(Solved): The cubic system features three Bravais lattices, the simple cubic lattice (S ...

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The cubic system features three Bravais lattices, the simple cubic lattice (SC), the body-centered cubic lattice (BCC) and the face-centered cubic lattice (FCC). The objective of this problem is the analysis of the diffractograms of the compounds $$\mathrm{KBr}$$ and $$\mathrm{KCl}$$ that crystallize in the cubic system. 1) Characterization of the cubic network and its reciprocal network 1.1) Characterize the parameters of the cubic network. What are the symmetry elements of the cubic lattice? Which point symmetry group? Sketch a figure to explain your answer. Represent the planes (001), (011) and (111) 1.2) Reciprocal network a) What is the reciprocal lattice of a cubic lattice? What is the parameter of the reciprocal elementary mesh? b) Calculate the interplanar distance dhkl for a family of lattice planes $$\{\mathrm{hkl}\}$$ 1.3) We consider the body-centered cubic lattice a) What is the multiplicity of the cubic mesh in this case? b) Which basis should be considered to use a simple cubic mesh? Express the structure factor of this basis as a function of the Miller indices $$\mathrm{h},\mathrm{k}$$ and $$\mathrm{I}$$ characterizing the vectors of the reciprocal space. c) Which nodes of the cubic network's reciprocal network must be eliminated (extinction rule)? Characterize the obtained reciprocal network.