Probing structural chirality with high-energy synchrotron radiation

The absolute structure has been determined for MnSi with data collected using synchrotron radiation with E = 78.3 keV (0.158 Å). At this energy, the resonant scattering contribution from MnSi is very small (f'_Mn = -0.0397, f''_Mn = 0.0385, f'_Si = -0.0197, f''_Si = 0.0027), but the large number of observed Bijvoet differences together with a wide Q range make absolute structure determination possible. A comparison with the data collected at E = 18 keV (0.68 Å) (f'_Mn = 0.2858, f''_Mn = 0.6739, f'_Si = 0.0653, f''_Si = 0.0646) for the same crystal shows the correctness of the absolute structure measured at the higher energy. A similar data collection has also been done at E = 65.3 keV (0.19 Å) for a single crystal of Fe_0.7Co_0.3Si with known absolute structure. In all cases, the absolute structure was correctly determined by analysing the statistical distribution of the chirality measure. Statistical descriptors of the refinements, the Flack parameter and the distribution of Parsons quotients are discussed for all presented experiments.

Computing details

For all compounds, program(s) used to refine structure: SHELXL2014/7 (Sheldrick, 2014).

(MnSi_18keV)

Crystal data

MnSi	Dx = 5.808 Mg m^−3
Mr = 83.03	Synchrotron radiation, λ = 0.68894 Å
Cubic, P213	Cell parameters from 715 reflections
a = 4.5622 (3) Å	θ = 4.3–32.3°
V = 94.96 (2) Å^3	µ = 12.76 mm^−1
Z = 4	T = 293 K
F(000) = 156	Block, metallic dark grey

Data collection

Pilatus@SNBL diffractometer	127 reflections with I > 2σ(I)
Radiation source: ESRF bending magnet	Rint = 0.026
Silicon monochromator	θmax = 32.3°, θmin = 6.1°
φ scan	h = −6→6
797 measured reflections	k = −7→7
127 independent reflections	l = −6→6

Refinement

Refinement on F^2	w = 1/[σ^2(Fo^2) + (0.053P)^2] where P = (Fo^2 + 2Fc^2)/3
Least-squares matrix: full	(Δ/σ)max < 0.001
R[F^2 > 2σ(F^2)] = 0.036	Δρmax = 0.96 e Å^−3
wR(F^2) = 0.074	Δρmin = −1.29 e Å^−3
S = 1.34	Extinction correction: SHELXL-2014/7 (Sheldrick 2014, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
127 reflections	Extinction coefficient: 0.63 (11)
8 parameters	Absolute structure: Flack x determined using 46 quotients [(I+)-(I-)]/[(I+)+(I-)] (Parsons, Flack and Wagner, Acta Cryst. B69 (2013) 249-259).
0 restraints	Absolute structure parameter: 0.06 (2)

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Mn01	0.13683 (11)	0.13683 (11)	0.13683 (11)	0.0169 (5)
Si02	0.8453 (2)	0.8453 (2)	0.8453 (2)	0.0182 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Mn01	0.0169 (5)	0.0169 (5)	0.0169 (5)	0.00003 (11)	0.00003 (11)	0.00003 (11)
Si02	0.0182 (5)	0.0182 (5)	0.0182 (5)	−0.0007 (2)	−0.0007 (2)	−0.0007 (2)

Geometric parameters (Å, º)

