The low-temperature crystal structure of the multiferroic melilite Ca₂CoSi₂O₇

In the antiferromagnetic ground state, below T_N ≃ 5.7 K, Ca₂CoSi₂O₇ exhibits strong magnetoelectric coupling. For a symmetry-consistent theoretical description of this multiferroic phase, precise knowledge of its crystal structure is a prerequisite. Here we report the results of single-crystal neutron diffraction on Ca₂CoSi₂O₇ at temperatures between 10 and 250 K. The low-temperature structure at 10 K was refined assuming twinning in the orthorhombic space group P2₁2₁2 with a 3 × 3 × 1 supercell [a = 23.52 (1), b = 23.52 (1), c = 5.030 (3) Å] compared with the high-temperature normal state [tetragonal space group , a = b ≃ 7.86, c ≃ 5.03 Å]. The precise structural parameters of Ca₂CoSi₂O₇ at 10 K are presented and compared with the literature X-ray diffraction results at 130 and 170 K (low-temperature commensurate phase), as well as at ∼ 500 K (high-temperature normal phase).

S1. Conclusions

Computing details

Figures

(I)

Crystal data

Ca2CoO7Si2	Z = 18
Mr = 307.26	F(000) = 2718
Orthorhombic, P21212	Dx = 3.304 Mg m^−3
Hall symbol: P 2 2ab	Neutron radiation, λ = 1.1695 Å
a = 23.52 (1) Å	µ = 0.02 mm^−1
b = 23.52 (1) Å	T = 10 K
c = 5.03 (1) Å	Cylinder, blue
V = 2782.5 Å^3	4 × 2 (radius) mm

Data collection

Four-circle diffractometer	θmax = 64.9°, θmin = 4.0°
3127 measured reflections	h = −20→36
2006 independent reflections	k = −30→36
1883 reflections with I > 3σ(I)	l = −7→7
Rint = 0.019

Refinement

Refinement on F^2	0 restraints
R[F^2 > 2σ(F^2)] = 0.043	51 constraints
wR(F^2) = 0.099	Weighting scheme based on measured s.u.'s w = 1/(σ^2(I) + 0.0004I^2)
S = 3.17	(Δ/σ)max = 0.0004
1883 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
168 parameters	Extinction coefficient: 360 (30)

