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There are three different experimental methods for x-ray diffraction that we are going to look at: The Laue method, the rotating crystal method and the powder (Debye-Scherrer) method. To help explain each method, the illuminating and very helpful Ewald construction will be explained.

The Ewald
construction is a simple geometric construction to aid in visualizing the
direction of allowable diffracted x-rays.
It is set up by drawing the incoming wave vector of the x-ray on the
reciprocal space which has the reciprocal lattice points. The incoming x-ray wave vector is drawn such
that it starts at the origin of the reciprocal space and is of course is in the
direction of the incident x-ray. Then a
circle with a radius equal to the magnitude of the incoming x-ray wave vector
is drawn with its center at the
endpoint of the incoming x-ray wave vector as shown in the figure below. For an allowable diffracted wave to exist,
the diffracted wave vector must be equal in magnitude but in a direction such
that **k-k’=K**, or the difference of incoming and outgoing wavevectors must
equal a reciprocal lattice vector. This
is a very restrictive condition and only reciprocal lattice points that lie on
the edge of this circle will satisfy this condition. This is all shown in the figure below in which only one scattered
x-ray is satisfies this condition and is therefore present.

The Laue method eases the restriction of illustrated by the figure above by using a range of wavelengths for the incoming x-rays. Hence the ewald construction is modified as follows.

Where x-rays of wave vector **k _{o} **through

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In the rotating crystal method, there is only one wavelength for the incoming x-rays but the crystal is rotated and hence the reciprocal lattice is rotated. This allows for more reciprocal lattice points to satisfy the diffraction conditions. The extreme of this is when you rotate the crystal over all possible angles such as you would have if you had a polycrystalline material where the grains are oriented in all directions. For example, if you crushed the crystal into small pieces, the incoming x-rays would pass through crystals that are oriented in all directions, hence the reciprocal lattice is rotated in all directions as illustrated in the following figure.

For real 3D crystals, there will be diffaction cones as illustrated in the following figure:

By measuring the angle between the incoming and outgoing wavevectors, you can calculate the magnitude of the reciprocal lattice vectors.

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The x-ray intensity cones are recorded on film as shown below: