Bragg-Lane equation

Lane equations Equations that, like the Bragg equation, express the conditions for diffraction in terms of the path difference of scattered waves. Laue considered the path length differences of waves that are diffracted by two atoms one lattice translation apart. These path differences must be an integral number of wavelengths for diffraction (that is, reinforcement) to occur. This condition must be true simultaneously in all three dimensions. 

While Max von Lane used crystals to perform an experiment with x-rays, William H. Bragg (1862-1942) and his son William Lawrence Bragg (1890-1971) used x-rays to determine the structures of crystals. In 1912 and 1913 the Braggs developed and applied the diffraction equation that bears their name ... 

Max von Lane, a German physicist, was the first to suggest the use of x rays for the determination of crystal structure. Soon afterward, in 1913, the British physicists WiUiam Bragg and his son Lawrence developed the method on which modem crystal-structure determination is based. They realized that the atoms in a crystal form reflecting planes for x rays, and from this idea they derived the fundamental equation of crystal-structure determination. 

The individual variants of the lattice model differ fi om each other in the way the spatial distribution of the molecules of the individual components is taken into account. The simplest solution is the Bragg-Williams (B-W) approach which assumes a random distribution of molecules within the bulk phase. The thermodynamical meaning of this assumption is that the mixture is regular. In the adsorption layer, however, it is only in two dimensions (i.e., within the individual sublayers that a statistical distribution of molecules is assumed). Pioneering work in this field was published by Ono [92-94] and Ono and Kondo [95,96]. The method was later applied to the description of L/G interfaces by Lane and Johnson [97] and later taken up by Altenberger and Stecki [98]. Analytic isotherm equations have also been derived from the above... 

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