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An X-ray diffraction study aimed at establishing the subtle details of the electron density and anharmonicity of the atomic vibrations in a stoichiometric monodomain single crystal of potassium niobate, KNbO3, has been conducted at room tem­per­ature (orthorhombic ferroelectric phase Amm2). The cation and anion displacements obtained from the experiment are weakly anharmonic without any manifestation of structural disorder. The chemical bond and interatomic interactions inside and between crystal substructures at the balance of intracrystalline forces are characterized in detail. The role of each of the ions in the formation of the ferroelectric phase was studied and the features of the electron-density deformation in the niobium and oxygen substructures, and the role of each of them in the occurrence of spontaneous polarization are established. The position-space distribution of electrostatic and quantum forces in KNbO3 is restored. It is emphasized that for the com­pleteness of the analysis of the nature of the ferroelectric properties it is necessary to consider both static and kinetic electronic factors, which are of a quantum origin. The experimental results and theoretical estimations by the Kohn–Sham calculation with periodic boundary conditions are in reasonable agreement, thus indicating the physical significance of the findings of this study.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S2052520621006892/yh5015sup1.cif
Contains datablock I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S2052520621006892/yh5015Isup2.hkl
Contains datablock I

pdf

Portable Document Format (PDF) file https://doi.org/10.1107/S2052520621006892/yh5015sup3.pdf
Additional figures

CCDC reference: 2094437

Computing details top

Data collection: CAD-4-PC V1.2 (Enraf-Nonius ,1993); cell refinement: CAD-4-PC V1.2 (Enraf-Nonius ,1993); data reduction: CAD-4-PC V1.2 (Enraf-Nonius ,1993); program(s) used to solve structure: SHELXT-2014/4 (Sheldrick, 2014); program(s) used to refine structure: SHELXL2018/3 (Sheldrick, 2018).

(I) top
Crystal data top
KNbO3Dx = 4.620 Mg m3
Mr = 180.01Mo Kα radiation, λ = 0.71073 Å
Orthorhombic, Amm2Cell parameters from 24 reflections
a = 3.9719 (7) Åθ = 45.5–47.3°
b = 5.6943 (9) ŵ = 5.99 mm1
c = 5.7209 (9) ÅT = 293 K
V = 129.39 (4) Å3Plate, colorless
Z = 20.20 × 0.12 × 0.04 mm
F(000) = 168
Data collection top
Enraf-Nonius CAD-4
diffractometer
1097 reflections with I > 2σ(I)
Radiation source: fine-focus tubeRint = 0.032
β-filter monochromatorθmax = 59.9°, θmin = 5.1°
ω/2θ scansh = 99
Absorption correction: analytical
(see. N.W. Alcock (1970). Cryst. Computing, p271)
k = 1313
Tmin = 0.498, Tmax = 0.795l = 1313
11554 measured reflections3 standard reflections every 60 min
1098 independent reflections intensity decay: 0.0%
Refinement top
Refinement on F2 w = 1/[σ2(Fo2) + (0.011P)2 + 0.0047P]
where P = (Fo2 + 2Fc2)/3
Least-squares matrix: full(Δ/σ)max = 0.001
R[F2 > 2σ(F2)] = 0.007Δρmax = 0.47 e Å3
wR(F2) = 0.017Δρmin = 0.91 e Å3
S = 1.08Extinction correction: SHELXL-2018/3 (Sheldrick 2018), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
1098 reflectionsExtinction coefficient: 0.091 (3)
19 parametersAbsolute structure: Flack x determined using 520 quotients [(I+)-(I-)]/[(I+)+(I-)] (Parsons, Flack and Wagner, Acta Cryst. B69 (2013) 249-259).
0 restraintsAbsolute structure parameter: 0.099 (13)
Special details top

