International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. B. ch. 2.4, p. 275
Section 2.4.5.1. Neutron anomalous scattering^{a}Molecular Biophysics Unit, Indian Institute of Science, Bangalore 560 012, India, and ^{b}Raman Research Institute, Bangalore 560 080, India |
Apart from the limitations introduced by experimental factors, such as the need for large crystals and the comparatively low flux of neutron beams, there are two fundamental reasons why neutrons are less suitable than X-rays for the ab initio determination of crystal structures. First, the neutron scattering lengths of different nuclei have comparable magnitudes whereas the atomic form factors for X-rays vary by two orders of magnitude. Therefore, Patterson techniques and the related heavy-atom method are much less suitable for use with neutron diffraction data than with X-ray data. Secondly, neutron scattering lengths could be positive or negative and hence, in general, the positivity criterion (Karle & Hauptman, 1950) or the squarability criterion (Sayre, 1952) does not hold good for nuclear density. Therefore, the direct methods based on these criteria are not strictly applicable to structure analysis using neutron data, although it has been demonstrated that these methods could be successfully used in favourable situations in neutron crystallography (Sikka, 1969). The anomalous-scattering method is, however, in principle more powerful in the neutron case than in the X-ray case for ab initio structure determination.
Thermal neutrons are scattered anomalously at appropriate wavelengths by several nuclei. In a manner analogous to (2.4.3.1), the neutron scattering length of these nuclei can be written as The correction terms b′ and b″ are strongly wavelength-dependent. In favourable cases, and can be of the order of 10 whereas they are small fractions in X-ray anomalous scattering. In view of this pronounced anomalous effect in neutron scattering, Ramaseshan (1966) suggested that it could be used for structure solution. Subsequently, Singh & Ramaseshan (1968) proposed a two-wavelength method for unique structure analysis using neutron diffraction. The first part of the method is the determination of the positions of the anomalous scatterers from the estimated values of . The method employed for estimating is analogous to that using (2.4.4.9) except that data collected at two appropriate wavelengths are used instead of those from two isomorphous crystals. The second stage of the two-wavelength method involves phase evaluation. Referring to Fig. 2.4.3.2 and in a manner analogous to (2.4.3.5), we have where and subscript 1 refers to data collected at wavelength . Singh and Ramaseshan showed that cos can also be determined when data are available at wavelength and . We may define and we have from (2.4.3.3), (2.4.3.4) and (2.4.5.3) Then, where x is the magnitude of the temperature-corrected geometrical part of . and hence can be calculated using (2.4.5.2) and (2.4.5.5). can also be obtained in a similar manner.
During the decade that followed Ramaseshan's suggestion, neutron anomalous scattering was used to solve half a dozen crystal structures, employing the multiple-wavelength methods as well as the methods developed for structure determination using X-ray anomalous scattering (Koetzle & Hamilton, 1975; Sikka & Rajagopal, 1975; Flook et al., 1977). It has also been demonstrated that measurable Bijvoet differences could be obtained, in favourable situations, in neutron diffraction patterns from protein crystals (Schoenborn, 1975). However, despite the early promise held by neutron anomalous scattering, the method has not been as successful as might have been hoped. In addition to the need for large crystals, the main problem with using this method appears to be the time and expense involved in data collection (Koetzle & Hamilton, 1975).
References
Flook, R. J., Freeman, H. C. & Scudder, M. L. (1977). An X-ray and neutron diffraction study of aqua(L-glutamato) cadmium(II) hydrate. Acta Cryst. B33, 801–809.Google ScholarKarle, J. & Hauptman, H. (1950). The phases and magnitudes of the structure factors. Acta Cryst. 3, 181–187.Google Scholar
Koetzle, T. F. & Hamilton, W. C. (1975). Neutron diffraction study of NaSmEDTA.8H_{2}O: an evaluation of methods of phase determination based on three-wavelength anomalous dispersion data. In Anomalous scattering, edited by S. Ramaseshan & S. C. Abrahams, pp. 489–502. Copenhagen: Munksgaard.Google Scholar
Ramaseshan, S. (1966). The use of anomalous scattering of neutrons in the solution of crystal structures containing large molecules. Curr. Sci. 35, 87–91.Google Scholar
Sayre, D. (1952). The squaring method: a new method for phase determination. Acta Cryst. 5, 60–65.Google Scholar
Schoenborn, B. P. (1975). Phasing of neutron protein data by anomalous dispersion. In Anomalous scattering, edited by S. Ramaseshan & S. C. Abrahams, pp. 407–416, Copenhagen: Munksgaard.Google Scholar
Sikka, S. K. (1969). On the application of the symbolic addition procedure in neutron diffraction structure determination. Acta Cryst. A25, 539–543.Google Scholar
Sikka, S. K. & Rajagopal, H. (1975). Application of neutron anomalous dispersion in the structure determination of cadmium tartrate pentahydrate. In Anomalous scattering, edited by S. Ramaseshan & S. C. Abrahams, pp. 503–514. Copenhagen: Munksgaard.Google Scholar
Singh, A. K. & Ramaseshan, S. (1968). The use of neutron anomalous scattering in crystal structure analysis. I. Non-centrosymmetric structures. Acta Cryst. B24, 35–39.Google Scholar