Lesson 1: X-Rays and Diffraction

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Lesson 1 X-rays & Diffraction

Nicola Döbelin RMS Foundation, Bettlach, Switzerland

October 16 – 17, 2013, Uppsala, Sweden Electromagnetic Spectrum

X rays: Wavelength λ: 0.01 – 10 nm Energy: 100 eV – 100 keV

Interatomic distances in crystals: Generation of X-radiation: typically 0.15 – 0.4 nm Shoot electrons on matter

Interference phenomena only for features ≈ λ

2 Generation of X-rays

Accelerated electron impinges on matter:

Bremsstrahlung (Deceleration radiation)

Electron is deflected and decelerated by the atomic nucleus. (Inelastic scattering)

Deflected electron emits electromagnetic radiation. Wavelength depends on the loss of energy.

3 Bremsstrahlung

Continuous spectrum

40 kV, 20 mA

30 kV, 20 mA

Intensity 20 kV, 20 mA

0.00 0.05 0.10 0.15 0.20 0.25 0.30 Wavelength (nm)

4 Bremsstrahlung

Continuous spectrum

30 kV, 40 mA

30 kV, 30 mA Intensity

30 kV, 20 mA

0.00 0.05 0.10 0.15 0.20 0.25 0.30 Wavelength (nm)

5 Characteristic Radiation

Cu Eb (eV) 0 M4,5 (3d)

M2,3 (3p) 76

M1 (3s) 122

M L K L3 (2p 3/2 ) 933 952 L1 (2p 1/2 )

L1 (2s) 1097

Kα1 Kα2 Kβ

K1 (1s) 8979

Wavelength of K α1, K α2, K β, L α... are characteristic for the atomic species.

6 X-rays: Spectrum

Kα1

Kα2

Kα2 Kβ

Kβ Intensity

0.00 0.05 0.10 0.15 0.20 0.25 0.30 Wavelength (nm)

7 X-ray Tube

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

‒ Acceleration e Be window Voltage Vacuum Filament

Filament Current

Generator settings: kV mA

8 Old X-ray tubes

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

Caution: Beryllium is toxic & carcinogenic! - Never touch the windows! - Use appropriate covers!

9 Focal Point

Typical target size: Take-off angle Length: 10-12 mm (typically 6°) Width: 0.4-1.0 mm

Target

Point focus

Line focus

10 X-rays: Summary

• Generated in an X-ray tube

• Spectrum contains Bremsstrahlung (continuous) and

characteristic radiation (K α1, K α2, K β) of target material

• Tube is characterized by: • Target material • Size and shape of target • Aceleration voltage and current

11 Diffraction Basics

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

CuK α1 Fe atom

FeK α1

1. Absorption and ionization 2. Relaxation and emission of characteristic radiation

12 Elastic Scattering

Fe atom

CuK α1 λp

λs

CuK α1

Electron oscillates in the electric field, Secondary wave is in phase emits photons of the same wavelength as (+ 180°) with primary wave.

the incoming radiation ( λs = λp).

13 Crystal Lattice

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

Electrons of each atom become a source of scattered radiation (spherical waves)

14 Positive interference (amplification) Negative interference (extinction)

More sources in ordered arrangement = More distinct interference pattern

xx.xx.xxxx 15 Tagung Image: http://www.forbes.com/ Bragg’s Law

n · λ = 2 · d · sin( θ)

θ d θ 2θ

Diffracted beam looks like a «reflection», but it is scattered radiation

16 Bragg’s Law

CuK α1 = 0.154056 nm a = 0.2 nm b = 0.5 nm

2θ = 17.72° θ = 22.65° 2θ = 45.30° θ = 8.86° d = 0.2 nm

d = 0.5 nm

a b a b

17 Lattice Planes and Miller Indices

d(-210) Definition: A lattice plane is a plane which intersects atoms of a unit cell across the whole 3‐dimensional lattice. d(010) - Each lattice plane generates a diffraction peak.

- The 2θ angle of the peak depends on the b plane’s d-spacing.

a - Diffraction peaks can d(100) d(110) be labelled with the plane’s Miller index.

18 Single Crystal

A single crystal must be rotated to bring each lattice plane in diffraction condition.

2θ 2θ 2θ

19 Polycrystals, Powders

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.

20 Diffraction Cones

Diffraction at an angle 2 θ° from the primary beam

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

21 Diffraction Cones

Powder sample: (120)

(100)

(010)

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

22 Debye Ring Gray Value Value Gray Gray

2θ Angle

23 Powder Diffractometer

Diffraction Cones «Secondary Beams»

X-ray tube Primary Beam X-ray Detector scanning X-ray intensity vs. 2 θ angle Powder Sample

24 Powder Diffraction Pattern

Lesson 2: All about powder diffractometers 2000

1500

1000 Intensity (cts) Intensity

500

0 10 20 30 40 50 60 Diffraction Angle (°2 θ)

25 Monochromatic X-radiation

Diffraction angle θ depends on wavelength λ:

n · λ = 2 · d · sin( θ)

Polychromatic X-ray Beam

We need monochromatic X-radiation!

http://fineartamerica.com

26 Monochromatic X-radiation

Kα1

Kα2 Kα1 Kβ Intensity

Kα 0.00 0.05 0.10 0.15 0.20 0.25 0.30 2 Wavelength (nm) Kβ

Bremsstrahlung

X-ray Beam from Tube

Monochromator: Remove every wavelength but K α1

27 Monochromator

X-radiation is absorbed by solid matter. Absorption coefficient depends on wavelength. There are steps (absorption edges) in the spectrum.

