt, N. Dupin, M. Hillert, L. Hoglund, H. L. Lukas, J. C. Schuster and N. Solak, Calphad, Vol 31 (2007) pp 28-37" />
    <Bibitem Id="09Sun" Text="B. Sundman, I. Ohnuma, N. Dupin, U. R. Kattner and S. G. Fries, An assessment of the entire Al-Fe system including D03 ordering, Acta Mater, Vol 57 (2009) pp 2896-2908" />
    <Bibitem Id="12Xio" Text="W. Xiong, Q. Chen, P. A. Korzhavyi and M. Selleby, An improved magnetic model for thermodynamic modeling, Calphad, Vol 39 (2012) pp 11-20" />
    <Bibitem Id="13Bec" Text="C. A. Becker, J. Agren, M. Baricco, Q Chen, S. A. Decterov, U. R. Kattner, J. H. Perepezko, G. R. Pottlacher and M. Selleby, Thermodynamic modelling of liquids: Calphad approaches and contributions from statistical physics, Phys Stat Sol B (2013) pp 1-20" />
    <Bibitem Id="18Dup" Text="N. Dupin, U. R. Kattner, B. Sundman, M. Palumbo and S. G. Fries, Implementation of an Effective Bond Energy Formalism in the Multicomponent Calphad Approach, J Res NIST, Vol 123 (2018) 123020" />
    <Bibitem Id="20Sun" Text="B. Sundman, U. R. Kattner, M. Hillert, M. Selleby, J. Agren, S. Bigdeli, Q. Chen, A. Dinsdale, B. Hallstedt, A. Khvan, H. Mao and R. Otis, A method for handling the extrapolation of solid crystalline phases to temperatures far above their melting point, Calphad, Vol 68 (2020) 101737" />
  </Bibliography>

\end{verbatim}
}

\subsection{Model parameter identifier, MPID}\label{sec:mpid}\label{sec:mpid2}

An MPID must start with a letter A-Z and contain letters and digits
and not exceed 8 charactes.  It cannot be abbreviated.  In
OpenCalphad some are defined, see Appendix~\ref{sec:mpid2} but there
should be a reserved list also for future MPIDs to avoid that
different software use the same for different things.
  
The letter ``\&'', frequently used for mobility parameters, is
forbidden in XML but it can be replaced by some other character, using
``\&amp;'' seems clumsy.  The special character ``\#'' is already used
by software to identify composition sets, i.e. miscibility gaps or
order/disorder sets of a phase or sublattice number.

At present the MPID "G'' is the Gibbs energy, TC Curie $T$, BMAGN the
Bohr magneton number etc.  An MPID must not be abbreviated in a
parameter.  Different software may use different MPID if they are well
defined.

The degree in a binary excess model parameter defines the power used
for the composition dependence in a binary Redlich-Kister polynomial.
For higher order excess models see section~\ref{sec:degree}.

The model parameter identifier ``L'' is frequently used for
interaction Gibbs energies, this or ``G'' can be accepted.  But the
should be an error to use ``L'' for a Gibbs energy of an endmember.

Some of the model parameter identifiers used in OC are listed in
Table~\ref{tab:mpis}.  In OC a parameter for a disordred part of a
{\bf DisorderedPart} use the same phase name and simply has fewer
sublattices.

\begin{table}[!h]
  \caption{Current set of model parameter identifiers in OC.  For each
    parameter it is indicated if it can depend on $T$, $P$ or have an
    extra constituent specification.  Most of them have no associated
    code.}\label{tab:mpis}

{\small
\begin{verbatim}
Indx Ident T P Specification                Status Note
   1 G     T P                                   0 Gibbs Energy
   2 TC    - P                                   2 Combined Curie/Neel T
   3 BMAG  - -                                   1 Average Bohr magneton number
   4 CTA   - P                                   2 Curie temperature
   5 NTA   - P                                   2 Neel temperature
   7 LNTH  - P                                   2 Einstein temperature
   8 V0    - -                                   1 Volume at T0, P0
   9 VA    T -                                   4 Thermal expansion
  10 VB    T P                                   0 Bulk modulus
  12 VS    T P                                   0 Diffusion volume parameter
  13 MQ    T P &<constituent#sublattice>;       10 Mobility activation energy
  14 MF    T P &<constituent#sublattice>;       10 RT*ln(mobility freq.fact.)
  15 MG    T P &<constituent#sublattice>;       10 Magnetic mobility factor
  16 G2    T P                                   0 Liquid two state parameter
  19 LPX   T P                                   0 Lattice param X axis
  20 LPY   T P                                   0 Lattice param Y axis
  21 LPZ   T P                                   0 Lattice param Z axis
  23 EC11  T P                                   0 Elastic const C11
  24 EC12  T P                                   0 Elastic const C12
  25 EC44  T P                                   0 Elastic const C44
  26 UQT   T P &<constituent#sublattice>;       10 UNIQUAC residual parameter (OC)
  27 RHO   T P                                   0 Electric resistivity
  28 VISC  T P                                   0 Viscosity
  29 LAMB  T P                                   0 Thermal conductivity
  30 HMVA  T P                                   0 Enthalpy of vacancy formation (MatCalc)
\end{verbatim}
  }
\end{table}

A replacement of the ``\&'' character is needed.

\newpage 

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\section{The Parameter tag and how it relates to models}\label{sec:partags}

A {\bf Parameter} {\em Id} attribute defined in
section~\ref{sec:parametertag} starts with a model parameter
identifier, MPID, see Appendix~\ref{sec:mpid}.  Then follows an
opening paramthesis, ``(``, and a {\bf Phase} {\em Id} and a comma and
the constituents as a list of {\bf Species}{\em Id} separated by
commas, ``,'' or colon ``:'' depedning on the model for the phase and
the composition dependence of the parameter.  After the last
constituent there is either just a closeing parenthesis, ``)'', or a
semicolon, ``;'', followed by a single digit, called the degree, and a
closing parenthesis.  Below is an example of a reciprocal parameter in
FCC\_4SL:

{\large
\begin{verbatim}
<Parameter Id="G(FCC_4SL,Au,Cu:Au:Au,Cu:Cu;0)" Expr="..." Bibref="..." />
\end{verbatim}
}

The reason for this rather complex parameter name is to specify the
position of the model parameter in a sometimes quite complex
mathematical model.  In most cases the MPID refers to a Gibbs energy
but there are MPID representing magnetic properties, mobilities,
Einsten $\theta$ etc.  In the explanation below how the {\bf
  Parameter} {\em Id} referes to the mathermatical model for the phase
will only use the Gibbs energy MPID but all properties represented by
different MPID can have the same composition dependence.

The $T$ and $P$ dependence is described by the {\em Expr} attribute
explained in section~\ref{sec:tpfunattr}.


\subsection{Excess model parameters and degree}\label{sec:degree}\label{sec:rkorder}

There has been a large number of excess parameters models proposed
during (and even before) the 50 years of Calphad development.  Most of
them can be converted between each other or are obsolete.  The excess
parameter represent an bond energy between two or more different
elements which are present in the same sublattice.  If there are
several sublattices this energy also depends on the surroundings,
i.e. one must specify the constituents on all sublattices for the
parameter.

There are also parameters which take into accound the simultaneous
mixing of two or more elements on two or more sublattices.  In fact
the CEF model allows simultaneous interaction of all constituents on
all sublattices.  Recently that has been explored to handle
interactions on intermetallic phases with many sublattices, see
section~\ref{sec:ebef}, using also the wildcard feature
in~\ref{sec:wildcard}.

\subsubsection{The binary Redlich-Kister model}\label{sec:RK}

Only the Redlich-Kister binary excess model is allowed.  Any other
binary excess moldel can always be transformed into a Redlich-Kister
model.  A phase can have different ternary extrapolation methods, see
section~\ref{sec:toop}.  The parameters for a Redlich-Kister expression
for interaction on a sublattice $s$:
\begin{eqnarray}
\Delta ~^{\rm RK}G_{\rm AB} &=& y_{s,\rm A}y_{s,\rm B} \sum_{\nu=0}^n (y_{s,\rm A}-y_{s,\rm B})^{\nu} \cdot ~^{\nu}L_{\rm A,B}
\end{eqnarray}
where $\nu$ is known as the degree.  Normally $\nu \le 3$ 
and the parameters would be in the XTDB file:

\begin{verbatim}
<Parameter Id="G(LIQUID,A,B;0)" Expr="..." Bibref="..." />
<Parameter Id="G(LIQUID,A,B;1)" Expr="..." Bibref="..." />
<Parameter Id="G(LIQUID,A,B;2)" Expr="..." Bibref="..." />
\end{verbatim}

In the binary Redlich-Kister series for a system A-B the composition
dependence depend on the difference $(y_{s,\rm A}-y_{s,\rm B})^n$, in
sublattice $s$ and $n$ is known as the degree.  The order of the
species in the fraction difference is by default alphabetical but
there is a {\em RKorder} attribute in the {\bf Defaults} tag to change
the default and use the ``actual'' order the constituents are
specified in the model parameter, for example L(liquid,C,A;1) would
mean to use the difference $(x_{\rm C}-x_{\rm A})$ and not $(x_{\rm
  A}-x_{\rm C})$.

