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dc.contributor.advisorParker, Travis J.
dc.creatorKlunk, David Griffith
dc.description.abstractIn studying the structure of matter, X-ray diffraction techniques are limited by a phenomenon known as the "Phase Problem". Previous contributions to the direct solution of crystal structures have made use of statistical relationships between measured diffraction intensities. This dissertation describes the application of a novel approach to three-dimensional centrosymmetric cases using an optimization methodology. The method involves casting the "Phase Problem" in terms of a classical integer linear programming problem. The variables, which represent the phases, are restricted to take on the values of zero or one. The assignment of zero to a phase angle, in effect, causes it to take on the value of 180°, just as the assignment of one corresponds to a phase angle of 0°. When a priori knowledge of atomic positions exists, the coefficients in the objective function may be biased accordingly to speed up the convergence process. The inequality constraints required by the problem formulation are based on a non-negativity restriction that applies to all points in the unit cell. Upper bound constraints may also be generated for points in real space that correspond to pronounced valleys in Patterson (vector) space. The operation of the method is described in detail and the results of the successful solution of two test cases are presented. The two structures involved are spirodienone, C��H₈O₂, and potassium lead hexanitrocuprate II, K₂PbCu(NO₂)₆. This direct method is significant in that it is a nonstatistical approach that has been shown to work with real structures by using measured intensities. A priori knowledge of, atomic positions Is not required and algorithm efficiency for small structures is comparable to other existing direct methods.en
dc.format.extent40 leavesen
dc.rightsThis thesis was part of a retrospective digitization project authorized by the Texas A&M University Libraries. Copyright remains vested with the author(s). It is the user's responsibility to secure permission from the copyright holder(s) for re-use of the work beyond the provision of Fair Use.en
dc.subject.classification1974 Dissertation K66
dc.titleThe direct solution of crystal structures by a Boolean programming optimization methodologyen
dc.typeThesisen Scienceen A&M Universityen of Philosophyen
dc.contributor.committeeMemberDeFord, R. K.
dc.contributor.committeeMemberFahlquist, Davis A.
dc.contributor.committeeMemberHoldredge, Edwin S.
dc.contributor.committeeMemberSchroeder, Melvin C.
dc.contributor.committeeMemberSeward, Clay
dc.format.digitalOriginreformatted digitalen
dc.publisher.digitalTexas A&M University. Libraries

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