Crystal structure and structural phase transition in bis­muth-containing HoFe₃(BO₃)₄ in the temperature range 11–500 K

An accurate single-crystal X-ray diffraction study of bis­muth-containing HoFe₃(BO₃)₄ between 11 and 500 K has revealed structural phase transition at T_str = 365 K. The Bi atoms enter the composition from Bi₂Mo₃O₁₂-based flux during crystal growth and significantly affect T_str. The content of Bi was estimated by two independent methods, establishing the composition as (Ho_0.96Bi_0.04)Fe₃(BO₃)₄. In the low-temperature (LT) phase below T_str the (Ho_0.96Bi_0.04)Fe₃(BO₃)₄ crystal symmetry is trigonal, of space group P3₁21, whereas at high temperature (HT) above 365 K the symmetry increases to space group R32. There is a sharp jump of oxygen O1 (LT) and O2 (LT) atomic displacement parameters (ADP) at T_str. O1 and O2 ADP ellipsoids are the most elongated over 90–500 K. In space group R32 specific distances decrease steadily or do not change with decreasing temperature. In space group P3₁21 the distortion of the polyhedra Ho(Bi)O₆, Fe1O₆ and Fe2O₆, B2O₃ and B3O₃ increases with decreasing temperature, whereas the triangles B1O₃ remain almost equilateral. All BO₃ triangles deviate from the ab plane with decreasing temperature. Fe–Fe distances in Fe1 chains decrease, while distances in Fe2 chains increase with decreasing temperature. The Mössbauer study confirms that the FeO₆ octahedra undergo complex dynamic distortions. However, all observed distortions are rather small, and the general change in symmetry during the structural phase transition has very little influence on the local environment of iron in oxygen octahedra. The Mössbauer spectra do not distinguish two structurally different Fe1 and Fe2 positions in the LT phase. The characteristic temperatures of cation thermal vibrations were calculated using X-ray diffraction and Mössbauer data.

Computing details

(90)

Crystal data

B4Bi0.037Fe3Ho0.963O12	Dx = 4.796 Mg m^−3
Mr = 569.3	Mo Kα radiation, λ = 0.71073 Å
Trigonal, P3121	Cell parameters from 21639 reflections
Hall symbol: P 31 2"	θ = 4.3–74.0°
a = 9.5177 (1) Å	µ = 15.87 mm^−1
c = 7.538 (1) Å	T = 90 K
V = 591.36 (1) Å^3	Sphere, light-green
Z = 3	0.16 mm (radius)
F(000) = 785

Data collection

Xcalibur, EosS2 with high theta cut diffractometer	6832 independent reflections
Radiation source: X-ray tube	6832 reflections with I > 0σ(I)
Graphite monochromator	Rint = 0.034
Detector resolution: 16.1745 pixels mm^-1	θmax = 74.4°, θmin = 3.7°
ω scans	h = −25→25
Absorption correction: for a sphere (Dudka, 2007)	k = −25→23
Tmin = 0.012, Tmax = 0.037	l = −18→19
59807 measured reflections

Refinement

Refinement on F^2	Weighting scheme based on measured s.u.'s w = 1/σ^2(I)
R[F^2 > 2σ(F^2)] = 0.018	(Δ/σ)max = 0.018
wR(F^2) = 0.045	Δρmax = 2.22 e Å^−3
S = 0.98	Δρmin = −0.91 e Å^−3
6832 reflections	Extinction correction: Becker_Coppens G_I Isotropic (Becker & Coppens, 1974)
94 parameters	Extinction coefficient: 0.364 (7)
0 restraints	Absolute structure: 3079 of Friedel pairs used in the refinement
5 constraints	Absolute structure parameter: 0.494 (5)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ho1	0.665142 (6)	0.665142 (6)	0	0.001302 (9)	0.9627
Bi1	0.665142 (6)	0.665142 (6)	0	0.001302 (9)	0.0373
Fe1	0.884333 (17)	0	0.333333	0.00098 (2)
Fe2	0.336417 (14)	0.548636 (15)	0.321750 (15)	0.001064 (19)
O1	0	0.92196 (10)	0.166667	0.00386 (16)
O2	0.41884 (9)	0.72347 (8)	0.12651 (9)	0.00357 (11)
O3	0.69588 (8)	0.87846 (8)	0.17766 (10)	0.00296 (12)
O4	0.85204 (8)	0.63698 (8)	0.18509 (10)	0.00289 (11)
O5	0.52480 (8)	0.67063 (8)	0.49039 (9)	0.00260 (12)
O6	0.81268 (10)	0.81268 (10)	0.5	0.00264 (13)
O7	0.46652 (8)	0.47569 (8)	0.18566 (10)	0.00305 (12)
B1	0.66814 (15)	0.66814 (15)	0.5	0.0017 (2)
B2	0.55137 (13)	0.87535 (13)	0.15148 (15)	0.00237 (19)
B3	0	0.77863 (15)	0.166667	0.0023 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ho1	0.001311 (11)	0.001311 (11)	0.001347 (14)	0.000703 (10)	−0.000108 (4)	0.000108 (4)
Bi1	0.001311 (11)	0.001311 (11)	0.001347 (14)	0.000703 (10)	−0.000108 (4)	0.000108 (4)
Fe1	0.00100 (3)	0.00075 (3)	0.00113 (3)	0.000374 (17)	−0.000006 (13)	−0.00001 (3)
Fe2	0.00095 (2)	0.00097 (2)	0.00129 (2)	0.00049 (2)	−0.00004 (2)	0.000014 (16)
O1	0.0041 (2)	0.00209 (15)	0.0060 (3)	0.00206 (12)	0.00307 (17)	0.00154 (9)
O2	0.00241 (15)	0.00208 (13)	0.00474 (16)	0.00000 (11)	−0.00093 (11)	0.00103 (10)
O3	0.00231 (13)	0.00365 (15)	0.00330 (17)	0.00178 (12)	−0.00102 (10)	−0.00095 (11)
O4	0.00216 (13)	0.00226 (13)	0.00323 (17)	0.00035 (11)	0.00010 (10)	0.00054 (10)
O5	0.00179 (13)	0.00281 (15)	0.0036 (2)	0.00147 (11)	−0.00071 (10)	−0.00124 (12)
O6	0.00152 (13)	0.00152 (13)	0.0035 (2)	−0.00026 (15)	−0.00043 (8)	0.00043 (8)
O7	0.00386 (15)	0.00182 (13)	0.00406 (17)	0.00187 (12)	0.00057 (11)	−0.00012 (10)
B1	0.0009 (2)	0.0009 (2)	0.0031 (3)	0.0003 (3)	0.00000 (12)	0.00000 (12)
B2	0.0015 (2)	0.0015 (2)	0.0039 (3)	0.0005 (2)	−0.00036 (17)	0.00010 (16)
B3	0.0010 (4)	0.0017 (2)	0.0039 (4)	0.00050 (18)	0.0007 (2)	0.00036 (12)

Geometric parameters (Å, º)

Ho1—Bi1	0	Fe1—O3^v	1.9640 (10)
Ho1—O3	2.3253 (8)	Fe1—O6^iv	2.0015 (7)
Ho1—O3^i	2.3253 (8)	Fe1—O6^vi	2.0015 (6)
Ho1—O4	2.3789 (8)	Fe2—O2	2.0603 (7)
Ho1—O4^i	2.3789 (8)	Fe2—O2^vii	2.0384 (11)
Ho1—O7	2.3184 (6)	Fe2—O4^viii	1.9663 (7)
Ho1—O7^i	2.3184 (6)	Fe2—O5	2.0241 (7)
Bi1—O3	2.3253 (8)	Fe2—O5^ix	2.0131 (9)
Bi1—O3^i	2.3253 (8)	Fe2—O7	1.9818 (9)
Bi1—O4	2.3789 (8)	O1—B3	1.3642 (17)
Bi1—O4^i	2.3789 (8)	O2—B2	1.3757 (10)
Bi1—O7	2.3184 (6)	O3—B2	1.3751 (16)
Bi1—O7^i	2.3184 (6)	O4—B3^x	1.3862 (9)
Fe1—O1^ii	2.0395 (6)	O5—B1	1.3781 (18)
Fe1—O1^iii	2.0395 (7)	O6—B1	1.3757 (12)
Fe1—O3^iv	1.9640 (7)	O7—B2^xi	1.3671 (19)
Bi1—Ho1—O3	0	O6^iv—Fe1—O6^vi	167.99 (5)
Bi1—Ho1—O3^i	0	O2—Fe2—O2^vii	86.30 (3)
Bi1—Ho1—O4	0	O2—Fe2—O4^viii	168.17 (3)
Bi1—Ho1—O4^i	0	O2—Fe2—O5	96.60 (3)
Bi1—Ho1—O7	0	O2—Fe2—O5^ix	75.70 (3)
Bi1—Ho1—O7^i	0	O2—Fe2—O7	82.00 (3)
O3—Ho1—O3^i	120.07 (2)	O2^vii—Fe2—O4^viii	93.60 (4)
O3—Ho1—O4	89.19 (3)	O2^vii—Fe2—O5	75.95 (3)
O3—Ho1—O4^i	72.36 (3)	O2^vii—Fe2—O5^ix	92.33 (4)
O3—Ho1—O7	91.67 (2)	O2^vii—Fe2—O7	160.41 (2)
O3—Ho1—O7^i	140.05 (3)	O4^viii—Fe2—O5	94.85 (3)
O3^i—Ho1—O4	72.36 (3)	O4^viii—Fe2—O5^ix	92.49 (3)
O3^i—Ho1—O4^i	89.19 (3)	O4^viii—Fe2—O7	101.05 (4)
O3^i—Ho1—O7	140.05 (3)	O5—Fe2—O5^ix	166.52 (4)
O3^i—Ho1—O7^i	91.67 (2)	O5—Fe2—O7	89.81 (3)
O4—Ho1—O4^i	142.97 (2)	O5^ix—Fe2—O7	99.88 (4)
O4—Ho1—O7	85.60 (3)	Fe1^xii—O1—Fe1^xiii	101.30 (4)
O4—Ho1—O7^i	125.64 (3)	Fe1^xii—O1—B3	129.35 (2)
O4^i—Ho1—O7	125.64 (3)	Fe1^xiii—O1—B3	129.35 (2)
O4^i—Ho1—O7^i	85.60 (3)	Fe2—O2—Fe2^ix	102.38 (3)
O7—Ho1—O7^i	74.39 (2)	Fe2—O2—B2	121.99 (7)
Ho1—Bi1—O3	0	Fe2^ix—O2—B2	127.82 (8)
Ho1—Bi1—O3^i	0	Ho1—O3—Bi1	0.0 (5)
Ho1—Bi1—O4	0	Ho1—O3—Fe1^xiv	122.51 (5)
Ho1—Bi1—O4^i	0	Ho1—O3—B2	102.17 (6)
Ho1—Bi1—O7	0	Bi1—O3—Fe1^xiv	122.51 (5)
Ho1—Bi1—O7^i	0	Bi1—O3—B2	102.17 (6)
O3—Bi1—O3^i	120.07 (2)	Fe1^xiv—O3—B2	135.03 (7)
O3—Bi1—O4	89.19 (3)	Ho1—O4—Bi1	0.0 (5)
O3—Bi1—O4^i	72.36 (3)	Ho1—O4—Fe2^v	123.12 (3)
O3—Bi1—O7	91.67 (2)	Ho1—O4—B3^x	106.56 (6)
O3—Bi1—O7^i	140.05 (3)	Bi1—O4—Fe2^v	123.12 (3)
O3^i—Bi1—O4	72.36 (3)	Bi1—O4—B3^x	106.56 (6)
O3^i—Bi1—O4^i	89.19 (3)	Fe2^v—O4—B3^x	130.06 (6)
O3^i—Bi1—O7	140.05 (3)	Fe2—O5—Fe2^vii	104.58 (4)
O3^i—Bi1—O7^i	91.67 (2)	Fe2—O5—B1	128.59 (6)
O4—Bi1—O4^i	142.97 (2)	Fe2^vii—O5—B1	126.72 (5)
O4—Bi1—O7	85.60 (3)	Fe1^xiv—O6—Fe1^xv	103.99 (3)
O4—Bi1—O7^i	125.64 (3)	Fe1^xiv—O6—B1	128.00 (6)
O4^i—Bi1—O7	125.64 (3)	Fe1^xv—O6—B1	128.00 (6)
O4^i—Bi1—O7^i	85.60 (3)	Ho1—O7—Bi1	0.0 (5)
O7—Bi1—O7^i	74.39 (2)	Ho1—O7—Fe2	116.70 (4)
O1^ii—Fe1—O1^iii	87.58 (3)	Ho1—O7—B2^xi	115.55 (7)
O1^ii—Fe1—O3^iv	85.28 (3)	Bi1—O7—Fe2	116.70 (4)
O1^ii—Fe1—O3^v	167.31 (3)	Bi1—O7—B2^xi	115.55 (7)
O1^ii—Fe1—O6^iv	93.89 (3)	Fe2—O7—B2^xi	127.68 (6)
O1^ii—Fe1—O6^vi	77.36 (4)	O5—B1—O5^xvi	121.80 (8)
O1^iii—Fe1—O3^iv	167.31 (4)	O5—B1—O6	119.10 (13)
O1^iii—Fe1—O3^v	85.28 (4)	O5^xvi—B1—O6	119.10 (13)
O1^iii—Fe1—O6^iv	77.36 (3)	O2—B2—O3	115.08 (11)
O1^iii—Fe1—O6^vi	93.89 (3)	O2—B2—O7^xvii	120.01 (10)
O3^iv—Fe1—O3^v	103.55 (4)	O3—B2—O7^xvii	124.90 (7)
O3^iv—Fe1—O6^iv	92.65 (3)	O1—B3—O4^xviii	117.69 (7)
O3^iv—Fe1—O6^vi	94.77 (3)	O1—B3—O4^xvii	117.69 (7)
O3^v—Fe1—O6^iv	94.77 (3)	O4^xviii—B3—O4^xvii	124.63 (12)
O3^v—Fe1—O6^vi	92.65 (4)

