import numpy as np
import warnings
[docs]
class BinaryCompset():
"""
Composition set for representations of a phase equilibria in a two
component system with a temperature condition.
Parameters
----------
phase_name : str
Name of phase
temperature : float
Temperature corresponding the the calculation
indep_comp : str
Name of the independent component
composition : float
Mole fraction of the independent component
site_fracs : np.ndarray
Array of floats corresponding to the site fractions.
Notes
-----
In the future, this representation could be phased out if `equilibrium` returned composition sets.
"""
# tolerances for defining equality between composition sets
SITE_FRAC_ATOL = 0.001
TEMPERATURE_ATOL = 0.1
def __init__(self, phase_name, temperature, indep_comp, composition, site_fracs):
self.phase_name = phase_name
self.temperature = temperature
self.indep_comp = indep_comp
self.composition = composition
self.site_fracs = site_fracs
def __repr__(self,):
return "<BinaryCompset({0}, T={1:0.3f}, X({2})={3:0.3f})>".format(self.phase_name, self.temperature, self.indep_comp, self.composition)
def __str__(self,):
return self.__repr__()
def __eq__(self, other):
if hasattr(other, 'phase_name') and hasattr(other, 'site_fracs') and hasattr(other, 'temperature'):
same_phase = self.phase_name == other.phase_name
site_frac_close = np.all(np.isclose(self.site_fracs, other.site_fracs, atol=self.__class__.SITE_FRAC_ATOL))
temp_close = np.isclose(self.temperature, other.temperature, atol=self.__class__.TEMPERATURE_ATOL)
return same_phase and site_frac_close and temp_close
else:
return False
[docs]
@classmethod
def from_dataset_vertices(cls, ds, indep_comp, indep_comp_idx, num_vertex):
compsets = []
Phase = ds["Phase"].squeeze()
T = np.array(ds["T"]).squeeze()
X = ds["X"].squeeze()
Y = ds["Y"].squeeze()
for i in range(num_vertex):
phase_name = Phase[i]
if phase_name != '':
compsets.append(cls(str(phase_name),
T,
indep_comp,
X[i, indep_comp_idx],
Y[i, :],
))
return compsets
[docs]
class CompsetPair():
"""
Pair of binary composition sets that make up an equilibrium
Parameters
----------
compsets : list of BinaryCompset
Attributes
----------
compsets : list of BinaryCompset
CompSets sorted by composition
a : BinaryCompset
Composition set in the pair with the lower composition
b : BinaryCompset
Composition set in the pair with the higher composition
phases : list of str
List of phase names, sorted by composition
unique_phases : set of str
Set of phase names
compositions : np.ndarray
Array of compositions, sorted
temperature : float
Temperature of the 2D compsets
same_phase : bool
Whether the composition sets are for the same phase
mean_composition : float
Mean composition of the CompSets
max_composition : float
Max composition of the CompSets
min_composition : float
Min composition of the CompSets
"""
def __init__(self, compsets):
_composition_key_func = lambda c: c.composition
sorted_compsets = sorted(compsets, key=_composition_key_func)
phases = [c.phase_name for c in sorted_compsets]
compositions = np.array([c.composition for c in sorted_compsets])
a = sorted_compsets[0]
b = sorted_compsets[1]
self._orig_compsets = compsets # with original sorting
self.compsets = sorted_compsets
self.phases = phases
self.unique_phases = frozenset(phases)
self.a = a
self.b = b
self.same_phase = a.phase_name == b.phase_name
self.compositions = compositions
self.mean_composition = np.mean(compositions)
self.min_composition = a.composition
self.max_composition = b.composition
if a.temperature == b.temperature:
self.temperature = a.temperature
else:
warnings.warn("Temperatures are different for CompSet objects {}. Assuming that the pair temperature is ".format(sorted_compsets, a.temperature))
self.temperature = a.temperature
[docs]
def xdiscrepancy(self, ignore_phase=False):
"""
Calculate the composition discrepancy (absolute difference) between this
composition set and another.
Parameters
----------
ignore_phase : bool
If False, unlike phases will give infinite discrepancy. If True, we
only care about the composition and the real discrepancy will be returned.
Returns
-------
np.float64
"""
if self.same_phase or ignore_phase:
return np.abs(self.a.composition - self.b.composition)
else:
return np.infty
[docs]
def ydiscrepancy(self):
"""
Calculate the discrepancy (absolute differences) between the site
fractions of the composition sets as an array of discrepancies.
