PHYS 570 - Introduction to Synchrotron Radiationcsrri.iit.edu/~segre/phys570/13F/lecture_01.pdfPHYS...

PHYS 570 - Introduction to Synchrotron Radiation

Term: Fall 2013Meetings: Monday & Wednesday 15:15-16:30Location: 239 Stuart Building

Instructor: Carlo SegreOffice: 166A Life SciencesPhone: 312.567.3498email: [email protected]

Book: Elements of Modern X-Ray Physics, 2nd ed.,J. Als-Nielsen and D. McMorrow (Wiley, 2011)

Web Site: http://csrri.iit.edu/∼segre/phys570/13F

C. Segre (IIT) PHYS 570 - Fall 2013 August 19, 2013 1 / 21

Course objectives

• Understand the means of production of synchrotron x-ray radiation

• Understand the function of various components of a synchrotronbeamline

• Be able to perform calculations in support of a synchrotronexperiment

• Understand the physics behind a variety of experimental techniques

• Be able to make an oral presentation of a synchrotron radiationresearch topic

• Be able to write a General User Proposal in the format used by theAdvanced Photon Source


Course objectives








Course objectives








Course objectives








Course objectives








Course objectives








Course syllabus

• Focus on applications of synchrotron radiation

• Homework assignments

• In-class student presentations on research topics

• Choose a research article which features a synchrotron technique• Timetable will be posted

• Final project - writing a General User Proposal

• Start thinking about a suitable project right away• Make proposal and get approval before starting

• Visits to Advanced Photon Source (outside class, not required)

• All students who plan to attend will need to request badges from APS• Go to http://www.aps.anl.gov/Users/New/ and register as a new user.• Use MRCAT (Sector 10) as location of experiment• Use Carlo Segre as local contact• State that your beamtime will be in the first week of October


Course syllabus










Course syllabus










Course syllabus










Course syllabus










Topics to be covered (at a minimum)

• X-rays and their interaction with matter

• Sources of x-rays

• Refraction and reflection from interfaces

• Kinematical diffraction

• Diffraction by perfect crystals

• Photoelectric absorption

• Resonant scattering

• Imaging

• Small angle scattering (not in book)


Resources for the course

• Orange x-ray data booklet:http://xdb.lbl.gov/xdb-new.pdf

• Center for X-Ray Optics web site:http://cxro.lbl.gov

• X-ray Oriented Programs:http://www.esrf.eu/computing/scientific/xop2.1

• Hephaestus from the horae suite:http://cars9.uchicago.edu/˜ravel/software/abouthephaestus.html

• McMaster data on the Web:http://csrri.iit.edu/periodic-table.html






























Today’s outline - August 19, 2013

• History of x-ray sources

• X-ray interactions with matter

• Thomson scattering

• Atomic form factor

Reading Assignment: Chapter 1.1–1.6; 2.1–2.2





































History of x-ray sources

• 1895 x-rays discovered byWilliam Rontgen

• 1st generationsynchrotrons initially usedin parasitic mode (SSRL,CHESS)

• 2nd generation werededicated sources (NSLS,SRC, CAMD)

• 3rd generation featuredinsertion devices (APS,ESRF, ALS)

• 4th generation are freeelectron lasers (LCLS)





































The classical x-ray

The classical plane wave representation of x-rays is:

E(r, t) = εEoei(k·r−ωt)

where ε is a unit vector in the direction of the electric field, k is thewavevector of the radiation along the propagation direction and ω is theangular frequency of oscillation of the radiation.

If E is in keV, the relationship among these quantities is given by:

~ω = hν = E , λν = c

λ = hc/E= (4.1357× 10−15 eV · s)(2.9979× 108 m/s)/E= (4.1357× 10−18 keV · s)(2.9979× 1017 nm/s)/E= 12.398 A · keV/E to give units of A


The classical x-ray



where ε is a unit vector in the direction of the electric field, k is thewavevector of the radiation along the propagation direction and ω is theangular frequency of oscillation of the radiation.If E is in keV, the relationship among these quantities is given by:

~ω = hν = E , λν = c



The classical x-ray



where ε is a unit vector in the direction of the electric field, k is thewavevector of the radiation along the propagation direction and ω is theangular frequency of oscillation of the radiation.If E is in keV, the relationship among these quantities is given by:

~ω = hν = E , λν = c



Interactions of x-rays with matter

For the purposes of this course, we care most about the interactions ofx-rays with matter.

