Lesson 1 X-rays & Diffraction Nicola Döbelin RMS Foundation, Bettlach, Switzerland February 11 14, 2013, Riga, Latvia
Electromagnetic Spectrum X rays: Wavelength λ: 0.01 10 nm Energy: 100 ev 100 kev Interatomic distances in crystals: typically 0.15 0.4 nm Generation of X-radiation: Shoot electrons on matter Interference phenomena only for features λ 5
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. 6
Bremsstrahlung Continuous spectrum 40 kv, 20 ma Intensity 30 kv, 20 ma 20 kv, 20 ma 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Wavelength (nm) 7
Bremsstrahlung Continuous spectrum 30 kv, 40 ma Intensity 30 kv, 30 ma 30 kv, 20 ma 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Wavelength (nm) 8
Characteristic Radiation M 4,5 (3d) M 2,3 (3p) M 1 (3s) Cu E b (ev) 0 76 122 M L K L 3 (2p 3/2 ) L 1 (2p 1/2 ) 933 952 L 1 (2s) 1097 Kα 1 Kα 2 Kβ K 1 (1s) 8979 Wavelength of Kα 1, Kα 2, Kβ, Lα... are characteristic for the atomic species. 9
X-rays: Spectrum Kα 1 Kα 1 Kα 2 Intensity Kβ Kβ Kα 2 Mo Cu 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Wavelength (nm) 10
X-ray Tube Target (Cu, Mo, Fe, Co,...) Acceleration Voltage Vacuum e Filament Be window Filament Current Generator settings: kv ma 11
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! 12
Focal Point Typical target size: Length: 10-12 mm Width: 0.4-1.0 mm Take-off angle (typically 6 ) Target Point focus Line focus 13
X-rays: Summary Generated in an X-ray tube Spectrum contains Bremsstrahlung (continuous) and characteristic radiation (Kα 1, Kα 2, Kβ) of target material Tube is characterized by: Target material Size and shape of target Aceleration voltage and current 14
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 CuKα 1 Fe atom FeKα 1 1. Absorption and ionization 2. Relaxation and emission of characteristic radiation 15
Elastic Scattering Fe atom CuKα 1 λ p λ s CuKα 1 Electron oscillates in the electric field, emits photons of the same wavelength as the incoming radiation (λ s = λ p ). Secondary wave is in phase (+ 180 ) with primary wave. 16
Crystal Lattice Crystal: Periodic arrangement of atoms/ions/molecules in 3 dimensions. Electrons of each atom become a source of scattered radiation (spherical waves) 17
Positive interference (amplification) Negative interference (extinction) More sources in ordered arrangement = More distinct interference pattern xx.xx.xxxx 18 Tagung Image: http://www.forbes.com/
Bragg s Law n λ = 2 d sin(θ) λ θ θ 2θ d Diffracted beam looks like a «reflection», but it is scattered radiation 19
Bragg s Law CuKα 1 = 0.154056 nm a = 0.2 nm b = 0.5 nm d = 0.2 nm θ = 22.65 2θ = 45.30 θ = 8.86 2θ = 17.72 d = 0.5 nm a b b a 20
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. b - The 2θ angle of the peak depends on the plane s d-spacing. a d(100) d(110) - Diffraction peaks can be labelled with the plane s Miller index. 21
Single Crystal A single crystal must be rotated to bring each lattice plane in diffraction condition. 2θ 2θ 2θ 22
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. 23
Diffraction Cones Diffraction at an angle 2θ from the primary beam All possible rays form a cone = diffraction cone = Debye cone 24
Diffraction Cones Powder sample: (120) (100) (010) One Debye Cone for each lattice plane spacing (d value) 25
Gray Value Debye Ring 26 2θ Angle
Powder Diffractometer Diffraction Cones «Secondary Beams» X-ray tube Primary Beam Powder Sample X-ray Detector scanning X-ray intensity vs. 2θ angle 27