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

	x	y	z	Uiso*/Ueq
Ca1	0.1086 (4)	0.0527 (4)	0.503 (3)	0.0075 (3)*
Ca2	0.1145 (4)	0.3923 (4)	0.490 (2)	0.0075 (3)*
Ca3	0.0554 (4)	0.2245 (5)	0.499 (3)	0.0075 (3)*
Ca4	0.2746 (5)	0.1114 (4)	0.515 (2)	0.0075 (3)*
Ca5	0.2677 (4)	0.4511 (4)	0.475 (2)	0.0075 (3)*
Ca6	0.2153 (4)	0.2664 (3)	0.519 (2)	0.0075 (3)*
Ca7	0.4409 (4)	0.0525 (4)	0.517 (2)	0.0075 (3)*
Ca8	0.4505 (4)	0.3973 (4)	0.516 (2)	0.0075 (3)*
Ca9	0.4028 (3)	0.2115 (4)	0.492 (2)	0.0075 (3)*
Co1	0	0	0.014 (5)	0.0033 (7)*
Co2	0.0057 (7)	0.3369 (7)	0.017 (3)	0.0033 (7)*
Co3	0.1634 (9)	0.1612 (6)	0.001 (5)	0.0033 (7)*
Co4	0.3347 (7)	0.0019 (8)	0.022 (3)	0.0033 (7)*
Co5	0.3332 (9)	0.3299 (8)	0.009 (5)	0.0033 (7)*
Si1	0.0418 (5)	0.1214 (5)	−0.066 (3)	0.0056 (3)*
Si2	0.0506 (5)	0.4568 (4)	−0.080 (2)	0.0056 (3)*
Si3	0.1241 (5)	0.2862 (4)	0.081 (2)	0.0056 (3)*
Si4	0.2124 (5)	0.0411 (5)	0.071 (3)	0.0056 (3)*
Si5	0.2160 (4)	0.3812 (5)	0.032 (2)	0.0056 (3)*
Si6	0.2827 (4)	0.2081 (4)	−0.037 (2)	0.0056 (3)*
Si7	0.3827 (5)	0.1234 (5)	−0.056 (3)	0.0056 (3)*
Si8	0.3830 (4)	0.4549 (5)	−0.065 (3)	0.0056 (3)*
Si9	0.4520 (4)	0.2811 (5)	0.056 (3)	0.0056 (3)*
O1	−0.0083 (3)	0.1647 (3)	0.822 (2)	0.00798 (16)*
O2	0.1740 (3)	−0.0146 (3)	0.1742 (19)	0.00798 (16)*
O3	0.1797 (3)	0.3265 (3)	0.1724 (18)	0.00798 (16)*
O4	0.3401 (3)	0.1758 (3)	0.836 (2)	0.00798 (16)*
O5	0.5	0	0.205 (2)	0.00798 (16)*
O6	0.0423 (3)	0.1183 (3)	0.245 (2)	0.00798 (16)*
O7	0.0505 (3)	0.4582 (3)	0.2354 (18)	0.00798 (16)*
O8	0.1247 (3)	0.2822 (3)	0.751 (2)	0.00798 (16)*
O9	0.2165 (3)	0.0436 (3)	0.754 (2)	0.00798 (16)*
O10	0.2080 (3)	0.3847 (3)	0.722 (2)	0.00798 (16)*
O11	0.2776 (3)	0.2032 (3)	0.2738 (16)	0.00798 (16)*
O12	0.3863 (3)	0.1209 (3)	0.258 (2)	0.00798 (16)*
O13	0.3862 (3)	0.4584 (3)	0.263 (2)	0.00798 (16)*
O14	0.4624 (3)	0.2760 (3)	0.7443 (19)	0.00798 (16)*
O15	0.0250 (3)	0.0620 (3)	0.771 (2)	0.00798 (16)*
O16	0.0986 (3)	0.1435 (3)	0.773 (2)	0.00798 (16)*
O17	0.0342 (2)	0.3955 (3)	0.7770 (18)	0.00798 (16)*
O18	0.1039 (3)	0.4798 (3)	0.7535 (17)	0.00798 (16)*
O19	0.1388 (3)	0.2266 (3)	0.2249 (19)	0.00798 (16)*
O20	0.0711 (3)	0.3125 (3)	0.2239 (19)	0.00798 (16)*
O21	0.1826 (3)	0.0953 (3)	0.2239 (19)	0.00798 (16)*
O22	0.2713 (3)	0.0301 (3)	0.230 (2)	0.00798 (16)*
O23	0.1864 (3)	0.4357 (3)	0.2064 (19)	0.00798 (16)*
O24	0.2779 (3)	0.3794 (3)	0.1706 (17)	0.00798 (16)*
O25	0.2870 (3)	0.2728 (3)	0.8338 (16)	0.00798 (16)*
O26	0.2301 (3)	0.1799 (3)	0.7953 (18)	0.00798 (16)*
O27	0.3562 (3)	0.0674 (3)	0.7915 (19)	0.00798 (16)*
O28	0.4403 (3)	0.1371 (3)	0.7877 (19)	0.00798 (16)*
O29	0.3809 (3)	0.3879 (3)	0.8310 (17)	0.00798 (16)*
O30	0.4350 (3)	0.4821 (3)	0.782 (2)	0.00798 (16)*
O31	0.4841 (3)	0.2276 (3)	0.2185 (18)	0.00798 (16)*
O32	0.3918 (3)	0.2831 (3)	0.1809 (17)	0.00798 (16)*

Geometric parameters (Å, º)

