X-ray analysis of ferroelectric domains in the paraelectric phase of NaNO<sub>2</sub>

Canut, M. L.; Hösemann, R.

doi:10.1107/s0365110x64002523

Cited by 24 publications

(7 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1). There are also similarities to the structure of the ferroelectric phase of sodium nitrite, NaNO2 (Canut & Hosemann, 1964) where NO~-groups in parallel planes are stacked along b and the Na + ion is six-coordinated to oxygen forming triangular prisms. In this case, of course, the NOz groups are oriented with their dipole moments parallel.…”

Section: Table 2 Distances (A) and Angles (°) Of Na + Coordination Imentioning

confidence: 80%

Anhydrous sodium chlorite

Tarımcı¹,

Rosenstein²,

Schempp³

1976

Acta Crystallogr Sect B

View full text Add to dashboard Cite

NaC1Oz, I2/a, monoclinic, a = 6.456 (2), b = 6.442 (2), c=6.813 (2)A, fl=120.6 (1) °, Z=4, D,= 2.468 gcm -3. The CI-O bond length is 1"564 (3) A and the OCIO bond angle is 108.6 (1) °, which are values close to those found in NaCIOz.3HzO. The CIO~ groups are oriented with antiparallel dipole moments along b and the O atoms form a sixfold coordination unit about the Na + ions in the form of a distorted triangular prism.Abstract. The space group is P] and not P 1 ; the asymmetric unit is [CsHsN4S.CuCI2.H20]. The structure has now been refined in P] to R =0-046 for 1584 observed data and yields satisfactory bond lengths and angles.

show abstract

Section: Table 2 Distances (A) and Angles (°) Of Na + Coordination Imentioning

confidence: 80%

Anhydrous sodium chlorite

Tarımcı¹,

Rosenstein²,

Schempp³

1976

Acta Crystallogr Sect B

View full text Add to dashboard Cite

show abstract

“…For the infinite crystal it concides with the Patterson function in current use, so that P(r) = lim ~ gav dis(r) = ν* Σ <F (hkl)> 2 e 2 "« hx + * + ">, In performing the convolution square of the real disordered infinite crystal, terms of two different kind are obtained (see also CANUT and HOSEMANN, 1964). A series of terms is due to the selfimages of each molecule, whose average value is proportional to Σ<2(τ) = ZQu(r).…”

Section: Q^^(r) = Qcqn(t)*zci(r)mentioning

confidence: 99%

On the significance of two new Patterson functions for disordered crystals

CANUT-AMORÓS¹

1967

Zeitschrift Für Kristallographie - Crystalline Materials

View full text Add to dashboard Cite

AuszugEs werden zwei neue Patterson-Funktionen definiert: die eine, AP 0T (r) = [P 0 (r) -P r (r)] · s Zelle (r), für den thermisch bewegten Kristall und die andere, ΔΡ ΟΑ {Γ) = [P B (r)-P(r)] · Szelle (r), für den ungeordneten Kristall. Diese Funktionen ergeben zwei neue FourierBeziehungen :Es ist möglich, aus den neuen Differenz-Pattersonfunktionen die stetigen Funktionen der diffusen Streuung, die von der Wärmebewegung oder der Lagenunordnung herrühren, ohne Kenntnis der Kristallstruktur zu berechnen. AbstractOn account of the Fourier-transform reciprocity theorem it is possible to go back and forth from physical space to reciprocal space. One mechanism involves Fourier summations of sampled values in one space, leading to a continuous, periodic function in the other. Two new Patterson functions are defined, one for a thermally agitated crystal, ZlP 0I ,(r) = [P 0 (r) -Pj-(r)] · s cel] (r), and another ΔΡ»ΑΓ) = [JVr) -P(Γ)] • *«"(r), 242 MABISA CANUT-AMOROS for a disordered crystal. These new functions yield to two new Fourier mates Τ Τ-1 and τ ^wW^Wf*)· τ~ι The new difference Patterson functions allow one to calculate the continuous diffuse-scattering functions arising from thermal and positional disorder, respectively, without any previous knowledege of the crystal structure. The quasi periodic Q functions of the thermally agitated or disordered molecular crystals are analyzed in terms of only two motifs calculated in terms of adequate Patterson functions.It is a well known fact that, in real crystals, at least thermal agitation disturbs the ideal periodicity. Wide use in crystal-structure analysis of Fourier series with coefficients l-i^il 2 (i-e · the Patterson series) implies, however, an infinite and strictly periodic structure, that is to an hypothetical structure whose electron density is identical in all unit cells, and which corresponds to the electron density of the real crystal under study, but averaged over time and space. The Patterson synthesis obtained from experimental data thus corresponds to the Patterson function of the hypothetical average crystal.On the other hand, the intensity diffracted by the real crystal is basically of two kinds: the Bragg intensities located at the lattice points of the reciprocal lattice, and a diffuse-scattering intensity. While the Patterson function corresponds to the inverse Fourier transform of the Bragg intensities only, the Q function corresponds to the inverse Fourier transform of the total intensity diffracted by the real crystal. HOSEMANN and BAGCHI (1962) pointed out that, instead of being ideally periodic as the Patterson function, the Q function, is only quasi-periodic.It was pointed out first by EWALD (1940), that it is not generally realized that the reciprocal lattice is only an incomplete representation of the Fourier transform of the crystal, and that much clearness of discussion can be gained by making full use of the conception of the Fourier transform. In order to successfully apply Fourier-transform theory to real crystals, it is necessary to...

