IdealSolidSolnPhase.h

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/**
 * @file IdealSolidSolnPhase.h Header file for an ideal solid solution model
 *      with incompressible thermodynamics (see \ref thermoprops and
 *      \link Cantera::IdealSolidSolnPhase IdealSolidSolnPhase\endlink).
 *
 * This class inherits from the Cantera class ThermoPhase and implements an
 * ideal solid solution model with incompressible thermodynamics.
 */

// This file is part of Cantera. See License.txt in the top-level directory or
// at http://www.cantera.org/license.txt for license and copyright information.

#ifndef CT_IDEALSOLIDSOLNPHASE_H
#define CT_IDEALSOLIDSOLNPHASE_H

#include "ThermoPhase.h"

namespace Cantera
{

/**
 * Class IdealSolidSolnPhase represents a condensed phase ideal solution
 * compound. The phase and the pure species phases which comprise the standard
 * states of the species are assumed to have zero volume expansivity and zero
 * isothermal compressibility. Each species does, however, have constant but
 * distinct partial molar volumes equal to their pure species molar volumes. The
 * class derives from class ThermoPhase, and overloads the virtual methods
 * defined there with ones that use expressions appropriate for ideal solution
 * mixtures.
 *
 * The generalized concentrations can have three different forms depending on
 * the value of the member attribute #m_formGC, which is supplied in the
 * constructor and in the XML file. The value and form of the generalized
 * concentration will affect reaction rate constants involving species in this
 * phase.
 *
 * @ingroup thermoprops
 */
class IdealSolidSolnPhase : public ThermoPhase
{
public:
    /**
     * Constructor for IdealSolidSolnPhase.
     * The generalized concentrations can have three different forms
     * depending on the value of the member attribute #m_formGC, which
     * is supplied in the constructor or read from the XML data file.
     *
     * @param formCG This parameter initializes the #m_formGC variable.
     */
    IdealSolidSolnPhase(int formCG=0);

    //! Construct and initialize an IdealSolidSolnPhase ThermoPhase object
    //! directly from an ASCII input file
    /*!
     * This constructor will also fully initialize the object.
     * The generalized concentrations can have three different forms
     * depending on the value of the member attribute #m_formGC, which
     * is supplied in the constructor or read from the XML data file.
     *
     * @param infile File name for the XML datafile containing information
     *               for this phase
     * @param id     The name of this phase. This is used to look up
     *               the phase in the XML datafile.
     * @param formCG This parameter initializes the #m_formGC variable.
     */
    IdealSolidSolnPhase(const std::string& infile, const std::string& id="", int formCG=0);

    //! Construct and initialize an IdealSolidSolnPhase ThermoPhase object
    //! directly from an XML database
    /*!
     * The generalized concentrations can have three different forms
     * depending on the value of the member attribute #m_formGC, which
     * is supplied in the constructor and/or read from the data file.
     *
     * @param root   XML tree containing a description of the phase.
     *               The tree must be positioned at the XML element
     *               named phase with id, "id", on input to this routine.
     * @param id     The name of this phase. This is used to look up
     *               the phase in the XML datafile.
     * @param formCG This parameter initializes the #m_formGC variable.
     */
    IdealSolidSolnPhase(XML_Node& root, const std::string& id="", int formCG=0);

    virtual std::string type() const {
        return "IdealSolidSoln";
    }

    //! @name Molar Thermodynamic Properties of the Solution
    //! @{

    /**
     * Molar enthalpy of the solution. Units: J/kmol. For an ideal, constant
     * partial molar volume solution mixture with pure species phases which
     * exhibit zero volume expansivity and zero isothermal compressibility:
     * \f[
     * \hat h(T,P) = \sum_k X_k \hat h^0_k(T) + (P - P_{ref}) (\sum_k X_k \hat V^0_k)
     * \f]
     * The reference-state pure-species enthalpies at the reference pressure Pref
     * \f$ \hat h^0_k(T) \f$, are computed by the species thermodynamic
     * property manager. They are polynomial functions of temperature.
     * @see MultiSpeciesThermo
     */
    virtual doublereal enthalpy_mole() const;

