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Page 1: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Today’s Outline - October 31, 2016

• Dumond diagrams

• Monochromators

• Photoelectric absorption

• Cross-section of an isolated atom

• X-ray absorption spectroscopy

• EXAFS of NFA steels

Homework Assignment #05:Chapter 5: 1, 3, 7, 9, 10due Wednesday, November 02, 2016

Homework Assignment #06:Chapter 6: 1,6,7,8,9due Monday, November 14, 2016

No class on Wednesday, November 09, 2016

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 1 / 21

Page 2: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Today’s Outline - October 31, 2016

• Dumond diagrams

• Monochromators

• Photoelectric absorption

• Cross-section of an isolated atom

• X-ray absorption spectroscopy

• EXAFS of NFA steels

Homework Assignment #05:Chapter 5: 1, 3, 7, 9, 10due Wednesday, November 02, 2016

Homework Assignment #06:Chapter 6: 1,6,7,8,9due Monday, November 14, 2016

No class on Wednesday, November 09, 2016

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 1 / 21

Page 3: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Today’s Outline - October 31, 2016

• Dumond diagrams

• Monochromators

• Photoelectric absorption

• Cross-section of an isolated atom

• X-ray absorption spectroscopy

• EXAFS of NFA steels

Homework Assignment #05:Chapter 5: 1, 3, 7, 9, 10due Wednesday, November 02, 2016

Homework Assignment #06:Chapter 6: 1,6,7,8,9due Monday, November 14, 2016

No class on Wednesday, November 09, 2016

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 1 / 21

Page 4: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Today’s Outline - October 31, 2016

• Dumond diagrams

• Monochromators

• Photoelectric absorption

• Cross-section of an isolated atom

• X-ray absorption spectroscopy

• EXAFS of NFA steels

Homework Assignment #05:Chapter 5: 1, 3, 7, 9, 10due Wednesday, November 02, 2016

Homework Assignment #06:Chapter 6: 1,6,7,8,9due Monday, November 14, 2016

No class on Wednesday, November 09, 2016

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 1 / 21

Page 5: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Today’s Outline - October 31, 2016

• Dumond diagrams

• Monochromators

• Photoelectric absorption

• Cross-section of an isolated atom

• X-ray absorption spectroscopy

• EXAFS of NFA steels

Homework Assignment #05:Chapter 5: 1, 3, 7, 9, 10due Wednesday, November 02, 2016

Homework Assignment #06:Chapter 6: 1,6,7,8,9due Monday, November 14, 2016

No class on Wednesday, November 09, 2016

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 1 / 21

Page 6: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Today’s Outline - October 31, 2016

• Dumond diagrams

• Monochromators

• Photoelectric absorption

• Cross-section of an isolated atom

• X-ray absorption spectroscopy

• EXAFS of NFA steels

Homework Assignment #05:Chapter 5: 1, 3, 7, 9, 10due Wednesday, November 02, 2016

Homework Assignment #06:Chapter 6: 1,6,7,8,9due Monday, November 14, 2016

No class on Wednesday, November 09, 2016

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 1 / 21

Page 7: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Today’s Outline - October 31, 2016

• Dumond diagrams

• Monochromators

• Photoelectric absorption

• Cross-section of an isolated atom

• X-ray absorption spectroscopy

• EXAFS of NFA steels

Homework Assignment #05:Chapter 5: 1, 3, 7, 9, 10due Wednesday, November 02, 2016

Homework Assignment #06:Chapter 6: 1,6,7,8,9due Monday, November 14, 2016

No class on Wednesday, November 09, 2016

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 1 / 21

Page 8: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Today’s Outline - October 31, 2016

• Dumond diagrams

• Monochromators

• Photoelectric absorption

• Cross-section of an isolated atom

• X-ray absorption spectroscopy

• EXAFS of NFA steels

Homework Assignment #05:Chapter 5: 1, 3, 7, 9, 10due Wednesday, November 02, 2016

Homework Assignment #06:Chapter 6: 1,6,7,8,9due Monday, November 14, 2016

No class on Wednesday, November 09, 2016

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 1 / 21

Page 9: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Today’s Outline - October 31, 2016

• Dumond diagrams

• Monochromators

• Photoelectric absorption

• Cross-section of an isolated atom

• X-ray absorption spectroscopy

• EXAFS of NFA steels

Homework Assignment #05:Chapter 5: 1, 3, 7, 9, 10due Wednesday, November 02, 2016

Homework Assignment #06:Chapter 6: 1,6,7,8,9due Monday, November 14, 2016

No class on Wednesday, November 09, 2016

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 1 / 21

Page 10: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Today’s Outline - October 31, 2016

• Dumond diagrams

• Monochromators

• Photoelectric absorption

• Cross-section of an isolated atom

• X-ray absorption spectroscopy

• EXAFS of NFA steels

Homework Assignment #05:Chapter 5: 1, 3, 7, 9, 10due Wednesday, November 02, 2016

Homework Assignment #06:Chapter 6: 1,6,7,8,9due Monday, November 14, 2016

No class on Wednesday, November 09, 2016

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 1 / 21

Page 11: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Today’s Outline - October 31, 2016

• Dumond diagrams

• Monochromators

• Photoelectric absorption

• Cross-section of an isolated atom

• X-ray absorption spectroscopy

• EXAFS of NFA steels

Homework Assignment #05:Chapter 5: 1, 3, 7, 9, 10due Wednesday, November 02, 2016

Homework Assignment #06:Chapter 6: 1,6,7,8,9due Monday, November 14, 2016

No class on Wednesday, November 09, 2016

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 1 / 21

Page 12: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Final projects & presentations

In-class student presentations on research topics

• Choose a research article which features a synchrotrontechnique

• Get it approved by instructor first!

• Schedule a 15 minute time on Final Exam Day(tentatively, Monday, December 5, 2016, will confirmtimes)

Final project - writing a General User Proposal

• Think of a research problem (could be yours) that canbe approached using synchrotron radiation techniques

• Make proposal and get approval from instructor beforestarting

• Must be different techique than your presentation!

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 2 / 21

Page 13: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Final projects & presentations

In-class student presentations on research topics

• Choose a research article which features a synchrotrontechnique

• Get it approved by instructor first!

• Schedule a 15 minute time on Final Exam Day(tentatively, Monday, December 5, 2016, will confirmtimes)

Final project - writing a General User Proposal

• Think of a research problem (could be yours) that canbe approached using synchrotron radiation techniques

• Make proposal and get approval from instructor beforestarting

• Must be different techique than your presentation!

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 2 / 21

Page 14: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Asymmetric geometry

In general the diffracting planes are not precisely aligned with the surfaceof the crystal.

Parameterized by the asymmetryangle 0 < α < θBragg

This leads to a beam compression

b =sin θisin θe

=sin(θ + α)

sin(θ − α)

He =Hi

b

according to Liouville’s theorem,the divergence of the beam mustalso change

δθe =√b(ζD tan θ)

δθi =1√b

(ζD tan θ)

δθiHi

=1√b

(ζD tan θ)bHe =√b(ζD tan θ)He

= δθeHe

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 3 / 21

Page 15: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Asymmetric geometry

In general the diffracting planes are not precisely aligned with the surfaceof the crystal.

Parameterized by the asymmetryangle 0 < α < θBragg

This leads to a beam compression

b =sin θisin θe

=sin(θ + α)

sin(θ − α)

He =Hi

b

according to Liouville’s theorem,the divergence of the beam mustalso change

δθe =√b(ζD tan θ)

δθi =1√b

(ζD tan θ)

δθiHi

=1√b

(ζD tan θ)bHe =√b(ζD tan θ)He

= δθeHe

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 3 / 21

Page 16: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Asymmetric geometry

In general the diffracting planes are not precisely aligned with the surfaceof the crystal.

Parameterized by the asymmetryangle 0 < α < θBragg

This leads to a beam compression

b =sin θisin θe

=sin(θ + α)

sin(θ − α)

He =Hi

b

according to Liouville’s theorem,the divergence of the beam mustalso change

δθe =√b(ζD tan θ)

δθi =1√b

(ζD tan θ)

δθiHi

=1√b

(ζD tan θ)bHe =√b(ζD tan θ)He

= δθeHe

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 3 / 21

Page 17: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Asymmetric geometry

In general the diffracting planes are not precisely aligned with the surfaceof the crystal.

Parameterized by the asymmetryangle 0 < α < θBragg

This leads to a beam compression

b =sin θisin θe

=sin(θ + α)

sin(θ − α)

He =Hi

b

according to Liouville’s theorem,the divergence of the beam mustalso change

δθe =√b(ζD tan θ)

δθi =1√b

(ζD tan θ)

δθiHi

=1√b

(ζD tan θ)bHe =√b(ζD tan θ)He

= δθeHe

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 3 / 21

Page 18: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Asymmetric geometry

In general the diffracting planes are not precisely aligned with the surfaceof the crystal.

Parameterized by the asymmetryangle 0 < α < θBragg

This leads to a beam compression

b =sin θisin θe

=sin(θ + α)

sin(θ − α)

He =Hi

b

according to Liouville’s theorem,the divergence of the beam mustalso change

δθe =√b(ζD tan θ)

δθi =1√b

(ζD tan θ)

δθiHi

=1√b

(ζD tan θ)bHe =√b(ζD tan θ)He

= δθeHe

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 3 / 21

Page 19: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Asymmetric geometry

In general the diffracting planes are not precisely aligned with the surfaceof the crystal.

Parameterized by the asymmetryangle 0 < α < θBragg

This leads to a beam compression

b =sin θisin θe

=sin(θ + α)

sin(θ − α)

He =Hi

b

according to Liouville’s theorem,the divergence of the beam mustalso change

δθe =√b(ζD tan θ)

δθi =1√b

(ζD tan θ)

δθiHi

=1√b

(ζD tan θ)bHe =√b(ζD tan θ)He

= δθeHe

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 3 / 21

Page 20: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Asymmetric geometry

In general the diffracting planes are not precisely aligned with the surfaceof the crystal.

Parameterized by the asymmetryangle 0 < α < θBragg

This leads to a beam compression

b =sin θisin θe

=sin(θ + α)

sin(θ − α)

He =Hi

b

according to Liouville’s theorem,the divergence of the beam mustalso change

δθe =√b(ζD tan θ)

δθi =1√b

(ζD tan θ)

δθiHi

=1√b

(ζD tan θ)bHe =√b(ζD tan θ)He

= δθeHe

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 3 / 21

Page 21: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Asymmetric geometry

In general the diffracting planes are not precisely aligned with the surfaceof the crystal.

Parameterized by the asymmetryangle 0 < α < θBragg

This leads to a beam compression

b =sin θisin θe

=sin(θ + α)

sin(θ − α)

He =Hi

b

according to Liouville’s theorem,the divergence of the beam mustalso change

δθe =√b(ζD tan θ)

δθi =1√b

(ζD tan θ)

δθiHi

=1√b

(ζD tan θ)bHe =√b(ζD tan θ)He

= δθeHe

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 3 / 21

Page 22: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Asymmetric geometry

In general the diffracting planes are not precisely aligned with the surfaceof the crystal.

Parameterized by the asymmetryangle 0 < α < θBragg

This leads to a beam compression

b =sin θisin θe

=sin(θ + α)

sin(θ − α)

He =Hi

b

according to Liouville’s theorem,the divergence of the beam mustalso change

δθe =√b(ζD tan θ)

δθi =1√b

(ζD tan θ)

δθiHi

=1√b

(ζD tan θ)bHe =√b(ζD tan θ)He

= δθeHe

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 3 / 21

Page 23: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Asymmetric geometry

In general the diffracting planes are not precisely aligned with the surfaceof the crystal.

Parameterized by the asymmetryangle 0 < α < θBragg

This leads to a beam compression

b =sin θisin θe

=sin(θ + α)

sin(θ − α)

He =Hi

b

according to Liouville’s theorem,the divergence of the beam mustalso change

δθe =√b(ζD tan θ)

δθi =1√b

(ζD tan θ)

δθiHi

=1√b

(ζD tan θ)bHe =√b(ζD tan θ)He = δθeHe

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 3 / 21

Page 24: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Asymmetric geometry

In general the diffracting planes are not precisely aligned with the surfaceof the crystal.

Parameterized by the asymmetryangle 0 < α < θBragg

This leads to a beam compression

b =sin θisin θe

=sin(θ + α)

sin(θ − α)

He =Hi

b

according to Liouville’s theorem,the divergence of the beam mustalso change

δθe =√b(ζD tan θ)

δθi =1√b

(ζD tan θ)

δθiHi =1√b

(ζD tan θ)bHe

=√b(ζD tan θ)He = δθeHe

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 3 / 21

Page 25: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Asymmetric geometry

In general the diffracting planes are not precisely aligned with the surfaceof the crystal.

Parameterized by the asymmetryangle 0 < α < θBragg

This leads to a beam compression

b =sin θisin θe

=sin(θ + α)

sin(θ − α)

He =Hi

b

according to Liouville’s theorem,the divergence of the beam mustalso change

δθe =√b(ζD tan θ)

δθi =1√b

(ζD tan θ)

δθiHi =1√b

(ζD tan θ)bHe =√b(ζD tan θ)He

= δθeHe

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 3 / 21

Page 26: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Asymmetric geometry

In general the diffracting planes are not precisely aligned with the surfaceof the crystal.

Parameterized by the asymmetryangle 0 < α < θBragg

This leads to a beam compression

b =sin θisin θe

=sin(θ + α)

sin(θ − α)

He =Hi

b

according to Liouville’s theorem,the divergence of the beam mustalso change

δθe =√b(ζD tan θ)

δθi =1√b

(ζD tan θ)

δθiHi =1√b

(ζD tan θ)bHe =√b(ζD tan θ)He = δθeHe

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 3 / 21

Page 27: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Rocking curve measurements

The measured “rocking” curve from a two crystal system is a convolutionof the Darwin curves of both crystals.

When the two crystals have amatched asymmetry, we get a triangle. When one asymmetry is muchhigher, then we can measure the Darwin curve of a single crystal.

output divergence on left, input divergence on right

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 4 / 21

Page 28: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Rocking curve measurements

The measured “rocking” curve from a two crystal system is a convolutionof the Darwin curves of both crystals. When the two crystals have amatched asymmetry, we get a triangle.