Mn01—Si02^i	2.304 (2)	Si02—Mn01^xiii	2.304 (2)
Mn01—Si02^ii	2.3977 (13)	Si02—Mn01^xiv	2.3977 (13)
Mn01—Si02^iii	2.3977 (13)	Si02—Mn01^xv	2.3977 (13)
Mn01—Si02^iv	2.3977 (13)	Si02—Mn01^xvi	2.3977 (13)
Mn01—Si02^v	2.5482 (9)	Si02—Mn01^xvii	2.5482 (9)
Mn01—Si02^vi	2.5482 (9)	Si02—Mn01^xviii	2.5482 (9)
Mn01—Si02^vii	2.5482 (9)	Si02—Mn01^xix	2.5482 (9)
Mn01—Mn01^viii	2.7980 (2)	Si02—Si02^xx	2.8200 (4)
Mn01—Mn01^ix	2.7980 (2)	Si02—Si02^xxi	2.8200 (4)
Mn01—Mn01^x	2.7980 (2)	Si02—Si02^xxii	2.8200 (4)
Mn01—Mn01^xi	2.7980 (2)	Si02—Si02^xxiii	2.8200 (4)
Mn01—Mn01^xii	2.7980 (2)	Si02—Si02^xxiv	2.8200 (4)
Si02^i—Mn01—Si02^ii	73.68 (2)	Mn01^xiii—Si02—Mn01^xiv	137.64 (3)
Si02^i—Mn01—Si02^iii	73.68 (2)	Mn01^xiii—Si02—Mn01^xv	137.64 (3)
Si02^ii—Mn01—Si02^iii	112.431 (17)	Mn01^xiv—Si02—Mn01^xv	71.39 (5)
Si02^i—Mn01—Si02^iv	73.68 (2)	Mn01^xiii—Si02—Mn01^xvi	137.64 (3)
Si02^ii—Mn01—Si02^iv	112.431 (17)	Mn01^xiv—Si02—Mn01^xvi	71.39 (5)
Si02^iii—Mn01—Si02^iv	112.431 (17)	Mn01^xv—Si02—Mn01^xvi	71.39 (5)
Si02^i—Mn01—Si02^v	140.288 (13)	Mn01^xiii—Si02—Mn01^xvii	70.22 (4)
Si02^ii—Mn01—Si02^v	69.45 (2)	Mn01^xiv—Si02—Mn01^xvii	114.19 (4)
Si02^iii—Mn01—Si02^v	107.34 (6)	Mn01^xv—Si02—Mn01^xvii	134.54 (5)
Si02^iv—Mn01—Si02^v	134.54 (5)	Mn01^xvi—Si02—Mn01^xvii	68.826 (14)
Si02^i—Mn01—Si02^vi	140.288 (13)	Mn01^xiii—Si02—Mn01^xviii	70.22 (4)
Si02^ii—Mn01—Si02^vi	134.54 (5)	Mn01^xiv—Si02—Mn01^xviii	134.54 (5)
Si02^iii—Mn01—Si02^vi	69.45 (2)	Mn01^xv—Si02—Mn01^xviii	68.826 (14)
Si02^iv—Mn01—Si02^vi	107.34 (6)	Mn01^xvi—Si02—Mn01^xviii	114.19 (4)
Si02^v—Mn01—Si02^vi	67.19 (2)	Mn01^xvii—Si02—Mn01^xviii	109.17 (4)
Si02^i—Mn01—Si02^vii	140.288 (13)	Mn01^xiii—Si02—Mn01^xix	70.22 (4)
Si02^ii—Mn01—Si02^vii	107.34 (6)	Mn01^xiv—Si02—Mn01^xix	68.826 (14)
Si02^iii—Mn01—Si02^vii	134.54 (5)	Mn01^xv—Si02—Mn01^xix	114.19 (4)
Si02^iv—Mn01—Si02^vii	69.45 (2)	Mn01^xvi—Si02—Mn01^xix	134.54 (5)
Si02^v—Mn01—Si02^vii	67.19 (2)	Mn01^xvii—Si02—Mn01^xix	109.17 (4)
Si02^vi—Mn01—Si02^vii	67.19 (2)	Mn01^xviii—Si02—Mn01^xix	109.17 (4)
Si02^i—Mn01—Mn01^viii	115.22 (3)	Mn01^xiii—Si02—Si02^xx	54.69 (5)
Si02^ii—Mn01—Mn01^viii	91.74 (2)	Mn01^xiv—Si02—Si02^xx	91.202 (14)
Si02^iii—Mn01—Mn01^viii	54.31 (2)	Mn01^xv—Si02—Si02^xx	162.01 (4)
Si02^iv—Mn01—Mn01^viii	155.83 (4)	Mn01^xvi—Si02—Si02^xx	108.02 (5)
Si02^v—Mn01—Mn01^viii	53.04 (4)	Mn01^xvii—Si02—Si02^xx	56.405 (10)
Si02^vi—Mn01—Mn01^viii	50.79 (5)	Mn01^xviii—Si02—Si02^xx	124.87 (9)
Si02^vii—Mn01—Mn01^viii	104.47 (4)	Mn01^xix—Si02—Si02^xx	52.76 (4)
Si02^i—Mn01—Mn01^ix	115.22 (3)	Mn01^xiii—Si02—Si02^xxi	54.69 (5)
Si02^ii—Mn01—Mn01^ix	54.31 (2)	Mn01^xiv—Si02—Si02^xxi	162.01 (4)
Si02^iii—Mn01—Mn01^ix	155.83 (4)	Mn01^xv—Si02—Si02^xxi	108.02 (5)
Si02^iv—Mn01—Mn01^ix	91.74 (2)	Mn01^xvi—Si02—Si02^xxi	91.202 (14)
Si02^v—Mn01—Mn01^ix	50.79 (5)	Mn01^xvii—Si02—Si02^xxi	52.76 (4)
Si02^vi—Mn01—Mn01^ix	104.47 (4)	Mn01^xviii—Si02—Si02^xxi	56.405 (10)
Si02^vii—Mn01—Mn01^ix	53.04 (4)	Mn01^xix—Si02—Si02^xxi	124.87 (9)
Mn01^viii—Mn01—Mn01^ix	103.16 (3)	Si02^xx—Si02—Si02^xxi	89.93 (8)
Si02^i—Mn01—Mn01^x	115.22 (3)	Mn01^xiii—Si02—Si02^xxii	54.69 (5)
Si02^ii—Mn01—Mn01^x	155.83 (4)	Mn01^xiv—Si02—Si02^xxii	108.02 (5)
Si02^iii—Mn01—Mn01^x	91.74 (2)	Mn01^xv—Si02—Si02^xxii	91.202 (14)
Si02^iv—Mn01—Mn01^x	54.31 (2)	Mn01^xvi—Si02—Si02^xxii	162.01 (4)
Si02^v—Mn01—Mn01^x	104.47 (4)	Mn01^xvii—Si02—Si02^xxii	124.87 (9)
Si02^vi—Mn01—Mn01^x	53.04 (4)	Mn01^xviii—Si02—Si02^xxii	52.76 (4)
Si02^vii—Mn01—Mn01^x	50.79 (5)	Mn01^xix—Si02—Si02^xxii	56.405 (10)
Mn01^viii—Mn01—Mn01^x	103.16 (3)	Si02^xx—Si02—Si02^xxii	89.93 (8)
Mn01^ix—Mn01—Mn01^x	103.16 (3)	Si02^xxi—Si02—Si02^xxii	89.93 (8)
Si02^i—Mn01—Mn01^xi	58.99 (3)	Mn01^xiii—Si02—Si02^xxiii	110.85 (6)
Si02^ii—Mn01—Mn01^xi	54.31 (2)	Mn01^xiv—Si02—Si02^xxiii	51.63 (5)
Si02^iii—Mn01—Mn01^xi	132.62 (4)	Mn01^xv—Si02—Si02^xxiii	57.79 (3)
Si02^iv—Mn01—Mn01^xi	58.13 (3)	Mn01^xvi—Si02—Si02^xxiii	111.37 (9)
Si02^v—Mn01—Mn01^xi	107.58 (4)	Mn01^xvii—Si02—Si02^xxiii	161.21 (3)
Si02^vi—Mn01—Mn01^xi	155.59 (4)	Mn01^xviii—Si02—Si02^xxiii	88.16 (3)
Si02^vii—Mn01—Mn01^xi	88.646 (19)	Mn01^xix—Si02—Si02^xxiii	56.405 (10)
Mn01^viii—Mn01—Mn01^xi	146.033 (7)	Si02^xx—Si02—Si02^xxiii	107.98 (2)
Mn01^ix—Mn01—Mn01^xi	60.0	Si02^xxi—Si02—Si02^xxiii	143.97 (4)
Mn01^x—Mn01—Mn01^xi	109.230 (4)	Si02^xxii—Si02—Si02^xxiii	60.0
Si02^i—Mn01—Mn01^xii	58.99 (3)	Mn01^xiii—Si02—Si02^xxiv	110.85 (6)
Si02^ii—Mn01—Mn01^xii	58.13 (3)	Mn01^xiv—Si02—Si02^xxiv	57.79 (3)
Si02^iii—Mn01—Mn01^xii	54.31 (2)	Mn01^xv—Si02—Si02^xxiv	111.37 (9)
Si02^iv—Mn01—Mn01^xii	132.62 (4)	Mn01^xvi—Si02—Si02^xxiv	51.63 (5)
Si02^v—Mn01—Mn01^xii	88.646 (19)	Mn01^xvii—Si02—Si02^xxiv	56.405 (10)
Si02^vi—Mn01—Mn01^xii	107.58 (4)	Mn01^xviii—Si02—Si02^xxiv	161.21 (3)
Si02^vii—Mn01—Mn01^xii	155.59 (4)	Mn01^xix—Si02—Si02^xxiv	88.16 (3)
Mn01^viii—Mn01—Mn01^xii	60.0	Si02^xx—Si02—Si02^xxiv	60.0
Mn01^ix—Mn01—Mn01^xii	109.230 (4)	Si02^xxi—Si02—Si02^xxiv	107.98 (2)
Mn01^x—Mn01—Mn01^xii	146.033 (7)	Si02^xxii—Si02—Si02^xxiv	143.97 (4)
Mn01^xi—Mn01—Mn01^xii	95.84 (3)	Si02^xxiii—Si02—Si02^xxiv	108.05 (6)

