research papers
Structure factors for rubidium oxotitanium arsenate, RbTiOAsO4, were measured at 293 K with focused synchrotron X-radiation [λ = 0.7500 (9) Å] using a fast avalanche photodiode counter. The accurate synchrotron single-crystal data are of sufficient quality and resolution to detect the splitting positions of the Rb cations at room temperature. Strong accumulation of the Δρ difference charge density near the Rb atoms at a distance of ∼0.5 Å in the −c direction can be attributed to the partial occupancy of additional sites related by pseudosymmetry. This type of static and/or dynamic disorder is temperature-dependent and seems to be universal for the KTiOPO4 family of compounds. The best modelling of the experimental data was obtained with the Rb atom in split positions described within the harmonic approximation and the multipole functions for the other atoms. The Δρ density features in the Ti—O and As—O covalent bonds can be related to the linear and non-linear susceptibility using bond-polarization theory. The charge-density maps reflect the anisotropy of non-linear susceptibility, which is larger for directions where locally antisymmetric components of Δρ are strong.
Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768100006285/os0048sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108768100006285/os00481sup2.hkl |
Computing details top
Data collection: bl14a; cell refinement: bl14a; data reduction: Xtal DIFDAT ADDREF SORTRF ABSORB; program(s) used to solve structure: Xtal; program(s) used to refine structure: Xtal CRYLSQ xd; molecular graphics: Xtal; software used to prepare material for publication: Xtal BONDLA CIFIO xd.
(RoomT) top
Crystal data top
RbTiOAsO4 | F(000) = 1056 |
Mr = 288.27 | Dx = 4.038 Mg m−3 |
Orthorhombic, Pna21 | Synchrotron xray vertical wiggler radiation, λ = 0.75 Å |
Hall symbol: P 2c -2n | Cell parameters from 12 reflections |
a = 13.2352 (11) Å | θ = 42.5–50.8° |
b = 6.6666 (7) Å | µ = 21.09 mm−1 |
c = 10.7483 (9) Å | T = 293 K |
V = 948.36 (15) Å3 | Rectangular, colourless |
Z = 8 | 0.06 × 0.06 × 0.04 mm |
Data collection top
Bl14a 4-circle diffractometer | 5982 reflections with F2 > 0 |
Radiation source: photon factory bl14a | Rint = 0.054 |
Si(111) monochromator | θmax = 60°, θmin = 3.3° |
ω–2θ scans | h = −30→30 |
Absorption correction: analytical Alcock (1974) | k = −15→15 |
Tmin = 0.344, Tmax = 0.494 | l = −24→24 |
46432 measured reflections | 6 standard reflections every 94 reflections |
6310 independent reflections | intensity decay: 8.8% |
Refinement top
Refinement on F | w = 1/σ2(F) |
Least-squares matrix: full | (Δ/σ)max = 0.01 |
R[F2 > 2σ(F2)] = 0.018 | Extinction correction: Becker-Coppens Gaussian |
wR(F2) = 0.015 | Extinction coefficient: 28925 (1184) |
S = 1.22 | Absolute structure: Flack XABS refined |
5982 reflections | Absolute structure parameter: 0.424 (3) |
533 parameters |
Crystal data top
RbTiOAsO4 | V = 948.36 (15) Å3 |