Ca1—Ca5^i	3.766 (14)	Ca9—Si7^iii	3.112 (15)
Ca1—Ca8^i	3.910 (14)	Ca9—Si9	2.969 (16)
Ca1—Ca8^ii	3.902 (14)	Ca9—O4	2.421 (13)
Ca1—Si1^iii	3.124 (18)	Ca9—O14	2.424 (12)
Ca1—Si4	3.279 (17)	Ca9—O31	2.385 (12)
Ca1—Si8^iv	3.190 (17)	Ca9—O32	2.312 (12)
Ca1—O15	2.391 (14)	Co1—O15^ix	1.991 (18)
Ca1—O30^i	2.420 (14)	Co1—O15^x	1.991 (18)
Ca2—Ca5	3.861 (13)	Co1—O30^i	1.890 (16)
Ca2—Ca6	3.795 (13)	Co1—O30^ii	1.890 (16)
Ca2—Ca7^v	3.987 (13)	Co2—O17^ix	1.950 (18)
Ca2—Si2^iii	3.036 (15)	Co2—O20	1.944 (18)
Ca2—Si3	3.241 (15)	Co2—O28^ii	1.925 (18)
Ca2—O17	2.376 (12)	Co2—O31^xi	1.988 (18)
Ca2—O23	2.437 (13)	Co3—O16^ix	1.95 (2)
Ca3—Ca6	3.888 (14)	Co3—O19	1.99 (2)
Ca3—Ca8^ii	3.782 (14)	Co3—O21	1.97 (2)
Ca3—Ca9^ii	3.893 (13)	Co3—O26^ix	1.93 (2)
Ca3—Si1^iii	3.280 (18)	Co4—O18^i	1.904 (18)
Ca3—Si3	3.020 (17)	Co4—O22	1.937 (18)
Ca3—Si9^ii	3.306 (18)	Co4—O23^iv	1.997 (19)
Ca3—O19	2.397 (14)	Co4—O27^ix	1.994 (19)
Ca4—Ca5^i	3.900 (14)	Co5—O24	1.93 (2)
Ca4—Ca6	3.904 (13)	Co5—O25^ix	1.94 (2)
Ca4—Ca9	3.826 (13)	Co5—O29^ix	1.98 (2)
Ca4—Si4	3.140 (17)	Co5—O32	1.97 (2)
Ca4—Si6^iii	3.205 (15)	Si1—O1^ix	1.655 (14)
Ca4—O9	2.420 (14)	Si1—O6	1.57 (2)
Ca4—O22	2.391 (14)	Si1—O15^ix	1.667 (15)
Ca4—O26	2.381 (13)	Si1—O16^ix	1.646 (15)
Ca5—Si4^v	3.149 (17)	Si2—O7	1.587 (15)
Ca5—Si5	3.024 (16)	Si2—O17^ix	1.654 (13)
Ca5—O2^v	2.375 (14)	Si2—O18^ix	1.602 (13)
Ca5—O10	2.441 (13)	Si3—O8^ix	1.663 (17)
Ca5—O23	2.369 (13)	Si3—O19	1.614 (13)
Ca5—O24	2.288 (13)	Si3—O20	1.564 (14)
Ca6—Si3	3.109 (16)	Si4—O2	1.674 (13)
Ca6—Si6^iii	3.059 (14)	Si4—O9^ix	1.597 (18)
Ca6—O3	2.395 (13)	Si4—O21	1.645 (14)
Ca6—O11	2.425 (12)	Si4—O22	1.620 (14)
Ca6—O25	2.317 (12)	Si5—O10^ix	1.570 (16)
Ca7—Ca7^vi	3.717 (14)	Si5—O24	1.615 (13)
Ca7—Ca9	3.848 (12)	Si6—O11	1.572 (14)
Ca7—Si2^iv	3.150 (15)	Si6—O25^ix	1.657 (12)
Ca7—Si7^iii	3.045 (16)	Si6—O26^ix	1.637 (12)
Ca7—O5	2.430 (12)	Si7—O12	1.582 (17)
Ca7—O12	2.435 (13)	Si7—O27^ix	1.646 (14)
Ca7—O18^i	2.425 (12)	Si7—O28^ix	1.600 (14)
Ca7—O28	2.411 (12)	Si8—O2^xii	1.615 (13)
Ca8—Si1^vii	3.151 (18)	Si8—O13	1.654 (18)
Ca8—Si8^iii	2.961 (17)	Si8—O29^ix	1.658 (13)
Ca8—O1^viii	2.441 (14)	Si8—O30^ix	1.579 (14)
Ca8—O13	2.444 (13)	Si9—O14^ix	1.592 (18)
Ca8—O29	2.287 (13)	Si9—O32	1.549 (13)
Ca8—O30	2.426 (13)
Ca5^i—Ca1—Ca8^i	71.5 (3)	Ca3^viii—Ca9—Ca7	99.2 (3)
Ca5^i—Ca1—Ca8^ii	158.2 (4)	Ca3^viii—Ca9—Si7^iii	112.9 (4)
