Effect of cationic substitution on the double-well hydrogen-bond potential in [K_1−x(NH₄)_x]₃H(SO₄)₂ proton conductors: a single-crystal neutron diffraction study

The structure of the mixed crystal [K_1−x(NH₄)_x]₃H(SO₄)₂ as obtained from single-crystal neutron diffraction is compared with the previously reported room-temperature neutron structure of crystalline K₃H(SO₄)₂. The two structures are very similar, as indicated by the high value of their isostructurality index (94.8%). It was found that the replacement of even a small amount (3%) of K⁺ with NH₄⁺ has a significant influence on the short strong hydrogen bond connecting the two SO₄²⁻ ions. Earlier optical measurements had revealed that the kinetics of the superionic transition in the solid solution [K_1−x(NH₄)_x]₃H(SO₄)₂ are much faster than in K₃H(SO₄)₂; this reported difference in the kinetics of the superionic phase transition in this class of crystal is explained on the basis of the difference in strength of the hydrogen-bond interactions in the two structures.

Computing details

Program(s) used to refine structure: SHELXL97 (Sheldrick, 1997).

(I)

Crystal data

HK2.91N0.09O8S2	Z = 2
Mr = 616.34	F(000) = 240
Monoclinic, C2/c	Dx = 2.574 Mg m^−3
a = 14.692 (2) Å	Neutron radiation, λ = 0.99600 Å
b = 5.681 (1) Å	Cell parameters from 50 reflections
c = 9.776 (1) Å	θ = 4.0–44.2°
β = 102.99 (1)°	T = 293 K
V = 795.08 (19) Å^3	, transparent

Data collection

Radiation source: Dhruva reactor	Rint = 0.040
Copper monochromator	θmax = 44.2°, θmin = 4.0°
1211 measured reflections	h = −20→12
1094 independent reflections	k = −7→7
606 reflections with I > 2σ(I)	l = −8→13

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.139	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.387	H atoms treated by a mixture of independent and constrained refinement
S = 1.10	w = 1/[σ^2(Fo^2) + (0.0853P)^2 + 0.8246P] where P = (Fo^2 + 2Fc^2)/3
1094 reflections	(Δ/σ)max < 0.001
65 parameters	Δρmax = 0.23 e Å^−3
0 restraints	Δρmin = −0.23 e Å^−3

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > 2sigma(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
K1	1.0000	−0.7536 (18)	0.7500	0.0279 (17)	0.97
N1	1.0000	−0.7536 (18)	0.7500	0.0279 (17)	0.03
K2	0.3045 (5)	0.7392 (13)	0.3503 (7)	0.0323 (14)	0.97
N2	0.3045 (5)	0.7392 (13)	0.3503 (7)	0.0323 (14)	0.03
S	0.3843 (5)	0.7653 (15)	0.0420 (8)	0.0221 (15)
O1	0.3478 (4)	0.9716 (8)	0.1016 (5)	0.0332 (11)
O2	0.4898 (4)	0.8071 (14)	0.0614 (10)	0.057 (2)
O3	0.3510 (4)	0.7563 (10)	0.8898 (5)	0.0349 (11)
O4	0.3644 (4)	0.5497 (8)	0.1075 (5)	0.0375 (13)
H1	0.5000	0.0000	0.0000	0.110 (15)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.035 (5)	0.027 (4)	0.021 (3)	0.000	0.005 (3)	0.000
N1	0.035 (5)	0.027 (4)	0.021 (3)	0.000	0.005 (3)	0.000
K2	0.043 (4)	0.024 (3)	0.031 (3)	−0.002	0.011 (3)	0.000 (3)
N2	0.043 (4)	0.024 (3)	0.031 (3)	−0.002	0.011 (3)	0.000 (3)
S	0.021 (3)	0.022 (3)	0.023 (3)	0.000 (3)	0.006 (2)	−0.001 (3)
O1	0.041 (3)	0.024 (2)	0.035 (2)	−0.0019 (18)	0.0093 (18)	−0.0071 (17)
O2	0.017 (2)	0.068 (5)	0.083 (6)	0.000 (3)	0.005 (3)	−0.030 (4)
O3	0.049 (3)	0.034 (2)	0.0251 (18)	−0.005 (2)	0.0149 (17)	−0.002 (2)
O4	0.057 (3)	0.025 (2)	0.029 (2)	0.006 (2)	0.005 (2)	0.0056 (18)
H1	0.021 (6)	0.25 (5)	0.055 (10)	0.018 (15)	−0.002 (6)	−0.07 (2)

Geometric parameters (Å, º)

S—O4	1.442 (10)	S—O2	1.537 (10)
S—O3^i	1.459 (9)	O3—S^ii	1.459 (9)
S—O1	1.464 (9)
O4—S—O3^i	111.6 (6)	O4—S—O2	112.1 (7)
O4—S—O1	112.0 (6)	O3^i—S—O2	103.2 (6)
O3^i—S—O1	111.4 (6)	O1—S—O2	106.1 (6)

Symmetry codes: (i) x, y, z−1; (ii) x, y, z+1.