Understanding ICSD data



In [9]:
from __future__ import division, print_function

# import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from pymatgen.core import Element, Composition

%matplotlib inline

In [4]:
import csv

with open("../../ICSD/icsd-ternaries.csv", "r") as f:
    csv_reader = csv.reader(f, dialect = csv.excel_tab)
    data = [line for line in csv_reader]

formulas = [line[2] for line in data]
compositions = [Composition(f) for f in formulas]

Structure Types

Structure types are assigned by hand by ICSD curators.


In [5]:
# How many ternaries have been assigned a structure type?
structure_types = [line[3] for line in data if line[3] is not '']
unique_structure_types = set(structure_types)
print("There are {} ICSD ternaries entries.".format(len(data)))
print("Structure types are assigned for {} entries.".format(len(structure_types)))
print("There are {} unique structure types.".format(len(unique_structure_types)))


There are 68064 ICSD ternaries entries.
Structure types are assigned for 59117 entries.
There are 4201 unique structure types.

Filter for stoichiometric compounds only:


In [6]:
def is_stoichiometric(composition):
    return np.all(np.mod(composition.values(), 1) == 0)

In [7]:
stoichiometric_compositions = [c for c in compositions if is_stoichiometric(c)]
print("Number of stoichiometric compositions: {}".format(len(stoichiometric_compositions)))
ternaries = set(c.formula for c in stoichiometric_compositions)
print("Number of unique stoichiometric compositions: {}".format(len(ternaries)))


Number of stoichiometric compositions: 49893
Number of unique stoichiometric compositions: 26255

In [10]:
data_stoichiometric = [x for x in data if is_stoichiometric(Composition(x[2]))]

In [11]:
from collections import Counter

struct_type_freq = Counter(x[3] for x in data_stoichiometric if x[3] is not '')

In [15]:
plt.loglog(range(1, len(struct_type_freq)+1),
             sorted(struct_type_freq.values(), reverse = True), 'o')
plt.xlabel("Structure Type")
plt.ylabel("Structure Type Frequency")
plt.title("Distribution of Frequencies of Structure Types")


Out[15]:
<matplotlib.text.Text at 0x1160cfd90>

In [55]:
sorted(struct_type_freq.items(), key = lambda x: x[1], reverse = True)