\subsubsection{The ternary excess model}\label{sec:hillert3}

For ternary parameters Hillert~\cite{80Hil} has proposed a symmetric
ternary composition dependent parameter L(PHASE,A,B,C;0..3):
\begin{eqnarray}
\Delta ^{\rm H3}G_{\rm ABC} &=& x_{\rm A}x_{\rm B}x_{\rm C}(v_{\rm A}~^0L_{\rm A,B,C}+v_{\rm B}~^1L_{\rm A,B,C}+v_{\rm C}~^2L_{\rm A,B,C}) \label{eq:hillert3}
\end{eqnarray}
where
\begin{eqnarray}
v_{\rm A} &=& (1+2x_{\rm A}-x_{\rm B}-x_{\rm C})/3\\
v_{\rm B} &=& (1+2x_{\rm B}-x_{\rm C}-x_{\rm A})/3\\
v_{\rm C} &=& (1+2x_{\rm C}-x_{\rm A}-x_{\rm B})/3
\end{eqnarray}
where the advantage of using $v$ is that the sum of them is always
unity and thus avoids any unintended skewness when extrapolating to
higher order system.  In TC and OC a single ternary parameter with
zero degree means no composition dependence, and in order to have a
composition dependence parameters for all 3 degrees must be given even
if one or two of them are zero.

\begin{verbatim}
<Parameter Id="G(LIQUID,A,B,C;0)" Expr="..." Bibref="..." />
<Parameter Id="G(LIQUID,A,B,C;1)" Expr="..." Bibref="..." />
<Parameter Id="G(LIQUID,A,B,C;2)" Expr="..." Bibref="..." />
\end{verbatim}

\subsubsection{The reciprocal model for phases with sublattices}\label{sec:recip}

In the sublattice model one can have independent binary and ternary
excess interaction on each sublattice.  One can also have simultaneous
interaction on two or more sublattices, and the so-called reciprocal
parameter signifies interaction with two constituents on two
sublattices.  This parameter has an important physical significance
for the thermodynamics and can approximate short range
ordering~\cite{98Sun}.
\begin{eqnarray}
\Delta ^{\rm reci}G_{\rm AB:CD} &=& y_{1,\rm A} y_{1,\rm B} y_{2,\rm C} y_{2,\rm D} L_{\rm A,B:C,D}
\end{eqnarray}

There is also a composition dependence proposed for reciprocal
parameters such as L(PHASE,A,B:C,D;0..3) which I think is:
\begin{eqnarray}
\Delta  ^{\rm reci}G_{\rm AB:CD} &=& y_{1,\rm A}y_{1,\rm B}y_{2,\rm C}y_{2,\rm D} (~^0L_{\rm A,B:C,D} +  (y_{1,\rm A}-y_{1,\rm B})~^1L_{\rm A,B,C} + (y_{2,\rm C}-y_{2,\rm D})~^2L_{\rm A,B,C})  \label{eq:hillert4}
\end{eqnarray}

\begin{verbatim}
<Parameter Id="G(BCC_A2,A,B:C,D;0)" Expr="..." Bibref="..." />
<Parameter Id="G(BCC_A2,A,B:C,D;1)" Expr="..." Bibref="..." />
<Parameter Id="G(BCC_A2,A,B:C,C;2)" Expr="..." Bibref="..." />
\end{verbatim}

\subsection{Ternary extrapolation methods}\label{sec:ternaryxpol}

\begin{figure}[!h]
  \includegraphics[width=\textwidth]{figs/MKT2.png}
  \caption{Various ternary extrapolation methods, the Muggianu in a),
    the Kohler in b), the Toop together with Kohler in c) and Toop
    together with Muggianu in d).  More complex extrapolations can be
    defined if necessary.}\label{fg:MKT2}
\end{figure}

In the Muggianu exgrapolation method the binary compositions are used
inside the ternary system without any modifications, see
Fig.~\ref{fg:MKT2} a).  For the Kohler and Toop methods the
compositions used for the binay contribution must be adjusted
according to the extrapolation method.  The method to handle differebt
kinds of ternary extrapolations have been explained by
Pelton~\cite{01Pel} but they are rarely used.  At present it is not
possible to have different ternary extrapolations on different
sublattices.  For more details see Appendix~\ref{sec:ternaryxpol}.

The ternary extrapolation in a multicomponent system can be different
for each ternary combination.  In some software one groups the
constituents in different groups and if all 3 are in the same group
the software use Kohler extrapolation, if one is different from the
other two that constituent is considered as Toop element and use a
Toop extrapolation of the binaries with that constituent and Kohler
for the binary without the Toop element.

In the XTDB there are no groups but for each ternary comination of
constituents one can specify the extrapolation of each ternary

\begin{verbatim}
<TernaryXpol Phase="LIQUID" Constituents="Fe Cr Ni" Xmode="MMM" />
<TernaryXpol Phase="LIQUID" Constituents="Fe Si Ni" Xmode="T2KT2" />
\end{verbatim}

In the {\em Xmode} attribute the letters K, M and T are usef for
Kohler, Muggianu and Toop extrapolation.  The letters are in the order
of the constituents forming the binaries: 1-2, 1-3 and 2-3.  For a
Toop extrapolation from a binary one must identify the Toop
constituent by its order in the {\em Constituents} attribute.

Each ternary extrapolation methods must be a separate tag.  If it is
found necessary one could create a tag to handle several
extrapolations in a more practical way.

For the attribute {\em Xmode} one can use only numbers if 0 is used
for a Muggianu extrapolation and the index of the ternary constituent
for a Kohler extrapolation and, for a Toop extrapolation the
constituent index of the Toop constituent used.  Thus "321" means all
3 binaries extrapolates as Kohler.  If a binary extrapolates as Toop
its Toop constituent index is used for the binary, thus "222" means
the same as "T2KT2" above.

As a special case one can use

\begin{verbatim}
<TernaryXpol Phase=``Liquid'' Constituents=``*'' Xmode="KKK" />
\end{verbatim}
\noindent
when all ternary extrapolations are Kohler.  More elaborate cases have
to be implemented later, for example arranging the phase constituetns
in groups and use Kohler if all 3 constituents are in the same group
and Toop if there is one from a different group.

\subsection{The use of wildcards for constituents in parameters}\label{sec:wildcard}

In some parameters a asterisk, ``*'', also known as wildcard is used
to indicate the parameter is independent of the constituent in this
sublattice.  For example if one has:

\begin{verbatim}
<Parameter Id="G(C14,A,B:*)" Expr="-10000" Bibref="someone" />
<Parameter Id="G(C14,A,B:C)" Expr="+30000" Bibref="someone" />
<Parameter Id="G(C14,A,B:D)" Expr="-20000" Bibref="someone" />
\end{verbatim}

When reading such a set of parameters from a database some software
just added the wildcard parameters to the other two.  That is
mathematically correct but this simple case but for more complex cases
with wildcards in several sublattices it is wrong.  The parameter with
the wildcard must be kept as a an individual parameter, independent of
the constituents in that sublattice.  The reason for this is explained
in the sections~\ref{sec:OD} and ~\ref{sec:ebef}.

\subsection{Modeling order/disorder transitions}\label{sec:OD}

Phases with very simple lattices such as BCC, FCC and HCP can have
order/disorder transitions which are important for their properties
and must be modeled correctly.  The ordering means that a set of sites
which have identical constitution in the disordered phase can tranform
to a state with different constitutions on ``identical'' sublattices,
for example BCC\_A2/B2/D0$_3$/B32 or FCC\_A1/L1$_2$/L1$_0$.  Such
order/disorder transition in multicomponent systems can be correctly
calculated using sublattices with approximate Short Range Ordering
(SRO) using a reciprocal parameter explained in
section~\ref{sec:recip}.  This means one must use models with 2 or 4
sublattices which, in the disordered state, are identical.  To
simplify the modeling of such phases the {\bf DisordorderdPart} tag
was developed.

The Gibbs energy description of the disordered phase, $~^{\rm dis}G_M$
in eq.~\ref{eq:nosub} include all the endmember parameters for the
constituents.  If the disordered phase is stable for a significant
composition and temperature ranges there can be parameters describing
this in $~^{\rm dis}G_M$.  In $~^{\rm ord}G_M$ all endmembers with the
same constituent in all sublattices are zero because those values are
in $~^{\rm dis}G_M$.  The endmember parameters in $~^{\rm ord}G_M$ has
two or more different constituents and represent the bond energy
between constituents on different sublattices.

Phases with order/disorder transition can use the {\bf DisorderedPart}
tag and {\em Subtract} attrubute model if the disordered phase can be
assessed independently from the ordered one.  But there are still a
large number of endmembers to assess for the ordered part and many of
them represent identical configurations.  This lead the the
permutation model described in the next section.

\subsection{Permutation of parameters in ordered phases}\label{sec:permut}

Using 4 sublattices to decribe the ordered FCC phase means that
many of the parameters are identical, for example
\begin{eqnarray}
G^{\rm FCC}_{\rm A:A:A:B} = G^{\rm FCC}_{\rm A:A:B:A} &=& G^{\rm FCC}_{\rm A:B:A:A} = G^{\rm FCC}_{\rm B:A:A:A} \label{eq:gl12}\\
G^{\rm FCC}_{\rm A:A:B:B} = G^{\rm FCC}_{\rm A:B:B:A} = G^{\rm FCC}_{\rm B:B:A:A} &=& G^{\rm FCC}_{\rm B:A:A:B} = G^{\rm FCC}_{\rm B:A:B:A} = = G^{\rm FCC}_{\rm A:B:B:A}  \label{eq:gl10}
\end{eqnarray}
because the B atom has exactly the same environment independent of
which of the 4 sublattices it occupies.  This initiated the
permutation feature in Thermo-Calc and OC which simplifies
significantly developing models for ordered phases and in the XTDB
file there will be just one parameter for each permutation:

The other 3 or 6 permutations will be generated by the software.
Sometimes $u_{\rm AB}$ is quite similar when $x_{\rm AB}$ is 0.25, 0.5
or 0.75 which simplifies the assessment.

