phys 570 - introduction to synchrotron radiationcsrri.iit.edu/~segre/phys570/10f/lecture_01.pdf ·...

PHYS 570 - Introduction to Synchrotron Radiation

Term: Fall 2010Meetings: Tuesday & Thursday 10:00-11:15Location: 245 Engineering 1 BuildingInstructor: Carlo SegreOffice: 166A Life SciencesPhone: 312.567.3498email: [email protected]: Elements of Modern X-Ray Physics,

J. Als-Nielsen and D. McMorrow (Wiley, 2001)Web Site: http://csrri.iit.edu/˜segre/phys570/10F

C. Segre (IIT) PHYS 570 - Fall 2010 August 24, 2010 1 / 19

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 Syllabus

• Focus on applications of synchrotron radiation

• Homework assignments, exams (?)

• 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)

• All students 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 second week of October

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

• 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

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× 10−15eV · s)(2.9979× 108m/s)/E= 12.398/E in 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

Elastic Scattering Geometry

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′

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

resulting in a scattering vector Q

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

Thomson Scattering

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

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

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

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 ′) where t ′ = t − R/c

ax(t ′) = − e

−iωt′cosψ = − e

−iωte iωR/ccosψ

ax(t ′) = − e

iωR/ccosψ

Thomson Scattering

ax(t ′) = − e

iωR/ccosψ

Thomson Scattering

ax(t ′) = − e

iωR/ccosψ

Thomson Scattering

EineiωR/ccosψ

Erad(R, t)

Ein= − e2

4πε0mc2e iωR/c

Rcosψ but k = ω/c

Thomson Scattering

EineiωR/ccosψ

Erad(R, t)

Ein= − e2

4πε0mc2e iωR/c

Rcosψ but k = ω/c

Thomson Scattering

Erad(R, t)

Ein= − e2

4πε0mc2e ikR

Rcosψ = −ro

Rcosψ

r0 = e2

4πε0mc2= 2.82× 10−5A

Scattering Cross-Section

detector of solid angle Ω at a distance R from electron

cross-section of incoming beam = Ao

Cross section of scattered beam (into detector) = R2Ω

IscattIo

=|Erad |2

|Ein|2R2Ω

detector of solid angle Ω at a distance R from electroncross-section of incoming beam = Ao

IscattIo

=|Erad |2

|Ein|2R2Ω

detector of solid angle Ω at a distance R from electroncross-section of incoming beam = Ao

IscattIo

=|Erad |2

|Ein|2R2Ω

differential cross-section is obtained by normalizing

Iscatt(Io/Ao) Ω

=|Erad |2

|Ein|2R2

|Erad |2

|Ein|2= r2o

e ikRe−ikR

R2R2cosψ2

Iscatt(Io/Ao) Ω

=|Erad |2

|Ein|2R2

|Erad |2

|Ein|2= r2o

e ikRe−ikR

R2R2cosψ2

Iscatt(Io/Ao) Ω

=|Erad |2

|Ein|2R2

|Erad |2

|Ein|2= r2o

e ikRe−ikR

R2R2cosψ2

|Erad |2

|Ein|2= r2o

e ikRe−ikR

R2R2cosψ2

dΩ= r2o cos

Total Cross-Section

σ =8π

3r2o = 0.665× 10−24cm2 = 0.665barn

Total Cross-Section

Polarization factor = cos2ψ1

(1 + cos2ψ

)C. Segre (IIT) PHYS 570 - Fall 2010 August 24, 2010 17 / 19

Atomic Scattering

phase shift arises from scattering off differentportions of extended electron distribution

∆φ(r) = (k− k′) · r = Q · r

|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

|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

3000 4000 5000 6000 7000Energy (eV)

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 (Q, ~ω) = f o(Q)+ f ′(~ω)+ if ′′(~ω)

Atomic Form Factor

3000 4000 5000 6000 7000Energy (eV)

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

Atomic Form Factor

3000 4000 5000 6000 7000Energy (eV)

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

phys 570 - introduction to synchrotron radiationcsrri.iit.edu/~segre/phys570/10f/lecture_01.pdf ·...

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