Returns
-------
Array of np.float64
Notes
-----
The phases must match for this to be meaningful.
"""
if self.same_phase:
return np.abs(self.a.site_fracs - self.b.site_fracs)
else:
return np.infty
[docs]
def ydiscrepancy_max(self):
"""
Calculate the maximum discrepancy (absolute difference) between the site
fractions of the composition sets.
Returns
-------
np.float64
Notes
-----
The phases must match for this to be meaningful.
"""
return np.max(np.abs(self.ydiscrepancy()))
[docs]
def Tdiscrepancy(self, other):
"""
Calculate the temperature discrepancy (absolute difference) between this
pair of composition sets and another.
Parameters
----------
other : CompsetPair
Returns
-------
np.float64
"""
return np.abs(self.temperature - other.temperature)
def __repr__(self,):
compset_strs = ", ".join(["{0}:<X({1})={2:0.3f}>".format(c.phase_name, c.indep_comp, c.composition) for c in self.compsets])
return "CompSet2D(T={0:0.3f}: ({1})".format(self.temperature, compset_strs)
def __str__(self,):
return self.__repr__()
[docs]
def pairwise_xdiscrepancy(self, other):
"""
Compute the ordered composition discrepancy between this and another
pair of CompSet2D objects.
Parameters
----------
other : CompsetPair
Returns
-------
float
"""
if self.phases == other.phases:
return np.abs(self.compositions - other.compositions)
else:
return np.full(self.compositions.shape, np.infty)
[docs]
def get_compsets(eq_dataset, indep_comp=None, indep_comp_index=None):
"""
Return a CompSet2D object if a pair of composition sets is found in an
equilibrium dataset. Otherwise return None.
Parameters
----------
eq_dataset :
indep_comp :
indep_comp_index :
Returns
-------
CompsetPair
"""
if indep_comp is None:
indep_comp = [c for c in eq_dataset.coords if 'X_' in c][0][2:]
if indep_comp_index is None:
indep_comp_index = eq_dataset.component.values.tolist().index(indep_comp)
extracted_compsets = BinaryCompset.from_dataset_vertices(eq_dataset, indep_comp, indep_comp_index, 3)
if len(extracted_compsets) == 2:
return CompsetPair(extracted_compsets)
else:
return None
[docs]
def find_two_phase_region_compsets(hull, temperature, indep_comp, indep_comp_idx, misc_gap_tol=0.1, minimum_composition=None):
"""
From a 1D convex hull at constant T and P, return the composition sets for
a two phase region or that have the smallest index composition coordinate
Parameters
----------
hull : EquilibriumResult
Equilibrium-like from pycalphad that has a `Phase` Data variable.
temperature : float
Temperature that the calculation was performed at
indep_comp : str
Name of the independent component
indep_comp_idx : str
Index of the independent component in the the sorted pure elements
misc_gap_tol : float
If any site fractions are different by at least this amount, the
composition sets are considered distinct and in a miscibility gap.
minimum_composition : float
Minimum composition in the convex hull to search for composition sets
Returns
-------
CompsetPair
"""
phases = hull.Phase.squeeze()
compositions = hull.X.squeeze()
site_fracs = hull.Y.squeeze()
grid_shape = phases.shape[:-1]
num_phases = phases.shape[-1]
it = np.nditer(np.empty(grid_shape), flags=['multi_index']) # empty grid for indexing
while not it.finished:
idx = it.multi_index
cs = []
# TODO: assumption of only two phases, seems like the third phase index can have bad points
# Three phases is probably an error anyways...
if minimum_composition is not None and np.all(compositions[idx][:, indep_comp_idx][:2] < minimum_composition):
it.iternext()
continue
for i in np.arange(num_phases):
if str(phases[idx][i]) != '':
stable_composition_sets = BinaryCompset(str(phases[idx][i]), temperature, indep_comp, compositions[idx][i, indep_comp_idx], site_fracs[idx][i, :])
cs.append(stable_composition_sets)
if len(cs) == 2:
compsets = CompsetPair(cs)
if len(compsets.unique_phases) == 2:
return compsets # found a multiphase region
else:
# Same phase, either single phase region or a miscibility gap.
y_discrep = compsets.ydiscrepancy()
if np.any(y_discrep[~np.isnan(y_discrep)] > misc_gap_tol):
return compsets # miscibility gap
it.iternext()
return None