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

(293)

Crystal data

B4Bi0.037Fe3Ho0.963O12	Dx = 4.783 Mg m^−3
Mr = 569.3	Mo Kα radiation, λ = 0.71073 Å
Trigonal, P3121	Cell parameters from 23636 reflections
Hall symbol: P 31 2"	θ = 4.3–73.8°
a = 9.5245 (1) Å	µ = 15.83 mm^−1
c = 7.5481 (1) Å	T = 293 K
V = 593.00 (1) Å^3	Sphere, light-green
Z = 3	0.16 mm (radius)
F(000) = 785

Data collection

Xcalibur, EosS2 with high theta cut diffractometer	6205 independent reflections
Radiation source: X-ray tube	6205 reflections with I > 0σ(I)
Graphite monochromator	Rint = 0.030
Detector resolution: 8.0872 pixels mm^-1	θmax = 74.4°, θmin = 3.7°
ω scans	h = −25→25
Absorption correction: for a sphere (Dudka, 2007)	k = −25→23
Tmin = 0.012, Tmax = 0.036	l = −18→19
60932 measured reflections

Refinement

Refinement on F^2	Weighting scheme based on measured s.u.'s w = 1/σ^2(I)
R[F^2 > 2σ(F^2)] = 0.012	(Δ/σ)max = 0.004
wR(F^2) = 0.025	Δρmax = 1.36 e Å^−3
S = 0.99	Δρmin = −0.69 e Å^−3
6205 reflections	Extinction correction: Becker_Coppens G_I Isotropic (Becker & Coppens, 1974)
94 parameters	Extinction coefficient: 0.35 (1)
0 restraints	Absolute structure: 2761 of Friedel pairs used in the refinement
5 constraints	Absolute structure parameter: 0.499 (1)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ho1	0.665940 (8)	0.665940 (8)	0	0.004953 (9)	0.9627
Bi1	0.665940 (8)	0.665940 (8)	0	0.004953 (9)	0.0373
Fe1	0.884173 (18)	0	0.333333	0.00307 (3)
Fe2	0.335915 (18)	0.548872 (16)	0.323717 (10)	0.00320 (2)
O1	0	0.92232 (9)	0.166667	0.00754 (19)
O2	0.41729 (8)	0.72624 (8)	0.13301 (9)	0.00762 (12)
O3	0.69544 (9)	0.87893 (9)	0.17839 (9)	0.00612 (15)
O4	0.85250 (9)	0.63790 (9)	0.18439 (9)	0.00585 (14)
O5	0.52461 (8)	0.66983 (10)	0.49216 (9)	0.00478 (13)
O6	0.81248 (11)	0.81248 (11)	0.5	0.00510 (17)
O7	0.46441 (9)	0.47646 (9)	0.18453 (9)	0.00643 (14)
B1	0.6682 (2)	0.6682 (2)	0.5	0.0036 (2)
B2	0.55189 (13)	0.87750 (12)	0.15441 (12)	0.0044 (2)
B3	0	0.77853 (15)	0.166667	0.0040 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ho1	0.005154 (9)	0.005154 (9)	0.004709 (8)	0.002695 (14)	−0.000259 (5)	0.000259 (5)
Bi1	0.005154 (9)	0.005154 (9)	0.004709 (8)	0.002695 (14)	−0.000259 (5)	0.000259 (5)
Fe1	0.00306 (3)	0.00260 (5)	0.00339 (3)	0.00130 (2)	−0.000086 (17)	−0.00017 (3)
Fe2	0.00314 (3)	0.00288 (2)	0.00365 (2)	0.00154 (3)	0.00001 (3)	0.000091 (18)
O1	0.0092 (3)	0.00400 (15)	0.0112 (3)	0.00459 (15)	0.0065 (2)	0.00326 (11)
O2	0.00486 (15)	0.00402 (14)	0.01097 (17)	−0.00005 (12)	−0.00278 (13)	0.00261 (12)
O3	0.00374 (17)	0.0072 (2)	0.00731 (19)	0.00268 (14)	−0.00158 (12)	−0.00156 (13)
O4	0.00503 (19)	0.00368 (16)	0.00680 (17)	0.00065 (14)	−0.00035 (12)	0.00081 (12)
O5	0.00313 (15)	0.00531 (16)	0.0067 (2)	0.00271 (13)	−0.00108 (11)	−0.00199 (14)
O6	0.00328 (18)	0.00328 (18)	0.0067 (3)	0.0001 (2)	−0.00105 (10)	0.00105 (10)
O7	0.0084 (2)	0.00519 (17)	0.00738 (17)	0.00464 (15)	0.00168 (13)	0.00025 (12)
B1	0.0032 (2)	0.0032 (2)	0.00439 (15)	0.0015 (4)	−0.00009 (16)	0.00009 (16)
B2	0.0039 (2)	0.0035 (2)	0.0054 (3)	0.0016 (2)	0.00027 (16)	0.00050 (15)
B3	0.0036 (4)	0.0029 (3)	0.0058 (3)	0.0018 (2)	0.0006 (3)	0.00031 (13)

Geometric parameters (Å, º)

Ho1—Bi1	0	Fe1—O3^v	1.9637 (11)
Ho1—O3	2.3318 (9)	Fe1—O6^iv	2.0048 (7)
Ho1—O3^i	2.3318 (9)	Fe1—O6^vi	2.0048 (6)
Ho1—O4	2.3749 (9)	Fe2—O2	2.0536 (7)
Ho1—O4^i	2.3749 (9)	Fe2—O2^vii	2.0359 (11)
Ho1—O7	2.3275 (7)	Fe2—O4^viii	1.9689 (7)
Ho1—O7^i	2.3275 (7)	Fe2—O5	2.0257 (7)
Bi1—O3	2.3318 (9)	Fe2—O5^ix	2.0166 (10)
Bi1—O3^i	2.3318 (9)	Fe2—O7	1.9802 (10)
Bi1—O4	2.3749 (9)	O1—B3	1.3695 (17)
Bi1—O4^i	2.3749 (9)	O2—B2	1.3777 (10)
Bi1—O7	2.3275 (7)	O3—B2	1.3725 (16)
Bi1—O7^i	2.3275 (7)	O4—B3^x	1.3798 (9)
Fe1—O1^ii	2.0404 (6)	O5—B1	1.376 (2)
Fe1—O1^iii	2.0404 (7)	O6—B1	1.3746 (16)
Fe1—O3^iv	1.9637 (7)	O7—B2^xi	1.366 (2)
Bi1—Ho1—O3	0	O6^iv—Fe1—O6^vi	167.96 (6)
Bi1—Ho1—O3^i	0	O2—Fe2—O2^vii	86.51 (3)
Bi1—Ho1—O4	0	O2—Fe2—O4^viii	168.22 (4)
Bi1—Ho1—O4^i	0	O2—Fe2—O5	96.29 (3)
Bi1—Ho1—O7	0	O2—Fe2—O5^ix	75.93 (3)
Bi1—Ho1—O7^i	0	O2—Fe2—O7	82.52 (3)
O3—Ho1—O3^i	120.63 (2)	O2^vii—Fe2—O4^viii	92.58 (4)
O3—Ho1—O4	89.31 (3)	O2^vii—Fe2—O5	76.13 (3)
O3—Ho1—O4^i	72.37 (3)	O2^vii—Fe2—O5^ix	92.65 (4)
O3—Ho1—O7	91.31 (3)	O2^vii—Fe2—O7	161.46 (3)
O3—Ho1—O7^i	140.31 (3)	O4^viii—Fe2—O5	94.90 (3)
O3^i—Ho1—O4	72.37 (3)	O4^viii—Fe2—O5^ix	92.39 (3)
O3^i—Ho1—O4^i	89.31 (3)	O4^viii—Fe2—O7	101.16 (4)
O3^i—Ho1—O7	140.31 (3)	O5—Fe2—O5^ix	166.86 (4)
O3^i—Ho1—O7^i	91.31 (3)	O5—Fe2—O7	90.23 (3)
O4—Ho1—O4^i	142.93 (2)	O5^ix—Fe2—O7	99.09 (4)
O4—Ho1—O7	86.30 (3)	Fe1^xii—O1—Fe1^xiii	101.46 (4)
O4—Ho1—O7^i	124.97 (3)	Fe1^xii—O1—B3	129.269 (19)
O4^i—Ho1—O7	124.97 (3)	Fe1^xiii—O1—B3	129.27 (2)
O4^i—Ho1—O7^i	86.30 (3)	Fe2—O2—Fe2^ix	102.63 (2)
O7—Ho1—O7^i	73.73 (2)	Fe2—O2—B2	123.31 (6)
Ho1—Bi1—O3	0	Fe2^ix—O2—B2	128.35 (7)
Ho1—Bi1—O3^i	0	Ho1—O3—Bi1	0.0 (5)
Ho1—Bi1—O4	0	Ho1—O3—Fe1^xiv	122.11 (5)
Ho1—Bi1—O4^i	0	Ho1—O3—B2	103.25 (5)
Ho1—Bi1—O7	0	Bi1—O3—Fe1^xiv	122.11 (5)
Ho1—Bi1—O7^i	0	Bi1—O3—B2	103.25 (5)
O3—Bi1—O3^i	120.63 (2)	Fe1^xiv—O3—B2	134.37 (7)
O3—Bi1—O4	89.31 (3)	Ho1—O4—Bi1	0.0 (5)
O3—Bi1—O4^i	72.37 (3)	Ho1—O4—Fe2^v	122.76 (3)
O3—Bi1—O7	91.31 (3)	Ho1—O4—B3^x	106.85 (6)
O3—Bi1—O7^i	140.31 (3)	Bi1—O4—Fe2^v	122.76 (3)
O3^i—Bi1—O4	72.37 (3)	Bi1—O4—B3^x	106.85 (6)
O3^i—Bi1—O4^i	89.31 (3)	Fe2^v—O4—B3^x	130.14 (7)
O3^i—Bi1—O7	140.31 (3)	Fe2—O5—Fe2^vii	104.32 (4)
O3^i—Bi1—O7^i	91.31 (3)	Fe2—O5—B1	128.63 (7)
O4—Bi1—O4^i	142.93 (2)	Fe2^vii—O5—B1	126.98 (6)
O4—Bi1—O7	86.30 (3)	Fe1^xiv—O6—Fe1^xv	103.99 (3)
O4—Bi1—O7^i	124.97 (3)	Fe1^xiv—O6—B1	128.01 (8)
O4^i—Bi1—O7	124.97 (3)	Fe1^xv—O6—B1	128.01 (8)
O4^i—Bi1—O7^i	86.30 (3)	Ho1—O7—Bi1	0.0 (5)
O7—Bi1—O7^i	73.73 (2)	Ho1—O7—Fe2	117.46 (4)
O1^ii—Fe1—O1^iii	87.56 (2)	Ho1—O7—B2^xi	114.38 (7)
O1^ii—Fe1—O3^iv	85.53 (3)	Bi1—O7—Fe2	117.46 (4)
O1^ii—Fe1—O3^v	167.38 (3)	Bi1—O7—B2^xi	114.38 (7)
O1^ii—Fe1—O6^iv	93.95 (4)	Fe2—O7—B2^xi	128.14 (6)
O1^ii—Fe1—O6^vi	77.27 (4)	O5—B1—O5^xvi	121.21 (11)
O1^iii—Fe1—O3^iv	167.38 (4)	O5—B1—O6	119.39 (17)
O1^iii—Fe1—O3^v	85.53 (4)	O5^xvi—B1—O6	119.39 (17)
O1^iii—Fe1—O6^iv	77.27 (3)	O2—B2—O3	115.30 (10)
O1^iii—Fe1—O6^vi	93.95 (3)	O2—B2—O7^xvii	119.63 (10)
O3^iv—Fe1—O3^v	103.10 (4)	O3—B2—O7^xvii	125.07 (8)
O3^iv—Fe1—O6^iv	92.67 (3)	O1—B3—O4^xviii	117.49 (7)
O3^iv—Fe1—O6^vi	94.81 (3)	O1—B3—O4^xvii	117.49 (7)
O3^v—Fe1—O6^iv	94.81 (3)	O4^xviii—B3—O4^xvii	125.02 (12)
O3^v—Fe1—O6^vi	92.67 (4)