When one asymmetry is muchhigher, then we can measure the Darwin curve of a single crystal.

output divergence on left, input divergence on right

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 4 / 21

Page 29: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Rocking curve measurements

The measured “rocking” curve from a two crystal system is a convolutionof the Darwin curves of both crystals. When the two crystals have amatched asymmetry, we get a triangle.

When one asymmetry is muchhigher, then we can measure the Darwin curve of a single crystal.

output divergence on left, input divergence on right

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 4 / 21

Page 30: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Rocking curve measurements

The measured “rocking” curve from a two crystal system is a convolutionof the Darwin curves of both crystals. When the two crystals have amatched asymmetry, we get a triangle. When one asymmetry is muchhigher, then we can measure the Darwin curve of a single crystal.

output divergence on left, input divergence on right

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 4 / 21

Page 31: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Dumond diagram: no Darwin width

Transfer function of an optical element parameterized by angle andwavelength.

Here Darwin width is ignored.

0 0θi-θB θe-θB

λ

2d

∆θ

cosθΒ ∆θ

sin

θB

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 5 / 21

Page 32: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Dumond diagram: no Darwin width

Transfer function of an optical element parameterized by angle andwavelength. Here Darwin width is ignored.

0 0θi-θB θe-θB

λ

2d

∆θ

cosθΒ ∆θ

sin

θB

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 5 / 21

Page 33: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Dumond diagram: symmetric Bragg

Including the Darwin width, we have a bandpass in wavelength.

If inputbeam is perfectly collimated, so is output (vertical black line).

0 0θi-θB θe-θB

λ

2d

w0=sinθB ζD

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 6 / 21

Page 34: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Dumond diagram: symmetric Bragg

Including the Darwin width, we have a bandpass in wavelength. If inputbeam is perfectly collimated, so is output (vertical black line).

0 0θi-θB θe-θB

λ

2d

w0=sinθB ζD

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 6 / 21

Page 35: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Dumond diagram: asymmetric Bragg

For asymmetric crystal, the output beam is no longer collimated butacquires a divergence αe

0 0θi-θB θe-θB

λ

2d w0 b

b

w0

αe

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 7 / 21

Page 36: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Double crystal monochromators

∆θin

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 8 / 21

Page 37: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Double crystal monochromators

∆θin

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 8 / 21

Page 38: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Double crystal monochromators

∆θin

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 9 / 21

Page 39: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Double crystal monochromators

∆θin

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 9 / 21

Page 40: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Total cross section

The total cross-section forphoton “absorption” in-cludes elastic (or coher-ent) scattering, Compton(inelastic) scattering, andphotoelectric absorption.

Characteristic absorptionjumps depend on the ele-ment

These quantities vary significantly over many decades but can easily puton an equal footing.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 10 / 21

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Total cross section

The total cross-section forphoton “absorption” in-cludes elastic (or coher-ent) scattering, Compton(inelastic) scattering, andphotoelectric absorption.

Characteristic absorptionjumps depend on the ele-ment

These quantities vary significantly over many decades but can easily puton an equal footing.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 10 / 21

Page 42: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Total cross section

The total cross-section forphoton “absorption” in-cludes elastic (or coher-ent) scattering, Compton(inelastic) scattering, andphotoelectric absorption.

Characteristic absorptionjumps depend on the ele-ment

These quantities vary significantly over many decades but can easily puton an equal footing.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 10 / 21

Page 43: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Scaled absorption

T =I

I0= e−µz

µ =ρmNA

Mσa

σa ∼Z 4

E 3

scale σa for different ele-ments by E 3/Z 4 and plottogether

remarkably, all values lie on a common curve above the K edge andbetween the L and K edges and below the L edge

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 11 / 21

Page 44: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Scaled absorption

T =I

I0= e−µz

µ =ρmNA

Mσa

σa ∼Z 4

E 3

scale σa for different ele-ments by E 3/Z 4 and plottogether

remarkably, all values lie on a common curve above the K edge andbetween the L and K edges and below the L edge

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 11 / 21

Page 45: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Scaled absorption

T =I

I0= e−µz

µ =ρmNA

Mσa

σa ∼Z 4

E 3

scale σa for different ele-ments by E 3/Z 4 and plottogether

remarkably, all values lie on a common curve above the K edge andbetween the L and K edges and below the L edge

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 11 / 21

Page 46: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Scaled absorption

T =I

I0= e−µz

µ =ρmNA

Mσa

σa ∼Z 4

E 3

scale σa for different ele-ments by E 3/Z 4 and plottogether

remarkably, all values lie on a common curve above the K edge andbetween the L and K edges and below the L edge

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 11 / 21

Page 47: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Scaled absorption

T =I

I0= e−µz

µ =ρmNA

Mσa

σa ∼Z 4

E 3

scale σa for different ele-ments by E 3/Z 4 and plottogether

remarkably, all values lie on a common curve above the K edge andbetween the L and K edges and below the L edgeC. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 11 / 21

Page 48: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Scaled absorption

T =I

I0= e−µz

µ =ρmNA

Mσa

σa ∼Z 4

E 3

scale σa for different ele-ments by E 3/Z 4 and plottogether

remarkably, all values lie on a common curve above the K edge andbetween the L and K edges and below the L edge

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 11 / 21

Page 49: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Calculation of σa

From first-order perturbation theory, the absorption cross section is givenby

σa =2π

~cV 2

4π3

∫|Mif |2δ(Ef − Ei )q2 sin θdqdθdϕ

where the matrix element Mif be-tween the initial, 〈i |, and final, |f 〉,states is given by

The interaction Hamiltonian is ex-pressed in terms of the electromag-netic vector potential

Mif = 〈i |HI |f 〉

HI =e~p · ~Am

+e2A2

2m

~A = ε̂

√~

2ε0Vω

[ake

i~k·~r + a†ke−i~k·~r

]The first term gives absorption while the second produces Thomsonscattering so we take only the first into consideration now.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 12 / 21

Page 50: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Calculation of σa

From first-order perturbation theory, the absorption cross section is givenby

σa =2π

~cV 2

4π3

∫|Mif |2δ(Ef − Ei )q2 sin θdqdθdϕ

where the matrix element Mif be-tween the initial, 〈i |, and final, |f 〉,states is given by

The interaction Hamiltonian is ex-pressed in terms of the electromag-netic vector potential

Mif = 〈i |HI |f 〉

HI =e~p · ~Am

+e2A2

2m

~A = ε̂

√~

2ε0Vω

[ake

i~k·~r + a†ke−i~k·~r

]The first term gives absorption while the second produces Thomsonscattering so we take only the first into consideration now.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 12 / 21

Page 51: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Calculation of σa

From first-order perturbation theory, the absorption cross section is givenby

σa =2π

~cV 2

4π3

∫|Mif |2δ(Ef − Ei )q2 sin θdqdθdϕ

where the matrix element Mif be-tween the initial, 〈i |, and final, |f 〉,states is given by

The interaction Hamiltonian is ex-pressed in terms of the electromag-netic vector potential

Mif = 〈i |HI |f 〉

HI =e~p · ~Am

+e2A2

2m

~A = ε̂

√~

2ε0Vω

[ake

i~k·~r + a†ke−i~k·~r

]The first term gives absorption while the second produces Thomsonscattering so we take only the first into consideration now.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 12 / 21

