Investigations of the bond-selective response in a piezoelectric Li₂SO₄·H₂O crystal to an applied external electric field

Piezoelectric lithium sulfate monohydrate, Li₂SO₄·H₂O, was analyzed with respect to the relationship between the static structural properties of the crystal and its response to an external electric field. The static electron density was determined via standard low-temperature X-ray data collection at 90 (5) K using an Enraf–Nonius CAD-4 diffractometer, Mo Kα radiation and multipole model refinement. Then a synchrotron-radiation experiment using the D3 beamline at HASYLAB was conducted in order to investigate the structural deformations in Li₂SO₄·H₂O caused by an applied external electric field. In particular, the shifts of Bragg-peak positions induced by the electric field were measured and the piezoelectric constants d₂₁₁, d₂₂₂, d₂₃₃ and d₂₁₃ of Li₂SO₄·H₂O were obtained from the shifts. With the same experimental setup the variations of more than 100 Bragg intensities were measured under an applied electric field. The data were used to refine the corresponding displacements of individual atoms within the unit cell. The distortions of the cation–anion bond lengths in the LiO₄, LiO₃(H₂O) and SO₄ tetrahedra were evaluated and then analyzed in terms of the electron-density-related properties of the Li—O and S—O bonds. The two lithium structural units were found to be strongly deformed by the applied electric field, while the SO₄ tetrahedron changed less. This is in agreement with the low bond strength of the Li—O bonds.

Computing details

Data collection: Enraf Nonius CAD-4; cell refinement: Enraf Nonius CAD-4; data reduction: JANA2000; program(s) used to refine structure: MOLLYN; molecular graphics: MOLLYN.

Figures

Lithium sulfate monohydrate

Crystal data

H2Li2O5S	F(000) = 128
Mr = 127.96	Mo Kα radiation, λ = 0.71073 Å
Monoclinic, P21	Cell parameters from 25 reflections
a = 5.4484 (2) Å	θ = 18–26°
b = 4.8339 (2) Å	µ = 0.68 mm^−1
c = 8.1407 (2) Å	T = 90 K
β = 107.191 (2)°	Sphere, colorless
V = 204.82 Å^3	0.24 × 0.24 × 0.24 × 0.12 (radius) mm
Z = 2

Data collection

Enraf Nonius CAD-4 diffractometer	3930 independent reflections
Radiation source: fine-focus sealed tube	3865 reflections with > 3σ(I)
Graphite monochromator	Rint = 0.028
profile data from ω/2θ scans	θmax = 58.5°, θmin = 4.0°
Absorption correction: for a sphere Spherical absorption correction with JANA2000, V. Petricek and M. Dusek, (Institute of Physics, Praha, Czech Republic, 2000), The crystallographic computing system JANA2000	h = −12→12
Tmin = 0.901, Tmax = 0.901	k = −11→11
7853 measured reflections	l = −19→19

Refinement

Refinement on F	1 restraint
R[F^2 > 2σ(F^2)] = 0.014	Only H-atom coordinates refined
wR(F^2) = 0.018	Weighting scheme based on measured s.u.'s
S = 5.18
3865 reflections	Extinction correction: B-C type 1 Lorentzian isotropic
127 parameters	Absolute structure: Karppinen et al., 1986, J. Phys. Chem. 85, 5521-5227

Special details

Refinement. Refinement of F against ALL reflections. The conventional R-factor, R, the weighted R-factor, wR, and goodness of fit,S, are based on F. The threshold expression of I > σ(I) is used to choose the reflections for refinement and for calculating R-factors(gt) etc.

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

	x	y	z	Biso*/Beq	Occ. (<1)
Li(1)	0.30339 (16)	0.4964 (2)	0.99293 (11)
Li(2)	0.56016 (17)	0.4888 (2)	0.39517 (11)
S	0.29250 (1)	0	0.20806 (1)
O(1)	0.02096 (6)	0.07358 (8)	0.17099 (5)
O(2)	0.43702 (6)	0.11091 (6)	0.37855 (4)
O(3)	0.39822 (6)	0.12064 (6)	0.07650 (4)
O(4)	0.32514 (6)	−0.30371 (6)	0.20988 (4)
O(5)	0.91357 (8)	0.46525 (8)	0.40340 (6)
H(1)	0.963 (4)	0.401 (6)	0.327 (3)
H(2)	0.996 (5)	0.603 (6)	0.438 (3)
DUM1	0.00076	0.77350	1.04600		0.0
DUM2	0.42000	0.32050	1.29350		0.0
DUM3	0.20200	0.31840	0.19330		0.0
DUM4	0.79040	0.08740	0.38680		0.0
DUM5	0.16550	0.18450	0.34150		0.0
DUM6	0.12670	0.19420	0.03940		0.0
DUM7	0.61690	0.07720	0.37200		0.0
DUM8	0.55730	0.61090	0.16890		0.0
DUM9	0.00500	0.62060	0.06230		0.0
DUM10	0.06840	−0.29600	−0.19240		0.0
DUM11	0.88240	0.26200	0.29190		0.0

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Li(1)	0.00883 (19)	0.0083 (2)	0.00831 (8)	0.0006 (5)	0.0029 (2)	0.0013 (3)
Li(2)	0.00875 (19)	0.0083 (3)	0.00824 (8)	0.0004 (5)	0.0020 (2)	0.0006 (3)
S	0.00396 (2)	0.00293 (2)	0.00316 (1)	0.00020 (3)	0.00114 (2)	0.00008 (2)
O(1)	0.00404 (7)	0.00944 (9)	0.00746 (3)	0.00117 (13)	0.00110 (8)	−0.00109 (9)
O(2)	0.00756 (6)	0.00560 (6)	0.00415 (2)	−0.001232 (10)	0.00033 (6)	−0.00078 (7)
O(3)	0.00863 (6)	0.00590 (6)	0.00636 (3)	0.00109 (12)	0.00462 (7)	0.00178 (7)
O(4)	0.00968 (7)	0.00306 (6)	0.00598 (3)	0.00049 (10)	0.00173 (7)	0.00017 (6)
O(5)	0.00862 (9)	0.01230 (12)	0.01352 (4)	−0.00078 (14)	0.00545 (9)	−0.00228 (11)