show abstract

“…Sharp satellite (1 AE )50 reflections disappear on approaching T N and are replaced by diffuse reflections. Canut & Hosemann (1964) investigated the diffuse scattering of NaNO 2 in the paraelectric phase 20 K above the Curie point and found microdomains of a characteristic shape which they called 'cigarillos'.…”

Section: Introduction and Summary Of Previous Workmentioning

confidence: 99%

Diffuse scattering and ordering in the short-range modulated paraelectric phase of sodium nitrite, NaNO₂

Łukaszewicz

Pietraszko

Kucharska

2005

Acta Crystallogr Sect B

View full text Add to dashboard Cite

The incommensurately modulated antiferroelectric phase of sodium nitrite, NaNO2, transforms at T(N) = 437.7 K to the short-range modulated paraelectric phase. The apparently discontinuous phase transition is accompanied by characteristic changes in the diffraction pattern. Contrary to the well known modulated structures with sharp satellite reflections, the diffraction pattern of a short-range modulated structure contains diffuse satellite reflections. The short-range modulated crystal structure of the paraelectric phase of sodium nitrite has been analysed by the Reverse Monte Carlo (RMC) simulation of X-ray diffuse scattering. The crystal structure of sodium nitrite may be regarded as consisting of [Na+NO2-]infinity rows running along the polar b axis. One can expect long fragments of rows with uniform polarity The assumption that single [Na+NO2-]infinity rows are polar with uniform polarity proved to be a convenient approximation which is in good agreement with the observed diffraction pattern. The distribution of (+)- and (-)-[Na+NO2-]infinity polar rows crossing the (010) plane of short-range modulated NaNO2 revealed by RMC shows nanodomains consisting of distorted fragments of a sinusoidally modulated crystal structure. The size of the nanodomains and the degree of order in paraelectric NaNO2 decreases with temperature.

show abstract

X-ray analysis of ferroelectric domains in the paraelectric phase of NaNO₂

Cited by 24 publications

References 1 publication

Anhydrous sodium chlorite

Anhydrous sodium chlorite

On the significance of two new Patterson functions for disordered crystals

Diffuse scattering and ordering in the short-range modulated paraelectric phase of sodium nitrite, NaNO₂

Contact Info

Product

Resources

About

X-ray analysis of ferroelectric domains in the paraelectric phase of NaNO2

Cited by 24 publications

References 1 publication

Anhydrous sodium chlorite

Anhydrous sodium chlorite

On the significance of two new Patterson functions for disordered crystals

Diffuse scattering and ordering in the short-range modulated paraelectric phase of sodium nitrite, NaNO2

Contact Info

Product

Resources

About

X-ray analysis of ferroelectric domains in the paraelectric phase of NaNO₂

Diffuse scattering and ordering in the short-range modulated paraelectric phase of sodium nitrite, NaNO₂