Page 52: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Calculation of σa

From first-order perturbation theory, the absorption cross section is givenby

σa =2π

~cV 2

4π3

∫|Mif |2δ(Ef − Ei )q2 sin θdqdθdϕ

where the matrix element Mif be-tween the initial, 〈i |, and final, |f 〉,states is given by

The interaction Hamiltonian is ex-pressed in terms of the electromag-netic vector potential

Mif = 〈i |HI |f 〉

HI =e~p · ~Am

+e2A2

2m

~A = ε̂

√~

2ε0Vω

[ake

i~k·~r + a†ke−i~k·~r

]The first term gives absorption while the second produces Thomsonscattering so we take only the first into consideration now.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 12 / 21

Page 53: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Calculation of σa

From first-order perturbation theory, the absorption cross section is givenby

σa =2π

~cV 2

4π3

∫|Mif |2δ(Ef − Ei )q2 sin θdqdθdϕ

where the matrix element Mif be-tween the initial, 〈i |, and final, |f 〉,states is given by

The interaction Hamiltonian is ex-pressed in terms of the electromag-netic vector potential

Mif = 〈i |HI |f 〉

HI =e~p · ~Am

+e2A2

2m

~A = ε̂

√~

2ε0Vω

[ake

i~k·~r + a†ke−i~k·~r

]The first term gives absorption while the second produces Thomsonscattering so we take only the first into consideration now.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 12 / 21

Page 54: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Calculation of σa

From first-order perturbation theory, the absorption cross section is givenby

σa =2π

~cV 2

4π3

∫|Mif |2δ(Ef − Ei )q2 sin θdqdθdϕ

where the matrix element Mif be-tween the initial, 〈i |, and final, |f 〉,states is given by

The interaction Hamiltonian is ex-pressed in terms of the electromag-netic vector potential

Mif = 〈i |HI |f 〉

HI =e~p · ~Am

+e2A2

2m

~A = ε̂

√~

2ε0Vω

[ake

i~k·~r + a†ke−i~k·~r

]

The first term gives absorption while the second produces Thomsonscattering so we take only the first into consideration now.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 12 / 21

Page 55: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Calculation of σa

From first-order perturbation theory, the absorption cross section is givenby

σa =2π

~cV 2

4π3

∫|Mif |2δ(Ef − Ei )q2 sin θdqdθdϕ

where the matrix element Mif be-tween the initial, 〈i |, and final, |f 〉,states is given by

The interaction Hamiltonian is ex-pressed in terms of the electromag-netic vector potential

Mif = 〈i |HI |f 〉

HI =e~p · ~Am

+e2A2

2m

~A = ε̂

√~

2ε0Vω

[ake

i~k·~r + a†ke−i~k·~r

]The first term gives absorption

while the second produces Thomsonscattering so we take only the first into consideration now.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 12 / 21

Page 56: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Calculation of σa

From first-order perturbation theory, the absorption cross section is givenby

σa =2π

~cV 2

4π3

∫|Mif |2δ(Ef − Ei )q2 sin θdqdθdϕ

where the matrix element Mif be-tween the initial, 〈i |, and final, |f 〉,states is given by

The interaction Hamiltonian is ex-pressed in terms of the electromag-netic vector potential

Mif = 〈i |HI |f 〉

HI =e~p · ~Am

+e2A2

2m

~A = ε̂

√~

2ε0Vω

[ake

i~k·~r + a†ke−i~k·~r

]The first term gives absorption while the second produces Thomsonscattering so we take only the first into consideration now.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 12 / 21

Page 57: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Free electron approximation

In order to evaluate the Mif matrix element we define the initial and finalstates

the initial state has a photon and a K electron(no free electron)

similarly, the final state has no photon and anejected free electron (ignoring the core holeand charged ion)

|i〉 = |1〉γ |0〉e

〈f | = e〈1|γ〈0|

Thus

Mif =e

m

√~

2ε0Vω

[e〈1|γ〈0|(~p · ε̂)ae i

~k·~r + (~p · ε̂)a†e−i~k·~r |1〉γ |0〉e

]The calculation is simplified if the interaction Hamiltonian is applied to theleft since the final state has only a free electron and no photon

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 13 / 21

Page 58: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Free electron approximation

In order to evaluate the Mif matrix element we define the initial and finalstates

the initial state has a photon and a K electron(no free electron)

similarly, the final state has no photon and anejected free electron (ignoring the core holeand charged ion)

|i〉 = |1〉γ |0〉e

〈f | = e〈1|γ〈0|

Thus

Mif =e

m

√~

2ε0Vω

[e〈1|γ〈0|(~p · ε̂)ae i

~k·~r + (~p · ε̂)a†e−i~k·~r |1〉γ |0〉e

]The calculation is simplified if the interaction Hamiltonian is applied to theleft since the final state has only a free electron and no photon

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 13 / 21

Page 59: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Free electron approximation

In order to evaluate the Mif matrix element we define the initial and finalstates

the initial state has a photon and a K electron(no free electron)

similarly, the final state has no photon and anejected free electron (ignoring the core holeand charged ion)

|i〉 = |1〉γ |0〉e

〈f | = e〈1|γ〈0|

Thus

Mif =e

m

√~

2ε0Vω

[e〈1|γ〈0|(~p · ε̂)ae i

~k·~r + (~p · ε̂)a†e−i~k·~r |1〉γ |0〉e

]The calculation is simplified if the interaction Hamiltonian is applied to theleft since the final state has only a free electron and no photon

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 13 / 21

Page 60: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Free electron approximation

In order to evaluate the Mif matrix element we define the initial and finalstates

the initial state has a photon and a K electron(no free electron)

similarly, the final state has no photon and anejected free electron (ignoring the core holeand charged ion)

|i〉 = |1〉γ |0〉e

〈f | = e〈1|γ〈0|

Thus

Mif =e

m

√~

2ε0Vω

[e〈1|γ〈0|(~p · ε̂)ae i

~k·~r + (~p · ε̂)a†e−i~k·~r |1〉γ |0〉e

]The calculation is simplified if the interaction Hamiltonian is applied to theleft since the final state has only a free electron and no photon

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 13 / 21

Page 61: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Free electron approximation

In order to evaluate the Mif matrix element we define the initial and finalstates

the initial state has a photon and a K electron(no free electron)

similarly, the final state has no photon and anejected free electron (ignoring the core holeand charged ion)

|i〉 = |1〉γ |0〉e

〈f | = e〈1|γ〈0|

Thus

Mif =e

m

√~

2ε0Vω

[e〈1|γ〈0|(~p · ε̂)ae i

~k·~r + (~p · ε̂)a†e−i~k·~r |1〉γ |0〉e

]The calculation is simplified if the interaction Hamiltonian is applied to theleft since the final state has only a free electron and no photon

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 13 / 21

Page 62: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Free electron approximation

In order to evaluate the Mif matrix element we define the initial and finalstates

the initial state has a photon and a K electron(no free electron)

similarly, the final state has no photon and anejected free electron (ignoring the core holeand charged ion)

|i〉 = |1〉γ |0〉e

〈f | = e〈1|γ〈0|

Thus

Mif =e

m

√~

2ε0Vω

[e〈1|γ〈0|(~p · ε̂)ae i

~k·~r + (~p · ε̂)a†e−i~k·~r |1〉γ |0〉e

]