Experimental. Initial single crystal of KNbO3

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.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Nb10.5000000.0000000.5000000.00419 (2)
K10.0000000.0000000.01529 (10)0.00796 (5)
O10.0000000.0000000.53578 (13)0.00726 (7)
O20.5000000.24702 (9)0.28431 (9)0.00733 (5)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Nb10.00533 (2)0.00388 (2)0.00335 (3)0.0000.0000.000
K10.00794 (4)0.00830 (4)0.00763 (16)0.0000.0000.000
O10.00442 (12)0.00921 (16)0.00814 (18)0.0000.0000.000
O20.00866 (12)0.00695 (11)0.00639 (13)0.0000.0000.00207 (11)
Geometric parameters (Å, º) top
Nb1—O21.8711 (5)K1—O1viii2.7433 (11)
Nb1—O2i1.8712 (5)K1—O2ix2.7866 (6)
Nb1—O1ii1.9965 (4)K1—O2x2.7866 (6)
Nb1—O11.9965 (4)K1—O2xi2.7866 (6)
Nb1—O2iii2.1727 (5)K1—O2xii2.7866 (6)
Nb1—O2iv2.1727 (5)K1—O1xiii2.8496 (5)
Nb1—K1ii3.4108 (6)K1—O1xii2.8496 (5)
Nb1—K13.4108 (6)K1—O22.8794 (6)
Nb1—K1v3.4725 (4)K1—O2i2.8795 (6)
Nb1—K1iv3.4725 (4)K1—O2xiv2.8795 (6)
Nb1—K1vi3.4725 (4)K1—O2xv2.8795 (6)
Nb1—K1vii3.4725 (4)K1—O12.9777 (11)
O2—Nb1—O2i97.48 (4)O1viii—K1—O1xii92.36 (2)
O2—Nb1—O1ii93.876 (14)O2ix—K1—O1xii60.198 (14)
O2i—Nb1—O1ii93.876 (14)O2x—K1—O1xii122.412 (17)
O2—Nb1—O193.877 (14)O2xi—K1—O1xii122.412 (17)
O2i—Nb1—O193.876 (14)O2xii—K1—O1xii60.198 (14)
O1ii—Nb1—O1168.23 (4)O1xiii—K1—O1xii175.29 (4)
O2—Nb1—O2iii89.729 (13)O1viii—K1—O2122.309 (15)
O2i—Nb1—O2iii172.79 (3)O2ix—K1—O2175.96 (3)
O1ii—Nb1—O2iii85.599 (16)O2x—K1—O260.620 (10)
O1—Nb1—O2iii85.598 (16)O2xi—K1—O2119.502 (10)
O2—Nb1—O2iv172.79 (3)O2xii—K1—O290.828 (12)
O2i—Nb1—O2iv89.729 (13)O1xiii—K1—O259.331 (14)
O1ii—Nb1—O2iv85.599 (16)O1xii—K1—O2117.782 (19)
O1—Nb1—O2iv85.598 (16)O1viii—K1—O2i122.309 (15)
O2iii—Nb1—O2iv83.06 (3)O2ix—K1—O2i119.502 (10)
O2—Nb1—K1ii57.578 (14)O2x—K1—O2i90.828 (12)
O2i—Nb1—K1ii57.579 (13)O2xi—K1—O2i175.96 (3)
O1ii—Nb1—K1ii60.27 (2)O2xii—K1—O2i60.620 (10)
O1—Nb1—K1ii131.49 (2)O1xiii—K1—O2i117.782 (19)
O2iii—Nb1—K1ii127.490 (12)O1xii—K1—O2i59.331 (13)
O2iv—Nb1—K1ii127.490 (12)O2—K1—O2i58.48 (2)
O2—Nb1—K157.578 (14)O1viii—K1—O2xiv122.309 (15)
O2i—Nb1—K157.579 (14)O2ix—K1—O2xiv60.620 (10)
O1ii—Nb1—K1131.49 (2)O2x—K1—O2xiv175.96 (3)
O1—Nb1—K160.27 (2)O2xi—K1—O2xiv90.828 (12)
O2iii—Nb1—K1127.490 (12)O2xii—K1—O2xiv119.502 (10)
O2iv—Nb1—K1127.490 (12)O1xiii—K1—O2xiv117.782 (19)
K1ii—Nb1—K171.219 (17)O1xii—K1—O2xiv59.331 (14)
O2—Nb1—K1v53.147 (16)O2—K1—O2xiv115.38 (3)
O2i—Nb1—K1v129.271 (14)O2i—K1—O2xiv87.21 (2)
O1ii—Nb1—K1v55.146 (7)O1viii—K1—O2xv122.309 (15)
O1—Nb1—K1v124.494 (7)O2ix—K1—O2xv90.828 (11)
O2iii—Nb1—K1v55.773 (15)O2x—K1—O2xv119.502 (10)