Out[55]:
[('ThCr2Si2', 1740),
 ('Spinel-Al2MgO4', 1529),
 ('Perovskite-GdFeO3', 1079),
 ('TiNiSi-MgSrSi', 861),
 ('Perovskite-CaTiO3', 852),
 ('ZrNiAl-Fe2P', 792),
 ('Heusler-AlCu2Mn', 627),
 ('Mn12Th', 601),
 ('PbClF/Cu2Sb', 581),
 ('Delafossite-NaCrS2', 455),
 ('NaCl', 427),
 ('Chalcopyrite-CuFeS2', 373),
 ('Pyrochlore-NaCa(Nb2O6)F', 369),
 ('Laves(2H)-MgZn2', 327),
 ('Heusler(alloy)-AlLiSi', 322),
 ('Zircon-ZrSiO4', 274),
 ('BaCuSn2-CeNi(1-x)Si2', 265),
 ('CaCu5', 254),
 ('Laves(cub)-Cu2Mg', 251),
 ('CaFe2O4', 250),
 ('Fe14Nd2B', 244),
 ('Calcite-CaCO3(hR10)', 237),
 ('K4Si23', 231),
 ('Si2U3', 230),
 ('La2O3', 229),
 ('Th3P4', 228),
 ('ZrBeSi', 222),
 ('Be2CaGe2', 212),
 ('Scheelite-CaWO4', 211),
 ('Perovskite-NdAlO3', 203),
 ('Olivine-Mg2SiO4', 203),
 ('K2PtCl6', 201),
 ('AuBe5', 196),
 ('Mn23Th6', 188),
 ('Brucite-Mg(OH)2', 184),
 ('Pr3Rh4Sn13', 178),
 ('K2MgF4', 177),
 ('LiNbO3', 164),
 ('Fe6Ge6Mg', 160),
 ('Th2Zn17', 160),
 ('Mo6PbS8', 156),
 ('LiGaGe', 144),
 ('Th2Zn17-filled', 139),
 ('Ilmenite-FeTiO3', 138),
 ('Ga4Ti5', 137),
 ('ZrCuSiAs-CuHfSi2', 136),
 ('CuHg2Ti', 134),
 ('Berlinite-AlPO4', 128),
 ('Zr2Fe12P7', 123),
 ('Cu4Zr3Si4', 123),
 ('AlCr2C', 122),
 ('BaNiSn3', 122),
 ('Barite-BaSO4', 120),
 ('FeSmB4-CrYB4', 120),
 ('Carbide(eta)-Fe3W3C', 119),
 ('Co3GdB2', 119),
 ('BaNiO3', 115),
 ('U3S5', 115),
 ('CeCu2', 113),
 ('LaFe4P12', 113),
 ('Carbide(tau)-Cr23C6', 111),
 ('CrNb2Se4-Cr3S4', 111),
 ('BaZn2P2', 107),
 ('Al2CdS4', 103),
 ('Cs2CuCl4', 101),
 ('Ni17Th2', 100),
 ('Al2CuMg', 98),
 ('Pseudobrookite-Fe2TiO5', 94),
 ('Perovskite-PbTiO3', 93),
 ('Aragonite-CaCO3(oP20)', 92),
 ('Co11Ga3La5', 89),
 ('Wolframite-NiWO4', 89),
 ('CaIn2', 86),
 ('Monazite-CePO4(mP)', 85),
 ('La2Sb', 84),
 ('Ni17Th2-filled', 83),
 ('Re7U4Si6', 83),
 ('Garnet-Al2Ca3Si3O12', 82),
 ('Y5S7', 82),
 ('Cu2Mg-filled-frame-', 82),
 ('Perovskite-SrTiO3-Cr3AsN', 80),
 ('YNbO4(mS24)', 77),
 ('Co3U2Si5', 77),
 ('Sphalerite-ZnS(cF8)', 77),
 ('K2SO4(beta)', 77),
 ('Mn5Si3', 75),
 ('Pyroxene-CaIrO3', 75),
 ('Pyrite-FeS2(cP12)', 74),
 ('NH4CdCl3/Sn2S3', 71),
 ('Al18Cr2Mg3', 71),
 ('CeNiC2', 70),
 ('LuMnO3', 70),
 ('Al11La3', 70),
 ('CeCo4B', 68),
 ('NaFeO2(beta)', 67),
 ('LiSbF6', 67),
 ('Ni3Pb2S2', 67),
 ('Al4NiY', 66),
 ('La2CuO4', 64),
 ('Co4Sc5Si10', 62),
 ('Ba5Sb4-Sm5Ge4', 62),
 ('CoHoGa5', 61),
 ('Fe3Sc2Si5', 61),
 ('Fe3TlTe3', 60),
 ('ZnSb2O6', 58),
 ('MnTiSi2', 57),
 ('Fe4Si2Zr', 57),
 ('La3NbO7(oS)', 57),
 ('Ca14MnAs11', 56),
 ('Ga5Ho2Ni5', 55),
 ('K4CdCl6', 55),
 ('HoNi3Hx-frame', 54),
 ('Cu2ErS2', 53),
 ('CdMn2O4', 53),
 ('ErPd2Si', 53),
 ('Nd2CuO4', 53),
 ('InSn2I5', 53),
 ('CrVO4', 52),
 ('Au3Sb4Y3', 52),
 ('Fluorite-CaF2', 52),
 ('Eu4Ga8Ge15', 51),
 ('Cr5BSi3', 51),
 ('CuLaS2', 50),
 ('Perovskite-PbZrO3', 49),
 ('AlB2', 49),
 ('Ce2Ni17Si9', 49),
 ('Cr3Si', 49),
 ('Sc2Si2O7', 49),
 ('Hf9Mo4B/Al5Co2', 48),
 ('InMg2', 48),
 ('InNi2', 48),
 ('FeOCl', 48),
 ('Perovskite-Ba2LaRuO6', 48),
 ('NiSSb', 47),
 ('TiAs', 47),
 ('ReY2B6', 47),
 ('AlOOH(Diaspore)', 46),
 ('Perovskite-Na3AlF6', 46),
 ('Pyroxene-MgSiO3', 46),
 ('Pd5TlAs', 45),
 ('Dy4CoCd', 44),
 ('Co4NdB4', 44),
 ('Pr7O12', 43),
 ('BaFeO2+x', 43),
 ('Th2TeN2', 43),
 ('FeBiO3', 43),
 ('Tl3AsS4', 43),
 ('ThSi2', 43),
 ('Ni12SrB6', 42),
 ('Nickeline-NiAs', 42),
 ('PbCl2', 42),
 ('Cs3CoCl5', 42),
 ('K2MnS2', 42),
 ('CeAsS', 41),
 ('Hf3Ni2Si3', 41),
 ('CeNi3', 41),
 ('SmNiSb', 41),
 ('Cr5CsS8', 41),
 ('NaZn13', 41),
 ('Minium-Pb3O4', 41),
 ('Pyroxene-CaMg(SiO3)2', 41),
 ('CeMn6Ni5', 41),
 ('Al2Zr3(tP20)', 40),
 ('Cu3VS4', 40),
 ('TlxNb6Se8', 39),
 ('Sillenite-Bi12SiO20', 39),
 ('Cs3Cr2Cl9', 39),
 ('CeCo4B4', 39),
 ('Ho6Mo4Al43', 38),
 ('Ce3Ni6Si2', 38),
 ('DyMn2O5', 38),
 ('Perovskite-BaTiO3(tet)', 38),
 ('K2GeF6', 38),
 ('NaLa6OsI12', 38),
 ('BaCuF4', 38),
 ('Ca11InSb9', 38),
 ('UCl3', 37),
 ('CaAl12O19', 37),
 ('CoGa8Ho2', 37),
 ('InTe-Tl2Se2', 37),
 ('GaMo4S8(HT)', 37),
 ('Cr5B3', 37),
 ('Eu2CuS3', 36),
 ('Rutile-TiO2', 36),
 ('CuCrSe2-AgCrSe2(R3m)', 36),
 ('IrYGe2', 36),
 ('AgFeO2', 36),
 ('Si2N2O', 35),
 ('Ce3Co11B4', 35),
 ('Bixbyite-Mn2O3', 35),
 ('Be2SiO4', 34),
 ('FeSiTi', 34),
 ('Co3Lu2Si5', 34),
 ('Perovskite-ScYS3', 34),
 ('K6HgS4', 33),
 ('MoUC2', 33),
 ('CoZr2Si2', 33),
 ('Al8CaCo2', 33),
 ('NaHS-HT', 33),
 ('BaPtSb', 33),
 ('Co4Hf2P3', 33),
 ('K2Pb(SO4)2', 33),
 ('Cu2HgI4', 32),
 ('Cs3Tl2Cl9', 32),
 ('La3CuSiS7', 32),
 ('Perovskite-BaPbO3', 32),
 ('Bi2Te3', 32),
 ('Mn2ZrHx-frame', 32),
 ('KInS2', 32),
 ('Na2HgO2', 32),
 ('MnP', 32),
 ('In5Bi3', 31),
 ('Ti3C2Si', 31),
 ('ReY3B7', 31),
 ('FeAsS-CoSb2', 31),
 ('PbPS3', 31),
 ('KAlO2', 31),
 ('FePS3', 30),
 ('BaGe2Se4', 30),
 ('Co2GaGd6', 30),
 ('K2WSe4', 30),
 ('LaPtSi', 30),
 ('Tm2S3', 30),
 ('CoNb3S6', 29),
 ('Na2Re3S6', 29),
 ('NdOF', 29),
 ('Elpasolite-K2NaAlF6', 29),
 ('CaSO4', 29),
 ('AgErSe2', 29),
 ('Li2ZrF6', 29),
 ('SmSI', 29),
 ('Nd3Ni13B2', 29),
 ('Y6RuI10', 28),
 ('Cr2Ho2C3', 28),
 ('CsCu2Cl3', 28),
 ('LuRu4B4', 28),
 ('YPtAs', 28),
 ('Al2(WO4)3', 28),
 ('Na2CO3(HT)', 28),
 ('Na2SiO3', 28),
 ('ZrSSi', 28),
 ('Na3AsS3', 28),
 ('Li2SnO3', 28),
 ('CrU8S17', 28),
 ('Ca2SiO4', 28),
 ('Co5YP3', 27),
 ('Al2SiO5-Andalusite', 27),
 ('LaIrSi', 27),
 ('Al2Mo3C', 27),
 ('KFeS2', 27),
 ('ErIr3B2', 27),
 ('BaSiF6', 27),
 ('MnPSe3', 27),
 ('Wurtzite-ZnS(2H)', 26),
 ('Al2Cu', 26),
 ('PrPS4', 26),
 ('Sr3Ti2O7', 26),
 ('Y2TiO5', 26),
 ('Cs2Au2Cl6', 26),
 ('BaNiS2', 26),
 ('LuRuB2', 26),
 ('PrOI', 26),
 ('AlFe2B2', 26),
 ('CuGeO3', 26),
 ('Na2SO4', 26),
 ('Co4Ge7Zr4', 26),
 ('KOsF6', 26),
 ('K2Cr2O7', 26),
 ('Ce4Ho11S22', 25),
 ('U2Mo3Si4', 25),
 ('SbPO4', 25),
 ('ZrP2O7', 25),
 ('Fluorite-CaF2(defect)', 25),
 ('InPt2Gd', 25),
 ('NiTi2', 25),
 ('CaV3O7', 25),
 ('Ni20Ho6P13', 25),
 ('K2RbC60', 25),
 ('Co3Tb4B6', 25),
 ('NaNbO3(mP5)', 24),
 ('Ca2AlFeO5(oI)', 24),
 ('Be3Nb', 24),
 ('Li2B4O7', 24),
 ('Al4Mo2Yb', 24),
 ('Nd2Te4O11', 24),
 ('Ho2Rh12As7', 24),
 ('Al2SiO5-Sillimanite', 24),
 ('KCuF3(tI20)', 24),
 ('Eu2Zr2O7', 24),
 ('SrGaSn', 24),
 ('NaV6O11', 23),
 ('Ga21Ho4Ni10', 23),
 ('Mo5Si3', 23),
 ('FeB', 23),
 ('V6Si5', 23),
 ('Kyanite', 23),
 ('YTaO4', 23),
 ('Ba(OH)2', 23),
 ('CrOOH(R3-m)', 23),
 ('LiFeO2-alpha', 23),
 ('RbNiCrF6', 23),
 ('AlOOH(oS16)', 23),
 ('Hf5Rh2In4', 22),
 ('MgNb2O6', 22),
 ('Na2MnCl4', 22),
 ('Zn(CN)2(disordered)', 22),
 ('Bi2Pb2Se5', 22),
 ('Cs2Zn3S4', 22),
 ('NaNO2', 22),
 ('AlCe', 22),
 ('K2ZnBr4', 22),
 ('Ce2Co7B3', 22),
 ('Enargite-Cu3AsS4', 22),
 ('DyB2C2', 22),
 ('KZnAs', 21),
 ('LiIO3', 21),
 ('Mg2Ga', 21),
 ('LiTiS2', 21),
 ('Proustite', 21),
 ('In2ZnS4(hR7)', 21),
 ('Bi2Al4O9', 21),
 ('CaLiSi2', 21),
 ('K2PtCl4', 21),
 ('NaNiO2(mS8)', 21),
 ('NaClO3', 21),
 ('ScUS3', 21),
 ('LaB2C2', 21),
 ('BiMnO3', 20),
 ('Pd3US4', 20),
 ('Co3Ga9Y2', 20),
 ('Brownmillerite-Ca2AlFeO5(oP)', 20),
 ('Ag8SiTe6', 20),
 ('Ca2Mn2O5', 20),
 ('Ca2MnO4', 20),
 ('Mo1+xMo6S8', 20),
 ('Mn23Th6-filled', 20),
 ('Tl3VS4', 20),
 ('Mn2GeO4', 20),
 ('CuSO4', 20),
 ('EuGa2S4', 19),
 ('CaC2', 19),
 ('NaTl', 19),
 ('ZnS(defect)-Cu2HgI4(HT)', 19),
 ('Mg2NiH4', 19),
 ('Cu2Sc2O5', 19),
 ('CsCl', 19),
 ('NaHS', 19),
 ('DyNi4Si', 19),
 ('CuInPt2', 19),
 ('KBrF4', 19),
 ('Auricupride-AuCu3', 19),
 ('Zr5Si4', 19),
 ('Eu4Ga8Ge16', 19),
 ('Perovskite-NaNbO3(tP10)', 19),
 ('GeSb2Te4', 19),
 ('Sr(NO3)2', 19),
 ('Rh3ScSi7', 19),
 ('Er3GaS6', 19),
 ('CsClO4', 19),
 ('NdTaO4', 19),
 ('KClO3', 19),
 ('BPO4', 19),
 ('La4Ge3S12', 19),
 ('CrOOH(oP8)', 19),
 ('RbNO3', 18),
 ('CoNb4Si', 18),
 ('Na2SiF6', 18),
 ('ZnMoO4', 18),
 ('Er4NiB13', 18),
 ('Ba2MnS3', 18),
 ('Y3TaO7', 18),
 ('MgSeO3', 18),
 ('MnNb4S8', 18),
 ('Sr4Mn3O10', 18),
 ('Cu4KS3', 18),
 ('Al10Fe2Yb', 18),
 ('Ba4OCl6', 18),
 ('Au3K2', 18),
 ('Hf2Ni3Si4', 18),
 ('In2Mo15Se19', 18),
 ('CsPrS2', 18),
 ('Cd4GeS6', 18),
 ('Ti4AlN3', 18),
 ('Gd5Si2Ge2', 18),
 ('Perovskite-NaNbO3', 18),
 ('Bi(IO3)3', 18),
 ('BaCd11', 18),
 ('Sn2F6', 18),
 ('La11Ni4In9', 18),
 ('AgBiSe2', 17),
 ('Perovskite-NaTaO3', 17),
 ('Rh(PO3)3', 17),
 ('LiCuO(I4-2m)', 17),
 ('TlI', 17),
 ('AlFeO3', 17),
 ('Pb3(PO4)2', 17),
 ('Na3As', 17),
 ('CoGa3Pr8', 17),
 ('YbV4O8(mP52)', 16),
 ('Bi4(SiO4)3', 16),
 ('Pyroxene-MgSiO3-LT', 16),
 ('Eu2(WO4)3', 16),
 ('Fe6Ga6Sc', 16),
 ('Ho11Ge10', 16),
 ('Mg3TeO6', 16),
 ('Ba4SiAs4', 16),
 ('Co19Zr5P12', 16),
 ('ScU3S6', 16),
 ('La3InS6', 16),
 ('NiAs2', 16),
 ('Li3LaSb2', 16),
 ('Zr3PbO4F6', 16),
 ('LaMo5O8', 16),
 ('Er2RhSi3(P6-2c)', 16),
 ('SrZrS3', 16),
 ('Ca2RuO4', 16),
 ('Ca2P2O7(beta)', 16),
 ('K5Sb3Sn', 16),
 ('NH3BH3', 16),
 ('NdRh2Sn4', 16),
 ('Lavenite', 16),
 ('CdI2', 15),
 ('Ce3Pt23Si11', 15),
 ('FeF3', 15),
 ('InOOH', 15),
 ('CeRu2B2', 15),
 ('BaRuO3', 15),
 ('Ca3PI3', 15),
 ('LiMnO2', 15),
 ('Sb2S3', 15),
 ('LiMnAs', 15),
 ('ThMoB4', 15),
 ('Na5ReO6', 15),
 ('Al5(BO3)O6', 15),
 ('K2ZnCl4', 15),
 ('CaRh2B2', 15),
 ('Co3HoP2', 15),
 ('Baddeleyite-ZrO2(mP12)', 15),
 ('Yb3S4', 15),
 ('Nolanite', 15),
 ('AlMgB14', 15),
 ('Co2InTb', 15),
 ('Ca3Ru2O7', 15),
 ('BaMo6S8', 15),
 ('Na4SiO4', 15),
 ('Stannite-Cu2FeSnS4', 15),
 ('UAsTe', 15),
 ('NaV(SO4)2', 15),
 ('Hg3S2Cl2', 15),
 ('Pr10S14O', 15),
 ('Na1.55Si17', 15),
 ('Bi2CuO4', 15),
 ('MnSiO3(aP50)', 15),
 ('Na4Sn3O8', 15),
 ('Ca3Ge2As4', 15),
 ('BaTi2Fe4O11', 15),
 ('Cr3C2', 14),
 ('NaPdC2', 14),
 ('Ce2CuGe6', 14),
 ('CaSiO3(HP)', 14),
 ('Dy3Ni7B2', 14),
 ('CaV2O5', 14),
 ('CuBiS2', 14),
 ('YAlGe', 14),
 ('Fe2BO3O', 14),
 ('CeNiSb3', 14),
 ('K2PdP2', 14),
 ('Er2RhSi3', 14),
 ('SrB4O7', 14),
 ('Gd2SiO5', 14),
 ('FeU2S5', 14),
 ('LaCoAl4', 14),
 ('Perovskite-BaTiO3(orh)', 14),
 ('YBO3', 14),
 ('BaCu2S2', 14),
 ('Ag3PO4', 14),
 ('LiBH4', 14),
 ('NiSmGe3', 14),
 ('CrUS3', 14),
