Instrumentation - making & detecting x-rays Read Roe - Chap 2 through 2.5.1 (ignore neutrons)
SCATTERING OF NEUTRONS AND X-RAYS
description
Transcript of SCATTERING OF NEUTRONS AND X-RAYS
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SCATTERING OF NEUTRONS AND X-RAYS
ki
ki - kf = qhω ENERGY TRANSFER
hq MOMENTUM TRANSFERkf
Dynamic structure factor
O
r,t
COHERENT INCOHERENT
SCATTERING SCATTERING
g (r,t) gs(r,t)
QUASIELASTIC DIFFUSIVE MOTIONS
INELASTIC VIBRATIONAL
COHERENT INCOHERENT
STRUCTURAL FT [gs (r, )]
NUCLEAR PROB.
DISTRIBUTION
ELASTICElastic
QuasielasticInelastic
Energy transfer, ω
Δωe
Δωqe
S (q,ω) = ei(ωt-q·r) g(r,t) dr dt
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Neutron Diffraction
1) Scattering from nuclei- combined x-n analysis of small molecules.
2) Scattering power does not depend on atomic number.- hydrogens scatter strongly- deuterium and hydrogen opposite signs.
3) Small-angle scattering - contrast matching.4) Solution scattering with isotope substitution
- partial structure factors.4) Enzyme structures
- proton positions- water structure
- no solution to phase problem- large crystals required- need nuclear reactor or spallation source.
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Protein Hydration.
Svergun et al: First 3Å hydration layer ~10% denser than bulk water
FRANCI MERZEL
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Geometric Rg from MD simulation = 14.10.1Å
SMALL-ANGLESCATTERING
RADII OF GYRATION
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Statistical Models of a Strongly Unfolded Protein
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Low q :Size
Radius of Gyration (Rg)
Include Higher q :Chain Configurational
Statistics
q(Å-1)
P(q)
Small Angle Neutron Scattering
rijbibj
0 0.1 0.2 0.30
0.2
0.4
0.6
0.8
1
ki
kf
ki
kfq
array detector
Sample
L ~ 5 - 50 m
n
1i
n
1jji qrij
qrsin ijbb
n21
)q(PqR
3
11~)q(P 2
g
0q
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P(q)
q(Å-1)
Freely Jointed Chains Excluded Volume Chains
Phosphoglycerate Kinase in 4M GdnDCl
RgNat~ 23Å
RgDen~ 90Å
FJChains
0 0.1 0.2 0.31
2
3
0 0.1 0.2 0.31
2
3
x 10 A-4 -2o
q P(q)2
q(A )-1o
EVC6_1.0
Best FJC
EVC5_0.7
ANDREI PETRESCUPATRICK CALMETTESDOMINIQUE DURAND
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EVB(Exluded Volume
Beta)
EVN(Exluded Volume
Native)
Ci-1
Ci
C,i+1
Low Resolution MC Simulation
Scattering Profile of the Models
Atomic Level Modeling
0 0.1 0.2 0.3 0.40
1
2
3
4
5
6
EVN
LE
EVB
x 10 A-4 -2o
q P(q)2
q(A )-1o
LE(Locally
Extended)
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EVN
EVB
LE
EVN
EVB
LE
Snapshots of Atomic-Detail Models of Strongly-Unfolded PGK
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Lattice Vibrations - PERIODIC in TIME and SPACE. - DISPERSION RELATIONSHIP between FREQUENCY and WAVEVECTOR
OPTICAL
ACOUSTICAL
0*a
q
1
l
=180o==2lq=/l
COHERENT INELASTIC NEUTRON SCATTERING
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CRYSTALLINE L-ALANINE : LATTICE DYNAMICS
EXPERIMENT - Triple-Axis Coherent Inelastic Neutron Scattering
THEORY - (i) Ab Initio Quantum Chemistry
H-Bond and Rotational Potentials (ii) Energy Minimization + Harmonic Analysis.PHONON DISPERSION CURVES
CM-1THz
Calculated Experimental
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COHERENT INELASTIC NEUTRON SCATTERING INTENSITIES22
.)( eQqF
INTENSITY SCATTERINGVECTOR
MODE POLARIZATION VECTOR
CALCULATED
EXPERIMENTAL
b*direction
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UREA-ALKANE INCLUSION COMPOUND
DIFFUSIVE ALKANE DYNAMICS AT 180K
Three SimulationModels
Urea ‘HOST’
C19H40 ‘GUEST’
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QUASIELASTIC INCOHERENT NEUTRON SCATTERING
Experiment compared with Simulation
DIRECTION PARALLELTO CHAIN AXIS
DIRECTION PERPENDICULARTO CHAIN AXIS
= experiment
1 chain
3 chains
5 chains
10 chains
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ROTATIONAL PROBABILITY DISTRIBUTIONS OF ALKANE CHAINS
ROTATIONAL ANGLE,
TWO SINGLE CHAINS
Average Over Chains
V()=RotationalPotential
Potential of Mean Force=-kTlogP()
Elastic Incoherent Structure Factor
Experiment & Simulation
Converged (t)
2)(( PFT
Probability Distributions, P()