Phase-angle determination by anomalous X-ray scattering with a four-circle SSD diffractometer

It is shown that the locus of the f' + if'' plot in the complex plane, f' being determined from measured f'' by using the dispersion relation, looks like a semicircle very near the absorption edge of Ge. The semicircular locus is derived from a quantum theory of X-ray resonant scattering when there is a sharp isolated peak in f'' just above the K-absorption edge. Using the semicircular behavior, an approach is proposed to determine the anomalous scattering factors in a crystal by fitting known calculated values based on an isolated-atom model to a semicircular focus. The determined anomalous scattering factors f' show excellent agreement with the measured values just below the absorption edge. In addition, the phase determination of a crystal structure factor has been considered by using the semicircular behavior.

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“…2. A similar semicircular locus of f 0 þ if 00 has been reported by Sakamaki et al (1980) near the K edge of Zn in hemimorphite.…”

Section: Methodssupporting

confidence: 79%

Anomalous scattering factor determined by semicircle fitting near theK-absorption edge of Ge

et al. 2005

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“…The results of a twowavelength Bijvoet difference procedure are greatly influenced if the two sets of data are not on a common scale [e.g. Sakamaki, Hosaya & Fukamachi (1980)]. In the paper by S&R (1968) the intensities are assumed to be on an absolute scale.…”

Section: Connection With the Sandr Methodsmentioning

confidence: 99%

The two-wavelength technique in crystal structure determination

Klop¹,

Krabbendam²,

Kroon³

1989

Acta Cryst Sect A

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(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.

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“…(7), it contains the centrosymmetric superposition of k • (k -1) vectors between all e-atoms [line 2 of Eq. If all b" are approximately zero, APC contains merely the Patterson function of the e-atom arrangement, as has been mentioned by Sakamaki et al (1980). (7)].…”

Section: (5)mentioning

confidence: 99%

Difference Patterson functions at 3 or 4 wavelengths

Fischer¹

1987

Zeitschrift Für Kristallographie - Crystalline Materials

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Difference Patterson functions from data sets measured at 3 or 4 selected wavelengths around the absorption edge of an anomalous scatterer, are used for solving crystal structures. Wavelength selection for each pair of measurements is made such that for the first pair /' is equal, with f" being as much different as possible. For the second pair, f" has little (or no), f a large difference. The two pairs of wavelengths can be reduced to three single ones, with some loss of contrast due to smaller Af" for λι, λ 2 and Af for λ 2 , λ 3 respectively. The real part of the first difference Patterson essentially contains the self-convolution of the anomalous scatterers (e-atoms). The imaginary part, added to the real part of the second difference Patterson, consists of the vectors from the e-atoms to all other ("normal") atoms (e->w vectors), the reverse w-»e vectors being suppressed. The solution of the «-atom structure, e.g. by a minimum function, is straight-forward in its "true" space group (including the correct enantiomer and/or polarity), provided the e-atom arrangement can be found from the first difference Patterson. Because the result of applying the minimum function consists of the (slightly modified) electron density distribution of the normal scatterers, atomic resolution for them is not a prerequesite. Determination of single reflection phases is neither necessary for, nor a direct result of this "lambda technique": it circumvents the phase problem for the «-atoms. For the e-atoms, the phase problem is separated and therefore to be solved more easily. The "lambda technique" has been put to a praxis test: re-determination of the pseudosymmetric (ferroelectric) KNb0 3 structure.

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Phase-angle determination by anomalous X-ray scattering with a four-circle SSD diffractometer

Cited by 14 publications

References 30 publications

Anomalous scattering factor determined by semicircle fitting near theK-absorption edge of Ge

Anomalous scattering factor determined by semicircle fitting near theK-absorption edge of Ge

The two-wavelength technique in crystal structure determination

Difference Patterson functions at 3 or 4 wavelengths

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