phys 570 - introduction to synchrotron radiationcsrri.iit.edu/~segre/phys570/18s/lecture_01.pdf ·...

PHYS 570 - Introduction to Synchrotron Radiation

Term: Spring 2018Meetings: Tuesday & Thursday 13:50-15:05Location: 213 Stuart Building

Instructor: Carlo SegreOffice: 136A 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/phys570/18S

C. Segre (IIT) PHYS 570 - Spring 2018 January 09, 2018 1 / 20

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• 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 the APS User Portal,

https://www1.aps.anl.gov/Users-Information and register as a newuser.

• 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 March

Course syllabus

• Homework assignments

• In-class student presentations on research topics• Choose a research article which features a synchrotron technique• Timetable will be posted

Course syllabus

Course grading

33% – Homework assignments

Weekly or bi-weeklyDue at beginning of classMay be turned in via Blackboard

33% – General User Proposal

33% – Final Exam Presentation

Grading scaleA – 80% to 100%B – 65% to 80%C – 50% to 65%E – 0% to 50%

Course grading

33% – Homework assignmentsWeekly or bi-weekly

Due at beginning of classMay be turned in via Blackboard

Course grading

33% – Homework assignmentsWeekly or bi-weeklyDue at beginning of class

May be turned in via Blackboard

Course grading

33% – Homework assignmentsWeekly or bi-weeklyDue at beginning of classMay be turned in via Blackboard

Course grading

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

• Small angle scattering

• Photoelectric absorption

• Resonant scattering

• Imaging

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

• Hephaestus from the Demeter suite:http://bruceravel.github.io/demeter/

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

• X-ray Oriented Programs:https://www1.aps.anl.gov/Science/Scientific-Software/XOP

Today’s outline - January 09, 2018

• The big picture

• 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

• The big picture

Why synchrotron radiation?

X-rays are the ideal structural probe for interatomic dis-tances with wavelengths of ∼1 A

Laboratory x-ray sources are extremely useful and havegotten much better in the past decades but some exper-iments can only be done at a synchrotron

Synchrotron sources provide superior flux, brilliance, andtunability

Synchrotron sources and particularly FELs produce co-herent beams

The broad range of techniques make synchrotron x-raysources to nearly any science or engineering field

A bit about my research. . .

Lithiation Delithiation

SnPx Sn LiySn

0 200 400 6000 200 400 6000

Capacity (mAh g-1)

| (R)|(Å-3)

“In situ EXAFS-derived mechanism of highly reversible tin phosphide/graphitecomposite anode for Li-ion batteries,” Y. Ding, Z. Li, E.V. Timofeeva, and C.U. Segre,Adv. Energy Mater. 1702134 (2017).

A bit about my research. . .

Lithiation Delithiation

SnPx Sn LiySn

0 200 400 6000 200 400 6000

Capacity (mAh g-1)

| (R)|(Å-3)

“In situ EXAFS-derived mechanism of highly reversible tin phosphide/graphitecomposite anode for Li-ion batteries,” Y. Ding, Z. Li, E.V. Timofeeva, and C.U. Segre,Adv. Energy Mater. 1702134 (2017).

History of x-ray sources

1900 1950 2000

Peak X

-ray B

Free electron lasers

Synchrotrons

X-ray tubes

• 1895 x-rays discovered by WilliamRontgen

• 1st generation synchrotrons initiallyused in parasitic mode (SSRL,CHESS)

• 2nd generation were dedicatedsources (NSLS, SRC, CAMD)

• 3rd generation featured insertiondevices (APS, ESRF, ALS)

• 4th generation are free electronlasers (LCLS, XFEL)

1900 1950 2000

Peak X

-ray B

Synchrotrons

X-ray tubes

1900 1950 2000

Peak X

-ray B

Synchrotrons

X-ray tubes

1900 1950 2000

Peak X

-ray B

Synchrotrons

X-ray tubes

1900 1950 2000

Peak X

-ray B

Synchrotrons

X-ray tubes

The classical x-ray

The classical plane wave representation of x-rays is:

E(r, t) = εE0ei(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 the energy, E is in keV, the relationship among these quantities is givenby:

~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× 1018 A/s)/E= 12.398 A · keV/E to give units of A

The classical x-ray

~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.