 ('Cr11Ge8', 14),
 ('Mg6MnO8', 14),
 ('La2SnS5', 14),
 ('Mg3(PO4)2', 14),
 ('Zr(MoO4)2(HT)', 14),
 ('VOSO4-alpha', 14),
 ('Rh2Y3Si2', 14),
 ('ErPtF7', 14),
 ('Ho5Au2Sb', 14),
 ('LaNi5Hx-frame', 14),
 ('In5Nd4S13', 14),
 ('MoNiP2', 14),
 ('CeCoC2', 14),
 ('LiYSn', 14),
 ('Sr2AlFeO5', 13),
 ('LuFe2O4', 13),
 ('CaGe2O5', 13),
 ('Ca5Ga2As6', 13),
 ('Os3(CO)12', 13),
 ('Sr2CuO3', 13),
 ('NdTe3', 13),
 ('NiTiO3', 13),
 ('Perovskite-BaBiO3(mS20)', 13),
 ('Ni5YSi3', 13),
 ('K3CrO8', 13),
 ('Ag3CsS2', 13),
 ('Na2Ti6O13', 13),
 ('Al3ScC3', 13),
 ('Ag5Te2Cl', 13),
 ('CeCu6', 13),
 ('AlPO4(C2221)', 13),
 ('LiCo6P4', 13),
 ('Kotoite', 13),
 ('FeYb2S4', 13),
 ('Sr2IrO4', 13),
 ('GdPS', 13),
 ('Zn(OH)2', 13),
 ('Yb3Sb5O12', 13),
 ('KOH', 13),
 ('AlCoPr2', 13),
 ('AgDyTe2', 13),
 ('In5S4', 13),
 ('Marcasite-FeS2(oP6)', 13),
 ('CaCrF5', 13),
 ('Ca2Sb2O7', 13),
 ('Rb2CuCl4', 13),
 ('TlPb2Cl5', 13),
 ('PtGeSe', 13),
 ('NaAlCl4', 12),
 ('Ag2NiO2', 12),
 ('Na4UO5', 12),
 ('Al2Sr3P4', 12),
 ('BaSO4(HT)', 12),
 ('CoMo2S4', 12),
 ('ErNiB4', 12),
 ('LuNiSn2', 12),
 ('Na2SnF6', 12),
 ('CoMoO4', 12),
 ('Yb5Sb3', 12),
 ('CoYC(tP6)', 12),
 ('Ce(SO4)2', 12),
 ('Cementite-Fe3C', 12),
 ('Ge2LaPt2', 12),
 ('La6Ni6P17', 12),
 ('La23Ni7Mg4', 12),
 ('Ce2Ni22C3', 12),
 ('NdNiGa2', 12),
 ('Ni60Yb11C6', 12),
 ('LiAlCl4', 12),
 ('CoGdGa', 12),
 ('CuSmP2', 12),
 ('TlSbS2', 12),
 ('SrV3O7', 12),
 ('CdIn2Se4', 12),
 ('CeNi5Sn', 12),
 ('Y2ReC2', 12),
 ('CeTmS3', 12),
 ('Protoenstatite', 12),
 ('CeNi12B6', 12),
 ('LiNH2', 12),
 ('CrSi2', 12),
 ('Ce2CuGa12', 12),
 ('YOOH', 12),
 ('NaOH', 12),
 ('La6MnSi2S14', 12),
 ('DyFe4Ge2', 12),
 ('K3SiF7', 12),
 ('K2PtS2', 12),
 ('K2NbF7', 12),
 ('K2CO3', 12),
 ('(Mn,Fe)2PO4F', 12),
 ('Ir3Ge7', 12),
 ('Cs2BeF4', 12),
 ('Ni3V2O8', 12),
 ('K2Pd3S4', 11),
 ('Li4CO4(Cm1)', 11),
 ('Nd2WO6(mS72)', 11),
 ('Fe2(SO4)3', 11),
 ('SbSI', 11),
 ('Co5Cr2Mo3', 11),
 ('UBC', 11),
 ('BaMnO3', 11),
 ('Rb3PdF5', 11),
 ('Mn7SiO12', 11),
 ('Nd(BO2)3', 11),
 ('Co5USi3', 11),
 ('Mo3Se4', 11),
 ('Na2CrO4', 11),
 ('CoW2B2', 11),
 ('Zn4B6O13', 11),
 ('Cs3Tb7Te12', 11),
 ('KNiCl3', 11),
 ('Tm4Zn5Ge6', 11),
 ('TbB2C', 11),
 ('CrEr2S4', 11),
 ('Sc3FeC4', 11),
 ('K2Al2Sb3', 11),
 ('BaUO4', 11),
 ('CrUO4', 11),
 ('LaNi4AlH4-frame', 11),
 ('Ce3Ni2-xSn7-y', 11),
 ('Fe4Y2Si9', 11),
 ('Ga41V8', 11),
 ('Na2ThF6', 11),
 ('Na3IrH6', 11),
 ('(Cu,Zn)WO4', 11),
 ('NaCl(defect)-VC.75', 11),
 ('Al2(SO4)3', 11),
 ('Ni4U3Si4', 11),
 ('(Ca8)xCa2', 11),
 ('Tl4HgBr6', 11),
 ('Ag4K2S3', 11),
 ('Sr4Fe4O11', 11),
 ('LaNiO2', 11),
 ('Ce3NiSi3', 10),
 ('PbO2-alpha', 10),
 ('Be3N2', 10),
 ('ZnSe2O5', 10),
 ('LiCuO', 10),
 ('K2SnCl6', 10),
 ('Eu3Sb4S9', 10),
 ('Dy12Mn5C15', 10),
 ('Mn23Y6Hx-frame', 10),
 ('NPBr2', 10),
 ('Er4Ni13C4', 10),
 ('KBO2', 10),
 ('Cu4NaAs2', 10),
 ('Fe3(PO4)2(mP26)', 10),
 ('Li2PdO2', 10),
 ('KAlF4', 10),
 ('Na3Pt4Ge4', 10),
 ('Li4CO4(C2)', 10),
 ('Al3Ti', 10),
 ('Ce2CrN3', 10),
 ('TbP5O14', 10),
 ('KYbSiS4', 10),
 ('SnTaS2', 10),
 ('K3AlSe3', 10),
 ('CuFe2S3', 10),
 ('Li8IrO6', 10),
 ('CsIO4', 10),
 ('Tb(BO2)3', 10),
 ('HoCuAl3', 10),
 ('Dy2Ni2Al', 10),
 ('Al9Co2Sr', 10),
 ('HgPbP14', 10),
 ('K6W2O3N4', 10),
 ('AlAu4', 10),
 ('BiB3O6', 10),
 ('Tilasite', 10),
 ('HgMoO4', 10),
 ('Ag8GeS6', 10),
 ('Ho2Ni15B9', 10),
 ('Pb2OSO4', 10),
 ('Co9S8', 10),
 ('Ag7NbS6', 10),
 ('Ca3AsN', 10),
 ('Ba4Y3F17', 10),
 ('Li5Mo9S12', 10),
 ('K2SO4(alpha)', 10),
 ('HoPdGe', 10),
 ('PbSnF4', 10),
 ('KV3O8', 10),
 ('Ba7Cl2F12', 9),
 ('Sm3NS3', 9),
 ('Al5C3N', 9),
 ('Ce2Li2Ge3', 9),
 ('Spinel-LiFe5O8', 9),
 ('Sm6Co2Si3/Co3Ho4', 9),
 ('Cu2P2O7', 9),
 ('Ag16Ca6N', 9),
 ('NaN3(beta)', 9),
 ('Er2Ge2O7', 9),
 ('H2SO4(H2O)4', 9),
 ('Ho4Mo4O11', 9),
 ('SiTa4Te4', 9),
 ('Nb2Co4O9', 9),
 ('Li7PN4', 9),
 ('RbAuS', 9),
 ('ThB2C', 9),
 ('Er2Ni3B6', 9),
 ('KRu4O8', 9),
 ('Ho2Ni10B5', 9),
 ('K6Fe2O6', 9),
 ('Mn2SnS4', 9),
 ('AlPO4(HT)', 9),
 ('Na5FeO4', 9),
 ('AuCaGe', 9),
 ('Sr2IrH5', 9),
 ('LiPr2Ge6', 9),
 ('Al3Y2Si2', 9),
 ('Gd2(MoO4)3(oP68)', 9),
 ('Lu3Co8Sn4', 9),
 ('CaMn7O12', 9),
 ('Al5Ni2Zr', 9),
 ('GaMo4S8', 9),
 ('In(OH)3', 9),
 ('NaBiO2', 9),
 ('Ag2SeO3', 9),
 ('Y3Co2', 9),
 ('K2MnF6', 9),
 ('Lu2Te5O13', 9),
 ('K4Ti3S14', 9),
 ('Eu6Rh30As19', 9),
 ('Au4KSn2', 9),
 ('Li2PbO3', 9),
 ('KTh2Se6', 9),
 ('NdYbS3', 9),
 ('TiMn2O4', 9),
 ('SrLaI4', 9),
 ('K4BeP2', 9),
 ('Ti2CuSb3', 9),
 ('K2B12H12', 9),
 ('Mo6Ni6C', 9),
 ('CeRhAl', 9),
 ('Pb3O2Cl2', 9),
 ('Cu2GeS3', 9),
 ('AuEuGe', 9),
 ('NH3BH3(I4mm)', 9),
 ('NdCu2O4-x', 9),
 ('YPdSi', 9),
 ('Tl2Ge2S5', 9),
 ('CeSe2O6', 9),
 ('KAlF4(tP12)', 9),
 ('CsCrBr3', 9),
 ('ThTi2O6', 9),
 ('Er2FeC4', 9),
 ('Yb2S2O', 9),
 ('CsNbN2', 9),
 ('Co11Ga6Sm26', 9),
 ('In3Mo15Se19', 9),
 ('GeS', 9),
 ('LiAlH4', 9),
 ('Co2Si', 9),
 ('U2O(PO4)2', 9),
 ('CePt2B', 9),
 ('PrAuAs2', 9),
 ('Zr(WO4)2', 9),
 ('Nb5Cu4Si4', 9),
 ('CaAl4O7', 9),
 ('K2ZrF6(C2/c)', 9),
 ('Sm3RuO7', 9),
 ('PbMo6Cl14', 9),
 ('SrFe2As2', 9),
 ('Al2S3', 9),
 ('Ludwigite', 9),
 ('HoFe6Sn6', 8),
 ('Cr(CO)6', 8),
 ('Al2Ca3Ge2', 8),
 ('FeAsO4', 8),
 ('BiZr3F15', 8),
 ('Na4CO4', 8),
 ('Pr2Si2O7', 8),
 ('Co7Gd2', 8),
 ('Ba2ZnO3', 8),
 ('AgYbS2', 8),
 ('SnWO4(oP24)', 8),
 ('NiCr2O4', 8),
 ('Cs3Bi2Br9', 8),
 ('Pb2Sb2S5', 8),
 ('CaSiO3(cI40)', 8),
 ('YbP5O14', 8),
 ('LiAlO2-gamma', 8),
 ('Co2B2O5', 8),
 ('SrCuO2', 8),
 ('YbV4O8', 8),
 ('AgSbO3', 8),
 ('Tl4Ge2S6', 8),
 ('La2SbO2', 8),
 ('Fe4LuGe2', 8),
 ('Th11Ru12C18', 8),
 ('Zr(MoO4)2', 8),
 ('Dy2Te', 8),
 ('FePO4', 8),
 ('SrSiO3', 8),
 ('LaPd2O4', 8),
 ('Zn3P2', 8),
 ('Ba3Yb4O9', 8),
 ('Li2MnO3', 8),
 ('SrO2(H2O)8', 8),
 ('CaB2O4', 8),
 ('Co7Ho6Ga21', 8),
 ('U4S3', 8),
 ('Ta2S2C', 8),
 ('Ce3B2N4', 8),
 ('Na3Fe2S4', 8),
 ('Spinel-Al2MgO4, reduced symmetry', 8),
 ('VO2(HT)', 8),
 ('LiMnSe2', 8),
 ('Re2(CO)10', 8),
 ('Rb2PtO4', 8),
 ('K3AuGe4', 8),
 ('BaV10O15', 8),
 ('CaIn2Te4', 8),
 ('CaGa2O4-LT', 8),
 ('Co40Ta13Si31', 8),
 ('K9Fe2S7', 8),
 ('TmRuGa3', 8),
 ('SrZnO2', 8),
 ('CsCuCl3', 8),
 ('Ce4MnSn7', 8),
 ('CaSiO3(tP40)', 8),
 ('Mn2Sb2O7', 8),
 ('Ca3InP3', 8),
 ('La2Ir3Sb4', 8),
 ('Zr3NiSb7', 8),
 ('Fe3(PO4)2(mP52)', 8),
 ('PrMn7O12', 8),
 ('S7NH', 8),
 ('Ag7PSe4Se2', 8),
 ('KCoO2(tP16)', 8),
 ('TbFe6Sn6', 8),
 ('K2SnCl6(LT)', 8),
 ('TaIrTe2', 8),
 ('FeZr6Cl14', 8),
 ('Ga2Gd3', 8),
 ('Ni3Bi2Se2', 8),
 ('CsHS', 8),
 ('La2SrCu2O6', 8),
 ('ZrSi2', 8),
 ('Hg(CN)2', 8),
 ('Gd2Fe2I', 8),
 ('CaSiO3(tI40)', 8),
 ('Cs4PbO4', 8),
 ('CsGdTe4', 8),
 ('Er3Ru4Si12', 8),
 ('Ni(N(CN)2)2', 8),
 ('Bi4Ti3O12', 8),
 ('Nd2WO6(oP36)', 8),
 ('Fe3Th7', 8),
 ('LiTiO2', 8),
 ('PbWO4(mP48)', 8),
 ('K2Mo9S11', 7),
 ('LiOHH2O', 7),
 ('KIO3', 7),
 ('Nd3Co3Ga', 7),
 ('K4Nb6Cl18', 7),
 ('Ca(BH4)2(tP22)', 7),
 ('Ho10In20Ni9', 7),
 ('Ca(BH4)2', 7),
 ('BaSi2', 7),
 ('Li8Al3Si5', 7),
 ('KHF2', 7),
 ('La2NiO4', 7),
 ('CuMoF6', 7),
 ('Ba2Nb5O9', 7),
 ('RbCuC2', 7),
 ('K2Cd3S4', 7),
 ('Rb4Re6S13', 7),
 ('CrB', 7),
 ('Perovskite-PbTiO3(Pmmm)', 7),
 ('Zn4Ta2O9', 7),
 ('TlAsS2', 7),
 ('BaAl2O4', 7),
 ('RbNO3(oP10)', 7),
 ('KMnF4', 7),
 ('Ag8SiS6', 7),
 ('LiMn2O4', 7),
 ('BaThF6', 7),
 ('TaN', 7),
 ('La2Ni5B4', 7),
 ('Hg2P3Cl', 7),
 ('Tb3Fe5O12', 7),
 ('Ni3TeO6', 7),
 ('CoYC(tP3)', 7),
 ('Al3Zr2C4', 7),
 ('V(PO3)3', 7),
 ('Al(OH)3(gibbsite)', 7),
 ('K3Na(SO4)2', 7),
 ('Yb(ReO4)3', 7),
 ('Am(IO3)3', 7),
 ('Zn2Te3O8', 7),
 ('K2UF6', 7),
 ('Sr3Al2Ge4', 7),
 ('V2Zr3Ga4', 7),
 ('CeSiP3', 7),
 ('Co(AlCl4)2', 7),
 ('Ag3AuTe2', 7),
 ('NH4NO3(IV)', 7),
 ('CaMn2O4', 7),
 ('Cu8Rb3Se6', 7),
 ('Ni2TbB2', 7),
 ('NaBH4', 7),
 ('Gd2C2Br2', 7),
 ('GePbS3', 7),
 ('Li4TeO5', 7),
 ('CaUO4', 7),
 ('(Ce,Zr)O2', 7),
 ('CaB2O4(HP)', 7),
 ('Rh3Y2Sn5', 7),
 ('Perovskite-PbVO3', 7),
 ('Zr2NiAs2', 7),
 ('LiB3O5', 7),
 ('La12I17(C2)3', 7),
 ('Cs6Ga2P4', 7),
 ('SCl3AlCl4', 7),
 ('MgB4O7', 7),
 ('Ni3SnP', 7),
 ('RbBSe3', 7),
 ('Ba3AlSb3', 7),
 ('CH5N3', 7),
 ('AgCN', 7),
 ('Nb2Se3', 7),
 ('AlFe(MoO4)3', 7),
 ('CoUC2', 7),
 ('Rb8Fe2O7', 7),
 ('Sm2F(AuF4)5', 7),
 ('CsTaN2', 7),
 ('NiZr2Hx-frame', 7),
 ('TlFeS2', 7),
 ('Na3FeS3', 7),
 ('Al5PrNi2', 7),
 ('K2MoO4', 7),
 ('PbU2Se5', 7),
 ('CaGaN', 7),
 ('Cu2TiTe3', 7),
 ('Sm4Co3Ga16', 7),
 ('Gd3MnI3', 7),
 ('Ca9Zn4Bi9', 7),
 ('Tl5Se2I', 7),
 ('Co2P2O7', 7),
 ('Mg2SiO4(oI56)', 7),
 ('Sr21Cd4Bi18', 7),
 ('(O2)PtF6', 7),
 ('Mg2NiH4(C2/c)', 7),
 ('PrAgAs2', 7),
 ('CuYS2', 7),
 ('CdGeO3', 7),
 ('(COOH)2(H2O)2', 7),
 ('AlPO4(cF24)', 7),
 ('CdSO4', 7),
 ('Eu(N(CN)2)3', 7),
 ('AuCN', 7),
 ('MnP4O11', 7),
 ('Perovskite-Sr2CoRuO6', 7),
 ('ErRh3Si2', 7),
 ('Ta2Pt3Se8', 7),
 ('Ho2S2Te', 7),
 ('Cs2Pt3S4', 7),
 ('Sr2Ga2S5', 7),
 ('SrNi4Sn2', 7),
 ('Zr(MoO4)2(hP11)', 7),
 ('KCuO2', 7),
 ('Ni2SiP', 7),
 ('K3FeO2', 6),
 ('Ce2AlGe2(Ge,Al)4', 6),
 ('Zr2P2O9', 6),
 ('CeTa7O19', 6),
 ('ZnB4O7', 6),
 ('Ba(OH)2H2O', 6),
 ('Pb(PO3)2', 6),
 ('K4Nb2S11', 6),
 ('Laves(4H)-MgNi2', 6),
 ('Ba5Ta4O15', 6),
 ('KCd4As3', 6),
 ('NH4F', 6),
 ('RhTe6Cl3', 6),
 ('MnTb2S4', 6),
 ('Cs5SiP3', 6),
 ('YNiSi3', 6),
 ('NaCu2O2', 6),
 ('Fe2Ta9S6', 6),
 ('Cd6Sr11Sb12', 6),
 ('Tl3AsSe3', 6),
 ('K2SnO3', 6),
 ('SrNi5P3', 6),
 ('Al2CuCl8', 6),
 ('Al9Na4Ge14', 6),
 ('ReBiO4', 6),
 ('SrAl2O4', 6),
 ('Pr3MoO7', 6),
 ('RbCr3S5', 6),
 ('Auricupride-AuCu3-filled', 6),
 ('(SeCl3)2ReCl6', 6),
 ('Sr2Zn2As3', 6),
 ('Fe(IO3)3', 6),
 ('Li5GaO4-alpha', 6),
 ('Y5Mo2O12', 6),
 ('Li3In2(PO4)3', 6),
 ('KCuO', 6),
 ('Cu2FeS2', 6),
 ('Rb2TiO3', 6),
 ('Na2Ta4O11', 6),
 ('ErMn2H2', 6),
 ('AgNb3S4', 6),
 ('MgV2O5', 6),
 ('CeLi2Ge', 6),
 ('Sr3SiO5', 6),
 ('Co5Ti3B2', 6),
 ('Rb3Mn2Cl7', 6),
 ('Cs9GaO4', 6),
 ('KVO3', 6),
 ('Rh2Y3', 6),
 ('Whitlockite', 6),
 ('Nd3NbO7', 6),
 ('K3NO4', 6),
 ('CrPS4', 6),
 ('Tl3PbBr5', 6),
 ('Skutterudite-CoAs3', 6),
 ('Co2Ge3S3', 6),
 ('Ca2CdAs2', 6),
 ...]

