X-ray study of deformation density and spontaneous polarization in ferroelectric NaNO₂

The deformation electron density of ferroelectric sodium nitrite has been determined from X-ray diffraction data at 30 K, using Hirshfeld deformation functions. Owing to the strong correlation between odd terms of the deformation coefficients, constraints were imposed in the refinement. The net charges for Na, N and O atoms were estimated to be 0.27, 0.20 and -0.24 e, respectively. The calculated spontaneous polarization using these net charges and atomic dipole terms, 7.8 µC cm^-2, is much closer to the recently measured value, 12 µC cm^-2, as compared with the value calculated from the formal point charges (74 µC cm^-2).

Computing details

Data collection: DIF4; cell refinement: LATCON (Lundgren, 1983); data reduction: STOEDATRED (Lundgren, 1983); program(s) used to refine structure: DUPALS (Lundgren, 1983).

Sodium Nitrite

Crystal data

NNaO2	F(000) = 68
Mr = 69.0	Dx = 2.203 Mg m^−3
Orthorhombic, Im2m	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: I -2 -2	Cell parameters from 15 reflections
a = 3.5024 (6) Å	θ = 26.4–27.4°
b = 5.5209 (5) Å	µ = 0.39 mm^−1
c = 5.3789 (9) Å	T = 30 K
V = 104.01 (2) Å^3	Hexagonal prism, colourless
Z = 2	0.22 × 0.18 × 0.08 mm

Data collection

HUBER/STOE/ARACOR diffractometer	384 reflections with I > −3σ(I)
Radiation source: fine focus Philips Mo tube	Rint = 0.012
Graphite monochromator	θmax = 53.0°, θmin = 5.3°
ω/2θ scans	h = −7→7
Absorption correction: integration ABSSTOE (Lundgren, 1983)	k = −12→12
Tmin = 0.923, Tmax = 0.948	l = −12→0
1396 measured reflections	5 standard reflections every 240 min
384 independent reflections	intensity decay: 0.1%

Refinement

Refinement on F^2	Weighting scheme based on measured s.u.'s w = 1/σ^2(F^2)
Least-squares matrix: full	(Δ/σ)max = 0.031
R[F^2 > 2σ(F^2)] = 0.014	Δρmax = 0.11 e Å^−3
wR(F^2) = 0.022	Δρmin = −0.12 e Å^−3
S = 1.79	Extinction correction: Becker & Coppens (1975) type 1 Lorentzian isotropic
1390 reflections	Extinction coefficient: '0.177E4 (7)
68 parameters

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Na	0	0.58833 (4)	0	0.00573 (3)	.25
N	0	0.12277 (4)	0	0.00595 (4)	.25
O	0	0	0.19646 (3)	0.00685 (4)	.5

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Na	0.00623 (3)	0.00538 (3)	0.00559 (3)	0	0	0
N	0.00836 (4)	0.00461 (5)	0.00490 (4)	0	0	0
O	0.00886 (4)	0.00706 (5)	0.00462 (4)	0	0	0.00076 (4)

Geometric parameters (Å, º)

Na—N	2.5703 (3)	Na—O^ii	2.4434 (3)
Na—O^i	2.5064 (2)	N—O	1.2554 (1)
O—N—O^iii	114.65 (1)

Symmetry codes: (i) x, y+1, z; (ii) x−1/2, y+1/2, z−1/2; (iii) x, y, −z.