The estimation of triplet invariants from multi-wavelength data

Self Cite

(1963) obtained agreement between observed and calculated fringe spacings within 25% in the highabsorption case and 70% in the low-absorption case. The reason for the deviation is that in their simple theory they considered only the effect of the phase relationship of waves upon the fringe spacing, but neglected the effect of the absorption and the intensities of the waves. In this paper, we have considered all factors affecting the spacings of fringes. Therefore we have obtained good agreement, within 14%, between observed and calculated fringe spacings in the high-and low-absorption cases. The computer simulation patterns also fit the experimental patterns very well. Through our theory the BL fringes are physically clearer. If this relationship is used as scaling scheme, the S&R method is algebraically equivalent to the ratio technique. For centric reflections the two methods are equivalent provided that the same scaling is applied.

Section: Connection With the Sandr Methodsmentioning

confidence: 97%

“…The definitions of Klop et al (1989) are used throughout, some of which are repeated here for convenience.…”

Section: Definitionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The two-wavelength technique in crystal structure determination

Klop¹,

Krabbendam²,

Kroon³

1989

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“…In order to get phase estimates the triplet phase sums of the heavy-atom substructure are assumed to be concentrated near zero (Karle, 1984). Recently, Klop, Krabbendam & Kroon (1989) combined algebraic analysis results of twowavelength anomalous-dispersive data of a single structure with the joint probability distribution (j.p.d.) of Hauptman (1982b) in order to estimate triplet invariants.…”

Section: Introductionmentioning

confidence: 99%

The joint probability distribution of structure factors incorporating anomalous-scattering and isomorphous-replacement data

Peschar¹,

Schenk²

1991

A method to derive joint probability distributions of structure factors is presented which incorporates anomalous-scattering and isomorphous-replacement data in a unified procedure. The structure factors F, and F_n, whose magnitudes are different due to anomalous scattering, are shown to be isomorphously related. This leads to a definition of isomorphism by means of which isomorphous-replacement and anomalous-scattering data can be handled simultaneously. The definition and calculation of the general term of the joint probability distribution for isomorphous structure factors turns out to be crucial. Its analytical form leads to an algorithm by means of which any particular joint probability distribution of structure factors can be constructed. The calculation of the general term is discussed for the case of four isomorphous structure factors in P1, assuming the atoms to be independently and uniformly distributed. A main result is the construction of the probability distribution of the 64 triplet phase sums present in space group P1 amongst four isomorphous structure factors F,, four isomorphous FK and four isomorphous F-H-K. The procedure is readily generalized in the case where an arbitrary number of isomorphous structure factors are available for FH, FK and F_n_K.

“…For the single-crystal case, phase-angle determination with two wavelengths has been reviewed recently by Klop, Krabbendam & Kroon (1989). Fischer (1987) discusses difference Patterson functions calculated from single-crystal data taken at three or four wavelengths as the 'lambda technique'.…”

Section: Introductionmentioning

confidence: 99%

Phase determination and Patterson maps from multiwave powder data

Prandl¹

1990

In the limit of unrestricted resolution, with Friedel pairs as the only coincidences, phase angles or signs can be determined uniquely from powder diffraction data using multiple-wavelength techniques. For a centrosymmetric structure one anomalously scattering species of atoms and data taken at two h's are sufficient. In the acentric case one needs two different anomalous scatterers and measurements at three )t's. The anomalous scatterers can be localized from difference Patterson maps: their peaks can be discriminated against the peaks due to non-anomalous scatterers.