Electron density and atomic displacements in KTaO₃

The atomic interactions and anharmonicity of atomic displacements in the virtual ferroelectric KTaO₃, potassium tantalate, have been studied using accurate single-crystal X-ray diffraction at room temperature. The multipole analysis of electron density and Gram-Charlier series description of anharmonic atomic displacements allowed us to perform a quantitative analysis of the chemical bonding and atomic motion in this crystal. Closed-shell interactions between Ta-O and K-O pairs of atoms were found, while no interaction was observed for the Ta-K and O-O atomic pairs. The character of the anharmonic atomic displacements is discussed and compared with those in SrTiO₃.

Computing details

Data reduction: Zucker et al. (1983); program(s) used to solve structure: Zucker et al. (1983); program(s) used to refine structure: Protas, J.(1997).

(KTaO3)

Crystal data

KO3Ta	Mo Kα radiation, λ = 0.71069 Å
Mr = 268.05	Cell parameters from 25 reflections
Cubic, Pm3m	θ = 30–45°
Hall symbol: -P 4 2 3	µ = 44.68 mm^−1
a = 3.9883 (2) Å	T = 298 K
V = 63.44 Å^3	Sphere, colorless
Z = 1	0.11 × 0.11 × 0.11 × 0.06 (1) (radius) mm
Dx = 7.016 Mg m^−3

Data collection

Enraf Nonius CAD-4 diffractometer	Rint = 0.020
ω/2θ scans	θmax = 64.5°
Absorption correction: for a sphere Zucker et al. (1983)	h = −10→10
	k = 0→7
2183 measured reflections	l = 0→5
148 independent reflections	3 standard reflections every 100 reflections
148 reflections with F > 3σ(F)	intensity decay: none

Refinement

Refinement on F	w = 1/(s**2 + 0.00002F**2)
R[F^2 > 2σ(F^2)] = 0.004	(Δ/σ)max < 0.001
wR(F^2) = 0.005	Δρmax = 0.1 e Å^−3
S = 1.05	Δρmin = −0.1 e Å^−3
148 reflections	Extinction correction: Becker-Coppens type 2
28 parameters	Extinction coefficient: 0.02085

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

	x	y	z	Uiso*/Ueq
K	0.5	0.5	0.5	0.0082 (2)*
O	0.5	0.0	0.0	0.0073 (8)
Ta	0.0	0.0	0.0	0.00332 (3)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O	0.0035 (8)	0.0092 (4)	0.0092 (4)	0.0	0.0	0.0

Geometric parameters (Å, º)

K—Ta	3.454	Ta—O	1.994
K—O	2.820
Ta—O—Ta	0.0	K—Ta—K	0.0
O—K—O	90.0	K—Ta—O	54.7