The structure of the incommensurate modulated phase of α-bis(<i>N</i>-methylsalicylaldiminato)nickel(II)

Steurer, W.; Adlhart, W.

doi:10.1107/s0108768183002529

Cited by 12 publications

(9 citation statements)

References 14 publications

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“…For R = H, see Stewart & Lingafelter (1959). For R = CH3, see Frasson, Panattoni & Sacconi (1959), Fox & Lingafelter (1967), and Steurer & Adlhart (1983). For R = C2Hs, see Shkol'nikova, Knyazeva & Voblikova (1967).…”

Section: Introductionmentioning

confidence: 99%

Bis(N-n-propylsalicylideneaminato)nickel(II)

Britton¹,

Pignolet²

1989

Acta Crystallogr C

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Section: Introductionmentioning

confidence: 99%

Bis(N-n-propylsalicylideneaminato)nickel(II)

Britton¹,

Pignolet²

1989

Acta Crystallogr C

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“…For example, in the case of rectangular modulation high orders of satellites can be found around all main reflections, in principle, whereas they appear for sinusoidal modulation around highly indexed ones only. This is a consequence of the fact that the structure factor of an ruth-order satellite is proportional If we assume phase fluctuations with a Gaussian distribution, equal for all atoms, then the limiting function can be written as f(m)=exp (-n/2m2(q,2)) (cf Steurer & Adlhart, 1983a) and its Fourier transform is…”

Section: Series Termination Errorsmentioning

confidence: 99%

“…However, it is easy to determine the phase difference from the position of the absolute maximum at T = 0.8 and the amplitudes from the 'bordering' peaks at T=0.3. A practical example, calculated with the intensities of the known modulated phase of a-bis(N-methylsalicylideneaminato)nickel(II) (Steurer & Adlhart, 1983a) is represented in Fig. 5.…”

Section: F(t)=[2~/(n(@2))] ~/2 Exp [-2~2t2/(n(~b2))] (34)mentioning

confidence: 99%

(3+1)-Dimensional Patterson and Fourier methods for the determination of one-dimensionally modulated structures

Steurer¹

1987

Acta Cryst Sect A

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Patterson and Fourier methods applied to onedimensionally modulated structures in the (3+ 1)-dimensional space R3+1 can be very helpful tools for the calculation of starting parameters of the atomic modulation functions. The characteristics of the (3+ 1)-dimensional Patterson function [(3 + 1)-PF] are discussed for some typical modulation waves from a geometrical point of view as well as with the aid of known modulated phases. The influence of series termination errors, resulting from incomplete data sets, is demonstrated. The (3+I)-PF, in any case, yields sufficient basic information even if first-order satellites only are accessible. Of course, it is necessary to include higher orders if one wants to learn something about the shape of the modulation wave. A comparison is made with the Patterson methods used for the solution of modulated structures until now, and it is shown that they are special cases of the (3+ 1)-PF. Some applications are given for Fourier methods in R3+1, for example, to detect fluctuations of the phase or the amplitude of the modulation wave.

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“…The number of IC structures which are determined using superspace formalism is increasing constantly (van Aalst, den Hollander, Peterse & de Wolff, 1976, Yamamoto, 1982a, c, 1985Yamada & Ikeda, 1984;Yamada, 1985;Baudour & Sanquer, 1983;Steurer & Adlhart, 1983;Kucharczyk & Paciorek, 1985;van Smaalen, Bronsema & Mahy, 1986;Madariaga, Zuniga, Perez-Mato & Tello, 1987). This formalism includes, in the form presently used, the definition of a 'supercrystal' in a (3+d)-dimensional space (superspace), where d is the number of independent modulation wave vectors.…”

Section: Introductionmentioning

confidence: 99%

On the structure and symmetry of incommensurate phases. A practical formulation

Perez-Mato¹,

Madariaga²,

Zúñiga³

et al. 1987

Acta Cryst Sect A

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PRECISE DIFFRACTION ANGLES BY FFTand the counter slit, t is the thickness of the specimen and 2A is the breadth of the spot on which the incident beam falls. In this case, where the vertical diversion of the beam is neglected, both t and A are variable factors in the experiment. If the value of /.1. = 143cm -1, estimated from the mass absorption coefficients of oxygen and silicon (Cullity, 1978) and the density of SiO2, and the goniometer radius of L= 175 mm are entered into (13), AO is found to be less than 9 x 10 -3° for 20 > 90 °. On the other hand, the analytical process of a personal computer is effective to six figures and its precision of calculation is better than 0.001 °. The difference between 20a and 20th is at most 0.02 ° because the goniometer has a precision of 20 =0.01 ° and is scanned with a step width of 0.01 ° in 20. All errors involved in the analysis can therefore be reduced through the mechanical accuracy of the goniometer. Consequently, it is definitely possible by adopting this analytical method to obtain a higher analytical accuracy when the accuracy of the goniometer is improved and the step width is reduced. AbstractThe structural description, symmetry and diffraction properties of incommensurate modulated phases are revised using a real-space framework. The superspace formalism usually employed is reformulated using a practical description where no multidimensional geometrical constructions are needed. The incommensurate structural distortion is described in terms of 'atomic modulation functions' where the internal space is only considered as a continuous label for the cells of the non-distorted structure. Hence, no atomic positions or thermal tensors in a multidimensional space are defined. By this means and with the introduction of the concept of 'atomic modulation factors' a general expression for the structure factor is proposed which constitutes a direct generalization of the standard expression for a commensurate structure. The concept of superspace symmetry is reduced in this approach to a simple relation between the defined atomic modulation functions, which can be 0108-7673/87/020216-11501.50 directly translated by means of the structure-factor expression into the symmetry and extinction rules of the diffraction diagram. The advantages of superspace formalism in the analysis of commensurate modulated phases are also discussed. The use of superspace groups for describing the symmetry of superstructures, contrary to some recent claims, does not formally reduce the number of structural parameters but may often allow some of them to be neglected.

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The structure of the incommensurate modulated phase of α-bis(N-methylsalicylaldiminato)nickel(II)

Cited by 12 publications

References 14 publications

Bis(N-n-propylsalicylideneaminato)nickel(II)

Bis(N-n-propylsalicylideneaminato)nickel(II)

(3+1)-Dimensional Patterson and Fourier methods for the determination of one-dimensionally modulated structures

On the structure and symmetry of incommensurate phases. A practical formulation

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