The crystal structure and electric charge distribution in LiNaSO4 have been studied at 296 K by X-ray diffraction using a spherical crystal. LiNaSO4 is pyroelectric, nonferroelectric and an optically uniaxial insulator which crystallizes in the space group P31c. Least-squares refinement (MOLLY) was based on 13 026 reflections. The asymmetric unit contains Li+, Na+ and three SO42− ions, where one O and S lie on a threefold axis about which three O atoms are related with a threefold symmetry in each sulfate ion. Two of the O—S—O groups suffer from disorder. The net charges of the atoms in three independent sulfate ions were determined under ionic charge constraints. The S atoms have positive net electric charges and O atoms are negative. The components of the significant electric multipole moments in the principal axis directions are determined from the distribution of net atomic charges in each sulfate ion. Electric moments in the unit cell generate macroscopic electric moments in the crystal which interact with light. This interaction results in two axial vectors of second rank associated with an optical indicatrix. The ratio of the calculated axial vector components in the principal axis directions originating from the asymmetric unit is 1.0061 (1), which compares well with the ratio of 1.006 for the corresponding optical refractive indices of LiNaSO4 for λNa = 589.29 nm.
Supporting information
CCDC reference: 1057951
Data collection: Enfrad-Nonius CAD4; cell refinement: STADI STOE; data reduction: ABSCAD(Lundgren,1983); program(s) used to solve structure: MOLLY(Hansen,Coppens,1978); program(s) used to refine structure: UPALS(Lundgren,1983); molecular graphics: ?; software used to prepare material for publication: ?.
Lithium Sodium Sulphate
top
Crystal data top
LiNaSO4 | Dx = 2.527 Mg m−3 |
Mr = 125.99 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, P31c | Cell parameters from 37 reflections |
a = 7.6281 (2) Å | θ = 3.0–32.6° |
c = 9.8562 (4) Å | µ = 0.94 mm−1 |
V = 496.68 (1) Å3 | T = 296 K |
Z = 6 | Sphere, colourless |
F(000) = 372 | 0.12 mm (radius) |
Data collection top
Enfrad-Nonius CAD4/PDP 8/a diffractometer | 13026 reflections with I > 2σ(I) |
Graphite monochromator | θmax = 42.0°, θmin = 2.7° |
φ and ω scans | h = −13→13 |
Absorption correction: for a sphere Radius =0.115 mm | k = −14→14 |
Tmin = 0.847, Tmax = 0.847 | l = −18→18 |
15855 measured reflections | 5 standard reflections every 120 min |
13026 independent reflections | intensity decay: 16% |
Refinement top
Refinement on F2 | 0 restraints |
Least-squares matrix: full | w = 1/[σ2(Fo2) + (0.0644P)2 + 0.3608P] where P = (Fo2 + 2Fc2)/3 |
R[F2 > 2σ(F2)] = 0.019 | (Δ/σ)max = 0.001 |
wR(F2) = 0.048 | Δρmax = 0.4 e Å−3 |
S = 1.02 | Δρmin = −0.6 e Å−3 |
13026 reflections | Extinction correction: Becker-Coppens(Ref.20),Type 1 Lorenzian anisotropic |
87 parameters | |
Special details top
Experimental. The "mu"-value is basing on mass absorption coefficients=("mu"/"rho") for
Li=0.198, Na=3.04, S=9.99 and for O=1.22, taken from:
http//chemistry.bd.psu.edu/jircitano/Absortion20%Coefficients.pdf,
which give the "Mu"-value=9.420cm(-1)=0.942 mm(-1). |
Refinement. "Refine_instruction_details" is not loaded in dictionaries!
The rest of "ALERT Level A problems" will be explained soon.
