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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 Co100 − xCrx 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.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768112006234/kd5058sup1.cif
Contains datablocks global, Co35LH, Co35RT, Co39LH, Co39RT, Co44LH, Co44RT

rtv

Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768112006234/kd5058Co35LHsup2.rtv
Contains datablock Co35LH

rtv

Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768112006234/kd5058Co35RTsup3.rtv
Contains datablock Co35RT

rtv

Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768112006234/kd5058Co39LHsup4.rtv
Contains datablock Co39LH

rtv

Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768112006234/kd5058Co39RTsup5.rtv
Contains datablock Co39RT

rtv

Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768112006234/kd5058Co44LHsup6.rtv
Contains datablock Co44LH

rtv

Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768112006234/kd5058Co44RTsup7.rtv
Contains datablock Co44RT

pdf

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
[Figure 1]
[Figure 2]
[Figure 3]
[Figure 4]
[Figure 5]
(Co35LH) top
Crystal data top
?c = 4.5266 (2) Å
Mr = ?V = 348.24 (3) Å3
Tetragonal, P42/mnmZ = ?
Hall symbol: -P 4n 2nConstant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7710 (5) Å?, ? × ? × ? mm
Data collection top
Radiation source: nuclear reactor2θmin = 0.348°, 2θmax = 160.148°, 2θstep = 0.050°
Refinement top
Rp = 1.6243197 data points
Rwp = 2.09331 parameters
Rexp = 1.4590 restraints
RBragg = 4.715
χ2 = NOT FOUND
Crystal data top
?V = 348.24 (3) Å3
Mr = ?Z = ?
Tetragonal, P42/mnmConstant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7710 (5) Å?, ? × ? × ? mm
c = 4.5266 (2) Å
Data collection top
2θmin = 0.348°, 2θmax = 160.148°, 2θstep = 0.050°
Refinement top
Rp = 1.624χ2 = NOT FOUND
Rwp = 2.0933197 data points
Rexp = 1.45931 parameters
RBragg = 4.7150 restraints
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Co010.000000.000000.000000.0026 (4)1.00 (4)
Co030.39792 (16)0.39792 (16)0.000000.0026 (4)0.16 (3)
Co070.7404 (2)0.0653 (3)0.000000.0026 (4)0.984 (18)
Co150.46413 (18)0.12918 (16)0.000000.0026 (4)0.03 (2)
Co230.18245 (10)0.18245 (10)0.2536 (6)0.0026 (4)0.051 (10)
CR010.000000.000000.000000.00289 (19)0.08 (4)
CR030.39792 (16)0.39792 (16)0.000000.00289 (19)0.93 (3)
CR070.7404 (2)0.0653 (3)0.000000.00289 (19)0.099 (18)
CR150.46413 (18)0.12918 (16)0.000000.00289 (19)1.05 (2)
CR230.18245 (10)0.18245 (10)0.2536 (6)0.00289 (19)1.04 (9)
(Co35RT) top
Crystal data top
?c = 4.53884 (15) Å
Mr = ?V = 350.61 (2) Å3
Tetragonal, P42/mnmZ = ?
Hall symbol: -P 4n 2nConstant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7890 (3) Å?, ? × ? × ? mm
Data collection top
Radiation source: nuclear reactor2θmin = 30.086°, 2θmax = 159.086°, 2θstep = 0.050°
Refinement top
Rp = 1.5322581 data points
Rwp = 2.00431 parameters
Rexp = 1.2120 restraints
RBragg = 4.466
χ2 = NOT FOUND
Crystal data top
?V = 350.61 (2) Å3
Mr = ?Z = ?
Tetragonal, P42/mnmConstant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7890 (3) Å?, ? × ? × ? mm
c = 4.53884 (15) Å
Data collection top