Even more interesting is that the interaction beteen two constituents
in the ordered state is fairly independent of the surrondings, even in
multicomponent systems.  This suggested the use of the wildcard for
such parameters:

\begin{verbatim}
<Parameter Id="L(FCC_4SL,A,B:*:*:*)" Expr="..." Bibref="someone" />
\end{verbatim}

\noindent
which will also be permuted on all 4 sublattices.  In this case it is
obvious that it would be totally wrong if the software did not treat
this parameter as independent of any other parameter.

\subsection{Modeling multicomponent phases with many sublattices}\label{sec:ms}

Binary systems with intermetallics can be well described using the
sublattice model but require often DFT calculations for their
endmembers as they are frequently stable only in a small composition
range.  These phases use the {\bf DisorderedPart} model without the
{\em Subtract} attribute.

But such binary intermetallics extrapolate badly to ternary and higher
order system because there is a large number of endmembers with 3 or
more different constituents and, contrary to the phases which can
totally disorder, there are no symmetry criteria to reduce them.
Using interaction parameters is also meaningless because each
sublattice represent only a small change in the overall composition.

This lead to the Effective Bond Enegery Formalism~\cite{18Dup} which
represent a totally new view of the parameters in the sublattice
model.

\subsection{The EBEF model use many wildcards}\label{sec:ebef}

In an intermetallic phase with many sublattices using the {\bf
  DisorderedPart} tag means that all the ordered endmember enegies
represent bond energies within the intermetallic phase itself.  The
``lattice stability'' between the stable phase of the constituent and
the intermetallic is in the endmember for the disordered part.  In the
ordered part all endmembers with all constituents same will be zero.
The ordered endmembers with 2 or more different constituents are quite
similar to interaction parameters but they are strongly related to the
crystalline lattice.

For a binary system one can by DFT calculations obtain a set of
endmember energies representing a specific constituent in each
sublattice.  These DFT values can be fitted to a another set of
endmembers energies where all but two of the sublattices have
wildcards and the other two have different constituents.  Several of
these wildcard endmembers have similar overall compositions and one
has to be careful that the new set of ``wildcard''-endmember energies
reproduces the sublattice occupancies for the original DFT
calculations.

The extrapolation from binaries to ternaries of such ``wildcard''
endmembers is very good as shown by Dupin~\cite{18Dup}.  The reason
for this is that fitting the ``wildcard'' endmembers create an
``average'' of the bond energies, originally calculated with a fixed
constituent in each sublattice, which becomes related to the overall
composition rather than the constitution.

This model use the same notation for parameters as in CEF, and require
fewer {\bf Parameter} tags.  In a binary $\sigma$ phase with 5
sublattices one has 32 endmembers but there are only 20 endmember with
pairs (as the sites are different the pair energy is not the same
switching the sites of the constituents)

\begin{verbatim}
<Parameter Id="G(sigma,FE:CR:*:*:*) Expr="..." Bibref="someone" />
<Parameter Id="G(sigma,CR:FE:*:*:*) Expr="..." Bibref="someone" />
\end{verbatim}

These endmembers can be compared with the excess Gibbs energies for an
ordered FCC or BCC when such a parameter has wildcards in the
sublattices without the interaction in section~\ref{sec:permut}.  But
these parameters cannot be permuted because the sublattices are not
identical.

\subsection{Maybe a simplified wildcard notation}\label{sec:useat}

This is not part of this proposal but may be included in a future
version.  The EBEF model may increase drastically the parameters with
wildcards and if there are more wildcards then actual constituents one
could consider using:

\begin{verbatim}
<Parameter Id="G(sigma,FE@1:CR@2) Expr="..." Bibref="someone" />
<Parameter Id="G(sigma,CR@1:FE@2) Expr="..." Bibref="someone" />
\end{verbatim}

This may be useful also gor the I2SL model which may exist with only
neutrals in the anion sublattice.  For example the species C and S can
be neutrals in the 2nd sublattice of the I2SL model without any cation.
Fir example the parameter for pure liquid C could be

\begin{verbatim}
<Parameter Id="G(LIQUID,C@2) Expr="..." Bibref="someone" />
\end{verbatim}

\subsection{CVM and the cluster site model}

Parameters and equations for these models should be included in the
XTDB format also.

\newpage

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\section{Complete examples}\label{sec:complete}

\subsection{The Al-C system with new unary models}\label{sec:alc}

{\small
\begin{verbatim}
<Database version="0.0.3">
  <metadata>
    <writer Software="OpenCalphad  6.068" Date="2023-10-26" />
  </metadata>
  <Defaults LowT="10" HighT="6000" Bibref="U.N. Known" Elements="VA /-" />
  <Element Id="AL" Refstate="FCC_A1" Mass="2.698200E+01" H298="4.577300E+03" S298="2.832200E+01" />
  <Element Id="C" Refstate="GRAPHITE" Mass="1.201100E+01" H298="1.054000E+03" S298="5.742300E+00" />
  <Species Id="VA" Stoichiometry="VA" />
  <Species Id="AL" Stoichiometry="AL" />
  <Species Id="C" Stoichiometry="C" />
  <TPfun Id="R"     Expr="8.31451;" />
  <TPfun Id="RTLNP" Expr="R*T*LN(1.0E-5)*P);" />
  <TPfun Id="G0AL4C3" Expr=" -277339-.005423368*T**2;" /> 
  <TPfun Id="GTSERAL" Expr=" -.001478307*T**2-7.83339395E-07*T**3;" /> 
  <TPfun Id="GTSERCC" Expr=" -.00029531332*T**2-3.3998492E-16*T**5;" /> 
  <TPfun Id="G0BCCAL" Expr=" +GHSERAL+10083;" /> 
  <TPfun Id="G0HCPAL" Expr=" +GHSERAL+5481;" /> 
  <TPfun Id="GHSERAL" Expr=" -8160+GTSERAL;" /> 
  <TPfun Id="GHSERCC" Expr=" -17752.213+GEGRACC+GTSERCC;" /> 
  <TPfun Id="G0DIACC" Expr=" -16275.202-9.1299452E-05*T**2-2.1653414E-16*T**5;" /> 
  <TPfun Id="GEDIACC" Expr=" +0.2318*GEIN(+813.63716)+.01148*GEIN(+345.35022)-0.236743*GEIN(+1601.4467);" /> 
  <TPfun Id="G0LIQAL" Expr=" -209-3.777*T-.00045*T**2;" /> 
  <TPfun Id="G0LIQCC" Expr=" +63887-8.2*T-.0004185*T**2;" /> 
  <TPfun Id="GEGRACC" Expr=" -0.5159523*GEIN(+1953.2502)+0.121519*GEIN(+447.96926)+0.3496843*GEIN(+947.01605)
     +.0388463*GEIN(+192.65039)+.005840323*GEIN(+64.463356);" /> 
  <Phase Id="LIQUID" Configuration="CEF" State="L" >
    <Sites NumberOf="1" Multiplicities="1" >
      <Constituents Sublattice="1" List="AL C" />
    </Sites>
    <AmendPhase Models="LIQ2STATE" />
  </Phase>
  <Phase Id="AL4C3" Configuration="CEF" State="S" >
    <Sites NumberOf="2" Multiplicities="4 3" >
      <Constituents Sublattice="1" List="AL" />
      <Constituents Sublattice="2" List="C" />
    </Sites>
    <AmendPhase Models="GEIN" />
  </Phase>
  <Phase Id="BCC_A2" Configuration="CEF" State="S" >
    <Sites NumberOf="2" Multiplicities="1 3" >
      <Constituents Sublattice="1" List="AL" />
      <Constituents Sublattice="2" List="C VA" />
    </Sites>
    <AmendPhase Models="GEIN" />
  </Phase>
  <Phase Id="DIAMOND" Configuration="CEF" State="S" >
    <Sites NumberOf="1" Multiplicities="1" >
      <Constituents Sublattice="1" List="C" />
    </Sites>
    <AmendPhase Models="GEIN" />
  </Phase>


