Lesson 1 X-Rays & Diffraction -...

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Lesson 1

X-Rays & Diffraction

Nicola Döbelin

RMS Foundation, Bettlach, Switzerland

June 07 – 09, 2017, Oslo, N

Electromagnetic Spectrum

2

X rays:

Wavelength λ: 0.01 – 10 nm

Energy: 100 eV – 100 keV

Generation of X-radiation:

Shoot electrons on matter

Interatomic distances in crystals:

typically 0.15 – 0.4 nm

Interference phenomena only

for features ≈ λ

X-ray Tube

3

e‒

Filament (W)

Target (Cu, Mo, Fe, Co, ...)

Be window

Acceleration

Voltage

Va

cu

um

Filament

Current

X-ray Tube

4

e‒

Filament (W)

Target (Cu, Mo, Fe, Co, ...)

Point focus

Line focus

Generation of X-rays

5

Accelerated electron impinges on matter:

Electron is deflected and decelerated by the atomic nucleus.

(Inelastic scattering)

Deflected electron emits electromagnetic radiation.

Wavelength depends on the loss of energy.

Bremsstrahlung (Deceleration radiation)

Bremsstrahlung

6

Wavelength (nm)

Inte

nsity

0.00 0.05 0.10 0.15 0.20

20 kV, 20 mA

30 kV, 20 mA

40 kV, 20 mA

Continuous spectrum

0.25 0.30

Acceleration Voltage:

Speed / Energy of Electrons

Bremsstrahlung

7

Wavelength (nm)

Inte

nsity

0.00 0.05 0.10 0.15 0.20

30 kV, 20 mA

Continuous spectrum

0.25 0.30

30 kV, 30 mA

30 kV, 40 mA Generator Current:

Number of Electrons

Characteristic Radiation

8

K L M

Eb (eV)

0

76

122

933 952

1097

8979

M4,5 (3d)

M2,3 (3p)

M1 (3s)

L3 (2p3/2)

L1 (2p1/2)

L1 (2s)

K1 (1s)

Kα1 Kα2 Kβ

Cu

Wavelength of Kα1, Kα2, Kβ, Lα... are characteristic for the atomic species.

X-rays: Spectrum

9

Wavelength (nm)

Inte

nsity

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Cu

Kα1

Kα2

Kβ

Kα1

Kα2

Kβ

Mo

Old X-ray tubes

10

Caution:

Beryllium is toxic & carcinogenic!

- Never touch the windows!

- Use appropriate covers!

Lifetime of a few years:

- Vacuum decreases

loss of intensity

- Tungsten from filament deposits

on target

contaminated spectrum (characteristic

W spectrum starts to appear)

- Monitor the intensity

- Replace old tubes

X-rays: Summary

11

• Generated in an X-ray tube

• Spectrum contains Bremsstrahlung (continuous) and

characteristic radiation (Kα1, Kα2, Kβ) of target material

• Tube is characterized by: • Target material

• Size and shape of target

• Aceleration voltage and

current

Diffraction Basics

12

Interaction of X-rays with matter:

- Absorption (photoelectric effect, giving rise to fluorescence)

- Elastic scattering (Thomson scattering)

- Inelastic scattering (Compton scattering)

Absorption Photoelectric effect, Fluorescence

1. Absorption and ionization

2. Relaxation and emission of characteristic radiation

CuKα1

FeKα1

Fe atom

Elastic Scattering

13

Electron oscillates in the electric field,

emits photons of the same wavelength as

the incoming radiation (λs = λp).

λp

λs

CuKα1

CuKα1

Fe atom

Secondary wave is in phase

(+ 180°) with primary wave.

Crystal Lattice

14

Crystal: Periodic arrangement of atoms/ions/molecules in 3 dimensions.

Electrons of each atom become a source of

scattered radiation (spherical waves)

15

Interference pattern

n=2

+ =

Positive / constructive

interference

Amplification

+ =

Negative / destructive

interference

Extinction

16

Interference pattern

n=4 n=8 n=12 n=25 n=50

Bragg’s Law

17

n ∙ λ = 2 ∙ d ∙ sin(θ)

d

λ

θ θ δ

2δ = n ∙ λ δ = d ∙ sin(θ)

d = (n ∙ λ) / (2 ∙ sin(θ))

Lattice Planes and Miller Indices

18

a

b

Definition:

A lattice plane is a plane

which intersects atoms of

a unit cell across the whole

3‐dimensional lattice.

d(100)

d(010)

d(110)

d(-210)

- Each lattice plane

generates a diffraction

peak.