2θmin = 30.086°, 2θmax = 159.086°, 2θstep = 0.050°
Refinement top
Rp = 1.532χ2 = NOT FOUND
Rwp = 2.0042581 data points
Rexp = 1.21231 parameters
RBragg = 4.4660 restraints
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Co010.000000.000000.000000.0008 (4)1.00 (4)
Co030.39737 (16)0.39737 (16)0.000000.0008 (4)0.14 (3)
Co070.7399 (2)0.0665 (2)0.000000.0008 (4)1.023 (18)
Co150.46425 (16)0.12847 (15)0.000000.0008 (4)0.04 (2)
Co230.18264 (10)0.18264 (10)0.2554 (6)0.0008 (4)0.066 (8)
CR010.000000.000000.000000.00595 (18)0.13 (4)
CR030.39737 (16)0.39737 (16)0.000000.00595 (18)0.99 (3)
CR070.7399 (2)0.0665 (2)0.000000.00595 (18)0.108 (18)
CR150.46425 (16)0.12847 (15)0.000000.00595 (18)1.09 (2)
CR230.18264 (10)0.18264 (10)0.2554 (6)0.00595 (18)1.063 (11)
(Co39LH) top
Crystal data top
?c = 4.5234 (2) Å
Mr = ?V = 346.94 (3) Å3
Tetragonal, P42/mnmZ = ?
Hall symbol: -P 4n 2nConstant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7578 (4) Å?, ? × ? × ? mm
Data collection top
Radiation source: nuclear reactor2θmin = 0.285°, 2θmax = 160.085°, 2θstep = 0.050°
Refinement top
Rp = 1.4503197 data points
Rwp = 1.87830 parameters
Rexp = 1.4490 restraints
RBragg = 4.267
χ2 = NOT FOUND
Crystal data top
?V = 346.94 (3) Å3
Mr = ?Z = ?
Tetragonal, P42/mnmConstant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7578 (4) Å?, ? × ? × ? mm
c = 4.5234 (2) Å
Data collection top
2θmin = 0.285°, 2θmax = 160.085°, 2θstep = 0.050°
Refinement top
Rp = 1.450χ2 = NOT FOUND
Rwp = 1.8783197 data points
Rexp = 1.44930 parameters
RBragg = 4.2670 restraints
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Co010.000000.000000.000000.00024 (13)1.00 (3)
Co030.39781 (14)0.39781 (14)0.000000.00024 (13)0.20 (2)
Co070.7400 (2)0.0652 (3)0.000000.00024 (13)1.046 (11)
Co150.46328 (17)0.13001 (14)0.000000.00024 (13)0.230 (16)
Co230.18232 (9)0.18232 (9)0.2523 (5)0.00024 (13)0.096 (8)
CR010.000000.000000.000000.00024 (13)0.23 (3)
CR030.39781 (14)0.39781 (14)0.000000.00024 (13)1.03 (2)
CR070.7400 (2)0.0652 (3)0.000000.00024 (13)0.184 (11)
CR150.46328 (17)0.13001 (14)0.000000.00024 (13)1.000 (16)
CR230.18232 (9)0.18232 (9)0.2523 (5)0.00024 (13)1.135 (8)
(Co39RT) top
Crystal data top
?c = 4.53521 (15) Å
Mr = ?V = 349.17 (2) Å3
Tetragonal, P42/mnmZ = ?
Hall symbol: -P 4n 2nConstant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7745 (3) Å?, ? × ? × ? mm
Data collection top
Radiation source: nuclear reactor2θmin = 0.198°, 2θmax = 159.998°, 2θstep = 0.050°
Refinement top
Rp = 1.5653197 data points
Rwp = 2.12431 parameters
Rexp = 1.3980 restraints
RBragg = 4.511
χ2 = NOT FOUND
Crystal data top
?V = 349.17 (2) Å3
Mr = ?Z = ?
Tetragonal, P42/mnmConstant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7745 (3) Å?, ? × ? × ? mm
c = 4.53521 (15) Å
Data collection top
2θmin = 0.198°, 2θmax = 159.998°, 2θstep = 0.050°
Refinement top
Rp = 1.565χ2 = NOT FOUND
Rwp = 2.1243197 data points
Rexp = 1.39831 parameters
RBragg = 4.5110 restraints
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Co010.000000.000000.000000.0029 (4)1.00 (4)
Co030.39770 (17)0.39770 (17)0.000000.0029 (4)0.12 (2)
Co070.7389 (2)0.0663 (3)0.000000.0029 (4)0.814 (15)
