Modulated structure of Lu₄AlCu₂B₉O₂₃ from low-temperature single-crystal X-ray data

A second-order phase transition with both displacive and disorder mechanisms was discovered in Lu₄AlCu₂B₉O₂₃ using single-crystal X-ray diffraction techniques by cooling down the sample to 110 K. Low-temperature structure modulations are mainly associated with Cu atoms surrounded by O atoms. The fivefold asymmetric environment leads to a special copper position splitting into a pair of general ones so that four O atoms coordinate each of them. Each copper site is 50% occupied at room temperature, but at lower temperature statistical disorder gives occupation and displacive modulations with a wavevector of q = 0.132c*. Tetragonal symmetry of the non-modulated phase transforms into an orthorhombic (3+1)-dimensional symmetry, P2₁2₁2(00γ)00s, whereas the axis becomes the twinning axis.

Computing details

Figures

(I)

Crystal data

AlB9Cu2Lu4O23	Z = 2
Mr = 1319.2	F(000) = 1168
Orthorhombic, P21212(00γ)00s†	Dx = 5.86 Mg m^−3
q = 0.132000c*	X-ray radiation, λ = 0.7093 Å
a = 12.591 (1) Å	µ = 29.12 mm^−1
b = 12.591 (1) Å	T = 110 K
c = 4.7144 (3) Å	Columnar, transparent emerald-green
V = 747.41 Å^3	0.09 × 0.02 × 0.02 mm

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₁, −x₂, x₃, x₄+1/2; (3) −x₁+1/2, x₂+1/2, −x₃, −x₄+1/2; (4) x₁+1/2, −x₂+1/2, −x₃, −x₄.

Data collection

IPDS STOE II diffractometer	3378 reflections with I > 3σ(I)
Graphite monochromator	Rint = 0.040
phi–scans	θmax = 29.2°, θmin = 1.7°
Absorption correction: gaussian Jana2006 (Petricek, Dusek & Palatinus, 2000)	h = −17→17
Tmin = 0.041, Tmax = 0.135	k = −17→17
40750 measured reflections	l = −6→6
6076 independent reflections

Refinement

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0004F^2)
R[F^2 > 2σ(F^2)] = 0.039	(Δ/σ)max = 0.046
wR(F^2) = 0.053	Δρmax = 2.27 e Å^−3
S = 1.19	Δρmin = −2.60 e Å^−3
6076 reflections	Extinction correction: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974)
217 parameters	Extinction coefficient: 3400 (120)
0 restraints	Absolute structure: 2663 of Friedel pairs used in the refinement
9 constraints

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Lu	0.65032 (4)	0.35435 (4)	0.00313 (13)	0.01138 (17)
Lu'	0.35243 (4)	0.35148 (4)	−0.00254 (13)	0.01254 (19)
Cu	0.8807 (3)	0.5713 (2)	−0.0292 (10)	0.0115 (2)*	0.5
Cu'	0.9158 (3)	0.6093 (3)	−0.0270 (8)	0.0115 (2)*	0.5
Al	0.5	0.5	0.4931 (16)	0.0101 (4)*
B1	0.7158 (10)	0.4979 (10)	0.525 (3)	0.0103 (8)*
B1'	0.4970 (11)	0.2845 (8)	0.448 (3)	0.0103 (8)*
B2	0.8511 (9)	0.6453 (10)	0.4656 (15)	0.0118 (11)*
B3	0.8208 (10)	0.3250 (10)	0.4787 (15)	0.0116 (11)*
B4	0	0.5	0.502 (2)	0.0157 (17)*
O1	0.6929 (8)	0.5024 (8)	0.249 (2)	0.0136 (5)*
O1'	0.4994 (9)	0.3068 (8)	0.757 (2)	0.0136 (5)*
O2	0.6159 (8)	0.4982 (7)	0.715 (2)	0.0140 (6)*
O2'	0.5048 (7)	0.3856 (7)	0.286 (2)	0.0140 (6)*
O3	0.7663 (7)	0.3998 (7)	0.650 (2)	0.0111 (6)*
O3'	0.6038 (6)	0.7678 (7)	0.370 (2)	0.0111 (6)*
O4	0.7763 (7)	0.5924 (7)	0.650 (2)	0.0121 (6)*
O4'	0.4088 (7)	0.7785 (7)	0.367 (2)	0.0121 (6)*
O5	0.7995 (7)	0.3024 (7)	0.2108 (9)	0.0096 (7)*
O6	0.9321 (6)	0.5619 (7)	0.3552 (9)	0.0140 (8)*
O7	0.8088 (7)	0.6856 (7)	0.1982 (9)	0.0130 (9)*
O8	0	0.5	0.7858 (14)	0.0213 (15)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Lu	0.0128 (3)	0.0113 (3)	0.0100 (2)	0.00030 (12)	0.0024 (2)	0.0000 (2)
Lu'	0.0135 (4)	0.0110 (3)	0.0131 (2)	−0.00014 (12)	0.0013 (2)	−0.0028 (2)