    /**
     * Molar entropy of the solution. Units: J/kmol/K. For an ideal, constant
     * partial molar volume solution mixture with pure species phases which
     * exhibit zero volume expansivity:
     * \f[
     * \hat s(T, P, X_k) = \sum_k X_k \hat s^0_k(T)  - \hat R \sum_k X_k log(X_k)
     * \f]
     * The reference-state pure-species entropies
     * \f$ \hat s^0_k(T,p_{ref}) \f$ are computed by the species thermodynamic
     * property manager. The pure species entropies are independent of
     * pressure since the volume expansivities are equal to zero.
     * @see MultiSpeciesThermo
     */
    virtual doublereal entropy_mole() const;

    /**
     * Molar Gibbs free energy of the solution. Units: J/kmol. For an ideal,
     * constant partial molar volume solution mixture with pure species phases
     * which exhibit zero volume expansivity:
     * \f[
     * \hat g(T, P) = \sum_k X_k \hat g^0_k(T,P) + \hat R T \sum_k X_k log(X_k)
     * \f]
     * The reference-state pure-species Gibbs free energies
     * \f$ \hat g^0_k(T) \f$ are computed by the species thermodynamic
     * property manager, while the standard state Gibbs free energies
     * \f$ \hat g^0_k(T,P) \f$ are computed by the member function, gibbs_RT().
     * @see MultiSpeciesThermo
     */
    virtual doublereal gibbs_mole() const;

    /**
     * Molar heat capacity at constant pressure of the solution.
     * Units: J/kmol/K.
     * For an ideal, constant partial molar volume solution mixture with
     * pure species phases which exhibit zero volume expansivity:
     * \f[
     * \hat c_p(T,P) = \sum_k X_k \hat c^0_{p,k}(T) .
     * \f]
     * The heat capacity is independent of pressure. The reference-state pure-
     * species heat capacities \f$ \hat c^0_{p,k}(T) \f$ are computed by the
     * species thermodynamic property manager.
     * @see MultiSpeciesThermo
     */
    virtual doublereal cp_mole() const;

    /**
     * Molar heat capacity at constant volume of the solution. Units: J/kmol/K.
     * For an ideal, constant partial molar volume solution mixture with pure
     * species phases which exhibit zero volume expansivity:
     * \f[ \hat c_v(T,P) = \hat c_p(T,P) \f]
     * The two heat capacities are equal.
     */
    virtual doublereal cv_mole() const {
        return cp_mole();
    }

    //@}
    /** @name Mechanical Equation of State Properties
     *
     * In this equation of state implementation, the density is a function only
     * of the mole fractions. Therefore, it can't be an independent variable.
     * Instead, the pressure is used as the independent variable. Functions
     * which try to set the thermodynamic state by calling setDensity() may
     * cause an exception to be thrown.
     */
    //@{

    /**
     * Pressure. Units: Pa. For this incompressible system, we return the
     * internally stored independent value of the pressure.
     */
    virtual doublereal pressure() const {
        return m_Pcurrent;
    }

    /**
     * Set the pressure at constant temperature. Units: Pa. This method sets a
     * constant within the object. The mass density is not a function of
     * pressure.
     *
     * @param p   Input Pressure (Pa)
     */
    virtual void setPressure(doublereal p);

    /**
     * Calculate the density of the mixture using the partial molar volumes and
     * mole fractions as input
     *
     * The formula for this is
     *
     * \f[
     * \rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}}
     * \f]
     *
     * where \f$X_k\f$ are the mole fractions, \f$W_k\f$ are the molecular
     * weights, and \f$V_k\f$ are the pure species molar volumes.
     *
     * Note, the basis behind this formula is that in an ideal solution the
     * partial molar volumes are equal to the pure species molar volumes. We
     * have additionally specified in this class that the pure species molar
     * volumes are independent of temperature and pressure.
     */
    void calcDensity();

    /**
     * Overridden setDensity() function is necessary because the density is not
     * an independent variable.
     *
     * This function will now throw an error condition
     *
     * @internal May have to adjust the strategy here to make the eos for these
     *     materials slightly compressible, in order to create a condition where
     *     the density is a function of the pressure.
     *
     * @param rho  Input density
     */
    virtual void setDensity(const doublereal rho);

    /**
     * Overridden setMolarDensity() function is necessary because the density
     * is not an independent variable.
     *
     * This function will now throw an error condition.
     *
     * @param rho   Input Density
     */
    virtual void setMolarDensity(const doublereal rho);

