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- W2043104549 abstract "Abstract For a centric crystal structure represented by m equal point scatterers at rest, absolute scaling of a small number n of reflection data reduced to relative geometrical structure amplitudes g ′( h ) = K · |∑ cos (2π i hr j )|, j = 1, …, m ; K = scaling factor) is obtained by dividing each amplitude through the r.m.s. average of the amplitudes to be considered. For the same batch of reflections, the resulting values e ( h , n ) are proportional to the well known normalized structure amplitudes | E ( h )| in Direct Methods. Choosing a set of n harmonic reflections of a central reciprocal lattice row, the e ( h , n ) serve to determine the m independent coordinates of the point scatterers projected onto the corresponding direct space direction, e.g . h 00-reflections for coordinates x j , hh 0-reflections for ( x + y ) j ( j = 1, …, m ), etc . This is achieved by applying the concept of an m -dimensional parameter space P m with asymmetric part A m containing ( m – 1)-dimensional iso-surfaces E ( h , n ; e ) determined by the values e ( h , n ), which define boundaries between forbidden and permitted solution regions (the latter containing test structure vectors Xt ) based on observed inequalities, e.g. e ( h , n ) < e ( k , n ). Due to the spatial resolution potential of the concept even less than m data suffice to yield in A m tractable amounts of such test structure vectors ready for conventional least-squares refinement based on n > m data in order to obtain the “best” solution of the considered one-dimensional structure projection. The refined coordinates of various different projections can then be combined for reconstructing the three-dimensional structure. Properties of the e ( h , n ) and their iso-surfaces E ( h , n ; e ) are discussed and determinations of two very small structures (centric and acentric) as well as of a centric 15-atom structure are presented as examples for the applicability of the method." @default.
- W2043104549 created "2016-06-24" @default.
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- W2043104549 date "2009-07-01" @default.
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- W2043104549 title "Structure determination without Fourier inversion. Part IV: Using quasi-normalized data" @default.
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- W2043104549 doi "https://doi.org/10.1524/zkri.2009.1130" @default.
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