Co150.46435 (17)0.12902 (16)0.000000.0029 (4)0.053 (18)
Co230.18298 (10)0.18298 (10)0.2546 (6)0.0029 (4)0.091 (9)
CR010.000000.000000.000000.0075 (2)0.09 (4)
CR030.39770 (17)0.39770 (17)0.000000.0075 (2)0.79 (2)
CR070.7389 (2)0.0663 (3)0.000000.0075 (2)0.092 (15)
CR150.46435 (17)0.12902 (16)0.000000.0075 (2)0.854 (18)
CR230.18298 (10)0.18298 (10)0.2546 (6)0.0075 (2)0.816 (9)
(Co44LH) top
Crystal data top
?c = 4.5193 (3) Å
Mr = ?V = 344.89 (4) Å3
Tetragonal, P42/mnmZ = ?
Hall symbol: -P 4n 2nConstant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7359 (5) Å?, ? × ? × ? mm
Data collection top
Radiation source: nuclear reactor2θmin = 0.433°, 2θmax = 160.233°, 2θstep = 0.050°
Refinement top
Rp = 1.6893197 data points
Rwp = 2.24730 parameters
Rexp = 1.2620 restraints
RBragg = 5.447
χ2 = NOT FOUND
Crystal data top
?V = 344.89 (4) Å3
Mr = ?Z = ?
Tetragonal, P42/mnmConstant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7359 (5) Å?, ? × ? × ? mm
c = 4.5193 (3) Å
Data collection top
2θmin = 0.433°, 2θmax = 160.233°, 2θstep = 0.050°
Refinement top
Rp = 1.689χ2 = NOT FOUND
Rwp = 2.2473197 data points
Rexp = 1.26230 parameters
RBragg = 5.4470 restraints
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Co010.000000.000000.000000.00299 (17)1.00 (4)
Co030.39874 (18)0.39874 (18)0.000000.00299 (17)0.23 (3)
Co070.7402 (2)0.0650 (3)0.000000.00299 (17)1.017 (12)
Co150.4637 (2)0.12972 (18)0.000000.00299 (17)0.194 (17)
Co230.18280 (12)0.18280 (12)0.2525 (7)0.00299 (17)0.230 (9)
CR010.000000.000000.000000.00299 (17)0.12 (4)
CR030.39874 (18)0.39874 (18)0.000000.00299 (17)0.89 (3)
CR070.7402 (2)0.0650 (3)0.000000.00299 (17)0.103 (12)
CR150.4637 (2)0.12972 (18)0.000000.00299 (17)0.926 (17)
CR230.18280 (12)0.18280 (12)0.2525 (7)0.00299 (17)0.890 (9)
(Co44RT) top
Crystal data top
?c = 4.5308 (3) Å
Mr = ?V = 347.10 (4) Å3
Tetragonal, P42/mnmZ = ?
Hall symbol: -P 4n 2nConstant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7526 (6) Å?, ? × ? × ? mm
Data collection top
Radiation source: nuclear reactor2θmin = 0.394°, 2θmax = 160.194°, 2θstep = 0.050°
Refinement top
Rp = 1.7523197 data points
Rwp = 2.34930 parameters
Rexp = 1.2820 restraints
RBragg = 6.795
χ2 = NOT FOUND
Crystal data top
?V = 347.10 (4) Å3
Mr = ?Z = ?
Tetragonal, P42/mnmConstant Wavelength Neutron Diffraction radiation, λ = 1.594000 Å
a = 8.7526 (6) Å?, ? × ? × ? mm
c = 4.5308 (3) Å
Data collection top
2θmin = 0.394°, 2θmax = 160.194°, 2θstep = 0.050°
Refinement top
Rp = 1.752χ2 = NOT FOUND
Rwp = 2.3493197 data points
Rexp = 1.28230 parameters
RBragg = 6.7950 restraints
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Co010.000000.000000.000000.00573 (19)1.00 (3)
Co030.3989 (2)0.3989 (2)0.000000.00573 (19)0.21 (3)
Co070.7402 (3)0.0649 (4)0.000000.00573 (19)0.895 (12)
Co150.4639 (2)0.13032 (19)0.000000.00573 (19)0.233 (17)
Co230.18231 (13)0.18231 (13)0.2531 (7)0.00573 (19)0.185 (9)
CR010.000000.000000.000000.00573 (19)0.03 (3)
CR030.3989 (2)0.3989 (2)0.000000.00573 (19)0.82 (3)
CR070.7402 (3)0.0649 (4)0.000000.00573 (19)0.140 (12)
CR150.4639 (2)0.13032 (19)0.000000.00573 (19)0.802 (17)
CR230.18231 (13)0.18231 (13)0.2531 (7)0.00573 (19)0.849 (9)