  <Phase Id="FCC_A1" Configuration="CEF" State="S" >
    <Sites NumberOf="2" Multiplicities="1 1" >
      <Constituents Sublattice="1" List="AL" />
      <Constituents Sublattice="2" List="C VA" />
    </Sites>
    <AmendPhase Models="GEIN" />
  </Phase>
  <Phase Id="GRAPHITE" Configuration="CEF" State="S" >
    <Sites NumberOf="1" Multiplicities="1" >
      <Constituents Sublattice="1" List="C" />
    </Sites>
    <AmendPhase Models="GEIN" />
  </Phase>
  <Phase Id="HCP_A3" Configuration="CEF" State="S" >
    <Sites NumberOf="2" Multiplicities="1 0.5" >
      <Constituents Sublattice="1" List="AL" />
      <Constituents Sublattice="2" List="C VA" />
    </Sites>
    <AmendPhase Models="GEIN" />
  </Phase>
  <Parameter Id="G(LIQUID,AL;0)"  Expr=" +G0LIQAL;"  Bibref="20HE" />
  <Parameter Id="LNTH(LIQUID,AL;0)"  Expr=" +LN(+254);"  Bibref="20HE" />
  <Parameter Id="G2(LIQUID,AL;0)"  Expr=" +13398-R*T-0.16597*T*LN(+T);"  Bibref="20HE" />
  <Parameter Id="G(LIQUID,C;0)"  Expr=" +G0LIQCC;"  Bibref="20HE" />
  <Parameter Id="LNTH(LIQUID,C;0)"  Expr=" +LN(+1400);"  Bibref="20HE" />
  <Parameter Id="G2(LIQUID,C;0)"  Expr=" +59147-49.61*T+2.9806*T*LN(+T);"  Bibref="20HE" />
  <Parameter Id="G(LIQUID,AL,C;0)"  Expr=" +20994-22*T;"  Bibref="20HE" />
  <Parameter Id="G(AL4C3,AL:C;0)"  Expr=" +G0AL4C3-3.08*GEIN(+401)+3.08*GEIN(+1077);"  Bibref="20HE" />
  <Parameter Id="LNTH(AL4C3,AL:C;0)"  Expr=" +LN(+401);"  Bibref="20HE" />
  <Parameter Id="G(BCC_A2,AL:C;0)"  Expr=" +GTSERAL+3*GTSERCC+1006844;"  Bibref="20HE" />
  <Parameter Id="LNTH(BCC_A2,AL:C;0)"  Expr=" +LN(+863);"  Bibref="20HE" />
  <Parameter Id="G(BCC_A2,AL:VA;0)"  Expr=" +G0BCCAL;"  Bibref="20HE" />
  <Parameter Id="LNTH(BCC_A2,AL:VA;0)"  Expr=" +LN(+233);"  Bibref="20HE" />
  <Parameter Id="G(BCC_A2,AL:C,VA;0)"  Expr=" -819896+14*T;"  Bibref="20HE" />
  <Parameter Id="G(DIAMOND,C;0)"  Expr=" +G0DIACC+GEDIACC;"  Bibref="20HE" />
  <Parameter Id="LNTH(DIAMOND,C;0)"  Expr=" +LN(+1601.4467);"  Bibref="20HE" />
  <Parameter Id="G(FCC_A1,AL:C;0)"  Expr=" +GTSERAL+GTSERCC+57338;"  Bibref="20HE" />
  <Parameter Id="LNTH(FCC_A1,AL:C;0)"  Expr=" +LN(+549);"  Bibref="20HE" />
  <Parameter Id="G(FCC_A1,AL:VA;0)"  Expr=" +GHSERAL;"  Bibref="20HE" />
  <Parameter Id="LNTH(FCC_A1,AL:VA;0)"  Expr=" +LN(+283);"  Bibref="20HE" />
  <Parameter Id="G(FCC_A1,AL:C,VA;0)"  Expr=" -70345;"  Bibref="20HE" />
  <Parameter Id="G(GRAPHITE,C;0)"  Expr=" +GHSERCC;"  Bibref="20HE" />
  <Parameter Id="LNTH(GRAPHITE,C;0)"  Expr=" +LN(+1953.2502);"  Bibref="20HE" />
  <Parameter Id="G(HCP_A3,AL:C;0)"  Expr=" +GTSERAL+0.5*GTSERCC+2176775;"  Bibref="20HE" />
  <Parameter Id="LNTH(HCP_A3,AL:C;0)"  Expr=" +LN(+452);"  Bibref="20HE" />
  <Parameter Id="G(HCP_A3,AL:VA;0)"  Expr=" +G0HCPAL;"  Bibref="20HE" />
  <Parameter Id="LNTH(HCP_A3,AL:VA;0)"  Expr=" +LN(+263);"  Bibref="20HE" />
  <Parameter Id="G(HCP_A3,AL:C,VA;0)"  Expr=" 0;"  Bibref="20HE" />
  <Bibliography>
    <Bibitem Id="20HE" Text="Zhangting He, Bartek Kaplan, Huahai Mao and Malin Selleby, Calphad Vol 72, (2021) 102250" /> 
    <Bibitem Id="Default" Text="U.N. Known" /> 
  </Bibliography>
</Database>
\end{verbatim}
}

\newpage

Calculated phase diagram and heat capacity curves from the assessment
of Zhangting He at al for Al-C using the new unary models.

\includegraphics[width=0.45\textwidth]{Figs/AlC-PD.png}
\includegraphics[width=0.45\textwidth]{Figs/Al-Cp-fcc+liquid.png}

\includegraphics[width=0.45\textwidth]{Figs/C-Cp-all.png}
\includegraphics[width=0.45\textwidth]{Figs/Al4C3-Cp.png}

It is nice to be able to extrapolate the heat capacity down to $T=0$~K
but I propose we set the low $T$ limit at 10~K.  The rapidly
increasing heat capacity for the extrapolated metastable FCC phase
requires the EEC model to prevent the FCC to become stable at high $T$.

Adding thermal vacancies to model the increase of the heat capacity of
FCC-Al just before melting may supress the increase of the
extrapolated heat capacity but reguires some extra parameters.

Alternatively one can introduce a break point in $T$ when the solid is
assumed no longer to be mechanically stable.

\newpage

\subsection{The Al-Li system with separated disordered FCC and BCC phases
  and with these integrated in the ordered phases}

The first version in section~\ref{sec:alli1} has been generated using
a TDB file where the disordered part of the 4 sublattice FCC and BCC
phases has been described by separate phases A1\_FCC and A2\_BCC.  In
the {\bf DisorderedPart} tag with the {\em Subtract} attribute this is
indicated by the {\em Disordered} attribute.  This is the way this
feature is implemented in TC.  The {\bf CrystalStructure} tag has no
direct influence on the thermodynamic calculations but if provided
should be stored internally and be provided as information to an
application software and written on any XTDB file generated by the
software.

The second version in section~\ref{sec:alli2} has been generated by OC
and in OC there are no A1\_FCC or A2\_BCC phases because they are
integrated as ``disordered parts'' of the ordered phases.  Thus the
{\bf DisorderedPart} tag in the XTDB file has no no attribute {\em
  Disordered} and the parameters have no sublattices for the ordering.

Both XTDB files have the same information but reflect the way the
different software handle the disordered part.  There should be
problem using slightly different ways to provide the thermodynamic
data on the XTDB files.  Each software can read the data and use its
own way to store the data and it should also implement ways to write
XTDB files in such a way that other software can read them.  It is
important that the software developers document their XTDB format to
allow other software to read their database files.


\subsubsection{The Al-Li system with ordering and crystal structures}\label{sec:alli1}

\begin{verbatim}
<Database version="0.0.1">
  <XTDB Version="0.0.3" Software="Manual" Date="2023.10.10" Signature="Bengt Hallstedt" />
  <Defaults LowT="298.15" HighT="6000" Elements="Va" />
  <DatabaseInfo>
    Database for Al-Li from B. Hallstedt and O. Kim 2007.
	B. Hallstedt, O. Kim, Int. J. Mater. Res., 98, 961-69(2007)
	Including 4-SL ordering models for fcc and bcc.
	
    Dataset created 2009.06.07 by Bengt Hallstedt.
    2016.10.22: Condensed version using option F and B.
    2020.12.20: Modified for use with GES6.
    2023.04.11: Corrected number of interstitial sites in BCC_4SL.
  </DatabaseInfo>

  <Element Id="Va" Refstate="Vacuum" Mass="0.0" H298="0.0" S298="0.0" />
  <Element Id="Al" Refstate="FCC_A1" Mass="26.98154" H298="4540.00" S298="28.30" />
  <Element Id="Li" Refstate="BCC_A2" Mass="6.941" H298="4632.00" S298="29.12" />

<!-- Do we really need these? -->
  <Species Id="Va" Stoichiometry="Va1" />
  <Species Id="Al" Stoichiometry="Al1" />
  <Species Id="Li" Stoichiometry="Li1" />

  <TPfun Id="ZERO"      Expr="0.0;" />
  <TPfun Id="UN_ASS"    Expr="0.0;" />
  <TPfun Id="R"         Expr="8.31451;" />

  <Phase Id="LIQUID" Configuration="CEF" State="L" >
    <Sites NumberOf="1" Multiplicities="1" >
      <Constituents List="Al Li" />
    </Sites>
  </Phase>

<!-- I have added crystal structure information with suggested element and attributes -->
<!-- FCC_A1 does not order -->
  <Phase Id="FCC_A1" Configuration="CEF" State="S" >
	<CrystalStructure Prototype="Cu" PearsonSymbol="cF4" SpaceGroup="Fm-3m" />
	<CrystalStructure Prototype="NaCl" PearsonSymbol="cF8" SpaceGroup="Fm-3m" />
    <Sites NumberOf="2" Multiplicities="1 1" >
      <Constituents Sublattice="1" List="Al Li" />
      <Constituents Sublattice="2" List="Va" />
    </Sites>
    <AmendPhase Models="IHJFCC" />
  </Phase>

<!-- Disordered part of FCC_4SL, identical to FCC_A1 -->
  <Phase Id="A1_FCC" Configuration="CEF" State="S" >
	<CrystalStructure Prototype="Cu" PearsonSymbol="cF4" SpaceGroup="Fm-3m" />
	<CrystalStructure Prototype="NaCl" PearsonSymbol="cF8" SpaceGroup="Fm-3m" />
    <Sites NumberOf="2" Multiplicities="1 1" >
      <Constituents Sublattice="1" List="Al Li" />
      <Constituents Sublattice="2" List="Va" />
    </Sites>
    <AmendPhase Models="IHJFCC" />
  </Phase>

