《XRD 教程02》.ppt

2.4 Diffraction Analysis The Structure Factor in the complex plane Interpretation of Diffracted Intensities 各晶面族的多重因子列表 We simplify the notation by setting h/3 + 2k/3 + l/2 = X; the complication is simply that X may be a fraction. The analysis is quite straightforward if we consider ?F?2, which is what we need in the expression for intensities. Then we can rearrange as follows Extending fcc and hcp to include a basis What we did in the previous section was to calculate the reciprocal lattice of a simple-cubic crystal with a basis of four atoms in fcc and two atoms in bcc. We can take this analysis one step further by starting with fcc and adding a basis. This extension both illustrates the technique and deduces structure-factor rules for three important materials. NaCl, GaAs, and Si: Each of these three crystal structures is an fcc lattice with a basis. In other words, We can separate out the atoms lying on the fcc lattice and those which make up the basis. We usually say that for every Na atom, there is a Cl atom related to it by the vector [0, 0, 0]. However, to emphasize the cubic symmetry, we can choose the alternative basis vector [1/2, 1/2, 1/2]. The phase factor for the Cl atom will be the same as for the Na atom , but with an additional phase of ?i(h + k + l). Of course, the atomic scattering amplitudes, f, are also different for the two atoms. We can write this expression for F as Thank you ! GaAs: You should repeat the above exercise with the Ga located on the fcc lattice and the As related to it by the basis vector [1/4, 1/4, 1/4]. (Crystallographers will immediately note that this puts the As atom in the tetrahedron instead of the octahedron, as found in NaCl.) Now the expression for F becomes (see equation 4 for Ffcc) Applying the bcc and fcc analysis to simple