In [16]:
uniq_phases = set()
for row in data_stoichiometric:
    spacegroup, formula, struct_type = row[1:4]
    phase = (spacegroup, Composition(formula).formula, struct_type)
    uniq_phases.add(phase)

In [18]:
uniq_struct_type_freq = Counter(x[2] for x in uniq_phases if x[2] is not '')
uniq_struct_type_freq_sorted = sorted(uniq_struct_type_freq.items(), key = lambda x: x[1], reverse = True)

In [20]:
plt.loglog(range(1, len(uniq_struct_type_freq_sorted)+1),
           [x[1] for x in uniq_struct_type_freq_sorted], 'o')
plt.xlabel("Structure Type")
plt.ylabel("Structure Type Frequency")
plt.title("Distribution of Frequencies of Structure Types")


Out[20]:
<matplotlib.text.Text at 0x116aff290>

In [21]:
uniq_struct_type_freq_sorted


Out[21]:
[('ThCr2Si2', 676),
 ('TiNiSi-MgSrSi', 586),
 ('ZrNiAl-Fe2P', 511),
 ('Perovskite-CaTiO3', 439),
 ('Heusler-AlCu2Mn', 343),
 ('Mn12Th', 339),
 ('PbClF/Cu2Sb', 334),
 ('Perovskite-GdFeO3', 314),
 ('Spinel-Al2MgO4', 305),
 ('Delafossite-NaCrS2', 278),
 ('NaCl', 258),
 ('Laves(2H)-MgZn2', 239),
 ('Laves(cub)-Cu2Mg', 209),
 ('Th3P4', 205),
 ('Si2U3', 194),
 ('Heusler(alloy)-AlLiSi', 185),
 ('BaCuSn2-CeNi(1-x)Si2', 179),
 ('ZrBeSi', 179),
 ('CaCu5', 178),
 ('Be2CaGe2', 163),
 ('CaFe2O4', 158),
 ('Pyrochlore-NaCa(Nb2O6)F', 146),
 ('Mn23Th6', 142),
 ('La2O3', 140),
 ('Ga4Ti5', 131),
 ('Th2Zn17', 130),
 ('K2PtCl6', 121),
 ('AuBe5', 114),
 ('Pr3Rh4Sn13', 113),
 ('CuHg2Ti', 112),
 ('LiGaGe', 108),
 ('Zircon-ZrSiO4', 101),
 ('U3S5', 100),
 ('FeSmB4-CrYB4', 99),
 ('ZrCuSiAs-CuHfSi2', 95),
 ('Carbide(eta)-Fe3W3C', 94),
 ('CeCu2', 93),
 ('BaNiSn3', 90),
 ('Carbide(tau)-Cr23C6', 89),
 ('Scheelite-CaWO4', 87),
 ('CrNb2Se4-Cr3S4', 85),
 ('Zr2Fe12P7', 84),
 ('Ni17Th2', 83),
 ('Al2CuMg', 82),
 ('K2MgF4', 79),
 ('CaIn2', 76),
 ('Cu4Zr3Si4', 75),
 ('Fe6Ge6Mg', 74),
 ('Mo6PbS8', 74),
 ('Re7U4Si6', 72),
 ('LaFe4P12', 70),
 ('Th2Zn17-filled', 69),
 ('Pyrite-FeS2(cP12)', 65),
 ('Al11La3', 64),
 ('K4Si23', 64),
 ('Al18Cr2Mg3', 63),
 ('Co3U2Si5', 62),
 ('Cu2Mg-filled-frame-', 62),
 ('Mn5Si3', 61),
 ('BaNiO3', 59),
 ('Olivine-Mg2SiO4', 59),
 ('Y5S7', 59),
 ('Ni17Th2-filled', 58),
 ('Co11Ga3La5', 58),
 ('Barite-BaSO4', 57),
 ('Chalcopyrite-CuFeS2', 57),
 ('NH4CdCl3/Sn2S3', 57),
 ('LiSbF6', 56),
 ('Ba5Sb4-Sm5Ge4', 55),
 ('YNbO4(mS24)', 50),
 ('Cr5BSi3', 49),
 ('Co3GdB2', 47),
 ('BaZn2P2', 47),
 ('Hf9Mo4B/Al5Co2', 46),
 ('Fluorite-CaF2', 46),
 ('ErPd2Si', 45),
 ('Cs2CuCl4', 45),
 ('CoHoGa5', 45),
 ('Dy4CoCd', 44),
 ('Al4NiY', 44),
 ('InMg2', 44),
 ('Fe4Si2Zr', 44),
 ('AlCr2C', 44),
 ('Co4Sc5Si10', 43),
 ('Sphalerite-ZnS(cF8)', 43),
 ('Au3Sb4Y3', 43),
 ('K2SO4(beta)', 43),
 ('La2Sb', 43),
 ('AlB2', 42),
 ('ThSi2', 41),
 ('MnTiSi2', 41),
 ('ReY2B6', 40),
 ('Pd5TlAs', 40),
 ('K2MnS2', 39),
 ('Fe3Sc2Si5', 39),
 ('CeCo4B', 38),
 ('Cu2ErS2', 38),
 ('Ga5Ho2Ni5', 38),
 ('NaZn13', 38),
 ('Ho6Mo4Al43', 37),
 ('CeNiC2', 37),
 ('ZnSb2O6', 37),
 ('Cr3Si', 37),
 ('CeNi3', 36),
 ('TlxNb6Se8', 36),
 ('NaLa6OsI12', 36),
 ('HoNi3Hx-frame', 35),
 ('Ilmenite-FeTiO3', 35),
 ('CeAsS', 34),
 ('InNi2', 34),
 ('Cr5CsS8', 34),
 ('La3NbO7(oS)', 34),
 ('FeOCl', 34),
 ('Ce2Ni17Si9', 34),
 ('Fe14Nd2B', 33),
 ('K4CdCl6', 33),
 ('Ni3Pb2S2', 33),
 ('Hf3Ni2Si3', 32),
 ('Eu2CuS3', 32),
 ('Ce3Ni6Si2', 31),
 ('Cs3CoCl5', 31),
 ('CrVO4', 31),
 ('Nickeline-NiAs', 31),
 ('Th2TeN2', 31),
 ('FeSiTi', 31),
 ('CoGa8Ho2', 31),
 ('K2GeF6', 31),
 ('Al2CdS4', 30),
 ('Garnet-Al2Ca3Si3O12', 30),
 ('NiSSb', 30),
 ('LiNbO3', 30),
 ('Co3Lu2Si5', 30),
 ('La3CuSiS7', 30),
 ('Al2Zr3(tP20)', 29),
 ('Tl3AsS4', 29),
 ('BaPtSb', 29),
 ('CeCo4B4', 29),
 ('Co4Hf2P3', 29),
 ('Tm2S3', 29),
 ('CuLaS2', 28),
 ('SmNiSb', 28),
 ('Y6RuI10', 28),
 ('TiAs', 28),
 ('Cr5B3', 28),
 ('FeAsS-CoSb2', 28),
 ('Perovskite-ScYS3', 28),
 ('MnP', 28),
 ('CoZr2Si2', 27),
 ('Co4NdB4', 27),
 ('Cs3Cr2Cl9', 27),
 ('Wolframite-NiWO4', 27),
 ('CdMn2O4', 27),
 ('Calcite-CaCO3(hR10)', 27),
 ('ReY3B7', 27),
 ('Monazite-CePO4(mP)', 27),
 ('Pr7O12', 26),
 ('NaFeO2(beta)', 26),
 ('Co5YP3', 26),
 ('Sc2Si2O7', 26),
 ('BaFeO2+x', 25),
 ('BaGe2Se4', 25),
 ('YPtAs', 25),
 ('PbCl2', 25),
 ('Ni20Ho6P13', 25),
 ('LuRuB2', 25),
 ('IrYGe2', 25),
 ('CeMn6Ni5', 25),
 ('Ce4Ho11S22', 24),
 ('Co2GaGd6', 24),
 ('PbPS3', 24),
 ('Al8CaCo2', 24),
 ('AgFeO2', 24),
 ('K6HgS4', 23),
 ('U2Mo3Si4', 23),
 ('MoUC2', 23),
 ('FeB', 23),
 ('Ni12SrB6', 23),
 ('Perovskite-NdAlO3', 23),
 ('Bi2Te3', 23),
 ('NiTi2', 23),
 ('Na3AsS3', 23),
 ('LaPtSi', 23),
 ('Ga21Ho4Ni10', 23),
 ('Bixbyite-Mn2O3', 23),
 ('Co3Tb4B6', 23),
 ('ErIr3B2', 23),
 ('Al2Cu', 22),
 ('Rutile-TiO2', 22),
 ('LuRu4B4', 22),
 ('Perovskite-Na3AlF6', 22),
 ('BaSiF6', 22),
 ('Be3Nb', 21),
 ('CoNb3S6', 21),
 ('In5Bi3', 21),
 ('Fe3TlTe3', 21),
 ('LaIrSi', 21),
 ('Cr2Ho2C3', 21),
 ('InPt2Gd', 21),
 ('K2WSe4', 21),
 ('KInS2', 21),
 ('KZnAs', 20),
 ('Elpasolite-K2NaAlF6', 20),
 ('Al4Mo2Yb', 20),
 ('Na2SiO3', 20),
 ('ZrSSi', 20),
 ('Li2ZrF6', 20),
 ('KOsF6', 20),
 ('SrGaSn', 20),
 ('Ca14MnAs11', 19),
 ('Mo5Si3', 19),
 ('CuCrSe2-AgCrSe2(R3m)', 19),
 ('CsCu2Cl3', 19),
 ('Co3Ga9Y2', 19),
 ('Nd2Te4O11', 19),
 ('Sillenite-Bi12SiO20', 19),
 ('Perovskite-SrTiO3-Cr3AsN', 19),
 ('FeBiO3', 19),
 ('YTaO4', 19),
 ('InTe-Tl2Se2', 19),
 ('Rh3ScSi7', 19),
 ('Hf5Rh2In4', 19),
 ('Na2HgO2', 19),
 ('K2Pb(SO4)2', 19),
 ('FePS3', 18),
 ('Na2Re3S6', 18),
 ('Y3TaO7', 18),
 ('Au3K2', 18),
 ('Mn2ZrHx-frame', 18),
 ('PrOI', 18),
 ('Mn23Th6-filled', 18),
 ('BaCuF4', 18),
 ('Co4Ge7Zr4', 18),
 ('Perovskite-Ba2LaRuO6', 18),
 ('LaB2C2', 18),
 ('CoNb4Si', 17),
 ('Wurtzite-ZnS(2H)', 17),
 ('CaC2', 17),
 ('Er4NiB13', 17),
 ('Fluorite-CaF2(defect)', 17),
 ('V6Si5', 17),
 ('NaTl', 17),
 ('La11Ni4In9', 17),
 ('CsPrS2', 17),
 ('Mo1+xMo6S8', 17),
 ('LiFeO2-alpha', 17),
 ('BaCd11', 17),
 ('K2Cr2O7', 17),
 ('DyMn2O5', 16),
 ('EuGa2S4', 16),
 ('MnPSe3', 16),
 ('Ho11Ge10', 16),
 ('NaHS-HT', 16),
 ('BaNiS2', 16),
 ('Ho2Rh12As7', 16),
 ('Ba4SiAs4', 16),
 ('CuInPt2', 16),
 ('Li3LaSb2', 16),
 ('Co19Zr5P12', 16),
 ('Auricupride-AuCu3', 16),
 ('AlCe', 16),
 ('K2ZnBr4', 16),
 ('CrU8S17', 16),
 ('K5Sb3Sn', 16),
 ('Eu2Zr2O7', 16),
 ('Nd3Ni13B2', 16),
 ('Ca3PI3', 15),
 ('CeRu2B2', 15),
 ('Al2Mo3C', 15),
 ('Cu2HgI4', 15),
 ('NdOF', 15),
 ('MnNb4S8', 15),
 ('TlI', 15),
 ('Pseudobrookite-Fe2TiO5', 15),
 ('Y2TiO5', 15),
 ('Ba4OCl6', 15),
 ('CaLiSi2', 15),
 ('KBrF4', 15),
 ('UCl3', 15),
 ('ScU3S6', 15),
 ('AgErSe2', 15),
 ('La3InS6', 15),
 ('In2Mo15Se19', 15),
 ('Bi(IO3)3', 15),
 ('Pyroxene-CaIrO3', 15),
 ('NdRh2Sn4', 15),
 ('CoGa3Pr8', 15),
 ('Ce2CuGe6', 14),
 ('Pd3US4', 14),
 ('LiTiS2', 14),