There are four basic types of such interactions:

1 Elastic scattering

2 Inelastic scattering

3 Absorption

4 Pair production

We will only discuss the first three.







3 Absorption

4 Pair production








3 Absorption

4 Pair production








3 Absorption

4 Pair production








3 Absorption

4 Pair production








3 Absorption

4 Pair production



Elastic scattering geometry

k’

k

Q

an incident x-ray of wave number k

scatters elastically to k′

resulting in a scattering vector Qor in terms of momentum transfer: ~Q = ~k− ~k′



k’

k

Q

an incident x-ray of wave number kscatters elastically to k′




k’

k

Q


resulting in a scattering vector Q

or in terms of momentum transfer: ~Q = ~k− ~k′



k’

k

Q




Thomson scattering

Assumptions:plane wave of x-rays incident on a single electrontotal scattered energy ≡ total incoming energyelectron is a point chargescattered intensity ∝ 1/R2


Thomson scattering

Assumptions:plane wave of x-rays incident on a single electron

total scattered energy ≡ total incoming energyelectron is a point chargescattered intensity ∝ 1/R2


Thomson scattering

Assumptions:plane wave of x-rays incident on a single electrontotal scattered energy ≡ total incoming energy

electron is a point chargescattered intensity ∝ 1/R2


Thomson scattering

Assumptions:plane wave of x-rays incident on a single electrontotal scattered energy ≡ total incoming energyelectron is a point charge

scattered intensity ∝ 1/R2


Thomson scattering

Assumptions:plane wave of x-rays incident on a single electrontotal scattered energy ≡ total incoming energyelectron is a point chargescattered intensity ∝ 1/R2


Thomson scattering

Erad(R, t) = − −e4πε0c2R

ax(t ′) sin Ψ

where t ′ = t − R/c

ax(t ′) = − e

mExoe

−iωt′

= − e

mExoe

−iωte iωR/c

ax(t ′) = − e

mEine

iωR/c


Thomson scattering


ax(t ′) sin Ψ where t ′ = t − R/c

ax(t ′) = − e

mExoe

−iωt′

= − e

mExoe

−iωte iωR/c

ax(t ′) = − e

mEine

iωR/c


Thomson scattering



ax(t ′) = − e

mExoe

−iωt′

= − e

mExoe

−iωte iωR/c

ax(t ′) = − e

mEine

iωR/c


Thomson scattering



ax(t ′) = − e

mExoe

−iωt′ = − e

mExoe

−iωte iωR/c

ax(t ′) = − e

mEine

iωR/c


Thomson scattering



ax(t ′) = − e

mExoe

−iωt′ = − e

mExoe

−iωte iωR/c

ax(t ′) = − e

mEine

iωR/c


Thomson scattering


−em

EineiωR/c sin Ψ

Erad(R, t)

Ein= − e2

4πε0mc2e iωR/c

Rsin Ψ but k = ω/c


Thomson scattering


−em

EineiωR/c sin Ψ

Erad(R, t)

Ein= − e2

4πε0mc2e iωR/c

Rsin Ψ

but k = ω/c


Thomson scattering


−em

EineiωR/c sin Ψ

Erad(R, t)

Ein= − e2

4πε0mc2e iωR/c

Rsin Ψ but k = ω/c


Thomson scattering

Erad(R, t)

Ein= − e2

4πε0mc2e ikR

Rsin Ψ = −ro

e ikR

Rsin Ψ

r0 =e2

4πε0mc2= 2.82× 10−5A


Thomson scattering

Erad(R, t)

Ein= − e2

4πε0mc2e ikR

Rsin Ψ = −ro

e ikR

Rsin Ψ

r0 =e2

4πε0mc2= 2.82× 10−5A


Scattering cross-section

Detector of solid angle ∆Ω at a distance R from electronCross-section of incoming beam = Ao

