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This documentation is for an old version of Cantera. You can find docs for newer versions here.

Elements and Species

Elements

The element entry defines an element or an isotope of an element. Note that these entries are not often needed, since the the database file elements.xml is searched for element definitions when importing phase and interface definitions. An explicit element entry is needed only if an isotope not in elements.xml is required:

element(symbol='C-13',
        atomic_mass=13.003354826)
element("O-!8", 17.9991603)

Species

For each species, a species entry is required. Species are defined at the top-level of the input file—their definitions are not embedded in a phase or interface entry.

Species Name

The name field may contain embedded parentheses, + or - signs to indicate the charge, or just about anything else that is printable and not a reserved character in XML. Some example name specifications:

name = 'CH4'
name = 'methane'
name = 'argon_2+'
name = 'CH2(singlet)'

Elemental Composition

The elemental composition is specified in the atoms entry, as follows:

atoms = "C:1 O:2"             # CO2
atoms = "C:1, O:2"            # CO2 with optional comma
atoms = "Y:1 Ba:2 Cu:3 O:6.5" # stoichiometric YBCO
atoms = ""                    # a surface species representing an empty site
atoms = "Ar:1 E:-2"           # Ar++

For gaseous species, the elemental composition is well-defined, since the species represent distinct molecules. For species in solid or liquid solutions, or on surfaces, there may be several possible ways of defining the species. For example, an aqueous species might be defined with or without including the water molecules in the solvation cage surrounding it.

For surface species, it is possible to omit the atoms field entirely, in which case it is composed of nothing, and represents an empty surface site. This can also be done to represent vacancies in solids. A charged vacancy can be defined to be composed solely of electrons:

species(name = 'ysz-oxygen-vacancy',
        atoms = 'O:0, E:2',
        ...)

Note that an atom number of zero may be given if desired, but is completely equivalent to omitting that element.

The number of atoms of an element must be non-negative, except for the special “element” E that represents an electron.

Thermodynamic Properties

The phase and ideal_interface entries discussed in the last chapter implement specific models for the thermodynamic properties appropriate for the type of phase or interface they represent. Although each one may use different expressions to compute the properties, they all require thermodynamic property information for the individual species. For the phase types implemented at present, the properties needed are:

1. the molar heat capacity at constant pressure \(\hat{c}^0_p(T)\) for a range of temperatures and a reference pressure \(P_0\);
2. the molar enthalpy \(\hat{h}(T_0, P_0)\) at \(P_0\) and a reference temperature \(T_0\);
3. the absolute molar entropy \(\hat{s}(T_0, P_0)\) at \((T_0, P_0)\).

See: Thermodynamic Property Models

Species Transport Coefficients

Transport property models in general require coefficients that express the effect of each species on the transport properties of the phase. The transport field may be assigned an embedded entry that provides species-specific coefficients.

Currently, the only entry type is gas_transport, which supplies parameters needed by the ideal-gas transport property models. The field values and their units of the gas_transport entry are compatible with the transport database parameters described by Kee et al. [1986]. Entries in transport databases in the format described in their report can be used directly in the fields of the gas_transport entry, without requiring any unit conversion. The numeric field values should all be entered as pure numbers, with no attached units string.

Thermodynamic Property Models

The entry types described in this section can be used to provide data for the thermo field of a species. Each implements a different parameterization (functional form) for the heat capacity. Note that there is no requirement that all species in a phase use the same parameterization; each species can use the one most appropriate to represent how the heat capacity depends on temperature.

Currently, three entry types are implemented, all of which provide species properties appropriate for models of ideal gas mixtures, ideal solutions, and pure compounds. Non-ideal phase models are not yet implemented, but may be in future releases. When they are, additional entry types may also be added that provide species-specific coefficients required by specific non-ideal equations of state.