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

(350)

Crystal data

B4Bi0.037Fe3Ho0.963O12	Dx = 4.771 Mg m^−3
Mr = 569.3	Mo Kα radiation, λ = 0.71073 Å
Trigonal, P3121	Cell parameters from 21154 reflections
Hall symbol: P 31 2"	θ = 4.3–73.7°
a = 9.5291 (1) Å	µ = 15.79 mm^−1
c = 7.5601 (1) Å	T = 350 K
V = 594.51 (1) Å^3	Sphere, light-green
Z = 3	0.16 mm (radius)
F(000) = 785

Data collection

Xcalibur, EosS2 with high theta cut diffractometer	4721 independent reflections
Radiation source: X-ray tube	4721 reflections with I > 0σ(I)
Graphite monochromator	Rint = 0.075
Detector resolution: 8.0872 pixels mm^-1	θmax = 74.4°, θmin = 3.7°
ω scans	h = −25→25
Absorption correction: for a sphere (Dudka, 2007)	k = −25→23
Tmin = 0.012, Tmax = 0.036	l = −18→19
60999 measured reflections

Refinement

Refinement on F^2	Weighting scheme based on measured s.u.'s w = 1/σ^2(I)
R[F^2 > 2σ(F^2)] = 0.021	(Δ/σ)max = 0.047
wR(F^2) = 0.052	Δρmax = 2.08 e Å^−3
S = 1.01	Δρmin = −0.93 e Å^−3
4721 reflections	Extinction correction: Becker_Coppens G_I Isotropic (Becker & Coppens, 1974)
94 parameters	Extinction coefficient: 0.68 (6)
0 restraints	Absolute structure: 2084 of Friedel pairs used in the refinement
5 constraints	Absolute structure parameter: 0.511 (5)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ho1	0.666333 (16)	0.666333 (16)	0	0.00668 (2)	0.9627
Bi1	0.666333 (16)	0.666333 (16)	0	0.00668 (2)	0.0373
Fe1	0.88392 (4)	0	0.333333	0.00407 (7)
Fe2	0.33544 (4)	0.54897 (4)	0.32583 (2)	0.00440 (5)
O1	0	0.9229 (2)	0.166667	0.0116 (5)
O2	0.41569 (18)	0.72942 (19)	0.1393 (2)	0.0122 (3)
O3	0.69441 (18)	0.87854 (19)	0.17872 (18)	0.0076 (3)
O4	0.85264 (19)	0.63869 (19)	0.18346 (19)	0.0075 (3)
O5	0.52396 (17)	0.6692 (2)	0.4941 (2)	0.0063 (3)
O6	0.8121 (2)	0.8121 (2)	0.5	0.0061 (4)
O7	0.4625 (2)	0.4776 (2)	0.1831 (2)	0.0086 (3)
B1	0.6675 (5)	0.6675 (5)	0.5	0.0043 (5)
B2	0.5518 (3)	0.8791 (3)	0.1567 (2)	0.0053 (4)
B3	0	0.7792 (4)	0.166667	0.0055 (6)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ho1	0.00691 (2)	0.00691 (2)	0.00640 (2)	0.00358 (3)	−0.000324 (12)	0.000324 (12)
Bi1	0.00691 (2)	0.00691 (2)	0.00640 (2)	0.00358 (3)	−0.000324 (12)	0.000324 (12)
Fe1	0.00421 (7)	0.00324 (11)	0.00442 (5)	0.00162 (6)	−0.00001 (4)	−0.00002 (9)
Fe2	0.00449 (7)	0.00376 (6)	0.00499 (4)	0.00208 (6)	−0.00001 (7)	0.00012 (4)
O1	0.0160 (9)	0.0063 (4)	0.0158 (7)	0.0080 (5)	0.0111 (6)	0.0056 (3)
O2	0.0061 (4)	0.0072 (4)	0.0182 (5)	−0.0005 (3)	−0.0050 (3)	0.0060 (3)
O3	0.0049 (4)	0.0100 (5)	0.0079 (4)	0.0038 (3)	−0.0023 (3)	−0.0026 (3)
O4	0.0070 (5)	0.0055 (4)	0.0076 (4)	0.0014 (3)	−0.0006 (3)	0.0011 (3)
O5	0.0043 (3)	0.0076 (4)	0.0086 (4)	0.0041 (3)	−0.0013 (2)	−0.0037 (3)
O6	0.0050 (5)	0.0050 (5)	0.0070 (5)	0.0015 (5)	−0.0002 (2)	0.0002 (2)
O7	0.0102 (5)	0.0067 (4)	0.0098 (4)	0.0050 (3)	0.0026 (3)	0.0002 (3)
B1	0.0046 (5)	0.0046 (5)	0.0061 (3)	0.0041 (9)	0.0002 (3)	−0.0002 (3)
B2	0.0035 (5)	0.0046 (5)	0.0072 (6)	0.0016 (4)	0.0002 (3)	0.0008 (3)
B3	0.0050 (10)	0.0048 (7)	0.0068 (7)	0.0025 (5)	0.0011 (6)	0.0005 (3)

Geometric parameters (Å, º)