Cross section of scattered beam (into detector) = R2∆Ω

IscattIo

=|Erad |2

|Ein|2R2∆Ω



Detector of solid angle ∆Ω at a distance R from electron

Cross-section of incoming beam = Ao


IscattIo

=|Erad |2

|Ein|2R2∆Ω





IscattIo

=|Erad |2

|Ein|2R2∆Ω





IscattIo

=|Erad |2

|Ein|2R2∆Ω





IscattIo

=|Erad |2

|Ein|2R2∆Ω



Differential cross-section is obtained by normalizing

dσ

dΩ=

Iscatt(Io/Ao) ∆Ω

=|Erad |2

|Ein|2R2 = r2o sin2 Ψ

|Erad |2

|Ein|2R2 = r2o

e ikRe−ikR

R2R2sin2 Ψ

= r2o sin2 Ψ




dσ

dΩ=

Iscatt(Io/Ao) ∆Ω

=|Erad |2


|Erad |2

|Ein|2R2 = r2o

e ikRe−ikR

R2R2sin2 Ψ

= r2o sin2 Ψ




dσ

dΩ=

Iscatt(Io/Ao) ∆Ω

=|Erad |2


|Erad |2

|Ein|2R2 = r2o

e ikRe−ikR

R2R2sin2 Ψ

= r2o sin2 Ψ




dσ

dΩ=

Iscatt(Io/Ao) ∆Ω

=|Erad |2

|Ein|2R2

= r2o sin2 Ψ

|Erad |2

|Ein|2R2 = r2o

e ikRe−ikR

R2R2sin2 Ψ

= r2o sin2 Ψ




dσ

dΩ=

Iscatt(Io/Ao) ∆Ω

=|Erad |2

|Ein|2R2

= r2o sin2 Ψ

|Erad |2

|Ein|2R2 = r2o

e ikRe−ikR

R2R2sin2 Ψ

= r2o sin2 Ψ




dσ

dΩ=

Iscatt(Io/Ao) ∆Ω

=|Erad |2

|Ein|2R2

= r2o sin2 Ψ

|Erad |2

|Ein|2R2 = r2o

e ikRe−ikR

R2R2sin2 Ψ = r2o sin2 Ψ




dσ

dΩ=

Iscatt(Io/Ao) ∆Ω

=|Erad |2


|Erad |2

|Ein|2R2 = r2o

e ikRe−ikR

R2R2sin2 Ψ = r2o sin2 Ψ


Total cross-section

Integrate to obtain the total Thomson scattering cross-section from anelectron.

If displacement is in vertical direction, sin Ψ term is replacedby unity and if the source is unpolarized, it is a combination.

σ =8π

3r2o

= 0.665× 10−24 cm2

= 0.665 barn

Polarization factor =

1

sin2 Ψ12

(1 + sin2 Ψ

)


Total cross-section



σ =8π

3r2o

= 0.665× 10−24 cm2

= 0.665 barn


1

sin2 Ψ12

(1 + sin2 Ψ

)


Total cross-section



σ =8π

3r2o

= 0.665× 10−24 cm2

= 0.665 barn


1

sin2 Ψ12

(1 + sin2 Ψ

)


Total cross-section

Integrate to obtain the total Thomson scattering cross-section from anelectron. If displacement is in vertical direction, sin Ψ term is replacedby unity and if the source is unpolarized, it is a combination.

σ =8π

3r2o

= 0.665× 10−24 cm2

= 0.665 barn


1

sin2 Ψ12

(1 + sin2 Ψ

)


Total cross-section

Integrate to obtain the total Thomson scattering cross-section from anelectron. If displacement is in vertical direction, sin Ψ term is replacedby unity and if the source is unpolarized, it is a combination.