 ('YAlGe', 14),
 ('K2PdP2', 14),
 ('Cr11Ge8', 14),
 ('PrPS4', 14),
 ('ZnS(defect)-Cu2HgI4(HT)', 14),
 ('Al2(WO4)3', 14),
 ('Perovskite-BaPbO3', 14),
 ('Hf2Ni3Si4', 14),
 ('CaRh2B2', 14),
 ('NiSmGe3', 14),
 ('CrUS3', 14),
 ('Co3HoP2', 14),
 ('LuMnO3', 14),
 ('AlFe2B2', 14),
 ('In2ZnS4(hR7)', 14),
 ('Li2SnO3', 14),
 ('ErPtF7', 14),
 ('InSn2I5', 14),
 ('LiYSn', 14),
 ('ScUS3', 14),
 ('CuSO4', 13),
 ('Al10Fe2Yb', 13),
 ('Rh(PO3)3', 13),
 ('Perovskite-BaTiO3(tet)', 13),
 ('Sb2S3', 13),
 ('CeNiSb3', 13),
 ('Be2SiO4', 13),
 ('Ce3Pt23Si11', 13),
 ('Ca3Ge2As4', 13),
 ('Sr4Mn3O10', 13),
 ('Ni5YSi3', 13),
 ('ThMoB4', 13),
 ('Cu2Sc2O5', 13),
 ('Fe6Ga6Sc', 13),
 ('Yb3S4', 13),
 ('Zr5Si4', 13),
 ('LiCo6P4', 13),
 ('GdPS', 13),
 ('GaMo4S8(HT)', 13),
 ('Er3GaS6', 13),
 ('Rh2Y3Si2', 13),
 ('Ho5Au2Sb', 13),
 ('AlCoPr2', 13),
 ('DyB2C2', 13),
 ('In5S4', 13),
 ('Aragonite-CaCO3(oP20)', 13),
 ('MoNiP2', 13),
 ('SmSI', 13),
 ('Co2InTb', 13),
 ('Enargite-Cu3AsS4', 13),
 ('Ca5Ga2As6', 12),
 ('Na2MnCl4', 12),
 ('Al2Sr3P4', 12),
 ('La2CuO4', 12),
 ('Cs3Tl2Cl9', 12),
 ('Ba2MnS3', 12),
 ('Na5ReO6', 12),
 ('FeU2S5', 12),
 ('Cementite-Fe3C', 12),
 ('ErNiB4', 12),
 ('La23Ni7Mg4', 12),
 ('Sr3Ti2O7', 12),
 ('Ag3CsS2', 12),
 ('Al3ScC3', 12),
 ('Brucite-Mg(OH)2', 12),
 ('Y2ReC2', 12),
 ('Na4SiO4', 12),
 ('CeTmS3', 12),
 ('Hg3S2Cl2', 12),
 ('Pr10S14O', 12),
 ('La6MnSi2S14', 12),
 ('LaMo5O8', 12),
 ('Sn2F6', 12),
 ('K3SiF7', 12),
 ('K2PtS2', 12),
 ('Ir3Ge7', 12),
 ('Ce3Co11B4', 12),
 ('Perovskite-PbTiO3', 12),
 ('NdTaO4', 12),
 ('MgNb2O6', 11),
 ('Cs2Zn3S4', 11),
 ('Na2SiF6', 11),
 ('Nd2WO6(mS72)', 11),
 ('Mg2Ga', 11),
 ('Yb5Sb3', 11),
 ('Ce(SO4)2', 11),
 ('Gd2SiO5', 11),
 ('Ge2LaPt2', 11),
 ('Tm4Zn5Ge6', 11),
 ('AlOOH(Diaspore)', 11),
 ('Nd(BO2)3', 11),
 ('K2Al2Sb3', 11),
 ('CuSmP2', 11),
 ('CaAl12O19', 11),
 ('Cs3Tb7Te12', 11),
 ('KAlO2', 11),
 ('BaMo6S8', 11),
 ('UAsTe', 11),
 ('Dy3Ni7B2', 11),
 ('Ce2Co7B3', 11),
 ('Co5USi3', 11),
 ('YOOH', 11),
 ('In5Nd4S13', 11),
 ('SrZrS3', 11),
 ('NaCl(defect)-VC.75', 11),
 ('CaCrF5', 11),
 ('Ga41V8', 11),
 ('La4Ge3S12', 11),
 ('Ce3NiSi3', 10),
 ('Dy12Mn5C15', 10),
 ('AgBiSe2', 10),
 ('CdI2', 10),
 ('Perovskite-NaTaO3', 10),
 ('Co5Cr2Mo3', 10),
 ('ZrP2O7', 10),
 ('KBO2', 10),
 ('Cu4NaAs2', 10),
 ('CoYC(tP6)', 10),
 ('SrB4O7', 10),
 ('Ni4U3Si4', 10),
 ('Al3Ti', 10),
 ('CoW2B2', 10),
 ('YBO3', 10),
 ('K3AlSe3', 10),
 ('CaSO4', 10),
 ('KClO3', 10),
 ('Al9Co2Sr', 10),
 ('GeSb2Te4', 10),
 ('Ce2CuGa12', 10),
 ('Fe4Y2Si9', 10),
 ('FeYb2S4', 10),
 ('K2RbC60', 10),
 ('Cu3VS4', 10),
 ('Ag8SiTe6', 10),
 ('CsClO4', 10),
 ('CrSi2', 10),
 ('Tl3VS4', 10),
 ('Na3As', 10),
 ('LiCuO', 10),
 ('CrOOH(R3-m)', 10),
 ('NaNiO2(mS8)', 10),
 ('(Mn,Fe)2PO4F', 10),
 ('CeCoC2', 10),
 ('Marcasite-FeS2(oP6)', 10),
 ('Dy2Ni2Al', 10),
 ('HoPdGe', 10),
 ('NdCu2O4-x', 9),
 ('Sr2IrH5', 9),
 ('CaSiO3(HP)', 9),
 ('K2SnCl6', 9),
 ('FeF3', 9),
 ('Er2FeC4', 9),
 ('BaSO4(HT)', 9),
 ('BaRuO3', 9),
 ('Bi2Pb2Se5', 9),
 ('MgSeO3', 9),
 ('Er2Ge2O7', 9),
 ('Er4Ni13C4', 9),
 ('Ho4Mo4O11', 9),
 ('Na2SnF6', 9),
 ('CoMoO4', 9),
 ('Ho2Ni10B5', 9),
 ('NdTe3', 9),
 ('Er2RhSi3', 9),
 ('Na3Pt4Ge4', 9),
 ('Co11Ga6Sm26', 9),
 ('Mg2NiH4', 9),
 ('Mo3Se4', 9),
 ('AlMgB14', 9),
 ('LaCoAl4', 9),
 ('TbP5O14', 9),
 ('Nd2CuO4', 9),
 ('Ce2Ni22C3', 9),
 ('DyNi4Si', 9),
 ('TbB2C', 9),
 ('LiAlCl4', 9),
 ('CrEr2S4', 9),
 ('TlSbS2', 9),
 ('CeCu6', 9),
 ('Mg6MnO8', 9),
 ('Tb(BO2)3', 9),
 ('HoCuAl3', 9),
 ('Mg3(PO4)2', 9),
 ('LaNi4AlH4-frame', 9),
 ('Ce3Ni2-xSn7-y', 9),
 ('KTh2Se6', 9),
 ('CeNi12B6', 9),
 ('SrLaI4', 9),
 ('K4BeP2', 9),
 ('NaV(SO4)2', 9),
 ('HgPbP14', 9),
 ('Cr3C2', 9),
 ('NiAs2', 9),
 ('Ag16Ca6N', 9),
 ('Er2RhSi3(P6-2c)', 9),
 ('Tl2Ge2S5', 9),
 ('Yb2S2O', 9),
 ('K2NbF7', 9),
 ('Co9S8', 9),
 ('Pyroxene-CaMg(SiO3)2', 9),
 ('Berlinite-AlPO4', 9),
 ('Co2Si', 9),
 ('Ba4Y3F17', 9),
 ('CoGdGa', 9),
 ('PbMo6Cl14', 9),
 ('TlPb2Cl5', 9),
 ('YPdSi', 9),
 ('NaPdC2', 8),
 ('BiZr3F15', 8),
 ('ZnSe2O5', 8),
 ('KNiCl3', 8),
 ('Y3Co2', 8),
 ('Ba2ZnO3', 8),
 ('Al2Ca3Ge2', 8),
 ('Eu3Sb4S9', 8),
 ('KFeS2', 8),
 ('Sm3NS3', 8),
 ('Lu2Te5O13', 8),
 ('Fe2(SO4)3', 8),
 ('LuNiSn2', 8),
 ('Eu2(WO4)3', 8),
 ('Ce4MnSn7', 8),
 ('LiCuO(I4-2m)', 8),
 ('Mg3TeO6', 8),
 ('Er2Ni3B6', 8),
 ('La2SbO2', 8),
 ('K6Fe2O6', 8),
 ('Sm3RuO7', 8),
 ('Dy2Te', 8),
 ('KOH', 8),
 ('Na5FeO4', 8),
 ('LaPd2O4', 8),
 ('Fe3Th7', 8),
 ('AuCaGe', 8),
 ('Co7Ho6Ga21', 8),
 ('Cu4KS3', 8),
 ('NaHS', 8),
 ('K2ZnCl4', 8),
 ('Na3Fe2S4', 8),
 ('LiMnSe2', 8),
 ('NdNiGa2', 8),
 ('BaCu2S2', 8),
 ('Ag2SeO3', 8),
 ('LiTiO2', 8),
 ('Ti4AlN3', 8),
 ('Co40Ta13Si31', 8),
 ('K9Fe2S7', 8),
 ('Au4KSn2', 8),
 ('La2SnS5', 8),
 ('TmRuGa3', 8),
 ('Nb5Cu4Si4', 8),
 ('Kotoite', 8),
 ('NdYbS3', 8),
 ('Rb2CuCl4', 8),
 ('K6W2O3N4', 8),
 ('AlAu4', 8),
 ('Cs4PbO4', 8),
 ('CeRhAl', 8),
 ('Ho2Ni15B9', 8),
 ('Na2SO4', 8),
 ('Ca2P2O7(beta)', 8),
 ('CeSe2O6', 8),
 ('CsCrBr3', 8),
 ('RbNiCrF6', 8),
 ('FeZr6Cl14', 8),
 ('Ga2Gd3', 8),
 ('GeS', 8),
 ('Ca3AsN', 8),
 ('K3AuGe4', 8),
 ('VOSO4-alpha', 8),
 ('Ni3V2O8', 8),
 ('CsGdTe4', 8),
 ('Er3Ru4Si12', 8),
 ('Nd2WO6(oP36)', 8),
 ('Al2S3', 8),
 ('Ba7Cl2F12', 7),
 ('Nd3Co3Ga', 7),
 ('K2Pd3S4', 7),
 ('CoYC(tP3)', 7),
 ('Co7Gd2', 7),
 ('Ni60Yb11C6', 7),
 ('Minium-Pb3O4', 7),
 ('Ce2Li2Ge3', 7),
 ('AgYbS2', 7),
 ('ZnMoO4', 7),
 ('Sm6Co2Si3/Co3Ho4', 7),
 ('K2Cd3S4', 7),
 ('Ca2AlFeO5(oI)', 7),
 ('YbP5O14', 7),
 ('Rb4Re6S13', 7),
 ('CrB', 7),
 ('Rb3PdF5', 7),
 ('SiTa4Te4', 7),
 ('CsNbN2', 7),
 ('BaMnO3', 7),
 ('TaN', 7),
 ('AgSbO3', 7),
 ('Tl4Ge2S6', 7),
 ('Th11Ru12C18', 7),
 ('Hg2P3Cl', 7),
 ('Li8IrO6', 7),
 ('SrSiO3', 7),
 ('Ba3Yb4O9', 7),
 ('V2Zr3Ga4', 7),
 ('La6Ni6P17', 7),
 ('K3Na(SO4)2', 7),
 ('Am(IO3)3', 7),
 ('Ni2TbB2', 7),
 ('Ce2CrN3', 7),
 ('Sr3Al2Ge4', 7),
 ('Lu3Co8Sn4', 7),
 ('Spinel-Al2MgO4, reduced symmetry', 7),
 ('Co(AlCl4)2', 7),
 ('GaMo4S8', 7),
 ('NaBiO2', 7),
 ('Na2Ti6O13', 7),
 ('Cd4GeS6', 7),
 ('K2MnF6', 7),
 ('Sc3FeC4', 7),
 ('(Ce,Zr)O2', 7),
 ('PrAuAs2', 7),
 ('CaIn2Te4', 7),
 ('BaUO4', 7),
 ('Rh3Y2Sn5', 7),
 ('K4Ti3S14', 7),
 ('Zr2NiAs2', 7),
 ('Eu6Rh30As19', 7),
 ('Cs6Ga2P4', 7),
 ('CrUO4', 7),
 ('SrZnO2', 7),
 ('RbBSe3', 7),
 ('Ba3AlSb3', 7),
 ('Sr(NO3)2', 7),
 ('Stannite-Cu2FeSnS4', 7),
 ('MnP4O11', 7),
 ('Nb2Se3', 7),
 ('Pyroxene-MgSiO3', 7),
 ('CoUC2', 7),
 ('Zn4Ta2O9', 7),
 ('NiZr2Hx-frame', 7),
 ('Na3FeS3', 7),
 ('Ca3InP3', 7),
 ('Na3IrH6', 7),
 ('Gd5Si2Ge2', 7),
 ('PbU2Se5', 7),
 ('Mo6Ni6C', 7),
 ('Sm4Co3Ga16', 7),
 ('Gd3MnI3', 7),
 ('Cu2GeS3', 7),
 ('LiPr2Ge6', 7),
 ('Al2(SO4)3', 7),
 ('AgDyTe2', 7),
 ('Sr21Cd4Bi18', 7),
 ('TbFe6Sn6', 7),