«K» edge Ni K: 0.14879 nm L-I: 1.22988 nm Absorption Coefficient Absorption

0.00 0.05 0.10 0.15 0.20 0.25 0.30 Wavelength (nm)

28 Ni-Filter

Kα1

Kα2

Kβ Intensity

0.00 0.05 0.10 0.15 0.20 0.25 0.30 Wavelength (nm)

Cu Radiation

Ni filter

29 Ni-Filter

Kα1

Kα2

Kβ Intensity

0.00 0.05 0.10 0.15 0.20 0.25 0.30 Wavelength (nm)

Cu Radiation Ni-filtered Cu Radiation

Ni filter Kβ and Bremsstrahlung attenuated

No elimination of Kα2

30 Ni-filtered Diffraction Pattern

500000 α Cu K 1

400000

300000

α Cu K 2

200000 Intensity

100000

0 27 28 29 30 31 32 Diffraction Angle (°2 θ)

31 Ni-filtered Diffraction Pattern

α α Cu K 1 & Cu K 2 duplet 20000

18000

16000

14000

12000 Cu Kα Satellites α 10000 (= CuK 3)

8000 Intensity Absorption Edge CuK β 6000

4000

2000 Impurity Remaining Bremsstrahlung

0 27 28 29 30 31 32 Diffraction Angle (°2 θ)

32 Ni Filter: Primary or Secondary Beam

Kα1 Primary beam filter

Kα2 Cu Radiation Ni-filtered primary beam

Kα1 Ni filter

Kα2 Secondary beam filter

Kβ Bremsstrahlung Ni filter Cu Radiation

33 Kβ Filter

Target Kα1 (nm) Kα2 (nm) Kβ (nm) Kβ Filter Absorption Element Edge λK (nm) Cr 0.228975 0.229365 0.20849 V 0.2269 Fe 0.193631 0.194002 0.17567 Mn 0.1896 Co 0.178900 0.179289 0.16208 Fe 0.1744 Ni 0.165794 0.166178 0.15002 Co 0.1608 Cu 0.154059 0.154441 0.139225 Ni 0.1488 Mo 0.709317 0.713607 0.63230 Zr 0.6889 Ag 0.559422 0.563813 0.49708 Rh 0.5339

Birkholz, M. «Thin Film Analysis by X-ray Scattering», Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2006.

34 Summary: Kβ Filter

Kβ Filter: - Mostly eliminates Kβ

- Does not eliminate Kα2

- Moderate loss of intensity of Kα1 and Kα2 - Leaves an absorption edge in the foot of the diffraction peaks - Attenuation of Kβ depends on thickness of filter foil - Can be placed in the primary or secondary beam

35 Monochromator Crystal

Kβ and most of the Bremsstrahlung (BS) are not in diffraction condition ‰ Extinction

θ = 13.3° 2θ = 26.6°

Graphite single crystal

d (002) = 0.3352 nm

n · λ = 2 · d · sin( θ) Emission Line Wavelength (nm) 2θ Bragg Diffraction Condition (°)

CuKα1 0.154059 26.57

CuKα2 0.154441 26.64 CuKβ 0.139225 23.97

36 Monochromator Crystal

Graphite Graphite Crystal monochromator BS Kβ

Kα2

Kα1

High-resolution Si / Ge Crystals Kα Kα monochromator 1 2

Kα1

37 Graphite Monochromator

10000 α Cu K 1 9000

8000

7000

6000

α 5000 Cu K 2

4000 Intensity

3000

2000

1000

0 27 28 29 30 31 32 Diffraction Angle (°2 θ)

38 Graphite Monochromator

α α Cu K 1 & Cu K 2 duplet 500

400

300

200 Cu Kα Satellites Intensity α (= CuK 3)

100

0 27 28 29 30 31 32 Diffraction Angle (°2 θ)

39 Monochromator Crystal

Monochromator Crystal: - Completely eliminates Kβ - Reduces background intensity

- Si / Ge eliminate Kα2, Graphite does not eliminate Kα2

- Severe loss of intensity of Kα1 (and Kα2) - Graphite crystal can be placed in primary or secondary beam - Si / Ge crystals are usually placed in the primary beam - Monochromatic beam is polarized

40 Energy-Dispersive Detector

Detector

Detector’s energy window

is set to Kα1/2 , other wavelengths are ignored («digital filtering»)

BS Kβ Kα1 Kα2

Powder Sample

41 Energy-Dispersive Detector

Energy-dispersive Detector: - Completely eliminates Kβ - Reduces background intensity

- Does not eliminate Kα2

- No loss of intensity of Kα1 and Kα2

42 Summary: Monochromators

• Monochromatic X-radiation is required for powder XRD

• Bremsstrahlung and Kβ must be eliminated from the tube’s spectrum

• 3 different types of monochromators: •Kβ filter (Cu tube + Ni filter, Mo tube + Zr filter) • Monochromator crystal • Energy-dispersive detector

• Most systems do not eliminate Kα2!

43 Overview of Instruments

Lab Instrument Monochromator Uppsala Uni Bruker D8 Ni-Filter RMS (Uni Bern) Panalytical X’Pert Ni-Filter RMS (Uni Bern) Panalytical CubiX Graphite Monochromator

Bruker D8 Panalytical X’Pert Panalytical CubiX