  <Phase Id="FCC_4SL" Configuration="CEF" State="S" >
	<CrystalStructure Prototype="Cu" PearsonSymbol="cF4" SpaceGroup="Fm-3m" />
	<CrystalStructure Prototype="AuCu" PearsonSymbol="tP4" SpaceGroup="P4/mmm" />
	<CrystalStructure Prototype="AuCu3" PearsonSymbol="cP4" SpaceGroup="Pm-3m" />
    <Sites NumberOf="5" Multiplicities="0.25 0.25 0.25 0.25 1" >
      <Constituents Sublattice="1" List="Al Li" />
      <Constituents Sublattice="2" List="Al Li" />
      <Constituents Sublattice="3" List="Al Li" />
      <Constituents Sublattice="4" List="Al Li" />
      <Constituents Sublattice="5" List="Va" />
    </Sites>
    <Disordered_3Part Disordered="A1_FCC" Sum="4" />
    <AmendPhase Models="IHJREST FCC4PERM" />
  </Phase>

<!-- BCC_A2 does not order -->
  <Phase Id="BCC_A2" Configuration="CEF" State="S" >
	<CrystalStructure Prototype="W" PearsonSymbol="cI2" SpaceGroup="Im-3m" />
    <Sites NumberOf="2" Multiplicities="1 3" >
      <Constituents Sublattice="1" List="Al Li" />
      <Constituents Sublattice="2" List="Va" />
    </Sites>
    <AmendPhase Models="IHJBCC" />
  </Phase>

<!-- Disordered part of BCC_4SL, identical to BCC_A2 -->
  <Phase Id="A2_BCC" Configuration="CEF" State="S" >
	<CrystalStructure Prototype="W" PearsonSymbol="cI2" SpaceGroup="Im-3m" />
    <Sites NumberOf="2" Multiplicities="1 3" >
      <Constituents Sublattice="1" List="Al Li" />
      <Constituents Sublattice="2" List="Va" />
    </Sites>
    <AmendPhase Models="IHJBCC" />
  </Phase>

  <Phase Id="BCC_4SL" Configuration="CEF" State="S" >
	<CrystalStructure Prototype="W" PearsonSymbol="cI2" SpaceGroup="Im-3m" />
	<CrystalStructure Prototype="CsCl" PearsonSymbol="cP2" SpaceGroup="Pm-3m" />
	<CrystalStructure Prototype="NaTl" PearsonSymbol="cF16" SpaceGroup="Fd-3m" />
	<CrystalStructure Prototype="AlFe3" PearsonSymbol="cF16" SpaceGroup="Fm-3m" />
	<CrystalStructure Prototype="AlCu2Mn" PearsonSymbol="cF16" SpaceGroup="Fm-3m" />
    <Sites NumberOf="5" Multiplicities="0.25 0.25 0.25 0.25 3" >
      <Constituents Sublattice="1" List="Al Li" />
      <Constituents Sublattice="2" List="Al Li" />
      <Constituents Sublattice="3" List="Al Li" />
      <Constituents Sublattice="4" List="Al Li" />
      <Constituents Sublattice="5" List="Va" />
    </Sites>
    <Disordered_3Part Disordered="A2_BCC" Sum="4" />
    <AmendPhase Models="IHJREST BCC4PERM" />
  </Phase>

  <Phase Id="HCP_A3" Configuration="CEF" State="S" >
	<CrystalStructure Prototype="Mg" PearsonSymbol="hP2" SpaceGroup="P6_3/mmc" />
	<CrystalStructure Prototype="NiAs" PearsonSymbol="hP4" SpaceGroup="P6_3/mmc" />
    <Sites NumberOf="2" Multiplicities="1 0.5" >
      <Constituents Sublattice="1" List="Al Li" />
      <Constituents Sublattice="2" List="Va" />
    </Sites>
    <AmendPhase Models="IHJREST" />
  </Phase>

  <Phase Id="AL2LI3" Configuration="CEF" State="S" >
	<CrystalStructure Prototype="Al2Li3" PearsonSymbol="hR5" SpaceGroup="R-3m" />
    <Sites NumberOf="2" Multiplicities="2 3" >
      <Constituents Sublattice="1" List="Al" />
      <Constituents Sublattice="2" List="Li" />
    </Sites>
  </Phase>

  <Phase Id="AL4LI9" Configuration="CEF" State="S" >
	<CrystalStructure Prototype="Al4Li9" PearsonSymbol="mC26" SpaceGroup="C2/m" />
    <Sites NumberOf="2" Multiplicities="4 9" >
      <Constituents Sublattice="1" List="Al" />
      <Constituents Sublattice="2" List="Li" />
    </Sites>
  </Phase>

<!-- Unary Al -->
  <Parameter Id="G(FCC_A1,AL:VA)"  Expr="GHSERAL;" HighT="2900"  Bibref="91Din" />
  <Parameter Id="G(A1_FCC,AL:VA)"  Expr="GHSERAL;" HighT="2900"  Bibref="91Din" />
  <Parameter Id="G(BCC_A2,AL:VA)"  Expr="GHSERAL+10083-4.813*T;" HighT="2900"  Bibref="91Din" />
  <Parameter Id="G(A2_BCC,AL:VA)"  Expr="GHSERAL+10083-4.813*T;" HighT="2900"  Bibref="91Din" />
  <Parameter Id="G(HCP_A3,AL:VA)"  Expr="GHSERAL+5481-1.8*T;" HighT="2900"  Bibref="91Din" />
  <Parameter Id="G(LIQUID,AL)"  Expr="GLIQAL;" HighT="2900"  Bibref="91Din" />

  <TPfun Id="GHSERAL" Expr="-7976.15+137.093038*T-24.3671976*T*LN(T)-0.001884662*T**2-8.77664E-07*T**3+74092*T**(-1);" HighT="700" >
    <Trange Expr="-11276.24+223.048446*T-38.5844296*T*LN(T)+0.018531982*T**2 -5.764227E-06*T**3+74092*T**(-1);" HighT="933.47" /> 
    <Trange Expr="-11278.361+188.684136*T-31.748192*T*LN(T)-1.230622E+28*T**(-9);" HighT="2900" /> 
  </TPfun>

  <TPfun Id="GLIQAL" Expr="+11005.045-11.84185*T+GHSERAL+7.9337E-20*T**7;" HighT="933.47" >
     <Trange Expr="-795.991+177.430209*T-31.748192*T*LN(T);" HighT="2900" /> 
  </TPfun>

<!-- Unary Li -->
  <Parameter Id="G(BCC_A2,LI:VA)"  LowT="200" Expr="GHSERLI;" HighT="3000"  Bibref="91Din" />
  <Parameter Id="G(A2_BCC,LI:VA)"  LowT="200" Expr="GHSERLI;" HighT="3000"  Bibref="91Din" />
  <Parameter Id="G(FCC_A1,LI:VA)"  LowT="200" Expr="GHSERLI-108+1.3*T;" HighT="3000"  Bibref="91Din" />
  <Parameter Id="G(A1_FCC,LI:VA)"  LowT="200" Expr="GHSERLI-108+1.3*T;" HighT="3000"  Bibref="91Din" />
  <Parameter Id="G(HCP_A3,AL:VA)"  LowT="200" Expr="GHSERLI-154+2*T;" HighT="3000"  Bibref="91Din" />
  <Parameter Id="G(LIQUID,LI)"  LowT="200" Expr="GLIQLI;" HighT="3000"  Bibref="91Din" />

  <TPfun Id="GHSERLI" Expr="-10583.817+217.637482*T-38.940488*T*LN(T)+0.035466931*T**2-1.9869816E-05*T**3+159994*T**(-1);" HighT="453" >
    <Trange Expr="-559579.123+10547.8799*T-1702.88865*T*LN(T)+2.25832944*T**2-5.71066077E-04*T**3+33885874*T**(-1);" HighT="500" /> 
    <Trange Expr="-9062.994+179.278285*T-31.2283718*T*LN(T)+0.002633221*T**2-4.38058E-07*T**3-102387*T**(-1);" HighT="3000" /> 
  </TPfun>

  <TPfun Id="GLIQLI" Expr="+2700.205-5.795621*T+GHSERLI;" HighT="250" >
    <Trange Expr="+12015.027-362.187078*T+61.6104424*T*LN(T)-0.182426463*T**2+6.3955671E-05*T**3-559968*T**(-1);" HighT="453" /> 
    <Trange Expr="-6057.31+172.652183*T-31.2283718*T*LN(T)+0.002633221*T**2-4.38058E-07*T**3-102387*T**(-1);" HighT="500" /> 
    <Trange Expr="+3005.684-6.626102*T+GHSERLI;" HighT="3000" /> 
  </TPfun>

<!-- Binary Al-Li -->
  <Parameter Id="G(LIQUID,AL,LI;0)"  Expr="-44200+20.6*T;" Bibref="07Hal" />
  <Parameter Id="G(LIQUID,AL,LI;1)"  Expr="+13600-5.3*T;" Bibref="07Hal" />
  <Parameter Id="G(LIQUID,AL,LI;2)"  Expr="+14200;" Bibref="07Hal" />
  <Parameter Id="G(LIQUID,AL,LI;3)"  Expr="-12100;" Bibref="07Hal" />
  <Parameter Id="G(LIQUID,AL,LI;4)"  Expr="-7100;" Bibref="07Hal" />