Mr = 288.27 | Z = 8 |
Orthorhombic, Pna21 | Synchrotron xray vertical wiggler radiation, λ = 0.75 Å |
a = 13.2352 (11) Å | µ = 21.09 mm−1 |
b = 6.6666 (7) Å | T = 293 K |
c = 10.7483 (9) Å | 0.06 × 0.06 × 0.04 mm |
Data collection top
Bl14a 4-circle diffractometer | 5982 reflections with F2 > 0 |
Absorption correction: analytical Alcock (1974) | Rint = 0.054 |
Tmin = 0.344, Tmax = 0.494 | 6 standard reflections every 94 reflections |
46432 measured reflections | intensity decay: 8.8% |
6310 independent reflections |
Refinement top
R[F2 > 2σ(F2)] = 0.018 | 533 parameters |
wR(F2) = 0.015 | Absolute structure: Flack XABS refined |
S = 1.22 | Absolute structure parameter: 0.424 (3) |
5982 reflections |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
x | y | z | Uiso*/Ueq | ||
Rb1 | 0.38246 (4) | 0.78159 (6) | 0.70236 (3) | 0.017 | |
Rb2 | 0.10885 (6) | 0.69335 (10) | 0.95521 (4) | 0.014 | |
Rb3 | 0.3871 (2) | 0.7878 (4) | 0.6741 (2) | 0.014 | |
Rb4 | 0.1110 (4) | 0.6983 (5) | 0.9340 (3) | 0.011 | |
Ti1 | 0.373747 (13) | 0.50505 (3) | 1.027988 (17) | 0.005 | |
Ti2 | 0.248776 (15) | 0.26999 (3) | 0.777903 (18) | 0.005 | |
As1 | 0.499652 (9) | 0.328210 (14) | 0.770681 (13) | 0.004 | |
As2 | 0.179890 (7) | 0.505071 (17) | 0.516443 (11) | 0.005 | |
O1 | 0.48731 (8) | 0.48947 (16) | 0.88714 (9) | 0.011 | |
O2 | 0.51039 (7) | 0.46126 (15) | 0.63784 (8) | 0.010 | |
O3 | 0.39509 (6) | 0.18744 (14) | 0.74880 (9) | 0.009 | |
O4 | 0.60025 (6) | 0.17655 (14) | 0.79062 (9) | 0.009 | |
O11 | 0.28160 (7) | 0.45211 (14) | 0.88764 (8) | 0.008 | |
O12 | 0.21791 (7) | 0.05542 (14) | 0.63748 (8) | 0.009 | |
O5 | 0.10983 (8) | 0.30341 (13) | 0.48072 (9) | 0.009 | |
O6 | 0.10713 (8) | 0.70414 (13) | 0.54832 (10) | 0.010 | |
O7 | 0.25824 (8) | 0.54470 (15) | 0.39454 (9) | 0.010 | |
O8 | 0.25779 (8) | 0.45857 (15) | 0.63651 (8) | 0.010 |
Atomic displacement parameters (Å2) top
U11 | U22 | U33 | U12 | U13 | U23 | |
Rb1 | 0.02131 (9) | 0.00722 (6) | 0.02104 (12) | 0.00289 (5) | −0.00609 (11) | −0.00211 (9) |
Rb2 | 0.01048 (8) | 0.01382 (10) | 0.01740 (17) | 0.00368 (6) | −0.00058 (12) | −0.00088 (10) |
Rb3 | 0.0159 (5) | 0.0073 (5) | 0.0181 (8) | 0.0028 (3) | −0.0055 (7) | −0.0020 (6) |
Rb4 | 0.0107 (5) | 0.0065 (4) | 0.0147 (9) | 0.0019 (3) | 0.0010 (7) | −0.0006 (6) |
Ti1 | 0.00519 (5) | 0.00489 (5) | 0.00490 (5) | −0.00005 (5) | 0.00018 (4) | −0.00091 (5) |
Ti2 | 0.00502 (4) | 0.00500 (5) | 0.00473 (5) | −0.00028 (5) | −0.00064 (5) | 0.00014 (5) |
As1 | 0.00378 (3) | 0.00446 (3) | 0.00510 (3) | −0.00004 (3) | 0.00065 (2) | −0.00029 (3) |
As2 | 0.00624 (3) | 0.00344 (3) | 0.00513 (3) | −0.00027 (3) | −0.00029 (3) | 0.00061 (2) |
O1 | 0.0100 (3) | 0.0117 (3) | 0.0105 (3) | −0.0033 (2) | 0.0038 (2) | −0.0062 (2) |
O2 | 0.0087 (3) | 0.0117 (3) | 0.0091 (2) | 0.0020 (2) | 0.0031 (2) | 0.0047 (2) |
O3 | 0.0058 (2) | 0.0073 (2) | 0.0127 (3) | −0.0015 (2) | 0.0005 (2) | −0.0019 (2) |
O4 | 0.0048 (2) | 0.0088 (2) | 0.0138 (3) | 0.0011 (2) | −0.0005 (2) | 0.0024 (2) |
