User:Ldm1954/Diff/Kinematical

Kinematical Diffraction
In Kinematical theory we approximate that the electrons are only scattered once, and we normally make life simpler by also assuming a simple, flat sample of a given thickness $$t$$. The intensity we will observe in a diffraction pattern is then proportional to
 * $$I_{hkl} = |F_{hkl}sin(\pi t s_z)/(\pi t s_z)|^2

$$ where $$F_{hkl}$$ is the structure factor:
 * $$F_{hkl} = \sum_{j=1}^N f_j \mathrm{e}^{[2 \pi i (h x_j + k y_j + \ell z_j) -T g^2]} $$

the sum being over all the atoms in the unit cell with $$f_j$$ the form factors mentioned earlier, $$g$$ is a reciprocal lattice vector of form $$ g = hA + kB + lC $$ and $$ A, B, C$$ are the three individual vectors of the reciprocal lattice and $$T$$ is a simplified Debye–Waller factor. This form is a reasonable first approximation within about 20% in many cases, but one has to use much more accurate forms where we include multiple scattering of the electrons to properly understand the intensities. These approaches are called dynamical diffraction.