Abstract
The mathematical solution of a set of relations among the phases of the structure factors of a crystal may be attempted either ab initio, or by starting from some partial or approximate information concerning the desired solution. In the first case one speaks of a direct method of phase determination, in the second case of a direct method of phase extension or refinement. The preceding chapters have dealt principally with the first case, although phase extension and refinement have been mentioned at some length as .components of methods whose overall purpose is ab initio phasing. Starting with this chapter, attention will shift to the second case. Mathematically the shift will involve a change in the type of relation system solved. Chapter 8 will discuss methods of phase extension and refinement based on the solution of convolutional and related systems of equations, and Chapters 9 and 10 will deal, respectively, with methods involving the maximization of Karle-Hauptman determinants and the solution of relation systems arising out of structural redundancy. The shift will involve also a change in solution technique.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Agarwal, R. C., and Isaacs, N. W. (1976). Private communication.
Ahmed, F. R., and Hall, S. R. (1975). In Crystallographic Computing Techniques, Ed. F. R. Ahmed, Munksgaard, Copenhagen, pp. 71–84.
Barrett, A. N., and Zwick, M. (1971). Acta Crystallogr. Sect. A 27, 6.
Carpenter, G. B. (1969). Principles of Crystal Structure Determination, W. A. Benjamin, New York.
Collins, D. M., Brice, M. D., la Cour, T. F. M., and Legg, M. J. (1975). In Crystallographic Computing Techniques, Ed. F. R. Ahmed, Munksgaard, Copenhagen, pp. 330–335.
Collins, D. M., Cotton, F. A., Hazen, E. E., Jr., Meyer, E. F., Jr., and Morimoto, C. N. (1975). Science 190, 1047.
Coulter, C. L. (1965). J. Mol. Biol. 12, 292.
Coulter, C. L., and Dewar, R. B. K. (1971). Acta Crystallogr. Sect. B 27, 1730.
Cutfield, J. F., Dodson, E. J., Dodson, G. G., Hodgkin, D. C., Isaacs, N. W., Sakabe, K., and Sakabe, N. (1975). Acta Crystallogr. Sect. A 31, S21.
Davies, A. R., and Rollett, J. S. (1976). Acta Crystallogr. Sect. A 32, 17.
Destro, R . (1972). Report of C.E.C.A.M. workshop, Orsay, France.
Gassmann, J . (1975). In Crystallographic Computing Techniques, Ed. F. R. Ahmed, Munksgaard, Copenhagen, pp. 144–154.
Gassmann, J. (1976). Acta Crystallogr. Sect. A 32, 274.
Gassmann, J., and Zechmeister, K. (1972). Acta Crystallogr. Sect. A 28, 270.
Hall, S. R . (1969). In Crystallographic Computing, Ed. F. R. Ahmed, Munksgaard, Copenhagen, pp. 67–70.
Hauptman, H. (1971). Abstract H3, American Crystallographic Association Winter Meeting, Columbia, South Carolina.
Hendrickson, W. A. (1973). Trans. Am. Crystallogr. Assoc. 9, 61.
Hendrickson, W. A. (1975), J. Mol. Biol. 91, 226.
Hendrickson, W. A., and Karle, J. (1973). J. Biol. Chem. 248, 3327.
Hendrickson, W. A., Love, W. E., and Karle, J. (1973). J. Mol. Biol. 74, 331.
Hoppe, W. (1962). Acta Crystallogr. 15, 13.
Hoppe, W. (1963), Z. Kristallogr. 118, 121.
Hoppe, W., and Gassmann, J. (1964). Ber. Bunsenges. Phys. Chem. 68, 808.
Hoppe, W., and Gassmann, J. (1968). Acta Crystallogr. Sect. B 24, 97.
Hoppe, W., Gassmann, J., and Zechmeister, K. (1969). In Crystallographic Computing, Ed. F. R. Ahmed, Munksgaard, Copenhagen, pp. 26–36.
Hughes, E. W. (1953). Acta Crystallogr. 6, 871.
Karle, J. (1964). Advances in Structure Research by Diffraction Methods, Interscience, New York, pp. 55–89.
Karle, J. (1969). Advances in Chemical Physics, Interscience, New York, Vol. XVI, pp. 131–222.
Karle, J., and Hauptman, H. (1950). Acta Crystallogr. 3, 181.
Karle, J., and Hauptman, H. (1956). Acta Crystallogr. 9, 635.
Karle, J., and Karle, I. L. (1966). Acta Crystallogr. 21, 849.
Kartha, G. (1969). Acta Crystallogr. Sect. A 25, S87.
Kolba, D. P., and Parks, T. W. (1977). IEEE Trans. Acoust. Speech Signal Process. 25, 281.
Krabbendam, H., and Kroon, J. (1971). Acta Crystallogr. Sect. A 27, 48.
Lessinger, L. (1976). Acta Crystallogr. Sect. A 32, 538.
Luenberger, D. G. (1969). Optimization by Vector Space Methods, Wiley, New York.
Podjarny, A . (1976). Talk given at International School for Crystallography, Erice, Sicily.
Reeke, G. N., Jr., and Lipscomb, W. N. (1969). Acta Crystallogr. Sect. B 25, 2614.
Rothbauer, R. (1976). Acta Crystallogr. Sect. A 32, 169.
Sayre, D. (1952). Acta Crystallogr. 5, 60.
Sayre, D. (1972). Acta Crystallogr. Sect. A 28, 210.
Sayre, D. (1974). Acta Crystallogr. Sect. A 30, 180.
Sayre, D . (1975). In Crystallographic Computing Techniques, Ed. F. R. Ahmed, Munksgaard, Copenhagen, pp. 322–327.
Sayre, D., and Toupin, R. (1975). Acta Crystallogr. Sect. A 31, S20.
Simonov, V. I. (1975). In Crystallographic Computing Techniques, Ed. F. R. Ahmed, Munksgaard, Copenhagen, pp. 138–143.
Simonov, V. I . (1976). Abstract SC1, American Crystallographic Association Summer Symposium, Buffalo, New York.
Silverman, H. F. (1977). IEEE Trans. Acoust. Speech Signal Process. 25, 152.
Slepian, D., and Pollack, H. O. (1961). Bell System Tech. J. 40, 43.
Stout, G. H., and Jensen, L. H. (1968). X-Ray Structure Determination, MacMillan, New York.
Tsoucaris, G. (1976). Private communication.
Weinzierl, J. E., Eisenberg, D., and Dickerson, R. E. (1969). Acta Crystallogr. Sect. B 25, 380.
White, P. S., and Woolfson, M. M. (1975). Acta Crystallogr. Sect. A 31, 53.
Zwick, M., Bantz, D., and Hughes, J. (1976). Ultramicroscopy 1, 275.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1980 Plenum Press, New York
About this chapter
Cite this chapter
Sayre, D. (1980). Phase Extension and Refinement Using Convolutional and Related Equation Systems. In: Ladd, M.F.C., Palmer, R.A. (eds) Theory and Practice of Direct Methods in Crystallography. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2979-4_8
Download citation
DOI: https://doi.org/10.1007/978-1-4613-2979-4_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-2981-7
Online ISBN: 978-1-4613-2979-4
eBook Packages: Springer Book Archive