Powder Diffraction Pattern 2000 Lesson 2: All about powder diffractometers 1500 Intensity (cts) 1000 500 0 10 20 30 40 50 60 Diffraction Angle ( 2θ) 28
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 29
Monochromatic X-radiation Kα 1 Intensity Kβ Kα 2 Kα 1 Cu 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Wavelength (nm) Bremsstrahlung X-ray Beam from Tube Kβ Kα 2 Monochromator: Remove every wavelength but Kα 1 30
Monochromator X-radiation is absorbed by solid matter. Absorption coefficient depends on wavelength. There are steps (absorption edges) in the spectrum. Ni Absorption Coefficient «K» edge Ni K: 0.14879 nm L-I: 1.22988 nm 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Wavelength (nm) 31
Ni-Filter Kα 1 Ni Kα 2 Intensity Kβ Cu 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Wavelength (nm) Cu Radiation Ni filter 32
Ni-Filter Kα 1 Ni Kα 2 Intensity Kβ 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 Kα 2 33
Ni-filtered Diffraction Pattern 500000 CuKα 1 400000 Intensity 300000 200000 CuKα 2 100000 0 27 28 29 30 31 32 Diffraction Angle ( 2θ) 34
Ni-filtered Diffraction Pattern 20000 CuKα 1 & CuKα 2 duplet 18000 16000 14000 Intensity 12000 10000 8000 6000 CuKβ Absorption Edge CuKα Satellites (= CuKα 3 ) 4000 2000 Impurity Remaining Bremsstrahlung 0 27 28 29 30 31 32 Diffraction Angle ( 2θ) 35
Ni Filter: Primary or Secondary Beam Primary beam filter Kα 1 Cu Radiation Ni-filtered primary beam Kα 2 Ni filter Kα 1 Secondary beam filter Kα 2 Cu Radiation Bremsstrahlung Kβ Ni filter 36
Kβ Filter Target Element Kα 1 (nm) Kα 2 (nm) Kβ(nm) KβFilter Absorption Edge λ K (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. 37
Summary: Kβ Filter Kβ Filter: - Mostly eliminates Kβ - Does not eliminate Kα 2 - Moderate loss of intensity of Kα 1 and Kα 2 - 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 38
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( ) CuKα 1 0.154059 26.57 CuKα 2 0.154441 26.64 CuKβ 0.139225 23.97 39
Monochromator Crystal Graphite monochromator BS Kβ Graphite Crystal Kα 2 Kα 1 High-resolution monochromator Si / Ge Crystals Kα 1 Kα 2 Kα 1 40
Graphite Monochromator 10000 9000 CuKα 1 Intensity 8000 7000 6000 5000 4000 3000 2000 1000 CuKα 2 0 27 28 29 30 31 32 Diffraction Angle ( 2θ) 41
Graphite Monochromator 500 CuKα 1 & CuKα 2 duplet 400 Intensity 300 200 CuKα Satellites (= CuKα 3 ) 100 0 27 28 29 30 31 32 Diffraction Angle ( 2θ) 42
Monochromator Crystal Monochromator Crystal: - Completely eliminates Kβ - Reduces background intensity - Si / Ge eliminate Kα 2, Graphite does not eliminate Kα 2 - Severe loss of intensity of Kα 1 (and Kα 2 ) - Graphite crystal can be placed in primary or secondary beam - Si / Ge crystals are usually placed in the primary beam - Monochromatic beam is polarized 43
Energy-Dispersive Detector Detector Detector s energy window is set to Kα 1/2, other wavelengths are ignored («digital filtering») BS Kβ Kα 1 Kα 2 Powder Sample 44
Energy-Dispersive Detector Energy-dispersive Detector: - Completely eliminates Kβ - Reduces background intensity - Does not eliminate Kα 2 - No loss of intensity of Kα 1 and Kα 2 45
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 Kα 2! 46
Overview of Instruments Lab Instrument Monochromator RTU Rigaku Ultima+ Graphite Monochromator RTU Panalytical X Pert Ni-Filter LU Bruker D8 Ni-Filter Uppsala Uni Bruker D8 Ni-Filter RTU Salaspils Bruker D8 Energy-dispersive Detector RMS (Uni Bern) Panalytical X Pert Ni-Filter RMS (Uni Bern) PanalyticalCubiX Graphite Monochromator 47