Ca5^i—Ca1—Si1^iii	134.1 (5)	Ca3^viii—Ca9—Si9	55.6 (3)
Ca5^i—Ca1—Si4	52.5 (3)	Ca3^viii—Ca9—O4	133.4 (5)
Ca5^i—Ca1—Si8^iv	61.0 (3)	Ca3^viii—Ca9—O14	38.6 (3)
Ca5^i—Ca1—O15	132.6 (5)	Ca3^viii—Ca9—O31	37.5 (3)
Ca5^i—Ca1—O30^i	84.8 (4)	Ca3^viii—Ca9—O32	80.2 (3)
Ca8^i—Ca1—Ca8^ii	86.7 (3)	Ca4—Ca9—Ca7	65.5 (2)
Ca8^i—Ca1—Si1^iii	108.8 (4)	Ca4—Ca9—Si7^iii	56.5 (3)
Ca8^i—Ca1—Si4	99.8 (4)	Ca4—Ca9—Si9	132.0 (4)
Ca8^i—Ca1—Si8^iv	48.0 (3)	Ca4—Ca9—O4	44.4 (3)
Ca8^i—Ca1—O15	78.9 (3)	Ca4—Ca9—O14	145.6 (5)
Ca8^i—Ca1—O30^i	36.3 (3)	Ca4—Ca9—O31	138.3 (4)
Ca8^ii—Ca1—Si1^iii	51.9 (3)	Ca4—Ca9—O32	112.4 (4)
Ca8^ii—Ca1—Si4	135.9 (5)	Ca7—Ca9—Si7^iii	50.5 (3)
Ca8^ii—Ca1—Si8^iv	105.0 (4)	Ca7—Ca9—Si9	117.9 (4)
Ca8^ii—Ca1—O15	37.2 (3)	Ca7—Ca9—O4	77.4 (3)
Ca8^ii—Ca1—O30^i	77.8 (3)	Ca7—Ca9—O14	117.1 (4)
Si1^iii—Ca1—Si4	151.1 (4)	Ca7—Ca9—O31	89.2 (3)
Si1^iii—Ca1—Si8^iv	151.9 (5)	Ca7—Ca9—O32	139.1 (4)
Si1^iii—Ca1—O15	31.8 (3)	Si7^iii—Ca9—Si9	164.8 (4)
Si1^iii—Ca1—O30^i	123.5 (5)	Si7^iii—Ca9—O4	32.4 (3)
Si4—Ca1—Si8^iv	55.7 (3)	Si7^iii—Ca9—O14	97.0 (4)
Si4—Ca1—O15	172.7 (6)	Si7^iii—Ca9—O31	130.4 (4)
Si4—Ca1—O30^i	82.3 (4)	Si7^iii—Ca9—O32	164.2 (4)
Si8^iv—Ca1—O15	120.3 (5)	Si9—Ca9—O4	162.8 (4)
Si8^iv—Ca1—O30^i	28.7 (3)	Si9—Ca9—O14	79.3 (4)
O15—Ca1—O30^i	92.7 (4)	Si9—Ca9—O31	34.4 (3)
Ca5—Ca2—Ca6	72.4 (3)	Si9—Ca9—O32	31.1 (3)
Ca5—Ca2—Ca7^v	88.1 (3)	O4—Ca9—O14	101.3 (5)
Ca5—Ca2—Si2^iii	107.3 (4)	O4—Ca9—O31	162.6 (5)
Ca5—Ca2—Si3	101.4 (4)	O4—Ca9—O32	131.9 (4)
Ca5—Ca2—O17	137.9 (5)	O14—Ca9—O31	74.8 (4)
Ca5—Ca2—O23	35.9 (3)	O14—Ca9—O32	87.9 (4)
Ca6—Ca2—Ca7^v	160.3 (3)	O31—Ca9—O32	65.4 (3)
Ca6—Ca2—Si2^iii	132.2 (4)	O15^ix—Co1—O15^x	104.3 (12)
Ca6—Ca2—Si3	51.7 (3)	O15^ix—Co1—O30^i	104.9 (3)
Ca6—Ca2—O17	119.9 (4)	O15^ix—Co1—O30^ii	114.2 (3)
Ca6—Ca2—O23	85.2 (3)	O15^x—Co1—O30^i	114.2 (3)
Ca7^v—Ca2—Si2^iii	51.1 (3)	O15^x—Co1—O30^ii	104.9 (3)
Ca7^v—Ca2—Si3	138.1 (4)	O30^i—Co1—O30^ii	114.1 (14)
Ca7^v—Ca2—O17	73.5 (3)	O17^ix—Co2—O20	105.6 (8)
Ca7^v—Ca2—O23	80.0 (3)	O17^ix—Co2—O28^ii	111.4 (8)
Si2^iii—Ca2—Si3	150.5 (4)	O17^ix—Co2—O31^xi	105.1 (8)
Si2^iii—Ca2—O17	32.8 (3)	O20—Co2—O28^ii	116.9 (9)
Si2^iii—Ca2—O23	123.4 (4)	O20—Co2—O31^xi	107.2 (8)
Si3—Ca2—O17	117.7 (4)	O28^ii—Co2—O31^xi	110.0 (9)
Si3—Ca2—O23	84.4 (4)	O16^ix—Co3—O19	105.7 (9)
O17—Ca2—O23	153.2 (5)	O16^ix—Co3—O21	110.3 (8)
