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Mean-square atomic displacements in lanthanum triiron cobalt dodecaantimonide, determined as a function of temperature using single-crystal neutron diffraction, show that the La atom exhibits an anomalously large displacement at room temperature, Ueq = 0.0196 (9) Å2, because it is too small to fill the atomic cage formed by the corner-linked octahedral framework of M4Sb12, M = Fe, Co. Site-occupancy refinements show 25% vacancies on the La site and an actual Fe:Co ratio of 2.17:1. Analysis of the temperature dependence of the atomic displacements identifies a significant temperature-independent component for the La atom ascribed to static disorder, which amounts to 19% of the room-temperature value. The large-amplitude rattling of the La atom can be effectively linked to the dramatic decrease of the lattice contribution to the thermal conductivity, which is a key factor for improving the thermoelectric behavior of these materials. This ­structure-property relationship offers a new paradigm for the exploration of thermoelectric materials.

Supporting information

cif

Crystallographic Information File (CIF)
Contains datablocks global, phase1, phase2, phase3, phase4, phase5, phase6, phase7, phase8, phase9

sft

Structure factor file (SHELXL table format)
Supplementary material

sft

Structure factor file (SHELXL table format)
Supplementary material

sft

Structure factor file (SHELXL table format)
Supplementary material

sft

Structure factor file (SHELXL table format)
Supplementary material

sft

Structure factor file (SHELXL table format)
Supplementary material

sft

Structure factor file (SHELXL table format)
Supplementary material

sft

Structure factor file (SHELXL table format)
Supplementary material

sft

Structure factor file (SHELXL table format)
Supplementary material

sft

Structure factor file (SHELXL table format)
Supplementary material

Computing details top

For all compounds, data collection: UCLA Crystallographic Computing Package (Strouse 1994); cell refinement: UCLA Crystallographic Computing Package - Program Least (Strouse 1994); data reduction: UCLA Crystallographic Computing Package - Program Reduce, Lehmann-Larson algorithm (Strouse 1994); program(s) used to refine structure: GSAS (Larson & Von Dreele 1986); molecular graphics: ATOMS (Dowty 1993).

