Site occupancy and lattice parameters in sigma-phase Co–Cr alloys

Cieslak, J.; Dubiel, S.M.; Reissner, M.

doi:10.1107/S0108768112006234

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Site occupancy and lattice parameters in sigma-phase Co–Cr alloys

J. Cieslak, S. M. Dubiel and M. Reissner

Neutron powder diffraction was used to study the distribution of Co and Cr atoms over different lattice sites as well as the lattice parameters of sigma-phase compounds Co_{100 − x}Cr_x with x = 57.0, 62.7 and 65.8. From the diffractograms recorded in the temperature range of 4.2–300 K it was found for the five crystallographically independent sites that A (2a) and D (8i) are predominantly occupied by Co atoms, while sites B (4f), C (8i) and E (8j) mainly accommodate Cr atoms. The lattice parameters a and c exhibit linear temperature dependencies, with different expansion coefficients in the temperature ranges of 4.2–100 and 100–300 K.

Keywords: sigma phase; intermetallics; site occupancy; neutron powder diffraction.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768112006234/kd5058sup1.cif Contains datablocks global, Co35LH, Co35RT, Co39LH, Co39RT, Co44LH, Co44RT
	Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768112006234/kd5058Co35LHsup2.rtv Contains datablock Co35LH
	Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768112006234/kd5058Co35RTsup3.rtv Contains datablock Co35RT
	Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768112006234/kd5058Co39LHsup4.rtv Contains datablock Co39LH
	Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768112006234/kd5058Co39RTsup5.rtv Contains datablock Co39RT
	Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768112006234/kd5058Co44LHsup6.rtv Contains datablock Co44LH
	Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768112006234/kd5058Co44RTsup7.rtv Contains datablock Co44RT
	Portable Document Format (PDF) file https://doi.org/10.1107/S0108768112006234/kd5058sup8.pdf Tables of atomic positions and parameters of best-fit analyses

Computing details top

For all compounds, program(s) used to refine structure: FULLPROF.

Figures top

(Co35LH) top

Crystal data top

?	c = 4.5266 (2) Å
M_r = ?	V = 348.24 (3) Å³
Tetragonal, P4₂/mnm	Z = ?
Hall symbol: -P 4n 2n	Constant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7710 (5) Å	?, ? × ? × ? mm

Data collection top

Radiation source: nuclear reactor

2θ_min = 0.348°, 2θ_max = 160.148°, 2θ_step = 0.050°

Refinement top

R_p = 1.624	3197 data points
R_wp = 2.093	31 parameters
R_exp = 1.459	0 restraints
R_Bragg = 4.715
χ² = NOT FOUND

Crystal data top

?	V = 348.24 (3) Å³
M_r = ?	Z = ?
Tetragonal, P4₂/mnm	Constant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7710 (5) Å	?, ? × ? × ? mm
c = 4.5266 (2) Å

Data collection top

2θ_min = 0.348°, 2θ_max = 160.148°, 2θ_step = 0.050°

Refinement top

R_p = 1.624	χ² = NOT FOUND
R_wp = 2.093	3197 data points
R_exp = 1.459	31 parameters
R_Bragg = 4.715	0 restraints

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Co01	0.00000	0.00000	0.00000	−0.0026 (4)	1.00 (4)
Co03	0.39792 (16)	0.39792 (16)	0.00000	−0.0026 (4)	0.16 (3)
Co07	0.7404 (2)	0.0653 (3)	0.00000	−0.0026 (4)	0.984 (18)
Co15	0.46413 (18)	0.12918 (16)	0.00000	−0.0026 (4)	0.03 (2)
Co23	0.18245 (10)	0.18245 (10)	0.2536 (6)	−0.0026 (4)	0.051 (10)
CR01	0.00000	0.00000	0.00000	0.00289 (19)	0.08 (4)
CR03	0.39792 (16)	0.39792 (16)	0.00000	0.00289 (19)	0.93 (3)
CR07	0.7404 (2)	0.0653 (3)	0.00000	0.00289 (19)	0.099 (18)
CR15	0.46413 (18)	0.12918 (16)	0.00000	0.00289 (19)	1.05 (2)
CR23	0.18245 (10)	0.18245 (10)	0.2536 (6)	0.00289 (19)	1.04 (9)

(Co35RT) top

Crystal data top

?	c = 4.53884 (15) Å
M_r = ?	V = 350.61 (2) Å³
Tetragonal, P4₂/mnm	Z = ?
Hall symbol: -P 4n 2n	Constant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7890 (3) Å	?, ? × ? × ? mm

Data collection top

Radiation source: nuclear reactor

2θ_min = 30.086°, 2θ_max = 159.086°, 2θ_step = 0.050°

Refinement top

R_p = 1.532	2581 data points
R_wp = 2.004	31 parameters
R_exp = 1.212	0 restraints
R_Bragg = 4.466
χ² = NOT FOUND

