A Machine for Synthesizing Two‐Dimensional Fourier Series in the Determination of Crystal Structures

1950 ◽  
Vol 21 (9) ◽  
pp. 779-783 ◽  
Author(s):  
H. Shimizu ◽  
P. J. Elsey ◽  
D. McLachlan
Keyword(s):  
Fourier Series ◽  
Crystal Structures ◽  
Two Dimensional

The use of a high-speed digital computer for the direct determination of crystal structures. I

1955 ◽  
Vol 227 (1171) ◽  
pp. 486-500 ◽  
Keyword(s):  
Crystal Structure ◽  
Fourier Series ◽  
Crystal Structures ◽  
Digital Computer ◽  
High Speed ◽  
Electronic Computer ◽  
Direct Determination ◽  
Direct Methods ◽  
Weighting Factor

A method is described whereby an electronic computer, the EDSAC, may be used to select a set, or sets, of signs for the coefficients F (h) of a Fourier series, such that the Fourier series, satisfies a certain condition. This condition is expressed as X ≡ Ʃ h Ʃ h ' P (h,h') S (h) S (h') S (h+h')≽ X 0 , where S (h) denotes the sign of F (h) and P (h, h') is a weighting factor related to the probability that S (h) S (h') = S (h+h'). In certain circumstances the determination of a crystal structure which is beyond the range of other direct methods is possible by this procedure.

scholarly journals Mercury Cyanamide / Carbodiimide Networks: Synthesis and Crystal Structures of Hg2(NCN)Cl2 and Hg3(NCN)2Cl2

2002 ◽  
Vol 57 (10) ◽  
pp. 1108-1114 ◽  
Author(s):  
Xiaohui Liu ◽  
Richard Dronskowski
Keyword(s):  
Crystal Structure ◽  
Crystal Structures ◽  
Structure Determination ◽  
Crystal Structure Determination ◽  
Two Dimensional ◽  
Synthesis And Crystal Structure ◽  
Packing Efficiency ◽  
Inorganic Network

AbstractWe report about the synthesis and crystal structure determination of Hg2(NCN)Cl2 (P21/c (No. 14), Z = 4, a = 806.7(1), b = 907.1(2), c = 788.0(1) pm, β = 106.446(3)°, 1374 independent reflections, 67 variables, R1 = 0.0463) and Hg3(NCN)2Cl2 (Pca21 (No. 29), Z = 4, a = 702.0(2), b = 1078.5(2), c = 1050.3(2) pm, 1977 independent reflections, 71 variables, R1 = 0.0380). Both compounds contain infinite -Hg-NCN-Hg- zigzag chains which are linked by additional Hg atoms to result in two-dimensional frameworks characterized by 20-membered rings sharing edges. The remarkably flexible structural backbone [Hg3(NCN)2]2+ hosts additional Cl! anions and HgCl2 molecules in Hg2(NCN)Cl2 but only Cl- anions in Hg3(NCN)2Cl2, by that reaching a high packing efficiency in both cases.While Hg2(NCN)Cl2 exclusively contains carbodiimide N=C=N2- species, Hg3(NCN)2Cl2 is the first structural example of an inorganic network built up from both carbodiimide N=C=N2- and cyanamide N-C≡N2- groups.

New NMR Methods that Probe the Structure of Glasses

1990 ◽  
Vol 215 ◽  
Author(s):  
Robert Tycko ◽  
Gary Dabbagh
Keyword(s):  
Crystal Structures ◽  
Short Range ◽  
Two Dimensional ◽  
Structure Of Glasses ◽  
Orientational Ordering ◽  
Nmr Methods

AbstractTwo-dimensional NMR methods allow a determination of the relative orientations of nearby molecules in polycrystalline and noncrystalline solids. We describe these methods and present applications to the determination of the crystal structures of two forms of polycrystalline methanol and to the investigation of short range molecular orientational ordering in methanol glass and in atactic PMMA.

scholarly journals The determination of parameters in crystal structures by means of Fourier series

1929 ◽  
Vol 123 (792) ◽  
pp. 537-559 ◽  
Keyword(s):  
Fourier Series ◽  
Crystal Structures ◽  
General Term ◽  
X Ray ◽  
Fourier Representation ◽  
Determination Of Parameters ◽  
Phase Angles

The Fourier representation of the results of X-ray analysis was first suggested by W. H. Bragg. It was developed independently by Duane, and used by Havighurst and Compton to give striking representations of the distribution of scattering matter in crystals. Duane and Havighurst were first in applying the method to the much more accurate X-ray measurements available in 1925, and in showing how useful it could be. Duane used a formula derived by Epstein and Ehrenfest. They showed that the intensity of an X-ray reflexion from a plane ( h k l ) of a crystal is proportional to the square of the coefficient of a term in the Fourier series, representing the density ρ ( x, y, z ) of the diffracting material in the crystal as a function of x, y, z . The general term may be written A ( h k l ) sin (2π hx/a — δ h ) sin (2π k/b — δ k ) sin (2π lz/c — δ i Duane reversed the line of thought, and showed that it is possible to deduce the density in the crystal from the measured intensities of X-ray reflexion. The X-ray measurements give the values of (A ( h k l ) ) 2 but not the phase angles δ h , δ k , δ i . This difficulty, Duane showed, could be surmounted in certain simple cases.

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