Origin of forbidden reflections in multiferroic Ba₂CoGe₂O₇ by neutron diffraction: symmetry lowering or Renninger effect?

For a symmetry-consistent theoretical description of the multiferroic phase of Ba₂CoGe₂O₇ a precise knowledge of its crystal structure is a prerequisite. In a previous synchrotron X-ray diffraction experiment on multiferroic Ba₂CoGe₂O₇ at room temperature, forbidden reflections were found that favour the tetragonal-to-orthorhombic symmetry lowering of the compound [Hutanu, Sazonov, Murakawa, Tokura, Náfrádi & Chernyshov (2011), Phys. Rev. B, 84, 212101]. Here, the results are reported of room-temperature single-crystal diffraction studies with both hot and cold neutrons to differentiate between genuine symmetry lowering and multiple diffraction (the Renninger effect). A comparison of the experimental multiple diffraction patterns with simulated ones rules out symmetry lowering. Thus, the structural model based on the tetragonal space group was selected to describe the Ba₂CoGe₂O₇ symmetry at room temperature. The precise structural parameters from neutron diffraction at 300 K are presented and compared with the previous X-ray diffraction results.

Computing details

(I)

Crystal data

Ba2CoGe2O7	Z = 2
Mr = 590.81	Dx = 5.010 Mg m^−3
Tetragonal, P421m	Neutron radiation, λ = 0.793 Å
Hall symbol: P -4 2ab	µ = 0.01 mm^−1
a = 8.392 (1) Å	T = 300 K
c = 5.561 (1) Å	Cylinder, blue
V = 391.64 (12) Å^3	4 × 2 (radius) mm

Data collection

Four-circle diffractometer	θmax = 49.7°, θmin = 3.8°
1746 measured reflections	h = 0→16
552 independent reflections	k = 0→16
552 reflections with I > 3σ(I)	l = −10→10
Rint = 0.024

Refinement

Refinement on F^2	0 constraints
R[F^2 > 2σ(F^2)] = 0.016	Weighting scheme based on measured s.u.'s w = 1/(σ^2(I) + 0.0004I^2)
wR(F^2) = 0.042	(Δ/σ)max = 0.003
S = 1.68	Extinction correction: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974)
551 reflections	Extinction coefficient: 24200 (700)
35 parameters	Absolute structure: 0 of Friedel pairs used in the refinement
0 restraints

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

	x	y	z	Uiso*/Ueq
Ba	0.33479 (7)	0.16521 (7)	0.49267 (17)	0.00731 (12)
Co	0	0	0	0.0063 (3)
Ge	0.14053 (5)	0.35947 (5)	0.03986 (9)	0.00520 (8)
O1	0	0.5	0.1581 (2)	0.00968 (18)
O2	0.13843 (8)	0.36157 (8)	0.72982 (15)	0.01017 (12)
O3	0.07949 (9)	0.18468 (7)	0.18715 (14)	0.00997 (12)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ba	0.00743 (18)	0.00743 (18)	0.0071 (2)	0.00247 (19)	−0.00058 (16)	0.00058 (16)
Co	0.0055 (4)	0.0055 (4)	0.0080 (8)	0	0	0
Ge	0.00514 (11)	0.00514 (11)	0.00532 (17)	0.00053 (13)	−0.00002 (8)	0.00002 (8)
O1	0.0108 (2)	0.0108 (2)	0.0074 (4)	0.0059 (3)	0	0
O2	0.01205 (19)	0.01205 (19)	0.0064 (2)	0.0023 (3)	0.00043 (14)	−0.00043 (14)
O3	0.0133 (3)	0.0066 (2)	0.01005 (17)	−0.00288 (15)	−0.00213 (18)	0.00046 (16)

Geometric parameters (Å, º)