Ca6—Ca3—Ca8^ii	145.5 (4)	O16^ix—Co3—O26^ix	111.7 (13)
Ca6—Ca3—Ca9^ii	142.5 (3)	O19—Co3—O21	110.6 (12)
Ca6—Ca3—Si1^iii	105.3 (4)	O19—Co3—O26^ix	111.2 (8)
Ca6—Ca3—Si3	51.6 (3)	O21—Co3—O26^ix	107.3 (10)
Ca6—Ca3—Si9^ii	134.7 (5)	O18^i—Co4—O22	111.0 (8)
Ca6—Ca3—O19	38.6 (3)	O18^i—Co4—O23^iv	108.4 (9)
Ca8^ii—Ca3—Ca9^ii	72.0 (3)	O18^i—Co4—O27^ix	111.3 (9)
Ca8^ii—Ca3—Si1^iii	52.4 (3)	O22—Co4—O23^iv	112.7 (9)
Ca8^ii—Ca3—Si3	134.3 (5)	O22—Co4—O27^ix	104.1 (9)
Ca8^ii—Ca3—Si9^ii	60.2 (3)	O23^iv—Co4—O27^ix	109.3 (8)
Ca8^ii—Ca3—O19	122.6 (5)	O24—Co5—O25^ix	103.4 (10)
Ca9^ii—Ca3—Si1^iii	100.8 (4)	O24—Co5—O29^ix	99.1 (9)
Ca9^ii—Ca3—Si3	108.4 (4)	O24—Co5—O32	128.8 (13)
Ca9^ii—Ca3—Si9^ii	47.9 (3)	O25^ix—Co5—O29^ix	126.2 (13)
Ca9^ii—Ca3—O19	138.9 (5)	O25^ix—Co5—O32	101.8 (9)
Si1^iii—Ca3—Si3	150.5 (5)	O29^ix—Co5—O32	100.8 (10)
Si1^iii—Ca3—Si9^ii	56.5 (4)	Ca1^ix—Si1—Ca3^ix	82.6 (5)
Si1^iii—Ca3—O19	118.6 (5)	Ca1^ix—Si1—Ca8^xi	76.9 (4)
Si3—Ca3—Si9^ii	151.9 (5)	Ca1^ix—Si1—O1^ix	116.2 (8)
Si3—Ca3—O19	32.1 (3)	Ca1^ix—Si1—O6	131.6 (7)
Si9^ii—Ca3—O19	172.4 (6)	Ca1^ix—Si1—O15^ix	49.1 (5)
Ca5^i—Ca4—Ca6	144.2 (3)	Ca1^ix—Si1—O16^ix	54.2 (5)
Ca5^i—Ca4—Ca9	142.8 (3)	Ca3^ix—Si1—Ca8^xi	72.0 (4)
Ca5^i—Ca4—Si4	51.8 (3)	Ca3^ix—Si1—O1^ix	52.4 (5)
Ca5^i—Ca4—Si6^iii	133.8 (4)	Ca3^ix—Si1—O6	134.4 (7)
Ca5^i—Ca4—O9	38.0 (3)	Ca3^ix—Si1—O15^ix	108.4 (8)
Ca5^i—Ca4—O22	39.3 (3)	Ca3^ix—Si1—O16^ix	50.2 (5)
Ca5^i—Ca4—O26	122.3 (4)	Ca8^xi—Si1—O1^ix	50.0 (5)
Ca6—Ca4—Ca9	73.0 (2)	Ca8^xi—Si1—O6	135.7 (7)
Ca6—Ca4—Si4	109.2 (4)	Ca8^xi—Si1—O15^ix	50.9 (5)
Ca6—Ca4—Si6^iii	49.8 (3)	Ca8^xi—Si1—O16^ix	104.2 (8)
Ca6—Ca4—O9	114.2 (4)	O1^ix—Si1—O6	111.8 (9)
Ca6—Ca4—O22	137.5 (5)	O1^ix—Si1—O15^ix	100.4 (8)
Ca6—Ca4—O26	37.6 (3)	O1^ix—Si1—O16^ix	102.6 (8)
Ca9—Ca4—Si4	132.0 (5)	O6—Si1—O15^ix	117.0 (9)
Ca9—Ca4—Si6^iii	62.5 (3)	O6—Si1—O16^ix	120.0 (9)
Ca9—Ca4—O9	150.0 (5)	O15^ix—Si1—O16^ix	102.5 (9)
Ca9—Ca4—O22	119.9 (4)	Ca2^ix—Si2—Ca7^xii	80.2 (4)
Ca9—Ca4—O26	87.0 (4)	Ca2^ix—Si2—O7	136.2 (6)
Si4—Ca4—Si6^iii	154.2 (5)	Ca2^ix—Si2—O17^ix	51.1 (4)
Si4—Ca4—O9	75.1 (4)	Ca2^ix—Si2—O18^ix	53.9 (4)
Si4—Ca4—O22	30.4 (3)	Ca7^xii—Si2—O7	132.9 (6)
Si4—Ca4—O26	124.8 (5)	Ca7^xii—Si2—O17^ix	109.6 (6)
Si6^iii—Ca4—O9	98.8 (5)	Ca7^xii—Si2—O18^ix	49.1 (4)
Si6^iii—Ca4—O22	172.1 (6)	O7—Si2—O17^ix	116.9 (8)
Si6^iii—Ca4—O26	29.7 (3)	O7—Si2—O18^ix	121.0 (8)