Experimental details

(Co35LH)(Co35RT)(Co39LH)(Co39RT)
Crystal data
Chemical formula????
Mr????
Crystal system, space groupTetragonal, P42/mnmTetragonal, P42/mnmTetragonal, P42/mnmTetragonal, 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)
V3)348.24 (3)350.61 (2)346.94 (3)349.17 (2)
Z????
Radiation typeConstant Wavelength Neutron Diffraction, λ = 1.594000 ÅConstant Wavelength Neutron Diffraction, λ = 1.594000 ÅConstant Wavelength Neutron Diffraction, λ = 1.594000 ÅConstant Wavelength Neutron Diffraction, λ = 1.594000 Å
Specimen shape, size (mm)?, ? × ? × ??, ? × ? × ??, ? × ? × ??, ? × ? × ?
Data collection
Diffractometer????
Specimen mounting????
Data collection mode????
Scan method????
2θ values (°)2θmin = 0.348 2θmax = 160.148 2θstep = 0.0502θmin = 30.086 2θmax = 159.086 2θstep = 0.0502θmin = 0.285 2θmax = 160.085 2θstep = 0.0502θmin = 0.198 2θmax = 159.998 2θstep = 0.050
Refinement
R factors and goodness of fitRp = 1.624, Rwp = 2.093, Rexp = 1.459, RBragg = 4.715, χ2 = NOT FOUNDRp = 1.532, Rwp = 2.004, Rexp = 1.212, RBragg = 4.466, χ2 = NOT FOUNDRp = 1.450, Rwp = 1.878, Rexp = 1.449, RBragg = 4.267, χ2 = NOT FOUNDRp = 1.565, Rwp = 2.124, Rexp = 1.398, RBragg = 4.511, χ2 = NOT FOUND
No. of data points3197258131973197
No. of parameters31313031


(Co44LH)(Co44RT)
Crystal data
Chemical formula??
Mr??
Crystal system, space groupTetragonal, P42/mnmTetragonal, P42/mnm
Temperature (K)??
a, c (Å)8.7359 (5), 4.5193 (3)8.7526 (6), 4.5308 (3)
V3)344.89 (4)347.10 (4)
Z??
Radiation typeConstant Wavelength Neutron Diffraction, λ = 1.594000 ÅConstant Wavelength Neutron Diffraction, λ = 1.594000 Å
Specimen shape, size (mm)?, ? × ? × ??, ? × ? × ?
Data collection
Diffractometer??
Specimen mounting??
Data collection mode??
Scan method??
2θ values (°)2θmin = 0.433 2θmax = 160.233 2θstep = 0.0502θmin = 0.394 2θmax = 160.194 2θstep = 0.050
Refinement
R factors and goodness of fitRp = 1.689, Rwp = 2.247, Rexp = 1.262, RBragg = 5.447, χ2 = NOT FOUNDRp = 1.752, Rwp = 2.349, Rexp = 1.282, RBragg = 6.795, χ2 = NOT FOUND
No. of data points31973197
No. of parameters3030

Computer programs: FULLPROF.

 

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