Ho1—Bi1	0	Fe1—O3^v	1.969 (2)
Ho1—O3	2.3335 (17)	Fe1—O6^iv	2.0091 (16)
Ho1—O3^i	2.3335 (17)	Fe1—O6^vi	2.0091 (14)
Ho1—O4	2.3691 (19)	Fe2—O2	2.0532 (16)
Ho1—O4^i	2.3691 (19)	Fe2—O2^vii	2.033 (2)
Ho1—O7	2.3304 (15)	Fe2—O4^viii	1.9706 (14)
Ho1—O7^i	2.3304 (15)	Fe2—O5	2.0246 (14)
Bi1—O3	2.3335 (17)	Fe2—O5^ix	2.016 (2)
Bi1—O3^i	2.3335 (17)	Fe2—O7	1.979 (2)
Bi1—O4	2.3691 (19)	O1—B3	1.369 (4)
Bi1—O4^i	2.3691 (19)	O2—B2	1.373 (2)
Bi1—O7	2.3304 (15)	O3—B2	1.371 (3)
Bi1—O7^i	2.3304 (15)	O4—B3^x	1.379 (2)
Fe1—O1^ii	2.0407 (13)	O5—B1	1.377 (5)
Fe1—O1^iii	2.0407 (15)	O6—B1	1.378 (4)
Fe1—O3^iv	1.9690 (14)	O7—B2^xi	1.370 (4)
Bi1—Ho1—O3	0	O6^iv—Fe1—O6^vi	167.95 (12)
Bi1—Ho1—O3^i	0	O2—Fe2—O2^vii	86.66 (8)
Bi1—Ho1—O4	0	O2—Fe2—O4^viii	168.10 (8)
Bi1—Ho1—O4^i	0	O2—Fe2—O5	95.97 (6)
Bi1—Ho1—O7	0	O2—Fe2—O5^ix	75.97 (6)
Bi1—Ho1—O7^i	0	O2—Fe2—O7	82.98 (8)
O3—Ho1—O3^i	121.24 (5)	O2^vii—Fe2—O4^viii	91.42 (8)
O3—Ho1—O4	89.41 (6)	O2^vii—Fe2—O5	76.24 (8)
O3—Ho1—O4^i	72.37 (6)	O2^vii—Fe2—O5^ix	92.85 (8)
O3—Ho1—O7	90.86 (6)	O2^vii—Fe2—O7	162.52 (6)
O3—Ho1—O7^i	140.58 (7)	O4^viii—Fe2—O5	94.98 (7)
O3^i—Ho1—O4	72.37 (6)	O4^viii—Fe2—O5^ix	92.41 (7)
O3^i—Ho1—O4^i	89.41 (6)	O4^viii—Fe2—O7	101.54 (9)
O3^i—Ho1—O7	140.58 (7)	O5—Fe2—O5^ix	166.94 (9)
O3^i—Ho1—O7^i	90.86 (6)	O5—Fe2—O7	90.85 (8)
O4—Ho1—O4^i	142.78 (5)	O5^ix—Fe2—O7	98.22 (8)
O4—Ho1—O7	87.02 (6)	Fe1^xii—O1—Fe1^xiii	101.72 (9)
O4—Ho1—O7^i	124.35 (7)	Fe1^xii—O1—B3	129.14 (4)
O4^i—Ho1—O7	124.35 (7)	Fe1^xiii—O1—B3	129.14 (4)
O4^i—Ho1—O7^i	87.02 (6)	Fe2—O2—Fe2^ix	102.76 (6)
O7—Ho1—O7^i	73.24 (5)	Fe2—O2—B2	124.54 (13)
Ho1—Bi1—O3	0	Fe2^ix—O2—B2	128.89 (16)
Ho1—Bi1—O3^i	0	Ho1—O3—Bi1	0.0 (5)
Ho1—Bi1—O4	0	Ho1—O3—Fe1^xiv	121.82 (10)
Ho1—Bi1—O4^i	0	Ho1—O3—B2	104.39 (11)
Ho1—Bi1—O7	0	Bi1—O3—Fe1^xiv	121.82 (10)
Ho1—Bi1—O7^i	0	Bi1—O3—B2	104.39 (11)
O3—Bi1—O3^i	121.24 (5)	Fe1^xiv—O3—B2	133.55 (14)
O3—Bi1—O4	89.41 (6)	Ho1—O4—Bi1	0.0 (5)
O3—Bi1—O4^i	72.37 (6)	Ho1—O4—Fe2^v	122.47 (7)
O3—Bi1—O7	90.86 (6)	Ho1—O4—B3^x	107.11 (13)
O3—Bi1—O7^i	140.58 (7)	Bi1—O4—Fe2^v	122.47 (7)
O3^i—Bi1—O4	72.37 (6)	Bi1—O4—B3^x	107.11 (13)
O3^i—Bi1—O4^i	89.41 (6)	Fe2^v—O4—B3^x	130.19 (14)
O3^i—Bi1—O7	140.58 (7)	Fe2—O5—Fe2^vii	104.38 (9)
O3^i—Bi1—O7^i	90.86 (6)	Fe2—O5—B1	128.27 (16)
O4—Bi1—O4^i	142.78 (5)	Fe2^vii—O5—B1	127.31 (14)
O4—Bi1—O7	87.02 (6)	Fe1^xiv—O6—Fe1^xv	103.96 (7)
O4—Bi1—O7^i	124.35 (7)	Fe1^xiv—O6—B1	128.02 (17)
O4^i—Bi1—O7	124.35 (7)	Fe1^xv—O6—B1	128.02 (17)
O4^i—Bi1—O7^i	87.02 (6)	Ho1—O7—Bi1	0.0 (5)
O7—Bi1—O7^i	73.24 (5)	Ho1—O7—Fe2	118.40 (9)
O1^ii—Fe1—O1^iii	87.54 (5)	Ho1—O7—B2^xi	113.25 (14)
O1^ii—Fe1—O3^iv	85.68 (6)	Bi1—O7—Fe2	118.40 (9)
O1^ii—Fe1—O3^v	167.27 (6)	Bi1—O7—B2^xi	113.25 (14)
O1^ii—Fe1—O6^iv	94.05 (8)	Fe2—O7—B2^xi	128.35 (13)
O1^ii—Fe1—O6^vi	77.16 (9)	O5—B1—O5^xvi	121.2 (3)
O1^iii—Fe1—O3^iv	167.27 (8)	O5—B1—O6	119.4 (4)
O1^iii—Fe1—O3^v	85.68 (8)	O5^xvi—B1—O6	119.4 (4)
O1^iii—Fe1—O6^iv	77.16 (6)	O2—B2—O3	115.5 (2)
O1^iii—Fe1—O6^vi	94.05 (7)	O2—B2—O7^xvii	119.3 (2)
O3^iv—Fe1—O3^v	102.89 (9)	O3—B2—O7^xvii	125.15 (16)
O3^iv—Fe1—O6^iv	92.57 (6)	O1—B3—O4^xviii	117.51 (15)
O3^iv—Fe1—O6^vi	94.93 (7)	O1—B3—O4^xvii	117.51 (16)
O3^v—Fe1—O6^iv	94.93 (7)	O4^xviii—B3—O4^xvii	125.0 (3)
O3^v—Fe1—O6^vi	92.57 (8)

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

(360)

Crystal data

B4Bi0.037Fe3Ho0.963O12	Dx = 4.769 Mg m^−3
Mr = 569.3	Mo Kα radiation, λ = 0.71073 Å
Trigonal, P3121	Cell parameters from 20477 reflections
Hall symbol: P 31 2"	θ = 4.3–73.7°
a = 9.5301 (2) Å	µ = 15.78 mm^−1
c = 7.5615 (1) Å	T = 360 K
V = 594.75 (2) Å^3	Sphere, light-green
Z = 3	0.16 mm (radius)
F(000) = 785

Data collection

Xcalibur, EosS2 with high theta cut diffractometer	4241 independent reflections
Radiation source: X-ray tube	4241 reflections with I > 0σ(I)
Graphite monochromator	Rint = 0.032
Detector resolution: 8.0872 pixels mm^-1	θmax = 74.4°, θmin = 3.7°
ω scans	h = −25→25
Absorption correction: for a sphere (Dudka, 2007)	k = −25→23
Tmin = 0.012, Tmax = 0.037	l = −18→19
60236 measured reflections

Refinement

Refinement on F^2	Weighting scheme based on measured s.u.'s w = 1/σ^2(I)
R[F^2 > 2σ(F^2)] = 0.014	(Δ/σ)max = 0.049
wR(F^2) = 0.030	Δρmax = 1.32 e Å^−3
S = 1.04	Δρmin = −1.13 e Å^−3
4241 reflections	Extinction correction: Becker_Coppens G_I Isotropic (Becker & Coppens, 1974)
94 parameters	Extinction coefficient: 0.29 (4)
0 restraints	Absolute structure: 1857 of Friedel pairs used in the refinement
5 constraints	Absolute structure parameter: 0.500 (5)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ho1	0.66644 (2)	0.66644 (2)	0	0.00646 (3)	0.9627
Bi1	0.66644 (2)	0.66644 (2)	0	0.00646 (3)	0.0373
Fe1	0.88394 (5)	0	0.333333	0.00384 (8)
Fe2	0.33521 (6)	0.54896 (5)	0.32655 (2)	0.00420 (6)
O1	0	0.9235 (2)	0.166667	0.0109 (5)
O2	0.4151 (2)	0.7304 (2)	0.1419 (2)	0.0117 (3)
O3	0.6941 (2)	0.8784 (2)	0.1789 (2)	0.0075 (4)
O4	0.8530 (2)	0.6391 (2)	0.1833 (2)	0.0073 (4)
O5	0.5235 (2)	0.6688 (3)	0.4948 (3)	0.0062 (4)
O6	0.8114 (3)	0.8114 (3)	0.5	0.0061 (6)
O7	0.4616 (3)	0.4778 (3)	0.1830 (2)	0.0084 (4)
B1	0.6672 (6)	0.6672 (6)	0.5	0.0048 (7)
B2	0.5523 (3)	0.8802 (3)	0.1583 (3)	0.0052 (5)
B3	0	0.7798 (4)	0.166667	0.0059 (9)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ho1	0.00666 (3)	0.00666 (3)	0.006178 (14)	0.00341 (5)	−0.000301 (16)	0.000301 (16)
Bi1	0.00666 (3)	0.00666 (3)	0.006178 (14)	0.00341 (5)	−0.000301 (16)	0.000301 (16)
Fe1	0.00423 (10)	0.00231 (14)	0.00434 (6)	0.00115 (7)	−0.00005 (6)	−0.00011 (12)
Fe2	0.00453 (9)	0.00331 (7)	0.00498 (5)	0.00214 (8)	−0.00002 (9)	0.00013 (5)
O1	0.0140 (9)	0.0048 (4)	0.0170 (7)	0.0070 (5)	0.0105 (6)	0.0052 (3)
O2	0.0064 (4)	0.0061 (4)	0.0178 (5)	−0.0004 (3)	−0.0045 (3)	0.0057 (3)
O3	0.0038 (5)	0.0096 (7)	0.0092 (5)	0.0034 (4)	−0.0020 (3)	−0.0018 (4)
O4	0.0067 (6)	0.0058 (5)	0.0079 (4)	0.0020 (5)	−0.0006 (3)	0.0013 (3)
O5	0.0037 (4)	0.0081 (5)	0.0090 (5)	0.0045 (4)	−0.0013 (3)	−0.0031 (4)
O6	0.0054 (7)	0.0054 (7)	0.0075 (7)	0.0028 (7)	−0.0008 (3)	0.0008 (3)
O7	0.0110 (6)	0.0064 (5)	0.0091 (4)	0.0054 (4)	0.0021 (3)	0.0002 (3)
B1	0.0077 (7)	0.0077 (7)	0.0050 (3)	0.0084 (11)	0.0006 (3)	−0.0006 (3)
B2	0.0028 (6)	0.0050 (6)	0.0091 (7)	0.0030 (5)	−0.0002 (4)	0.0001 (4)
B3	0.0103 (15)	0.0049 (8)	0.0043 (8)	0.0051 (8)	0.0016 (7)	0.0008 (4)

Geometric parameters (Å, º)

