1. Chemical order & disorder in metallic alloy Calculation of Bragg and Diffuse Scattering Correlation length in the Mean-Field approach Correlation Length

2. Chemical order & disorder in metallic alloy A x B 1-x Correlation Length site “n” site “m” Probability of having at any site: atom A : p(A) = x atom B : p(B) = 1-x Probability of having an atom A at site “m” knowing atom B at site “n”: P A (m) Probability of having an atom B at site “m” knowing atom A at site “n”: P B (m)

3. Chemical order & disorder in metallic alloy A x B 1-x Correlation Length Pair probabilities: pair AB : x · P B (m) pair AA : x · (1 - P B (m) ) pair BA : (1-x) · P A (m) pair BB : (1-x) · (1 - P A (m) ) site “n” site “m”

4. Scattering in metallic alloy A x B 1-x Correlation Length Scattering intensity: add and subtract Bragg peaks “Diffuse scattering” Reciprocal lattice vectors

5. Scattering in metallic alloy A x B 1-x Correlation Length Bragg Scattering : Spherical atoms: f A and f B are real. Case x = ½= ( 1-x ) :

6. Scattering in metallic alloy A x B 1-x Correlation Length Diffuse Scattering : sole non zero term when no correlation correlation effect

7. Correlation Length Scattering in metallic alloy A x B 1-x Diffuse Scattering :

8. Correlation Length Diffuse Scattering : Case P A (m) = x, totally disordered alloy : Case P A (m) > x, AB pairs are favored  cell doubling  ordered alloy Case P A (m) < x, AA & BB pairs are favored  phase separation (A & B) Scattering in metallic alloy A x B 1-x

9. Correlation length in the mean-field approach Correlation Length 1D illustration

10. Correlation length in the mean-field approach Correlation Length 1D illustration

11. Correlation length in the mean-field approach Correlation Length 1D illustration  0: I diff  I Bragg cell doubling