The NASA Polynomial Parameterization

The NASA polynomial parameterization is used to compute the species reference-state thermodynamic properties \(\hat{c}^0_p(T)\), \(\hat{h}^0(T)\) and \(\hat{s}^0(T)\).

The NASA parameterization represents \(\hat{c}^0_p(T)\) with a fourth-order polynomial:

\[\frac{c_p^0(T)}{R} = a_0 + a_1 T + a_2 T^2 + a_3 T^3 + a_4 T^4\]\[\frac{h^0(T)}{RT} = a_0 + \frac{a1}{2}T + \frac{a_2}{3} T^2 + \frac{a_3}{4} T^3 + \frac{a_4}{5} T^4 + a_5\]\[\frac{s^0(T)}{R} = a_o \ln T + a_1 T + \frac{a_2}{2} T^2 + \frac{a_3}{3} T^3 + \frac{a_4}{4} T^4 + a_6\]

Note that this is the “old” NASA polynomial form, used in the original NASA equilibrium program and in Chemkin. It is not compatible with the form used in the most recent version of the NASA equilibrium program, which uses 9 coefficients, not 7.

A NASA parameterization is defined by an embedded NASA entry. Very often, two NASA parameterizations are used for two contiguous temperature ranges. This can be specified by assigning the thermo field of the species entry a sequence of two NASA entries:

# use one NASA parameterization for T < 1000 K, and another for T > 1000 K.
species(name = "O2",
        atoms = " O:2 ",
        thermo = (
            NASA( [ 200.00, 1000.00], [ 3.782456360E+00, -2.996734160E-03,
                    9.847302010E-06, -9.681295090E-09, 3.243728370E-12,
                    -1.063943560E+03, 3.657675730E+00] ),
            NASA( [ 1000.00, 3500.00], [ 3.282537840E+00, 1.483087540E-03,
                    -7.579666690E-07, 2.094705550E-10, -2.167177940E-14,
                    -1.088457720E+03, 5.453231290E+00] ) ) )

The Shomate Parameterization

The Shomate parameterization is:

\[\hat{c}_p^0(T) = A + Bt + Ct^2 + Dt^3 | \frac{E}{t^2}\]\[\hat{h}^0(T) = At + \frac{Bt^2}{2} + \frac{Ct^3}{3} + \frac{Dt^4}{4} - \frac{E}{t} + F\]\[\hat{s}^0(T) = A \ln t + B t + \frac{Ct^2}{2} + \frac{Dt^3}{3} - \frac{E}{2t^2} + G\]

where \(t = T / 1000 K\). It requires 7 coefficients A, B, C, D, E, F, and G. This parameterization is used to represent reference-state properties in the NIST Chemistry WebBook. The values of the coefficients A through G should be entered precisely as shown there, with no units attached. Unit conversions to SI will be handled internally.

Example usage of the shomate directive:

# use a single Shomate parameterization.
species(name = "O2",
        atoms = " O:2 ",
        thermo = Shomate( [298.0, 6000.0],
                          [29.659, 6.137261, -1.186521, 0.09578, -0.219663,
                           -9.861391, 237.948] ) )

Constant Heat Capacity

In some cases, species properties may only be required at a single temperature or over a narrow temperature range. In such cases, the heat capacity can be approximated as constant, and simpler expressions used for the thermodynamic properties. The const_cp parameterization computes the properties as follows:

\[\hat{c}_p^0(T) = \hat{c}_p^0(T_0)\]\[\hat{h}^0(T) = \hat{h}^0(T_0) + \hat{c}_p^0\cdot(T-T_0)\]\[\hat{s}^0(T) = \hat{s}^0(T_0) + \hat{c}_p^0 \ln (T/T_0)\]

The parameterization uses four constants: \(T_0, \hat{c}_p^0(T_0), \hat{h}^0(T_0), \hat{s}^0(T)\).

Example:

thermo = const_cp( t0 = 1200.0,
                   h0 = (-5.0, 'kcal/mol') )