An improved numerical method of two-dimensional fourier synthesis for crystals

作者: H Lipson , C A Beevers

DOI: 10.1088/0959-5309/48/5/310

关键词: Fourier transformMathematical analysisDivision (mathematics)Trigonometric functionsGeometrySine and cosine transformsSine waveMathematicsSymmetry (physics)Numerical analysisSTRIPS

摘要: It is shown that a two-dimensional Fourier summation for crystal without centre of symmetry can be resolved into one-dimensional summations, and these latter calculated very rapidly by using set printed strips which give cosine sine waves different wave-lengths amplitudes. The most useful interval division the strips, various features concerning their use, are described.

参考文章(7)
J. Monteath Robertson, X. Numerical and mechanical methods in double Fourier synthesis Philosophical Magazine Series 1. ,vol. 21, pp. 176- 187 ,(1936) , 10.1080/14786443608561568
C.A. Beevers, H. Lipson, LXXII. A rapid method for the summation of a two-dimensional Fourier series Philosophical Magazine Series 1. ,vol. 17, pp. 855- 859 ,(1934) , 10.1080/14786443409462442
James Rawlinson, XXIX. Description of an improved mill for grinding painters' colours Philosophical Magazine. ,vol. 21, pp. 176- 180 ,(1805) , 10.1080/14786440508676695
C. A. BEEVERS, H. LIPSON, A Numerical Method for Two-dimensional Fourier Synthesis Nature. ,vol. 137, pp. 825- 826 ,(1936) , 10.1038/137825A0
W.L. Bragg, J. West, LXXV. A note on the representation of crystal structure by Fourier series Philosophical Magazine Series 1. ,vol. 10, pp. 823- 841 ,(1930) , 10.1080/14786443009461630
The Determination of Parameters in Crystal Structures by means of Fourier Series Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 123, pp. 537- 559 ,(1929) , 10.1098/RSPA.1929.0083
A. L. Patterson, A Direct Method for the Determination of the Components of Interatomic Distances in Crystals Zeitschrift Fur Kristallographie. ,vol. 90, pp. 517- 542 ,(1935) , 10.1524/ZKRI.1935.90.1.517