## Elements and Species¶

All phase() entries in Cantera are made up of one or more species() entries, which in turn consist element() entries. This section describes how element() entries and species() entries are defined.

## 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-18", 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 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 $$(T_0, P_0)$$.

### 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. 1. 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, several types are implemented that provide species properties appropriate for models of ideal gas mixtures, ideal solutions, and pure compounds.

### The NASA 7-Coefficient Polynomial Parameterization¶

The NASA 7-coefficient 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:

\begin{equation*} \frac{c_p^0(T)}{R} = a_0 + a_1 T + a_2 T^2 + a_3 T^3 + a_4 T^4 \end{equation*}
\begin{equation*} \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 + \frac{a_5}{T} \end{equation*}
\begin{equation*} \frac{s^0(T)}{R} = a_0 \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 \end{equation*}

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

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 NASA 9-Coefficient Polynomial Parameterization¶

The NASA 9-coefficient polynomial parameterization 2 (“NASA9” for short) is an extension of the NASA 7-coefficient polynomial parameterization which includes two additional terms in each temperature region, as well as supporting an arbitrary number of temperature regions.

The NASA9 parameterization represents the species thermodynamic properties with the following equations:

\begin{equation*} \frac{C_p^0(T)}{R} = a_0 T^{-2} + a_1 T^{-1} + a_2 + a_3 T + a_4 T^2 + a_5 T^3 + a_6 T^4 \end{equation*}
\begin{equation*} \frac{H^0(T)}{RT} = - a_0 T^{-2} + a_1 \frac{\ln T}{T} + a_2 + \frac{a_3}{2} T + \frac{a_4}{3} T^2 + \frac{a_5}{4} T^3 + \frac{a_6}{5} T^4 + \frac{a_7}{T} \end{equation*}
\begin{equation*} \frac{s^0(T)}{R} = - \frac{a_0}{2} T^{-2} - a_1 T^{-1} + a_2 \ln T + a_3 T + \frac{a_4}{2} T^2 + \frac{a_5}{3} T^3 + \frac{a_6}{4} T^4 + a_8 \end{equation*}

The following is an example of a species defined using the NASA9() parameterization in three different temperature regions:

species(name=u'CO2',
atoms='C:1 O:2',
thermo=(NASA9([200.00, 1000.00],
[ 4.943650540E+04, -6.264116010E+02,  5.301725240E+00,
2.503813816E-03, -2.127308728E-07, -7.689988780E-10,
2.849677801E-13, -4.528198460E+04, -7.048279440E+00]),
NASA9([1000.00, 6000.00],
[ 1.176962419E+05, -1.788791477E+03,  8.291523190E+00,
-9.223156780E-05,  4.863676880E-09, -1.891053312E-12,
6.330036590E-16, -3.908350590E+04, -2.652669281E+01]),
NASA9([6000.00, 20000.00],
[-1.544423287E+09,  1.016847056E+06, -2.561405230E+02,
3.369401080E-02, -2.181184337E-06,  6.991420840E-11,
-8.842351500E-16, -8.043214510E+06,  2.254177493E+03])),
note='Gurvich,1991 pt1 p27 pt2 p24. [g 9/99]')


Thermodynamic data for a range of species can be obtained from the NASA ThermoBuild tool. Using the web interface, an input file can be obtained for a set of species. This input file should then be modified so that the first line reads “thermo nasa9“, as in the following example:

thermo nasa9
200.000  1000.000  6000.000 20000.000   9/09/04
CO                Gurvich,1979 pt1 p25 pt2 p29.
3 tpis79 C   1.00O   1.00    0.00    0.00    0.00 0   28.0101000    -110535.196
200.000   1000.0007 -2.0 -1.0  0.0  1.0  2.0  3.0  4.0  0.0         8671.104
1.489045326D+04-2.922285939D+02 5.724527170D+00-8.176235030D-03 1.456903469D-05
-1.087746302D-08 3.027941827D-12                -1.303131878D+04-7.859241350D+00
1000.000   6000.0007 -2.0 -1.0  0.0  1.0  2.0  3.0  4.0  0.0         8671.104
4.619197250D+05-1.944704863D+03 5.916714180D+00-5.664282830D-04 1.398814540D-07
-1.787680361D-11 9.620935570D-16                -2.466261084D+03-1.387413108D+01
6000.000  20000.0007 -2.0 -1.0  0.0  1.0  2.0  3.0  4.0  0.0         8671.104
8.868662960D+08-7.500377840D+05 2.495474979D+02-3.956351100D-02 3.297772080D-06
-1.318409933D-10 1.998937948D-15                 5.701421130D+06-2.060704786D+03
CO2               Gurvich,1991 pt1 p27 pt2 p24.
3 g 9/99 C   1.00O   2.00    0.00    0.00    0.00 0   44.0095000    -393510.000
200.000   1000.0007 -2.0 -1.0  0.0  1.0  2.0  3.0  4.0  0.0         9365.469
4.943650540D+04-6.264116010D+02 5.301725240D+00 2.503813816D-03-2.127308728D-07
-7.689988780D-10 2.849677801D-13                -4.528198460D+04-7.048279440D+00
1000.000   6000.0007 -2.0 -1.0  0.0  1.0  2.0  3.0  4.0  0.0         9365.469
1.176962419D+05-1.788791477D+03 8.291523190D+00-9.223156780D-05 4.863676880D-09
-1.891053312D-12 6.330036590D-16                -3.908350590D+04-2.652669281D+01
6000.000  20000.0007 -2.0 -1.0  0.0  1.0  2.0  3.0  4.0  0.0         9365.469
-1.544423287D+09 1.016847056D+06-2.561405230D+02 3.369401080D-02-2.181184337D-06
6.991420840D-11-8.842351500D-16                -8.043214510D+06 2.254177493D+03
END PRODUCTS
END REACTANTS


This file (saved for example as nasathermo.dat) can then be converted to the CTI format using the ck2cti script:

ck2cti --thermo=nasathermo.dat


To generate a full phase definition, create an input file defining the phase as well, saved for example as nasa.inp:

elements
C O
end

species
CO CO2
end


The two input files can then be converted together by calling:

ck2cti --input=nasa.inp --thermo=nasathermo.dat


### The Shomate Parameterization¶

The Shomate parameterization is:

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

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 can be used for the thermodynamic properties. The const_cp() parameterization computes the properties as follows:

\begin{equation*} \hat{c}_p^0(T) = \hat{c}_p^0(T_0) \end{equation*}
\begin{equation*} \hat{h}^0(T) = \hat{h}^0(T_0) + \hat{c}_p^0\cdot(T-T_0) \end{equation*}
\begin{equation*} \hat{s}^0(T) = \hat{s}^0(T_0) + \hat{c}_p^0 \ln (T/T_0) \end{equation*}

The parameterization uses four constants: $$T_0, \hat{c}_p^0(T_0), \hat{h}^0(T_0), \hat{s}^0(T)$$. The default value of $$T_0$$ is 298.15 K; the default value for the other parameters is 0.0.

Example:

thermo = const_cp(h0=(-393.51, 'kJ/mol'),
s0=(213.785, 'J/mol/K'),
cp0=(37.12, 'J/mol/K'))


Assuming that the units() function has been used to set the default energy units to Joules and the default quantity unit to kmol, this may be equivalently written as:

thermo = const_cp(h0=-3.9351e8, s0=2.13785e5, cp0=3.712e4)


References

1

R. J. Kee, G. Dixon-Lewis, J. Warnatz, M. E. Coltrin, and J. A. Miller. A FORTRAN Computer Code Package for the Evaluation of Gas-Phase, Multicomponent Transport Properties. Technical Report SAND86-8246, Sandia National Laboratories, 1986.

2

B. J. McBride, M. J. Zehe, S. Gordon. “NASA Glenn Coefficients for Calculating Thermodynamic Properties of Individual Species,” NASA/TP-2002-211556, Sept. 2002.