Ho1—Bi1	0	Fe1—O3^v	1.971 (3)
Ho1—O3	2.334 (2)	Fe1—O6^iv	2.013 (2)
Ho1—O3^i	2.334 (2)	Fe1—O6^vi	2.0134 (18)
Ho1—O4	2.369 (2)	Fe2—O2	2.0500 (16)
Ho1—O4^i	2.369 (2)	Fe2—O2^vii	2.034 (3)
Ho1—O7	2.3344 (17)	Fe2—O4^viii	1.9706 (17)
Ho1—O7^i	2.3344 (17)	Fe2—O5	2.0230 (19)
Bi1—O3	2.334 (2)	Fe2—O5^ix	2.016 (3)
Bi1—O3^i	2.334 (2)	Fe2—O7	1.976 (3)
Bi1—O4	2.369 (2)	O1—B3	1.370 (5)
Bi1—O4^i	2.369 (2)	O2—B2	1.377 (2)
Bi1—O7	2.3344 (17)	O3—B2	1.369 (4)
Bi1—O7^i	2.3344 (17)	O4—B3^x	1.377 (2)
Fe1—O1^ii	2.0368 (15)	O5—B1	1.378 (7)
Fe1—O1^iii	2.0368 (18)	O6—B1	1.374 (5)
Fe1—O3^iv	1.9707 (17)	O7—B2^xi	1.368 (5)
Bi1—Ho1—O3	0	O6^iv—Fe1—O6^vi	168.17 (16)
Bi1—Ho1—O3^i	0	O2—Fe2—O2^vii	86.71 (8)
Bi1—Ho1—O4	0	O2—Fe2—O4^viii	168.13 (10)
Bi1—Ho1—O4^i	0	O2—Fe2—O5	95.83 (8)
Bi1—Ho1—O7	0	O2—Fe2—O5^ix	76.01 (7)
Bi1—Ho1—O7^i	0	O2—Fe2—O7	83.26 (9)
O3—Ho1—O3^i	121.42 (6)	O2^vii—Fe2—O4^viii	91.07 (10)
O3—Ho1—O4	89.43 (7)	O2^vii—Fe2—O5	76.20 (9)
O3—Ho1—O4^i	72.34 (7)	O2^vii—Fe2—O5^ix	92.94 (10)
O3—Ho1—O7	90.69 (7)	O2^vii—Fe2—O7	162.89 (7)
O3—Ho1—O7^i	140.71 (9)	O4^viii—Fe2—O5	94.96 (9)
O3^i—Ho1—O4	72.34 (7)	O4^viii—Fe2—O5^ix	92.48 (9)
O3^i—Ho1—O4^i	89.43 (7)	O4^viii—Fe2—O7	101.50 (11)
O3^i—Ho1—O7	140.71 (9)	O5—Fe2—O5^ix	166.92 (12)
O3^i—Ho1—O7^i	90.69 (7)	O5—Fe2—O7	91.04 (10)
O4—Ho1—O4^i	142.64 (6)	O5^ix—Fe2—O7	98.01 (10)
O4—Ho1—O7	87.32 (7)	Fe1^xii—O1—Fe1^xiii	102.00 (10)
O4—Ho1—O7^i	124.15 (8)	Fe1^xii—O1—B3	129.00 (5)
O4^i—Ho1—O7	124.15 (8)	Fe1^xiii—O1—B3	129.00 (5)
O4^i—Ho1—O7^i	87.32 (7)	Fe2—O2—Fe2^ix	102.81 (6)
O7—Ho1—O7^i	73.12 (6)	Fe2—O2—B2	124.94 (15)
Ho1—Bi1—O3	0	Fe2^ix—O2—B2	128.99 (18)
Ho1—Bi1—O3^i	0	Ho1—O3—Bi1	0.0 (5)
Ho1—Bi1—O4	0	Ho1—O3—Fe1^xiv	121.71 (12)
Ho1—Bi1—O4^i	0	Ho1—O3—B2	105.07 (14)
Ho1—Bi1—O7	0	Bi1—O3—Fe1^xiv	121.71 (12)
Ho1—Bi1—O7^i	0	Bi1—O3—B2	105.07 (14)
O3—Bi1—O3^i	121.42 (6)	Fe1^xiv—O3—B2	132.98 (18)
O3—Bi1—O4	89.43 (7)	Ho1—O4—Bi1	0.0 (5)
O3—Bi1—O4^i	72.34 (7)	Ho1—O4—Fe2^v	122.22 (9)
O3—Bi1—O7	90.69 (7)	Ho1—O4—B3^x	107.07 (16)
O3—Bi1—O7^i	140.71 (9)	Bi1—O4—Fe2^v	122.22 (9)
O3^i—Bi1—O4	72.34 (7)	Bi1—O4—B3^x	107.07 (16)
O3^i—Bi1—O4^i	89.43 (7)	Fe2^v—O4—B3^x	130.46 (18)
O3^i—Bi1—O7	140.71 (9)	Fe2—O5—Fe2^vii	104.44 (11)
O3^i—Bi1—O7^i	90.69 (7)	Fe2—O5—B1	128.2 (2)
O4—Bi1—O4^i	142.64 (6)	Fe2^vii—O5—B1	127.35 (18)
O4—Bi1—O7	87.32 (7)	Fe1^xiv—O6—Fe1^xv	103.67 (9)
O4—Bi1—O7^i	124.15 (8)	Fe1^xiv—O6—B1	128.2 (2)
O4^i—Bi1—O7	124.15 (8)	Fe1^xv—O6—B1	128.2 (2)
O4^i—Bi1—O7^i	87.32 (7)	Ho1—O7—Bi1	0.0 (5)
O7—Bi1—O7^i	73.12 (6)	Ho1—O7—Fe2	118.67 (11)
O1^ii—Fe1—O1^iii	87.57 (7)	Ho1—O7—B2^xi	112.62 (17)
O1^ii—Fe1—O3^iv	85.76 (7)	Bi1—O7—Fe2	118.67 (11)
O1^ii—Fe1—O3^v	167.16 (7)	Bi1—O7—B2^xi	112.62 (17)
O1^ii—Fe1—O6^iv	94.21 (10)	Fe2—O7—B2^xi	128.71 (15)
O1^ii—Fe1—O6^vi	77.17 (12)	O5—B1—O5^xvi	121.1 (3)
O1^iii—Fe1—O3^iv	167.16 (10)	O5—B1—O6	119.5 (5)
O1^iii—Fe1—O3^v	85.76 (10)	O5^xvi—B1—O6	119.5 (5)
O1^iii—Fe1—O6^iv	77.17 (8)	O2—B2—O3	115.4 (3)
O1^iii—Fe1—O6^vi	94.21 (10)	O2—B2—O7^xvii	119.1 (3)
O3^iv—Fe1—O3^v	102.77 (10)	O3—B2—O7^xvii	125.47 (19)
O3^iv—Fe1—O6^iv	92.39 (8)	O1—B3—O4^xviii	117.70 (19)
O3^iv—Fe1—O6^vi	94.99 (9)	O1—B3—O4^xvii	117.70 (19)
O3^v—Fe1—O6^iv	94.99 (9)	O4^xviii—B3—O4^xvii	124.6 (3)
O3^v—Fe1—O6^vi	92.39 (11)

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

(365)

Crystal data

B4Bi0.037Fe3Ho0.963O12	Dx = 4.415 Mg m^−3
Mr = 569.3	Mo Kα radiation, λ = 0.71073 Å
Trigonal, R32	Cell parameters from 19433 reflections
Hall symbol: R 3 2"	θ = 4.3–74.1°
a = 9.5351 (1) Å	µ = 15.66 mm^−1
c = 7.5633 (1) Å	T = 365 K
V = 595.52 (1) Å^3	Sphere
Z = 3	0.16 mm (radius)
F(000) = 785

Data collection

Xcalibur, EosS2 with high theta cut diffractometer	2724 independent reflections
Radiation source: X-ray tube	2724 reflections with I > 0σ(I)
Graphite monochromator	Rint = 0.075
Detector resolution: 8.0872 pixels mm^-1	θmax = 74.3°, θmin = 3.7°
ω scans	h = −25→25
Absorption correction: for a sphere (Dudka, 2007)	k = −25→24
Tmin = 0.012, Tmax = 0.036	l = −18→19
20114 measured reflections

Refinement

Refinement on F^2	Weighting scheme based on measured s.u.'s w = 1/σ^2(I)
R[F^2 > 2σ(F^2)] = 0.020	(Δ/σ)max = 0.047
wR(F^2) = 0.050	Δρmax = 1.75 e Å^−3
S = 1.03	Δρmin = −1.89 e Å^−3
2724 reflections	Extinction correction: Becker_Coppens G_I Isotropic (Becker & Coppens, 1974)
34 parameters	Extinction coefficient: 0.83 (2)
0 restraints	Absolute structure: 1239 of Friedel pairs used in the refinement
2 constraints	Absolute structure parameter: 0.493 (5)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ho1	0	0	0	0.007349 (17)	0.9627
Bi1	0	0	0	0.007349 (17)	0.0373
Fe1	0.215788 (17)	0.333333	0.333333	0.00468 (3)
O1	0.14438 (8)	0.14438 (8)	0.5	0.00663 (12)
O2	0.40788 (11)	0.40788 (11)	0.5	0.0163 (3)
O3	0.02455 (8)	0.21094 (10)	0.18141 (11)	0.00825 (13)
B1	0	0	0.5	0.0042 (2)
B2	0.55121 (13)	0.55121 (13)	0.5	0.0060 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ho1	0.00758 (2)	0.00758 (2)	0.00689 (3)	0.003791 (11)	0	0
Bi1	0.00758 (2)	0.00758 (2)	0.00689 (3)	0.003791 (11)	0	0
Fe1	0.00425 (3)	0.00429 (3)	0.00552 (5)	0.002146 (17)	0.000056 (12)	0.00011 (2)
O1	0.00422 (11)	0.00422 (11)	0.0092 (2)	0.00040 (13)	−0.00123 (8)	0.00123 (8)
O2	0.00774 (17)	0.00774 (17)	0.0254 (7)	−0.0023 (2)	−0.0085 (3)	0.0085 (3)
O3	0.00587 (14)	0.01057 (19)	0.00888 (19)	0.00455 (13)	−0.00183 (12)	−0.00219 (14)
B1	0.0034 (2)	0.0034 (2)	0.0058 (5)	0.00171 (12)	0	0
B2	0.0049 (2)	0.0049 (2)	0.0079 (3)	0.0022 (3)	−0.00082 (16)	0.00082 (16)

Geometric parameters (Å, º)

Ho1—Bi1	0	Bi1—O3^iv	2.3477 (8)
Ho1—O3	2.3477 (9)	Bi1—O3^v	2.3477 (12)
Ho1—O3^i	2.3477 (8)	Fe1—O1	2.0179 (6)
Ho1—O3^ii	2.3477 (12)	Fe1—O1^vi	2.0179 (5)
Ho1—O3^iii	2.3477 (9)	Fe1—O2	2.0364 (8)
Ho1—O3^iv	2.3477 (8)	Fe1—O2^vi	2.0364 (13)
Ho1—O3^v	2.3477 (12)	Fe1—O3	1.9696 (7)
Bi1—O3	2.3477 (9)	Fe1—O3^vii	1.9696 (12)
Bi1—O3^i	2.3477 (8)	O1—B1	1.3767 (6)
Bi1—O3^ii	2.3477 (12)	O2—B2	1.3667 (12)
Bi1—O3^iii	2.3477 (9)	O3—B2^viii	1.3738 (17)
Bi1—Ho1—O3	0	O3^ii—Bi1—O3^v	141.63 (2)
Bi1—Ho1—O3^i	0	O3^iii—Bi1—O3^iv	89.29 (3)
Bi1—Ho1—O3^ii	0	O3^iii—Bi1—O3^v	89.29 (3)
Bi1—Ho1—O3^iii	0	O3^iv—Bi1—O3^v	89.29 (3)
Bi1—Ho1—O3^iv	0	O1—Fe1—O1^vi	167.48 (4)
Bi1—Ho1—O3^v	0	O1—Fe1—O2	76.59 (3)
O3—Ho1—O3^i	89.29 (3)	O1—Fe1—O2^vi	94.24 (3)
O3—Ho1—O3^ii	89.29 (3)	O1—Fe1—O3	92.08 (3)
O3—Ho1—O3^iii	122.86 (2)	O1—Fe1—O3^vii	95.80 (3)
O3—Ho1—O3^iv	141.63 (4)	O1^vi—Fe1—O2	94.24 (3)
O3—Ho1—O3^v	72.42 (3)	O1^vi—Fe1—O2^vi	76.59 (4)
O3^i—Ho1—O3^ii	89.29 (3)	O1^vi—Fe1—O3	95.80 (3)
O3^i—Ho1—O3^iii	141.63 (4)	O1^vi—Fe1—O3^vii	92.08 (4)
O3^i—Ho1—O3^iv	72.42 (3)	O2—Fe1—O2^vi	87.08 (4)
O3^i—Ho1—O3^v	122.86 (4)	O2—Fe1—O3	166.55 (4)
O3^ii—Ho1—O3^iii	72.42 (3)	O2—Fe1—O3^vii	86.57 (4)
O3^ii—Ho1—O3^iv	122.86 (4)	O2^vi—Fe1—O3	86.57 (4)
O3^ii—Ho1—O3^v	141.63 (2)	O2^vi—Fe1—O3^vii	166.55 (3)
O3^iii—Ho1—O3^iv	89.29 (3)	O3—Fe1—O3^vii	101.97 (4)
O3^iii—Ho1—O3^v	89.29 (3)	Fe1—O1—Fe1^ix	104.08 (3)
O3^iv—Ho1—O3^v	89.29 (3)	Fe1—O1—B1	127.96 (4)
Ho1—Bi1—O3	0	Fe1^ix—O1—B1	127.96 (4)
Ho1—Bi1—O3^i	0	Fe1—O2—Fe1^ix	102.75 (3)
Ho1—Bi1—O3^ii	0	Fe1—O2—B2	128.63 (6)
Ho1—Bi1—O3^iii	0	Fe1^ix—O2—B2	128.63 (6)
Ho1—Bi1—O3^iv	0	Ho1—O3—Bi1	0.0 (5)
Ho1—Bi1—O3^v	0	Ho1—O3—Fe1	120.98 (5)
O3—Bi1—O3^i	89.29 (3)	Ho1—O3—B2^viii	108.11 (5)
O3—Bi1—O3^ii	89.29 (3)	Bi1—O3—Fe1	120.98 (5)
O3—Bi1—O3^iii	122.86 (2)	Bi1—O3—B2^viii	108.11 (5)
O3—Bi1—O3^iv	141.63 (4)	Fe1—O3—B2^viii	130.76 (7)
O3—Bi1—O3^v	72.42 (3)	O1—B1—O1^i	120.00 (6)
O3^i—Bi1—O3^ii	89.29 (3)	O1—B1—O1^ii	120.00 (6)
O3^i—Bi1—O3^iii	141.63 (4)	O1^i—B1—O1^ii	120.00 (6)
O3^i—Bi1—O3^iv	72.42 (3)	O2—B2—O3^x	117.50 (12)
O3^i—Bi1—O3^v	122.86 (4)	O2—B2—O3^xi	117.50 (12)
O3^ii—Bi1—O3^iii	72.42 (3)	O3^x—B2—O3^xi	125.00 (8)
O3^ii—Bi1—O3^iv	122.86 (4)

