pycalphad package¶
Subpackages¶
- pycalphad.codegen package
- pycalphad.core package
- Submodules
- pycalphad.core.cache module
- pycalphad.core.calculate module
- pycalphad.core.cartesian module
- pycalphad.core.composition_set module
- pycalphad.core.constants module
- pycalphad.core.constraints module
- pycalphad.core.eqsolver module
- pycalphad.core.equilibrium module
- pycalphad.core.errors module
- pycalphad.core.halton module
- pycalphad.core.hyperplane module
- pycalphad.core.light_dataset module
- pycalphad.core.lower_convex_hull module
- pycalphad.core.minimizer module
- pycalphad.core.phase_rec module
- pycalphad.core.solver module
- pycalphad.core.starting_point module
- pycalphad.core.utils module
- Module contents
- pycalphad.io package
- pycalphad.models package
- pycalphad.plot package
Submodules¶
pycalphad.model module¶
The model module provides support for using a Database to perform calculations under specified conditions.
- class pycalphad.model.Model(*args, **kwargs)[source]¶
Bases:
object
Models use an abstract representation of the function for calculation of values under specified conditions.
- Parameters
dbe (Database) – Database containing the relevant parameters.
comps (list) – Names of components to consider in the calculation.
phase_name (str) – Name of phase model to build.
parameters (dict or list) – Optional dictionary of parameters to be substituted in the model. A list of parameters will cause those symbols to remain symbolic. This will overwrite parameters specified in the database
- constituents¶
A list of sublattices containing the sets of species on each sublattice.
- Type
List[Set[Species]]
- None yet.
Examples
None yet.
Notes
The two sublattice ionic liquid model has several special cases compared to typical models within the compound energy formalism. A few key differences arise. First, variable site ratios (modulated by vacancy site fractions) are used to charge balance the phase. Second, endmembers for neutral species and interactions among only neutral species should be specified using only one sublattice (dropping the cation sublattice). For understanding the special cases used throughout this class, users are referred to: Sundman, “Modification of the two-sublattice model for liquids”, Calphad 15(2) (1991) 109-119 https://doi.org/d3jppb
- BMAG = 0¶
- property CPM¶
- property CPM_MIX¶
- property DOO¶
- property G¶
- property GM¶
- property GM_MIX¶
- property HM¶
- property HM_MIX¶
- NT = 0¶
- property SM¶
- property SM_MIX¶
- TC = 0¶
- property ast¶
Return the full abstract syntax tree of the model.
- atomic_ordering_energy(dbe)[source]¶
Return the atomic ordering contribution in symbolic form.
If the current phase is anything other than the ordered phase in a paritioned order/disorder Gibbs energy model, this method will return zero. If the current phase is the ordered phase, ordering energy is computed by equation (18) of Connetable et al. 1: \(\Delta G^\mathrm{ord}(y_i) = G^\mathrm{ord}(y_i) - G^\mathrm{ord}(y_i = x_i)\)
This method must be the last energy contribution called because it plays several roles that require all other contributions to be defined:
1. The current AST in self.models represents the ordered energy \(G^\mathrm{ord}(y_i)\). To compute the ordering energy, all contributions to the ordered energy must have already been counted.
2. The true energy of the phase should be the sum of the disordered phase’s energy and the ordering energy. That is, \(G = G^\mathrm{dis} + \Delta G^\mathrm{ord}(y_i)\). This method not only computes the ordering energy, but also replaces the other model contributions by the disordered phase’s energy.
3. Physical properties are partitioned in the same way as the energy. See Section 5.8.6 of Lukas, Fries and Sundman 2.
Notes
Caution
This method overwrites the
self.models
dictionary with the model contributions for the disordered phase.This method assumes that the first sublattice of the disordered phase is the substitutional sublattice and all other sublattices are interstitial. In the ordered phase, all sublattices with constituents that match the disordered substitutional sublattice will be treated as disordered (with site fractions replaced by quasi mole fractions in the ordered sublattices) and the interstitial sublattices will not have any site fractions substituted.
References
- beta = 0¶
- build_phase(dbe)[source]¶
Generate the symbolic form of all the contributions to this phase.