O11 | 0.0082 (2) | 0.0090 (2) | 0.0078 (2) | 0.0005 (2) | −0.0027 (2) | −0.0031 (2) |
O12 | 0.0092 (3) | 0.0092 (3) | 0.0085 (2) | 0.0005 (2) | −0.0031 (2) | −0.0022 (2) |
O5 | 0.0116 (3) | 0.0048 (2) | 0.0119 (3) | −0.0018 (2) | −0.0039 (2) | 0.0007 (2) |
O6 | 0.0123 (3) | 0.0053 (2) | 0.0139 (3) | 0.0009 (2) | 0.0038 (2) | −0.0003 (2) |
O7 | 0.0106 (3) | 0.0103 (3) | 0.0090 (2) | 0.0032 (2) | 0.0031 (2) | 0.0045 (2) |
O8 | 0.0117 (3) | 0.0110 (3) | 0.0081 (2) | −0.0039 (2) | −0.0043 (2) | 0.0044 (2) |
Bond lengths (Å) top
Rb1—Rb3 | 0.312 (3) | Ti2—O11 | 1.7476 (8) |
Rb2—Rb3i | 3.585 (3) | Ti2—O12 | 2.1192 (9) |
Rb2—Rb4 | 0.233 (4) | Ti2—O7i | 1.9586 (9) |
Rb3—Rb4ii | 3.762 (4) | Ti2—O8 | 1.9760 (9) |
Ti1—O1 | 2.1358 (9) | As1—O1 | 1.6581 (8) |
Ti1—O2iii | 1.9484 (9) | As1—O2 | 1.6869 (8) |
Ti1—O11 | 1.9716 (8) | As1—O3 | 1.6885 (9) |
Ti1—O12iv | 1.7232 (8) | As1—O4 | 1.6855 (8) |
Ti1—O5iv | 2.0644 (9) | As2—O5 | 1.6777 (9) |
Ti1—O6i | 2.0337 (8) | As2—O6 | 1.6751 (9) |
Ti2—O3 | 2.0374 (9) | As2—O7 | 1.6917 (9) |
Ti2—O4v | 2.0025 (8) | As2—O8 | 1.6806 (9) |
Symmetry codes: (i) −x+1/2, y−1/2, z+1/2; (ii) −x+1/2, y+1/2, z−1/2; (iii) −x+1, −y+1, z+1/2; (iv) −x+1/2, y+1/2, z+1/2; (v) x−1/2, −y+1/2, z. |
Experimental details
Crystal data | |
Chemical formula | RbTiOAsO4 |
Mr | 288.27 |
Crystal system, space group | Orthorhombic, Pna21 |
Temperature (K) | 293 |
a, b, c (Å) | 13.2352 (11), 6.6666 (7), 10.7483 (9) |
V (Å3) | 948.36 (15) |
Z | 8 |
Radiation type | Synchrotron xray vertical wiggler, λ = 0.75 Å |
µ (mm−1) | 21.09 |
Crystal size (mm) | 0.06 × 0.06 × 0.04 |
Data collection | |
Diffractometer | Bl14a 4-circle diffractometer |
Absorption correction | Analytical Alcock (1974) |
Tmin, Tmax | 0.344, 0.494 |
No. of measured, independent and observed (F2 > 0) reflections | 46432, 6310, 5982 |
Rint | 0.054 |
(sin θ/λ)max (Å−1) | 1.155 |
Refinement | |
R[F2 > 2σ(F2)], wR(F2), S | 0.018, 0.015, 1.22 |
No. of reflections | 5982 |
No. of parameters | 533 |
No. of restraints | ? |
Δρmax, Δρmin (e Å−3) | ?, ? |
Absolute structure | Flack XABS refined |
Absolute structure parameter | 0.424 (3) |
Computer programs: bl14a, Xtal DIFDAT ADDREF SORTRF ABSORB, Xtal CRYLSQ xd, Xtal BONDLA CIFIO xd.
Selected bond lengths (Å) top
Rb1—Rb3 | 0.312 (3) | Ti2—O11 | 1.7476 (8) |
Rb2—Rb3i | 3.585 (3) | Ti2—O12 | 2.1192 (9) |
Rb2—Rb4 | 0.233 (4) | Ti2—O7i | 1.9586 (9) |
Rb3—Rb4ii | 3.762 (4) | Ti2—O8 | 1.9760 (9) |
Ti1—O1 | 2.1358 (9) | As1—O1 | 1.6581 (8) |
Ti1—O2iii | 1.9484 (9) | As1—O2 | 1.6869 (8) |
Ti1—O11 | 1.9716 (8) | As1—O3 | 1.6885 (9) |
Ti1—O12iv | 1.7232 (8) | As1—O4 | 1.6855 (8) |
Ti1—O5iv | 2.0644 (9) | As2—O5 | 1.6777 (9) |
Ti1—O6i | 2.0337 (8) | As2—O6 | 1.6751 (9) |
Ti2—O3 | 2.0374 (9) | As2—O7 | 1.6917 (9) |
Ti2—O4v | 2.0025 (8) | As2—O8 | 1.6806 (9) |
Symmetry codes: (i) −x+1/2, y−1/2, z+1/2; (ii) −x+1/2, y+1/2, z−1/2; (iii) −x+1, −y+1, z+1/2; (iv) −x+1/2, y+1/2, z+1/2; (v) x−1/2, −y+1/2, z. |