Crystal structure, atomic net charges and electric moments in pyroelectric LiNaSO₄ at 296 K

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 λ_Na = 589.29 nm.

Computing details

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

Crystal data

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) Å^3	T = 296 K
Z = 6	Sphere, colourless
F(000) = 372	0.12 mm (radius)

Data collection

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

Refinement on F^2	0 restraints
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0644P)^2 + 0.3608P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.019	(Δ/σ)max = 0.001
wR(F^2) = 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

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 (Ų)

	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 (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
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)

S1—O1	1.5021 (4)	Li—O6^ii	1.8922 (7)
S1—O4	1.4708 (2)	Na—O2	2.4975 (3)
S2—O2	1.4670 (5)	Na—O3^i	2.4081 (3)
S2—O5	1.4738 (3)	Na—O4^i	2.9623 (3)
S3—O3	1.4623 (5)	Na—O4^iii	2.4213 (3)
S3—O6	1.4635 (3)	Na—O5^iv	2.6811 (3)
Li—O1	2.0435 (7)	Na—O5^iii	2.4724 (3)
Li—O4^i	2.0368 (7)	Na—O6^v	2.9835 (4)
Li—O5	1.9270 (7)	Na—O6^ii	2.3933 (4)
O1—S1—O4	109.41 (1)	O3^i—Na—O4^iii	90.00 (1)
O4—S1—O4^ii	109.53 (1)	O3^i—Na—O5^iv	99.68 (1)
O2—S2—O5	110.28 (1)	O3^i—Na—O5^iii	107.33 (1)
O5—S2—O5^vi	108.65 (1)	O3^i—Na—O6^ii	140.41 (1)
O3—S3—O6	110.45 (2)	O3^i—Na—O6^v	163.14 (1)
O6—S3—O6^vii	108.48 (2)	O4^i—Na—O4^iii	152.09 (1)
O1—Li—O4^i	105.52 (3)	O4^i—Na—O5^iv	70.18 (1)
O1—Li—O5	99.14 (3)	O4^i—Na—O5^iii	125.34 (1)
O1—Li—O6^ii	129.05 (4)	O4^i—Na—O6^ii	64.58 (1)
O4^i—Li—O5	120.60 (3)	O4^i—Na—O6^v	115.46 (1)
O4^i—Li—O6^ii	95.11 (3)	O4^iii—Na—O5^iv	137.35 (1)
O5—Li—O6^ii	109.47 (3)	O4^iii—Na—O5^iii	82.23 (1)
O2—Na—O3^i	65.41 (1)	O4^iii—Na—O6^ii	116.57 (1)
O2—Na—O4^i	71.07 (1)	O4^iii—Na—O6^v	73.34 (1)
O2—Na—O4^iii	81.02 (1)	O5^iv—Na—O5^iii	55.19 (1)
O2—Na—O5^iv	140.60 (1)	O5^iv—Na—O6^ii	80.75 (1)
O2—Na—O5^iii	161.69 (1)	O5^iv—Na—O6^v	94.53 (1)
O2—Na—O6^ii	89.07 (1)	O5^iii—Na—O6^ii	105.06 (1)
O2—Na—O6^v	108.29 (1)	O5^iii—Na—O6^v	73.62 (1)
O3^i—Na—O4^i	78.22 (1)	O6^ii—Na—O6^v	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.