From Wikipedia,
the free encyclopedia
In
solid state physics, in
particular
crystallography, the Ewald
construction is a method for
reconstructing a
crystal structure by examining
and interpreting an
x-ray
diffraction pattern.
To every
crystallographic spatial
structure, there corresponds
exactly one so-called
reciprocal lattice. The
reciprocal
lattice is the set of all
allowed values of
crystal momentum that a
particle (or
wave) inside the
periodic potential of the
lattice may have. For example, the
lattice dual to a
simple cubic spatial structure
is a simple cubic structure (in
momentum or k-space).
These allowed values of momentum
form a cubic lattice.
Ewald construction for
plane waves of wave vector
q, incident on a
square crystal lattice
The Ewald construction for
plane waves of
wave-vector q incident
on a crystal (that is to say,
going in the direction that q
points in, with
wavelength 2 Pi / |q|)
tells you to pick any point in the
lattice, and draw a
sphere of
radius |q| about the
point at the tip of
vector q of the points
in the dual lattice. In general,
this sphere will only have the
origin you chose on its
surface, and will not have any
other points of the lattice on its
surface. If it does, then denote
by K the vector
corresponding to this second
point. If one then performs a
diffraction pattern experiment
with waves of wave vector q
incident on the crystal, one will
then see a large peak in the
spectrum of the diffraction
pattern at K.