- The 2θ angle of the

peak depends on the

plane’s d-spacing.

- Diffraction peaks can

be labelled with the

plane’s Miller index.

Bragg’s Law

19

CuKα1 = 0.154056 nm

a = 0.2 nm

b = 0.5 nm

b a

b

a

2θ = 45.30°

2θ = 17.72°

d = 0.2 nm

d = 0.5 nm

θ = 22.65°

θ = 8.86°

Single Crystal

20

A single crystal must be rotated

to bring each lattice plane in

diffraction condition.

Polycrystals, Powders

21

In an ideal powder every

possible orientation of

crystals occurs.

In a random powder

no orientation is preferred.

In an ideal powder all possible diffraction peaks

are generated, regardless of sample orientation.

Diffraction Cones

22

Diffraction at an angle 2θ° from

the primary beam

All possible rays form a cone = diffraction cone = Debye cone

Diffraction Cones

23

(120)

(100)

(010)

One Debye Cone for each lattice plane spacing (d value)

Powder sample:

Debye Ring

24

Gra

y V

alu

e

2 Angle

Powder Diffractometer

25

X-ray tube

Primary Beam

Powder

Sample

Diffraction Cones

«Secondary Beams»

X-ray Detector scanning X-ray intensity

vs. 2θ angle

Powder Diffraction Pattern

26

10 20 30 40 50 60

0

500

1000

1500

2000

Inte

nsity (

cts

)

Diffraction Angle (°2)

Lesson 2: All about powder diffractometers

Monochromatic X-radiation

27

n ∙ λ = 2 ∙ d ∙ sin(θ)

http://fineartamerica.com

Diffraction angle θ depends on wavelength λ:

Polychromatic X-ray Beam

We need monochromatic X-radiation!

28

Monochromatic X-Radiation

Cu Radiation

Kβ absorption filter

filtered Radiation

Ideally: Isolate Kα1

Reality: Suppress Kβ and Bremsstrahlung

Wavelength (nm)

Inte

nsity

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Cu

Kα1

Kα2

Kβ

Bremsstrahlung Cu Radiation

Monochromator Crystal

(Graphite, d = 0.3352 nm)

CuKα1/2 Radiation

n ∙ λ = 2 ∙ d ∙ sin(θ)

Cu Radiation Energy dispersive

Detector

Digital filtering

Kβ-filtered Diffraction Pattern

29

27 28 29 30 31 32

0

100000

200000

300000

400000

500000In

ten

sity


CuKα1

CuKα2

LaB6 pattern, Cu radiation, Ni filter in primary beam (Bruker D8 Advance)

Kβ-filtered Diffraction Pattern

30

27 28 29 30 31 32

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Inte

nsity


CuKβ

CuKα1 & CuKα2 duplet

Remaining Bremsstrahlung

Absorption Edge

Impurity

CuKα Satellites

(= CuKα3)

LaB6 pattern, Cu radiation, Ni filter in primary beam (Bruker D8 Advance)

Graphite Monochromator

31

27 28 29 30 31 32

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000In

ten

sity


CuKα1

CuKα2

LaB6 pattern, Cu radiation, Graphite monochromator, secondary beam (PANalytical CubiX3)

Graphite Monochromator

32

27 28 29 30 31 32

0

100

200

300

400

500In

ten

sity



CuKα Satellites

(= CuKα3)

LaB6 pattern, Cu radiation, Graphite monochromator, secondary beam (PANalytical CubiX3)

31 32 33 34 35 36

0

10000

20000

30000

40000

50000

taken from file NIST-SRM1976b-150105-03.brml

Inte

nsity (

co

un

ts)


Energy-Dispersive Detector

33

Al2O3 pattern, Cu radiation, LynxEyeXE detector (Bruker D8 Advance)

CuKα1

CuKα2

31 32 33 34 35 36

0

1000

2000

3000

4000

5000

taken from file NIST-SRM1976b-150105-03.brml

Inte

nsity (

co

un

ts)


Energy-Dispersive Detector

34

CuKβ


Edge of

Energy Window


31 32 33 34 35 36

0

5000

10000

15000

20000

25000

30000

taken from file NIST-SRM1976b-150106-01-NiFilter.brml

Inte

nsity (

co

un

ts)


Energy-Dispersive Detector + Kβ filter

35

CuKα1

CuKα2

50% loss of intensity

(0.0125 mm Ni filter)


31 32 33 34 35 36

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

taken from file NIST-SRM1976b-150106-01-NiFilter.brml

Inte

nsity (

co

un

ts)