Crystal data top

?	V = 350.61 (2) Å³
M_r = ?	Z = ?
Tetragonal, P4₂/mnm	Constant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7890 (3) Å	?, ? × ? × ? mm
c = 4.53884 (15) Å

Data collection top

2θ_min = 30.086°, 2θ_max = 159.086°, 2θ_step = 0.050°

Refinement top

R_p = 1.532	χ² = NOT FOUND
R_wp = 2.004	2581 data points
R_exp = 1.212	31 parameters
R_Bragg = 4.466	0 restraints

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Co01	0.00000	0.00000	0.00000	0.0008 (4)	1.00 (4)
Co03	0.39737 (16)	0.39737 (16)	0.00000	0.0008 (4)	0.14 (3)
Co07	0.7399 (2)	0.0665 (2)	0.00000	0.0008 (4)	1.023 (18)
Co15	0.46425 (16)	0.12847 (15)	0.00000	0.0008 (4)	0.04 (2)
Co23	0.18264 (10)	0.18264 (10)	0.2554 (6)	0.0008 (4)	0.066 (8)
CR01	0.00000	0.00000	0.00000	0.00595 (18)	0.13 (4)
CR03	0.39737 (16)	0.39737 (16)	0.00000	0.00595 (18)	0.99 (3)
CR07	0.7399 (2)	0.0665 (2)	0.00000	0.00595 (18)	0.108 (18)
CR15	0.46425 (16)	0.12847 (15)	0.00000	0.00595 (18)	1.09 (2)
CR23	0.18264 (10)	0.18264 (10)	0.2554 (6)	0.00595 (18)	1.063 (11)

(Co39LH) top

Crystal data top

?	c = 4.5234 (2) Å
M_r = ?	V = 346.94 (3) Å³
Tetragonal, P4₂/mnm	Z = ?
Hall symbol: -P 4n 2n	Constant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7578 (4) Å	?, ? × ? × ? mm

Data collection top

Radiation source: nuclear reactor

2θ_min = 0.285°, 2θ_max = 160.085°, 2θ_step = 0.050°

Refinement top

R_p = 1.450	3197 data points
R_wp = 1.878	30 parameters
R_exp = 1.449	0 restraints
R_Bragg = 4.267
χ² = NOT FOUND

Crystal data top

?	V = 346.94 (3) Å³
M_r = ?	Z = ?
Tetragonal, P4₂/mnm	Constant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7578 (4) Å	?, ? × ? × ? mm
c = 4.5234 (2) Å

Data collection top

2θ_min = 0.285°, 2θ_max = 160.085°, 2θ_step = 0.050°

Refinement top

R_p = 1.450	χ² = NOT FOUND
R_wp = 1.878	3197 data points
R_exp = 1.449	30 parameters
R_Bragg = 4.267	0 restraints

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Co01	0.00000	0.00000	0.00000	0.00024 (13)	1.00 (3)
Co03	0.39781 (14)	0.39781 (14)	0.00000	0.00024 (13)	0.20 (2)
Co07	0.7400 (2)	0.0652 (3)	0.00000	0.00024 (13)	1.046 (11)
Co15	0.46328 (17)	0.13001 (14)	0.00000	0.00024 (13)	0.230 (16)
Co23	0.18232 (9)	0.18232 (9)	0.2523 (5)	0.00024 (13)	0.096 (8)
CR01	0.00000	0.00000	0.00000	0.00024 (13)	0.23 (3)
CR03	0.39781 (14)	0.39781 (14)	0.00000	0.00024 (13)	1.03 (2)
CR07	0.7400 (2)	0.0652 (3)	0.00000	0.00024 (13)	0.184 (11)
CR15	0.46328 (17)	0.13001 (14)	0.00000	0.00024 (13)	1.000 (16)
CR23	0.18232 (9)	0.18232 (9)	0.2523 (5)	0.00024 (13)	1.135 (8)

(Co39RT) top

Crystal data top

?	c = 4.53521 (15) Å
M_r = ?	V = 349.17 (2) Å³
Tetragonal, P4₂/mnm	Z = ?
Hall symbol: -P 4n 2n	Constant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7745 (3) Å	?, ? × ? × ? mm

Data collection top

Radiation source: nuclear reactor

2θ_min = 0.198°, 2θ_max = 159.998°, 2θ_step = 0.050°

Refinement top

R_p = 1.565	3197 data points
R_wp = 2.124	31 parameters
R_exp = 1.398	0 restraints
R_Bragg = 4.511
χ² = NOT FOUND

Crystal data top

?	V = 349.17 (2) Å³
M_r = ?	Z = ?
Tetragonal, P4₂/mnm	Constant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7745 (3) Å	?, ? × ? × ? mm
c = 4.53521 (15) Å