Symmetry codes: (i) x−1, y−1, z−1; (ii) −x+1, y−1/2, −z+1/2; (iii) −x+1/2, −y+1, z−1/2; (iv) x−1/2, −y+1/2, −z+1; (v) x−1/2, −y+3/2, −z+1; (vi) −x+1, y−1/2, −z+3/2; (vii) −x+3/2, −y+1, z−1/2; (viii) −x, y+1/2, −z+1/2; (ix) x+1/2, −y+1/2, −z; (x) −x+1/2, −y, z+1/2; (xi) −x+1/2, −y, z−1/2; (xii) x−1/2, −y+1/2, −z; (xiii) x+1, y+1, z+1; (xiv) −x+1, y+1/2, −z+1/2; (xv) x+1/2, −y+1/2, −z+1; (xvi) −x+1/2, −y+1, z+1/2; (xvii) x+1/2, −y+3/2, −z+1; (xviii) −x+1, y+1/2, −z+3/2; (xix) −x+3/2, −y+1, z+1/2; (xx) −x+2, y+1/2, −z+3/2; (xxi) −x+3/2, −y+2, z+1/2; (xxii) x+1/2, −y+3/2, −z+2; (xxiii) −x+2, y−1/2, −z+3/2; (xxiv) −x+3/2, −y+2, z−1/2.

