Bulk Structural

33 Pages·2012·0.38 MB·Romanian

Bulk Structure
Characterization
Apurva Mehta
Linda Lim
Outline
 What do diffraction peaks tell us?

 Structure Refinement Intro

 Refinement Details - Linda
Diffraction Physics
X-ray lens with resolution better than ~10nm don’t exist
image
sample
light
lens
Sample Image
SRceactitperroincga l
Space Space
SSppaaccee
X-ray Scattering/diffraction is about probing the structure without a lens
Diffraction Physics

Elastic
Scattering
Momentum change
DK = 2sin(q) * 2p/l

Momentum
2q DK = Q = 4p sin(q) /l
K = 2p/l
0
K = 2p/l
0
Diffraction Physics
e
f iwt
0
e
iwt 2pi (r1sin(2q)/l)
e e
iwt
f
1
Phase
r1
difference
2pi (r2sin(2q)/l)
e e
iwt
f
2
r2
Phase
difference
DK = Q = 4p sin(q) /l
2pi (risin(2q)/l)
A(DK = (s-s0)) = ei wt Sf e
i
amplitude
A(Q) = Fourier Transform ( r )
i
i (ri Q)
S
e
A(DK) = f
i
Fourier Transform Recap

 FT (large) ~ 1/large  small
la rge structures in real space  small in reciprocal space
 FT (periodic fn) ~ periodic
Rec iprocal and space have the same point group symmetry
 FT (FT (S) ) ~ S
FT FT
FT (r eal space)  reciprocal space: FT (rec. space)  image of
real space
 Convolution Theorem:
 FT (a multiply b) = FT (a) conv FT (b)
 FT (a conv b) = FT (a) mult FT (b)
Diffraction Physics
FT FT
Sample
Scattering
Space
Space
Fourier
Transform
Multiplication vs Convolution
x
FT (a multiply b) = FT (a) conv FT (b)
Convolution
FT (a conv b) = FT (a) mult FT (b)
Multiplication
Deconstructing the Sample space
Sample = S x P * M

= x *
M
o
t
i
f
Sample size
Infinite Periodic Lattice
(S)
(M)
(P)
Reciprocal Space Peaks
I (Q) = FT(sample) x FT(sample)

= FT ( S x P * M) x FT ( S x P * M)

= {FT (S x P) x FT (M)} { ….}

= {FT(S) * FT(P) x FT(M)} {…..}