(phase1) top
Crystal data top
La.743Fe2.74Co1.26Sb12Dx = 7.901 Mg m3
Mr = 1791.49Neutron radiation, λ = 0.8387 Å
Cubic, Im3Cell parameters from 31 reflections
Hall symbol: -I 2 2 3θ = 18.2–42.6°
a = 9.0971 (6) ŵ = 0.02 mm1
V = 752.85 Å3T = 295 K
Z = 2Sawn parallelepiped, silver
F(000) = 20.633.5 × 2.5 × 2.5 mm
Data collection top
Huber 4-circle, Crystal Logic Controller, Helium-3 detector, DEC Alpha computer
diffractometer
θmax = 50°
Radial–scansh = 016
1405 measured reflectionsk = 016
463 independent reflectionsl = 016
321 reflections with 0.03 standard reflections every 200 reflections
Rint = 0.046 intensity decay: none
Refinement top
Refinement on F0 restraints
Least-squares matrix: fullw = (2Fo/σFo2)2
R[F2 > 2σ(F2)] = 0.045(Δ/σ)max < 0.001
wR(F2) = 0.035Δρmax = 1.05 e Å3
S = 1.31Δρmin = 0.48 e Å3
321 reflectionsExtinction correction: B-C type I Gaussian isotropic
13 parametersExtinction coefficient: 2.32E-04
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
La0.00.00.00.0196 (9).743 (17)
Fe0.250.250.250.0053 (1).685 (8)
Co0.250.250.250.0053 (1).315 (8)
Sb0.00.33678 (9)0.16021 (8)0.0074 (3)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
La0.0197 (9)0.0197 (9)0.0197 (9)0.00.00.0
Fe0.00535 (18)0.00535 (18)0.00535 (18)0.00047 (16)0.00047 (16)0.00047 (16)
Co0.00535 (18)0.00535 (18)0.00535 (18)0.00047 (16)0.00047 (16)0.00047 (16)
Sb0.0052 (3)0.0100 (3)0.0070 (3)0.00.00.0013 (3)
Geometric parameters (Å, º) top
La—Sb3.3927 (9)Sb—Sb2.969 (1)
Fe,Co—Sb2.5422 (4)Sb—Sb3.4294 (8)
Sb—Sb2.914 (1)
Sb—Fe,Co—Sb95.17 (2)Fe,Co—Sb—Fe,Co126.91 (3)
Sb—Fe,Co—Sb84.83 (2)
(phase2) top
Crystal data top
La.743Fe2.74Co1.26Sb12Dx = 7.931 Mg m3
Mr = 1791.49Neutron radiation, λ = 0.8387 Å
Cubic, Im3Cell parameters from 31 reflections
Hall symbol: -I 2 2 3θ = 18.2–42.6°
a = 9.0854 (11) ŵ = 0.02 mm1
V = 749.95 Å3T = 200 K
Z = 2Sawn parallelepiped, silver
F(000) = 20.633.5 × 2.5 × 2.5 mm
Data collection top
Huber 4-circle, Crystal Logic Controller, Helium-3 detector, DEC Alpha computer
diffractometer
θmax = 50°
Radial–scansh = 016
1486 measured reflectionsk = 016
470 independent reflectionsl = 016
316 reflections with 0.03 standard reflections every 200 reflections
Rint = 0.051 intensity decay: none
Refinement top
Refinement on F0 restraints
Least-squares matrix: fullw = (2Fo/σFo2)2
R[F2 > 2σ(F2)] = 0.048(Δ/σ)max < 0.001
wR(F2) = 0.036Δρmax = 0.82 e Å3
S = 1.34Δρmin = 0.43 e Å3
316 reflectionsExtinction correction: B-C type I Gaussian isotropic
11 parametersExtinction coefficient: 2.2E-04
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
La0.00.00.00.0151 (5).743
Fe0.250.250.250.0042 (1).686
Co0.250.250.250.0042 (1).314
Sb0.00.33668 (9)0.15998 (8)0.0057 (3)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
La0.0152 (6)0.0152 (6)0.0152 (6)0.00.00.0
Fe0.00425 (15)0.00425 (15)0.00425 (15)0.00039 (18)0.00039 (18)0.00039 (18)