(MnSi_78keV)

Crystal data

MnSi	Dx = 5.793 Mg m^−3
Mr = 83.03	Cell parameters from 14604 reflections
Cubic, P213	θ = 2.0–19.9°
a = 4.5662 (1) Å	µ = 0.26 mm^−1
V = 95.21 (1) Å^3	T = 293 K
Z = 4	Block, metallic dark grey
F(000) = 156

Data collection

Huber χ at ID11@ESRF diffractometer	θmax = 15.2°, θmin = 1.7°
φ scan	h = −15→14
12145 measured reflections	k = −15→15
12145 independent reflections	l = −15→15
11972 reflections with I > 2σ(I)

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0218P)^2 + 0.0116P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.015	(Δ/σ)max < 0.001
wR(F^2) = 0.037	Δρmax = 0.59 e Å^−3
S = 1.08	Δρmin = −1.39 e Å^−3
12145 reflections	Absolute structure: Flack x determined using 529 quotients [(I+)-(I-)]/[(I+)+(I-)] (Parsons, Flack and Wagner, Acta Cryst. B69 (2013) 249-259).
7 parameters	Absolute structure parameter: −0.02 (12)

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Mn01	0.13688 (2)	0.13688 (2)	0.13688 (2)	0.004460 (10)
Si02	−0.15445 (4)	−0.15445 (4)	−0.15445 (4)	0.00570 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Mn01	0.004460 (10)	0.004460 (10)	0.004460 (10)	−0.000040 (10)	−0.000040 (10)	−0.000040 (10)
Si02	0.00570 (3)	0.00570 (3)	0.00570 (3)	−0.00061 (3)	−0.00061 (3)	−0.00061 (3)

Geometric parameters (Å, º)