The calculation is simplified if the interaction Hamiltonian is applied to theleft since the final state has only a free electron and no photon

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 13 / 21

Page 63: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Free electron approximation

In order to evaluate the Mif matrix element we define the initial and finalstates

the initial state has a photon and a K electron(no free electron)

similarly, the final state has no photon and anejected free electron (ignoring the core holeand charged ion)

|i〉 = |1〉γ |0〉e

〈f | = e〈1|γ〈0|

Thus

Mif =e

m

√~

2ε0Vω

[e〈1|γ〈0|(~p · ε̂)ae i

~k·~r + (~p · ε̂)a†e−i~k·~r |1〉γ |0〉e

]The calculation is simplified if the interaction Hamiltonian is applied to theleft since the final state has only a free electron and no photon

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 13 / 21

Page 64: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Free electron approximation

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

The free electron state is an eigen-function of the electron momentumoperator

The annihilation operator appliedto the left creates a photon whilethe creation operator annihilates aphoton when applied to the left.

e〈1|γ〈0|(~p · ε̂)a = ~(~q · ε̂)e〈1|γ〈1|

e〈1|γ〈0|(~p · ε̂)a† = 0

Mif =e

m

√~

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

=e~m

√~

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 14 / 21

Page 65: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Free electron approximation

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

The free electron state is an eigen-function of the electron momentumoperator

The annihilation operator appliedto the left creates a photon whilethe creation operator annihilates aphoton when applied to the left.

e〈1|γ〈0|(~p · ε̂)a = ~(~q · ε̂)e〈1|γ〈1|

e〈1|γ〈0|(~p · ε̂)a† = 0

Mif =e

m

√~

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

=e~m

√~

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 14 / 21

Page 66: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Free electron approximation

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

The free electron state is an eigen-function of the electron momentumoperator

The annihilation operator appliedto the left creates a photon

whilethe creation operator annihilates aphoton when applied to the left.

e〈1|γ〈0|(~p · ε̂)a = ~(~q · ε̂)e〈1|γ〈1|

e〈1|γ〈0|(~p · ε̂)a† = 0

Mif =e

m

√~

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

=e~m

√~

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 14 / 21

Page 67: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Free electron approximation

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

The free electron state is an eigen-function of the electron momentumoperator

The annihilation operator appliedto the left creates a photon

whilethe creation operator annihilates aphoton when applied to the left.

e〈1|γ〈0|(~p · ε̂)a = ~(~q · ε̂)e〈1|γ〈1|

e〈1|γ〈0|(~p · ε̂)a† = 0

Mif =e

m

√~

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

=e~m

√~

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 14 / 21

Page 68: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Free electron approximation

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

The free electron state is an eigen-function of the electron momentumoperator

The annihilation operator appliedto the left creates a photon whilethe creation operator annihilates aphoton when applied to the left.

e〈1|γ〈0|(~p · ε̂)a = ~(~q · ε̂)e〈1|γ〈1|

e〈1|γ〈0|(~p · ε̂)a† = 0

Mif =e

m

√~

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

=e~m

√~

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 14 / 21

Page 69: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Free electron approximation

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

The free electron state is an eigen-function of the electron momentumoperator

The annihilation operator appliedto the left creates a photon whilethe creation operator annihilates aphoton when applied to the left.

e〈1|γ〈0|(~p · ε̂)a = ~(~q · ε̂)e〈1|γ〈1|

e〈1|γ〈0|(~p · ε̂)a† = 0

Mif =e

m

√~

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

=e~m

√~

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 14 / 21

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Free electron approximation

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

The free electron state is an eigen-function of the electron momentumoperator

The annihilation operator appliedto the left creates a photon whilethe creation operator annihilates aphoton when applied to the left.

e〈1|γ〈0|(~p · ε̂)a = ~(~q · ε̂)e〈1|γ〈1|

e〈1|γ〈0|(~p · ε̂)a† = 0

Mif =e

m

√~

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

=e~m

√~

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 14 / 21

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Free electron approximation

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

The free electron state is an eigen-function of the electron momentumoperator

The annihilation operator appliedto the left creates a photon whilethe creation operator annihilates aphoton when applied to the left.

e〈1|γ〈0|(~p · ε̂)a = ~(~q · ε̂)e〈1|γ〈1|

e〈1|γ〈0|(~p · ε̂)a† = 0

Mif =e

m

√~

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

=e~m

√~

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 14 / 21

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Free electron approximation

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

The free electron state is an eigen-function of the electron momentumoperator

The annihilation operator appliedto the left creates a photon whilethe creation operator annihilates aphoton when applied to the left.

e〈1|γ〈0|(~p · ε̂)a = ~(~q · ε̂)e〈1|γ〈1|

e〈1|γ〈0|(~p · ε̂)a† = 0

Mif =e

m

√~

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

=e~m

√~

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 14 / 21

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Free electron approximation

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

The free electron state is an eigen-function of the electron momentumoperator

The annihilation operator appliedto the left creates a photon whilethe creation operator annihilates aphoton when applied to the left.

e〈1|γ〈0|(~p · ε̂)a = ~(~q · ε̂)e〈1|γ〈1|

e〈1|γ〈0|(~p · ε̂)a† = 0

Mif =e

m

√~

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

=e~m

√~

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e

=e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 14 / 21

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Free electron approximation

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

The free electron state is an eigen-function of the electron momentumoperator

The annihilation operator appliedto the left creates a photon whilethe creation operator annihilates aphoton when applied to the left.

e〈1|γ〈0|(~p · ε̂)a = ~(~q · ε̂)e〈1|γ〈1|

e〈1|γ〈0|(~p · ε̂)a† = 0

Mif =e

m

√~

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

=e~m

√~

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 14 / 21

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Photoelectron integral

Mif =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

=e~m

√~

2ε0Vω(~q · ε̂)φ(~Q)

ψi = ψ1s(~r) ψf =

√1

Ve i~q·~r

φ(~Q) =

√1

V

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

=

√1

V

∫ψ1s(~r)e i(

~k−~q)·~rd~r

=

√1

V

∫ψ1s(~r)e i

~Q·~rd~r

The initial electron wavefunction issimply that of a 1s atomic statewhile the final state is approxi-mated as a plane wave

The integral thus becomes

which is the Fourier transform ofthe initial state 1s electron wavefunction

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 15 / 21

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Photoelectron integral

Mif =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r =e~m

√~

2ε0Vω(~q · ε̂)φ(~Q)

ψi = ψ1s(~r) ψf =

√1

Ve i~q·~r

φ(~Q) =

√1

V

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

=

√1

V

∫ψ1s(~r)e i(

~k−~q)·~rd~r

=

√1

V

∫ψ1s(~r)e i

~Q·~rd~r

The initial electron wavefunction issimply that of a 1s atomic statewhile the final state is approxi-mated as a plane wave

The integral thus becomes

which is the Fourier transform ofthe initial state 1s electron wavefunction

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 15 / 21

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Photoelectron integral

Mif =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r =e~m

√~

2ε0Vω(~q · ε̂)φ(~Q)