Data collection top

2θ_min = 0.198°, 2θ_max = 159.998°, 2θ_step = 0.050°

Refinement top

R_p = 1.565	χ² = NOT FOUND
R_wp = 2.124	3197 data points
R_exp = 1.398	31 parameters
R_Bragg = 4.511	0 restraints

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Co01	0.00000	0.00000	0.00000	0.0029 (4)	1.00 (4)
Co03	0.39770 (17)	0.39770 (17)	0.00000	0.0029 (4)	0.12 (2)
Co07	0.7389 (2)	0.0663 (3)	0.00000	0.0029 (4)	0.814 (15)
Co15	0.46435 (17)	0.12902 (16)	0.00000	0.0029 (4)	0.053 (18)
Co23	0.18298 (10)	0.18298 (10)	0.2546 (6)	0.0029 (4)	0.091 (9)
CR01	0.00000	0.00000	0.00000	0.0075 (2)	0.09 (4)
CR03	0.39770 (17)	0.39770 (17)	0.00000	0.0075 (2)	0.79 (2)
CR07	0.7389 (2)	0.0663 (3)	0.00000	0.0075 (2)	0.092 (15)
CR15	0.46435 (17)	0.12902 (16)	0.00000	0.0075 (2)	0.854 (18)
CR23	0.18298 (10)	0.18298 (10)	0.2546 (6)	0.0075 (2)	0.816 (9)

(Co44LH) top

Crystal data top

?	c = 4.5193 (3) Å
M_r = ?	V = 344.89 (4) Å³
Tetragonal, P4₂/mnm	Z = ?
Hall symbol: -P 4n 2n	Constant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7359 (5) Å	?, ? × ? × ? mm

Data collection top

Radiation source: nuclear reactor

2θ_min = 0.433°, 2θ_max = 160.233°, 2θ_step = 0.050°

Refinement top

R_p = 1.689	3197 data points
R_wp = 2.247	30 parameters
R_exp = 1.262	0 restraints
R_Bragg = 5.447
χ² = NOT FOUND

Crystal data top

?	V = 344.89 (4) Å³
M_r = ?	Z = ?
Tetragonal, P4₂/mnm	Constant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7359 (5) Å	?, ? × ? × ? mm
c = 4.5193 (3) Å

Data collection top

2θ_min = 0.433°, 2θ_max = 160.233°, 2θ_step = 0.050°

Refinement top

R_p = 1.689	χ² = NOT FOUND
R_wp = 2.247	3197 data points
R_exp = 1.262	30 parameters
R_Bragg = 5.447	0 restraints

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Co01	0.00000	0.00000	0.00000	0.00299 (17)	1.00 (4)
Co03	0.39874 (18)	0.39874 (18)	0.00000	0.00299 (17)	0.23 (3)
Co07	0.7402 (2)	0.0650 (3)	0.00000	0.00299 (17)	1.017 (12)
Co15	0.4637 (2)	0.12972 (18)	0.00000	0.00299 (17)	0.194 (17)
Co23	0.18280 (12)	0.18280 (12)	0.2525 (7)	0.00299 (17)	0.230 (9)
CR01	0.00000	0.00000	0.00000	0.00299 (17)	0.12 (4)
CR03	0.39874 (18)	0.39874 (18)	0.00000	0.00299 (17)	0.89 (3)
CR07	0.7402 (2)	0.0650 (3)	0.00000	0.00299 (17)	0.103 (12)
CR15	0.4637 (2)	0.12972 (18)	0.00000	0.00299 (17)	0.926 (17)
CR23	0.18280 (12)	0.18280 (12)	0.2525 (7)	0.00299 (17)	0.890 (9)

(Co44RT) top

Crystal data top

?	c = 4.5308 (3) Å
M_r = ?	V = 347.10 (4) Å³
Tetragonal, P4₂/mnm	Z = ?
Hall symbol: -P 4n 2n	Constant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7526 (6) Å	?, ? × ? × ? mm

Data collection top

Radiation source: nuclear reactor

2θ_min = 0.394°, 2θ_max = 160.194°, 2θ_step = 0.050°

Refinement top

R_p = 1.752	3197 data points
R_wp = 2.349	30 parameters
R_exp = 1.282	0 restraints
R_Bragg = 6.795
χ² = NOT FOUND

Crystal data top

?	V = 347.10 (4) Å³
M_r = ?	Z = ?
Tetragonal, P4₂/mnm	Constant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7526 (6) Å	?, ? × ? × ? mm
c = 4.5308 (3) Å

Data collection top

2θ_min = 0.394°, 2θ_max = 160.194°, 2θ_step = 0.050°

Refinement top

R_p = 1.752	χ² = NOT FOUND
R_wp = 2.349	3197 data points
R_exp = 1.282	30 parameters
R_Bragg = 6.795	0 restraints

