Ewald's sphere

The Ewald sphere is a geometric construction used in electron, neutron, and x-ray diffraction which shows the relationship between:

the wavevector of the incident and diffracted beams,
the diffraction angle for a given reflection,
the reciprocal lattice of the crystal.

It was conceived by Paul Peter Ewald, a German physicist and crystallographer.^[1] Ewald himself spoke of the sphere of reflection.^[2] It is often simplified to the two-dimensional "Ewald's circle" model or may be referred to as the Ewald sphere.

^ Ewald, P. P. (1921). "Die Berechnung optischer und elektrostatischer Gitterpotentiale". Annalen der Physik (in German). 369 (3): 253–287. Bibcode:1921AnP...369..253E. doi:10.1002/andp.19213690304.
^ Ewald, P. P. (1969). "Introduction to the dynamical theory of X-ray diffraction". Acta Crystallographica Section A. 25 (1): 103–108. Bibcode:1969AcCrA..25..103E. doi:10.1107/S0567739469000155.

[1] Ewald, P. P. (1921). "Die Berechnung optischer und elektrostatischer Gitterpotentiale". Annalen der Physik (in German). 369 (3): 253–287. Bibcode:1921AnP...369..253E. doi:10.1002/andp.19213690304.

[2] Ewald, P. P. (1969). "Introduction to the dynamical theory of X-ray diffraction". Acta Crystallographica Section A. 25 (1): 103–108. Bibcode:1969AcCrA..25..103E. doi:10.1107/S0567739469000155.

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