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Dr. Abhijit Yadav, Assistant Professor at Rajarshi Shahu Mahavidyalaya, Latur, explains the structure factor determination for SnO2 (casseterite) with tetragonal rutile structure. Calculation involves atomic positions and lattice parameters.
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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, ½u, ½) and (u+½, ½u, 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 factorFfor 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, ½u, ½) and (u+½, ½u, 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)
FromPeiser, Rooksby and Wilson – X-Ray diffraction by Polycrystalline Materials, IoP, 1955.
