import time
from copy import deepcopy
import numpy as np
from pycalphad import calculate, variables as v
from pycalphad.codegen.callables import build_phase_records
from pycalphad.core.eqsolver import _solve_eq_at_conditions
from pycalphad.core.equilibrium import _adjust_conditions
from pycalphad.core.starting_point import starting_point
from pycalphad.core.utils import instantiate_models, get_state_variables, \
unpack_components, unpack_condition, filter_phases, get_pure_elements
from .compsets import get_compsets, find_two_phase_region_compsets
from .zpf_boundary_sets import ZPFBoundarySets
[docs]
def map_binary(dbf, comps, phases, conds, eq_kwargs=None, calc_kwargs=None,
boundary_sets=None, verbose=False, summary=False,):
"""
Map a binary T-X phase diagram
Parameters
----------
dbf : Database
comps : list of str
phases : list of str
List of phases to consider in mapping
conds : dict
Dictionary of conditions
eq_kwargs : dict
Dictionary of keyword arguments to pass to equilibrium
verbose : bool
Print verbose output for mapping
boundary_sets : ZPFBoundarySets
Existing ZPFBoundarySets
Returns
-------
ZPFBoundarySets
Notes
-----
Assumes conditions in T and X.
Simple algorithm to map a binary phase diagram in T-X. More or less follows
the algorithm described in Figure 2 by Snider et al. [1] with the small
algorithmic improvement of constructing a convex hull to find the next
potential two phase region.
For each temperature, proceed along increasing composition, skipping two
over two phase regions, once calculated.
[1] J. Snider, I. Griva, X. Sun, M. Emelianenko, Set based framework for Gibbs energy minimization, Calphad. 48 (2015) 18-26. doi: 10.1016/j.calphad.2014.09.005
"""
eq_kwargs = eq_kwargs or {}
calc_kwargs = calc_kwargs or {}
# implicitly add v.N to conditions
if v.N not in conds:
conds[v.N] = [1.0]
if 'pdens' not in calc_kwargs:
calc_kwargs['pdens'] = 50
species = unpack_components(dbf, comps)
phases = filter_phases(dbf, species, phases)
parameters = eq_kwargs.get('parameters', {})
models = eq_kwargs.get('model')
statevars = sorted(get_state_variables(models=models, conds=conds), key=str)
if models is None:
models = instantiate_models(dbf, comps, phases, model=eq_kwargs.get('model'),
parameters=parameters, symbols_only=True)
prxs = build_phase_records(dbf, species, phases, conds, models, output='GM',
parameters=parameters, build_gradients=True, build_hessians=True)
indep_comp = [key for key, value in conds.items() if isinstance(key, v.MoleFraction) and len(np.atleast_1d(value)) > 1]
indep_pot = [key for key, value in conds.items() if (type(key) is v.StateVariable) and len(np.atleast_1d(value)) > 1]
if (len(indep_comp) != 1) or (len(indep_pot) != 1):
raise ValueError('Binary map requires exactly one composition and one potential coordinate')
if indep_pot[0] != v.T:
raise ValueError('Binary map requires that a temperature grid must be defined')
# binary assumption, only one composition specified.
comp_cond = [k for k in conds.keys() if isinstance(k, v.X)][0]
indep_comp = comp_cond.name[2:]
indep_comp_idx = sorted(get_pure_elements(dbf, comps)).index(indep_comp)
composition_grid = unpack_condition(conds[comp_cond])
dX = composition_grid[1] - composition_grid[0]
Xmax = composition_grid.max()
temperature_grid = unpack_condition(conds[v.T])
dT = temperature_grid[1] - temperature_grid[0]
boundary_sets = boundary_sets or ZPFBoundarySets(comps, comp_cond)
equilibria_calculated = 0
equilibrium_time = 0
convex_hulls_calculated = 0
convex_hull_time = 0
curr_conds = {key: unpack_condition(val) for key, val in conds.items()}
str_conds = sorted([str(k) for k in curr_conds.keys()])
grid_conds = _adjust_conditions(curr_conds)
for T_idx in range(temperature_grid.size):
T = temperature_grid[T_idx]
iter_equilibria = 0
if verbose:
print("=== T = {} ===".format(float(T)))
curr_conds[v.T] = [float(T)]
eq_conds = deepcopy(curr_conds)
Xmax_visited = 0.0
hull_time = time.time()
grid = calculate(dbf, comps, phases, fake_points=True, output='GM',
T=T, P=grid_conds[v.P], N=1, model=models,
parameters=parameters, to_xarray=False, **calc_kwargs)
hull = starting_point(eq_conds, statevars, prxs, grid)
convex_hull_time += time.time() - hull_time
convex_hulls_calculated += 1
while Xmax_visited < Xmax:
hull_compsets = find_two_phase_region_compsets(hull, T, indep_comp, indep_comp_idx, minimum_composition=Xmax_visited, misc_gap_tol=2*dX)
if hull_compsets is None:
if verbose:
print("== Convex hull: max visited = {} - no multiphase phase compsets found ==".format(Xmax_visited, hull_compsets))
break
Xeq = hull_compsets.mean_composition
eq_conds[comp_cond] = [float(Xeq)]
eq_time = time.time()
start_point = starting_point(eq_conds, statevars, prxs, grid)
eq_ds = _solve_eq_at_conditions(start_point, prxs, grid, str_conds, statevars, False)
equilibrium_time += time.time() - eq_time
equilibria_calculated += 1
iter_equilibria += 1
# composition sets in the plane of the calculation:
# even for isopleths, this should always be two.
compsets = get_compsets(eq_ds, indep_comp, indep_comp_idx)
if verbose:
print("== Convex hull: max visited = {:0.4f} - hull compsets: {} equilibrium compsets: {} ==".format(Xmax_visited, hull_compsets, compsets))
if compsets is None:
# equilibrium calculation, didn't find a valid multiphase composition set
# we need to find the next feasible one from the convex hull.
Xmax_visited += dX
continue
else:
boundary_sets.add_compsets(compsets, Xtol=0.10, Ttol=2*dT)
if compsets.max_composition > Xmax_visited:
Xmax_visited = compsets.max_composition
# this seems kind of sloppy, but captures the effect that we want to
# keep doing equilibrium calculations, if possible.
while Xmax_visited < Xmax and compsets is not None:
eq_conds[comp_cond] = [float(Xmax_visited + dX)]
eq_time = time.time()
# TODO: starting point could be improved by basing it off the previous calculation
start_point = starting_point(eq_conds, statevars, prxs, grid)
eq_ds = _solve_eq_at_conditions(start_point, prxs, grid, str_conds, statevars, False)
equilibrium_time += time.time() - eq_time
equilibria_calculated += 1
compsets = get_compsets(eq_ds, indep_comp, indep_comp_idx)
if compsets is not None:
Xmax_visited = compsets.max_composition
boundary_sets.add_compsets(compsets, Xtol=0.10, Ttol=2*dT)
else:
Xmax_visited += dX
if verbose:
print("Equilibrium: at X = {:0.4f}, found compsets {}".format(Xmax_visited, compsets))
if verbose:
print(iter_equilibria, 'equilibria calculated in this iteration.')
if verbose or summary:
print("{} Convex hulls calculated ({:0.1f}s)".format(convex_hulls_calculated, convex_hull_time))
print("{} Equilbria calculated ({:0.1f}s)".format(equilibria_calculated, equilibrium_time))
print("{:0.0f}% of brute force calculations skipped".format(100*(1-equilibria_calculated/(composition_grid.size*temperature_grid.size))))
return boundary_sets