    //@}

    /**
     * @name Chemical Potentials and Activities
     *
     * The activity \f$a_k\f$ of a species in solution is related to the
     * chemical potential by
     * \f[
     *  \mu_k(T,P,X_k) = \mu_k^0(T,P)
     * + \hat R T \log a_k.
     *  \f]
     * The quantity \f$\mu_k^0(T,P)\f$ is the standard state chemical potential
     * at unit activity. It may depend on the pressure and the temperature.
     * However, it may not depend on the mole fractions of the species in the
     * solid solution.
     *
     * The activities are related to the generalized concentrations, \f$\tilde
     * C_k\f$, and standard concentrations, \f$C^0_k\f$, by the following
     * formula:
     *
     *  \f[
     *  a_k = \frac{\tilde C_k}{C^0_k}
     *  \f]
     * The generalized concentrations are used in the kinetics classes to
     * describe the rates of progress of reactions involving the species. Their
     * formulation depends upon the specification of the rate constants for
     * reaction, especially the units used in specifying the rate constants. The
     * bridge between the thermodynamic equilibrium expressions that use a_k and
     * the kinetics expressions which use the generalized concentrations is
     * provided by the multiplicative factor of the standard concentrations.
     * @{
     */

    /**
     * This method returns the array of generalized concentrations. The
     * generalized concentrations are used in the evaluation of the rates of
     * progress for reactions involving species in this phase. The generalized
     * concentration divided by the standard concentration is also equal to the
     * activity of species.
     *
     * For this implementation the activity is defined to be the mole fraction
     * of the species. The generalized concentration is defined to be equal to
     * the mole fraction divided by the partial molar volume. The generalized
     * concentrations for species in this phase therefore have units of
     * kmol/m^3. Rate constants must reflect this fact.
     *
     * On a general note, the following must be true. For an ideal solution, the
     * generalized concentration must consist of the mole fraction multiplied by
     * a constant. The constant may be fairly arbitrarily chosen, with
     * differences adsorbed into the reaction rate expression. 1/V_N, 1/V_k, or
     * 1 are equally good, as long as the standard concentration is adjusted
     * accordingly. However, it must be a constant (and not the concentration,
     * btw, which is a function of the mole fractions) in order for the ideal
     * solution properties to hold at the same time having the standard
     * concentration to be independent of the mole fractions.
     *
     * In this implementation the form of the generalized concentrations
     * depend upon the member attribute, #m_formGC.
     *
     * HKM Note: We have absorbed the pressure dependence of the pure species
     *        state into the thermodynamics functions. Therefore the standard
     *        state on which the activities are based depend on both temperature
     *        and pressure. If we hadn't, it would have appeared in this
     *        function in a very awkward exp[] format.
     *
     * @param c  Pointer to array of doubles of length m_kk, which on exit
     *           will contain the generalized concentrations.
     */
    virtual void getActivityConcentrations(doublereal* c) const;

    /**
     * The standard concentration \f$ C^0_k \f$ used to normalize the
     * generalized concentration. In many cases, this quantity will be the
     * same for all species in a phase. However, for this case, we will return
     * a distinct concentration for each species. This is the inverse of the
     * species molar volume. Units for the standard concentration are kmol/m^3.
     *
     * @param k Species number: this is a require parameter, a change from the
     *     ThermoPhase base class, where it was an optional parameter.
     */
    virtual doublereal standardConcentration(size_t k) const;

    //! Get the array of species activity coefficients
    /*!
     * @param ac output vector of activity coefficients. Length: m_kk
     */
    virtual void getActivityCoefficients(doublereal* ac) const;

    /**
     * Get the species chemical potentials. Units: J/kmol.
     *
     * This function returns a vector of chemical potentials of the
     * species in solution.
     * \f[
     *    \mu_k = \mu^{ref}_k(T) + V_k * (p - p_o) + R T ln(X_k)
     * \f]
     *  or another way to phrase this is
     * \f[
     *    \mu_k = \mu^o_k(T,p) + R T ln(X_k)
     * \f]
     *  where \f$ \mu^o_k(T,p) = \mu^{ref}_k(T) + V_k * (p - p_o)\f$
     *
     * @param mu  Output vector of chemical potentials.
     */
    virtual void getChemPotentials(doublereal* mu) const;