Mn01—Si02	2.3040 (3)	Si02—Mn01^x	2.4015 (2)
Mn01—Si02^i	2.4014 (2)	Si02—Mn01^xi	2.4015 (2)
Mn01—Si02^ii	2.4014 (2)	Si02—Mn01^xii	2.4015 (2)
Mn01—Si02^iii	2.4014 (2)	Si02—Mn01^ix	2.5494 (1)
Mn01—Si02^iv	2.5495 (1)	Si02—Mn01^vii	2.5494 (1)
Mn01—Si02^v	2.5495 (1)	Si02—Mn01^viii	2.5494 (1)
Mn01—Si02^vi	2.5495 (1)	Si02—Si02^i	2.8220 (1)
Mn01—Mn01^vii	2.8004 (1)	Si02—Si02^ii	2.8220 (1)
Mn01—Mn01^viii	2.8004 (1)	Si02—Si02^iii	2.8220 (1)
Mn01—Mn01^ix	2.8004 (1)	Si02—Si02^x	2.8220 (1)
Mn01—Mn01^v	2.8004 (1)	Si02—Si02^xi	2.8220 (1)
Mn01—Mn01^vi	2.8004 (1)
Si02—Mn01—Si02^i	73.666 (2)	Mn01—Si02—Mn01^x	137.680 (5)
Si02—Mn01—Si02^ii	73.666 (2)	Mn01—Si02—Mn01^xi	137.680 (5)
Si02^i—Mn01—Si02^ii	112.418 (2)	Mn01^x—Si02—Mn01^xi	71.333 (7)
Si02—Mn01—Si02^iii	73.666 (2)	Mn01—Si02—Mn01^xii	137.680 (5)
Si02^i—Mn01—Si02^iii	112.418 (2)	Mn01^x—Si02—Mn01^xii	71.333 (7)
Si02^ii—Mn01—Si02^iii	112.418 (2)	Mn01^xi—Si02—Mn01^xii	71.333 (7)
Si02—Mn01—Si02^iv	140.278 (2)	Mn01—Si02—Mn01^ix	70.270 (6)
Si02^i—Mn01—Si02^iv	134.507 (7)	Mn01^x—Si02—Mn01^ix	114.152 (5)
Si02^ii—Mn01—Si02^iv	69.425 (3)	Mn01^xi—Si02—Mn01^ix	68.819 (2)
Si02^iii—Mn01—Si02^iv	107.420 (10)	Mn01^xii—Si02—Mn01^ix	134.507 (7)
Si02—Mn01—Si02^v	140.278 (2)	Mn01—Si02—Mn01^vii	70.270 (6)
Si02^i—Mn01—Si02^v	107.420 (10)	Mn01^x—Si02—Mn01^vii	68.819 (2)
Si02^ii—Mn01—Si02^v	134.507 (7)	Mn01^xi—Si02—Mn01^vii	134.507 (7)
Si02^iii—Mn01—Si02^v	69.425 (3)	Mn01^xii—Si02—Mn01^vii	114.152 (5)
Si02^iv—Mn01—Si02^v	67.207 (3)	Mn01^ix—Si02—Mn01^vii	109.211 (6)
Si02—Mn01—Si02^vi	140.278 (2)	Mn01—Si02—Mn01^viii	70.270 (6)
Si02^i—Mn01—Si02^vi	69.425 (3)	Mn01^x—Si02—Mn01^viii	134.507 (7)
Si02^ii—Mn01—Si02^vi	107.420 (10)	Mn01^xi—Si02—Mn01^viii	114.152 (5)
Si02^iii—Mn01—Si02^vi	134.507 (7)	Mn01^xii—Si02—Mn01^viii	68.819 (2)
Si02^iv—Mn01—Si02^vi	67.207 (3)	Mn01^ix—Si02—Mn01^viii	109.211 (6)
Si02^v—Mn01—Si02^vi	67.207 (3)	Mn01^vii—Si02—Mn01^viii	109.211 (6)
Si02—Mn01—Mn01^vii	58.974 (3)	Mn01—Si02—Si02^i	54.750 (9)
Si02^i—Mn01—Mn01^vii	58.090 (5)	Mn01^x—Si02—Si02^i	107.985 (7)
Si02^ii—Mn01—Mn01^vii	54.334 (4)	Mn01^xi—Si02—Si02^i	161.951 (7)
Si02^iii—Mn01—Mn01^vii	132.594 (5)	Mn01^xii—Si02—Si02^i	91.184 (2)
Si02^iv—Mn01—Mn01^vii	107.552 (6)	Mn01^ix—Si02—Si02^i	124.980 (15)
Si02^v—Mn01—Mn01^vii	155.640 (6)	Mn01^vii—Si02—Si02^i	56.3960 (10)
Si02^vi—Mn01—Mn01^vii	88.669 (3)	Mn01^viii—Si02—Si02^i	52.817 (7)
Si02—Mn01—Mn01^viii	58.974 (3)	Mn01—Si02—Si02^ii	54.750 (9)
Si02^i—Mn01—Mn01^viii	54.334 (4)	Mn01^x—Si02—Si02^ii	91.184 (2)
Si02^ii—Mn01—Mn01^viii	132.594 (5)	Mn01^xi—Si02—Si02^ii	107.985 (7)
Si02^iii—Mn01—Mn01^viii	58.090 (5)	Mn01^xii—Si02—Si02^ii	161.951 (7)
Si02^iv—Mn01—Mn01^viii	155.640 (6)	Mn01^ix—Si02—Si02^ii	56.3960 (10)
Si02^v—Mn01—Mn01^viii	88.669 (3)	Mn01^vii—Si02—Si02^ii	52.817 (7)
Si02^vi—Mn01—Mn01^viii	107.552 (6)	Mn01^viii—Si02—Si02^ii	124.980 (15)
Mn01^vii—Mn01—Mn01^viii	95.826 (4)	Si02^i—Si02—Si02^ii	90.020 (12)
Si02—Mn01—Mn01^ix	58.974 (3)	Mn01—Si02—Si02^iii	54.750 (9)
Si02^i—Mn01—Mn01^ix	132.594 (5)	Mn01^x—Si02—Si02^iii	161.951 (7)
Si02^ii—Mn01—Mn01^ix	58.090 (5)	Mn01^xi—Si02—Si02^iii	91.184 (2)
Si02^iii—Mn01—Mn01^ix	54.334 (4)	Mn01^xii—Si02—Si02^iii	107.985 (7)
Si02^iv—Mn01—Mn01^ix	88.669 (3)	Mn01^ix—Si02—Si02^iii	52.817 (7)
Si02^v—Mn01—Mn01^ix	107.552 (6)	Mn01^vii—Si02—Si02^iii	124.980 (15)
Si02^vi—Mn01—Mn01^ix	155.640 (6)	Mn01^viii—Si02—Si02^iii	56.3960 (10)
Mn01^vii—Mn01—Mn01^ix	95.826 (4)	Si02^i—Si02—Si02^iii	90.020 (12)
Mn01^viii—Mn01—Mn01^ix	95.826 (4)	Si02^ii—Si02—Si02^iii	90.020 (12)
Si02—Mn01—Mn01^v	115.212 (3)	Mn01—Si02—Si02^x	110.920 (9)
Si02^i—Mn01—Mn01^v	155.872 (5)	Mn01^x—Si02—Si02^x	51.584 (8)
Si02^ii—Mn01—Mn01^v	91.709 (4)	Mn01^xi—Si02—Si02^x	111.274 (14)
Si02^iii—Mn01—Mn01^v	54.333 (4)	Mn01^xii—Si02—Si02^x	57.758 (4)
Si02^iv—Mn01—Mn01^v	53.091 (6)	Mn01^ix—Si02—Si02^x	161.178 (4)
Si02^v—Mn01—Mn01^v	50.756 (7)	Mn01^vii—Si02—Si02^x	56.3960 (10)
Si02^vi—Mn01—Mn01^v	104.492 (4)	Mn01^viii—Si02—Si02^x	88.197 (4)
Mn01^vii—Mn01—Mn01^v	146.0300 (10)	Si02^i—Si02—Si02^x	60.0
Mn01^viii—Mn01—Mn01^v	109.2	Si02^ii—Si02—Si02^x	108.006 (3)
Mn01^ix—Mn01—Mn01^v	60.0	Si02^iii—Si02—Si02^x	144.009 (6)
Si02—Mn01—Mn01^vi	115.212 (3)	Mn01—Si02—Si02^xi	110.920 (9)
Si02^i—Mn01—Mn01^vi	54.333 (4)	Mn01^x—Si02—Si02^xi	57.758 (4)
Si02^ii—Mn01—Mn01^vi	155.872 (5)	Mn01^xi—Si02—Si02^xi	51.584 (8)
Si02^iii—Mn01—Mn01^vi	91.709 (4)	Mn01^xii—Si02—Si02^xi	111.274 (14)
Si02^iv—Mn01—Mn01^vi	104.492 (4)	Mn01^ix—Si02—Si02^xi	56.3960 (10)
Si02^v—Mn01—Mn01^vi	53.091 (6)	Mn01^vii—Si02—Si02^xi	88.197 (4)
Si02^vi—Mn01—Mn01^vi	50.756 (7)	Mn01^viii—Si02—Si02^xi	161.177 (4)
Mn01^vii—Mn01—Mn01^vi	109.2	Si02^i—Si02—Si02^xi	144.009 (6)
Mn01^viii—Mn01—Mn01^vi	60.0	Si02^ii—Si02—Si02^xi	60.0
Mn01^ix—Mn01—Mn01^vi	146.0300 (10)	Si02^iii—Si02—Si02^xi	108.006 (4)
Mn01^v—Mn01—Mn01^vi	103.169 (3)	Si02^x—Si02—Si02^xi	107.985 (9)

