Structure Factor determination

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Presentation transcript:

Structure Factor determination Dr. Abhijit Yadav Assistant Professor, Department of Physics Rajarshi Shahu Mahavidyalaya, Latur

X-ray analysis: SnO2 (casseterite) has a tetragonal rutile structure, with two molecules per unit cell. The space group is and the atomic positions are Sn (two atoms) in (0, 0, 0) and (½, ½, ½) O (four atoms) in +(u, u, 0), (u, u, 0), (u+½, ½u, ½) and  (u+½, ½u, ½), with u = 0.307. The lattice parameters are given as: a0 = 4.7372 Ao. c0 = 3.186383 Ao.

Knowing the atomic coordinates it is possible to calculate the structure factor F for each (hkl) reflection, which for SnO2 is: Where f is the atomic scattering factor, B is the Debye-Waller temperature factor  is the Bragg angle.

Considering now the possible presence of fluorine atoms in substitutional Oxygen positions +(u, u, 0), (u, u, 0), (u+½, ½u, ½) and  (u+½, ½u, ½), and interstitial positions (0, ½, ½) and (½, 0, ½), we can write the expression for the Structure factor in a compact form: Where j represents tin, oxygen or fluorine atoms fj and Bj their atomic scattering factors and temperature factors resp. Oj the occupation probability for each (xj, yj, zj)

From Peiser, Rooksby and Wilson – X-Ray diffraction by Polycrystalline Materials, IoP, 1955.