    /**
     * Get the array of non-dimensional species solution
     * chemical potentials at the current T and P
     * \f$\mu_k / \hat R T \f$.
     * \f[
     *  \mu^0_k(T,P) = \mu^{ref}_k(T) + (P - P_{ref}) * V_k + RT ln(X_k)
     * \f]
     * where \f$V_k\f$ is the molar volume of pure species *k*.
     * \f$ \mu^{ref}_k(T)\f$ is the chemical potential of pure
     * species *k* at the reference pressure, \f$P_{ref}\f$.
     *
     * @param mu   Output vector of dimensionless chemical potentials.
     *             Length = m_kk.
     */
    virtual void getChemPotentials_RT(doublereal* mu) const;

    //@}
    /// @name  Partial Molar Properties of the Solution
    //@{

    //! Returns an array of partial molar enthalpies for the species in the
    //! mixture.
    /*!
     * Units (J/kmol). For this phase, the partial molar enthalpies are equal to
     * the pure species enthalpies
     *  \f[
     * \bar h_k(T,P) = \hat h^{ref}_k(T) + (P - P_{ref}) \hat V^0_k
     * \f]
     * The reference-state pure-species enthalpies, \f$ \hat h^{ref}_k(T) \f$,
     * at the reference pressure,\f$ P_{ref} \f$, are computed by the species
     * thermodynamic property manager. They are polynomial functions of
     * temperature.
     * @see MultiSpeciesThermo
     *
     * @param hbar Output vector containing partial molar enthalpies.
     *             Length: m_kk.
     */
    virtual void getPartialMolarEnthalpies(doublereal* hbar) const;

    /**
     * Returns an array of partial molar entropies of the species in the
     * solution. Units: J/kmol/K. For this phase, the partial molar entropies
     * are equal to the pure species entropies plus the ideal solution
     * contribution.
     *  \f[
     * \bar s_k(T,P) =  \hat s^0_k(T) - R log(X_k)
     * \f]
     * The reference-state pure-species entropies,\f$ \hat s^{ref}_k(T) \f$, at
     * the reference pressure, \f$ P_{ref} \f$, are computed by the species
     * thermodynamic property manager. They are polynomial functions of
     * temperature.
     * @see MultiSpeciesThermo
     *
     * @param sbar Output vector containing partial molar entropies.
     *             Length: m_kk.
     */
    virtual void getPartialMolarEntropies(doublereal* sbar) const;

    /**
     * Returns an array of partial molar Heat Capacities at constant pressure of
     * the species in the solution. Units: J/kmol/K. For this phase, the partial
     * molar heat capacities are equal to the standard state heat capacities.
     *
     * @param cpbar  Output vector of partial heat capacities. Length: m_kk.
     */
    virtual void getPartialMolarCp(doublereal* cpbar) const;

    /**
     * returns an array of partial molar volumes of the species
     * in the solution. Units: m^3 kmol-1.
     *
     * For this solution, the partial molar volumes are equal to the
     * constant species molar volumes.
     *
     * @param vbar  Output vector of partial molar volumes. Length: m_kk.
     */
    virtual void getPartialMolarVolumes(doublereal* vbar) const;

    //@}
    /// @name  Properties of the Standard State of the Species in the Solution
    //@{

    /**
     * Get the standard state chemical potentials of the species. This is the
     * array of chemical potentials at unit activity \f$ \mu^0_k(T,P) \f$. We
     * define these here as the chemical potentials of the pure species at the
     * temperature and pressure of the solution. This function is used in the
     * evaluation of the equilibrium constant Kc. Therefore, Kc will also depend
     * on T and P. This is the norm for liquid and solid systems.
     *
     *  units = J / kmol
     *
     * @param mu0   Output vector of standard state chemical potentials.
     *              Length: m_kk.
     */
    virtual void getStandardChemPotentials(doublereal* mu0) const {
        getPureGibbs(mu0);
    }

    //! Get the array of nondimensional Enthalpy functions for the standard
    //! state species at the current *T* and *P* of the solution.
    /*!
     * We assume an incompressible constant partial molar volume here:
     * \f[
     *  h^0_k(T,P) = h^{ref}_k(T) + (P - P_{ref}) * V_k
     * \f]
     * where \f$V_k\f$ is the molar volume of pure species *k*.
     * \f$ h^{ref}_k(T)\f$ is the enthalpy of the pure species *k* at the
     * reference pressure, \f$P_{ref}\f$.
     *
     * @param hrt Vector of length m_kk, which on return hrt[k] will contain the
     *            nondimensional standard state enthalpy of species k.
     */
    virtual void getEnthalpy_RT(doublereal* hrt) const;