Symmetry codes: (i) x+1/2, −y−1/2, −z; (ii) −x, y+1/2, −z−1/2; (iii) −x−1/2, −y, z+1/2; (iv) x+1/2, −y+1/2, −z; (v) −x, y+1/2, −z+1/2; (vi) −x+1/2, −y, z+1/2; (vii) −x+1/2, −y, z−1/2; (viii) −x, y−1/2, −z+1/2; (ix) x−1/2, −y+1/2, −z; (x) −x, y−1/2, −z−1/2; (xi) −x−1/2, −y, z−1/2; (xii) x−1/2, −y−1/2, −z.

(FeCoSi_65keV)

Crystal data

Co0.30Fe0.70Si	Dx = 6.298 Mg m^−3
Mr = 84.86	Cell parameters from 5730 reflections
Cubic, P213	θ = 1.7–19.6°
a = 4.4732 (5) Å	µ = 0.48 mm^−1
V = 89.51 (3) Å^3	T = 120 K
Z = 4	Block, metallic dark grey
F(000) = 161

Data collection

Huber χ at ID11@ESRF diffractometer	θmax = 19.7°, θmin = 1.7°
φ scan	h = −14→14
8860 measured reflections	k = −14→15
8860 independent reflections	l = −12→12
8781 reflections with I > 2σ(I)

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0331P)^2 + 0.1327P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.024	(Δ/σ)max < 0.001
wR(F^2) = 0.062	Δρmax = 0.99 e Å^−3
S = 1.06	Δρmin = −2.26 e Å^−3
8860 reflections	Absolute structure: Flack x determined using 509 quotients [(I+)-(I-)]/[(I+)+(I-)] (Parsons, Flack and Wagner, Acta Cryst. B69 (2013) 249-259).
7 parameters	Absolute structure parameter: −0.08 (10)

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Fe01	0.13757 (2)	0.13757 (2)	0.13757 (2)	0.00264 (2)	0.6999
Co01	0.13757 (2)	0.13757 (2)	0.13757 (2)	0.00264 (2)	0.3
Si01	0.84218 (7)	0.84218 (7)	0.84218 (7)	0.00333 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Fe01	0.00264 (2)	0.00264 (2)	0.00264 (2)	0.00004 (2)	0.00004 (2)	0.00004 (2)
Co01	0.00264 (2)	0.00264 (2)	0.00264 (2)	0.00004 (2)	0.00004 (2)	0.00004 (2)
Si01	0.00333 (5)	0.00333 (5)	0.00333 (5)	−0.00021 (5)	−0.00021 (5)	−0.00021 (5)

Geometric parameters (Å, º)