Bond lengths (Å)

	Average	Minimum	Maximum
Lu—O1	2.260 (13)	2.234 (13)	2.286 (13)
Lu—O1'^i	2.304 (14)	2.295 (14)	2.312 (14)
Lu—O2^i	2.305 (12)	2.293 (12)	2.318 (12)
Lu—O2'	2.301 (12)	2.289 (12)	2.313 (12)
Lu—O3^i	2.286 (13)	2.274 (13)	2.298 (13)
Lu—O4'^ii	2.509 (13)	2.457 (12)	2.560 (12)
Lu—O5	2.217 (11)	2.186 (11)	2.249 (11)
Lu—O7^iii	2.383 (11)	2.356 (11)	2.411 (11)
Lu'—O1^ii	2.262 (13)	2.229 (13)	2.296 (13)
Lu'—O1'^i	2.241 (14)	2.220 (14)	2.262 (14)
Lu'—O2^iv	2.349 (12)	2.339 (12)	2.358 (12)
Lu'—O2'	2.392 (12)	2.362 (12)	2.421 (12)
Lu'—O3'^ii	2.377 (13)	2.348 (12)	2.405 (12)
Lu'—O4^iv	2.409 (13)	2.360 (13)	2.459 (13)
Lu'—O5^v	2.273 (11)	2.261 (11)	2.285 (11)
Lu'—O7^ii	2.289 (11)	2.269 (11)	2.309 (11)
Cu—Cu'	0.650 (8)	0.479 (8)	0.822 (8)
Cu—O4^i	2.019 (14)	1.972 (14)	2.068 (14)
Cu—O4'^vi	2.496 (13)	2.471 (14)	2.522 (14)
Cu—O6	1.928 (12)	1.894 (12)	1.963 (12)
Cu—O7	2.011 (12)	1.979 (12)	2.042 (12)
Cu—O8^vii	1.969 (15)	1.901 (14)	2.062 (15)
Cu'—B2	2.505 (18)	2.452 (18)	2.559 (18)
Cu'—O4^i	2.332 (14)	2.210 (14)	2.459 (14)
Cu'—O4'^vi	2.140 (14)	2.033 (14)	2.248 (14)
Cu'—O6	1.912 (12)	1.883 (12)	1.947 (12)
Cu'—O7	1.968 (12)	1.902 (12)	2.034 (12)
Cu'—O8^vii	1.952 (14)	1.906 (15)	1.995 (14)
Al—O2	1.796 (16)	1.790 (16)	1.801 (16)
Al—O2^ii	1.795 (16)	1.790 (16)	1.801 (16)
Al—O2'	1.740 (14)	1.724 (14)	1.757 (14)
Al—O2'^ii	1.740 (14)	1.724 (14)	1.757 (14)
B1—B2	2.54 (3)	2.48 (3)	2.59 (3)
B1—O1	1.33 (3)	1.28 (3)	1.39 (3)
B1—O2	1.54 (3)	1.51 (3)	1.58 (3)
B1—O3	1.51 (2)	1.49 (2)	1.53 (2)
B1—O4	1.53 (2)	1.49 (2)	1.57 (2)
B1'—O1'	1.49 (2)	1.49 (2)	1.49 (2)
B1'—O2'	1.49 (2)	1.49 (2)	1.49 (2)
B1'—O3'^ii	1.48 (2)	1.47 (2)	1.48 (2)
B1'—O4'^ii	1.48 (2)	1.47 (3)	1.48 (3)
B2—O4	1.45 (2)	1.42 (2)	1.47 (2)