- Parameters
dbe (Database) –
- contributions = [('ref', 'reference_energy'), ('idmix', 'ideal_mixing_energy'), ('xsmix', 'excess_mixing_energy'), ('mag', 'magnetic_energy'), ('2st', 'twostate_energy'), ('ein', 'einstein_energy'), ('ord', 'atomic_ordering_energy')]¶
- curie_temperature = 0¶
- property degree_of_ordering¶
- einstein_energy(dbe)[source]¶
Return the energy based on the Einstein model. Note that THETA parameters are actually LN(THETA). All Redlich-Kister summation is done in log-space, then exp() is called on the result.
- property endmember_reference_model¶
Return a Model containing only energy contributions from endmembers.
- Return type
Notes
The endmember_reference_model is used for
_MIX
properties of Model objects. It is defined such that subtracting it from the model will set the energy of the endmembers to zero. The endmember_reference_model AST can be modified in the same way as any Model.Partitioned models have energetic contributions from the ordered compound energies/interactions and the disordered compound energies/interactions. The endmembers to choose as the reference is ambiguous. If the current model has an ordered energy as part of a partitioned model, then the model energy contributions are set to
nan
.The endmember reference model is built lazily and stored for later re-use because it needs to copy the Database and instantiate a new Model.
- property energy¶
- property enthalpy¶
- property entropy¶
- excess_mixing_energy(dbe)[source]¶
Build the binary, ternary and higher order interaction term Here we use Redlich-Kister polynomial basis by default Here we use the Muggianu ternary extension by default Replace y_i -> y_i + (1 - sum(y involved in parameter)) / m, where m is the arity of the interaction parameter
- property formulaenergy¶
- gradient = None¶
- property heat_capacity¶
- magnetic_energy(dbe)[source]¶
Return the energy from magnetic ordering in symbolic form. The implemented model is the Inden-Hillert-Jarl formulation. The approach follows from the background of W. Xiong et al, Calphad, 2012.
- property mixing_energy¶
- property mixing_enthalpy¶
- property mixing_entropy¶
- property mixing_heat_capacity¶
- neel_temperature = 0¶
- redlich_kister_sum(phase, param_search, param_query)[source]¶
Construct parameter in Redlich-Kister polynomial basis, using the Muggianu ternary parameter extension.
- reference_energy(dbe)[source]¶
Returns the weighted average of the endmember energies in symbolic form.
- shift_reference_state(reference_states, dbe, contrib_mods=None, output=('GM', 'HM', 'SM', 'CPM'), fmt_str='{}R')[source]¶
Add new attributes for calculating properties w.r.t. an arbitrary pure element reference state.
- Parameters
reference_states (Iterable of ReferenceState) – Pure element ReferenceState objects. Must include all the pure elements defined in the current model.
dbe (Database) – Database containing the relevant parameters.
output (Iterable, optional) – Parameters to subtract the ReferenceState from, defaults to (‘GM’, ‘HM’, ‘SM’, ‘CPM’).
contrib_mods (Mapping, optional) – Map of {model contribution: new value}. Used to adjust the pure reference model contributions at the time this is called, since the models attribute of the pure element references are effectively static after calling this method.
fmt_str (str, optional) – String that will be formatted with the output parameter name. Defaults to “{}R”, e.g. the transformation of ‘GM’ -> ‘GMR’
- static symbol_replace(obj, symbols)[source]¶
Substitute values of symbols into ‘obj’.
- Parameters
obj (SymEngine object) –
symbols (dict mapping symengine.Symbol to SymEngine object) –
- Return type
SymEngine object
- property variables¶
Return state variables in the model.
- class pycalphad.model.ReferenceState(species, reference_phase, fixed_statevars=None)[source]¶
Bases:
object
Define the phase and any fixed state variables as a reference state for a component.
- fixed_statevars¶
Dictionary of {StateVariable: value} that will be fixed, e.g. {v.T: 298.15, v.P: 101325}
- Type
dict
- phase_name¶
Name of phase
- Type
str
- class pycalphad.model.TestModel(*args, **kwargs)[source]¶
Bases:
pycalphad.model.Model
Test Model object for global minimization.