~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.

~ω = hν = E , λν = c

The classical x-ray

~ω = hν = E , λν = c

The classical x-ray

~ω = hν = E , λν = c

The classical x-ray

~ω = hν = E , λν = c

The classical x-ray

~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

Most of the phenomena we will discuss can be treated classically as elasticscattering of electromagnetic waves (x-rays)

The typical scattering geometry is

where an incident x-ray of wave number k

scatters elastically from an electron to k′

resulting in a scattering vector Q

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

Start with the scattering from a single electron, then build up to morecomplexity

Elastic scattering

Thomson scattering

Assumptions:

incident x-ray plane waveelectron is a point chargescattering is elasticscattered intensity ∝ 1/R2

The electron is exposed to theincident electric field Ein(t ′) andis accelerated

The acceleration of the electron,ax(t ′), results in the radiation ofa spherical wave with the samefrequency

The observer at R “sees” a scat-tered electric field Erad(R, t) ata later time t = t ′ + R/c

Using this, calculate the elasticscattering cross-section

Thomson scattering

Assumptions:

incident x-ray plane wave

electron is a point chargescattering is elasticscattered intensity ∝ 1/R2

Thomson scattering

Assumptions:

incident x-ray plane waveelectron is a point charge

scattering is elasticscattered intensity ∝ 1/R2

Thomson scattering

Assumptions:

incident x-ray plane waveelectron is a point chargescattering is elastic

scattered intensity ∝ 1/R2

Thomson scattering

Assumptions:

Thomson scattering

Assumptions:

Thomson scattering

Assumptions:

Thomson scattering

Assumptions:

Thomson scattering

Assumptions:

Thomson scattering

Erad(R, t) = − −e4πε0c2R

ax(t ′) sin Ψ

where t ′ = t − R/c

ax(t ′) = − e

−iωt′

= − e

−iωte iωR/c

ax(t ′) = − e

iωR/c

Thomson scattering

ax(t ′) sin Ψ where t ′ = t − R/c

ax(t ′) = − e

−iωt′

= − e

−iωte iωR/c

ax(t ′) = − e

iωR/c

Thomson scattering

ax(t ′) = − e

−iωt′

= − e

−iωte iωR/c

ax(t ′) = − e

iωR/c

Thomson scattering

ax(t ′) = − e

−iωt′ = − e

−iωte iωR/c

ax(t ′) = − e

iωR/c

Thomson scattering

ax(t ′) = − e

−iωt′ = − e

−iωte iωR/c

ax(t ′) = − e

iωR/c

Thomson scattering

EineiωR/c sin Ψ

Erad(R, t)

Ein= − e2

4πε0mc2e iωR/c

Rsin Ψ but k = ω/c

Thomson scattering

EineiωR/c sin Ψ

Erad(R, t)

Ein= − e2

4πε0mc2e iωR/c

Rsin Ψ

but k = ω/c

Thomson scattering

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 = −r0

Rsin Ψ

r0 =e2

4πε0mc2= 2.82× 10−5A

Thomson scattering

Erad(R, t)

Ein= − e2

4πε0mc2e ikR

Rsin Ψ = −r0

Rsin Ψ

r0 =e2

4πε0mc2= 2.82× 10−5A

Scattering cross-section

Detector of solid angle ∆Ω at a dis-tance R from electronCross-section of incoming beam isA0