Fe01—Si01^i	2.2886 (6)	Si01—Co01^xi	2.2886 (6)
Fe01—Si01^ii	2.3348 (5)	Si01—Fe01^xi	2.2886 (6)
Fe01—Si01^iii	2.3348 (5)	Si01—Co01^xii	2.3348 (5)
Fe01—Si01^iv	2.3348 (5)	Si01—Fe01^xii	2.3348 (5)
Fe01—Si01^v	2.5023 (4)	Si01—Co01^xiii	2.3348 (5)
Fe01—Si01^vi	2.5023 (4)	Si01—Co01^xiv	2.3348 (5)
Fe01—Si01^vii	2.5023 (4)	Si01—Fe01^xiii	2.3348 (5)
Fe01—Fe01^viii	2.7439 (3)	Si01—Fe01^xiv	2.3348 (5)
Fe01—Co01^viii	2.7439 (3)	Si01—Co01^xv	2.5023 (4)
Fe01—Fe01^ix	2.7439 (3)	Si01—Fe01^xv	2.5023 (4)
Fe01—Co01^ix	2.7439 (3)	Si01—Co01^xvi	2.5023 (4)
Fe01—Co01^x	2.7439 (3)	Si01—Co01^xvii	2.5023 (4)
Si01^i—Fe01—Si01^ii	73.624 (5)	Co01^xi—Si01—Fe01^xi	0.0
Si01^i—Fe01—Si01^iii	73.624 (5)	Co01^xi—Si01—Co01^xii	137.274 (9)
Si01^ii—Fe01—Si01^iii	112.381 (4)	Fe01^xi—Si01—Co01^xii	137.274 (9)
Si01^i—Fe01—Si01^iv	73.624 (5)	Co01^xi—Si01—Fe01^xii	137.3
Si01^ii—Fe01—Si01^iv	112.381 (4)	Fe01^xi—Si01—Fe01^xii	137.274 (9)
Si01^iii—Fe01—Si01^iv	112.381 (4)	Co01^xii—Si01—Fe01^xii	0.0
Si01^i—Fe01—Si01^v	140.265 (3)	Co01^xi—Si01—Co01^xiii	137.274 (9)
Si01^ii—Fe01—Si01^v	69.788 (6)	Fe01^xi—Si01—Co01^xiii	137.274 (9)
Si01^iii—Fe01—Si01^v	106.615 (18)	Co01^xii—Si01—Co01^xiii	71.973 (13)
Si01^iv—Fe01—Si01^v	135.236 (12)	Fe01^xii—Si01—Co01^xiii	71.973 (13)
Si01^i—Fe01—Si01^vi	140.265 (3)	Co01^xi—Si01—Co01^xiv	137.274 (9)
Si01^ii—Fe01—Si01^vi	135.236 (12)	Fe01^xi—Si01—Co01^xiv	137.274 (9)
Si01^iii—Fe01—Si01^vi	69.788 (6)	Co01^xii—Si01—Co01^xiv	71.973 (13)
Si01^iv—Fe01—Si01^vi	106.615 (18)	Fe01^xii—Si01—Co01^xiv	71.973 (13)
Si01^v—Fe01—Si01^vi	67.228 (5)	Co01^xiii—Si01—Co01^xiv	71.973 (13)
Si01^i—Fe01—Si01^vii	140.265 (3)	Co01^xi—Si01—Fe01^xiii	137.3
Si01^ii—Fe01—Si01^vii	106.615 (18)	Fe01^xi—Si01—Fe01^xiii	137.274 (9)
Si01^iii—Fe01—Si01^vii	135.236 (12)	Co01^xii—Si01—Fe01^xiii	72.0
Si01^iv—Fe01—Si01^vii	69.788 (6)	Fe01^xii—Si01—Fe01^xiii	71.973 (13)
Si01^v—Fe01—Si01^vii	67.228 (5)	Co01^xiii—Si01—Fe01^xiii	0.0
Si01^vi—Fe01—Si01^vii	67.228 (5)	Co01^xiv—Si01—Fe01^xiii	72.0
Si01^i—Fe01—Fe01^viii	58.806 (6)	Co01^xi—Si01—Fe01^xiv	137.3
Si01^ii—Fe01—Fe01^viii	132.366 (10)	Fe01^xi—Si01—Fe01^xiv	137.274 (9)
Si01^iii—Fe01—Fe01^viii	58.374 (9)	Co01^xii—Si01—Fe01^xiv	72.0
Si01^iv—Fe01—Fe01^viii	54.014 (7)	Fe01^xii—Si01—Fe01^xiv	71.973 (13)
Si01^v—Fe01—Fe01^viii	155.349 (10)	Co01^xiii—Si01—Fe01^xiv	72.0
Si01^vi—Fe01—Fe01^viii	88.480 (5)	Co01^xiv—Si01—Fe01^xiv	0.0
Si01^vii—Fe01—Fe01^viii	108.214 (11)	Fe01^xiii—Si01—Fe01^xiv	71.973 (13)
Si01^i—Fe01—Co01^viii	58.806 (6)	Co01^xi—Si01—Co01^xv	69.717 (11)
Si01^ii—Fe01—Co01^viii	132.366 (10)	Fe01^xi—Si01—Co01^xv	69.717 (11)
Si01^iii—Fe01—Co01^viii	58.374 (9)	Co01^xii—Si01—Co01^xv	69.018 (3)
Si01^iv—Fe01—Co01^viii	54.014 (7)	Fe01^xii—Si01—Co01^xv	69.018 (3)
