Source code for ase.phasediagram

from __future__ import division, print_function
import fractions
import functools
import re

import numpy as np
from scipy.spatial import ConvexHull, Delaunay

import ase.units as units
from ase.atoms import string2symbols
from ase.utils import hill


_solvated = []


def parse_formula(formula):
    aq = formula.endswith('(aq)')
    if aq:
        formula = formula[:-4]
    charge = formula.count('+') - formula.count('-')
    if charge:
        formula = formula.rstrip('+-')
    count = {}
    for symbol in string2symbols(formula):
        count[symbol] = count.get(symbol, 0) + 1
    return count, charge, aq

    
def float2str(x):
    f = fractions.Fraction(x).limit_denominator(100)
    n = f.numerator
    d = f.denominator
    if abs(n / d - f) > 1e-6:
        return '{0:.3f}'.format(f)
    if d == 0:
        return '0'
    if f.denominator == 1:
        return str(n)
    return '{0}/{1}'.format(f.numerator, f.denominator)
    
    
[docs]def solvated(symbols): """Extract solvation energies from database. symbols: str Extract only those molecules that contain the chemical elements given by the symbols string (plus water and H+). Data from: Johnson JW, Oelkers EH, Helgeson HC (1992) Comput Geosci 18(7):899. doi:10.1016/0098-3004(92)90029-Q and: Pourbaix M (1966) Atlas of electrochemical equilibria in aqueous solutions. No. v. 1 in Atlas of Electrochemical Equilibria in Aqueous Solutions. Pergamon Press, New York. Returns list of (name, energy) tuples. """ if isinstance(symbols, str): symbols = set(string2symbols(symbols)) if len(_solvated) == 0: for line in _aqueous.splitlines(): energy, formula = line.split(',') name = formula + '(aq)' count, charge, aq = parse_formula(name) energy = float(energy) * 0.001 * units.kcal / units.mol _solvated.append((name, count, charge, aq, energy)) references = [] for name, count, charge, aq, energy in _solvated: for symbol in count: if symbol not in 'HO' and symbol not in symbols: break else: references.append((name, energy)) return references
def bisect(A, X, Y, f): a = [] for i in [0, -1]: for j in [0, -1]: if A[i, j] == -1: A[i, j] = f(X[i], Y[j]) a.append(A[i, j]) if np.ptp(a) == 0: A[:] = a[0] return if a[0] == a[1]: A[0] = a[0] if a[1] == a[3]: A[:, -1] = a[1] if a[3] == a[2]: A[-1] = a[3] if a[2] == a[0]: A[:, 0] = a[2] if not (A == -1).any(): return i = len(X) // 2 j = len(Y) // 2 bisect(A[:i + 1, :j + 1], X[:i + 1], Y[:j + 1], f) bisect(A[:i + 1, j:], X[:i + 1], Y[j:], f) bisect(A[i:, :j + 1], X[i:], Y[:j + 1], f) bisect(A[i:, j:], X[i:], Y[j:], f) def print_results(results): total_energy = 0.0 print('reference coefficient energy') print('------------------------------------') for name, coef, energy in results: total_energy += coef * energy if abs(coef) < 1e-7: continue print('{0:14}{1:>10}{2:12.3f}'.format(name, float2str(coef), energy)) print('------------------------------------') print('Total energy: {0:22.3f}'.format(total_energy)) print('------------------------------------')
