def binplot(dbf, comps, phases, x_variable, low_temp, high_temp,
steps=None, ax=None, **kwargs):
"""
Calculate the binary isobaric phase diagram for the given temperature
range.
Parameters
----------
dbf : Database
Thermodynamic database containing the relevant parameters.
comps : list
Names of components to consider in the calculation.
phases : list
Names of phases to consider in the calculation.
x_variable : string
Name of the x-axis variable to plot, e.g., 'X(FE)'
low_temp : float
Lower bound of temperature to calculate.
high_temp : float
Upper bound of temperature to calculate.
steps : int, optional
Number of temperature steps to take between `low_temp` and `high_temp`.
ax : Matplotlib Axes object, optional
pdens : int, optional
Number of points to sample per sublattice, per degree of freedom.
ast : ['numpy', 'numexpr'], optional
Specify how we should construct the callable for the energy.
Returns
-------
A phase diagram as a figure.
Examples
--------
None yet.
"""
assert high_temp > low_temp
tie_lines = []
tie_line_colors = []
tie_line_widths = []
tsteps = steps or int((high_temp-low_temp) / 10) # Take 10 K steps by def.
temps = np.array(np.linspace(low_temp, high_temp, num=tsteps),
dtype=np.float64)
# Convert all phase names to uppercase
phases = [phase.upper() for phase in phases]
try:
pdens = kwargs.pop('pdens')
except KeyError:
pdens = 1000 # points per d.o.f
# Calculate energy surface at each temperature
full_df = energy_surf(dbf, comps, phases, T=temps, pdens=pdens,
**kwargs)
# Select only the P, T, etc., of interest
full_df = full_df.groupby('T', sort=False)
for temp, hull_frame in full_df:
# Calculate the convex hull for the desired points
hull_points = hull_frame[[x_variable, 'GM']].values
hull = None
try:
hull = scipy.spatial.ConvexHull(
hull_points, qhull_options='QJ'
)
del hull_points
except RuntimeError:
print('temperature: '+str(temp))
raise
# keep track of tie line orientations
# this is for invariant reaction detection
tieline_normals = []
current_tielines = []
# this was factored out of the loop based on profiling
coordinates = hull_frame.iloc[np.asarray(hull.simplices).ravel()].values
# Reshape coordinates into rank 3 ndarray of simplex coordinates
# Each point is ordered as: Energy, Phase Name, Coordinates
coordinates.shape = (len(hull.simplices), len(hull.simplices[0]),
len(coordinates[0]))
columns = list(hull_frame.columns)
for coords, equ in \
zip(coordinates, hull.equations):
if equ[-2] > -1e-6:
# simplex oriented 'upwards' in energy direction
# must not be part of the energy surface
continue
#distances = scipy.spatial.distance.pdist(coords)
#simplex_edges = \
# np.asarray(list(itertools.combinations(simplex, 2)))
#phase_edge_list = hull_frame['Phase'].values[simplex_edges]
#edge_phases_match = \
## np.array(phase_edge_list[:, 0] == phase_edge_list[:, 1])
#new_lines = simplex_edges
# Check if this is a two phase region
first_endpoint = coords[0]
second_endpoint = coords[1]
phases_match = first_endpoint[columns.index('Phase')] == \
second_endpoint[columns.index('Phase')]
if phases_match:
# Is this a miscibility gap region?
# Check that the average of the tieline energy is less than
# the energy calculated at the midpoint
# If not, this is a single-phase region and should be dropped
#phase_name = first_endpoint[columns.index('Phase')]
#input_cols = [x for x in hull_frame.columns if phase_name in x]
#midpoint = np.mean([first_endpoint.ix[input_cols].values, \
# second_endpoint.ix[input_cols].values], axis=0)
# chebyshev distance returns maximum difference between any
# dimension
#pxd = scipy.spatial.distance.chebyshev(
# first_endpoint.ix[input_cols].values, \
# second_endpoint.ix[input_cols].values)
pxd = scipy.spatial.distance.chebyshev(
first_endpoint[columns.index(x_variable)], \
second_endpoint[columns.index(x_variable)])
if pxd < 0.03:
continue
# energy at midpoint
#midpoint_nrg = nrg[phase_name](*midpoint)
# average energy of endpoints
#average_nrg = (0.5 * (first_endpoint.ix['GM'] + \
# second_endpoint.ix['GM']))
#if average_nrg >= midpoint_nrg:
# # not a true tieline, drop this simplex
# continue
# if we get here, this is a miscibility gap region or a
# two-phase region
current_tielines.append(
[[first_endpoint[columns.index(x_variable)], temp, \
first_endpoint[columns.index('Phase')]], \
[second_endpoint[columns.index(x_variable)], temp, \
second_endpoint[columns.index('Phase')]]]
)
tieline_norm = equ[:-1]
tieline_normals.append(tieline_norm)
# enumerate all normals but the one we just added
for idx, normal in enumerate(tieline_normals[:-1]):
continue
dihedral = np.dot(normal, tieline_norm)
if dihedral > (1.0 - 1e-11):
# nearly coplanar: we are near a 3-phase boundary
# red for an invariant
tie_lines.append(current_tielines[-1])
tie_lines.append(current_tielines[idx])
# prevent double counting
#del current_tielines[idx]
#del current_tielines[-1]
tie_line_colors.append([1, 0, 0, 1])
tie_line_widths.append(2)
tie_line_colors.append([1, 0, 0, 1])
tie_line_widths.append(2)
for line in current_tielines:
# Green for a tie line
tie_lines.append(line)
tie_line_colors.append([0, 1, 0, 1])
tie_line_widths.append(0.5)
tie_lines = np.asarray(tie_lines)
if ax is None:
ax = plt.gca()
ax = _binplot_setup(ax, phases, tie_lines, tie_line_colors, tie_line_widths)
plot_title = '-'.join([x.title() for x in sorted(comps) if x != 'VA'])
ax.set_title(plot_title, fontsize=20)
ax.set_xlim([-0.01, 1.01])
ax.set_ylim([low_temp, high_temp])
ax.set_xlabel(x_variable, labelpad=15, fontsize=20)
ax.set_ylabel("Temperature (K)", fontsize=20)
return ax
def binplot(dbf,
comps,
phases,
x_variable,
low_temp,
high_temp,
steps=None,
ax=None,
**kwargs):
"""
Calculate the binary isobaric phase diagram for the given temperature
range.
Parameters
----------
dbf : Database
Thermodynamic database containing the relevant parameters.
comps : list
Names of components to consider in the calculation.
phases : list
Names of phases to consider in the calculation.
x_variable : string
Name of the x-axis variable to plot, e.g., 'X(FE)'
low_temp : float
Lower bound of temperature to calculate.
high_temp : float
Upper bound of temperature to calculate.
steps : int, optional
Number of temperature steps to take between `low_temp` and `high_temp`.
ax : Matplotlib Axes object, optional
pdens : int, optional
Number of points to sample per sublattice, per degree of freedom.
ast : ['numpy', 'numexpr'], optional
Specify how we should construct the callable for the energy.
Returns
-------
A phase diagram as a figure.
Examples
--------
None yet.
"""
assert high_temp > low_temp
tie_lines = []
tie_line_colors = []
tie_line_widths = []
tsteps = steps or int(
(high_temp - low_temp) / 10) # Take 10 K steps by def.
temps = np.array(np.linspace(low_temp, high_temp, num=tsteps),
dtype=np.float64)
# Convert all phase names to uppercase
phases = [phase.upper() for phase in phases]
try:
pdens = kwargs.pop('pdens')
except KeyError:
pdens = 1000 # points per d.o.f
# Calculate energy surface at each temperature
full_df = energy_surf(dbf, comps, phases, T=temps, pdens=pdens, **kwargs)
# Select only the P, T, etc., of interest
full_df = full_df.groupby('T', sort=False)
for temp, hull_frame in full_df:
# Calculate the convex hull for the desired points
hull_points = hull_frame[[x_variable, 'GM']].values
hull = None
try:
hull = scipy.spatial.ConvexHull(hull_points, qhull_options='QJ')
del hull_points
except RuntimeError:
print('temperature: ' + str(temp))
raise
# keep track of tie line orientations
# this is for invariant reaction detection
tieline_normals = []
current_tielines = []
# this was factored out of the loop based on profiling
coordinates = hull_frame.iloc[np.asarray(
hull.simplices).ravel()].values
# Reshape coordinates into rank 3 ndarray of simplex coordinates
# Each point is ordered as: Energy, Phase Name, Coordinates
coordinates.shape = (len(hull.simplices), len(hull.simplices[0]),
len(coordinates[0]))
columns = list(hull_frame.columns)
for coords, equ in \
zip(coordinates, hull.equations):
if equ[-2] > -1e-6:
# simplex oriented 'upwards' in energy direction
# must not be part of the energy surface
continue
#distances = scipy.spatial.distance.pdist(coords)
#simplex_edges = \
# np.asarray(list(itertools.combinations(simplex, 2)))
#phase_edge_list = hull_frame['Phase'].values[simplex_edges]
#edge_phases_match = \
## np.array(phase_edge_list[:, 0] == phase_edge_list[:, 1])
#new_lines = simplex_edges
# Check if this is a two phase region
first_endpoint = coords[0]
second_endpoint = coords[1]
phases_match = first_endpoint[columns.index('Phase')] == \
second_endpoint[columns.index('Phase')]
if phases_match:
