Modeling and analysis of x-ray diffraction in square and triangular arrays

Document Type : Research Paper

Authors

1 Physics Department, Semnan University, Semnan, Iran

2 physics department, Semnan University, Semnan, Iran

Abstract

X-ray diffraction is a very practical and useful method for characterizing crystals, viruses, including influenza viruses, microscopic particles in biological sciences etc. So, X-ray diffraction is simulated and analyzed in the paper. The calculations are performed using the Green's function by written FORTRAN codes. Also, atoms in a crystal are proposed to be the same as circular apertures and diffraction patterns of square and triangular arrays are studied. In this approach the apertures represent the core of the crystal atoms, and the X-ray diffraction pattern is simulated by passing electromagnetic waves from these apertures. The results show that the general diffraction patterns are independent of the number of crystal atoms, so they can be used as a fingerprint to examine a variety of crystal structures. Also, the increase in the atoms sizes (atomic radius) leads to raise the intensity of the diffraction pattern. The increase in the crystal lattice constant reduces divergence and higher order diffraction patterns appear.

Keywords


[1] W. Friedrich, P. Knipping, and M. V. Laue; “Laue's geometrical theory”;
Annalen der Physik, 41(1912) 971-988
[2] H. Freiser; Concepts and Calculations in Analytical Chemistry, CRC,
Florida.1992
[3] D. A. Skoog, D. M. West; Principles of Instrumental Analysis, Holt-Saunders,
Tokyo, (1987)
[4] H. Xu, J. S. J. Van Deventer; “Microstructural characterization of geopolymers
synthesized from kaolinite/stilbite mixtures using XRD, MAS-NMR, SEM/EDX,
TEM/EDX, and HREM”; Cement and Concrete Research, 32, No. 11(2002) 17051716.
[5] H. Liu, X. Shen, D. Zhu, and S. Han; “Fourier-transform ghost imaging with
pure far-field correlated thermal light”; Phys. Rev. A 76, No.5 (2007) 05380810538085.

[6] F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David; “Phase retrieval and
differential phase-contrast imaging with low-brilliance X-ray sources”; Nat. Phys. 2,
No. 4 (2006) 258–261.
[7] D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganin; “Experimental
X-Ray ghost imaging”; Phys. Rev. Lett. 117, No. 11 (2016) 1139021-1139025.
[8] H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu; “Fourier-transform
ghost imaging with hard X rays”; Phys. Rev. Lett 117, No. 11 (2016) 113901-5.
[9] A. Schori and S. Shwartz; “X-ray ghost imaging with a laboratory source”;
Optics Express 25, No. 13 (2017) 14822-14828.
[10] S. A. Wynne, R. A. Crowther, A. G. W. Leslie; “The crystal structure of the
human hepatitis B virus
capsid”; Mol Cell 3 (1999) 771–780.
[11] N. E. Chayen, J. R. Helliwell, E. H. Snell; “Macromolecular crystallization and
crystal perfection”; Oxford University Press, Oxford (2010).
[12] E. Garman; “Cool crystals: macromolecular cryocrystallography and radiation
damage”; Curr Opin Struct Biol 13 (2003) 545–551.
[13] N. Verdaguer, D. Garriga, I. Fita; “X-Ray Crystallography of Viruses”;
Structure and Physics of Viruses, Part of the Subcellular Biochemistry book series,
SCBI, volume 68(2013) 117-144.
[14] Z. Sayers, B. Avşar, E. Cholak, I. Karmous; “Application of advanced X-ray
methods in life sciences”; Biochimica et Biophysica Acta (BBA)1861, No. 1, Part B
(2017) 3671–3685.
[15] C. Amabil, L. Farina, V. Lopresto et al.; “Tissue shrinkage in microwave
ablation of liver: an ex vivo predictive model”; International Journal of
Hyperthermia 33, No. 1 (2016) 101-109.
[16] M. Kemerink, T. J. Dierichs, J. Dierichs et al.; “The Application of X-Rays in
Radiology: From Difficult and Dangerous to Simple and Safe”; AJR American
Journal of Roentgenology 198, No. 4 (2012) 754-759.
[17] A. C. Thompson, E. M. Westbrook, W. M. Lavender and J. C. Nix; “A large
area CMOS detector for shutterless collection of x-ray diffraction data”; Journal of
Physics: Conference Series 493 (2014) 1-4.
[18] M. C Zdora, P Thibault, T Zhou et al.; “X-ray Phase-Contrast Imaging and
Metrology through Unified Modulated Pattern Analysis”; Phys. Rev. Lett. 118, No.
20 (2017) 2039031- 2039036.
[19] J. Liu, Y. Yang, W. Zhu et al.; “Nanoscale metal-organic frameworks for
combined photodynamic & radiation therapy in cancer treatment”; Biomaterials 97
(2016) 1–9.
[20] M
. Oldham, P. Yoon, Z. Fathi, et al.; “X-Ray Psoralen Activated Cancer
Therapy (X-PACT)”; PLoS ONE journal 11, No. 9 (2016) 1-13.