Dynamic structure factors for excitations in modulated structures

Adlhart, W.

doi:10.1107/s0567739482001065

Cited by 17 publications

(14 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We observe intense diffuse scattering around the satellite reflections and we assume that it is caused by phase fluctuations. In § 4 the diffuse scattering is discussed in connection with calculations of the dynamic structure factor for phase and amplitude fluctuations (Adlhart, 1982).…”

Section: * Iupac Name: A-bis(n-methylsalicylideneiminato)copper(ii)mentioning

confidence: 99%

See 1 more Smart Citation

X-ray study on the incommensurate phase of α-bis(N-methylsalicylaldiminato)copper(II) (α-CuNSal)

Adlhart¹,

Blank²,

Jagodziñski³

1982

Acta Cryst Sect A

Self Cite

View full text Add to dashboard Cite

The temperature dependence of satellite reflections and diffuse scattering of a-CuNSal, Cu(CsHsNO)2 , was studied with X-ray film and counter techniques. At T t = 305 (2)K a continuous and reversible phase transition from a commensurate to an incommensurate orthorhombic structure was observed. At T C = 241 (2) K there occurs a first-order transition from the incommensurate to a commensurate monoclinic structure. In the incommensurate phase an intense diffuse scattering at the satellite reflections was observed, which is explained by phase fluctuations of the static displacement wave.

show abstract

Section: * Iupac Name: A-bis(n-methylsalicylideneiminato)copper(ii)mentioning

confidence: 99%

“…We would like to discuss our experiments with the help of recent dynamic structure-factor calculations (Adlhart, 1982). We anticipate that the main part of the diffuse scattering around the satellites is caused by phasons, since their dispersion relation approaches zero at the site of the satellite reflections.…”

Section: Phase Fluctuationsmentioning

confidence: 99%

X-ray study on the incommensurate phase of α-bis(N-methylsalicylaldiminato)copper(II) (α-CuNSal)

Adlhart¹,

Blank²,

Jagodziñski³

1982

Acta Cryst Sect A

Self Cite

View full text Add to dashboard Cite

show abstract

“…Another possibility provided that higher-order satellites are included is finding indications to the existence of fluctuations of the phase or the amplitude of the modulation wave (cf. Adlhart, 1982) if they are of the order of the Debye-Waller factor.…”

Section: P(xyzt) = 1/v~ E E E ~ Fhklmmentioning

confidence: 99%

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

Steurer¹

1987

Acta Cryst Sect A

View full text Add to dashboard Cite

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.

show abstract

“…This may be one cause for the rather high U33 but it is expected that far away from the second-order phase-transition temperature the phase fluctuations are more important than amplitude fluctuations. A deter-A would only be possible by mination of both w~' and w k studying the diffuse scattering (Adlhart, 1982).…”

Section: Phason and Amplitudon Factor According Tomentioning

confidence: 99%

“…The merging of the two data sets collected with different crystal mounting was carded out with the batch scale factors calculated in part I. Considering anomalous-dispersion effects the structure-factor equations (for the structure-factor formulae of Table 1) The formula (a) is derived in the Appendix, (b) and (c) are taken from Adlhart (1982). [Q = G -mq, G = 2nH.fk(Q) is the atomic scattering factor for atom k, w, the temperature factor, ¢)k the phase term, A, the amplitude, J,.…”

Section: Structure Refinementmentioning

confidence: 99%

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

Steurer¹,

Adlhart²

1983

Acta Crystallogr Sect B

Self Cite

View full text Add to dashboard Cite

The modulated structure of the title compound (aNiNSal) was determined at 160 K by single-crystal X-ray methods. The refinements were performed in the superspace group otba2 (a00). Different models considering thermal fluctuations in the phase and the amplitude of the static modulation wave were calculated. The best refinement yielded the overall R factors R = 0.088, R w = 0.051 for 4322 independent reflexions including 2725 first-order and 118 secondorder reflexions. The positional parameters of the basic structure and of the average structure are nearly equal. The amplitudes of the one-dimensional displacive modulation waves decrease due to steric interactions between adjacent molecule stacks from 0.30 A at the central Ni u ion to 0.22 A at the peripheral C atoms. The modulation functions were found to be sinusoidal. Calculations with a phason factor yielded only slightly better R factors -no reliable proof for the existence of amplitude and phase fluctuations.

show abstract

Dynamic structure factors for excitations in modulated structures

Cited by 17 publications

References 6 publications

X-ray study on the incommensurate phase of α-bis(N-methylsalicylaldiminato)copper(II) (α-CuNSal)

X-ray study on the incommensurate phase of α-bis(N-methylsalicylaldiminato)copper(II) (α-CuNSal)

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

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

Contact Info

Product

Resources

About