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

(370)

Crystal data

B4Bi0.037Fe3Ho0.963O12	Dx = 4.762 Mg m^−3
Mr = 569.3	Mo Kα radiation, λ = 0.71073 Å
Trigonal, R32	Cell parameters from 19339 reflections
Hall symbol: R 3 2"	θ = 4.3–73.7°
a = 9.5349 (2) Å	µ = 15.76 mm^−1
c = 7.5641 (1) Å	T = 370 K
V = 595.55 (2) Å^3	Sphere, light-green
Z = 3	0.16 mm (radius)
F(000) = 785

Data collection

Xcalibur, EosS2 with high theta cut diffractometer	2727 independent reflections
Radiation source: X-ray tube	2727 reflections with I > 0σ(I)
Graphite monochromator	Rint = 0.041
Detector resolution: 8.0872 pixels mm^-1	θmax = 74.0°, θmin = 3.7°
ω scans	h = −25→25
Absorption correction: for a sphere (Dudka, 2007)	k = −25→23
Tmin = 0.012, Tmax = 0.036	l = −18→19
20376 measured reflections

Refinement

Refinement on F^2	Weighting scheme based on measured s.u.'s w = 1/σ^2(I)
R[F^2 > 2σ(F^2)] = 0.016	(Δ/σ)max = 0.050
wR(F^2) = 0.039	Δρmax = 1.29 e Å^−3
S = 0.99	Δρmin = −1.38 e Å^−3
2727 reflections	Extinction correction: Becker_Coppens G_I Isotropic (Becker & Coppens, 1974)
34 parameters	Extinction coefficient: 0.97 (3)
0 restraints	Absolute structure: 1240 of Friedel pairs used in the refinement
2 constraints	Absolute structure parameter: 0.495 (5)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ho1	0	0	0	0.007256 (12)	0.9627
Bi1	0	0	0	0.007256 (12)	0.0373
Fe1	0.215778 (15)	0.333333	0.333333	0.00453 (2)
O1	0.14433 (7)	0.14433 (7)	0.5	0.00648 (10)
O2	0.40784 (9)	0.40784 (9)	0.5	0.0152 (2)
O3	0.02446 (7)	0.21102 (8)	0.18117 (9)	0.00817 (11)
B1	0	0	0.5	0.00437 (19)
B2	0.55116 (11)	0.55116 (11)	0.5	0.00579 (17)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ho1	0.007428 (15)	0.007428 (15)	0.00691 (2)	0.003714 (7)	0	0
Bi1	0.007428 (15)	0.007428 (15)	0.00691 (2)	0.003714 (7)	0	0
Fe1	0.00401 (2)	0.00409 (3)	0.00552 (4)	0.002046 (13)	0.000026 (9)	0.000052 (19)
O1	0.00418 (9)	0.00418 (9)	0.0088 (2)	0.00035 (11)	−0.00141 (7)	0.00141 (7)
O2	0.00715 (14)	0.00715 (14)	0.0240 (5)	−0.00199 (19)	−0.0079 (2)	0.0079 (2)
O3	0.00549 (11)	0.01038 (16)	0.00926 (16)	0.00443 (11)	−0.00200 (10)	−0.00234 (12)
B1	0.0037 (2)	0.0037 (2)	0.0056 (4)	0.00187 (10)	0	0
B2	0.00443 (16)	0.00443 (16)	0.0078 (3)	0.0017 (3)	−0.00056 (13)	0.00056 (13)

Geometric parameters (Å, º)

Ho1—Bi1	0	Bi1—O3^iv	2.3477 (6)
Ho1—O3	2.3477 (8)	Bi1—O3^v	2.3477 (10)
Ho1—O3^i	2.3477 (6)	Fe1—O1	2.0183 (5)
Ho1—O3^ii	2.3477 (10)	Fe1—O1^vi	2.0183 (4)
Ho1—O3^iii	2.3477 (8)	Fe1—O2	2.0364 (7)
Ho1—O3^iv	2.3477 (6)	Fe1—O2^vi	2.0364 (11)
Ho1—O3^v	2.3477 (10)	Fe1—O3	1.9711 (6)
Bi1—O3	2.3477 (8)	Fe1—O3^vii	1.9711 (10)
Bi1—O3^i	2.3477 (6)	O1—B1	1.3762 (5)
Bi1—O3^ii	2.3477 (10)	O2—B2	1.3665 (10)
Bi1—O3^iii	2.3477 (8)	O3—B2^viii	1.3726 (14)
Bi1—Ho1—O3	0	O3^ii—Bi1—O3^v	141.561 (19)
Bi1—Ho1—O3^i	0	O3^iii—Bi1—O3^iv	89.36 (3)
Bi1—Ho1—O3^ii	0	O3^iii—Bi1—O3^v	89.36 (3)
Bi1—Ho1—O3^iii	0	O3^iv—Bi1—O3^v	89.36 (3)
Bi1—Ho1—O3^iv	0	O1—Fe1—O1^vi	167.49 (4)
Bi1—Ho1—O3^v	0	O1—Fe1—O2	76.58 (2)
O3—Ho1—O3^i	89.36 (3)	O1—Fe1—O2^vi	94.25 (3)
O3—Ho1—O3^ii	89.36 (3)	O1—Fe1—O3	92.12 (2)
O3—Ho1—O3^iii	122.866 (19)	O1—Fe1—O3^vii	95.74 (3)
O3—Ho1—O3^iv	141.56 (3)	O1^vi—Fe1—O2	94.25 (3)
O3—Ho1—O3^v	72.32 (3)	O1^vi—Fe1—O2^vi	76.58 (3)
O3^i—Ho1—O3^ii	89.36 (3)	O1^vi—Fe1—O3	95.74 (3)
O3^i—Ho1—O3^iii	141.56 (3)	O1^vi—Fe1—O3^vii	92.12 (3)
O3^i—Ho1—O3^iv	72.32 (2)	O2—Fe1—O2^vi	87.08 (3)
O3^i—Ho1—O3^v	122.87 (3)	O2—Fe1—O3	166.59 (4)
O3^ii—Ho1—O3^iii	72.32 (3)	O2—Fe1—O3^vii	86.57 (4)
O3^ii—Ho1—O3^iv	122.87 (3)	O2^vi—Fe1—O3	86.57 (3)
O3^ii—Ho1—O3^v	141.561 (19)	O2^vi—Fe1—O3^vii	166.59 (3)
O3^iii—Ho1—O3^iv	89.36 (3)	O3—Fe1—O3^vii	101.95 (4)
O3^iii—Ho1—O3^v	89.36 (3)	Fe1—O1—Fe1^ix	104.06 (2)
O3^iv—Ho1—O3^v	89.36 (3)	Fe1—O1—B1	127.97 (3)
Ho1—Bi1—O3	0	Fe1^ix—O1—B1	127.97 (3)
Ho1—Bi1—O3^i	0	Fe1—O2—Fe1^ix	102.77 (3)
Ho1—Bi1—O3^ii	0	Fe1—O2—B2	128.62 (5)
Ho1—Bi1—O3^iii	0	Fe1^ix—O2—B2	128.62 (5)
Ho1—Bi1—O3^iv	0	Ho1—O3—Bi1	0.0 (5)
Ho1—Bi1—O3^v	0	Ho1—O3—Fe1	120.92 (4)
O3—Bi1—O3^i	89.36 (3)	Ho1—O3—B2^viii	108.16 (4)
O3—Bi1—O3^ii	89.36 (3)	Bi1—O3—Fe1	120.92 (4)
O3—Bi1—O3^iii	122.866 (19)	Bi1—O3—B2^viii	108.16 (4)
O3—Bi1—O3^iv	141.56 (3)	Fe1—O3—B2^viii	130.75 (6)
O3—Bi1—O3^v	72.32 (3)	O1—B1—O1^i	120.00 (5)
O3^i—Bi1—O3^ii	89.36 (3)	O1—B1—O1^ii	120.00 (5)
O3^i—Bi1—O3^iii	141.56 (3)	O1^i—B1—O1^ii	120.00 (5)
O3^i—Bi1—O3^iv	72.32 (2)	O2—B2—O3^x	117.55 (10)
O3^i—Bi1—O3^v	122.87 (3)	O2—B2—O3^xi	117.55 (10)
O3^ii—Bi1—O3^iii	72.32 (3)	O3^x—B2—O3^xi	124.90 (7)
O3^ii—Bi1—O3^iv	122.87 (3)

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

(380)

Crystal data

B4Bi0.037Fe3Ho0.963O12	Dx = 4.418 Mg m^−3
Mr = 569.3	Mo Kα radiation, λ = 0.71073 Å
Trigonal, R32	Cell parameters from 19271 reflections
Hall symbol: R 3 2"	θ = 4.3–73.7°
a = 9.5359 (2) Å	µ = 15.81 mm^−1
c = 7.5659 (2) Å	T = 380 K
V = 595.82 (2) Å^3	Sphere, light-green
Z = 3	0.16 mm (radius)
F(000) = 713

Data collection

Xcalibur, EosS2 with high theta cut diffractometer	2726 independent reflections
Radiation source: X-ray tube	2726 reflections with I > 0σ(I)
Graphite monochromator	Rint = 0.095
Detector resolution: 8.0872 pixels mm^-1	θmax = 74.0°, θmin = 3.7°
ω scans	h = −25→25
Absorption correction: for a sphere (Dudka, 2007)	k = −25→23
Tmin = 0.012, Tmax = 0.036	l = −18→19
20378 measured reflections

