today’s outline - march 27, 2018 - iitphys.iit.edu/~segre/phys570/18s/lecture_19.pdfhomework...

Today’s Outline - March 27, 2018

• Dumond diagrams

• Monochromators

• Photoelectric absorption

• Cross-section of an isolated atom

• X-ray absorption spectroscopy

Homework Assignment #05:Chapter 5: 1, 3, 7, 9, 10due Thursday, March 29, 2018

Homework Assignment #06:Chapter 6: 1,6,7,8,9due Tuesday, April 10, 2018

C. Segre (IIT) PHYS 570 - Spring 2018 March 27, 2018 1 / 20

• Dumond diagrams

• Monochromators

• Dumond diagrams

• Monochromators

• Dumond diagrams

• Monochromators

• Dumond diagrams

• Monochromators

• Dumond diagrams

• Monochromators

• Dumond diagrams

• Monochromators

• Dumond diagrams

• Monochromators

PHYS 570 day at 10-BM

1. Friday, March 30, 2018, 09:00 – 16:00

2. Activities

• Absolute flux measurement• Rocking curve measurement• SDD setup & measurement• EXAFS measurement

3. Make sure your badge is ready

4. Leave plenty of time to get the badge

5. Let me know when you plan to come!

1. Friday, March 30, 2018, 09:00 – 16:00

2. Activities• Absolute flux measurement• Rocking curve measurement• SDD setup & measurement• EXAFS measurement

1. Friday, March 30, 2018, 09:00 – 16:00

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, April 30, 2018, 10:30-12:30)

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!

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, April 30, 2018, 10:30-12:30)

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!

Dumond diagram: no Darwin width

Transfer function of an optical element parametrized by angle andwavelength.

Here Darwin width is ignored.

0 0θi-θB θe-θB

cosθΒ ∆θ

for small angular de-viations sin θ is lin-ear with a slope ofcos θB

non-zero diffractedbeam only for pointson the line

a horizontal linetransfers inputto output beamcharacteristics

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

0 0θi-θB θe-θB

cosθΒ ∆θ

0 0θi-θB θe-θB

cosθΒ ∆θ

0 0θi-θB θe-θB

cosθΒ ∆θ

0 0θi-θB θe-θB

cosθΒ ∆θ

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

w0=sinθB ζD

the bandwidth ofa collimated (noangular divergence)beam denoted bythe black line canbe accepted by theinput function ofthe crystal

this input band-width is transferredto a similar outputbandwidth which isalso collimated

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

w0=sinθB ζD

0 0θi-θB θe-θB

w0=sinθB ζD

0 0θi-θB θe-θB

w0=sinθB ζD

Dumond diagram: asymmetric Bragg

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

0 0θi-θB θe-θB

2d w0 b

a perfectly colli-mated input beamtransfers to anoutput beam thathas an angulardivergence whichdepends on theasymmetry factor b

this is in additionto a compression (inthis case) of thebeam height (Liou-ville’s theorem!)

0 0θi-θB θe-θB

2d w0 b

0 0θi-θB θe-θB

2d w0 b

Double crystal monochromator: Non-dispersive

∆θin

the transfer functions ofthe the two crystalsmatch and full bandwithand divergence is pre-served

∆θin

Double crystal monochromators: Dispersive

∆θin

the transfer functionmatches only in smallband that varies withangle of the secondcrystal

∆θin

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.

Total cross section

Scaled absorption

I0= e−µz

µ =ρmNA

σa ∼Z 4

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

Scaled absorption

I0= e−µz

µ =ρmNA

σa ∼Z 4

Scaled absorption

I0= e−µz

µ =ρmNA

σa ∼Z 4

Scaled absorption

I0= e−µz

µ =ρmNA

σa ∼Z 4

Scaled absorption

I0= e−µz

µ =ρmNA

σa ∼Z 4

Scaled absorption

I0= e−µz

µ =ρmNA

σa ∼Z 4

Calculation of σa

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

σa =2π

∫|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

~A = ε̂

2ε0Vω

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.

Calculation of σa

σa =2π

HI =e~p · ~Am

~A = ε̂

2ε0Vω

Calculation of σa

σa =2π

HI =e~p · ~Am

~A = ε̂

2ε0Vω

Calculation of σa

σa =2π

HI =e~p · ~Am

~A = ε̂

2ε0Vω

Calculation of σa

σa =2π

HI =e~p · ~Am

~A = ε̂

2ε0Vω

Calculation of σa

σa =2π

HI =e~p · ~Am

~A = ε̂

2ε0Vω

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

Calculation of σa

σa =2π

HI =e~p · ~Am

~A = ε̂

2ε0Vω

]The first term gives absorption

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

Calculation of σa

σa =2π

HI =e~p · ~Am

~A = ε̂

2ε0Vω

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|

Mif =e

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

|i〉 = |1〉γ |0〉e

〈f | = e〈1|γ〈0|

Mif =e

2ε0Vω

[e〈1|γ〈0|(~p · ε̂)ae i

~k·~r + (~p · ε̂)a†e−i~k·~r |1〉γ |0〉e

|i〉 = |1〉γ |0〉e

〈f | = e〈1|γ〈0|

Mif =e

2ε0Vω

[e〈1|γ〈0|(~p · ε̂)ae i

~k·~r + (~p · ε̂)a†e−i~k·~r |1〉γ |0〉e

|i〉 = |1〉γ |0〉e

〈f | = e〈1|γ〈0|

Mif =e

2ε0Vω

[e〈1|γ〈0|(~p · ε̂)ae i

~k·~r + (~p · ε̂)a†e−i~k·~r |1〉γ |0〉e

|i〉 = |1〉γ |0〉e

〈f | = e〈1|γ〈0|

Mif =e

2ε0Vω

[e〈1|γ〈0|(~p · ε̂)ae i

~k·~r + (~p · ε̂)a†e−i~k·~r |1〉γ |0〉e

|i〉 = |1〉γ |0〉e

〈f | = e〈1|γ〈0|

Mif =e

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

|i〉 = |1〉γ |0〉e

〈f | = e〈1|γ〈0|

Mif =e

2ε0Vω

[e〈1|γ〈0|(~p · ε̂)ae i

~k·~r + (~p · ε̂)a†e−i~k·~r |1〉γ |0〉e

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

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

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

e〈1|γ〈0|(~p · ε̂)a† = 0

Mif =e

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

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

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

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

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

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

e〈1|γ〈0|(~p · ε̂)a† = 0

Mif =e

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

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

e〈1|γ〈0|(~p · ε̂)a† = 0

Mif =e

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

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

e〈1|γ〈0|(~p · ε̂)a† = 0

Mif =e

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

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

e〈1|γ〈0|(~p · ε̂)a† = 0

Mif =e

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

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

e〈1|γ〈0|(~p · ε̂)a† = 0

Mif =e

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

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

e〈1|γ〈0|(~p · ε̂)a† = 0

Mif =e

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

e〈1|~p = (~~q)e〈1|

γ〈n|a = (√n + 1)γ〈n + 1|a

γ〈n|a† = (√n)γ〈n − 1|a

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

e〈1|γ〈0|(~p · ε̂)a† = 0

Mif =e

2ε0Vω

[~(~q · ε̂)e〈1|γ〈1|e i

~k·~r |1〉γ |0〉e + 0]

2ε0Vω(~q · ε̂)e〈1|e i

~k·~r |0〉e =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

Photoelectron integral

Mif =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r

2ε0Vω(~q · ε̂)φ(~Q)

ψi = ψ1s(~r) ψf =

Ve i~q·~r

φ(~Q) =

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

∫ψ1s(~r)e i(

~k−~q)·~rd~r

∫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

Mif =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r =e~m

2ε0Vω(~q · ε̂)φ(~Q)

Ve i~q·~r

φ(~Q) =

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

∫ψ1s(~r)e i(

~k−~q)·~rd~r

∫ψ1s(~r)e i

~Q·~rd~r

Mif =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r =e~m

2ε0Vω(~q · ε̂)φ(~Q)

Ve i~q·~r

φ(~Q) =

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

∫ψ1s(~r)e i(

~k−~q)·~rd~r

∫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

Mif =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r =e~m

2ε0Vω(~q · ε̂)φ(~Q)

ψi = ψ1s(~r)

Ve i~q·~r

φ(~Q) =

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

∫ψ1s(~r)e i(

~k−~q)·~rd~r

∫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

Mif =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r =e~m

2ε0Vω(~q · ε̂)φ(~Q)