Ueq-values down are calculated according to Ueq=(1/3)Σi[Σj(UijAiAjaiaj)],
where Ai,Aj are cell dimensions in real and ai,aj in reciprocal space
respectively. Intern Tables(2005)Vol.G p.103. Cross terms are omitted! |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
Li | 0.03235 (10) | 0.24471 (10) | 0.25838 (7) | 0.0221 (3) | |
Na | 0.02360 (2) | 0.54565 (2) | 0.486529 (19) | 0.02234 (7) | |
S1 | 0 | 0 | 0 | 0.01304 (4) | |
O1 | 0 | 0 | 0.15240 (4) | 0.01458 (10) | |
O4 | 0.20993 (3) | 0.10891 (3) | −0.04959 (3) | 0.01784 (9) | |
S2 | 0.333333 | 0.666667 | 0.194782 (19) | 0.01304 (4) | |
O2 | 0.333333 | 0.666667 | 0.34362 (5) | 0.02316 (14) | |
O5 | 0.22613 (4) | 0.45742 (4) | 0.14297 (3) | 0.02263 | |
S3 | 0.666667 | 0.333333 | 0.261023 (19) | 0.01356 (4) | |
O3 | 0.666667 | 0.333333 | 0.11266 (5) | 0.02517 (15) | |
O6 | 0.47505 (5) | 0.16841 (5) | 0.31290 (4) | 0.025573 (13) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Li | 0.0220 (3) | 0.0160 (3) | 0.0157 (3) | 0.0021 (2) | 0.0027 (2) | 0.0113 (2) |
Na | 0.01608 (6) | 0.02144 (7) | 0.01699 (7) | −0.00254 (6) | 0.00152 (6) | 0.00553 (5) |
S1 | 0.01142 (2) | 0.01142 (2) | 0.00865 (5) | 0 | 0 | 0.00571 (1) |
O1 | 0.01329 (8) | 0.01329 (8) | 0.00830 (15) | 0 | 0 | 0.00665 (4) |
O4 | 0.01301 (9) | 0.01602 (9) | 0.01481 (9) | 0.00001 (7) | 0.00440 (7) | 0.00565 (7) |
S2 | 0.01127 (2) | 0.01127 (2) | 0.00907 (5) | 0 | 0 | 0.00563 (1) |
O2 | 0.02269 (13) | 0.02269 (13) | 0.00896 (16) | 0 | 0 | 0.01134 (6) |
O5 | 0.02479 (12) | 0.01216 (9) | 0.01863 (10) | −0.00361 (7) | 0.00204 (8) | 0.00578 (8) |
S3 | 0.01156 (2) | 0.01156 (2) | 0.00986 (5) | 0 | 0 | 0.00578 (1) |
O3 | 0.02528 (13) | 0.02528 (13) | 0.00810 (18) | 0 | 0 | 0.01264 (7) |
O6 | 0.01739 (12) | 0.02893 (16) | 0.02375 (14) | 0.00730 (11) | 0.00217 (9) | −0.00282 (10) |
Geometric parameters (Å, º) top
S1—O1 | 1.5021 (4) | Li—O6ii | 1.8922 (7) |
S1—O4 | 1.4708 (2) | Na—O2 | 2.4975 (3) |
S2—O2 | 1.4670 (5) | Na—O3i | 2.4081 (3) |
S2—O5 | 1.4738 (3) | Na—O4i | 2.9623 (3) |
S3—O3 | 1.4623 (5) | Na—O4iii | 2.4213 (3) |
S3—O6 | 1.4635 (3) | Na—O5iv | 2.6811 (3) |
Li—O1 | 2.0435 (7) | Na—O5iii | 2.4724 (3) |
Li—O4i | 2.0368 (7) | Na—O6v | 2.9835 (4) |
Li—O5 | 1.9270 (7) | Na—O6ii | 2.3933 (4) |
| | | |
O1—S1—O4 | 109.41 (1) | O3i—Na—O4iii | 90.00 (1) |
O4—S1—O4ii | 109.53 (1) | O3i—Na—O5iv | 99.68 (1) |
O2—S2—O5 | 110.28 (1) | O3i—Na—O5iii | 107.33 (1) |
O5—S2—O5vi | 108.65 (1) | O3i—Na—O6ii | 140.41 (1) |
O3—S3—O6 | 110.45 (2) | O3i—Na—O6v | 163.14 (1) |
O6—S3—O6vii | 108.48 (2) | O4i—Na—O4iii | 152.09 (1) |
O1—Li—O4i | 105.52 (3) | O4i—Na—O5iv | 70.18 (1) |
