Dynamical Diffraction in Two Waves Approximation

The system (5.84) can also be transformed by scalar multiplying its first equation with and the second with Z) and, then, taking into accoimt of the relations (5.79), and (5.85) there is obtained  

The linear and homogeneous system (5.86) will have non-trivial solutions if the associated determinant will be identical null, wherefrom results the equation  

The solution (5.89) is not yet completed until the possible values for the refraction indices (respectively for Sg and S, quantities) associated to the transmitted and diffracted waves are determined. 

These quantities are connected through the Eq. (5.88) - also called as the dispersion equation just for the correlation that it includes, between the refraction indices associated to the transmitted and diffracted directions and along the structure factor of the crystal and the incident wave vector. The last correlation is even better emphasized if the relations (5.1), (5.68), and (5.85) are considered wherefrom another connection between the quantities 6 and 8, can be expressed namely  

Quantum Nanochemistry—Volume IV Quantum Solids and Orderability 

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