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 Kα1 Kα2 Kα2 Kβ Kβ Intensity Mo Cu 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) λ 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 Cu 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. Ni «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 Ni Kα2 Kβ Intensity Cu 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Wavelength (nm) Cu Radiation Ni filter 29 Ni-Filter Kα1 Ni 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 44.