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## Ewald's sphereThe - the wavelength of the incident and diffracted x-ray beams,
- the diffraction angle for a given reflection,
- the reciprocal lattice of the crystal
## Additional recommended knowledgeIt was conceived by Paul Peter Ewald, a German physicist and crystallographer. Ewald's sphere can be used to find the maximum resolution available for a given x-ray wavelength and the unit cell dimensions. It is often simplified to the two-dimensional "Ewald's circle" model or may be referred to as the Ewald sphere. ## Ewald Construction
A crystal can be described as a lattice of points of equal symmetry. The requirement for constructive interference in a diffraction experiment means that in momentum or reciprocal space the values of momentum transfer where constructive interference occurs also form a lattice (the reciprocal lattice). For example, the reciprocal lattice of a simple cubic real-space lattice is also a simple cubic structure. The aim of the Ewald sphere is to determine which lattice planes (represented by the grid points on the reciprocal lattice) will result in a diffracted signal for a given wavelength, λ, of incident radiation.
. If no energy is gained or lost in the diffraction process (it is elastic) then K_{f} has the same length as K_{f}. The amount the beam is diffracted by is defined by the scattering vector K_{i}Δ. Since K = K_{f} − K_{i} and K_{i} have the same length the scattering vector must lie on the surface of a sphere of radius 2π / λ. This sphere is called the Ewald sphere.
K_{f}
Categories: Condensed matter physics | Crystallography |

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Ewald's_sphere". A list of authors is available in Wikipedia. |