Correlation Length Chemical order disorder in metallic alloy

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

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

Correlation Length • Chemical order & disorder in metallic alloy Ax. B 1 -x • Pair probabilities: site “m” site “n” ü pair AB : x · PB(m) ü pair AA : x · (1 - PB(m) ) ü pair BA : (1 -x) · PA(m) ü pair BB : (1 -x) · (1 - PA(m) )

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

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

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

Correlation Length • Scattering in metallic alloy Ax. B 1 -x • Diffuse Scattering :

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

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

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

Correlation Length • Correlation length in the mean-field approach • 1 D illustration 0: Idiff IBragg cell doubling