Refinement

Refinement on F^2	Weighting scheme based on measured s.u.'s w = 1/σ^2(I)
R[F^2 > 2σ(F^2)] = 0.021	(Δ/σ)max = 0.050
wR(F^2) = 0.055	Δρmax = 1.44 e Å^−3
S = 1.00	Δρmin = −1.26 e Å^−3
2726 reflections	Extinction correction: Becker_Coppens G_I Isotropic (Becker & Coppens, 1974)
34 parameters	Extinction coefficient: 0.97 (9)
0 restraints	Absolute structure: 1240 of Friedel pairs used in the refinement
2 constraints	Absolute structure parameter: 0.497 (5)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ho1	0	0	0	0.007624 (18)	0.9627
Bi1	0	0	0	0.007624 (18)	0.0373
Fe1	0.215802 (18)	0.333333	0.333333	0.00479 (3)
O1	0.14438 (9)	0.14438 (9)	0.5	0.00654 (12)
O2	0.40802 (11)	0.40802 (11)	0.5	0.0142 (2)
O3	0.02462 (9)	0.21097 (11)	0.18071 (12)	0.00846 (14)
B1	0	0	0.5	0.0045 (2)
B2	0.55115 (13)	0.55115 (13)	0.5	0.0061 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ho1	0.00785 (2)	0.00785 (2)	0.00718 (3)	0.003923 (11)	0	0
Bi1	0.00785 (2)	0.00785 (2)	0.00718 (3)	0.003923 (11)	0	0
Fe1	0.00428 (3)	0.00439 (3)	0.00574 (5)	0.002194 (17)	0.000038 (11)	0.00008 (2)
O1	0.00449 (11)	0.00449 (11)	0.0082 (2)	0.00038 (13)	−0.00147 (8)	0.00147 (8)
O2	0.00749 (17)	0.00749 (17)	0.0206 (6)	−0.0016 (2)	−0.0071 (2)	0.0071 (2)
O3	0.00593 (14)	0.0108 (2)	0.00932 (19)	0.00472 (14)	−0.00211 (12)	−0.00252 (14)
B1	0.0035 (3)	0.0035 (3)	0.0064 (5)	0.00176 (13)	0	0
B2	0.0046 (2)	0.0046 (2)	0.0082 (3)	0.0016 (3)	−0.00064 (16)	0.00064 (16)

Geometric parameters (Å, º)

Ho1—Bi1	0	Bi1—O3^iv	2.3451 (8)
Ho1—O3	2.3451 (10)	Bi1—O3^v	2.3451 (13)
Ho1—O3^i	2.3451 (8)	Fe1—O1	2.0183 (6)
Ho1—O3^ii	2.3451 (13)	Fe1—O1^vi	2.0183 (5)
Ho1—O3^iii	2.3451 (10)	Fe1—O2	2.0376 (8)
Ho1—O3^iv	2.3451 (8)	Fe1—O2^vi	2.0376 (13)
Ho1—O3^v	2.3451 (13)	Fe1—O3	1.9727 (8)
Bi1—O3	2.3451 (10)	Fe1—O3^vii	1.9727 (13)
Bi1—O3^i	2.3451 (8)	O1—B1	1.3768 (6)
Bi1—O3^ii	2.3451 (13)	O2—B2	1.3649 (12)
Bi1—O3^iii	2.3451 (10)	O3—B2^viii	1.3742 (18)
Bi1—Ho1—O3	0	O3^ii—Bi1—O3^v	141.60 (2)
Bi1—Ho1—O3^i	0	O3^iii—Bi1—O3^iv	89.44 (4)
Bi1—Ho1—O3^ii	0	O3^iii—Bi1—O3^v	89.44 (3)
Bi1—Ho1—O3^iii	0	O3^iv—Bi1—O3^v	89.44 (4)
Bi1—Ho1—O3^iv	0	O1—Fe1—O1^vi	167.49 (4)
Bi1—Ho1—O3^v	0	O1—Fe1—O2	76.61 (3)
O3—Ho1—O3^i	89.44 (4)	O1—Fe1—O2^vi	94.22 (3)
O3—Ho1—O3^ii	89.44 (3)	O1—Fe1—O3	92.19 (3)
O3—Ho1—O3^iii	122.76 (2)	O1—Fe1—O3^vii	95.67 (3)
O3—Ho1—O3^iv	141.60 (4)	O1^vi—Fe1—O2	94.22 (3)
O3—Ho1—O3^v	72.23 (4)	O1^vi—Fe1—O2^vi	76.61 (4)
O3^i—Ho1—O3^ii	89.44 (4)	O1^vi—Fe1—O3	95.67 (3)
O3^i—Ho1—O3^iii	141.60 (4)	O1^vi—Fe1—O3^vii	92.19 (4)
O3^i—Ho1—O3^iv	72.23 (3)	O2—Fe1—O2^vi	87.09 (4)
O3^i—Ho1—O3^v	122.76 (4)	O2—Fe1—O3	166.62 (4)
O3^ii—Ho1—O3^iii	72.23 (4)	O2—Fe1—O3^vii	86.46 (5)
O3^ii—Ho1—O3^iv	122.76 (4)	O2^vi—Fe1—O3	86.46 (4)
O3^ii—Ho1—O3^v	141.60 (2)	O2^vi—Fe1—O3^vii	166.62 (3)
O3^iii—Ho1—O3^iv	89.44 (4)	O3—Fe1—O3^vii	102.13 (5)
O3^iii—Ho1—O3^v	89.44 (3)	Fe1—O1—Fe1^ix	104.08 (3)
O3^iv—Ho1—O3^v	89.44 (4)	Fe1—O1—B1	127.96 (4)
Ho1—Bi1—O3	0	Fe1^ix—O1—B1	127.96 (4)
Ho1—Bi1—O3^i	0	Fe1—O2—Fe1^ix	102.70 (3)
Ho1—Bi1—O3^ii	0	Fe1—O2—B2	128.65 (6)
Ho1—Bi1—O3^iii	0	Fe1^ix—O2—B2	128.65 (6)
Ho1—Bi1—O3^iv	0	Ho1—O3—Bi1	0.0 (5)
Ho1—Bi1—O3^v	0	Ho1—O3—Fe1	121.01 (5)
O3—Bi1—O3^i	89.44 (4)	Ho1—O3—B2^viii	108.24 (5)
O3—Bi1—O3^ii	89.44 (3)	Bi1—O3—Fe1	121.01 (5)
O3—Bi1—O3^iii	122.76 (2)	Bi1—O3—B2^viii	108.24 (5)
O3—Bi1—O3^iv	141.60 (4)	Fe1—O3—B2^viii	130.56 (7)
O3—Bi1—O3^v	72.23 (4)	O1—B1—O1^i	120.00 (6)
O3^i—Bi1—O3^ii	89.44 (4)	O1—B1—O1^ii	120.00 (6)
O3^i—Bi1—O3^iii	141.60 (4)	O1^i—B1—O1^ii	120.00 (6)
O3^i—Bi1—O3^iv	72.23 (3)	O2—B2—O3^x	117.55 (12)
O3^i—Bi1—O3^v	122.76 (4)	O2—B2—O3^xi	117.55 (12)
O3^ii—Bi1—O3^iii	72.23 (4)	O3^x—B2—O3^xi	124.91 (8)
O3^ii—Bi1—O3^iv	122.76 (4)

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

(390)

Crystal data

B4Bi0.037Fe3Ho0.963O12	Dx = 4.412 Mg m^−3
Mr = 569.3	Mo Kα radiation, λ = 0.71073 Å
Trigonal, R32	Cell parameters from 19306 reflections
Hall symbol: R 3 2"	θ = 4.3–73.7°
a = 9.5364 (2) Å	µ = 15.64 mm^−1
c = 7.5677 (2) Å	T = 390 K
V = 596.02 (2) Å^3	Sphere, light-green
Z = 3	0.16 mm (radius)
F(000) = 785

Data collection

Xcalibur, EosS2 with high theta cut diffractometer	2726 independent reflections
Radiation source: X-ray tube	2726 reflections with I > 0σ(I)
Graphite monochromator	Rint = 0.093
Detector resolution: 8.0872 pixels mm^-1	θmax = 74.1°, θmin = 3.7°
ω scans	h = −25→25
Absorption correction: for a sphere (Dudka, 2007)	k = −25→23
Tmin = 0.012, Tmax = 0.036	l = −18→19
20162 measured reflections

Refinement

Refinement on F^2	Weighting scheme based on measured s.u.'s w = 1/σ^2(I)
R[F^2 > 2σ(F^2)] = 0.021	(Δ/σ)max = 0.050
wR(F^2) = 0.058	Δρmax = 1.52 e Å^−3
S = 1.03	Δρmin = −1.26 e Å^−3
2726 reflections	Extinction correction: Becker_Coppens G_I Isotropic (Becker & Coppens, 1974)
34 parameters	Extinction coefficient: 0.99 (7)
0 restraints	Absolute structure: 1239 of Friedel pairs used in the refinement
2 constraints	Absolute structure parameter: 0.495 (5)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ho1	0	0	0	0.007821 (19)	0.9627
Bi1	0	0	0	0.007821 (19)	0.0373
Fe1	0.215793 (19)	0.333333	0.333333	0.00493 (3)
O1	0.14444 (9)	0.14444 (9)	0.5	0.00664 (13)
O2	0.40788 (12)	0.40788 (12)	0.5	0.0147 (2)
O3	0.02475 (9)	0.21105 (11)	0.18085 (12)	0.00859 (15)
B1	0	0	0.5	0.0046 (2)
B2	0.55135 (14)	0.55135 (14)	0.5	0.0063 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ho1	0.00806 (2)	0.00806 (2)	0.00735 (3)	0.004029 (11)	0	0
Bi1	0.00806 (2)	0.00806 (2)	0.00735 (3)	0.004029 (11)	0	0
Fe1	0.00443 (3)	0.00449 (4)	0.00588 (5)	0.002246 (18)	0.000023 (12)	0.00005 (2)
O1	0.00459 (12)	0.00459 (12)	0.0082 (2)	0.00038 (14)	−0.00146 (9)	0.00146 (9)
O2	0.00782 (18)	0.00782 (18)	0.0208 (6)	−0.0017 (2)	−0.0073 (3)	0.0073 (3)
O3	0.00609 (15)	0.0107 (2)	0.0097 (2)	0.00469 (15)	−0.00225 (13)	−0.00248 (15)
B1	0.0037 (3)	0.0037 (3)	0.0065 (5)	0.00184 (13)	0	0
B2	0.0047 (2)	0.0047 (2)	0.0086 (3)	0.0018 (3)	−0.00077 (17)	0.00077 (17)

Geometric parameters (Å, º)