Energy-Dispersive Detector + Kβ filter

36



Edge of

Energy Window

50% loss of intensity

(0.0125 mm Ni filter)

Monochromators

37

Kβ Filter:

Selectively suppresses Kβ

and parts of Bremsstrahlung

Monochromator crystal and

energy dispersive detector:

Suppress everything BUT Kα

Important difference for

fluorescent samples

«Notch filter»

«Bandpass filter»

38

Ni-Filtered Cu Radiation, Fe Fluorescence

10 20 30 40 50 60 70 80

0

500

1000

1500

2000

G:\Auftr_Proj\S-Auftraege\2012\S12_0008 XRD Course Riga\Paper Andris\Paper2\XRD-Fluorescence.opj

Inte

nsity [cts

]

Diffraction Angle [°2]

T0

T05

T10

T25

T50

T75

CuK radiation, Ni-filternot stacked

10 20 30 40 50 60 70 80

0

500

1000

1500

2000


Inte

nsity [cts

]


T0

T05

T10

T25

T50

T75


10 20 30 40 50 60 70 80

0

500

1000

1500

2000


Inte

nsity [cts

]


T0

T05

T10

T25

T50

T75


10 20 30 40 50 60 70 80

0

500

1000

1500

2000


Inte

nsity [cts

]


T0

T05

T10

T25

T50

T75


10 20 30 40 50 60 70 80

0

500

1000

1500

2000


Inte

nsity [cts

]


T0

T05

T10

T25

T50

T75


10 20 30 40 50 60 70 80

0

500

1000

1500

2000


Inte

nsity [cts

]


T0

T05

T10

T25

T50

T75


Cu radiation, Ni filter in 2nd beam

(PANalytical X’Pert Pro)

100% TiO2

95% TiO2

+ 5% NiFe2O4

90% TiO2

+ 10% NiFe2O4

75% TiO2

+ 25% NiFe2O4

50% TiO2

+ 50% NiFe2O4

25% TiO2

+ 75% NiFe2O4

Secondary-monochromated Cu-Radiation

39

10 20 30 40 50 60 70 80

0

200

400

600

800

1000

1200

not stackedCuK radiation, Graphite monochromator

Inte

nsity [cts

]


T0

T05

T10

T25

T50

T75

T100


10 20 30 40 50 60 70 80

0

200

400

600

800

1000

1200


Inte

nsity [cts

]


T0

T05

T10

T25

T50

T75

T100


10 20 30 40 50 60 70 80

0

200

400

600

800

1000

1200


Inte

nsity [cts

]


T0

T05

T10

T25

T50

T75

T100


10 20 30 40 50 60 70 80

0

200

400

600

800

1000

1200


Inte

nsity [cts

]


T0

T05

T10

T25

T50

T75

T100


10 20 30 40 50 60 70 80

0

200

400

600

800

1000

1200


Inte

nsity [cts

]


T0

T05

T10

T25

T50

T75

T100


10 20 30 40 50 60 70 80

0

200

400

600

800

1000

1200


Inte

nsity [cts

]


T0

T05

T10

T25

T50

T75

T100


TiO2 + NiFe2O4,

Cu radiation, 2nd graphite monochromator

(PANalytical CubiX3)

95% TiO2

+ 5% NiFe2O4

90% TiO2

+ 10% NiFe2O4

75% TiO2

+ 25% NiFe2O4

50% TiO2

+ 50% NiFe2O4

25% TiO2

+ 75% NiFe2O4

100% NiFe2O4

In case of Fluorescence, use:

- Secondary-beam monochromator

- Energy-dispersive Detector

- Different X-ray tube (Cr / Fe / Co)

Summary: Monochromators

40

Optical Element Effect on Spectrum Effect on Intensity

Kβ Filter Reduces Kβ peaks Moderate loss

Graphite Monochromator Eliminates Kβ peaks Eliminates Fluorescence

Strong loss

Multi-bounce Monochromator Eliminates Kβ and Kα2 Eliminates Fluorescence

Massive loss (mostly used on Synchrotrons)

Energy dispersive Detector Reduces Kβ peaks Eliminates Fluorescence

No loss

Overview of Instruments

41

Lab Instrument Monochromator

RMS Foundation Bruker D8 Energy dispersive Detector

Uni Bern Panalytical X’Pert Kβ-Filter

Uni Bern Panalytical CubiX Graphite Monochromator

Bruker D8 Panalytical X’Pert Panalytical CubiX

Lesson 1 X-Rays & Diffraction -...

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