[docs]class Pourbaix: def __init__(self, references, formula=None, T=300.0, **kwargs): """Pourbaix object. references: list of (name, energy) tuples Examples of names: ZnO2, H+(aq), H2O(aq), Zn++(aq), ... formula: str Stoichiometry. Example: ``'ZnO'``. Can also be given as keyword arguments: ``Pourbaix(refs, Zn=1, O=1)``. T: float Temperature in Kelvin. """ if formula: assert not kwargs kwargs = parse_formula(formula)[0] self.kT = units.kB * T self.references = [] for name, energy in references: if name == 'O': continue count, charge, aq = parse_formula(name) for symbol in count: if aq: if not (symbol in 'HO' or symbol in kwargs): break else: if symbol not in kwargs: break else: self.references.append((count, charge, aq, energy, name)) self.references.append(({}, -1, False, 0.0, 'e-')) # an electron self.count = kwargs if 'O' not in self.count: self.count['O'] = 0 self.N = {'e-': 0, 'H': 1} for symbol in kwargs: if symbol not in self.N: self.N[symbol] = len(self.N)
[docs] def decompose(self, U, pH, verbose=True, concentration=1e-6): """Decompose material. U: float Potential in eV. pH: float pH value. verbose: bool Default is True. concentration: float Concentration of solvated references. Returns optimal coefficients and energy. """ alpha = np.log(10) * self.kT entropy = -np.log(concentration) * self.kT # We want to minimize np.dot(energies, x) under the constraints: # # np.dot(x, eq2) == eq1 # # with bounds[i,0] <= x[i] <= bounds[i, 1]. # # First two equations are charge and number of hydrogens, and # the rest are the remaining species. eq1 = [0, 0] + list(self.count.values()) eq2 = [] energies = [] bounds = [] names = [] for count, charge, aq, energy, name in self.references: eq = np.zeros(len(self.N)) eq[0] = charge for symbol, n in count.items(): eq[self.N[symbol]] = n eq2.append(eq) if name in ['H2O(aq)', 'H+(aq)', 'e-']: bounds.append((-np.inf, np.inf)) if name == 'e-': energy = -U elif name == 'H+(aq)': energy = -pH * alpha else: bounds.append((0, 1)) if aq: energy -= entropy if verbose: print('{0:<5}{1:10}{2:10.3f}'.format(len(energies), name, energy)) energies.append(energy) names.append(name) try: from scipy.optimize import linprog except ImportError: from ase.utils._linprog import linprog result = linprog(energies, None, None, np.transpose(eq2), eq1, bounds) if verbose: print_results(zip(names, result.x, energies)) return result.x, result.fun
[docs] def diagram(self, U, pH, plot=True, show=True): """Calculate Pourbaix diagram. U: list of float Potentials in eV. pH: list of float pH values. plot: bool Create plot. show: bool Show plot. """ a = np.empty((len(U), len(pH)), int) a[:] = -1 colors = {} f = functools.partial(self.colorfunction, colors=colors) bisect(a, U, pH, f) compositions = [None] * len(colors) names = [ref[-1] for ref in self.references] for indices, color in colors.items(): compositions[color] = ' + '.join(names[i] for i in indices if names[i] not in ['H2O(aq)', 'H+(aq)', 'e-']) text = [] for i, name in enumerate(compositions): b = (a == i) x = np.dot(b.sum(1), U) / b.sum() y = np.dot(b.sum(0), pH) / b.sum() name = re.sub('(\S)([+-]+)', r'\1$^{\2}$', name) name = re.sub('(\d+)', r'$_{\1}$', name) text.append((x, y, name)) if plot: import matplotlib.pyplot as plt import matplotlib.cm as cm plt.pcolormesh(pH, U, a, cmap=cm.Accent) for x, y, name in text: plt.text(y, x, name, horizontalalignment='center') plt.xlabel('pH') plt.ylabel('potential [eV]') plt.xlim(min(pH), max(pH)) plt.ylim(min(U), max(U)) if show: plt.show() return a, compositions, text