O1—Li—O5 | 99.14 (3) | O4i—Na—O5iii | 125.34 (1) |
O1—Li—O6ii | 129.05 (4) | O4i—Na—O6ii | 64.58 (1) |
O4i—Li—O5 | 120.60 (3) | O4i—Na—O6v | 115.46 (1) |
O4i—Li—O6ii | 95.11 (3) | O4iii—Na—O5iv | 137.35 (1) |
O5—Li—O6ii | 109.47 (3) | O4iii—Na—O5iii | 82.23 (1) |
O2—Na—O3i | 65.41 (1) | O4iii—Na—O6ii | 116.57 (1) |
O2—Na—O4i | 71.07 (1) | O4iii—Na—O6v | 73.34 (1) |
O2—Na—O4iii | 81.02 (1) | O5iv—Na—O5iii | 55.19 (1) |
O2—Na—O5iv | 140.60 (1) | O5iv—Na—O6ii | 80.75 (1) |
O2—Na—O5iii | 161.69 (1) | O5iv—Na—O6v | 94.53 (1) |
O2—Na—O6ii | 89.07 (1) | O5iii—Na—O6ii | 105.06 (1) |
O2—Na—O6v | 108.29 (1) | O5iii—Na—O6v | 73.62 (1) |
O3i—Na—O4i | 78.22 (1) | O6ii—Na—O6v | 51.00 (1) |
Symmetry codes: (i) y, x, z+1/2; (ii) −y, x−y, z; (iii) x−y, −y+1, z+1/2; (iv) −x, y−x, z+1/2; (v) y−x, −x+1, z; (vi) −y+1, x−y+1, z; (vii) −y+1, x−y, z. |
Atomic coordinates,charges and kappa top | x | y | z | Charge | Kappa |
Li+ | 0.032352 (99) | 0.244714 (96) | 0.258378 (69) | +1 | 1 |
Na+ | 0.023595 (23) | 0.545654 (24) | 0.486529 (19) | +1 | 1 |
S(1) | 0 | 0 | 0 | +1.388 | 1.008 (1) |
O(1) | 0 | 0 | 0.152400 (39) | -0.829 | 0.981 (1) |
O(4) | 0.209934 (30) | 0.108907 (34) | -0.049591 (28) | -0.853 | 0.981 (2) |
S(2) | 1/3 | 2/3 | 0.194782 (19) | +1.918 | 1.142 (3) |
O(2) | 1/3 | 2/3 | 0.343620 (48) | -0.816 | 0.968 (1) |
O(5) | 0.226127 (42) | 0.457422 (36) | 0.142966 (31) | -1.034 | 0.974 (2) |
S(3) | 2/3 | 1/3 | 0.261023 (19) | +1.228 | 1.008 (2) |
O(3) | 2/3 | 1/3 | 0.112664 (50) | - 0.813 | 0.979 (1) |
O(6) | 0.475046 (45) | 0.168414 (54) | 0.312901 (38) | - 0.805 | 0.976 (2) |
Anisotropic temperature coefficients Uij top | U11 | U22 | U33 | U12 | U13 | U23 |
Li+ | 0.02197 (25) | 0.01598 (26) | 0.01569 (26) | 0.01125 (22) | 0.00267 (22) | .0.00205 (21) |
Na+ | 0.01608 (6) | 0.02144 (7) | 0.01699 (7) | 0.00553 (5) | 0.00152 (6) | -0.00254 (6) |
S(1) | 0.01142 (2) | 0.01142 (2) | 0.0865 (5) | 0.00571 (1) | 0 | 0 |
O(1) | 0.01329 (8) | 0.01329 (8) | 0.00830 (15) | 0.00665 (4) | 0 | 0 |
O(4) | 0.01301 (9) | 0.01602 (9) | 0.01481 (9) | 0.00565 (7) | 0.00440 (7) | 0.0001 (7) |
S(2) | 0.01127 (2) | 0.01127 (2) | 0.00907 (5) | 0.00563 (1) | 0 | 0 |
O(2) | 0.02269 (13) | 0.02269 (13) | 0.00896 (16) | 0.01134 (6) | 0 | 0 |
O(5) | 0.02479 (12) | 0.01216 (9) | 0.01863 (10) | 0.00578 (8) | 0.00204 (8) | -0.00361 (7) |
S(3) | 0.01156 (2) | 0.01156 (2) | 0.00986 (5) | 0.00578 (1) | 0 | 0 |
O(3) | 0.02528 (13) | 0.02528 (13) | 0.00810 (18) | 0.01264 (7) | 0 | 0 |
O(6) | 0.01739 (12) | 0.02893 (16) | 0.02375 (14) | -0.00282 (10) | 0.00217 (9) | 0.00730 (11) |