 ('HoFe6Sn6', 7),
 ('Ca2SiO4', 7),
 ('ThTi2O6', 7),
 ('PrAgAs2', 7),
 ('Ag7NbS6', 7),
 ('In3Mo15Se19', 7),
 ('CuYS2', 7),
 ('Ag4K2S3', 7),
 ('CePt2B', 7),
 ('Ca2Sb2O7', 7),
 ('ZrSi2', 7),
 ('Eu(N(CN)2)3', 7),
 ('Gd2Fe2I', 7),
 ('ErRh3Si2', 7),
 ('Li5Mo9S12', 7),
 ('Cs2Pt3S4', 7),
 ('Lavenite', 7),
 ('CrOOH(oP8)', 7),
 ('Ce2AlGe2(Ge,Al)4', 6),
 ('ZnB4O7', 6),
 ('Sr2AlFeO5', 6),
 ('K2SnCl6(LT)', 6),
 ('Sr2Zn2As3', 6),
 ('BiMnO3', 6),
 ('K4Nb2S11', 6),
 ('Laves(4H)-MgNi2', 6),
 ('K4Nb6Cl18', 6),
 ('KCd4As3', 6),
 ('LuFe2O4', 6),
 ('RhTe6Cl3', 6),
 ('MnTb2S4', 6),
 ('Cs5SiP3', 6),
 ('K3CrO8', 6),
 ('CuMoF6', 6),
 ('ReBiO4', 6),
 ('RbCuC2', 6),
 ('Sr2ZnP2', 6),
 ('Pb2Sb2S5', 6),
 ('Ca2CdAs2', 6),
 ('NaN3(beta)', 6),
 ('Co5Ti3B2', 6),
 ('SrNi5P3', 6),
 ('Nb2Co4O9', 6),
 ('KCuO', 6),
 ('RbAuS', 6),
 ('AgNb3S4', 6),
 ('CaB2O4(HP)', 6),
 ('K3NO4', 6),
 ('SrNi4Sn2', 6),
 ('Zn3P2', 6),
 ('CrPS4', 6),
 ('Skutterudite-CoAs3', 6),
 ('Yb(ReO4)3', 6),
 ('Zn2Te3O8', 6),
 ('U4S3', 6),
 ('Al3Y2Si2', 6),
 ('Tm7Cu3Te12', 6),
 ('Al5Ni2Zr', 6),
 ('La2Zn6Ge3', 6),
 ('Ba3FeN3', 6),
 ('CeSiP3', 6),
 ('KYbSiS4', 6),
 ('CeErS3', 6),
 ('Ba4Li2Si6', 6),
 ('Li4TeO5', 6),
 ('BaV10O15', 6),
 ('KRu4O8', 6),
 ('CaGa2O4-LT', 6),
 ('PrZn3As3', 6),
 ('Al4Cu9', 6),
 ('Na1.55Si17', 6),
 ('La12I17(C2)3', 6),
 ('CdIn2Se4', 6),
 ('K3BP2', 6),
 ('K6Sn2Te6', 6),
 ('SCl3AlCl4', 6),
 ('Ag8GeS6', 6),
 ('MgB4O7', 6),
 ('CeNi5Sn', 6),
 ('Perovskite-NaNbO3(tP10)', 6),
 ('Ni3SnP', 6),
 ('Nd3Ni7P5', 6),
 ('Li3In2(PO4)3', 6),
 ('Cr3B4', 6),
 ('Ho3Ni19B10', 6),
 ('TiMn2O4', 6),
 ('Sm2F(AuF4)5', 6),
 ('Dy8Rh5C12', 6),
 ('Na52Au81Si29', 6),
 ('Ce3Pd6Sb5', 6),
 ('K2VO2F3', 6),
 ('CeLi2Ge', 6),
 ('UBC', 6),
 ('Sm9Sb5O5', 6),
 ('Cr12P7', 6),
 ('Yb3Sb5O12', 6),
 ('NaOH', 6),
 ('Al3Zr2C4', 6),
 ('Ca9Zn4Bi9', 6),
 ('GeRh3Y2', 6),
 ('Ag7PSe4Se2', 6),
 ('KCoO2(tP16)', 6),
 ('K2PtCl4', 6),
 ('Cs3Bi2Br9', 6),
 ('TaIrTe2', 6),
 ('AlCr2-MoSi2', 6),
 ('Li2MnF6', 6),
 ('Mn23Y6Hx-frame', 6),
 ('Ca11InSb9', 6),
 ('CdGeO3', 6),
 ('NiSc3Si3', 6),
 ('BaTi2Fe4O11', 6),
 ('AlOOH(oS16)', 6),
 ('Ti2CuSb3', 6),
 ('Fe2TiO5(C2/c)', 6),
 ('Sm3SbO3', 6),
 ('Ta2Pt3Se8', 6),
 ('Ho2S2Te', 6),
 ('Sr2Ga2S5', 6),
 ('Na4Ge4S10', 6),
 ('Ce2Cu9In3', 6),
 ('Li7SbO6', 6),
 ('Ho10In20Ni9', 6),
 ('MnNi2Ga', 5),
 ('CeTa7O19', 5),
 ('Th7Se12', 5),
 ('La2Zn3Ge6', 5),
 ('Pb(PO3)2', 5),
 ('Li4CO4(Cm2)', 5),
 ('ScAuSi', 5),
 ('Rb4In2S5', 5),
 ('Rb3TlF6', 5),
 ('Pr2Si2O7', 5),
 ('ZnAu2F8', 5),
 ('RbNO3', 5),
 ('AgTlTe2', 5),
 ('Al5C3N', 5),
 ('Tb117Fe52Ge112', 5),
 ('Pr2MoC2', 5),
 ('PH4I', 5),
 ('Tl4HgBr6', 5),
 ('Zn(CN)2(disordered)', 5),
 ('Zr3PbO4F6', 5),
 ('Pyroxene-MgSiO3-LT', 5),
 ('Be3N2', 5),
 ('SnWO4(oP24)', 5),
 ('K2SnO3', 5),
 ('NaV6O11', 5),
 ('AuEuGe', 5),
 ('Al2CuCl8', 5),
 ('Ge3Nd4Rh4', 5),
 ('InOOH', 5),
 ('BiCa2VO6', 5),
 ('Pr3MoO7', 5),
 ('Er(PO3)3', 5),
 ('Cu2P2O7', 5),
 ('(SeCl3)2ReCl6', 5),
 ('K2B2S7', 5),
 ('NaxBa7F12Cl2', 5),
 ('Li5GaO4-alpha', 5),
 ('Y5Mo2O12', 5),
 ('Na2Zn2O3', 5),
 ('ScRhSi2', 5),
 ('CsCd4As3', 5),
 ('Mg7ScH16', 5),
 ('CdP3Cl', 5),
 ('Ag8SiS6', 5),
 ('Rb2TiO3', 5),
 ('Na2Ta4O11', 5),
 ('PdTa2S6', 5),
 ('Fe3(PO4)2(mP26)', 5),
 ('Sr3SiO5', 5),
 ('La2Ti2O7(mP44)', 5),
 ('Cs9GaO4', 5),
 ('Li2PdO2', 5),
 ('KAlF4', 5),
 ('Na3GdCl6', 5),
 ('Ce2S3', 5),
 ('Mn2SnS4', 5),
 ('KVO3', 5),
 ('Na2PtS2', 5),
 ('Li4CO4(C2)', 5),
 ('Rh2Y3', 5),
 ('MnPt3O6', 5),
 ('UTe2', 5),
 ('Perovskite-BaBiO3(mS20)', 5),
 ('CsCu3S2', 5),
 ('Nd3Br5S2', 5),
 ('CaAl4O7', 5),
 ('Auricupride-AuCu3-filled', 5),
 ('V(PO3)3', 5),
 ('Pr4O4Se(Se2)', 5),
 ('Rb3Nb2S11', 5),
 ('Hf3Mn2Ga6', 5),
 ('CsCl', 5),
 ('Ba5Si3', 5),
 ('Gd2(MoO4)3(oP68)', 5),
 ('CaMn7O12', 5),
 ('Ta2S2C', 5),
 ('Ag51Gd14', 5),
 ('ThB2C', 5),
 ('Zn4B6O13', 5),
 ('SnTaS2', 5),
 ('VO2(HT)', 5),
 ('Cu4Mn3Bi4', 5),
 ('Rb2PtO4', 5),
 ('Nd4N2Te3', 5),
 ('Na3AgO2', 5),
 ('Cu8Rb3Se6', 5),
 ('Baddeleyite-ZrO2(mP12)', 5),
 ('CuClSe2', 5),
 ('CeCr2B6', 5),
 ('Ca11Ga7', 5),
 ('Cd6Sr11Sb12', 5),
 ('Co6Ho7Sn23', 5),
 ('Ga2NiHf', 5),
 ('NbOCl3', 5),
 ('Er3Pd7P4', 5),
 ('CaV3O7', 5),
 ('YVO3', 5),
 ('Nolanite', 5),
 ('Whitlockite', 5),
 ('Al2Ca5Bi6', 5),
 ('BaZn5', 5),
 ('Er3B5O12', 5),
 ('Proustite', 5),
 ('TbNi10Si2', 5),
 ('La4NiS7', 5),
 ('Ca3Ru2O7', 5),
 ('Ce2SiS5', 5),
 ('AlFe(MoO4)3', 5),
 ('Ca9Al6O18', 5),
 ('Cs3HgCl5', 5),
 ('Li6ZnO4', 5),
 ('La3Ru8B6', 5),
 ('Ni3Sn', 5),
 ('La10Ga5Cl4', 5),
 ('In(OH)3', 5),
 ('Ni2(PO3)4', 5),
 ('Dy5Co6Sn18', 5),
 ('Ce4Ni7In8', 5),
 ('CeBS3', 5),
 ('La4Au2O9', 5),
 ('La6MnSb15', 5),
 ('K2B12H12', 5),
 ('CaGaN', 5),
 ('Ce7Li8Ge10', 5),
 ('Mg(NH2)2', 5),
 ('La2Ir3Sb4', 5),
 ('LaNi5Hx-frame', 5),
 ('Ti3C2Si', 5),
 ('Rb4CO4(II)', 5),
 ('Tl2Pt4Te6', 5),
 ('Th2FeB10', 5),
 ('Li4CO4(P4-3m)', 5),
 ('Fe3(PO4)2(mP52)', 5),
 ('Co2P2O7', 5),
 ('K3Cu2P2', 5),
 ('Na5Al3F14', 5),
 ('Ca2RuO4', 5),
 ('SrFe2As2', 5),
 ('Ni3Zr2P3', 5),
 ('Sc3RhC4', 5),
 ('NbSeBr3', 5),
 ('AgGdS2', 5),
 ('BaMg4Si3', 5),
 ('CoW3B3', 5),
 ('CsCuSe4', 5),
 ('(Ca8)xCa2', 5),
 ('KFeF4', 5),
 ('Nb2TiO7', 5),
 ('Ni3Bi2Se2', 5),
 ('Hg5Ga2Se8', 5),
 ('Rb4CO4(I)', 5),
 ('V4Sb2Si', 5),
 ('CdSO4', 5),
 ('La2SrCu2O6', 5),
 ('PrNiSb2', 5),
 ('Pr2Re3B6', 5),
 ('Rb6Si3O9', 5),
 ('fcc(ccp)-Cu', 5),
 ('KCuF3(tI20)', 5),
 ('Ca2V2O7', 5),
 ('Ce4Mg7Ge6', 5),
 ('K4Nb2S9Se2', 5),
 ('RbB5O8', 5),
 ('K2SO4(alpha)', 5),
 ('LaNiO2', 5),
 ('CeNiSb3(oP60)', 5),
 ('Ni(N(CN)2)2', 5),
 ('Y14Co3In3', 5),
 ('KCuO2', 5),
 ('KV3O8', 5),
 ('PtGeSe', 5),
 ('K2Mo9S11', 4),
 ('Ba(OH)2H2O', 4),
 ('FeZrGa2', 4),
 ('KNH2', 4),
 ('NaMo6Cl13', 4),
 ('Pr4Cl5C2', 4),
 ('YBC', 4),
 ('PbO2-alpha', 4),
 ('Ce16Mo21O56', 4),
 ('Cr(CO)6', 4),
 ('CuSeO3', 4),
 ('Bi10(HfCl6)3', 4),
 ('PdSO4', 4),
 ('Ce3Rh3Si2', 4),
 ('Li7PN4', 4),
 ('FeAsO4', 4),
 ('Perovskite-K2LiAlF6', 4),
 ('Pr2C3', 4),
 ('Ba5Ta4O15', 4),
 ('SbPO4', 4),
 ('Ca2H3Br', 4),
 ('CdS2O7', 4),
 ('ErLiO2', 4),
 ('Tl6I4S', 4),
 ('Na4CO4', 4),
 ('BaAl2O4', 4),
 ('Re6S8Br2', 4),
 ('Ag8GeSe6', 4),
 ('Al9YNi3', 4),
 ('Na4UO5', 4),
 ('Ca6GaN5', 4),
 ('Li4CO4(Cm1)', 4),
 ('YNiSi3', 4),
 ('PrBN2', 4),
 ('Ca(BH4)2', 4),
 ('NdSi2-x', 4),
 ('FeSO3', 4),
 ('Tl3AsSe3', 4),
 ('La2NiO4', 4),
 ('Nd2Ni7P4', 4),
 ('Ti4CoFeH6', 4),
 ('BaAlF5', 4),
 ('Gd2Si2O7', 4),
 ('CeMgSi2', 4),
 ('Al9Na4Ge14', 4),
 ('NiCr2O4', 4),
 ('Mg3Ti(BO3)2O2', 4),
 ('U(beta)-CrFe', 4),
 ('CsMo6Te7', 4),
 ('MoS2(4H)', 4),
 ('TiMn2P12', 4),
 ('Sr6NGa5', 4),
 ('Li4CO4', 4),
 ('BaHg11', 4),
 ('RbCr3S5', 4),
 ('Fe(IO3)3', 4),
 ('Spinel-defect', 4),
 ('LiMnO2', 4),
 ('Ru4Sn6Y', 4),
 ('TlAsS2', 4),
 ('CoMo2S4', 4),
 ('Ba4Zr3S10', 4),
 ('Al23Gd4Ni6', 4),
 ...]

