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A second-order phase transition with both displacive and disorder mechanisms was discovered in Lu
4AlCu
2B
9O
23 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 = 0.132
c*. Tetragonal
symmetry of the non-modulated phase transforms into an orthorhombic (3+1)-dimensional symmetry,
P2
12
12(00γ)00
s, whereas the
axis becomes the twinning axis.
Supporting information
B-IncStrDB reference: 8012ELVkXA
Crystal data top
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 Å3 | 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 top
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 top
Refinement on F | Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0004F2) |
R[F2 > 2σ(F2)] = 0.039 | (Δ/σ)max = 0.046 |
wR(F2) = 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 | |
Crystal data top
AlB9Cu2Lu4O23 | V = 747.41 Å3 |
Mr = 1319.2 | Z = 2 |
Orthorhombic, P21212(00γ)00s† | X-ray radiation, λ = 0.7093 Å |
q = 0.132000c* | µ = 29.12 mm−1 |
a = 12.591 (1) Å | T = 110 K |
b = 12.591 (1) Å | 0.09 × 0.02 × 0.02 mm |
c = 4.7144 (3) Å | |
† 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 top
IPDS STOE II diffractometer | 6076 independent reflections |
Absorption correction: gaussian Jana2006 (Petricek, Dusek & Palatinus, 2000) | 3378 reflections with I > 3σ(I) |
Tmin = 0.041, Tmax = 0.135 | Rint = 0.040 |
40750 measured reflections | |
Refinement top
R[F2 > 2σ(F2)] = 0.039 | 0 restraints |
wR(F2) = 0.053 | Δρmax = 2.27 e Å−3 |
S = 1.19 | Δρmin = −2.60 e Å−3 |
6076 reflections | Absolute structure: 2663 of Friedel pairs used in the refinement |
217 parameters | |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | 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 (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
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) top | 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—O2i | 2.305 (12) | 2.293 (12) | 2.318 (12) |
Lu—O2' | 2.301 (12) | 2.289 (12) | 2.313 (12) |
Lu—O3i | 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—O7iii | 2.383 (11) | 2.356 (11) | 2.411 (11) |
Lu'—O1ii | 2.262 (13) | 2.229 (13) | 2.296 (13) |
Lu'—O1'i | 2.241 (14) | 2.220 (14) | 2.262 (14) |
Lu'—O2iv | 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'—O4iv | 2.409 (13) | 2.360 (13) | 2.459 (13) |
Lu'—O5v | 2.273 (11) | 2.261 (11) | 2.285 (11) |
Lu'—O7ii | 2.289 (11) | 2.269 (11) | 2.309 (11) |
Cu—Cu' | 0.650 (8) | 0.479 (8) | 0.822 (8) |
Cu—O4i | 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—O8vii | 1.969 (15) | 1.901 (14) | 2.062 (15) |
Cu'—B2 | 2.505 (18) | 2.452 (18) | 2.559 (18) |
Cu'—O4i | 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'—O8vii | 1.952 (14) | 1.906 (15) | 1.995 (14) |
Al—O2 | 1.796 (16) | 1.790 (16) | 1.801 (16) |
Al—O2ii | 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—O6x | 1.35 (2) | 1.34 (2) | 1.35 (2) |
B4—O6ii | 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'—O5xi | 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'—O6xii | 2.418 (16) | 2.406 (16) | 2.430 (16) |
O4'—O7xii | 2.449 (17) | 2.402 (17) | 2.496 (17) |
O6—O6xiii | 2.314 (15) | 2.314 (16) | 2.314 (15) |
O6—O7 | 2.320 (15) | 2.297 (15) | 2.344 (15) |
O6—O8xiv | 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. |
Experimental details
Crystal data |
Chemical formula | AlB9Cu2Lu4O23 |
Mr | 1319.2 |
Crystal system, space group | Orthorhombic, P21212(00γ)00s† |
Temperature (K) | 110 |
Wave vectors | q = 0.132000c* |
a, b, c (Å) | 12.591 (1), 12.591 (1), 4.7144 (3) |
V (Å3) | 747.41 |
Z | 2 |
Radiation type | X-ray, λ = 0.7093 Å |
µ (mm−1) | 29.12 |
Crystal size (mm) | 0.09 × 0.02 × 0.02 |
|
Data collection |
Diffractometer | IPDS STOE II diffractometer |
Absorption correction | Gaussian Jana2006 (Petricek, Dusek & Palatinus, 2000) |
Tmin, Tmax | 0.041, 0.135 |
No. of measured, independent and observed [I > 3σ(I)] reflections | 40750, 6076, 3378 |
Rint | 0.040 |
(sin θ/λ)max (Å−1) | 0.688 |
|
Refinement |
R[F2 > 2σ(F2)], wR(F2), S | 0.039, 0.053, 1.19 |
No. of reflections | 6076 |
No. of parameters | 217 |
Δρmax, Δρmin (e Å−3) | 2.27, −2.60 |
Absolute structure | 2663 of Friedel pairs used in the refinement |
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