# Is this a miscibility gap region?
# Check that the average of the tieline energy is less than
# the energy calculated at the midpoint
# If not, this is a single-phase region and should be dropped
#phase_name = first_endpoint[columns.index('Phase')]
#input_cols = [x for x in hull_frame.columns if phase_name in x]
#midpoint = np.mean([first_endpoint.ix[input_cols].values, \
# second_endpoint.ix[input_cols].values], axis=0)
# chebyshev distance returns maximum difference between any
# dimension
#pxd = scipy.spatial.distance.chebyshev(
# first_endpoint.ix[input_cols].values, \
# second_endpoint.ix[input_cols].values)
pxd = scipy.spatial.distance.chebyshev(
first_endpoint[columns.index(x_variable)], \
second_endpoint[columns.index(x_variable)])
if pxd < 0.03:
continue
# energy at midpoint
#midpoint_nrg = nrg[phase_name](*midpoint)
# average energy of endpoints
#average_nrg = (0.5 * (first_endpoint.ix['GM'] + \
# second_endpoint.ix['GM']))
#if average_nrg >= midpoint_nrg:
# # not a true tieline, drop this simplex
# continue
# if we get here, this is a miscibility gap region or a
# two-phase region
current_tielines.append(
[[first_endpoint[columns.index(x_variable)], temp, \
first_endpoint[columns.index('Phase')]], \
[second_endpoint[columns.index(x_variable)], temp, \
second_endpoint[columns.index('Phase')]]]
)
tieline_norm = equ[:-1]
tieline_normals.append(tieline_norm)
# enumerate all normals but the one we just added
for idx, normal in enumerate(tieline_normals[:-1]):
continue
dihedral = np.dot(normal, tieline_norm)
if dihedral > (1.0 - 1e-11):
# nearly coplanar: we are near a 3-phase boundary
# red for an invariant
tie_lines.append(current_tielines[-1])
tie_lines.append(current_tielines[idx])
# prevent double counting
#del current_tielines[idx]
#del current_tielines[-1]
tie_line_colors.append([1, 0, 0, 1])
tie_line_widths.append(2)
tie_line_colors.append([1, 0, 0, 1])
tie_line_widths.append(2)
for line in current_tielines:
# Green for a tie line
tie_lines.append(line)
tie_line_colors.append([0, 1, 0, 1])
tie_line_widths.append(0.5)
tie_lines = np.asarray(tie_lines)
if ax is None:
ax = plt.gca()
ax = _binplot_setup(ax, phases, tie_lines, tie_line_colors,
tie_line_widths)
plot_title = '-'.join([x.title() for x in sorted(comps) if x != 'VA'])
ax.set_title(plot_title, fontsize=20)
ax.set_xlim([-0.01, 1.01])
ax.set_ylim([low_temp, high_temp])
ax.set_xlabel(x_variable, labelpad=15, fontsize=20)
ax.set_ylabel("Temperature (K)", fontsize=20)
return ax
def test_unknown_model_attribute():
"Sampling an unknown model attribute raises exception."
energy_surf(DBF, ['AL', 'CR', 'NI'], ['L12_FCC'],
T=1400.0, output='_fail_')
def test_surface():
"Bare minimum: energy_surf produces a result."
energy_surf(DBF, ['AL', 'CR', 'NI'], ['L12_FCC'],
T=1273., mode='numpy')
def test_surface():
energy_surf(DBF, ['AL', 'CR', 'NI'], ['L12_FCC'],
T=1273, pdens=10, mode='numpy')
def test_unknown_model_attribute():
"Sampling an unknown model attribute raises exception."
energy_surf(DBF, ['AL', 'CR', 'NI'], ['L12_FCC'],
T=1400.0,
output='_fail_')
def test_surface():
"Bare minimum: energy_surf produces a result."
energy_surf(DBF, ['AL', 'CR', 'NI'], ['L12_FCC'], T=1273., mode='numpy')