Circle of a sphere the Equator the only great circle. By contrast, all meridians of longitude, paired with their opposite meridian in the other hemisphere, form great circles. The diameter of the sphere which passes through the center of the circle is called its axis and the endpoints of this diameter are called its poles. A circle of a sphere can also be defined as the set of points at a given angular distance from a given pole. When the intersection of a sphere and a plane is not empty or a single point, it is a circle. This can be seen as follows:
Ewald's sphere falling on the crystal has a wave vector formula_2 whose length is formula_3. The diffracted plane wave has a wave vector formula_4. If no energy is gained or lost in the diffraction process (it is elastic) then formula_4 has the same length as formula_2. The difference between the wave-vectors of diffracted and incident wave is defined as scattering vector formula_7. Since formula_2 and formula_4 have the same length the scattering vector must lie on the surface of a sphere of radius formula_3. This sphere is called the Ewald sphere. The reciprocal lattice points are the values of momentum transfer where