O9—Ca4—O22	75.7 (4)	O17^ix—Si2—O18^ix	104.5 (7)
O9—Ca4—O26	84.5 (5)	Ca2—Si3—Ca3	83.8 (4)
O22—Ca4—O26	151.7 (5)	Ca2—Si3—Ca6	73.4 (4)
Ca1^v—Ca5—Ca2	161.4 (3)	Ca2—Si3—O8^ix	132.6 (6)
Ca1^v—Ca5—Ca4^v	65.4 (3)	Ca2—Si3—O19	113.6 (7)
Ca1^v—Ca5—Si4^v	55.8 (3)	Ca2—Si3—O20	49.5 (4)
Ca1^v—Ca5—Si5	132.6 (5)	Ca3—Si3—Ca6	78.7 (4)
Ca1^v—Ca5—O2^v	46.9 (3)	Ca3—Si3—O8^ix	132.2 (7)
Ca1^v—Ca5—O10	146.7 (5)	Ca3—Si3—O19	52.2 (5)
Ca1^v—Ca5—O23	137.5 (5)	Ca3—Si3—O20	56.3 (5)
Ca1^v—Ca5—O24	114.0 (4)	Ca6—Si3—O8^ix	133.8 (7)
Ca2—Ca5—Ca4^v	96.2 (3)	Ca6—Si3—O19	53.5 (5)
Ca2—Ca5—Si4^v	111.4 (4)	Ca6—Si3—O20	106.5 (7)
Ca2—Ca5—Si5	56.3 (3)	O8^ix—Si3—O19	113.3 (8)
Ca2—Ca5—O2^v	130.2 (5)	O8^ix—Si3—O20	119.1 (8)
Ca2—Ca5—O10	39.0 (3)	O19—Si3—O20	108.0 (8)
Ca2—Ca5—O23	37.1 (3)	Ca1—Si4—Ca4	80.3 (4)
Ca2—Ca5—O24	81.2 (3)	Ca1—Si4—Ca5^i	71.7 (4)
Ca4^v—Ca5—Si4^v	51.6 (3)	Ca1—Si4—O2	57.2 (5)
Ca4^v—Ca5—Si5	115.6 (4)	Ca1—Si4—O9^ix	134.7 (6)
Ca4^v—Ca5—O2^v	79.0 (3)	Ca1—Si4—O21	46.3 (4)
Ca4^v—Ca5—O10	117.7 (4)	Ca1—Si4—O22	108.9 (7)
Ca4^v—Ca5—O23	87.0 (4)	Ca4—Si4—Ca5^i	76.7 (4)
Ca4^v—Ca5—O24	138.4 (5)	Ca4—Si4—O2	116.3 (8)
Si4^v—Ca5—Si5	163.6 (4)	Ca4—Si4—O9^ix	131.4 (6)
Si4^v—Ca5—O2^v	31.5 (3)	Ca4—Si4—O21	57.2 (5)
Si4^v—Ca5—O10	98.4 (5)	Ca4—Si4—O22	48.3 (5)
Si4^v—Ca5—O23	129.4 (4)	Ca5^i—Si4—O2	47.9 (5)
Si4^v—Ca5—O24	164.7 (5)	Ca5^i—Si4—O9^ix	137.6 (7)
Si5—Ca5—O2^v	164.6 (5)	Ca5^i—Si4—O21	104.2 (7)
Si5—Ca5—O10	78.2 (4)	Ca5^i—Si4—O22	53.8 (5)
Si5—Ca5—O23	34.2 (3)	O2—Si4—O9^ix	111.7 (8)
Si5—Ca5—O24	31.7 (3)	O2—Si4—O21	103.5 (8)
O2^v—Ca5—O10	99.9 (5)	O2—Si4—O22	100.6 (8)
O2^v—Ca5—O23	160.2 (5)	O9^ix—Si4—O21	117.6 (8)
O2^v—Ca5—O24	133.3 (5)	O9^ix—Si4—O22	116.4 (8)
O10—Ca5—O23	74.2 (4)	O21—Si4—O22	104.9 (8)
O10—Ca5—O24	85.9 (4)	Ca5—Si5—O10^ix	138.6 (7)
O23—Ca5—O24	65.9 (4)	Ca5—Si5—O24	48.2 (4)
Ca2—Ca6—Ca3	66.0 (3)	O10^ix—Si5—O24	122.6 (8)
Ca2—Ca6—Ca4	162.1 (3)	Ca4^ix—Si6—Ca6^ix	77.1 (4)
Ca2—Ca6—Si3	54.9 (3)	Ca4^ix—Si6—O11	129.9 (6)
Ca2—Ca6—Si6^iii	134.5 (4)	Ca4^ix—Si6—O25^ix	112.4 (6)
Ca2—Ca6—O3	45.1 (3)	Ca4^ix—Si6—O26^ix	46.1 (4)
Ca2—Ca6—O11	146.7 (5)	Ca6^ix—Si6—O11	135.9 (6)
Ca2—Ca6—O25	115.5 (4)	Ca6^ix—Si6—O25^ix	48.4 (4)
Ca3—Ca6—Ca4	96.3 (3)	Ca6^ix—Si6—O26^ix	54.3 (4)
Ca3—Ca6—Si3	49.6 (3)	O11—Si6—O25^ix	117.5 (7)
Ca3—Ca6—Si6^iii	114.0 (4)	O11—Si6—O26^ix	115.1 (7)
Ca3—Ca6—O3	78.1 (3)	O25^ix—Si6—O26^ix	102.6 (7)
Ca3—Ca6—O11	114.6 (4)	Ca7^ix—Si7—Ca9^ix	77.4 (4)
Ca3—Ca6—O25	137.7 (5)	Ca7^ix—Si7—O12	131.3 (6)
Ca4—Ca6—Si3	112.5 (4)	Ca7^ix—Si7—O27^ix	53.4 (5)
Ca4—Ca6—Si6^iii	53.1 (3)	Ca7^ix—Si7—O28^ix	51.8 (5)
Ca4—Ca6—O3	132.2 (4)	Ca9^ix—Si7—O12	138.2 (6)
Ca4—Ca6—O11	37.7 (3)	Ca9^ix—Si7—O27^ix	104.4 (7)
Ca4—Ca6—O25	78.7 (3)	Ca9^ix—Si7—O28^ix	51.6 (5)
Si3—Ca6—Si6^iii	160.2 (4)	O12—Si7—O27^ix	117.2 (8)
Si3—Ca6—O3	32.4 (3)	O12—Si7—O28^ix	116.9 (8)
Si3—Ca6—O11	98.5 (4)	O27^ix—Si7—O28^ix	104.6 (8)
Si3—Ca6—O25	167.4 (4)	Ca1^xii—Si8—Ca8^ix	78.8 (4)
Si6^iii—Ca6—O3	167.3 (4)	Ca1^xii—Si8—O2^xii	59.8 (5)
Si6^iii—Ca6—O11	77.5 (4)	Ca1^xii—Si8—O13	130.5 (6)
Si6^iii—Ca6—O25	32.3 (3)	Ca1^xii—Si8—O29^ix	118.0 (8)
O3—Ca6—O11	101.6 (5)	Ca1^xii—Si8—O30^ix	47.5 (5)
O3—Ca6—O25	135.4 (4)	Ca8^ix—Si8—O2^xii	114.0 (8)
O11—Ca6—O25	86.9 (4)	Ca8^ix—Si8—O13	135.0 (6)
Ca2^i—Ca7—Ca7^vi	67.4 (3)	Ca8^ix—Si8—O29^ix	50.2 (5)
Ca2^i—Ca7—Ca9	147.3 (3)	Ca8^ix—Si8—O30^ix	54.9 (5)
Ca2^i—Ca7—Si2^iv	48.6 (3)	O2^xii—Si8—O13	110.6 (8)
Ca2^i—Ca7—Si7^iii	112.1 (4)	O2^xii—Si8—O29^ix	106.8 (7)
Ca2^i—Ca7—O5	72.6 (3)	O2^xii—Si8—O30^ix	107.3 (8)
Ca2^i—Ca7—O12	116.6 (4)	O13—Si8—O29^ix	111.3 (8)
Ca2^i—Ca7—O18^i	35.6 (3)	O13—Si8—O30^ix	115.5 (8)
Ca2^i—Ca7—O28	141.5 (5)	O29^ix—Si8—O30^ix	104.8 (8)
Ca7^vi—Ca7—Ca9	145.1 (3)	Ca3^viii—Si9—Ca9	76.5 (4)
Ca7^vi—Ca7—Si2^iv	58.5 (3)	Ca3^viii—Si9—O14^ix	123.4 (6)
Ca7^vi—Ca7—Si7^iii	134.4 (4)	Ca3^viii—Si9—O32	113.6 (8)
Ca7^vi—Ca7—O5	40.1 (3)	Ca9—Si9—O14^ix	138.1 (6)
Ca7^vi—Ca7—O12	146.5 (5)	Ca9—Si9—O32	50.3 (5)
Ca7^vi—Ca7—O18^i	81.8 (3)	O14^ix—Si9—O32	122.8 (9)
Ca7^vi—Ca7—O28	123.5 (4)	Ca8^ii—O1—Si1^iii	98.8 (6)
Ca9—Ca7—Si2^iv	133.4 (4)	Ca5^i—O2—Si4	100.6 (6)
Ca9—Ca7—Si7^iii	52.1 (3)	Ca5^i—O2—Si8^iv	125.4 (6)
Ca9—Ca7—O5	127.3 (4)	Si4—O2—Si8^iv	133.7 (9)
Ca9—Ca7—O12	38.5 (3)	Ca7—O5—Ca7^vi	99.8 (5)
Ca9—Ca7—O18^i	124.4 (4)	Ca4—O9—Si4^iii	123.6 (7)
Ca9—Ca7—O28	38.3 (3)	Ca5—O10—Si5^iii	118.0 (6)
Si2^iv—Ca7—Si7^iii	155.7 (5)	Ca6—O11—Si6	120.5 (6)
Si2^iv—Ca7—O5	32.0 (2)	Ca7—O12—Si7	125.8 (6)
Si2^iv—Ca7—O12	97.7 (4)	Ca8—O13—Si8	121.2 (6)
Si2^iv—Ca7—O18^i	29.9 (3)	Ca9—O14—Si9^iii	118.3 (6)
Si2^iv—Ca7—O28	169.6 (5)	Ca1—O15—Co1^iii	121.4 (5)
Si7^iii—Ca7—O5	171.9 (5)	Ca1—O15—Si1^iii	99.1 (6)
Si7^iii—Ca7—O12	77.1 (4)	Co1^iii—O15—Si1^iii	112.4 (10)
Si7^iii—Ca7—O18^i	125.8 (5)	Co3^iii—O16—Si1^iii	114.4 (10)