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Co01	0.00000	0.00000	0.00000	0.00573 (19)	1.00 (3)
Co03	0.3989 (2)	0.3989 (2)	0.00000	0.00573 (19)	0.21 (3)
Co07	0.7402 (3)	0.0649 (4)	0.00000	0.00573 (19)	0.895 (12)
Co15	0.4639 (2)	0.13032 (19)	0.00000	0.00573 (19)	0.233 (17)
Co23	0.18231 (13)	0.18231 (13)	0.2531 (7)	0.00573 (19)	0.185 (9)
CR01	0.00000	0.00000	0.00000	0.00573 (19)	0.03 (3)
CR03	0.3989 (2)	0.3989 (2)	0.00000	0.00573 (19)	0.82 (3)
CR07	0.7402 (3)	0.0649 (4)	0.00000	0.00573 (19)	0.140 (12)
CR15	0.4639 (2)	0.13032 (19)	0.00000	0.00573 (19)	0.802 (17)
CR23	0.18231 (13)	0.18231 (13)	0.2531 (7)	0.00573 (19)	0.849 (9)

Experimental details

	(Co35LH)	(Co35RT)	(Co39LH)	(Co39RT)
Crystal data
Chemical formula	?	?	?	?
M_r	?	?	?	?
Crystal system, space group	Tetragonal, P4₂/mnm	Tetragonal, P4₂/mnm	Tetragonal, P4₂/mnm	Tetragonal, P4₂/mnm
Temperature (K)	?	?	?	?
a, c (Å)	8.7710 (5), 4.5266 (2)	8.7890 (3), 4.53884 (15)	8.7578 (4), 4.5234 (2)	8.7745 (3), 4.53521 (15)
V (Å³)	348.24 (3)	350.61 (2)	346.94 (3)	349.17 (2)
Z	?	?	?	?
Radiation type	Constant Wavelength Neutron Diffraction, λ = 1.594000 Å	Constant Wavelength Neutron Diffraction, λ = 1.594000 Å	Constant Wavelength Neutron Diffraction, λ = 1.594000 Å	Constant Wavelength Neutron Diffraction, λ = 1.594000 Å
Specimen shape, size (mm)	?, ? × ? × ?	?, ? × ? × ?	?, ? × ? × ?	?, ? × ? × ?

Data collection
Diffractometer	?	?	?	?
Specimen mounting	?	?	?	?
Data collection mode	?	?	?	?
Scan method	?	?	?	?
2θ values (°)	2θ_min = 0.348 2θ_max = 160.148 2θ_step = 0.050	2θ_min = 30.086 2θ_max = 159.086 2θ_step = 0.050	2θ_min = 0.285 2θ_max = 160.085 2θ_step = 0.050	2θ_min = 0.198 2θ_max = 159.998 2θ_step = 0.050

Refinement
R factors and goodness of fit	R_p = 1.624, R_wp = 2.093, R_exp = 1.459, R_Bragg = 4.715, χ² = NOT FOUND	R_p = 1.532, R_wp = 2.004, R_exp = 1.212, R_Bragg = 4.466, χ² = NOT FOUND	R_p = 1.450, R_wp = 1.878, R_exp = 1.449, R_Bragg = 4.267, χ² = NOT FOUND	R_p = 1.565, R_wp = 2.124, R_exp = 1.398, R_Bragg = 4.511, χ² = NOT FOUND
No. of data points	3197	2581	3197	3197
No. of parameters	31	31	30	31

	(Co44LH)	(Co44RT)
Crystal data
Chemical formula	?	?
M_r	?	?
Crystal system, space group	Tetragonal, P4₂/mnm	Tetragonal, P4₂/mnm
Temperature (K)	?	?
a, c (Å)	8.7359 (5), 4.5193 (3)	8.7526 (6), 4.5308 (3)
V (Å³)	344.89 (4)	347.10 (4)
Z	?	?
Radiation type	Constant Wavelength Neutron Diffraction, λ = 1.594000 Å	Constant Wavelength Neutron Diffraction, λ = 1.594000 Å
Specimen shape, size (mm)	?, ? × ? × ?	?, ? × ? × ?

Data collection
Diffractometer	?	?
Specimen mounting	?	?
Data collection mode	?	?
Scan method	?	?
2θ values (°)	2θ_min = 0.433 2θ_max = 160.233 2θ_step = 0.050	2θ_min = 0.394 2θ_max = 160.194 2θ_step = 0.050

Refinement
R factors and goodness of fit	R_p = 1.689, R_wp = 2.247, R_exp = 1.262, R_Bragg = 5.447, χ² = NOT FOUND	R_p = 1.752, R_wp = 2.349, R_exp = 1.282, R_Bragg = 6.795, χ² = NOT FOUND
No. of data points	3197	3197
No. of parameters	30	30

Computer programs: FULLPROF.

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