The phases and magnitudes of the structure factors

Karle, J.; Hauptman, H.

doi:10.1107/s0365110x50000446

Cited by 207 publications

(110 citation statements)

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“…An algebraic method by Ott (1927) to directly solve the structure-factor equations for the atom coordinates could not be developed into a practically useful method. More successful were the HarkerKasper (Harker & Kasper, 1948) and Karle-Hauptman (Karle & Hauptman, 1950) inequalities. The foundations of modern direct methods were laid with Sayre's equation (Sayre, 1952a), and by Hauptman & Karle (1953).…”

Section: Solution Of the Phase Problemmentioning

confidence: 99%

The success story of crystallographyThis Laue centennial article has also been published inZeitschrift für Kristallographie[Schwarzenbach (2012).Z. Kristallogr.227, 52–62].

Schwarzenbach

2011

Acta Cryst Sect A

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Diffractionists usually place the birth of crystallography in 1912 with the first X-ray diffraction experiment of Friedrich, Knipping and Laue. This discovery propelled the mathematical branch of mineralogy to global importance and enabled crystal structure determination. Knowledge of the geometrical structure of matter at atomic resolution had revolutionary consequences for all branches of the natural sciences: physics, chemistry, biology, earth sciences and material science. It is scarcely possible for a single person in a single article to trace and appropriately value all of these developments. This article presents the limited, subjective view of its author and a limited selection of references. The bulk of the article covers the history of X-ray structure determination from the NaCl structure to aperiodic structures and macromolecular structures. The theoretical foundations were available by 1920. The subsequent success of crystallography was then due to the development of diffraction equipment, the theory of the solution of the phase problem, symmetry theory and computers. The many structures becoming known called for the development of crystal chemistry and of data banks. Diffuse scattering from disordered structures without and with partial long-range order allows determination of short-range order. Neutron and electron scattering and diffraction are also mentioned.

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Section: Solution Of the Phase Problemmentioning

confidence: 99%

The success story of crystallographyThis Laue centennial article has also been published inZeitschrift für Kristallographie[Schwarzenbach (2012).Z. Kristallogr.227, 52–62].

Schwarzenbach

2011

Acta Cryst Sect A

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“…Although the triplet relation in its centrosymmetric form is already implicitly present in the Harker-Kasper inequalities (Harker & Kasper, 1948) and the determinant inequalities of Karle & Hauptman (1950), the first explicit formulation was given by Sayre (1952), Cochran (1952) and Zachariasen (1952). The noncentrosymmetric form of (1) was first formulated by Cochran (1955), although again this expression was implicitly present in many older papers.…”

Section: Introductionmentioning

confidence: 99%

The negative-quartet relation from electron-density considerations

Schenk¹

1981

Acta Cryst Sect A

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“…N fluo is counted for E fluo ≥ 6 keV. Assuming that the fluorescence yield is linearly proportional to σ P and using (19), the MAD coefficient c is converted byc where γ is a single scaling factor applied for all the thick curves in figure 3, as well as the relation between c andc in (16). In the low-intensity limit, the curves converted from the fluorescence yield (thick) and calculated by (4c) (thin) are very similar.…”

Section: Fluorescence Measurementmentioning

confidence: 99%

“…Note that the molecular replacement technique, which still needs a structurally similar reference structure to phase the new structure, was employed in [14]. The phase determination without any previously known structure has been, and still is, a longlasting challenge in x-ray crystallography [19,20].…”

Section: Introductionmentioning

confidence: 99%

Determination of multiwavelength anomalous diffraction coefficients at high x-ray intensity

Son

Chapman

Santra

2013

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. The high-intensity version of multiwavelength anomalous diffraction (MAD) has a potential for solving the phase problem in femtosecond crystallography with x-ray free-electron lasers (XFELs). For MAD phasing, it is required to calculate or measure the MAD coefficients involved in the key equation, which depend on XFEL pulse parameters. In the present work, we revisit the generalized KarleHendrickson equation to clarify the importance of configurational fluctuations of heavy atoms induced by intense x-ray pulses, and investigate the high-intensity cases of transmission and fluorescence measurements of samples containing heavy atoms. Based on transmission/fluorescence and diffraction experiments with crystalline samples of known structures, we propose an experimental procedure to determine all MAD coefficients at high x-ray intensity, which can be used in ab initio phasing for unknown structures.

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The phases and magnitudes of the structure factors

Cited by 207 publications

References 0 publications

The success story of crystallographyThis Laue centennial article has also been published inZeitschrift für Kristallographie[Schwarzenbach (2012).Z. Kristallogr.227, 52–62].

The success story of crystallographyThis Laue centennial article has also been published inZeitschrift für Kristallographie[Schwarzenbach (2012).Z. Kristallogr.227, 52–62].

The negative-quartet relation from electron-density considerations

Determination of multiwavelength anomalous diffraction coefficients at high x-ray intensity

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