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

Φ0 ≡I0A0

= c|Ein|2

Isc ∝ c(R2∆Ω)|Erad |2

~ωIscI0

=|Erad |2

|Ein|2R2∆Ω

Detector of solid angle ∆Ω at a dis-tance R from electron

Cross-section of incoming beam isA0

Φ0 ≡I0A0

= c|Ein|2

~ωIscI0

=|Erad |2

|Ein|2R2∆Ω

Φ0 ≡I0A0

= c|Ein|2

~ωIscI0

=|Erad |2

|Ein|2R2∆Ω

Φ0 ≡I0A0

= c|Ein|2

~ωIscI0

=|Erad |2

|Ein|2R2∆Ω

Φ0 ≡I0A0

= c|Ein|2

=|Erad |2

|Ein|2R2∆Ω

Φ0 ≡I0A0

= c|Ein|2

=|Erad |2

|Ein|2R2∆Ω

Φ0 ≡I0A0

= c|Ein|2

~ωIscI0

=|Erad |2

|Ein|2R2∆Ω

Differential cross-section is obtained by normalizing

Φ0∆Ω=

Isc(I0/A0) ∆Ω

=|Erad |2

|Ein|2R2 = r20 sin2 Ψ

Ein= −r0

∣∣ε · ε′∣∣ = −r0e ikR

∣∣cos(π2 −Ψ

)∣∣ = −r0e ikR

Rsin Ψ

Φ0∆Ω=

Isc(I0/A0) ∆Ω

=|Erad |2

Ein= −r0

∣∣ε · ε′∣∣ = −r0e ikR

∣∣cos(π2 −Ψ

)∣∣ = −r0e ikR

Rsin Ψ

IscΦ0∆Ω

(I0/A0) ∆Ω=|Erad |2

Ein= −r0

∣∣ε · ε′∣∣ = −r0e ikR

∣∣cos(π2 −Ψ

)∣∣ = −r0e ikR

Rsin Ψ

IscΦ0∆Ω

(I0/A0) ∆Ω

=|Erad |2

Ein= −r0

∣∣ε · ε′∣∣ = −r0e ikR

∣∣cos(π2 −Ψ

)∣∣ = −r0e ikR

Rsin Ψ

IscΦ0∆Ω

(I0/A0) ∆Ω=|Erad |2

|Ein|2R2

= r20 sin2 Ψ

Ein= −r0

∣∣ε · ε′∣∣ = −r0e ikR

∣∣cos(π2 −Ψ

)∣∣ = −r0e ikR

Rsin Ψ

IscΦ0∆Ω

(I0/A0) ∆Ω=|Erad |2

|Ein|2R2

= r20 sin2 Ψ

Ein= −r0

∣∣ε · ε′∣∣

= −r0e ikR

∣∣cos(π2 −Ψ

)∣∣ = −r0e ikR

Rsin Ψ

IscΦ0∆Ω

(I0/A0) ∆Ω=|Erad |2

|Ein|2R2

= r20 sin2 Ψ

Ein= −r0

∣∣ε · ε′∣∣ = −r0e ikR

∣∣cos(π2 −Ψ

)∣∣

= −r0e ikR

Rsin Ψ

IscΦ0∆Ω

(I0/A0) ∆Ω=|Erad |2

|Ein|2R2

= r20 sin2 Ψ

Ein= −r0

∣∣ε · ε′∣∣ = −r0e ikR

∣∣cos(π2 −Ψ

)∣∣ = −r0e ikR

Rsin Ψ

IscΦ0∆Ω

(I0/A0) ∆Ω=|Erad |2

Ein= −r0

∣∣ε · ε′∣∣ = −r0e ikR

∣∣cos(π2 −Ψ

)∣∣ = −r0e ikR

Rsin 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

= 0.665× 10−24 cm2

= 0.665 barn

Polarization factor =

sin2 Ψ12

(1 + sin2 Ψ

Total cross-section

σ =8π

= 0.665× 10−24 cm2

= 0.665 barn

sin2 Ψ12

(1 + sin2 Ψ

Total cross-section

σ =8π

= 0.665× 10−24 cm2

= 0.665 barn

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

= 0.665× 10−24 cm2

= 0.665 barn

sin2 Ψ12

(1 + sin2 Ψ

)C. Segre (IIT) PHYS 570 - Spring 2018 January 09, 2018 20 / 20

phys 570 - introduction to synchrotron radiationcsrri.iit.edu/~segre/phys570/18s/lecture_01.pdf ·...

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