    //! Get the nondimensional Entropies for the species standard states at the
    //! current T and P of the solution.
    /*!
     * Note, this is equal to the reference state entropies due to the zero
     * volume expansivity: i.e., (dS/dP)_T = (dV/dT)_P = 0.0
     *
     * @param sr Vector of length m_kk, which on return sr[k] will contain the
     *           nondimensional standard state entropy for species k.
     */
    virtual void getEntropy_R(doublereal* sr) const;

    /**
     * Get the nondimensional Gibbs function for the species standard states at
     * the current T and P of the solution.
     *
     * \f[
     *  \mu^0_k(T,P) = \mu^{ref}_k(T) + (P - P_{ref}) * V_k
     * \f]
     * where \f$V_k\f$ is the molar volume of pure species *k*.
     * \f$ \mu^{ref}_k(T)\f$ is the chemical potential of pure species *k*
     * at the reference pressure, \f$P_{ref}\f$.
     *
     * @param grt Vector of length m_kk, which on return sr[k] will contain the
     *           nondimensional standard state Gibbs function for species k.
     */
    virtual void getGibbs_RT(doublereal* grt) const;

    /**
     * Get the Gibbs functions for the pure species at the current *T* and *P*
     * of the solution. We assume an incompressible constant partial molar
     * volume here:
     * \f[
     *  \mu^0_k(T,P) = \mu^{ref}_k(T) + (P - P_{ref}) * V_k
     * \f]
     * where \f$V_k\f$ is the molar volume of pure species *k*.
     * \f$ \mu^{ref}_k(T)\f$ is the chemical potential of pure species *k* at
     * the reference pressure, \f$P_{ref}\f$.
     *
     * @param gpure  Output vector of Gibbs functions for species. Length: m_kk.
     */
    virtual void getPureGibbs(doublereal* gpure) const;

    virtual void getIntEnergy_RT(doublereal* urt) const;

    /**
     * Get the nondimensional heat capacity at constant pressure function for
     * the species standard states at the current T and P of the solution.
     * \f[
     *  Cp^0_k(T,P) = Cp^{ref}_k(T)
     * \f]
     * where \f$V_k\f$ is the molar volume of pure species *k*.
     * \f$ Cp^{ref}_k(T)\f$ is the constant pressure heat capacity of species
     * *k* at the reference pressure, \f$p_{ref}\f$.
     *
     * @param cpr Vector of length m_kk, which on return cpr[k] will contain the
     *           nondimensional constant pressure heat capacity for species k.
     */
    virtual void getCp_R(doublereal* cpr) const;

    virtual void getStandardVolumes(doublereal* vol) const;

    //@}
    /// @name Thermodynamic Values for the Species Reference States
    //@{

    virtual void getEnthalpy_RT_ref(doublereal* hrt) const;
    virtual void getGibbs_RT_ref(doublereal* grt) const;
    virtual void getGibbs_ref(doublereal* g) const;
    virtual void getEntropy_R_ref(doublereal* er) const;
    virtual void getIntEnergy_RT_ref(doublereal* urt) const;
    virtual void getCp_R_ref(doublereal* cprt) const;

    /**
     * Returns a reference to the vector of nondimensional enthalpies of the
     * reference state at the current temperature. Real reason for its existence
     * is that it also checks to see if a recalculation of the reference
     * thermodynamics functions needs to be done.
     */
    const vector_fp& enthalpy_RT_ref() const;

    /**
     * Returns a reference to the vector of nondimensional enthalpies of the
     * reference state at the current temperature. Real reason for its existence
     * is that it also checks to see if a recalculation of the reference
     * thermodynamics functions needs to be done.
     */
    const vector_fp& gibbs_RT_ref() const {
        _updateThermo();
        return m_g0_RT;
    }

    /**
     * Returns a reference to the vector of nondimensional enthalpies of the
     * reference state at the current temperature. Real reason for its existence
     * is that it also checks to see if a recalculation of the reference
     * thermodynamics functions needs to be done.
     */
    const vector_fp& entropy_R_ref() const;