ψi = ψ1s(~r) ψf =

√1

Ve i~q·~r

φ(~Q) =

√1

V

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

=

√1

V

∫ψ1s(~r)e i(

~k−~q)·~rd~r

=

√1

V

∫ψ1s(~r)e i

~Q·~rd~r

The initial electron wavefunction issimply that of a 1s atomic state

while the final state is approxi-mated as a plane wave

The integral thus becomes

which is the Fourier transform ofthe initial state 1s electron wavefunction

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 15 / 21

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Photoelectron integral

Mif =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r =e~m

√~

2ε0Vω(~q · ε̂)φ(~Q)

ψi = ψ1s(~r)

ψf =

√1

Ve i~q·~r

φ(~Q) =

√1

V

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

=

√1

V

∫ψ1s(~r)e i(

~k−~q)·~rd~r

=

√1

V

∫ψ1s(~r)e i

~Q·~rd~r

The initial electron wavefunction issimply that of a 1s atomic state

while the final state is approxi-mated as a plane wave

The integral thus becomes

which is the Fourier transform ofthe initial state 1s electron wavefunction

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 15 / 21

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Photoelectron integral

Mif =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r =e~m

√~

2ε0Vω(~q · ε̂)φ(~Q)

ψi = ψ1s(~r)

ψf =

√1

Ve i~q·~r

φ(~Q) =

√1

V

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

=

√1

V

∫ψ1s(~r)e i(

~k−~q)·~rd~r

=

√1

V

∫ψ1s(~r)e i

~Q·~rd~r

The initial electron wavefunction issimply that of a 1s atomic statewhile the final state is approxi-mated as a plane wave

The integral thus becomes

which is the Fourier transform ofthe initial state 1s electron wavefunction

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 15 / 21

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Photoelectron integral

Mif =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r =e~m

√~

2ε0Vω(~q · ε̂)φ(~Q)

ψi = ψ1s(~r) ψf =

√1

Ve i~q·~r

φ(~Q) =

√1

V

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

=

√1

V

∫ψ1s(~r)e i(

~k−~q)·~rd~r

=

√1

V

∫ψ1s(~r)e i

~Q·~rd~r

The initial electron wavefunction issimply that of a 1s atomic statewhile the final state is approxi-mated as a plane wave

The integral thus becomes

which is the Fourier transform ofthe initial state 1s electron wavefunction

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 15 / 21

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Photoelectron integral

Mif =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r =e~m

√~

2ε0Vω(~q · ε̂)φ(~Q)

ψi = ψ1s(~r) ψf =

√1

Ve i~q·~r

φ(~Q) =

√1

V

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

=

√1

V

∫ψ1s(~r)e i(

~k−~q)·~rd~r

=

√1

V

∫ψ1s(~r)e i

~Q·~rd~r

The initial electron wavefunction issimply that of a 1s atomic statewhile the final state is approxi-mated as a plane wave

The integral thus becomes

which is the Fourier transform ofthe initial state 1s electron wavefunction

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 15 / 21

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Photoelectron integral

Mif =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r =e~m

√~

2ε0Vω(~q · ε̂)φ(~Q)

ψi = ψ1s(~r) ψf =

√1

Ve i~q·~r

φ(~Q) =

√1

V

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

=

√1

V

∫ψ1s(~r)e i(

~k−~q)·~rd~r

=

√1

V

∫ψ1s(~r)e i

~Q·~rd~r

The initial electron wavefunction issimply that of a 1s atomic statewhile the final state is approxi-mated as a plane wave

The integral thus becomes

which is the Fourier transform ofthe initial state 1s electron wavefunction

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 15 / 21

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Photoelectron integral

Mif =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r =e~m

√~

2ε0Vω(~q · ε̂)φ(~Q)

ψi = ψ1s(~r) ψf =

√1

Ve i~q·~r

φ(~Q) =

√1

V

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

=

√1

V

∫ψ1s(~r)e i(

~k−~q)·~rd~r

=

√1

V

∫ψ1s(~r)e i

~Q·~rd~r

The initial electron wavefunction issimply that of a 1s atomic statewhile the final state is approxi-mated as a plane wave

The integral thus becomes

which is the Fourier transform ofthe initial state 1s electron wavefunction

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 15 / 21

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Photoelectron integral

Mif =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r =e~m

√~

2ε0Vω(~q · ε̂)φ(~Q)

ψi = ψ1s(~r) ψf =

√1

Ve i~q·~r

φ(~Q) =

√1

V

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

=

√1

V

∫ψ1s(~r)e i(

~k−~q)·~rd~r

=

√1

V

∫ψ1s(~r)e i

~Q·~rd~r

The initial electron wavefunction issimply that of a 1s atomic statewhile the final state is approxi-mated as a plane wave

The integral thus becomes

which is the Fourier transform ofthe initial state 1s electron wavefunction

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 15 / 21

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Photoelectron integral

Mif =e~m

√~

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r =e~m

√~

2ε0Vω(~q · ε̂)φ(~Q)

ψi = ψ1s(~r) ψf =

√1

Ve i~q·~r

φ(~Q) =

√1

V

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

=

√1

V

∫ψ1s(~r)e i(

~k−~q)·~rd~r

=

√1

V

∫ψ1s(~r)e i

~Q·~rd~r

The initial electron wavefunction issimply that of a 1s atomic statewhile the final state is approxi-mated as a plane wave

The integral thus becomes

which is the Fourier transform ofthe initial state 1s electron wavefunction

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 15 / 21

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Photoelectron cross-section

the overall matrix element squared for a particular photoelectron finaldirection (ϕ, θ) is

|Mif |2 =

(e~m

)2 ~2ε0V 2ω

(q2 sin2 θ cos2 ϕ)φ2(~Q)

and the final cross-section per K electron can now be computed as

σa =2π

~cV 2

4π3

(e~m

)2 ~2ε0V 2ω

I3 =

(e~m

)2 1

4π2ε0cωI3

where the integral I3 is given by

I3 =

∫φ2(~Q)q2 sin2 θ cos2 ϕδ(Ef − Ei )q2 sin θdqdθdφ

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 16 / 21

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Photoelectron cross-section

the overall matrix element squared for a particular photoelectron finaldirection (ϕ, θ) is

|Mif |2 =

(e~m

)2 ~2ε0V 2ω

(q2 sin2 θ cos2 ϕ)φ2(~Q)

and the final cross-section per K electron can now be computed as

σa =2π

~cV 2

4π3

(e~m

)2 ~2ε0V 2ω

I3 =

(e~m

)2 1

4π2ε0cωI3

where the integral I3 is given by

I3 =

∫φ2(~Q)q2 sin2 θ cos2 ϕδ(Ef − Ei )q2 sin θdqdθdφ

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 16 / 21

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Photoelectron cross-section

the overall matrix element squared for a particular photoelectron finaldirection (ϕ, θ) is

|Mif |2 =

(e~m

)2 ~2ε0V 2ω

(q2 sin2 θ cos2 ϕ)φ2(~Q)

and the final cross-section per K electron can now be computed as

σa =2π

~cV 2

4π3

(e~m

)2 ~2ε0V 2ω

I3 =

(e~m

)2 1

4π2ε0cωI3

where the integral I3 is given by

I3 =

∫φ2(~Q)q2 sin2 θ cos2 ϕδ(Ef − Ei )q2 sin θdqdθdφ

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 16 / 21

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Photoelectron cross-section

the overall matrix element squared for a particular photoelectron finaldirection (ϕ, θ) is

