Miller indices and Braggs law

When the coordinates of all atoms within the cell (actually, within the asymmetric unit. Section 5.1) are known, the structure factors can be calculated in modulus, Fhki, and phase, (l)hk i these are called F-air hiri. The single-crystal X-ray diffraction experiment starts by measuring the observed diffracted intensities  

A number of corrections allow the retrieval of the observed structure factors, Fobs,hki, and the game of X-ray crystallography, also known as the solution of the phase problem, is to find the set of atomic coordinates that give a close match between the Fcaic,hki and the Fobs,hki- A first guess must be somehow prepared this problem is now routinely and robustly solved by a technique called direct methods (see Section 5.9). The agreement between observed and calculated structure factors is coded into a discrepancy index traditionally called the F-factor  

Atomic coordinates can be refined by automatic least-squares to lower the F-factor as much as possible. Weights can be assigned to each stmcture factor according to 

One final point concerns thermal motion. Atoms are never at rest, and thermal motion causes a further decay in the intensity of diffracted beams. The atomic structure 

The genius of sir Lawrence Bragg provided a simple physical model of constructive scattering of X-rays by crystals, an immediate counterpart of the mathematics in term of simple phenomena. The conditions for constructive interference in a crystal will now be rewritten using Bragg s approach. 

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