ψi = ψ1s(~r)

Ve i~q·~r

φ(~Q) =

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

∫ψ1s(~r)e i(

~k−~q)·~rd~r

∫ψ1s(~r)e i

~Q·~rd~r

Mif =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r =e~m

2ε0Vω(~q · ε̂)φ(~Q)

Ve i~q·~r

φ(~Q) =

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

∫ψ1s(~r)e i(

~k−~q)·~rd~r

∫ψ1s(~r)e i

~Q·~rd~r

Mif =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r =e~m

2ε0Vω(~q · ε̂)φ(~Q)

Ve i~q·~r

φ(~Q) =

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

∫ψ1s(~r)e i(

~k−~q)·~rd~r

∫ψ1s(~r)e i

~Q·~rd~r

Mif =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r =e~m

2ε0Vω(~q · ε̂)φ(~Q)

Ve i~q·~r

φ(~Q) =

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

∫ψ1s(~r)e i(

~k−~q)·~rd~r

∫ψ1s(~r)e i

~Q·~rd~r

Mif =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r =e~m

2ε0Vω(~q · ε̂)φ(~Q)

Ve i~q·~r

φ(~Q) =

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

∫ψ1s(~r)e i(

~k−~q)·~rd~r

∫ψ1s(~r)e i

~Q·~rd~r

Mif =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r =e~m

2ε0Vω(~q · ε̂)φ(~Q)

Ve i~q·~r

φ(~Q) =

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

∫ψ1s(~r)e i(

~k−~q)·~rd~r

∫ψ1s(~r)e i

~Q·~rd~r

Mif =e~m

2ε0Vω(~q · ε̂)

∫ψ∗f e

i~k·~rψid~r =e~m

2ε0Vω(~q · ε̂)φ(~Q)

Ve i~q·~r

φ(~Q) =

∫e−i~q·~re i

~k·~rψ1s(~r)d~r

∫ψ1s(~r)e i(

~k−~q)·~rd~r

∫ψ1s(~r)e i

~Q·~rd~r

Photoelectron cross-section

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

|Mif |2 =

)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

)2 ~2ε0V 2ω

4π2ε0cωI3

where the integral I3 is given by

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

|Mif |2 =

)2 ~2ε0V 2ω

σa =2π

)2 ~2ε0V 2ω

4π2ε0cωI3

|Mif |2 =

)2 ~2ε0V 2ω

σa =2π

)2 ~2ε0V 2ω

4π2ε0cωI3

|Mif |2 =

)2 ~2ε0V 2ω

σa =2π

)2 ~2ε0V 2ω

4π2ε0cωI3

|Mif |2 =

)2 ~2ε0V 2ω

σa =2π

)2 ~2ε0V 2ω

4π2ε0cωI3

|Mif |2 =

)2 ~2ε0V 2ω

σa =2π

)2 ~2ε0V 2ω

4π2ε0cωI3

|Mif |2 =

)2 ~2ε0V 2ω

σa =2π

)2 ~2ε0V 2ω

4π2ε0cωI3

Calculated cross section

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.

E (eV)

77007600750074007300720071007000

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

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

photo−electron

Continuum

x−ray

photo−electron

Continuum

x−ray

photo−electron

Continuum

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.

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.

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.

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.

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.

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

EXAFS data extraction

normalize by fitting pre-edgeand post-edge trends

remove “smooth” µ0 back-ground

convert to photoelectron mo-mentum space

k =2π

√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

k =2π

√E − E0

11500 12000 12500

k =2π

√E − E0

11500 12000 12500

k =2π

√E − E0

0 5 10 15

k(Å-1

k =2π

√E − E0

0 5 10 15

k(Å-1

k =2π

√E − E0

0 2 4 6

XANES edge shifts and pre-edge peaks

5460 5470 5480 5490 5500

V metal

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.

5460 5470 5480 5490 5500

V metal

LiVOPO4

5460 5470 5480 5490 5500

V metal

LiVOPO4

5460 5470 5480 5490 5500

V metal

LiVOPO4

5460 5470 5480 5490 5500

V metal

LiVOPO4

today’s outline - march 27, 2018 - iitphys.iit.edu/~segre/phys570/18s/lecture_19.pdfhomework...

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