Ba—Ba^i	3.9213 (9)	Ba—O3	2.7392 (11)
Ba—Ba^ii	4.4315 (9)	Ba—O3^vi	2.7392 (11)
Ba—Ba^iii	4.4315 (9)	Co—O3	1.9825 (7)
Ba—Ba^iv	4.4315 (9)	Co—O3^vii	1.9825 (7)
Ba—Ba^v	4.4315 (9)	Co—O3^viii	1.9825 (7)
Ba—Ge	3.4141 (9)	Co—O3^ix	1.9825 (7)
Ba—O1^ii	2.7595 (12)	Ge—O1	1.7928 (6)
Ba—O2	2.6777 (10)	Ge—O2^x	1.7244 (10)
Ba—O2^ii	2.8415 (10)	Ge—O3	1.7563 (8)
Ba—O2^v	2.8415 (10)	Ge—O3^vi	1.7563 (8)
Ba^i—Ba—Ba^ii	63.741 (15)	Ge—Ba—O3	30.748 (18)
Ba^i—Ba—Ba^iii	153.72 (2)	Ge—Ba—O3^vi	30.748 (18)
Ba^i—Ba—Ba^iv	153.72 (2)	O1^ii—Ba—O2	105.77 (4)
Ba^i—Ba—Ba^v	63.741 (15)	O1^ii—Ba—O2^ii	79.41 (3)
Ba^i—Ba—Ge	132.48 (3)	O1^ii—Ba—O2^v	79.41 (3)
Ba^i—Ba—O1^ii	44.72 (3)	O1^ii—Ba—O3	149.25 (3)
Ba^i—Ba—O2	150.49 (4)	O1^ii—Ba—O3^vi	149.25 (3)
Ba^i—Ba—O2^ii	46.37 (2)	O2—Ba—O2^ii	144.58 (3)
Ba^i—Ba—O2^v	46.37 (2)	O2—Ba—O2^v	144.58 (3)
Ba^i—Ba—O3	126.53 (3)	O2—Ba—O3	77.73 (3)
Ba^i—Ba—O3^vi	126.53 (3)	O2—Ba—O3^vi	77.73 (3)
Ba^ii—Ba—Ba^iii	142.471 (19)	O2^ii—Ba—O2^v	70.65 (3)
Ba^ii—Ba—Ba^iv	89.981 (16)	O2^ii—Ba—O3	81.10 (3)
Ba^ii—Ba—Ba^v	127.432 (18)	O2^ii—Ba—O3^vi	115.85 (4)
Ba^ii—Ba—Ge	108.20 (2)	O2^v—Ba—O3	115.85 (4)
Ba^ii—Ba—O1^ii	70.895 (18)	O2^v—Ba—O3^vi	81.10 (3)
Ba^ii—Ba—O2	112.09 (3)	O3—Ba—O3^vi	61.44 (3)
Ba^ii—Ba—O2^ii	35.35 (2)	O3—Co—O3^vii	116.67 (3)
Ba^ii—Ba—O2^v	102.78 (2)	O3—Co—O3^viii	106.00 (3)
Ba^ii—Ba—O3	79.44 (2)	O3—Co—O3^ix	106.00 (3)
Ba^ii—Ba—O3^vi	137.12 (3)	O3^vii—Co—O3^viii	106.00 (3)
Ba^iii—Ba—Ba^iv	52.519 (13)	O3^vii—Co—O3^ix	106.00 (3)
Ba^iii—Ba—Ba^v	89.981 (16)	O3^viii—Co—O3^ix	116.67 (3)
Ba^iii—Ba—Ge	53.707 (16)	Ba—Ge—O1	110.95 (4)
Ba^iii—Ba—O1^ii	128.62 (3)	Ba—Ge—O2^x	138.35 (3)
Ba^iii—Ba—O2	37.87 (2)	Ba—Ge—O3	52.88 (3)
Ba^iii—Ba—O2^ii	151.94 (3)	Ba—Ge—O3^vi	52.88 (3)
Ba^iii—Ba—O2^v	111.77 (2)	O1—Ge—O2^x	110.69 (5)
Ba^iii—Ba—O3	72.77 (2)	O1—Ge—O3	100.74 (4)
Ba^iii—Ba—O3^vi	41.55 (2)	O1—Ge—O3^vi	100.74 (4)
Ba^iv—Ba—Ba^v	142.471 (19)	O2^x—Ge—O3	118.15 (4)
Ba^iv—Ba—Ge	53.707 (16)	O2^x—Ge—O3^vi	118.15 (4)
Ba^iv—Ba—O1^ii	128.62 (3)	O3—Ge—O3^vi	105.64 (4)
Ba^iv—Ba—O2	37.87 (2)	Ba^iii—O1—Ba^iv	90.55 (4)
Ba^iv—Ba—O2^ii	111.77 (2)	Ba^iii—O1—Ge	104.96 (3)
Ba^iv—Ba—O2^v	151.94 (3)	Ba^iii—O1—Ge^xi	104.96 (3)
Ba^iv—Ba—O3	41.55 (2)	Ba^iv—O1—Ge	104.96 (3)
Ba^iv—Ba—O3^vi	72.77 (2)	Ba^iv—O1—Ge^xi	104.96 (3)
Ba^v—Ba—Ge	108.20 (2)	Ge—O1—Ge^xi	136.95 (8)
Ba^v—Ba—O1^ii	70.895 (18)	Ba—O2—Ba^iii	106.78 (3)
Ba^v—Ba—O2	112.09 (3)	Ba—O2—Ba^iv	106.78 (3)
Ba^v—Ba—O2^ii	102.78 (2)	Ba—O2—Ge^xii	118.68 (4)
Ba^v—Ba—O2^v	35.35 (2)	Ba^iii—O2—Ba^iv	87.26 (3)
Ba^v—Ba—O3	137.12 (3)	Ba^iii—O2—Ge^xii	116.34 (4)
Ba^v—Ba—O3^vi	79.44 (2)	Ba^iv—O2—Ge^xii	116.34 (4)
Ge—Ba—O1^ii	177.20 (4)	Ba—O3—Co	122.83 (3)
Ge—Ba—O2	77.03 (2)	Ba—O3—Ge	96.37 (4)
Ge—Ba—O2^ii	98.33 (3)	Co—O3—Ge	120.41 (4)
Ge—Ba—O2^v	98.33 (3)

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