Kinematic diffraction

Kinematic diffraction is an approximation for diffraction of waves. It assumes that the waves are only scattered once, neglecting multiple scattering. For linear wave equations, it involves summing the contribution of the partial waves emanating from different scatterers, where only the incident field drives the scattering.

As a consequence, the far-field amplitude essentially corresponds to the Fourier transform of the scattering length density. It would be the charge density for x-rays and the electrostatic potential for electrons. It is typically understood as the Born approximation applied to a number of scatterers, and as such is often used for X-ray crystallography.

In the kinematic approximation, the scattered amplitude can be written as the Fourier transform of the scattering density,

A (𝐪) = \int ρ (𝐫) e^{i 𝐪 \cdot 𝐫} d^{3} r,

where $𝐪$ is the scattering vector and $ρ (𝐫)$ is the scattering density. The corresponding diffracted intensity is proportional to the squared magnitude of the amplitude,

I (𝐪) \propto | A (𝐪) |^{2} .

The corresponding full theory is called the dynamical theory of diffraction. For x-rays and in electron diffraction different approaches are used for calculating the dynamical diffraction for transmission: with high-energy electrons, for low energy electron diffraction, or reflection high-energy electron diffraction

References

↑ Als-Nielsen, Jens; McMorrow, Des (2011). Elements of Modern X‐ray Physics. John Wiley & Sons, Ltd. doi:10.1002/9781119998365. ISBN 9781119998365.
↑ Cowley, J. M. (1995). Diffraction physics. North-Holland personal library (3rd ed.). Amsterdam; New York: Elsevier Science B.V. ISBN 978-0-444-82218-5.
↑ Cullity, B. D. (2001). Elements of x-ray diffraction. Prentice Hall. ISBN 0-201-61091-4.
↑ Warren, B. E. (1990). X-ray Diffraction. New York: Dover Publications. ISBN 978-0-486-66317-3.
↑ Authier, Andre (2003-11-06). "Elementary dynamical theory". Dynamical Theory of X-Ray Diffraction. Oxford University PressOxford. pp. 68–112. ISBN 0-19-852892-2. Retrieved 2025-01-19.
↑ Humphreys, C J (1979-11-01). "The scattering of fast electrons by crystals". Reports on Progress in Physics. 42 (11): 1825–1887. doi:10.1088/0034-4885/42/11/002. ISSN 0034-4885.
↑ Peng, L -M; Dudarev, S L; Whelan, M J (2004-01-08), "Dynamical Theory Ii. Transmission High-Energy Electron Diffraction", High-Energy Electron Diffraction And Microscopy, Oxford University PressOxford, pp. 75–116, ISBN 978-0-19-850074-2, retrieved 2025-01-19
↑ J B Pendry (1971-11-18). "Ion core scattering and low energy electron diffraction. I". Journal of Physics C: Solid State Physics. 4 (16): 2501–2513. doi:10.1088/0022-3719/4/16/015. ISSN 0022-3719.
↑ Maksym, P.A.; Beeby, J.L. (1981). "A theory of rheed". Surface Science. 110 (2): 423–438. doi:10.1016/0039-6028(81)90649-X.

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[alsnielsen-1] Als-Nielsen, Jens; McMorrow, Des (2011). Elements of Modern X‐ray Physics. John Wiley & Sons, Ltd. doi:10.1002/9781119998365. ISBN 9781119998365.

[2] Cowley, J. M. (1995). Diffraction physics. North-Holland personal library (3rd ed.). Amsterdam; New York: Elsevier Science B.V. ISBN 978-0-444-82218-5.

[3] Cullity, B. D. (2001). Elements of x-ray diffraction. Prentice Hall. ISBN 0-201-61091-4.

[Warren1990-4] Warren, B. E. (1990). X-ray Diffraction. New York: Dover Publications. ISBN 978-0-486-66317-3.

[5] Authier, Andre (2003-11-06). "Elementary dynamical theory". Dynamical Theory of X-Ray Diffraction. Oxford University PressOxford. pp. 68–112. ISBN 0-19-852892-2. Retrieved 2025-01-19.

[6] Humphreys, C J (1979-11-01). "The scattering of fast electrons by crystals". Reports on Progress in Physics. 42 (11): 1825–1887. doi:10.1088/0034-4885/42/11/002. ISSN 0034-4885.

[7] Peng, L -M; Dudarev, S L; Whelan, M J (2004-01-08), "Dynamical Theory Ii. Transmission High-Energy Electron Diffraction", High-Energy Electron Diffraction And Microscopy, Oxford University PressOxford, pp. 75–116, ISBN 978-0-19-850074-2, retrieved 2025-01-19

[8] J B Pendry (1971-11-18). "Ion core scattering and low energy electron diffraction. I". Journal of Physics C: Solid State Physics. 4 (16): 2501–2513. doi:10.1088/0022-3719/4/16/015. ISSN 0022-3719.

[9] Maksym, P.A.; Beeby, J.L. (1981). "A theory of rheed". Surface Science. 110 (2): 423–438. doi:10.1016/0039-6028(81)90649-X.