σ =8π

3r2o

= 0.665× 10−24 cm2

= 0.665 barn


1

sin2 Ψ12

(1 + sin2 Ψ

)C. Segre (IIT) PHYS 570 - Fall 2013 August 19, 2013 17 / 21

Atomic scattering

phase shift arises from scattering off differentportions of extended electron distribution

∆φ(r) = (k− k′) · r = Q · r

r θ

k’

k

Q

θ

|Q| = 2 |k| sinθ = 4πλ sinθ


Atomic scattering

phase shift arises from scattering off differentportions of extended electron distribution

∆φ(r) = (k− k′) · r = Q · r

r θ

k’

k

Q

θ

|Q| = 2 |k| sinθ = 4πλ sinθ


Atomic form factor

the volume element at r contributes −roρ(r)d3r with phase factor e iQ·r

for an entire atom, integrate to get the atomic form factor f o(Q):

−ro f o(Q) = −ro∫ρ(r)e iQ·rd3r

Electrons which are tightly bound cannot respond like a free electron. Thisresults in a depression of the atomic form factor, called f ′ and a lossy termnear an ionization energy, called f ′′. Together these are the anomalouscorrections to the atomic form factor.

3000 4000 5000 6000 7000Energy (eV)

f

f

the total atomic scattering factor is

f (Q, ~ω) = f o(Q) + f ′(~ω) + if ′′(~ω)


Atomic form factor





3000 4000 5000 6000 7000Energy (eV)

f

f


f (Q, ~ω) = f o(Q) + f ′(~ω) + if ′′(~ω)


Atomic form factor





3000 4000 5000 6000 7000Energy (eV)

f

f


f (Q, ~ω) = f o(Q) + f ′(~ω) + if ′′(~ω)


Atomic form factor





3000 4000 5000 6000 7000Energy (eV)

f

f


f (Q, ~ω) = f o(Q) + f ′(~ω) + if ′′(~ω)


Atomic form factor





3000 4000 5000 6000 7000Energy (eV)

f

f


f (Q, ~ω) = f o(Q) + f ′(~ω) + if ′′(~ω)


Atomic form factor





3000 4000 5000 6000 7000Energy (eV)

f

f


f (Q, ~ω) = f o(Q) + f ′(~ω) + if ′′(~ω)


Atomic form factor





3000 4000 5000 6000 7000Energy (eV)

f

f


f (Q, ~ω) = f o(Q) + f ′(~ω) + if ′′(~ω)


Atomic form factor

The atomic form factor has an angulardependence

Q =4π

λsin θ

Lighter atoms (blue is oxygen) havewider form factor


Atomic form factor


Q =4π

λsin θ



Atomic form factor


Q =4π

λsin θ



Scattering from atoms: all effects

Scattering from an atom is built up from component quantities:

Thomson scattering from a single electron

atomic form factor

anomalous scattering terms

polarization factor

−ro = − e2

4πε0mc2

f o(Q) =

∫ρ(r)e iQ·rd3r

f ′(~ω) + if ′′(~ω)

P =

1

sin2 Ψ12(1 + sin2 Ψ)

− ro f (Q, ~ω) sin2 Ψ = −ro[f o(Q)

+ f ′(~ω) + if ′′(~ω)

]sin2 Ψ





atomic form factor


polarization factor

−ro = − e2

4πε0mc2

f o(Q) =

∫ρ(r)e iQ·rd3r

f ′(~ω) + if ′′(~ω)

P =

1


− ro

f (Q, ~ω) sin2 Ψ

= −ro

[f o(Q)

+ f ′(~ω) + if ′′(~ω)

]sin2 Ψ





atomic form factor


polarization factor

−ro = − e2

4πε0mc2

f o(Q) =

∫ρ(r)e iQ·rd3r

f ′(~ω) + if ′′(~ω)

P =

1


− ro f (Q, ~ω)

sin2 Ψ

= −ro[f o(Q)

+ f ′(~ω) + if ′′(~ω)

]

sin2 Ψ





atomic form factor


polarization factor

−ro = − e2

4πε0mc2

f o(Q) =

∫ρ(r)e iQ·rd3r

f ′(~ω) + if ′′(~ω)

P =

1


− ro f (Q, ~ω)

sin2 Ψ

= −ro[f o(Q) + f ′(~ω) + if ′′(~ω)

]

sin2 Ψ





atomic form factor


polarization factor

−ro = − e2

4πε0mc2

f o(Q) =

∫ρ(r)e iQ·rd3r

f ′(~ω) + if ′′(~ω)

P =

1


− ro f (Q, ~ω) sin2 Ψ = −ro[f o(Q) + f ′(~ω) + if ′′(~ω)

]sin2 Ψ


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