Si01^v—Fe01—Co01^viii	155.349 (10)	Co01^xiii—Si01—Co01^xv	135.237 (12)
Si01^vi—Fe01—Co01^viii	88.480 (5)	Co01^xiv—Si01—Co01^xv	114.331 (9)
Si01^vii—Fe01—Co01^viii	108.214 (11)	Fe01^xiii—Si01—Co01^xv	135.237 (12)
Fe01^viii—Fe01—Co01^viii	0.000 (5)	Fe01^xiv—Si01—Co01^xv	114.331 (9)
Si01^i—Fe01—Fe01^ix	58.806 (6)	Co01^xi—Si01—Fe01^xv	69.7
Si01^ii—Fe01—Fe01^ix	54.014 (7)	Fe01^xi—Si01—Fe01^xv	69.717 (11)
Si01^iii—Fe01—Fe01^ix	132.366 (10)	Co01^xii—Si01—Fe01^xv	69.0
Si01^iv—Fe01—Fe01^ix	58.374 (9)	Fe01^xii—Si01—Fe01^xv	69.018 (3)
Si01^v—Fe01—Fe01^ix	108.214 (11)	Co01^xiii—Si01—Fe01^xv	135.2
Si01^vi—Fe01—Fe01^ix	155.349 (10)	Co01^xiv—Si01—Fe01^xv	114.3
Si01^vii—Fe01—Fe01^ix	88.480 (5)	Fe01^xiii—Si01—Fe01^xv	135.237 (12)
Fe01^viii—Fe01—Fe01^ix	95.601 (8)	Fe01^xiv—Si01—Fe01^xv	114.331 (9)
Co01^viii—Fe01—Fe01^ix	95.6	Co01^xv—Si01—Fe01^xv	0.0
Si01^i—Fe01—Co01^ix	58.806 (6)	Co01^xi—Si01—Co01^xvi	69.717 (11)
Si01^ii—Fe01—Co01^ix	54.014 (7)	Fe01^xi—Si01—Co01^xvi	69.717 (11)
Si01^iii—Fe01—Co01^ix	132.366 (10)	Co01^xii—Si01—Co01^xvi	135.237 (12)
Si01^iv—Fe01—Co01^ix	58.374 (9)	Fe01^xii—Si01—Co01^xvi	135.237 (12)
Si01^v—Fe01—Co01^ix	108.214 (11)	Co01^xiii—Si01—Co01^xvi	114.331 (9)
Si01^vi—Fe01—Co01^ix	155.349 (10)	Co01^xiv—Si01—Co01^xvi	69.018 (3)
Si01^vii—Fe01—Co01^ix	88.480 (5)	Fe01^xiii—Si01—Co01^xvi	114.331 (9)
Fe01^viii—Fe01—Co01^ix	95.601 (8)	Fe01^xiv—Si01—Co01^xvi	69.018 (3)
Co01^viii—Fe01—Co01^ix	95.601 (8)	Co01^xv—Si01—Co01^xvi	108.648 (11)
Fe01^ix—Fe01—Co01^ix	0.000 (5)	Fe01^xv—Si01—Co01^xvi	108.648 (11)
Si01^i—Fe01—Co01^x	58.806 (6)	Co01^xi—Si01—Co01^xvii	69.717 (11)
Si01^ii—Fe01—Co01^x	58.374 (9)	Fe01^xi—Si01—Co01^xvii	69.717 (11)
Si01^iii—Fe01—Co01^x	54.014 (7)	Co01^xii—Si01—Co01^xvii	114.331 (9)
Si01^iv—Fe01—Co01^x	132.366 (10)	Fe01^xii—Si01—Co01^xvii	114.331 (9)
Si01^v—Fe01—Co01^x	88.480 (5)	Co01^xiii—Si01—Co01^xvii	69.018 (3)
Si01^vi—Fe01—Co01^x	108.214 (11)	Co01^xiv—Si01—Co01^xvii	135.237 (12)
Si01^vii—Fe01—Co01^x	155.349 (10)	Fe01^xiii—Si01—Co01^xvii	69.018 (3)
Fe01^viii—Fe01—Co01^x	95.601 (7)	Fe01^xiv—Si01—Co01^xvii	135.237 (12)
Co01^viii—Fe01—Co01^x	95.601 (7)	Co01^xv—Si01—Co01^xvii	108.648 (11)
Fe01^ix—Fe01—Co01^x	95.601 (8)	Fe01^xv—Si01—Co01^xvii	108.648 (11)
Co01^ix—Fe01—Co01^x	95.601 (8)	Co01^xvi—Si01—Co01^xvii	108.648 (11)

Symmetry codes: (i) x−1, y−1, z−1; (ii) x−1/2, −y+1/2, −z+1; (iii) −x+1, y−1/2, −z+1/2; (iv) −x+1/2, −y+1, z−1/2; (v) −x+3/2, −y+1, z−1/2; (vi) x−1/2, −y+3/2, −z+1; (vii) −x+1, y−1/2, −z+3/2; (viii) x−1/2, −y+1/2, −z; (ix) −x, y−1/2, −z+1/2; (x) −x+1/2, −y, z−1/2; (xi) x+1, y+1, z+1; (xii) x+1/2, −y+1/2, −z+1; (xiii) −x+1, y+1/2, −z+1/2; (xiv) −x+1/2, −y+1, z+1/2; (xv) −x+1, y+1/2, −z+3/2; (xvi) x+1/2, −y+3/2, −z+1; (xvii) −x+3/2, −y+1, z+1/2.