  <Parameter Id="G(FCC_A1,AL,LI:VA;0)"  Expr="+LDF0ALLI;" Bibref="07Hal" />
  <Parameter Id="G(FCC_A1,AL,LI:VA;1)"  Expr="+LDF1ALLI;" Bibref="07Hal" />
  <Parameter Id="G(FCC_A1,AL,LI:VA;2)"  Expr="+LDF2ALLI;" Bibref="07Hal" />

  <Parameter Id="G(A1_FCC,AL,LI:VA;0)"  Expr="+LDF0ALLI;" Bibref="07Hal" />
  <Parameter Id="G(A1_FCC,AL,LI:VA;1)"  Expr="+LDF1ALLI;" Bibref="07Hal" />
  <Parameter Id="G(A1_FCC,AL,LI:VA;2)"  Expr="+LDF2ALLI;" Bibref="07Hal" />

  <Parameter Id="G(BCC_A2,AL,LI:VA;0)"  Expr="+LDB0ALLI;" Bibref="07Hal" />
  <Parameter Id="G(BCC_A2,AL,LI:VA;1)"  Expr="+LDB1ALLI;" Bibref="07Hal" />
  <Parameter Id="G(BCC_A2,AL,LI:VA;2)"  Expr="+LDB2ALLI;" Bibref="07Hal" />

  <Parameter Id="G(A2_BCC,AL,LI:VA;0)"  Expr="+LDB0ALLI;" Bibref="07Hal" />
  <Parameter Id="G(A2_BCC,AL,LI:VA;1)"  Expr="+LDB1ALLI;" Bibref="07Hal" />
  <Parameter Id="G(A2_BCC,AL,LI:VA;2)"  Expr="+LDB2ALLI;" Bibref="07Hal" />

  <Parameter Id="G(FCC_4SL,AL:AL:AL:LI:VA)"  Expr="+GFAL3LI;" Bibref="07Hal" />
  <Parameter Id="G(FCC_4SL,AL:AL:LI:LI:VA)"  Expr="+GFALLI2;" Bibref="07Hal" />
  <Parameter Id="G(FCC_4SL,AL:LI:LI:LI:VA)"  Expr="+GFALLI3;" Bibref="07Hal" />
  <Parameter Id="G(FCC_4SL,AL,LI:*:*:*:VA;0)"  Expr="+L0FALLI;" Bibref="07Hal" />
  <Parameter Id="G(FCC_4SL,AL,LI:*:*:*:VA;1)"  Expr="+L1FALLI;" Bibref="07Hal" />
  <Parameter Id="G(FCC_4SL,AL,LI:*:*:*:VA;2)"  Expr="+L2FALLI;" Bibref="07Hal" />
  <Parameter Id="G(FCC_4SL,AL,LI:AL,LI:*:*:VA;0)"  Expr="+SFALLI;" Bibref="07Hal" />

  <Parameter Id="G(BCC_4SL,AL:AL:AL:LI:VA)"  Expr="+GBAL3LI;" Bibref="07Hal" />
  <Parameter Id="G(BCC_4SL,AL:AL:LI:LI:VA)"  Expr="+GB2ALLI;" Bibref="07Hal" />
  <Parameter Id="G(BCC_4SL,AL:LI:AL:LI:VA)"  Expr="+GB2ALLI;" Bibref="07Hal" />
  <Parameter Id="G(BCC_4SL,AL:LI:LI:LI:VA)"  Expr="+GBALLI3;" Bibref="07Hal" />
  <Parameter Id="G(BCC_4SL,AL,LI:*:*:*:VA;0)"  Expr="+L0BALLI;" Bibref="07Hal" />
  <Parameter Id="G(BCC_4SL,AL,LI:*:*:*:VA;1)"  Expr="+L1BALLI;" Bibref="07Hal" />
  <Parameter Id="G(BCC_4SL,AL,LI:*:*:*:VA;2)"  Expr="+L2BALLI;" Bibref="07Hal" />
  <Parameter Id="G(BCC_4SL,AL,LI:AL,LI:*:*:VA;0)"  Expr="+SB1ALLI;" Bibref="07Hal" />
  <Parameter Id="G(BCC_4SL,AL,LI:*:AL,LI:*:VA;0)"  Expr="+SB2ALLI;" Bibref="07Hal"  />
  
  <Parameter Id="G(AL2LI3,AL:LI)"  Expr="+2*GHSERAL+3*GHSERLI-93990+34.5*T;" Bibref="07Hal" />
  <Parameter Id="G(AL4LI),AL:LI)"  Expr="+4*GHSERAL+9*GHSERLI-193780+71.7*T;" Bibref="07Hal" />

<!-- metastable -->
  <Parameter Id="G(HCP_A3,AL,LI:VA;0)"  Expr="-27000+8*T;" Bibref="98Sau2" />

  <TPfun Id="UFALLI" Expr="-3270+1.96*T;" />
  <TPfun Id="L0FALLI" Expr="+2960-1.56*T;" />
  <TPfun Id="L2FALLI" Expr="0;" />
  <TPfun Id="L2FALLI" Expr="0;" />
  <TPfun Id="GFAL3LI" Expr="+3*UFALLI+1750-4.7*T;" />
  <TPfun Id="GFAL2LI2" Expr="+4*UFALLI;" />
  <TPfun Id="GFALLI3" Expr="+3*UFALLI+4900;" />
  <TPfun Id="SFALLI" Expr="+UFALLI;" />
  <TPfun Id="LDF0ALLI" Expr="+GFAL3LI+1.5*GFAL2LI2+GFALLI3+1.5*SFALLI+4*L0FALLI;" />
  <TPfun Id="LDF1ALLI" Expr="+2*GFAL3LI-2*GFALLI3+4*L1FALLI;" />
  <TPfun Id="LDF2ALLI" Expr="+GFAL3LI-1.5*GFAL2LI2+GFALLI3-1.5*SFALLI+4*L2FALLI;" />

  <TPfun Id="UB1ALLI" Expr="-3360+1.8*T;" />
  <TPfun Id="UB2ALLI" Expr="-4230+1.86*T;" />
  <TPfun Id="L0BALLI" Expr="0;" />
  <TPfun Id="L2BALLI" Expr="0;" />
  <TPfun Id="L2BALLI" Expr="0;" />
  <TPfun Id="GBAL3LI" Expr="+2*UB1ALLI+1.5*UB2ALLI+3700;" />
  <TPfun Id="GB2ALLI" Expr="+4*UB1ALLI;" />
  <TPfun Id="GB32ALLI" Expr="+2*UB1ALLI+3*UB2ALLI;" />
  <TPfun Id="GBALLI3" Expr="+2*UB1ALLI+1.5*UB2ALLI+3250;" />
  <TPfun Id="SB1ALLI" Expr="+15000;" />
  <TPfun Id="SB2ALLI" Expr="+15000;" />
  <TPfun Id="LDB0ALLI" Expr="+GBAL3LI+0.5*GB2ALLI+GB32ALLI+GBALLI3+4*L0BALLI;" />
  <TPfun Id="LDB1ALLI" Expr="+2*GBAL3LI-2*GBALLI3+4*L1BALLI;" />
  <TPfun Id="LDB2ALLI" Expr="+GBAL3LI-0.5*GB2ALLI-GB32ALLI+GBALLI3+4*L2BALLI;" />

  <Bibliography>
    <Bibitem Id="91Din" Text="A.T. Dinsdale, Calphad, 15, 317-425(1991)." />
    <Bibitem Id="98Sau2" Text="N. Saunders, COST 507, Final report round 2, 1998; Al-Li" />
    <Bibitem Id="07Hal" Text="B. Hallstedt, O. Kim, Int. J. Mater. Res., 98, 961-69(2007); Al-Li" />
  </Bibliography> 

</Database>
\end{verbatim}

\subsubsection{The Al-Li system with the disordered parameters
  integrated in the ordered phases}\label{sec:alli2}

This XTDB file for Al-Ni is generated from OC with the
``DisorderedPart'' parameters together with in the ordered FCC and BCC
phases.  The parameters for the disordered phas have one sublattices
replacing the ordered sublattices.