In [22]:
for struct_type,freq in uniq_struct_type_freq_sorted[:10]:
    print("{} : {}".format(struct_type, freq))
    fffs = [p[1] for p in uniq_phases if p[2] == struct_type]
    fmt = "  ".join(["{:14}"]*5)
    print(fmt.format(*fffs[0:5]))
    print(fmt.format(*fffs[5:10]))
    print(fmt.format(*fffs[10:15]))
    print(fmt.format(*fffs[15:20]))


ThCr2Si2 : 676
Sm1 Ni2 Sb2     Yb1 Si2 Ag2     Pr1 Fe2 Si2     Np1 Si2 Au2     Tb1 Co2 B2    
Ce1 Al3 Cu1     Nd1 P2 Pd2      Yb1 Co2 Ge2     Np1 Ni2 Ge2     U1 Si2 Ir2    
Gd1 Ni2 Sb2     Ho1 Si2 Pt2     Sm1 Fe2 Si2     Dy1 Mn2 Ge2     Er1 Mn2 Si2   
Pr1 Co2 B2      La1 Mn2 Ge2     Ba1 Ag2 Ge2     Ba1 Al2 Si2     Sm1 Fe2 Ge2   
TiNiSi-MgSrSi : 586
Ti1 As1 Rh1     Gd1 Zn1 Rh1     Pr1 Ge1 Rh1     Hf1 Si1 Rh1     Er1 Ga1 Pd1   
Gd1 Ge1 Rh1     Nb1 Fe1 Si1     Yb1 Ni1 Sn1     Sr1 Li1 Bi1     Yb1 Mg1 Pd1   
Ti1 Co1 P1      U1 Co1 Ge1      Gd1 Ge1 Ir1     Tm1 Ga1 Pt1     Tb1 Ni1 Ge1   
Y1 Si1 Pt1      Ti1 Si1 Ru1     Ho1 Ge1 Ru1     Sm1 Ge1 Pt1     Co1 Mo1 P1    
ZrNiAl-Fe2P : 511
Gd1 Zn1 Pd1     Dy1 Mg1 Pd1     Cr1 Ni1 P1      Ho6 Mn1 Te2     Gd1 Pd1 Pb1   
U1 Al1 Rh1      Sm1 Cd1 Cu1     Nb1 Fe1 B1      Ce1 Cd1 Pt1     Pu1 Al1 Ni1   
Dy1 Sn1 Pt1     Ho1 Al1 Cu1     Na1 Sr1 P1      La1 Mg1 Tl1     Th1 Al1 Pd1   
Ho1 Mg1 In1     Gd1 In1 Rh1     Yb1 Cd1 Ge1     Zr1 Ga1 Pt1     Tm1 Ag1 Sn1   
Perovskite-CaTiO3 : 439
Eu1 D3 Pd1      Th1 Ta1 N3      Cs1 I1 O3       Rb1 U1 O3       La1 B1 Rh3    
Ca1 Zr1 O3      Ba1 Nb1 O3      Y3 Tl1 C1       Ti3 In1 N1      Ho3 Tl1 C1    
Gd3 In1 N1      K3 Cl1 O1       Nd3 Tl1 C1      Ca3 Au1 N1      Sc3 In1 N1    
Ho1 B1 Rh3      Ce3 Tl1 C1      Ta1 Sn1 O3      Ti3 In1 C1      Ca3 Sn1 O1    
Heusler-AlCu2Mn : 343
Sc1 Al1 Au2     Zr1 In1 Pt2     Li2 Mg1 Sb1     Ce4 Mg9 Fe3     Ce1 In1 Cu2   
Sc1 In1 Pt2     Li2 Mg1 In1     Hf1 Co2 Sn1     Dy1 In1 Au2     Mn1 Ga1 Fe2   
Li2 Sn1 Pt1     Ho1 In1 Au2     Li2 Cd1 Sb1     V1 Co2 Si1      As1 Pd6 Pb1   
Y1 Sb1 Pd2      Mn1 Ga1 Ir2     Cu1 Sn1 Rh2     Li2 Cd1 Ge1     Sc2 Mn1 Si1   
Mn12Th : 339
Ce1 In7 Cu5     Gd1 V2 Fe10     Tm1 Al6 Cu6     Er1 Mn4 Al8     Gd1 Mn6 Al6   
Ho1 Al8 Cr4     Gd1 Fe10 Si2    Ho1 V2 Fe10     Tb1 Fe11 Mo1    Yb1 Mn6 Al6   
Ce3 Fe20 Mo3    Y1 Mn6 Co6      Sm1 Al8 Fe4     Ce1 Al8 Fe4     Sm1 Ti1 Fe11  
La1 Al8 Cr4     Tb1 Si2 Ni10    Yb1 Al6 Cu6     Lu1 Al8 Cu4     Sm1 V2 Fe10   
PbClF/Cu2Sb : 334
Tb1 S1 F1       Na1 Zn1 P1      Ba1 Mn1 Ge1     La1 Co1 Ge1     U1 Ge1 S1     
K1 Li1 S1       Tb1 Co1 Si1     Mg1 Co1 Ge1     Mn1 Cr1 As1     Dy1 Fe1 Si1   
Ba1 H1 Cl1      Bi1 I1 O1       U1 Te1 As1      Pr1 Sb1 Te1     Rb1 Ca1 As1   
Cs1 Mn1 Sb1     Ca1 Mn1 Ge1     Na1 Zn1 P1      Sr1 Cl1 F1      Ac1 Br1 O1    
Perovskite-GdFeO3 : 314
La1 Ga1 O3      Cd1 Tc1 O3      Tb1 Cr1 O3      Lu1 V1 O3       Ba1 Pu1 O3    
K1 Ca1 F3       Ho1 Ni1 O3      Na1 Fe1 F3      Y1 Mn1 O3       La1 Sc1 O3    
La1 Tm1 O3      Y1 Fe1 O3       Ba1 Ce1 O3      Nd1 Rh1 O3      Tb1 Rh1 O3    
Sr1 Ru1 O3      Dy1 Co1 O3      Sm1 Co1 O3      Lu1 Rh1 O3      Ca1 Nb1 O3    
Spinel-Al2MgO4 : 305
Tm2 Cd1 Se4     Li1 V2 O4       Mn1 In2 S4      Mn3 Fe3 O8      Cr1 Fe2 O4    
Zn1 In2 O4      In2 Fe1 S4      Cd1 In2 O4      Sc2 Mn1 Se4     Zn1 Cr2 Se4   
Yb2 Cd1 S4      Fe2 Cu1 O4      Mg1 Rh2 O4      Sc2 Cd1 S4      Li2 Cd1 Cl4   
Mg1 Fe2 O4      Ho2 Cd1 S4      V1 Zn2 O4       Lu2 Mn1 Se4     Zn1 Ga2 O4    
Delafossite-NaCrS2 : 278
Na1 Y1 S2       Cs1 Lu1 S2      Cu1 Rh1 O2      Na1 Dy1 S2      K1 Cr1 O2     
Eu1 Cu1 O2      Tl1 Bi1 Se2     Cs1 Nd1 S2      Eu2 P1 I1       Sr2 Br1 N1    
Mg2 N1 Cl1      Rb1 Tl1 O2      K1 Er1 S2       Sm1 Tl1 Te2     Rb1 Sm1 O2    
Na1 Sm1 Se2     Rb1 Gd1 S2      Li2 Mo1 O3      Y1 Tl1 Te2      Li1 Cr1 O2    

Long Formulas


In [6]:
# What are the longest formulas?
for formula in sorted(formulas, key = lambda x: len(x), reverse = True)[:20]:
    print(formula)


((Si (C H3)2)2 (Si (Si (C H3)3)2) (Si (C H3) (Si (C H3)3)) (Si (C H3) (Si (C H3)2 (Si (Si (C H3)3)3))))
((Si (C H3)2)2 (Si (Si (C H3)3)2) (Si (C H3) (Si (C H3)3)) (Si (C H3) (Si (Si (C H3)3)3)))
(((C H3) ((C H3)3 Si)2 Si (C H3)2 Si)2 Si (C H3) Si (C H3)2 Si (Si (C H3)3)2 Si (C H3)2)2
((((C H3)3 Si)3 Si (C H3)2 Si)2 Si (C H3) Si (C H3)2 Si (Si (C H3)3)2 Si (C H3)2)2
((Si (C H3)2)2 (Si (Si (C H3)3)2)2 (Si (C H3) (Si (C H3)2 (Si (Si (C H3)3)3))))
((Si (C H3)2)3 (Si (Si (C H3)3)2) (Si (C H3) (Si (C H3)2 (Si (Si (C H3)3)3))))
((Si (C H3)2)3 (Si (Si (C H3)3)2) (Si (C H3) (Si (Si (C H3)3)3)))
((Si (C H3)2)2 (Si (Si (C H3)3)2)2 (Si (C H3) (Si (C H3)3)))
((Si (C H3)2)4 (Si (C H3) (Si (C H3)3)) (Si (Si (C H3)3)2))
Ba8 (Si2.63 Al3.28) (Si11.3 Al4.32) (Si16.9 Al6.48)
(Mo138 O410 (O H)20 (H2 O)46) (H3 O)40 (H2 O)108
(Mo138 O410 (O H)20 (H2 O)38) (H3 O)40 (H2 O)78
(Mo138 O406 (O H)16 (H2 O)46) (H3 O)28 (H2 O)88
(Mo142 O400 (O H)52 (H2 O)38) (H3 O)28 (H2 O)34
(Mo148 O436 (O H)15 (H2 O)58) (H3 O)27 (H2 O)86
(Mo150 O451 (O H)5 (H2 O)61) (H3 O)35 (H2 O)139
Al1.5 (Al0.805 Nb0.195) (Al1.5 Ir1.5) Ir0.5 Nb3
(Li0.508 Fe0.192) (Li1.192 Fe0.808) (Fe2 O4)
(Si (C H3)3)4 ((C H3)11 Si6)2 (Si4 (C H3)4)
((Si (C H3)3)3 (C H3)8 Si6)2  (Si2 (C H3)4)

Two key insights:

  1. Just because there are three elements in the formula doesn't mean the compound is fundamentally a ternary. There are doped binaries which masquerade as ternaries. And there are doped ternaries which masquerade as quaternaries, or even quintenaries. Because I only asked for compositions with 3 elements, this data is missing.
  2. ICSD has strategically placed parentheses in the formulas which give hints as to logical groupings. For example: (Ho1.3 Ti0.7) ((Ti0.64 Ho1.36) O6.67) is in fact in the pyrochlore family, A2B2O7.

Intermetallics

How many intermetallics does the ICSD database contain?


In [8]:
def filter_in_set(compound, universe):
    return all((e in universe) for e in Composition(compound))

transition_metals = [e for e in Element if e.is_transition_metal]
tm_ternaries = [c for c in formulas if filter_in_set(c, transition_metals)]
print("Number of intermetallics:", len(tm_ternaries))


Number of intermetallics: 1021

In [15]:
unique_tm_ternaries = set([Composition(c).formula for c in tm_ternaries])
print("Number of unique intermetallics:", len(unique_tm_ternaries))