O2iv—Nb1—K1v121.652 (14)O2xi—K1—O2xv60.620 (10)
K1ii—Nb1—K1v71.789 (8)O2xii—K1—O2xv175.96 (3)
K1—Nb1—K1v110.700 (12)O1xiii—K1—O2xv59.331 (14)
O2—Nb1—K1iv129.271 (14)O1xii—K1—O2xv117.782 (19)
O2i—Nb1—K1iv53.147 (16)O2—K1—O2xv87.21 (2)
O1ii—Nb1—K1iv124.494 (7)O2i—K1—O2xv115.38 (3)
O1—Nb1—K1iv55.146 (6)O2xiv—K1—O2xv58.48 (2)
O2iii—Nb1—K1iv121.652 (15)O1viii—K1—O1180.0
O2iv—Nb1—K1iv55.773 (15)O2ix—K1—O1118.307 (16)
K1ii—Nb1—K1iv110.700 (12)O2x—K1—O1118.307 (16)
K1—Nb1—K1iv71.789 (8)O2xi—K1—O1118.307 (16)
K1v—Nb1—K1iv177.113 (18)O2xii—K1—O1118.307 (16)
O2—Nb1—K1vi53.147 (16)O1xiii—K1—O187.64 (2)
O2i—Nb1—K1vi129.271 (14)O1xii—K1—O187.64 (2)
O1ii—Nb1—K1vi124.494 (7)O2—K1—O157.691 (15)
O1—Nb1—K1vi55.146 (6)O2i—K1—O157.691 (15)
O2iii—Nb1—K1vi55.773 (15)O2xiv—K1—O157.691 (15)
O2iv—Nb1—K1vi121.652 (14)O2xv—K1—O157.691 (15)
K1ii—Nb1—K1vi110.700 (12)Nb1xv—O1—Nb1168.23 (4)
K1—Nb1—K1vi71.789 (8)Nb1xv—O1—K1xvi95.88 (2)
K1v—Nb1—K1vi69.768 (13)Nb1—O1—K1xvi95.88 (2)
K1iv—Nb1—K1vi110.155 (13)Nb1xv—O1—K1iv89.758 (3)
O2—Nb1—K1vii129.271 (14)Nb1—O1—K1iv89.758 (3)
O2i—Nb1—K1vii53.147 (16)K1xvi—O1—K1iv92.36 (2)
O1ii—Nb1—K1vii55.146 (6)Nb1xv—O1—K1vi89.758 (3)
O1—Nb1—K1vii124.494 (7)Nb1—O1—K1vi89.758 (3)
O2iii—Nb1—K1vii121.652 (14)K1xvi—O1—K1vi92.36 (2)
O2iv—Nb1—K1vii55.773 (15)K1iv—O1—K1vi175.29 (4)
K1ii—Nb1—K1vii71.789 (8)Nb1xv—O1—K184.12 (2)
K1—Nb1—K1vii110.700 (12)Nb1—O1—K184.12 (2)
K1v—Nb1—K1vii110.155 (13)K1xvi—O1—K1180.0
K1iv—Nb1—K1vii69.768 (13)K1iv—O1—K187.64 (2)
K1vi—Nb1—K1vii177.113 (18)K1vi—O1—K187.64 (2)
O1viii—K1—O2ix61.693 (16)Nb1—O2—Nb1xiii172.79 (3)
O1viii—K1—O2x61.693 (16)Nb1—O2—K1v94.35 (2)
O2ix—K1—O2x123.39 (3)Nb1xiii—O2—K1v90.702 (18)
O1viii—K1—O2xi61.693 (16)Nb1—O2—K1vi94.35 (2)
O2ix—K1—O2xi62.25 (2)Nb1xiii—O2—K1vi90.702 (18)
O2x—K1—O2xi90.91 (2)K1v—O2—K1vi90.91 (2)
O1viii—K1—O2xii61.693 (16)Nb1—O2—K189.155 (19)
O2ix—K1—O2xii90.91 (2)Nb1xiii—O2—K185.628 (19)
O2x—K1—O2xii62.25 (2)K1v—O2—K1175.96 (3)
O2xi—K1—O2xii123.39 (3)K1vi—O2—K190.828 (12)
O1viii—K1—O1xiii92.36 (2)Nb1—O2—K1ii89.155 (19)
O2ix—K1—O1xiii122.412 (17)Nb1xiii—O2—K1ii85.628 (19)
O2x—K1—O1xiii60.198 (14)K1v—O2—K1ii90.828 (11)
O2xi—K1—O1xiii60.198 (14)K1vi—O2—K1ii175.96 (3)
O2xii—K1—O1xiii122.412 (17)K1—O2—K1ii87.21 (2)
Symmetry codes: (i) x+1, y, z; (ii) x+1, y, z; (iii) x+1, y+1/2, z+1/2; (iv) x, y1/2, z+1/2; (v) x+1, y+1/2, z+1/2; (vi) x, y+1/2, z+1/2; (vii) x+1, y1/2, z+1/2; (viii) x, y, z1; (ix) x1, y1/2, z1/2; (x) x+1, y+1/2, z1/2; (xi) x, y+1/2, z1/2; (xii) x, y1/2, z1/2; (xiii) x, y+1/2, z1/2; (xiv) x, y, z; (xv) x1, y, z; (xvi) x, y, z+1.
 

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