In this listing all {\bf TPfun} tags are in the beginning, the {\bf
  CrystalStructure} tag is missing and the parameters for all phases
listed together at the end.  The list of parameters has been edited
manually and may contain some errors.

\begin{verbatim}
<Database version="0.0.3">
  <metadata>
    <writer Software="OpenCalphad  6.067" Date="2023-10-15" />
  </metadata>
  <Defaults LowT="298.15" HighT="6000" Bibref="U.N. Known" Elements="VA /-" />
  <Element Id="AL" Refstate="FCC_A1" Mass="2.698154E+01" H298="4.540000E+03" S298="2.830000E+01" />
  <Element Id="LI" Refstate="BCC_A2" Mass="6.941000E+00" H298="4.632000E+03" S298="2.912000E+01" />
  <Species Id="VA" Stoichiometry="VA" />
  <Species Id="AL" Stoichiometry="AL" />
  <Species Id="LI" Stoichiometry="LI" />
  <TPfun Id="R"     Expr="8.31451;" />
  <TPfun Id="RTLNP" Expr="R*T*LN(1.0E-5)*P);" />
  <TPfun Id="GHSERAL" Expr=" -7976.15+137.093038*T-24.3671976*T*LN(+T)-.001884662*T**2-8.77664E-07*T**3+74092*T**(-1);" HighT="700" >
    <Trange Expr="-11276.24+223.048446*T-38.5844296*T*LN(+T)+.018531982*T**2-5.764227E-06*T**3+74092*T**(-1);" HighT="933.47" />
    <Trange Expr="-11278.378+188.684153*T-31.748192*T*LN(+T)-1.230524E+28*T**(-9);" HighT="2900" /> 
  </TPfun>
  <TPfun Id="GLIQAL" Expr=" +11005.029-11.841867*T+GHSERAL+7.9337E-20*T**7;" HighT="933.47" >
    <Trange Expr="-795.996+177.430178*T-31.748192*T*LN(+T);" HighT="2900" /> 
  </TPfun>
  <TPfun Id="GHSERLI" LowT="200" Expr=" -10583.817+217.637482*T-38.940488*T*LN(+T)+.035466931*T**2-1.9869816E-05*T**3+159994*T**(-1);" HighT="453.6" >
    <Trange Expr="-559579.123+10547.8799*T-1702.88865*T*LN(+T)+2.25832944*T**2-.000571066077*T**3+33885874*T**(-1);" HighT="500" />
    <Trange Expr="-9062.994+179.278285*T-31.2283718*T*LN(+T)+.002633221*T**2-4.38058E-07*T**3-102387*T**(-1);" HighT="3000" /> 
  </TPfun>
  <TPfun Id="GLIQLI" LowT="200" Expr=" +2700.205-5.795621*T+GHSERLI;" HighT="250" >
    <Trange Expr="+12015.027-362.187078*T+61.6104424*T*LN(+T)-0.182426463*T**2+6.3955671E-05*T**3-559968*T**(-1);" HighT="453.6" />
    <Trange Expr="-6057.31+172.652183*T-31.2283718*T*LN(+T)+.002633221*T**2-4.38058E-07*T**3-102387*T**(-1);" HighT="500" />
    <Trange Expr="+3005.684-6.626102*T+GHSERLI;" HighT="3000" /> 
  </TPfun>
  <TPfun Id="LDF0ALLI" Expr=" +GFAL3LI+1.5*GFAL2LI2+GFALLI3+1.5*SFALLI+4*L0FALLI;" /> 
  <TPfun Id="LDF1ALLI" Expr=" +2*GFAL3LI-2*GFALLI3+4*L1FALLI;" /> 
  <TPfun Id="LDF2ALLI" Expr=" +GFAL3LI-1.5*GFAL2LI2+GFALLI3-1.5*SFALLI+4*L2FALLI;" /> 
  <TPfun Id="LDB0ALLI" Expr=" +GBAL3LI+0.5*GB2ALLI+GB32ALLI+GBALLI3+4*L0BALLI;" /> 
  <TPfun Id="LDB1ALLI" Expr=" +2*GBAL3LI-2*GBALLI3+4*L1BALLI;" /> 
  <TPfun Id="LDB2ALLI" Expr=" +GBAL3LI-0.5*GB2ALLI-GB32ALLI+GBALLI3+4*L2BALLI;" /> 
  <TPfun Id="GFAL3LI" Expr=" +3*UFALLI+1750-4.7*T;" /> 
  <TPfun Id="GFAL2LI2" Expr=" +4*UFALLI;" /> 
  <TPfun Id="L0FALLI" Expr=" +2960-1.56*T;" /> 
  <TPfun Id="L1FALLI" Expr=" 0;" /> 
  <TPfun Id="L2FALLI" Expr=" 0;" /> 
  <TPfun Id="SFALLI" Expr=" +UFALLI;" /> 
  <TPfun Id="GBAL3LI" Expr=" +2*UB1ALLI+1.5*UB2ALLI+3700;" /> 
  <TPfun Id="GB2ALLI" Expr=" +4*UB1ALLI;" /> 
  <TPfun Id="GBALLI3" Expr=" +2*UB1ALLI+1.5*UB2ALLI+3250;" /> 
  <TPfun Id="L0BALLI" Expr=" 0;" /> 
  <TPfun Id="L1BALLI" Expr=" 0;" /> 
  <TPfun Id="L2BALLI" Expr=" 0;" /> 
  <TPfun Id="SB1ALLI" Expr=" +15000;" /> 
  <TPfun Id="UFALLI" Expr=" -3270+1.96*T;" /> 
  <TPfun Id="GFALLI3" Expr=" +3*UFALLI+4900;" /> 
  <TPfun Id="UB1ALLI" Expr=" -3360+1.8*T;" /> 
  <TPfun Id="UB2ALLI" Expr=" -4230+1.86*T;" /> 
  <TPfun Id="GB32ALLI" Expr=" +2*UB1ALLI+3*UB2ALLI;" /> 
  <Phase Id="LIQUID" Configuration="CEF" State="L" >
    <Sites NumberOf="1" Multiplicities="1" >
      <Constituents List="AL LI" />
    </Sites>
  </Phase>
  <Phase Id="AL2LI3" Configuration="CEF" State="S" >
    <Sites NumberOf="2" Multiplicities="2 3" >
      <Constituents Sublattice="1" List="AL" />
      <Constituents Sublattice="2" List="LI" />
    </Sites>
  </Phase>
  <Phase Id="AL4LI9" Configuration="CEF" State="S" >
    <Sites NumberOf="2" Multiplicities="4 9" >
      <Constituents Sublattice="1" List="AL" />
      <Constituents Sublattice="2" List="LI" />
    </Sites>
  </Phase>
  <Phase Id="BCC_A2" Configuration="CEF" State="S" >
    <Sites NumberOf="2" Multiplicities="1 3" >
      <Constituents Sublattice="1" List="AL LI" />
      <Constituents Sublattice="2" List="VA" />
    </Sites>
  </Phase>
  <Phase Id="HCP_A3" Configuration="CEF" State="S" >
    <Sites NumberOf="2" Multiplicities="1 0.5" >
      <Constituents Sublattice="1" List="AL LI" />
      <Constituents Sublattice="2" List="VA" />
    </Sites>
  </Phase>
  <Phase Id="BD3_BCC" Configuration="CEF" State="S" >
    <Sites NumberOf="5" Multiplicities="0.25 0.25 0.25 0.25 1" >
      <Constituents Sublattice="1" List="AL LI" />
      <Constituents Sublattice="2" List="AL LI" />
      <Constituents Sublattice="3" List="AL LI" />
      <Constituents Sublattice="4" List="AL LI" />
      <Constituents Sublattice="5" List="VA" />
    </Sites>
    <DisorderedPart Sum="4" Subtract="Y"/>
    <AmendPhase Models="BCC4PERM" />
  </Phase>
  <Phase Id="FCC_A1" Configuration="CEF" State="S" >
    <Sites NumberOf="2" Multiplicities="1 1" >
      <Constituents Sublattice="1" List="AL LI" />
      <Constituents Sublattice="2" List="VA" />
    </Sites>
  </Phase>
  <Phase Id="L102_FCC" Configuration="CEF" State="S" >
    <Sites NumberOf="5" Multiplicities="0.25 0.25 0.25 0.25 1" >
      <Constituents Sublattice="1" List="AL LI" />
      <Constituents Sublattice="2" List="AL LI" />
      <Constituents Sublattice="3" List="AL LI" />
      <Constituents Sublattice="4" List="AL LI" />
      <Constituents Sublattice="5" List="VA" />
    </Sites>
    <DisorderedPart Sum="4" Subtract="Y"/>
    <AmendPhase Models="FCC4PERM" />
  </Phase>
  <Parameter Id="G(LIQUID,AL;0)"  Expr=" +GLIQAL;" HighT="2900"  Bibref="91DIN" />
  <Parameter Id="G(LIQUID,LI;0)"  LowT="200" Expr=" +GLIQLI;" HighT="3000"  Bibref="91DIN" />
  <Parameter Id="G(LIQUID,AL,LI;0)"  Expr=" -44200+20.6*T;"  Bibref="07HAL" />
  <Parameter Id="G(LIQUID,AL,LI;1)"  Expr=" +13600-5.3*T;"  Bibref="07HAL" />
  <Parameter Id="G(LIQUID,AL,LI;2)"  Expr=" +14200;"  Bibref="07HAL" />
  <Parameter Id="G(LIQUID,AL,LI;3)"  Expr=" -12100;"  Bibref="07HAL" />
  <Parameter Id="G(LIQUID,AL,LI;4)"  Expr=" -7100;"  Bibref="07HAL" />

  <Parameter Id="G(AL2LI3,AL:LI;0)"  Expr=" +2*GHSERAL+3*GHSERLI-93990+34.5*T;"  Bibref="07HAL" />
  <Parameter Id="G(AL4LI9,AL:LI;0)"  Expr=" +4*GHSERAL+9*GHSERLI-193780+71.7*T;"  Bibref="07HAL" />

  <Parameter Id="G(BCC_A2,AL:VA;0)"  Expr=" +GHSERAL+10083-4.813*T;" HighT="2900"  Bibref="91DIN" />
  <Parameter Id="G(BCC_A2,LI:VA;0)"  LowT="200" Expr=" +GHSERLI;" HighT="3000"  Bibref="91DIN" />
  <Parameter Id="G(BCC_A2,AL,LI:VA;0)"  Expr=" +LDB0ALLI;"  Bibref="07HAL" />
  <Parameter Id="G(BCC_A2,AL,LI:VA;1)"  Expr=" +LDB1ALLI;"  Bibref="07HAL" />
  <Parameter Id="G(BCC_A2,AL,LI:VA;2)"  Expr=" +LDB2ALLI;"  Bibref="07HAL" />
  <Parameter Id="G(HCP_A3,AL:VA;0)"  Expr=" +GHSERAL+5481-1.8*T;" HighT="2900"  Bibref="91DIN" />
  <Parameter Id="G(HCP_A3,LI:VA;0)"  LowT="200" Expr=" +GHSERLI-154+2*T;" HighT="3000"  Bibref="91DIN" />
  <Parameter Id="G(HCP_A3,AL,LI:VA;0)"  Expr=" -27000+8*T;"  Bibref="98SAU2" />

