Dynamical Diffraction Theory for Wave Packet Propagation in Deformed Crystals
Abstract
We develop a theory for the trajectory of an x ray in the presence of a crystal deformation. A set of equations of motion for an xray wave packet including the dynamical diffraction is derived, taking into account the Berry phase as a correction to geometrical optics. The trajectory of the wave packet has a shift of the center position due to a crystal deformation. Remarkably, in the vicinity of the Bragg condition, the shift is enhanced by a factor ({omega}/{delta}{omega}) ({omega}: frequency of an x ray, {delta}{omega}: gap frequency induced by the Bragg reflection). Comparison with the conventional dynamical diffraction theory is also made.
 Authors:
 Department of Applied Physics, University of Tokyo, 731, Hongo, Bunkyoku, Tokyo 1138656 (Japan)
 (CERC), National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 4, Tsukuba 3058562 (Japan)
 (JST) (Japan)
 Publication Date:
 OSTI Identifier:
 20775176
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review Letters; Journal Volume: 96; Journal Issue: 15; Other Information: DOI: 10.1103/PhysRevLett.96.154802; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BRAGG REFLECTION; COMPARATIVE EVALUATIONS; CRYSTALS; DEFORMATION; DIFFRACTION; EQUATIONS OF MOTION; TRAJECTORIES; WAVE PACKETS; WAVE PROPAGATION; X RADIATION
Citation Formats
Sawada, Kei, Murakami, Shuichi, Nagaosa, Naoto, Correlated Electron Research Center, and CREST, Japan Science and Technology Agency. Dynamical Diffraction Theory for Wave Packet Propagation in Deformed Crystals. United States: N. p., 2006.
Web. doi:10.1103/PhysRevLett.96.154802.
Sawada, Kei, Murakami, Shuichi, Nagaosa, Naoto, Correlated Electron Research Center, & CREST, Japan Science and Technology Agency. Dynamical Diffraction Theory for Wave Packet Propagation in Deformed Crystals. United States. doi:10.1103/PhysRevLett.96.154802.
Sawada, Kei, Murakami, Shuichi, Nagaosa, Naoto, Correlated Electron Research Center, and CREST, Japan Science and Technology Agency. Fri .
"Dynamical Diffraction Theory for Wave Packet Propagation in Deformed Crystals". United States.
doi:10.1103/PhysRevLett.96.154802.
@article{osti_20775176,
title = {Dynamical Diffraction Theory for Wave Packet Propagation in Deformed Crystals},
author = {Sawada, Kei and Murakami, Shuichi and Nagaosa, Naoto and Correlated Electron Research Center and CREST, Japan Science and Technology Agency},
abstractNote = {We develop a theory for the trajectory of an x ray in the presence of a crystal deformation. A set of equations of motion for an xray wave packet including the dynamical diffraction is derived, taking into account the Berry phase as a correction to geometrical optics. The trajectory of the wave packet has a shift of the center position due to a crystal deformation. Remarkably, in the vicinity of the Bragg condition, the shift is enhanced by a factor ({omega}/{delta}{omega}) ({omega}: frequency of an x ray, {delta}{omega}: gap frequency induced by the Bragg reflection). Comparison with the conventional dynamical diffraction theory is also made.},
doi = {10.1103/PhysRevLett.96.154802},
journal = {Physical Review Letters},
number = 15,
volume = 96,
place = {United States},
year = {Fri Apr 21 00:00:00 EDT 2006},
month = {Fri Apr 21 00:00:00 EDT 2006}
}
Other availability
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Lagrangedistributed approximatingfunctional approach to wavepacket propagation: Application to the timeindependent wavepacket reactantproduct decoupling method
A connection is made between a recently introduced Lagrangedistributed approximatingfunctional and the PaleyWiener sampling theorem. The Lagrangedistributed approximatingfunctional sampling is found to provide much superior results to that of PaleyWiener sampling. The relations between discrete variable representation and Lagrangedistributed approximating functionals are discussed. The latter is used to provide an even spaced, interpolative grid representation of the Hamiltonian, in which the kinetic energy matrix has a banded, Toeplitz structure. In this paper we demonstrate that the Lagrangedistributed approximatingfunctional representation is an accurate and reliable representation for use in fastFouriertransform wavepacket propagation methods and apply it to the timeindependent wavepacket reactantproductmore » 
Peculiarities of the diffraction contrast in planewave Xray topographs of weakly deformed crystals in the bragg geometry
The regularities of the topographic contrast formation in weakly deformed nonabsorbing crystals in the Bragg geometry for the diffraction of a plane Xray wave have been investigated by the method of Riemann functions. It is shown that in this case the extinction contrast has an interference character, alternates, and is proportional to the strain gradient rather than to the squared strain (like in the case of strong lattice distortions). The data of the analysis are compared with the results of a model numerical experiment. The possibility of implementing an Xrayacoustic resonance in the Bragg geometry is shown. 
Generalization of the nonstandard approach in the dynamic theory of diffraction for deformed crystals
The nonstandard theory of Xray scattering in a deformed crystal has been generalized. The vector of atomicplane displacement is introduced into the crystal polarizability model like in the generalized Takagi dynamic theory. The solution to the wave equation is sought for using the procedure of expanding the field amplitude and vector operators in the Fourier components of polarizability χ{sub H} in a series according to the multiscale method. It is shown that considering lattice strain generally calls for introducing various characteristic spatial regions for the diffraction equation, which is in complete agreement with the main concept of the multiscale method.more »