Co0.00425 (15)0.00425 (15)0.00425 (15)0.00039 (18)0.00039 (18)0.00039 (18)
Sb0.0039 (3)0.0083 (3)0.0049 (3)0.00.00.0008 (3)
Geometric parameters (Å, º) top
La—Sb3.386 (1)Sb—Sb2.967 (1)
Fe,Co—Sb2.5393 (4)Sb—Sb3.4272 (9)
Sb—Sb2.907 (1)
Sb—Fe,Co—Sb95.11 (2)Fe,Co—Sb—Fe,Co126.88 (3)
Sb—Fe,Co—Sb84.88 (2)
(phase3) top
Crystal data top
La.743Fe2.74Co1.26Sb12Dx = 7.931 Mg m3
Mr = 1791.49Neutron radiation, λ = 0.8387 Å
Cubic, Im3Cell parameters from 31 reflections
Hall symbol: -I 2 2 3θ = 18.2–42.6°
a = 9.0857 (11) ŵ = 0.02 mm1
V = 750.02 Å3T = 150 K
Z = 2Sawn parallelepiped, silver
F(000) = 20.633.5 × 2.5 × 2.5 mm
Data collection top
Huber 4-circle, Crystal Logic Controller, Helium-3 detector, DEC Alpha computer
diffractometer
θmax = 50°
Radial–scansh = 016
1492 measured reflectionsk = 016
471 independent reflectionsl = 016
318 reflections with 0.03 standard reflections every 200 reflections
Rint = 0.053 intensity decay: none
Refinement top
Refinement on F0 restraints
Least-squares matrix: fullw = (2Fo/σFo2)2
R[F2 > 2σ(F2)] = 0.045(Δ/σ)max < 0.001
wR(F2) = 0.036Δρmax = 1.11 e Å3
S = 1.35Δρmin = 0.63 e Å3
318 reflectionsExtinction correction: B-C type I Gaussian isotropic
11 parametersExtinction coefficient: 2.2E-04
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
La0.00.00.00.0127 (5).743
Fe0.250.250.250.0032 (1).686
Co0.250.250.250.0032 (1).314
Sb0.00.33659 (9)0.15999 (9)0.0046 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
La0.0127 (5)0.0127 (5)0.0127 (5)0.00.00.0
Fe0.00328 (15)0.00328 (15)0.00328 (15)0.00003 (17)0.00003 (17)0.00003 (17)
Co0.00328 (15)0.00328 (15)0.00328 (15)0.00003 (17)0.00003 (17)0.00003 (17)
Sb0.0031 (3)0.0067 (3)0.0041 (3)0.00.00.0002 (3)
Geometric parameters (Å, º) top
La—Sb3.3861 (9)Sb—Sb2.969 (1)
Fe,Co—Sb2.5391 (4)Sb—Sb3.4276 (9)
Sb—Sb2.907 (1)
Sb—Fe,Co—Sb95.09 (2)Fe,Co—Sb—Fe,Co126.90 (3)
Sb—Fe,Co—Sb84.90 (2)
(phase4) top
Crystal data top
La.743Fe2.74Co1.26Sb12Dx = 7.942 Mg m3
Mr = 1791.49Neutron radiation, λ = 0.8387 Å
Cubic, Im3Cell parameters from 31 reflections
Hall symbol: -I 2 2 3θ = 18.2–42.6°
a = 9.0813 (5) ŵ = 0.02 mm1
V = 748.93 Å3T = 125 K
Z = 2Sawn parallelepiped, silver
F(000) = 20.633.5 × 2.5 × 2.5 mm
Data collection top
Huber 4-circle, Crystal Logic Controller, Helium-3 detector, DEC Alpha computer
diffractometer
θmax = 50°
Radial–scansh = 016
484 measured reflectionsk = 016
337 independent reflectionsl = 016
264 reflections with 0.03 standard reflections every 200 reflections
Rint = 0.024 intensity decay: none
Refinement top
Refinement on F0 restraints
Least-squares matrix: fullw = (2Fo/σFo2)2
R[F2 > 2σ(F2)] = 0.062(Δ/σ)max < 0.001
wR(F2) = 0.043Δρmax = 0.44 e Å3
S = 1.26Δρmin = 0.25 e Å3
264 reflectionsExtinction correction: B-C type I Gaussian isotropic
11 parametersExtinction coefficient: 2.5E-04