def colorfunction(self, U, pH, colors): coefs, energy = self.decompose(U, pH, verbose=False) indices = tuple(sorted(np.where(abs(coefs) > 1e-7)[0])) color = colors.get(indices) if color is None: color = len(colors) colors[indices] = color return color
[docs]class PhaseDiagram: def __init__(self, references, filter='', verbose=True): """Phase-diagram. references: list of (name, energy) tuples List of references. The names can also be dicts like ``{'Zn': 1, 'O': 2}`` which would be equivalent to ``'ZnO2'``. filter: str or list of str Use only those references that match the given filter. Example: ``filter='ZnO'`` will select those that contain zinc or oxygen. verbose: bool Write information. """ filter = parse_formula(filter)[0] self.verbose = verbose self.species = {} self.references = [] for name, energy in references: if isinstance(name, str): count = parse_formula(name)[0] else: count = name name = hill(count) if filter and any(symbol not in filter for symbol in count): continue natoms = 0 for symbol, n in count.items(): natoms += n if symbol not in self.species: self.species[symbol] = len(self.species) self.references.append((count, energy, name, natoms)) if verbose: print('Species:', ', '.join(self.species)) print('References:', len(self.references)) for i, (count, energy, name, natoms) in enumerate(self.references): print('{0:<5}{1:10}{2:10.3f}'.format(i, name, energy)) self.points = np.zeros((len(self.references), len(self.species) + 1)) for s, (count, energy, name, natoms) in enumerate(self.references): for symbol, n in count.items(): self.points[s, self.species[symbol]] = n / natoms self.points[s, -1] = energy / natoms hull = ConvexHull(self.points[:, 1:]) # Find relevant vertices: ok = hull.equations[:, -2] < 0 vertices = set() for simplex in hull.simplices[ok]: vertices.update(simplex) self.vertices = np.array(list(vertices)) if verbose: print('Simplices:', ok.sum()) # Create triangulation: if len(self.species) == 2: D = Delaunay1D # scipy's Delaunay doesn't like 1-d! else: D = Delaunay self.tri = D(self.points[self.vertices, 1:-1])
[docs] def decompose(self, formula=None, **kwargs): """Find the combination of the references with the lowest energy. formula: str Stoichiometry. Example: ``'ZnO'``. Can also be given as keyword arguments: ``decompose(Zn=1, O=1)``. Example:: pd = PhaseDiagram(...) pd.decompose(Zn=1, O=3) Returns energy, indices of references and coefficients.""" if formula: assert not kwargs kwargs = parse_formula(formula)[0] point = np.zeros(len(self.species)) natoms = 0 for symbol, n in kwargs.items(): point[self.species[symbol]] = n natoms += n i = self.tri.find_simplex(point[1:] / natoms) indices = self.vertices[self.tri.simplices[i]] points = self.points[indices] scaledcoefs = np.linalg.solve(points[:, :-1].T, point) energy = np.dot(scaledcoefs, points[:, -1]) coefs = [] results = [] for coef, s in zip(scaledcoefs, indices): count, e, name, natoms = self.references[s] coef /= natoms coefs.append(coef) results.append((name, coef, e)) if self.verbose: print_results(results) return energy, indices, np.array(coefs)
[docs] def plot(self): """Plot datapoints and convex hull. Works only for 2 and 3 components systems. """ if len(self.species) == 2: self.plot2d() elif len(self.species) == 3: self.plot3d() else: raise ValueError('...')