|Mif |2 =

(e~m

)2 ~2ε0V 2ω

(q2 sin2 θ cos2 ϕ)φ2(~Q)

and the final cross-section per K electron can now be computed as

σa =2π

~cV 2

4π3

(e~m

)2 ~2ε0V 2ω

I3

=

(e~m

)2 1

4π2ε0cωI3

where the integral I3 is given by

I3 =

∫φ2(~Q)q2 sin2 θ cos2 ϕδ(Ef − Ei )q2 sin θdqdθdφ

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 16 / 21

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Photoelectron cross-section

the overall matrix element squared for a particular photoelectron finaldirection (ϕ, θ) is

|Mif |2 =

(e~m

)2 ~2ε0V 2ω

(q2 sin2 θ cos2 ϕ)φ2(~Q)

and the final cross-section per K electron can now be computed as

σa =2π

~cV 2

4π3

(e~m

)2 ~2ε0V 2ω

I3 =

(e~m

)2 1

4π2ε0cωI3

where the integral I3 is given by

I3 =

∫φ2(~Q)q2 sin2 θ cos2 ϕδ(Ef − Ei )q2 sin θdqdθdφ

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 16 / 21

Page 91: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

Photoelectron cross-section

the overall matrix element squared for a particular photoelectron finaldirection (ϕ, θ) is

|Mif |2 =

(e~m

)2 ~2ε0V 2ω

(q2 sin2 θ cos2 ϕ)φ2(~Q)

and the final cross-section per K electron can now be computed as

σa =2π

~cV 2

4π3

(e~m

)2 ~2ε0V 2ω

I3 =

(e~m

)2 1

4π2ε0cωI3

where the integral I3 is given by

I3 =

∫φ2(~Q)q2 sin2 θ cos2 ϕδ(Ef − Ei )q2 sin θdqdθdφ

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 16 / 21

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Photoelectron cross-section

the overall matrix element squared for a particular photoelectron finaldirection (ϕ, θ) is

|Mif |2 =

(e~m

)2 ~2ε0V 2ω

(q2 sin2 θ cos2 ϕ)φ2(~Q)

and the final cross-section per K electron can now be computed as

σa =2π

~cV 2

4π3

(e~m

)2 ~2ε0V 2ω

I3 =

(e~m

)2 1

4π2ε0cωI3

where the integral I3 is given by

I3 =

∫φ2(~Q)q2 sin2 θ cos2 ϕδ(Ef − Ei )q2 sin θdqdθdφ

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 16 / 21

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Calculated cross section

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 17 / 21

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Calculated cross section

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 17 / 21

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Calculated cross section

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 17 / 21

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What is XAFS?

X-ray Absorption Fine-Structure (XAFS) is the modulation of the x-rayabsorption coefficient at energies near and above an x-ray absorption edge.XAFS is also referred to as X-ray Absorption Spectroscopy (XAS) and isbroken into 2 regimes:

XANES X-ray Absorption Near-Edge SpectroscopyEXAFS Extended X-ray Absorption Fine-Structure

which contain related, but slightly different information about an element’slocal coordination and chemical state.

EXAFS

XANES

E (eV)

µ

(

E

)

77007600750074007300720071007000

2.0

1.5

1.0

0.5

0.0

Fe K-edge XAFS for FeO

XAFS Characteristics:

• local atomic coordination

• chemical / oxidation state

• applies to any element

• works at low concentrations

• minimal sample requirements

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 18 / 21

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The x-ray absorption process

An x-ray is absorbed by anatom when the energy of thex-ray is transferred to a core-level electron (K, L, or Mshell).

The atom is in an excitedstate with an empty elec-tronic level: a core hole.

Any excess energy fromthe x-ray is given to anejected photoelectron

, whichexpands as a spherical wave,reaches the neighboring elec-tron clouds, and scattersback to the core hole, cre-ating interference patternscalled XANES and EXAFS.

x−ray

L

K

M

Energy

photo−electron

Continuum

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 19 / 21

Page 98: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

The x-ray absorption process

An x-ray is absorbed by anatom when the energy of thex-ray is transferred to a core-level electron (K, L, or Mshell).

The atom is in an excitedstate with an empty elec-tronic level: a core hole.

Any excess energy fromthe x-ray is given to anejected photoelectron

, whichexpands as a spherical wave,reaches the neighboring elec-tron clouds, and scattersback to the core hole, cre-ating interference patternscalled XANES and EXAFS.

x−ray

L

K

M

Energy

photo−electron

Continuum

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 19 / 21

Page 99: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

The x-ray absorption process

An x-ray is absorbed by anatom when the energy of thex-ray is transferred to a core-level electron (K, L, or Mshell).

The atom is in an excitedstate with an empty elec-tronic level: a core hole.

Any excess energy fromthe x-ray is given to anejected photoelectron

, whichexpands as a spherical wave,reaches the neighboring elec-tron clouds, and scattersback to the core hole, cre-ating interference patternscalled XANES and EXAFS.

x−ray

L

K

M

Energy

photo−electron

Continuum

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 19 / 21

Page 100: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

The x-ray absorption process

An x-ray is absorbed by anatom when the energy of thex-ray is transferred to a core-level electron (K, L, or Mshell).

The atom is in an excitedstate with an empty elec-tronic level: a core hole.

Any excess energy fromthe x-ray is given to anejected photoelectron, whichexpands as a spherical wave

,reaches the neighboring elec-tron clouds, and scattersback to the core hole, cre-ating interference patternscalled XANES and EXAFS.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 19 / 21

Page 101: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

The x-ray absorption process

An x-ray is absorbed by anatom when the energy of thex-ray is transferred to a core-level electron (K, L, or Mshell).

The atom is in an excitedstate with an empty elec-tronic level: a core hole.

Any excess energy fromthe x-ray is given to anejected photoelectron, whichexpands as a spherical wave

,reaches the neighboring elec-tron clouds, and scattersback to the core hole, cre-ating interference patternscalled XANES and EXAFS.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 19 / 21

Page 102: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

The x-ray absorption process

An x-ray is absorbed by anatom when the energy of thex-ray is transferred to a core-level electron (K, L, or Mshell).

The atom is in an excitedstate with an empty elec-tronic level: a core hole.

Any excess energy fromthe x-ray is given to anejected photoelectron, whichexpands as a spherical wave,reaches the neighboring elec-tron clouds

, and scattersback to the core hole, cre-ating interference patternscalled XANES and EXAFS.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 19 / 21

Page 103: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

The x-ray absorption process

An x-ray is absorbed by anatom when the energy of thex-ray is transferred to a core-level electron (K, L, or Mshell).

The atom is in an excitedstate with an empty elec-tronic level: a core hole.

Any excess energy fromthe x-ray is given to anejected photoelectron, whichexpands as a spherical wave,reaches the neighboring elec-tron clouds, and scattersback to the core hole

, cre-ating interference patternscalled XANES and EXAFS.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 19 / 21

Page 104: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

The x-ray absorption process

An x-ray is absorbed by anatom when the energy of thex-ray is transferred to a core-level electron (K, L, or Mshell).

The atom is in an excitedstate with an empty elec-tronic level: a core hole.