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
La0.00.00.00.0107 (6).743
Fe0.250.250.250.0030 (2).686
Co0.250.250.250.0030 (2).314
Sb0.00.33679 (12)0.16008 (11)0.0039 (4)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
La0.0108 (7)0.0108 (7)0.0108 (7)0.00.00.0
Fe0.0031 (2)0.0031 (2)0.0031 (2)0.0002 (3)0.0002 (3)0.0002 (3)
Co0.0031 (2)0.0031 (2)0.0031 (2)0.0002 (3)0.0002 (3)0.0002 (3)
Sb0.0027 (3)0.0058 (3)0.0031 (3)0.00.00.0014 (4)
Geometric parameters (Å, º) top
La—Sb3.386 (1)Sb—Sb2.964 (2)
Fe,Co—Sb2.5382 (5)Sb—Sb3.424 (1)
Sb—Sb2.907 (2)
Sb—Fe,Co—Sb95.15 (3)Fe,Co—Sb—Fe,Co126.88 (4)
Sb—Fe,Co—Sb84.84 (3)
(phase5) top
Crystal data top
La.743Fe2.74Co1.26Sb12Dx = 7.943 Mg m3
Mr = 1791.49Neutron radiation, λ = 0.8387 Å
Cubic, Im3Cell parameters from 31 reflections
Hall symbol: -I 2 2 3θ = 18.2–42.6°
a = 9.0809 (4) ŵ = 0.02 mm1
V = 748.83 Å3T = 100 K
Z = 2Sawn parallelepiped, silver
F(000) = 20.633.5 × 2.5 × 2.5 mm
Data collection top
Huber 4-circle, Crystal Logic Controller, Helium-3 detector, DEC Alpha computer
diffractometer
θmax = 50°
Radial–scansh = 016
1400 measured reflectionsk = 016
459 independent reflectionsl = 016
330 reflections with 0.03 standard reflections every 200 reflections
Rint = 0.041 intensity decay: none
Refinement top
Refinement on F0 restraints
Least-squares matrix: fullw = (2Fo/σFo2)2
R[F2 > 2σ(F2)] = 0.041(Δ/σ)max < 0.001
wR(F2) = 0.031Δρmax = 0.43 e Å3
S = 1.23Δρmin = 0.42 e Å3
330 reflectionsExtinction correction: B-C type I Gaussian isotropic
11 parametersExtinction coefficient: 2.4E-04
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
La0.00.00.00.0100 (3).743
Fe0.250.250.250.0032 (1).686
Co0.250.250.250.0032 (1).314
Sb0.00.33678 (7)0.15995 (7)0.0039 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
La0.0100 (4)0.0100 (4)0.0100 (4)0.00.00.0
Fe0.00320 (13)0.00320 (13)0.00320 (13)0.00051 (14)0.00051 (14)0.00051 (14)
Co0.00320 (13)0.00320 (13)0.00320 (13)0.00051 (14)0.00051 (14)0.00051 (14)
Sb0.00250 (19)0.0058 (2)0.0032 (2)0.00.00.0005 (2)
Geometric parameters (Å, º) top
La—Sb3.3857 (7)Sb—Sb2.964 (1)
Fe,Co—Sb2.5384 (2)Sb—Sb3.4254 (7)
Sb—Sb2.904 (1)
Sb—Fe,Co—Sb95.13 (2)Fe,Co—Sb—Fe,Co126.84 (2)
Sb—Fe,Co—Sb84.86 (2)
(phase6) top
Crystal data top
La.743Fe2.74Co1.26Sb12Dx = 7.942 Mg m3
Mr = 1791.49Neutron radiation, λ = 0.8387 Å
Cubic, Im3Cell parameters from 31 reflections
Hall symbol: -I 2 2 3θ = 18.2–42.6°
a = 9.0814 (5) ŵ = 0.02 mm1
V = 748.95 Å3T = 75 K
Z = 2Sawn parallelepiped, silver
F(000) = 20.633.5 × 2.5 × 2.5 mm
Data collection top
Huber 4-circle, Crystal Logic Controller, Helium-3 detector, DEC Alpha computer
diffractometer
θmax = 50°
Radial–scansh = 016
1390 measured reflectionsk = 016
459 independent reflectionsl = 016
328 reflections with 0.03 standard reflections every 200 reflections
Rint = 0.042 intensity decay: none
Refinement top
Refinement on F0 restraints
