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Diffuse scattering - displacive disorder. Diffuse scattering - displacive disorder 1-D model lattice spacing a o random longitudinal displacements x i Then spacing d i = x i - x i-1 + a o. Diffuse scattering - displacive disorder 1-D model lattice spacing a o

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Diffuse scattering - displacive disorder

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Diffuse scattering - displacive disorder

Diffuse scattering - displacive disorder

1-D model

lattice spacing ao

random longitudinal displacements xi

Then

spacing di = xi - xi-1 + ao

Diffuse scattering - displacive disorder

1-D model

lattice spacing ao

random longitudinal displacements xi

Then

spacing di = xi - xi-1 + ao

Note: substitutional model xi = 0 or 1

displacement model xi continuously variable

Diffuse scattering - displacive disorder

1-D model

lattice spacing ao

random longitudinal displacements xi

Then

spacing di = xi - xi-1 + ao

All xi normally distributed in same manner

P(xi) = K exp (-xi2/2L2)

Diffuse scattering - displacive disorder

1-D model

lattice spacing ao

random longitudinal displacements xi

Then

spacing di = xi - xi-1 + ao

All xi normally distributed in same manner

P(xi) = K exp (-xi2/2L2)

Joint distribution of neighboring xi also normal

P(xi|xi-1) = K exp (-(xi-12 + xi2 - 2rxi-1xi)/(2L2(1 -r2)))

Diffuse scattering - displacive disorder

1-D model

All xi normally distributed in same manner

P(xi) = K exp (-xi2/2L2)

joint distribution of neighboring xi also normal

P(xi,xi-1) = K exp (-(xi-12 + xi2 - 2rxi-1xi)/(2L2(1 -r2)))

r is correlation coeff.

r = <xi-1xi>/L2

Diffuse scattering - displacive disorder

1-D model

All xi normally distributed in same manner

P(xi) = K exp (-xi2/2L2)

joint distribution of neighboring xi also normal

P(xi,xi-1) = K exp (-(xi-12 + xi2 - 2rxi-1xi)/(2L2(1 -r2))

P(xi|xi-1) = P(xi,xi-1)/P(xi)

= K exp (-(xi- 2rxi-1)2/(2L2(1 -r2))

ith site defined by i-1th site

Diffuse scattering - displacive disorder

1-D model

Diffuse scattering - displacive disorder

1-D model

Diffuse scattering - displacive disorder

1-D model