Any excess energy fromthe x-ray is given to anejected photoelectron, whichexpands as a spherical wave,reaches the neighboring elec-tron clouds, and scattersback to the core hole

, cre-ating interference patternscalled XANES and EXAFS.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 19 / 21

Page 105: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

The x-ray absorption process

An x-ray is absorbed by anatom when the energy of thex-ray is transferred to a core-level electron (K, L, or Mshell).

The atom is in an excitedstate with an empty elec-tronic level: a core hole.

Any excess energy fromthe x-ray is given to anejected photoelectron, whichexpands as a spherical wave,reaches the neighboring elec-tron clouds, and scattersback to the core hole, cre-ating interference patternscalled XANES and EXAFS.

11500 12000 12500

E(eV)

-2

-1.5

-1

-0.5

0

0.5

ln(I

o/I

)

EXAFS

XA

NE

S /

NE

XA

FS

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 19 / 21

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EXAFS data extraction

normalize by fitting pre-edgeand post-edge trends

remove “smooth” µ0 back-ground

convert to photoelectron mo-mentum space

k =2π

hc

√E − E0

weight by appropriate powerof k to obtain “good” enve-lope which clearly shows thatEXAFS is a sum of oscilla-tions with varying frequen-cies and phases

Fourier transform to get realspace EXAFS

11500 12000 12500

E(eV)

-2

-1.5

-1

-0.5

0

0.5

ln(I

o/I

)

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 20 / 21

Page 107: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

EXAFS data extraction

normalize by fitting pre-edgeand post-edge trends

remove “smooth” µ0 back-ground

convert to photoelectron mo-mentum space

k =2π

hc

√E − E0

weight by appropriate powerof k to obtain “good” enve-lope which clearly shows thatEXAFS is a sum of oscilla-tions with varying frequen-cies and phases

Fourier transform to get realspace EXAFS

11500 12000 12500

E(eV)

0

0.5

1

ln(I

o/I

)

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 20 / 21

Page 108: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

EXAFS data extraction

normalize by fitting pre-edgeand post-edge trends

remove “smooth” µ0 back-ground

convert to photoelectron mo-mentum space

k =2π

hc

√E − E0

weight by appropriate powerof k to obtain “good” enve-lope which clearly shows thatEXAFS is a sum of oscilla-tions with varying frequen-cies and phases

Fourier transform to get realspace EXAFS

11500 12000 12500

E(eV)

0

0.5

1

ln(I

o/I

)

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 20 / 21

Page 109: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

EXAFS data extraction

normalize by fitting pre-edgeand post-edge trends

remove “smooth” µ0 back-ground

convert to photoelectron mo-mentum space

k =2π

hc

√E − E0

weight by appropriate powerof k to obtain “good” enve-lope which clearly shows thatEXAFS is a sum of oscilla-tions with varying frequen-cies and phases

Fourier transform to get realspace EXAFS

0 5 10 15

k(Å-1

)

-0.2

-0.1

0

0.1

0.2

χ

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 20 / 21

Page 110: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

EXAFS data extraction

normalize by fitting pre-edgeand post-edge trends

remove “smooth” µ0 back-ground

convert to photoelectron mo-mentum space

k =2π

hc

√E − E0

weight by appropriate powerof k to obtain “good” enve-lope which clearly shows thatEXAFS is a sum of oscilla-tions with varying frequen-cies and phases

Fourier transform to get realspace EXAFS

0 5 10 15

k(Å-1

)

-0.2

-0.1

0

0.1

0.2

χ

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 20 / 21

Page 111: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

EXAFS data extraction

normalize by fitting pre-edgeand post-edge trends

remove “smooth” µ0 back-ground

convert to photoelectron mo-mentum space

k =2π

hc

√E − E0

weight by appropriate powerof k to obtain “good” enve-lope which clearly shows thatEXAFS is a sum of oscilla-tions with varying frequen-cies and phases

Fourier transform to get realspace EXAFS

0 2 4 6

R(Å)

0

5

10

15

20

25

30

χ(R

)

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 20 / 21

Page 112: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

XANES edge shifts and pre-edge peaks

5460 5470 5480 5490 5500

E(eV)

0

0.2

0.4

0.6

0.8

1

1.2

ln(I

o/I)

V metal

V2O

3

V2O

5

LiVOPO4

The shift of the edge positioncan be used to determine thevalence state.

The heights and positions ofpre-edge peaks can also be re-liably used to determine ionicratios for many atomic species.

XANES can be used as a fin-gerprint of phases and XANESanalysis can be as simple asmaking linear combinations of“known” spectra to get com-position.

Modern codes, such as FEFF9,are able to accurately computeXANES features.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 21 / 21

Page 113: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

XANES edge shifts and pre-edge peaks

5460 5470 5480 5490 5500

E(eV)

0

0.2

0.4

0.6

0.8

1

1.2

ln(I

o/I)

V metal

V2O

3

V2O

5

LiVOPO4

The shift of the edge positioncan be used to determine thevalence state.

The heights and positions ofpre-edge peaks can also be re-liably used to determine ionicratios for many atomic species.

XANES can be used as a fin-gerprint of phases and XANESanalysis can be as simple asmaking linear combinations of“known” spectra to get com-position.

Modern codes, such as FEFF9,are able to accurately computeXANES features.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 21 / 21

Page 114: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

XANES edge shifts and pre-edge peaks

5460 5470 5480 5490 5500

E(eV)

0

0.2

0.4

0.6

0.8

1

1.2

ln(I

o/I)

V metal

V2O

3

V2O

5

LiVOPO4

The shift of the edge positioncan be used to determine thevalence state.

The heights and positions ofpre-edge peaks can also be re-liably used to determine ionicratios for many atomic species.

XANES can be used as a fin-gerprint of phases and XANESanalysis can be as simple asmaking linear combinations of“known” spectra to get com-position.

Modern codes, such as FEFF9,are able to accurately computeXANES features.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 21 / 21

Page 115: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

XANES edge shifts and pre-edge peaks

5460 5470 5480 5490 5500

E(eV)

0

0.2

0.4

0.6

0.8

1

1.2

ln(I

o/I)

V metal

V2O

3

V2O

5

LiVOPO4

The shift of the edge positioncan be used to determine thevalence state.

The heights and positions ofpre-edge peaks can also be re-liably used to determine ionicratios for many atomic species.

XANES can be used as a fin-gerprint of phases and XANESanalysis can be as simple asmaking linear combinations of“known” spectra to get com-position.

Modern codes, such as FEFF9,are able to accurately computeXANES features.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 21 / 21

Page 116: Today’s Outline - October 31, 2016csrri.iit.edu/~segre/phys570/16F/lecture_19.pdfToday’s Outline - October 31, 2016 Dumond diagrams Monochromators Photoelectric absorption Cross-section

XANES edge shifts and pre-edge peaks

5460 5470 5480 5490 5500

E(eV)

0

0.2

0.4

0.6

0.8

1

1.2

ln(I

o/I)

V metal

V2O

3

V2O

5

LiVOPO4

The shift of the edge positioncan be used to determine thevalence state.

The heights and positions ofpre-edge peaks can also be re-liably used to determine ionicratios for many atomic species.

XANES can be used as a fin-gerprint of phases and XANESanalysis can be as simple asmaking linear combinations of“known” spectra to get com-position.

Modern codes, such as FEFF9,are able to accurately computeXANES features.

C. Segre (IIT) PHYS 570 - Fall 2016 October 31, 2016 21 / 21