Ho1—Bi1	0	Bi1—O3^iv	2.3462 (9)
Ho1—O3	2.3462 (11)	Bi1—O3^v	2.3462 (13)
Ho1—O3^i	2.3462 (9)	Fe1—O1	2.0182 (6)
Ho1—O3^ii	2.3462 (13)	Fe1—O1^vi	2.0182 (6)
Ho1—O3^iii	2.3462 (11)	Fe1—O2	2.0371 (8)
Ho1—O3^iv	2.3462 (9)	Fe1—O2^vi	2.0371 (14)
Ho1—O3^v	2.3462 (13)	Fe1—O3	1.9714 (8)
Bi1—O3	2.3462 (11)	Fe1—O3^vii	1.9714 (13)
Bi1—O3^i	2.3462 (9)	O1—B1	1.3774 (6)
Bi1—O3^ii	2.3462 (13)	O2—B2	1.3682 (12)
Bi1—O3^iii	2.3462 (11)	O3—B2^viii	1.3743 (18)
Bi1—Ho1—O3	0	O3^ii—Bi1—O3^v	141.66 (3)
Bi1—Ho1—O3^i	0	O3^iii—Bi1—O3^iv	89.40 (4)
Bi1—Ho1—O3^ii	0	O3^iii—Bi1—O3^v	89.40 (4)
Bi1—Ho1—O3^iii	0	O3^iv—Bi1—O3^v	89.40 (4)
Bi1—Ho1—O3^iv	0	O1—Fe1—O1^vi	167.47 (5)
Bi1—Ho1—O3^v	0	O1—Fe1—O2	76.56 (3)
O3—Ho1—O3^i	89.40 (4)	O1—Fe1—O2^vi	94.26 (4)
O3—Ho1—O3^ii	89.40 (4)	O1—Fe1—O3	92.20 (3)
O3—Ho1—O3^iii	122.73 (3)	O1—Fe1—O3^vii	95.67 (4)
O3—Ho1—O3^iv	141.66 (4)	O1^vi—Fe1—O2	94.26 (3)
O3—Ho1—O3^v	72.29 (4)	O1^vi—Fe1—O2^vi	76.56 (4)
O3^i—Ho1—O3^ii	89.40 (4)	O1^vi—Fe1—O3	95.67 (3)
O3^i—Ho1—O3^iii	141.66 (4)	O1^vi—Fe1—O3^vii	92.20 (4)
O3^i—Ho1—O3^iv	72.29 (3)	O2—Fe1—O2^vi	87.10 (4)
O3^i—Ho1—O3^v	122.73 (4)	O2—Fe1—O3	166.59 (5)
O3^ii—Ho1—O3^iii	72.29 (4)	O2—Fe1—O3^vii	86.45 (5)
O3^ii—Ho1—O3^iv	122.73 (4)	O2^vi—Fe1—O3	86.45 (4)
O3^ii—Ho1—O3^v	141.66 (3)	O2^vi—Fe1—O3^vii	166.59 (4)
O3^iii—Ho1—O3^iv	89.40 (4)	O3—Fe1—O3^vii	102.13 (5)
O3^iii—Ho1—O3^v	89.40 (4)	Fe1—O1—Fe1^ix	104.11 (3)
O3^iv—Ho1—O3^v	89.40 (4)	Fe1—O1—B1	127.94 (4)
Ho1—Bi1—O3	0	Fe1^ix—O1—B1	127.94 (4)
Ho1—Bi1—O3^i	0	Fe1—O2—Fe1^ix	102.76 (4)
Ho1—Bi1—O3^ii	0	Fe1—O2—B2	128.62 (7)
Ho1—Bi1—O3^iii	0	Fe1^ix—O2—B2	128.62 (7)
Ho1—Bi1—O3^iv	0	Ho1—O3—Bi1	0.0 (5)
Ho1—Bi1—O3^v	0	Ho1—O3—Fe1	121.05 (5)
O3—Bi1—O3^i	89.40 (4)	Ho1—O3—B2^viii	108.22 (6)
O3—Bi1—O3^ii	89.40 (4)	Bi1—O3—Fe1	121.05 (5)
O3—Bi1—O3^iii	122.73 (3)	Bi1—O3—B2^viii	108.22 (6)
O3—Bi1—O3^iv	141.66 (4)	Fe1—O3—B2^viii	130.56 (8)
O3—Bi1—O3^v	72.29 (4)	O1—B1—O1^i	120.00 (6)
O3^i—Bi1—O3^ii	89.40 (4)	O1—B1—O1^ii	120.00 (6)
O3^i—Bi1—O3^iii	141.66 (4)	O1^i—B1—O1^ii	120.00 (6)
O3^i—Bi1—O3^iv	72.29 (3)	O2—B2—O3^x	117.50 (13)
O3^i—Bi1—O3^v	122.73 (4)	O2—B2—O3^xi	117.50 (13)
O3^ii—Bi1—O3^iii	72.29 (4)	O3^x—B2—O3^xi	125.00 (9)
O3^ii—Bi1—O3^iv	122.73 (4)

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

(500)

Crystal data

B4Bi0.037Fe3Ho0.963O12	Dx = 4.408 Mg m^−3
Mr = 569.3	Mo Kα radiation, λ = 0.71073 Å
Trigonal, R32	Cell parameters from 18802 reflections
Hall symbol: R 3 2"	θ = 4.3–73.9°
a = 9.5394 (2) Å	µ = 15.63 mm^−1
c = 7.5693 (1) Å	T = 500 K
V = 596.53 (2) Å^3	Sphere, light-green
Z = 3	0.16 mm (radius)
F(000) = 785

Data collection

Xcalibur, EosS2 with high theta cut diffractometer	2730 independent reflections
Radiation source: X-ray tube	2730 reflections with I > 0σ(I)
Graphite monochromator	Rint = 0.097
Detector resolution: 8.0872 pixels mm^-1	θmax = 74.3°, θmin = 3.7°
ω scans	h = −25→25
Absorption correction: for a sphere (Dudka, 2007)	k = −25→23
Tmin = 0.012, Tmax = 0.036	l = −18→19
19721 measured reflections

Refinement

Refinement on F^2	Weighting scheme based on measured s.u.'s w = 1/σ^2(I)
R[F^2 > 2σ(F^2)] = 0.023	(Δ/σ)max = 0.050
wR(F^2) = 0.064	Δρmax = 1.08 e Å^−3
S = 0.99	Δρmin = −1.47 e Å^−3
2730 reflections	Extinction correction: Becker_Coppens G_I Isotropic (Becker & Coppens, 1974)
34 parameters	Extinction coefficient: 0.78 (7)
0 restraints	Absolute structure: 1241 of Friedel pairs used in the refinement
2 constraints	Absolute structure parameter: 0.495 (5)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ho1	0	0	0	0.00987 (2)	0.9627
Bi1	0	0	0	0.00987 (2)	0.0373
Fe1	0.21578 (2)	0.333333	0.333333	0.00610 (3)
O1	0.14438 (10)	0.14438 (10)	0.5	0.00837 (15)
O2	0.40794 (13)	0.40794 (13)	0.5	0.0175 (3)
O3	0.02459 (10)	0.21101 (13)	0.18111 (14)	0.01042 (17)
B1	0	0	0.5	0.0054 (3)
B2	0.55151 (14)	0.55151 (14)	0.5	0.0072 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ho1	0.01014 (3)	0.01014 (3)	0.00934 (4)	0.005069 (14)	0	0
Bi1	0.01014 (3)	0.01014 (3)	0.00934 (4)	0.005069 (14)	0	0
Fe1	0.00560 (3)	0.00569 (4)	0.00703 (5)	0.002846 (19)	−0.000003 (13)	−0.00001 (3)
O1	0.00550 (13)	0.00550 (13)	0.0109 (3)	0.00033 (15)	−0.00171 (10)	0.00171 (10)
O2	0.0091 (2)	0.0091 (2)	0.0255 (8)	−0.0021 (3)	−0.0085 (3)	0.0085 (3)
O3	0.00735 (17)	0.0135 (2)	0.0112 (2)	0.00580 (17)	−0.00260 (15)	−0.00291 (18)
B1	0.0043 (3)	0.0043 (3)	0.0077 (5)	0.00213 (14)	0	0
B2	0.0056 (2)	0.0056 (2)	0.0100 (3)	0.0024 (4)	−0.00075 (19)	0.00075 (19)

Geometric parameters (Å, º)

Ho1—Bi1	0	Bi1—O3^iv	2.3481 (10)
Ho1—O3	2.3481 (12)	Bi1—O3^v	2.3481 (15)
Ho1—O3^i	2.3481 (10)	Fe1—O1	2.0191 (7)
Ho1—O3^ii	2.3481 (15)	Fe1—O1^vi	2.0191 (6)
Ho1—O3^iii	2.3481 (12)	Fe1—O2	2.0381 (9)
Ho1—O3^iv	2.3481 (10)	Fe1—O2^vi	2.0381 (14)
Ho1—O3^v	2.3481 (15)	Fe1—O3	1.9717 (9)
Bi1—O3	2.3481 (12)	Fe1—O3^vii	1.9717 (15)
Bi1—O3^i	2.3481 (10)	O1—B1	1.3773 (6)
Bi1—O3^ii	2.3481 (15)	O2—B2	1.3695 (13)
Bi1—O3^iii	2.3481 (12)	O3—B2^viii	1.3730 (19)
Bi1—Ho1—O3	0	O3^ii—Bi1—O3^v	141.62 (3)
Bi1—Ho1—O3^i	0	O3^iii—Bi1—O3^iv	89.36 (4)
Bi1—Ho1—O3^ii	0	O3^iii—Bi1—O3^v	89.36 (4)
Bi1—Ho1—O3^iii	0	O3^iv—Bi1—O3^v	89.36 (4)
Bi1—Ho1—O3^iv	0	O1—Fe1—O1^vi	167.48 (5)
Bi1—Ho1—O3^v	0	O1—Fe1—O2	76.59 (3)
O3—Ho1—O3^i	89.36 (4)	O1—Fe1—O2^vi	94.24 (4)
O3—Ho1—O3^ii	89.36 (4)	O1—Fe1—O3	92.15 (4)
O3—Ho1—O3^iii	122.82 (3)	O1—Fe1—O3^vii	95.72 (4)
O3—Ho1—O3^iv	141.62 (5)	O1^vi—Fe1—O2	94.24 (3)
O3—Ho1—O3^v	72.34 (4)	O1^vi—Fe1—O2^vi	76.59 (4)
O3^i—Ho1—O3^ii	89.36 (4)	O1^vi—Fe1—O3	95.72 (4)
O3^i—Ho1—O3^iii	141.62 (5)	O1^vi—Fe1—O3^vii	92.15 (4)
O3^i—Ho1—O3^iv	72.34 (4)	O2—Fe1—O2^vi	87.09 (5)
O3^i—Ho1—O3^v	122.82 (5)	O2—Fe1—O3	166.59 (5)
O3^ii—Ho1—O3^iii	72.34 (4)	O2—Fe1—O3^vii	86.52 (5)
O3^ii—Ho1—O3^iv	122.82 (5)	O2^vi—Fe1—O3	86.52 (5)
O3^ii—Ho1—O3^v	141.62 (3)	O2^vi—Fe1—O3^vii	166.59 (4)
O3^iii—Ho1—O3^iv	89.36 (4)	O3—Fe1—O3^vii	102.03 (5)
O3^iii—Ho1—O3^v	89.36 (4)	Fe1—O1—Fe1^ix	104.09 (3)
O3^iv—Ho1—O3^v	89.36 (4)	Fe1—O1—B1	127.95 (4)
Ho1—Bi1—O3	0	Fe1^ix—O1—B1	127.95 (4)
Ho1—Bi1—O3^i	0	Fe1—O2—Fe1^ix	102.73 (4)
Ho1—Bi1—O3^ii	0	Fe1—O2—B2	128.63 (7)
Ho1—Bi1—O3^iii	0	Fe1^ix—O2—B2	128.63 (7)
Ho1—Bi1—O3^iv	0	Ho1—O3—Bi1	0.0 (5)
Ho1—Bi1—O3^v	0	Ho1—O3—Fe1	120.99 (6)
O3—Bi1—O3^i	89.36 (4)	Ho1—O3—B2^viii	108.23 (6)
O3—Bi1—O3^ii	89.36 (4)	Bi1—O3—Fe1	120.99 (6)
O3—Bi1—O3^iii	122.82 (3)	Bi1—O3—B2^viii	108.23 (6)
O3—Bi1—O3^iv	141.62 (5)	Fe1—O3—B2^viii	130.61 (9)
O3—Bi1—O3^v	72.34 (4)	O1—B1—O1^i	120.00 (7)
O3^i—Bi1—O3^ii	89.36 (4)	O1—B1—O1^ii	120.00 (7)
O3^i—Bi1—O3^iii	141.62 (5)	O1^i—B1—O1^ii	120.00 (7)
O3^i—Bi1—O3^iv	72.34 (4)	O2—B2—O3^x	117.43 (13)
O3^i—Bi1—O3^v	122.82 (5)	O2—B2—O3^xi	117.43 (13)
O3^ii—Bi1—O3^iii	72.34 (4)	O3^x—B2—O3^xi	125.15 (9)
O3^ii—Bi1—O3^iv	122.82 (5)

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