## The Ewald Construction for the surface.

The X-ray diffraction experiment is carried out so that the wavelength and the direction for the incident X-ray beam are known. This information may be put into the surface reciprocal lattice as follows (see figure).

1. Draw a vector in the incident direction of length 2p/l terminating at the origin. This is an incident wave-vector.

2. Construct a circle of radius 2p/l with center at the origin of incident wave-vector. Note whether this circle passes through any point of the reciprocal lattice; if it does:

3. Draw a vector from the origin of the incident wave-vector to the point of the intersection. This is reflected wave-vector.

4. Draw a vector from the origin to the point of the intersection. This is a reciprocal lattice vector.

5. Draw a line perpendicular to the reciprocal lattice vector. This line represents a reflecting plane. Any crystal plane which is parallel to that plane and is spaced according to the magnitude of the reciprocal lattice vector is participating in Bragg reflection.

6. There usually is more than one point of intersection of the circle with the Bragg rod indicating that there is more than one plane which can reflect the incident beam according to the Bragg law.

It is important to realize that the construction has been drawn in two dimensions for simplicity of demonstration. In three dimensions the Ewald construction is represented by a sphere of corresponding radius, and so the number of intersecting points (and therefore diffracting planes ) is accordingly increased.

To see the Ewald construction for the surface click on the Figure or here !!!

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