    /**
     * Returns a reference to the vector of nondimensional enthalpies of the
     * reference state at the current temperature. Real reason for its existence
     * is that it also checks to see if a recalculation of the reference
     * thermodynamics functions needs to be done.
     */
    const vector_fp& cp_R_ref() const {
        _updateThermo();
        return m_cp0_R;
    }

    virtual void setPotentialEnergy(int k, doublereal pe) {
        m_pe[k] = pe;
        _updateThermo();
    }

    virtual doublereal potentialEnergy(int k) const {
        return m_pe[k];
    }

    //@}
    /// @name Utility Functions
    //@{

    virtual bool addSpecies(shared_ptr<Species> spec);
    virtual void initThermoXML(XML_Node& phaseNode, const std::string& id);
    virtual void setToEquilState(const doublereal* lambda_RT);

    //! Set the form for the standard and generalized concentrations
    /*!
     * Must be one of 'unity', 'molar_volume', or 'solvent_volume'.
     * The default is 'unity'.
     *
     *  | m_formGC       | GeneralizedConc | StandardConc |
     *  | -----------    | --------------- | ------------ |
     *  | unity          | X_k             | 1.0          |
     *  | molar_volume   | X_k / V_k       | 1.0 / V_k    |
     *  | solvent_volume | X_k / V_N       | 1.0 / V_N    |
     *
     *  The value and form of the generalized concentration will affect
     *  reaction rate constants involving species in this phase.
     */
    void setStandardConcentrationModel(const std::string& model);

    /**
     * Report the molar volume of species k
     *
     * units - \f$ m^3 kmol^-1 \f$
     *
     * @param  k species index
     */
    double speciesMolarVolume(int k) const;

    /**
     * Fill in a return vector containing the species molar volumes.
     *
     * units - \f$ m^3 kmol^-1 \f$
     *
     * @param smv  output vector containing species molar volumes.
     *             Length: m_kk.
     */
    void getSpeciesMolarVolumes(doublereal* smv) const;

    //@}

protected:
    virtual void compositionChanged();

    /**
     * The standard concentrations can have one of three different forms:
     * 0 = 'unity', 1 = 'molar_volume', 2 = 'solvent_volume'. See
     * setStandardConcentrationModel().
     */
    int m_formGC;

    /**
     * Value of the reference pressure for all species in this phase. The T
     * dependent polynomials are evaluated at the reference pressure. Note,
     * because this is a single value, all species are required to have the same
     * reference pressure.
     */
    doublereal m_Pref;

    /**
     * m_Pcurrent = The current pressure
     * Since the density isn't a function of pressure, but only of the
     * mole fractions, we need to independently specify the pressure.
     * The density variable which is inherited as part of the State class,
     * m_dens, is always kept current whenever T, P, or X[] change.
     */
    doublereal m_Pcurrent;

    //! Vector of molar volumes for each species in the solution
    /**
     * Species molar volumes \f$ m^3 kmol^-1 \f$
     */
    vector_fp m_speciesMolarVolume;

    //! Vector containing the species reference enthalpies at T = m_tlast
    mutable vector_fp m_h0_RT;

    //! Vector containing the species reference constant pressure heat
    //! capacities at T = m_tlast
    mutable vector_fp m_cp0_R;

    //! Vector containing the species reference Gibbs functions at T = m_tlast
    mutable vector_fp m_g0_RT;

    //! Vector containing the species reference entropies at T = m_tlast
    mutable vector_fp m_s0_R;

    //! Vector containing the species reference exp(-G/RT) functions at
    //! T = m_tlast
    mutable vector_fp m_expg0_RT;

    //! Vector of potential energies for the species.
    mutable vector_fp m_pe;

    //! Temporary array used in equilibrium calculations
    mutable vector_fp m_pp;

private:
    /// @name Utility Functions
    //@{
    /**
     * This function gets called for every call to functions in this class. It
     * checks to see whether the temperature has changed and thus the reference
     * thermodynamics functions for all of the species must be recalculated. If
     * the temperature has changed, the species thermo manager is called to
     * recalculate G, Cp, H, and S at the current temperature.
     */
    void _updateThermo() const;

    //@}
};
}

#endif