def plot2d(self): import matplotlib.pyplot as plt x, y = self.points[:, 1:].T xsymbol = [symbol for symbol, id in self.species.items() if id == 1][0] plt.plot(x, y, 'or') for i, j in self.tri.simplices: plt.plot([x[i], x[j]], [y[i], y[j]], '-g') for count, energy, name, natoms in self.references: name = re.sub('(\d+)', r'$_{\1}$', name) plt.text(count.get(xsymbol, 0) / natoms, energy / natoms, name, horizontalalignment='center', verticalalignment='bottom') plt.xlabel(xsymbol) plt.ylabel('energy') plt.show()
class Delaunay1D: """Simple 1-d implementation.""" def __init__(self, points): self.points = points[:, 0] a = self.points.argsort() self.simplices = np.array([a[:-1], a[1:]]).T def find_simplex(self, point): p = point[0] for i, s in enumerate(self.simplices[:, 1]): if p < self.points[s]: return i return i + 1 _aqueous = """\ -525700,SiF6-- -514100,Rh(SO4)3---- -504800,Ru(SO4)3---- -499900,Pd(SO4)3---- -495200,Ru(SO4)3--- -485700,H4P2O7 -483700,Rh(SO4)3--- -483600,H3P2O7- -480400,H2P2O7-- -480380,Pt(SO4)3---- -471400,HP2O7--- -458700,P2O7---- -447500,LaF4- -437600,LaH2PO4++ -377900,LaF3 -376299,Ca(HSiO3)+ -370691,BeF4-- -355400,BF4- -353025,Mg(HSiO3)+ -346900,LaSO4+ -334100,Rh(SO4)2-- -325400,Ru(SO4)2-- -319640,Pd(SO4)2-- -317900,Ru(SO4)2- -312970,Cr2O7-- -312930,CaSO4 -307890,NaHSiO3 -307800,LaF2+ -307000,LaHCO3++ -306100,Rh(SO4)2- -302532,BeF3- -300670,Pt(SO4)2-- -299900,LaCO3+ -289477,MgSO4 -288400,LaCl4- -281500,HZrO3- -279200,HHfO3- -276720,Sr(HCO3)+ -275700,Ba(HCO3)+ -273830,Ca(HCO3)+ -273100,H3PO4 -270140,H2PO4- -266500,S2O8-- -264860,Sr(CO3) -264860,SrCO3 -263830,Ba(CO3) -263830,BaCO3 -262850,Ca(CO3) -262850,CaCO3 -260310,HPO4-- -257600,LaCl3 -250200,Mg(HCO3)+ -249200,H3VO4 -248700,S4O6-- -246640,KSO4- -243990,H2VO4- -243500,PO4--- -243400,KHSO4 -242801,HSiO3- -241700,HYO2 -241476,NaSO4- -239700,HZrO2+ -239300,LaO2H -238760,Mg(CO3) -238760,MgCO3 -237800,HHfO2+ -236890,Ag(CO3)2--- -236800,HNbO3 -236600,LaF++ -235640,MnSO4 -233400,ZrO2 -233000,HVO4-- -231600,HScO2 -231540,B(OH)3 -231400,HfO2 -231386,BeF2 -231000,S2O6-- -229000,S3O6-- -229000,S5O6-- -228460,HTiO3- -227400,YO2- -227100,NbO3- -226700,LaCl2+ -223400,HWO4- -221700,LaO2- -218500,WO4-- -218100,ScO2- -214900,VO4--- -210000,YOH++ -208900,LaOH++ -207700,HAlO2 -206400,HMoO4- -204800,H3PO3 -202350,H2PO3- -202290,SrF+ -201807,BaF+ -201120,BaF+ -200400,MoO4-- -200390,CaF+ -199190,SiO2 -198693,AlO2- -198100,YO+ -195900,LaO+ -195800,LaCl++ -194000,CaCl2 -194000,HPO3-- -191300,LaNO3++ -190400,ZrOH+++ -189000,HfOH+++ -189000,S2O5-- -187600,ZrO++ -186000,HfO++ -183700,HCrO4- -183600,ScO+ -183100,H3AsO4 -180630,HSO4- -180010,H2AsO4- -177930,SO4-- -177690,MgF+ -174800,CrO4-- -173300,SrOH+ -172300,BaOH+ -172200,HBeO2- -171300,CaOH+ -170790,HAsO4-- -166000,ReO4- -165800,SrCl+ -165475,Al(OH)++ -165475,AlOH++ -164730,BaCl+ -164000,La+++ -163800,Y+++ -163100,CaCl+ -162240,BO2- -158493,BeF+ -158188,AlO+ -155700,VOOH+ -155164,CdF2 -154970,AsO4--- -153500,Rh(SO4) -152900,BeO2-- -152370,HSO5- -151540,RuCl6--- -149255,MgOH+ -147400,H2S2O4 -146900,HS2O4- -146081,CdCl4-- -145521,BeCl2 -145200,Ru(SO4) -145056,PbF2 -143500,S2O4-- -140330,H2AsO3- -140300,VO2+ -140282,HCO3- -140200,Sc+++ -139900,BeOH+ -139700,MgCl+ -139200,Ru(SO4)+ -139000,Pd(SO4) -138160,HF2- -138100,HCrO2 -138000,TiO++ -137300,HGaO2 -136450,RbF -134760,Sr++ -134030,Ba++ -133270,Zr++++ -133177,PbCl4-- -132600,Hf++++ -132120,Ca++ -129310,ZnCl3- -128700,GaO2- -128600,BeO -128570,NaF -128000,H2S2O3 -127500,Rh(SO4)+ -127200,HS2O3- -126191,CO3-- -126130,HSO3- -125300,CrO2- -125100,H3PO2 -124900,S2O3-- -123641,MnF+ -122400,H2PO2- -121000,HMnO2- -120700,RuCl5-- -120400,MnO4-- -120300,Pt(SO4) -119800,HInO2 -116300,SO3-- -115971,CdCl3- -115609,Al+++ -115316,BeCl+ -112280,AgCl4--- -111670,TiO2++ -111500,VOH++ -111430,Ag(CO3)- -110720,HZnO2- -108505,Mg++ -108100,HSeO4- -108000,LiOH -107600,MnO4- -106988,HgCl4-- -106700,InO2- -106700,VO++ -106100,VO+ -105500,SeO4-- -105100,RbOH -105000,CsOH -104500,KOH -104109,ZnF+ -103900,PdCl4-- -103579,CuCl4-- -102600,MnO2-- -102150,PbCl3- -101850,H2SeO3 -101100,HFeO2 -100900,CsCl -100500,CrOH++ -99900,NaOH -99800,VOH+ -99250,LiCl -98340,HSeO3- -98300,ZnCl2 -97870,RbCl -97400,HSbO2 -97300,HSnO2- -97300,MnOH+ -97016,InF++ -96240,HAsO2 -95430,KCl -95400,HFeO2- -94610,CsBr -93290,ZnO2-- -93250,RhCl4-- -92910,NaCl -92800,CrO+ -92250,CO2 -91210,PtCl4-- -91157,FeF+ -91100,GaOH++ -91010,RbBr -90550,Be++ -90010,KBr -89963,CuCl3-- -89730,RuCl4- -88400,SeO3-- -88000,FeO2- -87373,CdF+ -86600,GaO+ -86500,HCdO2- -86290,MnCl+ -85610,NaBr -84851,CdCl2 -83900,RuCl4-- -83650,AsO2- -83600,Ti+++ -83460,CsI -83400,HCoO2- -82710,AgCl3-- -82400,SbO2- -81980,HNiO2- -81732,CoF+ -81500,MnO -81190,ZnOH+ -81000,HPbO2- -79768,NiF+ -79645,FeF++ -79300,HBiO2 -78900,RbI -77740,KI -77700,La++ -77500,RhCl4- -75860,PbF+ -75338,CuCl3- -75216,TlF -75100,Ti++ -74600,InOH++ -74504,HgCl3- -73480,FeCl2 -72900,NaI -71980,SO2 -71662,HF -71600,RuO4-- -71200,PbCl2 -69933,Li+ -69810,PdCl3- -69710,Cs+ -69400,InO+ -67811,AuCl3-- -67800,Rb+ -67510,K+ -67420,ZnO -67340,F- -67300,CdO2-- -66850,ZnCl+ -65850,FeOH+ -65550,TlOH -64200,NiO2-- -63530,RhCl3- -63200,CoO2-- -62591,Na+ -61700,BiO2- -61500,CdOH+ -60100,HCuO2- -59226,InCl++ -58600,SnOH+ -58560,RuCl3 -58038,CuCl2- -57900,V+++ -57800,FeOH++ -57760,PtCl3- -57600,HTlO2 -56690,H2O -56025,CoOH+ -55100,Mn++ -54380,RuCl3- -53950,PbOH+ -53739,CuF+ -53600,SnO -53100,FeO+ -53030,FeCl+ -52850,NiOH+ -52627,CdCl+ -52000,V++ -51560,AgCl2- -50720,FeO -49459,AgF -49300,Cr+++ -47500,CdO -46190,RhCl3 -46142,CuCl2 -45200,HHgO2- -45157,CoCl+ -44000,CoO -42838,HgCl2 -41600,TlO2- -41200,CuO2-- -40920,NiCl+ -39815,TlCl -39400,Cr++ -39350,PbO -39340,NiO -39050,PbCl+ -38000,Ga+++ -37518,FeCl++ -36781,AuCl2- -35332,AuCl4- -35200,Zn++ -35160,PdCl2 -33970,RhCl2 -32300,BiOH++ -31700,HIO3 -31379,Cl- -30600,IO3- -30410,HCl -30204,HgF+ -30200,CuOH+ -29300,BiO+ -28682,CO -26507,NO3- -26440,RuCl2+ -25590,Br3- -25060,RuCl2 -24870,Br- -24730,HNO3 -23700,HIO -23400,In+++ -23280,OCN- -23000,CoOH++ -22608,CuCl -22290,PtCl2 -21900,AgOH -21870,Fe++ -20800,CuO -20300,Mn+++ -20058,Pb(HS)2 -19700,HBrO -19100,HClO -19100,ScOH++ -18990,NH4+ -18971,Pb(HS)3- -18560,Cd++ -18290,Rh(OH)+ -17450,AgCl -16250,CuCl+ -14780,RhCl2+ -14000,IO4- -13130,Pd(OH)+ -13000,Co++ -12700,HgOH+ -12410,I- -12300,I3- -12190,Ru(OH)++ -12100,HNO2 -11500,PdO -10900,Ni++ -10470,Ru(OH)+ -10450,RuO+ -9200,IO- -8900,HgO -8800,ClO- -8000,BrO- -7740,Tl+ -7738,AgNO3 -7700,NO2- -7220,RhO -6673,H2S -6570,Sn++ -6383,NH3 -5710,Pb++ -5500,AgO- -4500,TlOH++ -4120,Fe+++ -3380,RhCl+ -3200,TlO+ -3184,AuCl -2155,HgCl+ -2040,ClO4- -1900,ClO3- -1130,PtO -820,Rh(OH)++ 0,Ag(HS)2- 0,H+ 230,RuO 1400,HClO2 1560,Pt(OH)+ 2429,Au(HS)2- 2500,PdCl+ 2860,HS- 3140,RhO+ 3215,Xe 3554,Kr 3890,Ar 4100,ClO2- 4347,N2 4450,BrO3- 4565,Ne 4658,He 5210,RuCl+ 7100,RuCl++ 8600,H2N2O2 9375,TlCl++ 10500,HSe- 11950,Cu+ 15675,Cu++ 15700,S5-- 16500,S4-- 17600,S3-- 18200,HN2O2- 18330,RhCl++ 18380,PtCl+ 18427,Ag+ 19000,S2-- 19500,SeCN- 19700,N2H5+ 21100,N2H6++ 22160,SCN- 22880,Bi+++ 27700,Rh++ 28200,BrO4- 28600,HCN 32000,Co+++ 33200,N2O2-- 35900,Ru++ 36710,Hg2++ 39360,Hg++ 41200,CN- 41440,Ru+++ 42200,Pd++ 51300,Tl+++ 52450,Rh+++ 61600,Pt++ 64300,Ag++ 103600,Au+++"""