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A method of calculating coherent X-ray diffraction from a bent nanowire, simulated by the molecular dynamics technique under the bent periodic boundary condition, is reported. The segment of nanowire under the X-ray beam consists of the central box and 2N image boxes. X-ray diffraction from this segment of nanowire is obtained from a single calculation of the amplitude of diffraction from the atoms in the central box according to the kinematic theory. Contributions from the image boxes are then obtained by rotations of this amplitude in the reciprocal space and additional phase factors to take into account the position of the image boxes with respect to the central box. This method will be called rotation in the reciprocal space (RRS). Comparison between the RRS and the full calculation of the diffracted amplitude from all the atoms in the central box and the 2N image boxes (full kinematic sum) is done in the Cu nanowire case. The bending of an FCC Cu nanowire oriented along a direction with an equilibrium shape made up of {100} and {111} facets is calculated by using the SMA (The second-moment approximation of the density of states in the tight-binding formalism) potential. The Cartesian x, y, and z axes correspond, respectively, to [112], [111] and [110] directions. The bending occurs in the y-z plane. The calculation time of the RRS method is about 1/(2N+1) times that obtained by doing the full kinematic sum, the RRS method being more efficient when the number of image boxes N is a bigger one. A very small difference in the calculated intensity between the RRS and the full kinematic sum comes from the interpolation in the reciprocal space. So the RRS method is more accurate, when there are more points calculated in the reciprocal space. Similarly, the RRS method can be applied to tension, compression and torsion of the nanowires, When using the molecular dynamics simulation under periodic boundary conditions. In the cases of tension and compression, it is simpler as only the phase factors have to be considered. Results are also reported in this paper.
[1] Somogyi A, Tucoulou R, Martinez-Criado G, Homs A, Cauzid J, Bleuet P, Bohic S, Simionovici A 2005 J. Synchrotron Rad. 12 208
[2] Bonanno P L, Gautier S, Gmili Y El, Moudakir T, Sirenko A A, Kazimirov A, Cai Z H, Martin J, Goh W H, Martinez A, Ramdane A, Gratiet L L, Malouf N, Assouar M B, Ougazzaden A 2013 Thin Solid Films. 541 46
[3] Hong X G, Du L C, Ye M P, Weng Y X 2004 Chin. Phys. Soc. 13 720
[4] Wang C L, Tsai S J, Chen J W, Shiu H W, Chang L Y, Lin K H, Hsu H C, Chen Y C, Chen C H, Wu C L 2014 App. Phy. Let. 105 123115
[5] Yamada T, Wang J, Sakata, O, Sandu C S, He Z B, Kamo T, Yasui S, Setter N, Funakubo H 2010 J. Eur. Ceram. Soc. 30 3259
[6] Chamard V, Diaz A, Stangl J, Labat S 2009 J. Strain Anal. Eng. Des. 44 533
[7] Chamard V, Stangl J, Labat S, Mandl B, Lechner R T, Metzger T H 2008 J. Appl. Crystallogr. 41 272
[8] Keplinger M, Kriegner D, Stangl J, ThomasM, Bernhard M, Wintersberger E, Bauer G 2010 Nucl. Instr. Meth. Phys. Res B 268 316
[9] Ren Z, Mastropietro F, Davydok A, Langlais S, Richard M I, Furter J J, Thomas O, Dupraz M, Verdier M, Beutier G, Boesecke P, Cornelius T W 2014 J. Synchrotron Rad. 21 1128
[10] Cai W, Fong W, Elsen E, Weinberger C R 2008 J. Mech. Phys. Solids 56 3242
[11] Rosato V, Guillope M, Legrand B 1989 Philos. Mag. A 59 321
[12] Gailhanou M, Roussel J M 2013 Phy. Rev. B 88 224101
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[1] Somogyi A, Tucoulou R, Martinez-Criado G, Homs A, Cauzid J, Bleuet P, Bohic S, Simionovici A 2005 J. Synchrotron Rad. 12 208
[2] Bonanno P L, Gautier S, Gmili Y El, Moudakir T, Sirenko A A, Kazimirov A, Cai Z H, Martin J, Goh W H, Martinez A, Ramdane A, Gratiet L L, Malouf N, Assouar M B, Ougazzaden A 2013 Thin Solid Films. 541 46
[3] Hong X G, Du L C, Ye M P, Weng Y X 2004 Chin. Phys. Soc. 13 720
[4] Wang C L, Tsai S J, Chen J W, Shiu H W, Chang L Y, Lin K H, Hsu H C, Chen Y C, Chen C H, Wu C L 2014 App. Phy. Let. 105 123115
[5] Yamada T, Wang J, Sakata, O, Sandu C S, He Z B, Kamo T, Yasui S, Setter N, Funakubo H 2010 J. Eur. Ceram. Soc. 30 3259
[6] Chamard V, Diaz A, Stangl J, Labat S 2009 J. Strain Anal. Eng. Des. 44 533
[7] Chamard V, Stangl J, Labat S, Mandl B, Lechner R T, Metzger T H 2008 J. Appl. Crystallogr. 41 272
[8] Keplinger M, Kriegner D, Stangl J, ThomasM, Bernhard M, Wintersberger E, Bauer G 2010 Nucl. Instr. Meth. Phys. Res B 268 316
[9] Ren Z, Mastropietro F, Davydok A, Langlais S, Richard M I, Furter J J, Thomas O, Dupraz M, Verdier M, Beutier G, Boesecke P, Cornelius T W 2014 J. Synchrotron Rad. 21 1128
[10] Cai W, Fong W, Elsen E, Weinberger C R 2008 J. Mech. Phys. Solids 56 3242
[11] Rosato V, Guillope M, Legrand B 1989 Philos. Mag. A 59 321
[12] Gailhanou M, Roussel J M 2013 Phy. Rev. B 88 224101
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