Least-squares matrix: fullw = (2Fo/σFo2)2
R[F2 > 2σ(F2)] = 0.042(Δ/σ)max < 0.001
wR(F2) = 0.034Δρmax = 0.58 e Å3
S = 1.36Δρmin = 0.41 e Å3
328 reflectionsExtinction correction: B-C type I Gaussian isotropic
11 parametersExtinction coefficient: 2.3E-04
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
La0.00.00.00.0088 (4).743
Fe0.250.250.250.0030 (1).686
Co0.250.250.250.0030 (1).314
Sb0.00.33671 (8)0.15994 (7)0.0034 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
La0.0089 (4)0.0089 (4)0.0089 (4)0.00.00.0
Fe0.00303 (14)0.00303 (14)0.00303 (14)0.00012 (15)0.00012 (15)0.00012 (15)
Co0.00303 (14)0.00303 (14)0.00303 (14)0.00012 (15)0.00012 (15)0.00012 (15)
Sb0.0026 (2)0.0052 (2)0.0024 (2)0.00.00.0006 (2)
Geometric parameters (Å, º) top
La—Sb3.3852 (8)Sb—Sb2.965 (1)
Fe,Co—Sb2.5384 (3)Sb—Sb3.4260 (7)
Sb—Sb2.904 (1)
Sb—Fe,Co—Sb95.11 (2)Fe,Co—Sb—Fe,Co126.86 (2)
Sb—Fe,Co—Sb84.88 (2)
(phase7) top
Crystal data top
La.743Fe2.74Co1.26Sb12Dx = 7.935 Mg m3
Mr = 1791.49Neutron radiation, λ = 0.8387 Å
Cubic, Im3Cell parameters from 31 reflections
Hall symbol: -I 2 2 3θ = 18.2–42.6°
a = 9.0839 (6) ŵ = 0.02 mm1
V = 749.57 Å3T = 50 K
Z = 2Sawn parallelepiped, silver
F(000) = 20.633.5 × 2.5 × 2.5 mm
Data collection top
Huber 4-circle, Crystal Logic Controller, Helium-3 detector, DEC Alpha computer
diffractometer
θmax = 50°
Radial–scansh = 016
1390 measured reflectionsk = 016
459 independent reflectionsl = 016
329 reflections with 0.03 standard reflections every 200 reflections
Rint = 0.041 intensity decay: none
Refinement top
Refinement on F0 restraints
Least-squares matrix: fullw = (2Fo/σFo2)2
R[F2 > 2σ(F2)] = 0.039(Δ/σ)max < 0.001
wR(F2) = 0.031Δρmax = 0.52 e Å3
S = 1.24Δρmin = 0.46 e Å3
329 reflectionsExtinction correction: B-C type I Gaussian isotropic
11 parametersExtinction coefficient: 2.2E-04
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
La0.00.00.00.0078 (3).743
Fe0.250.250.250.0028 (1).686
Co0.250.250.250.0028 (1).314
Sb0.00.33684 (7)0.16002 (7)0.0031 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
La0.0078 (4)0.0078 (4)0.0078 (4)0.00.00.0
Fe0.00283 (13)0.00283 (13)0.00283 (13)0.00030 (14)0.00030 (14)0.00030 (14)
Co0.00283 (13)0.00283 (13)0.00283 (13)0.00030 (14)0.00030 (14)0.00030 (14)
Sb0.0024 (2)0.0049 (2)0.0022 (2)0.00.00.0004 (2)
Geometric parameters (Å, º) top
La—Sb3.3876 (7)Sb—Sb2.964 (1)
Fe,Co—Sb2.5392 (3)Sb—Sb3.4257 (7)
Sb—Sb2.907 (1)
Sb—Fe,Co—Sb95.16 (2)Fe,Co—Sb—Fe,Co126.85 (2)
Sb—Fe,Co—Sb84.83 (2)
(phase8) top
Crystal data top
La.743Fe2.74Co1.26Sb12Dx = 7.953 Mg m3
Mr = 1791.49Neutron radiation, λ = 0.8387 Å
Cubic, Im3Cell parameters from 31 reflections
Hall symbol: -I 2 2 3θ = 18.2–42.6°
a = 9.0771 (4) ŵ = 0.02 mm1
V = 747.89 Å3T = 25 K
Z = 2Sawn parallelepiped, silver
F(000) = 20.633.5 × 2.5 × 2.5 mm
Data collection top