Equation 15.2 in: P.M. Pardalos, H.E. Romeijn (Eds.), Handbook of Global Optimization, vol. 2. Kluwer Academic Publishers, Boston/Dordrecht/London (2002)
- Parameters
dbf (Database) – Ignored by TestModel but retained for API compatibility.
comps (sequence) – Names of components to consider in the calculation.
phase (str) – Name of phase model to build.
solution (sequence, optional) – Float array locating the true minimum. Same length as ‘comps’. If not specified, randomly generated and saved to self.solution
- None yet.
Examples
None yet.
pycalphad.variables module¶
Classes and constants for representing thermodynamic variables.
- class pycalphad.variables.ChemicalPotential(species)[source]¶
Bases:
pycalphad.variables.StateVariable
Chemical potentials are symbols with built-in assumptions of being real.
- pycalphad.variables.MU¶
- class pycalphad.variables.MassFraction(*args)[source]¶
Bases:
pycalphad.variables.StateVariable
Weight fractions are symbols with built-in assumptions of being real and nonnegative.
- class pycalphad.variables.MoleFraction(*args)[source]¶
Bases:
pycalphad.variables.StateVariable
MoleFractions are symbols with built-in assumptions of being real and nonnegative.
- pycalphad.variables.NP¶
alias of
pycalphad.variables.PhaseFraction
- class pycalphad.variables.PhaseFraction(phase_name)[source]¶
Bases:
pycalphad.variables.StateVariable
Phase fractions are symbols with built-in assumptions of being real and nonnegative. The constructor handles formatting of the name.
- class pycalphad.variables.SiteFraction(phase_name, subl_index, species)[source]¶
Bases:
pycalphad.variables.StateVariable
Site fractions are symbols with built-in assumptions of being real and nonnegative. The constructor handles formatting of the name.
- class pycalphad.variables.Species(name, constituents=None, charge=0)[source]¶
Bases:
object
A chemical species.
- name¶
Name of the specie
- Type
string
- constituents¶
Dictionary of {element: quantity} where the element is a string and the quantity a float.
- Type
dict
- charge¶
Integer charge. Can be positive or negative.
- Type
int
- property escaped_name¶
Name safe to embed in the variable name of complex arithmetic expressions.
- property number_of_atoms¶
Number of atoms per formula unit. Vacancies do not count as atoms.
- property weight¶
Number of grams per formula unit.
- class pycalphad.variables.StateVariable(name)[source]¶
Bases:
symengine.lib.symengine_wrapper.Symbol
State variables are symbols with built-in assumptions of being real.
- pycalphad.variables.W¶
alias of
pycalphad.variables.MassFraction
- pycalphad.variables.X¶
alias of
pycalphad.variables.MoleFraction
- pycalphad.variables.Y¶
alias of
pycalphad.variables.SiteFraction
- pycalphad.variables.get_mass_fractions(mole_fractions, dependent_species, pure_element_mass_dict)[source]¶
Return a mapping of MassFractions for a point composition.
- Parameters
mass_fractions (Mapping[MoleFraction, float]) –
dependent_species (Union[Species, str]) – Dependent species not appearing in the independent mass fractions.
pure_element_mass_dict (Union[Mapping[str, float], pycalphad.Database]) – Either a mapping from pure elements to their mass, or a Database from which they can be retrieved.
- Return type
Dict[MassFraction, float]
- pycalphad.variables.get_mole_fractions(mass_fractions, dependent_species, pure_element_mass_dict)[source]¶
Return a mapping of MoleFractions for a point composition.
- Parameters
mass_fractions (Mapping[MassFraction, float]) –
dependent_species (Union[Species, str]) – Dependent species not appearing in the independent mass fractions.
pure_element_mass_dict (Union[Mapping[str, float], pycalphad.Database]) – Either a mapping from pure elements to their mass, or a Database from which they can be retrieved.
- Return type
Dict[MoleFraction, float]
- pycalphad.variables.site_fraction¶
alias of
pycalphad.variables.SiteFraction