  <Parameter Id="G(BD3_BCC,AL:AL:AL:LI:VA;0)"  Expr=" +GBAL3LI;"  Bibref="07HAL" />
  <Parameter Id="G(BD3_BCC,AL:LI:AL:AL:VA;0)"  Expr=" +GBAL3LI;"  Bibref="07HAL" />
  <Parameter Id="G(BD3_BCC,AL:AL:LI:LI:VA;0)"  Expr=" +GB2ALLI;"  Bibref="07HAL" />
  <Parameter Id="G(BD3_BCC,LI:LI:AL:AL;VA;0)"  Expr=" +GB32ALLI;"  Bibref="07HAL" />
  <Parameter Id="G(BD3_BCC,AL:LI:AL:LI:VA;0)"  Expr=" +GBALLI3;"  Bibref="07HAL" />
  <Parameter Id="G(BD3_BCC,LI:LI:AL:LI:VA;0)"  Expr=" +GBALLI3;"  Bibref="07HAL" />
  <Parameter Id="G(BD3_BCC,AL,LI:AL,LI:*:*:VA;0)"  Expr=" +SB1ALLI;"  Bibref="07HAL" />
  <Parameter Id="G(BD3_BCC,AL,LI:*:*:*:VA;0)"  Expr=" +L0BALLI;"  Bibref="07HAL" />
  <Parameter Id="G(BD3_BCC,AL,LI:*:*:*:VA;1)"  Expr=" +L1BALLI;"  Bibref="07HAL" />
  <Parameter Id="G(BD3_BCC,AL,LI:*:*:*:VA;2)"  Expr=" +L2BALLI;"  Bibref="07HAL" />
<!-- Disordered fraction set factor:     1.0000 Sublattices:   2 with suffix D -->
  <Parameter Id="G(BD3_BCC,AL:VA;0)"  Expr=" +GHSERAL+10083-4.813*T;" HighT="2900"  Bibref="91DIN" />
  <Parameter Id="G(BD3_BCC,LI:VA;0)"  LowT="200" Expr=" +GHSERLI;" HighT="3000"  Bibref="91DIN" />
  <Parameter Id="G(BD3_BCC,AL,LI:VA;0)"  Expr=" +LDB0ALLI;"  Bibref="07HAL" />
  <Parameter Id="G(BD3_BCC,AL,LI:VA;1)"  Expr=" +LDB1ALLI;"  Bibref="07HAL" />
  <Parameter Id="G(BD3_BCC,AL,LI:VA;2)"  Expr=" +LDB2ALLI;"  Bibref="07HAL" />

  <Parameter Id="G(FCC_A1,AL:VA;0)"  Expr=" +GHSERAL;" HighT="2900"  Bibref="91DIN" />
  <Parameter Id="G(FCC_A1,LI:VA;0)"  LowT="200" Expr=" +GHSERLI-108+1.3*T;" HighT="3000"  Bibref="91DIN" />
  <Parameter Id="G(FCC_A1,AL,LI:VA;0)"  Expr=" +LDF0ALLI;"  Bibref="07HAL" />
  <Parameter Id="G(FCC_A1,AL,LI:VA;1)"  Expr=" +LDF1ALLI;"  Bibref="07HAL" />
  <Parameter Id="G(FCC_A1,AL,LI:VA;2)"  Expr=" +LDF2ALLI;"  Bibref="07HAL" />

  <Parameter Id="G(L102_FCC,AL:AL:AL:LI:VA;0)"  Expr=" +GFAL3LI;"  Bibref="07HAL" />
  <Parameter Id="G(L102_FCC,AL:AL:LI:LI:VA;0)"  Expr=" +GFAL2LI2;"  Bibref="07HAL" />
  <Parameter Id="G(L102_FCC,AL:LI:LI:LI:VA;0)"  Expr=" +GFALLI3;"  Bibref="07HAL" />
  <Parameter Id="G(L102_FCC,*:*:AL,LI:AL,LI:VA;0)"  Expr=" +SFALLI;"  Bibref="07HAL" />
  <Parameter Id="G(L102_FCC,*:*:*:AL,LI:VA;0)"  Expr=" +L0FALLI;"  Bibref="07HAL" />
  <Parameter Id="G(L102_FCC,*:*:*:AL,LI:VA;1)"  Expr=" +L1FALLI;"  Bibref="07HAL" />
  <Parameter Id="G(L102_FCC,*:*:*:AL,LI:VA;2)"  Expr=" +L2FALLI;"  Bibref="07HAL" />
<!-- Disordered fraction set factor:     1.0000 Sublattices:   2 with suffix D-->
  <Parameter Id="G(L102_FCC,AL:VA;0)"  Expr=" +GHSERAL;" HighT="2900"  Bibref="91DIN" />
  <Parameter Id="G(L102_FCC,LI:VA;0)"  LowT="200" Expr=" +GHSERLI-108+1.3*T;" HighT="3000"  Bibref="91DIN" />
  <Parameter Id="G(L102_FCC,AL,LI:VA;0)"  Expr=" +LDF0ALLI;"  Bibref="07HAL" />
  <Parameter Id="G(L102_FCC,AL,LI:VA;1)"  Expr=" +LDF1ALLI;"  Bibref="07HAL" />
  <Parameter Id="G(L102_FCC,AL,LI:VA;2)"  Expr=" +LDF2ALLI;"  Bibref="07HAL" />
  <Bibliography>
    <Bibitem Id="91DIN" Text="A.T. Dinsdale, Calphad, 15, 317-425(1991)." /> 
    <Bibitem Id="07HAL" Text="B. Hallstedt, O. Kim, Int. J. Mater. Res., 98, 961-69(2007); Al-Li" /> 
    <Bibitem Id="98SAU2" Text="N. Saunders, COST 507, Final report round 2, 1998; Al-Li" /> 
    <Bibitem Id="Default" Text="U.N. Known" /> 
  </Bibliography>


</Database>
\end{verbatim}

\newpage

\setcounter{equation}{0}
\renewcommand{\theequation}{E\arabic{equation}}
\setcounter{figure}{0}
\renewcommand{\thefigure}{E\arabic{figure}}

\section{Some highlights and significant changes from earlier versions}\label{sec:changes}

\begin{enumerate}
\item The {\bf Disordered\_3Part} and {\bf Disordered\_2Part} have
  been merged to a single tag with an additional optional attribute
  {\em Subtract}.  The {\bf Subtract} attribute is needed when the
  ordered phases should be subtracted (i.e. the Disordered\_3Part) and
  could have any value.  Without any {\bf Subtract} attribute the {\bf
    DisorderedPart} tag means the same as the {\bf Disordered\_2Part}.

\item The tags {\bf FCC4PERM} and {\bf BCC4PERM} are removed and
  replaced by an attribute {\em Permutation} in the {\bf AmendPhase}
  tag.  The value of the {\em Permutation} attribute can be either
  FCC4PERM or BCC4PERM.

\item I have added several attributes for the {\bf AppendXTDB} tag
  indicating the content of the appended file with the idea to
  simplify and speed up reading the XTDB file

  While writing the software to read XTDB file my suggestion is that
  after opening the principal XTDB file the software should first read
  the {\em Model} attribute file which may introduce the models and
  MPIDs for the model parameters in the database.  Then it should
  continue reading the principal XTDB file with the {\bf Elements,
    Species} and {\bf Phase} tags with subtags defining {\bf
    Sublattices, Constituens} and {\bf AmendPhase} tags.  The
  principal XTDB file can include {\bf Parameter} and {\bf TPfun} tags
  but in a large XTDB file only few of those may be relevant for the
  selected set of elements.  As a {\bf TPfun} may depend on other {\bf
    TPfun}s it may be necessary to rewind and read the sequential XTDB
  file several time to catch all {\bf TPfun}s.  Thus it may be
  interesting to have them in a smaller separate file.

  The file with the {\bf Bibliography} tags can be read at the end to
  provide the references for the selected parameters.

\item The {\em Sublattice} attribute of the {\bf Constituents} tag is
  maybe redundant if we prescribe that the {\bf Constituent} tags must
  be in the same order as used for the {\em Multiplicity} attribute in
  the {\bf Sublattices} tag.  This order must also apply to the
  constituents in {\em Id} of the {\bf Parameter} tags.

\item The implementation of wildcards, in parameters as described in
  section~\ref{sec:wildcard} may need attention in the software.

\item The mathematical expression used for the {\em Expr} attribute in
  the tags {\bf TPfun, Parameter} and {\bf Parameter2} must be as
  simple as in the current TDB files, see section~\ref{sec:expr}.  The
  GEIN function has been added.

\item The previous {\bf Toop} and {\bf Kohler} tags are integrated in
  a new {\bf TernaryXpol} tag which can be handled according to the
  suggestions in the paper by Pelton~\cite{01Pel}.

\end{enumerate}

\end{appendices}

\end{document}