Huber 4-circle, Crystal Logic Controller, Helium-3 detector, DEC Alpha computer
diffractometer
θmax = 50°
Radial–scansh = 016
1362 measured reflectionsk = 016
459 independent reflectionsl = 016
348 reflections with 0.03 standard reflections every 200 reflections
Rint = 0.041 intensity decay: none
Refinement top
Refinement on F0 restraints
Least-squares matrix: fullw = (2Fo/σFo2)2
R[F2 > 2σ(F2)] = 0.049(Δ/σ)max < 0.001
wR(F2) = 0.036Δρmax = 0.40 e Å3
S = 1.39Δρmin = 0.34 e Å3
348 reflectionsExtinction correction: B-C type I Gaussian isotropic
11 parametersExtinction coefficient: 1.8E-04
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
La0.00.00.00.0066 (3).743
Fe0.250.250.250.0026 (1).686
Co0.250.250.250.0026 (1).314
Sb0.00.33674 (8)0.15996 (7)0.0032 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
La0.0066 (4)0.0066 (4)0.0066 (4)0.00.00.0
Fe0.00264 (14)0.00264 (14)0.00264 (14)0.00016 (15)0.00016 (15)0.00016 (15)
Co0.00264 (14)0.00264 (14)0.00264 (14)0.00016 (15)0.00016 (15)0.00016 (15)
Sb0.0025 (2)0.0049 (2)0.0021 (2)0.00.00.0004 (2)
Geometric parameters (Å, º) top
La—Sb3.3839 (8)Sb—Sb2.963 (1)
Fe,Co—Sb2.5372 (3)Sb—Sb3.4241 (7)
Sb—Sb2.903 (1)
Sb—Fe,Co—Sb95.12 (2)Fe,Co—Sb—Fe,Co126.86 (2)
Sb—Fe,Co—Sb84.87 (2)
(phase9) top
Crystal data top
La.743Fe2.74Co1.26Sb12Dx = 7.955 Mg m3
Mr = 1791.49Neutron radiation, λ = 0.8387 Å
Cubic, Im3Cell parameters from 31 reflections
Hall symbol: -I 2 2 3θ = 18.2–42.6°
a = 9.0762 (12) ŵ = 0.02 mm1
V = 747.67 Å3T = 10 K
Z = 2Sawn parallelepiped, silver
F(000) = 20.633.5 × 2.5 × 2.5 mm
Data collection top
Huber 4-circle, Crystal Logic Controller, Helium-3 detector, DEC Alpha computer
diffractometer
θmax = 50°
Radial–scansh = 016
1492 measured reflectionsk = 016
472 independent reflectionsl = 016
323 reflections with 0.03 standard reflections every 200 reflections
Rint = 0.047 intensity decay: none
Refinement top
Refinement on F0 restraints
Least-squares matrix: fullw = (2Fo/σFo2)2
R[F2 > 2σ(F2)] = 0.037(Δ/σ)max < 0.001
wR(F2) = 0.029Δρmax = 0.72 e Å3
S = 1.16Δρmin = 0.57 e Å3
323 reflectionsExtinction correction: B-C type I Gaussian isotropic
11 parametersExtinction coefficient: 3.1E-04
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
La0.00.00.00.0069 (3).743
Fe0.250.250.250.0026 (1).686
Co0.250.250.250.0026 (1).314
Sb0.00.33669 (7)0.15998 (6)0.0029 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
La0.0069 (3)0.0069 (3)0.0069 (3)0.00.00.0
Fe0.00263 (12)0.00263 (12)0.00263 (12)0.00010 (13)0.00010 (13)0.00010 (13)
Co0.00263 (12)0.00263 (12)0.00263 (12)0.00010 (13)0.00010 (13)0.00010 (13)
Sb0.00188 (19)0.0046 (2)0.00223 (19)0.00.00.00040 (19)
Geometric parameters (Å, º) top
La—Sb3.3833 (8)Sb—Sb2.964 (1)
Fe,Co—Sb2.5368 (4)Sb—Sb3.4237 (8)
Sb—Sb2.904 (1)
Sb—Fe,Co—Sb95.12 (2)Fe,Co—Sb—Fe,Co126.88 (2)
Sb—Fe,Co—Sb84.87 (2)
 
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