Number of unique intermetallics: 848

In [16]:
unique_tm_ternaries


Out[16]:
{u'Ag0.25 Pd0.5 Au0.25',
 u'Cd0.99 Ag0.09 Au0.91',
 u'Cd2 Ag1 Au1',
 u'Co0.05 Pd0.9 Rh0.05',
 u'Co0.5 Ni0.5 Pt1',
 u'Co1 Ni1 Pt2',
 u'Cr0.176 Co0.442 Mo0.382',
 u'Cr0.2 Fe0.6 Mo0.2',
 u'Cr0.2 Ni0.72 W0.08',
 u'Cr0.21 Fe0.62 Mo0.17',
 u'Cr0.26 Fe0.62 Co0.12',
 u'Cr0.4 Fe0.475 W0.125',
 u'Cr0.4 Mo0.32 W0.28',
 u'Cr0.8 Fe3 Re1.2',
 u'Cr0.8 Ni0.8 Mo0.4',
 u'Cr0.84 Co0.28 Re0.84',
 u'Cr0.86 Co0.286 Re0.853',
 u'Cr1 Co1 Pt2',
 u'Cr1.14 Ni0.71 W0.14',
 u'Cr1.67 Fe3.1 Mo0.23',
 u'Cr15.01 Co22.99 W15',
 u'Cr2.6 Co7.8 W2.6',
 u'Cr6 Fe18 Mo5',
 u'Cr9.54 Ni21.22 Mo25.24',
 u'Cr9.61 Ni21.27 Mo25.12',
 u'Cu0.33 Ni0.34 Au0.33',
 u'Cu0.333 Ni0.333 Pd0.333',
 u'Cu0.453 Pt0.047 Au0.5',
 u'Cu0.75 Pd0.25 Au1',
 u'Cu0.76 Pd0.24 Au1',
 u'Cu0.84 Ni0.14 Au0.98',
 u'Cu0.86 Ni0.14 Au1',
 u'Cu0.94 Pt0.06 Au1',
 u'Cu0.95 Pt0.05 Au1',
 u'Cu1 Ag0.05 Au0.95',
 u'Cu1 Ag0.08 Au0.92',
 u'Cu1 Ni0.1 Au0.9',
 u'Cu1 Ni0.14 Au0.86',
 u'Cu1.33 Ni1.33 Pd1.33',
 u'Fe0.01 Cu0.49 Au0.5',
 u'Fe0.129 Co0.853 Au0.018',
 u'Fe0.15 Ni0.55 Rh0.3',
 u'Fe0.333 Cu0.333 Ni0.334',
 u'Fe0.4 Ni0.5 Pt0.1',
 u'Fe0.5 Co0.5 Pt1',
 u'Fe0.5 Cu0.5 Pt1',
 u'Fe0.5 Ni0.5 Pt1',
 u'Fe0.5 Ni0.5 Pt3',
 u'Fe0.75 Ni0.125 Pt0.125',
 u'Fe1 Co1 Pt2',
 u'Fe1 Cu1 Pt2',
 u'Fe1 Ir0.05 Rh0.95',
 u'Fe1 Ni1 Pt2',
 u'Fe1 Pd1.5 Au1.5',
 u'Fe1 Rh0.5 Pt0.5',
 u'Fe1.5 Ni0.25 Pt0.25',
 u'Fe1.5 Ni1.5 Pt1',
 u'Fe2 Rh1 Pt1',
 u'Fe5.6 Ni22.4 Mo28',
 u'Hf0.08 Mo1.12 Ru0.8',
 u'Hf0.1 Ti0.9 Ni1',
 u'Hf0.1 Ti0.95 Ni0.95',
 u'Hf0.1 Ti1 Ni0.9',
 u'Hf0.16 Zr3.04 Mn8.8',
 u'Hf0.16675 Ti0.16675 Mo0.667',
 u'Hf0.16675 Ti0.16675 W0.667',
 u'Hf0.16675 Zr0.16675 Mo0.667',
 u'Hf0.167 Zr0.167 W0.666',
 u'Hf0.17 Os0.5 W0.33',
 u'Hf0.17 Ti1 Ni0.83',
 u'Hf0.172 Zr3.268 Mn8.56',
 u'Hf0.24 Ti0.76 Ni1',
 u'Hf0.25 Ti0.89 Ni0.86',
 u'Hf0.3 Zr0.7 Zn2',
 u'Hf0.32 Zr1.68 Fe1',
 u'Hf0.36 Ti0.64 Ni1',
 u'Hf0.4 Ti0.8 Ni0.8',
 u'Hf0.4 Ti1 Ni0.6',
 u'Hf0.4 Zr0.4 Nb1.2',
 u'Hf0.42 Ti0.91 Ni0.67',
 u'Hf0.46 Ti0.75 Ni0.79',
 u'Hf0.5 Ta0.5 Fe2',
 u'Hf0.5 Ti0.5 Fe2',
 u'Hf0.5 Ti0.5 Mo2',
 u'Hf0.5 Ti0.5 Ru1',
 u'Hf0.5 Zr0.5 Fe2',
 u'Hf0.5 Zr0.5 Mo2',
 u'Hf0.51 Ti0.59 Ni0.9',
 u'Hf0.667 Ti0.333 Ni1',
 u'Hf0.8 Ta0.2 Co2',
 u'Hf0.8 Ta0.2 Fe2',
 u'Hf0.8 Ti0.2 V2',
 u'Hf0.8 Zr0.6 Nb0.6',
 u'Hf0.84 Nb0.16 V2',
 u'Hf0.87 Ta0.13 V2',
 u'Hf0.9 Ta0.9 V1.2',
 u'Hf1 Cu1 Hg2',
 u'Hf1 Ta1 V4',
 u'Hf1 Ti1 W4',
 u'Hf1 V0.8 Fe1.2',
 u'Hf1 V1.5 Ru0.5',
 u'Hf1 Zn20 Ru2',
 u'Hf1 Zr1 Fe1',
 u'Hf1 Zr1 V4',
 u'Hf1 Zr1 W4',
 u'Hf1.2 Zr6.8 Zn16',
 u'Hf1.5 Zn0.5 Cu1',
 u'Hf2 Co0.94 Ni0.06',
 u'Hf2 Ni0.52 Rh0.48',
 u'Hf2 Ni0.58 Ir0.42',
 u'Hf2 Ni0.7 Os0.3',
 u'Hf2 Ni0.7 Ru0.3',
 u'Hf4 Ag1 Pd1',
 u'Hf6 Zn16 Cu7',
 u'Hf9 Co1 Mo4',
 u'Hf9 Co1 Re4',
 u'Hf9 Co1 W4',
 u'Hf9 Fe1 Mo4',
 u'Hf9 Fe1 Re4',
 u'Hf9 Fe1 W4',
 u'Hf9 Ni1 Mo4',
 u'Hf9 Ni1 W4',
 u'Hf9 Re4 Ni1',
 u'Ir0.55 Os0.25 Au0.2',
 u'La0.4 Y0.6 Co5',
 u'La0.5 Y0.5 Co5',
 u'La0.5 Y0.5 Ni5',
 u'La0.5 Zn11 Co0.5',
 u'La0.7 Y0.3 Mn2',
 u'La0.8 Ti0.2 Ni5',
 u'La0.875 Cu1.32 Ni3.93',
 u'La0.899 Cu0.86 Ni4.34',
 u'La0.952 Cu0.94 Ni4.15',
 u'La0.983 Mn1.8 Ni3.24',
 u'La0.989 Mn0.32 Ni4.71',
 u'La0.99 Mn0.32 Ni4.71',
 u'La0.995 Mn0.91 Ni4.1',
 u'La1 Cd1 Au1',
 u'La1 Cd1 Pd1',
 u'La1 Cd2 Ni0.958',
 u'La1 Cd2 Pd1',
 u'La1 Cd20 Ni2',
 u'La1 Co0.3 Ni4.7',
 u'La1 Co1 Cu12',
 u'La1 Co1 Ni4',
 u'La1 Co2.5 Ni2.5',
 u'La1 Cr0.5 Ni4.5',
 u'La1 Cu0.6 Ni4.4',
 u'La1 Cu1 Ni4',
 u'La1 Cu1.2 Ni3.8',
 u'La1 Cu1.5 Ni0.5',
 u'La1 Cu2 Ni3',
 u'La1 Cu2.5 Ni2.5',
 u'La1 Cu3 Ni2',
 u'La1 Fe1 Ni4',
 u'La1 Fe1.4 Ni3.6',
 u'La1 Hg1 Pd1',
 u'La1 Mn0.1 Ni4.9',
 u'La1 Mn0.2 Ni4.8',
 u'La1 Mn0.3 Ni4.7',
 u'La1 Mn0.4 Ni4.6',
 u'La1 Mn0.5 Ni4.5',
 u'La1 Mn0.91 Ni4.1',
 u'La1 Mn1 Ni4',
 u'La1 Mn1.13 Ni3.87',
 u'La1 Mn2 Ni3',
 u'La1 Mn3 Ni2',
 u'La1 Mn6 Ni5',
 u'La1 Ni2 Pt3',
 u'La1 Ni2 Rh3',
 u'La1 Ni3 Rh2',
 u'La1 Ni4 Pt1',
 u'La1 Ni4 Rh1',
 u'La1 Ni4.5 Pt0.5',
 u'La1 Y2 Ni9',
 u'La1 Zn0.39 Ni4.61',
 u'La1 Zn0.91 Au1.09',
 u'La1 Zn0.96 Ni0.04',
 u'La1 Zn1 Ni1',
 u'La1 Zn1 Ni4',
 u'La1 Zn1 Pd1',
 u'La1 Zn1 Rh1',
 u'La1 Zn2.05 Ni2.95',
 u'La1 Zn3.05 Ni1.95',
 u'La1 Zn4 Co9',
 u'La1 Zn4.05 Ni0.95',
 u'La1.092 Mn0.44 Ni4.46',
 u'La1.29 Mn0.46 Ni4.25',
 u'La1.36 Zn9.5 Co8.14',
 u'La15 Cd2 Rh5',
 u'La2 Cd1 Ni1.66',
 u'La2 Cd1 Rh2',
 u'La2 Ni1 Pt1',
 u'La2 Ta0.48 Co16.52',
 u'La2 Ti1 Co16',
 u'La2 V1 Co16',
 u'La2 Zn1 Ni2',
 u'La2.2 V12.8 Co11.7',
 u'La23 Cd4 Pt7',
 u'La23 Cd4 Ru7',
 u'La3 Mn0.92 Ni8.08',
 u'La3 Zn0.52 Cu0.48',
 u'La3 Zn1 Ni3',
 u'La3 Zn4 Pd4',
 u'La3 Zn4 Pt4',
 u'La3.43 Mn1.5 Ni1.07',
 u'La4 Cd1 Co1',
 u'La4 Cd1 Ru1',
 u'La4.18 Mn0.82 Ni1.01',
 u'La6 Cd4 Pd13',
 u'La6 Zn4 Pd13',
 u'La6 Zn4.46 Pd12.54',
 u'La7 Zn1 Ni2',
 u'Mn0.08 Cr0.23 Ni0.69',
 u'Mn0.2 Fe0.5 Ni0.3',
 u'Mn0.2 Zn1.5 Ag0.3',
 u'Mn0.4 Co0.6 Pt1',
 u'Mn0.4 Fe1 Pt2.6',
 u'Mn0.4 Zn0.4 Cu3.2',
 u'Mn0.5 Cr0.5 Pt3',
 u'Mn0.5 Fe0.5 Pd3',
 u'Mn0.5 Fe0.5 Pt1',
 u'Mn1 Fe1 Pt2',
 u'Mn1 Hg0.75 Au0.25',
 u'Mn1.2 Fe2.6 Ni0.2',
 u'Mn2.58 Fe0.42 Pt1',
 u'Mn3 Rh0.5 Pt0.5',
 u'Mn3.31 Co3.31 Mo3.31',
 u'Mo0.2 Pd0.6 Rh0.2',
 u'Mo0.25 Ru0.35 Pd0.4',
 u'Mo0.25 Ru0.5 Pd0.25',
 u'Mo0.3 Ru0.3 Rh0.4',
 u'Mo0.4 Pd0.35 Rh0.25',
 u'Mo0.45 Os0.1 W0.45',
 u'Mo0.5 Pd0.45 Rh0.05',
 u'Mo0.66 Ru0.66 Rh0.66',
 u'Mo0.67 Ru0.67 W0.67',
 u'Mo0.8 Pd0.4 Rh0.8',
 u'Mo3 Ru0.5 Ir0.5',
 u'Mo6 Ru1 Os1',
 u'Nb0.3 Co0.4 Pt0.3',
 u'Nb0.333 Mo0.333 W0.333',
 u'Nb0.333 Re0.333 Mo0.333',
 u'Nb0.333 V0.333 Re0.333',
 u'Nb0.4 Cr0.2 Mo0.4',
 u'Nb0.5 Ni3 Mo0.5',
 u'Nb0.5 V0.5 Co3',
 u'Nb1 Co0.2 Pt0.8',
 u'Nb1 Cr0.44 Co1.56',
 u'Nb1 Cr0.66 Co1.34',
 u'Nb1 Cr1 Fe1',
 u'Nb1 Cr1 Ni1',
 u'Nb1 Cr1.02 Ni0.98',
 u'Nb1 Cr1.04 Co0.96',
 u'Nb1 Cr1.38 Co0.62',
 u'Nb1 Fe1.4 Co1.6',
 u'Nb1 V1 Co1',
 u'Nb1 V1 Cr1',
 u'Nb1 V1 Ni1',
 u'Nb1.026 Zn20 Fe1.97',
 u'Nb1.12 Ni26.88 Mo28',
 u'Nb2 Fe1 Co3',
 u'Nb3 Cr0.062 Au0.938',
 u'Nb3 Fe0.062 Au0.938',
 u'Nb3 Fe0.2 Pt0.8',
 u'Nb3 Ir0.25 Au0.75',
 u'Nb3 Os0.5 Au0.5',
 u'Nb3 Pt0.5 Au0.5',
 u'Nb3 Pt0.7 Au0.3',
 u'Nb3 V3 Ir2',
 u'Nb3 Zn1 Au1',
 u'Nb6 Pd1 Pt1',
 u'Nb6 Pd1 Rh1',
 u'Nb6 Pt0.6 Au1.4',
 u'Nb6 Pt1 Au1',
 u'Nb6 Ru1 Rh1',
 u'Nb6.18 Ni6.18 Mo0.64',
 u'Nb6.5 Co4.55 Pt1.95',
 u'Nb6.5 Fe3.25 Co3.25',
 u'Nb7 Pd8.4 Rh12.6',
 u'Pd0.33 Pt0.34 Au0.33',
 u'Re0.12 Ni1.92 Mo5.46',
 u'Re0.37 Mo1.08 Ru0.55',
 u'Re12.9 Ni2.4 Mo14.7',
 u'Re16.74 Ni5.58 Mo7.68',
 u'Re3 Ni3 Mo8',
 u'Re8.7 Ni5.7 Mo15.6',
 u'Ru0.1 Ir0.43 Os0.47',
 u'Ru0.34 Ir0.33 Os0.33',
 u'Ru0.7 Pd0.15 Rh0.15',
 u'Sc0.35 Ti0.65 Fe2',
 u'Sc1 Cd1 Ni4',
 u'Sc1 Fe1.5 Ru0.5',
 u'Sc1 Mn0.7 Ni1.3',
 u'Sc1 Mn1 Cr1',
 u'Sc1 Ni4 Au1',
 u'Sc1 Zn1 Cu1',
 u'Sc1 Zn1 Pd1',
 u'Sc1 Zn1 Pt1',
 u'Sc3 Zn16.06 Cu2.19',
 u'Sc3 Zn16.514 Cu1.486',
 u'Sc3 Zn17.34 Cu0.66',
 u'Ta0.038 Cr0.904 Mo0.058',
 u'Ta0.066 Cr0.792 Mo0.142',
 u'Ta0.167 Nb0.167 Re0.667',
 u'Ta0.17 Ti0.83 Co3',
 u'Ta0.17 Ti0.83 Ni3',
 u'Ta0.33 Mo0.33 W0.34',
 u'Ta0.33 Nb0.33 V0.34',
 u'Ta0.33 Nb0.33 W0.34',
 u'Ta0.33 Ti0.67 Ni3',
 u'Ta0.333 Nb0.333 Mo0.333',
 u'Ta0.4 Mo0.8 Ru0.8',
 u'Ta0.5 Co3 Mo0.5',
 u'Ta0.5 Fe2 W0.5',
 u'Ta0.5 Nb0.5 Re1',
 u'Ta0.5 Ni3 Mo0.5',
 u'Ta0.5 Ti0.5 Fe2',
 u'Ta0.75 Co2.09 Mo0.16',
 u'Ta0.75 Pd2.06 Rh0.19',
 u'Ta1 Co0.5 Ni2.5',
 u'Ta1 Co1 Ni2',
 u'Ta1 Co1.8 Pt1.2',
 u'Ta1 Co4 Mo1',
 u'Ta1 Cr1 Co1',
 u'Ta1 Cr1 Ni1',
 u'Ta1 Cu0.75 Ni2.25',
 u'Ta1 Pd1.5 Rh1.5',
 u'Ta1 Pd2.01 Rh0.99',
 u'Ta1 Pd2.16 Rh0.84',
 u'Ta1 Pd2.25 Rh0.75',
 u'Ta1 Ru0.33 Pd2.67',
 u'Ta1 Ru0.67 Pd2.33',
 u'Ta1 Ru0.75 Pd2.25',
 u'Ta1 Ru1.5 Pd1.5',
 u'Ta1 Ti1 Co1',
 u'Ta1 Ti1 Fe4',
 u'Ta1 V1 Co1',
 u'Ta1 V1 Cu1',
 u'Ta1 V1 Ni1',
 u'Ta1.46 Co1 Mo0.54',
 u'Ta2 Cr3 Cu1',
 u'Ta2 Cu0.3 Ni0.7',
 u'Ta2 Mn1 V3',
 u'Ta2 V3 Cu1',
 u'Ta2.6 Co6.5 Mo3.9',
 u'Ta3 Ni0.4 Ir0.6',
 u'Ta4 Co1 Ni1',
 u'Ta6.5 Cu3.25 Ni3.25',
 u'Ta6.5 Ni5.85 Mo0.65',
 u'Ti0.048 Cr0.144 Ni0.808',
 u'Ti0.05 Mn0.6 Co0.35',
 u'Ti0.092 V0.828 Fe0.08',
 u'Ti0.1 Mn0.45 Fe0.45',
 u'Ti0.1 Mn0.85 Co0.05',
 u'Ti0.125 Nb0.125 Ni0.75',
 u'Ti0.17 Cr0.21 Fe0.62',
 u'Ti0.18 V0.72 Fe0.1',
 u'Ti0.2 Mn0.2 V0.6',
 u'Ti0.22 V0.5 Cr0.28',
 u'Ti0.25 Nb0.75 Ni3',
 u'Ti0.32 V0.25 Cr0.43',
 u'Ti0.333 Mn0.333 V0.333',
 u'Ti0.5 Ni3 Mo0.5',
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