B2—O4'^viii	1.44 (2)	1.42 (2)	1.46 (2)
B2—O6	1.55 (2)	1.53 (2)	1.58 (2)
B2—O7	1.46 (2)	1.42 (2)	1.50 (2)
B3—O3	1.42 (2)	1.38 (2)	1.46 (2)
B3—O3'^ix	1.39 (2)	1.37 (2)	1.41 (2)
B3—O5	1.32 (2)	1.27 (2)	1.38 (2)
B4—O6^x	1.35 (2)	1.34 (2)	1.35 (2)
B4—O6^ii	1.35 (2)	1.34 (2)	1.35 (2)
B4—O8	1.356 (12)	1.340 (12)	1.371 (13)
O1—O2	2.40 (2)	2.39 (2)	2.41 (2)
O1—O3	2.471 (19)	2.445 (19)	2.498 (19)
O1—O4	2.444 (19)	2.424 (19)	2.463 (19)
O1'—O2'	2.434 (18)	2.423 (18)	2.446 (18)
O1'—O3'^ii	2.430 (18)	2.420 (18)	2.440 (18)
O1'—O4'^ii	2.426 (18)	2.410 (18)	2.443 (18)
O2—O3	2.284 (17)	2.278 (17)	2.289 (17)
O2—O4	2.363 (17)	2.341 (17)	2.385 (17)
O2'—O3'^ii	2.400 (16)	2.393 (16)	2.407 (16)
O2'—O4'^ii	2.367 (16)	2.352 (16)	2.381 (16)
O3—O3'^ix	2.334 (15)	2.329 (15)	2.339 (15)
O3—O4	2.429 (15)	2.407 (15)	2.450 (15)
O3—O5	2.444 (17)	2.414 (17)	2.475 (17)
O3'—O4'	2.460 (15)	2.446 (15)	2.474 (15)
O3'—O5^xi	2.361 (17)	2.311 (17)	2.410 (17)
O4—O4'^viii	2.331 (16)	2.320 (16)	2.341 (16)
O4—O6	2.436 (16)	2.424 (16)	2.448 (16)
O4—O7	2.468 (17)	2.430 (17)	2.506 (17)
O4'—O6^xii	2.418 (16)	2.406 (16)	2.430 (16)
O4'—O7^xii	2.449 (17)	2.402 (17)	2.496 (17)
O6—O6^xiii	2.314 (15)	2.314 (16)	2.314 (15)
O6—O7	2.320 (15)	2.297 (15)	2.344 (15)
O6—O8^xiv	2.350 (14)	2.327 (14)	2.377 (14)

Symmetry codes: (i) x₁, x₂, x₃−1, x₄; (ii) −x₁+1, −x₂+1, x₃, x₄+1/2; (iii) −x₁+3/2, x₂−1/2, −x₃, −x₄+1/2; (iv) −x₁+1, −x₂+1, x₃−1, x₄+1/2; (v) x₁−1/2, −x₂+1/2, −x₃, −x₄; (vi) x₁+1/2, −x₂+3/2, −x₃, −x₄; (vii) x₁+1, x₂, x₃−1, x₄; (viii) x₁+1/2, −x₂+3/2, −x₃+1, −x₄; (ix) −x₁+3/2, x₂−1/2, −x₃+1, −x₄+1/2; (x) x₁−1, x₂, x₃, x₄; (xi) −x₁+3/2, x₂+1/2, −x₃+1, −x₄+1/2; (xii) x₁−1/2, −x₂+3/2, −x₃+1, −x₄; (xiii) −x₁+2, −x₂+1, x₃, x₄+1/2; (xiv) x₁+1, x₂, x₃, x₄.