Si7^iii—Ca7—O28	31.5 (3)	Ca2—O17—Co2^iii	128.7 (6)
O5—Ca7—O12	107.1 (5)	Ca2—O17—Si2^iii	96.1 (5)
O5—Ca7—O18^i	61.9 (3)	Co2^iii—O17—Si2^iii	115.3 (8)
O5—Ca7—O28	141.9 (5)	Ca7^v—O18—Co4^v	118.0 (7)
O12—Ca7—O18^i	86.4 (4)	Ca7^v—O18—Si2^iii	100.9 (6)
O12—Ca7—O28	75.7 (4)	Co4^v—O18—Si2^iii	112.1 (8)
O18^i—Ca7—O28	153.6 (5)	Ca3—O19—Co3	123.1 (7)
Ca1^v—Ca8—Ca1^viii	93.2 (3)	Ca3—O19—Si3	95.7 (6)
Ca1^v—Ca8—Ca3^viii	159.9 (4)	Co3—O19—Si3	118.7 (9)
Ca1^v—Ca8—Si1^vii	110.8 (4)	Co2—O20—Si3	120.1 (9)
Ca1^v—Ca8—Si8^iii	53.2 (3)	Co3—O21—Si4	116.2 (10)
Ca1^v—Ca8—O1^viii	132.9 (5)	Ca4—O22—Co4	124.9 (7)
Ca1^v—Ca8—O13	38.5 (3)	Ca4—O22—Si4	101.3 (6)
Ca1^v—Ca8—O29	81.6 (3)	Co4—O22—Si4	116.6 (9)
Ca1^v—Ca8—O30	36.2 (3)	Ca2—O23—Ca5	106.9 (5)
Ca1^viii—Ca8—Ca3^viii	66.8 (3)	Ca2—O23—Co4^xii	119.4 (6)
Ca1^viii—Ca8—Si1^vii	51.2 (3)	Ca5—O23—Co4^xii	114.2 (6)
Ca1^viii—Ca8—Si8^iii	113.0 (4)	Ca5—O24—Co5	142.9 (8)
Ca1^viii—Ca8—O1^viii	77.5 (3)	Ca5—O24—Si5	100.1 (6)
Ca1^viii—Ca8—O13	113.5 (4)	Co5—O24—Si5	116.2 (9)
Ca1^viii—Ca8—O29	136.8 (5)	Ca6—O25—Co5^iii	139.7 (7)
Ca1^viii—Ca8—O30	84.8 (3)	Ca6—O25—Si6^iii	99.3 (5)
Ca3^viii—Ca8—Si1^vii	55.6 (3)	Co5^iii—O25—Si6^iii	119.6 (9)
Ca3^viii—Ca8—Si8^iii	135.2 (5)	Ca4—O26—Co3^iii	121.3 (6)
Ca3^viii—Ca8—O1^viii	43.5 (3)	Ca4—O26—Si6^iii	104.3 (5)
Ca3^viii—Ca8—O13	147.0 (5)	Co3^iii—O26—Si6^iii	115.6 (9)
Ca3^viii—Ca8—O29	114.1 (4)	Co4^iii—O27—Si7^iii	116.3 (8)
Ca3^viii—Ca8—O30	137.0 (5)	Ca7—O28—Co2^viii	123.1 (6)
Si1^vii—Ca8—Si8^iii	159.9 (4)	Ca7—O28—Si7^iii	96.7 (6)
Si1^vii—Ca8—O1^viii	31.3 (3)	Co2^viii—O28—Si7^iii	119.3 (9)
Si1^vii—Ca8—O13	97.4 (5)	Ca8—O29—Co5^iii	141.6 (7)
Si1^vii—Ca8—O29	166.2 (5)	Ca8—O29—Si8^iii	96.0 (6)
Si1^vii—Ca8—O30	127.7 (5)	Co5^iii—O29—Si8^iii	122.0 (9)
Si8^iii—Ca8—O1^viii	168.7 (5)	Ca1^v—O30—Ca8	107.6 (6)
Si8^iii—Ca8—O13	76.7 (4)	Ca1^v—O30—Co1^v	120.8 (5)
Si8^iii—Ca8—O29	33.9 (3)	Ca1^v—O30—Si8^iii	103.8 (6)
Si8^iii—Ca8—O30	32.2 (3)	Ca8—O30—Co1^v	111.2 (5)
O1^viii—Ca8—O13	103.5 (5)	Ca8—O30—Si8^iii	92.9 (6)
O1^viii—Ca8—O29	135.2 (5)	Co1^v—O30—Si8^iii	116.8 (10)
O1^viii—Ca8—O30	159.0 (5)	Ca9—O31—Co2^vii	115.3 (6)
O13—Ca8—O29	88.5 (4)	Ca9—O32—Co5	141.6 (7)
O13—Ca8—O30	73.2 (4)	Ca9—O32—Si9	98.6 (6)
O29—Ca8—O30	65.9 (4)	Co5—O32—Si9	118.7 (9)
Ca3^viii—Ca9—Ca4	164.5 (3)

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