Values of h, k, 1 which satisfy the following equation are

simultaneous solutions to the intersection of the Ewald

sphere with the reciprocal lattice:

(h/a UR/IBI)2 + (k/a VR/IBI)2 + (1/a WR/IBI)2 = R2.

Expansion and rearrangement of this equation yield

 h2+k2+12 + R2(U2+V2+W2) 2(hU+kV+lW) R = R2.
 a (U2+V2+W2) a TB

This can be simplified to

 h2+k2+12 = 2 g-B. (1)


This equation says that the sum of the squares of the

planar indices of a diffracting plane is equal to a

constant for a given electron accelerating potential,

lattice parameter, beam direction and cubic Bravais

lattice type.
 To solve the equation, one must know the microscope

accelerating potential, the approximate lattice parameter

of the examined crystal, and the beam direction in the
crystal. The accelerating potential is never known to

great accuracy. When only relative and comparative

lattice parameter measurements are to be made, this

uncertainty cancels. The lattice parameter can be

approximately derived from either a calibrated selected

area diffraction pattern, or from a calibrated CBED

pattern. The beam direction must be known.