Material structure elucidation methods X-ray analysis dr. Éva Makó 1
Major branches of science -X-ray radiography, Computed Tomography -X-ray fluorescence spectrometry (XRF) -X-ray crystallography X-ray powder diffractometry (XRD) 2
History 1895. The discovery of X-rays by W. K. Röntgen. (Crookes tube, the medical use, Röntgen rays, the 1901 Nobel Prize) 1906. Charles Barkla discovered that X-rays could be scattered by gases, and that each element had a characteristic X-ray spectrum (the 1917 Nobel Prize). 1912. Max von Laue, P. Knipping, and W. Friedrich first observed the diffraction of X-rays by crystals (the 1914 Nobel Prize). 1915. W. H. Bragg shared a Nobel Prize with his son W. L. Bragg: "for their services in the analysis of crystal structure by means of X-rays„. 1917. Philips starts to manufacture X-ray tubes in Eindhoven. 1935. The first X-ray powder diffractometer was developed by Le Galley. 1945. Friedman was working on „X-ray spectrometer”. 1947. The first commercial X-ray powder diffractometer by Philips. 1954. The first commercial X-ray spectrometer by Philips… 3
X-rays • X-rays are electromagnetic waves with associated wavelength, or beams of photons with associated energies. Properties: • Energy: E=h · ν =h · c/ λ 0.125 – 125 keV • Wavelength: 0.01 - 10 nm • Types: white radiation; characteristic radiation. 4
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Generation of X-rays • The sealed X-ray tube. 6
Generation of X-rays White radiation : The interaction of accelerated electron with the anode leads to a loss in energy, resulting in the emission of X-rays in a continuous spectrum. Characteristic radiation : Irradiating an atom with electrons with sufficient energy can expel an electron from the atom. The emission of an electron produces a void in a shell (e.g. in the K-shell). The atom wants to restore the original configuration by transferring an electron from an outer shell (e.g. L-shell). When an L- shell electron is transferred to the K-shell, the energy excess is emitted as an X-ray photon. 7
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Interaction of X-rays with matter X 9
1. Absorption I – x , thickness, − µ ρ = x e m – ρ , density, I 0 – µ m , absorption coefficient. • The µ m of the material depends on: – Z , atomic number, – λ, wavelength, N – N A , Avogadro number, µ = λ ≈ λ 4 3 3 3 k Z Z A – A , atomic mass. m A • Mixtures and compounds: n µ m,T : – The average µ µ µ = ∑ µ µ w – w i , atomic mass fraction. m T m i i , , 10 = i 1
1. Absorption • Absorption edges: K-, L I -, L II -, L III -, M I-V , N I-VII , ... etc. – High energies are hardly absorbed. – The highest yield is reached when the energy of the photon is just above the binding energy of the electron. – An edge can be seen: the energy is too low to expel electrons from that shell. 11
2. Fluorescence ∆ E � E=h · c/ λ The emission of X-ray photons. ∆ ∆ ∆ λ λ λ 3 λ 3 3 3 λ λ 0 λ λ λ 1 λ λ λ 1 1 1 V N M ∆ E 3 ∆ ∆ ∆ L ∆ ∆ E 2 ∆ ∆ ∆ E 1 ∆ ∆ ∆ K X-ray photons can expel an electron from the atom. The stabilization is occurred through the emission of E i =h ν ν i = ∆ ν ν ∆ ∆ ∆ E i characteristic X-ray photons. • Characteristic lines – Heavy elements have more characteristic lines. – λ λ λ λ 0 < λ λ 1 , λ λ λ λ 2 , λ λ λ λ λ 3 , ...of emitted characteristic X-rays. λ 12
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3. Diffraction (Rayleigh scatter) A crystal can be seen as a 3D grating with a spacing ( d crystal ), and diffraction effect • can be observed when the wavelength ( λ λ λ λ X-ray ) of the incoming X-ray photon is of similar size. Bragg’s law: ∆ = λ = θ s n d ( ) 2 sin � s, the optical path difference. • As a consequence of the regular arrangement of atoms in solid matter coherent scattering of X-rays at the atoms results in constructive interference at certain well- defined angles (Bragg’s law). λ λ λ λ , wavelength (Å), – n = 1, 2, 3, ..., ‘order of the interference, normally n=1, – d , interplanar spacing (Å), – θ , angle of the incident and diffracted X-ray. θ θ θ – 14
3. Diffraction (Rayleigh scatter) 15 15
X-ray diffraction (XRD) It is a versatile, non-destructive analytical method to analyze material properties like phase composition, structure, texture, etc. of powder, solid and liquid samples. 16
XRD is used for: - Characterization of (new) materials at universities and research centers; - Process control (e.g. in cement industry); - Determination of polymorphism (active pharmaceutical ingredient); - Phase identification of minerals in geological samples; - Optimization of fabrication parameters for ceramics; - Determination of crystallinity; - Determination of amorphous phase contents. 17
Crystalline and amorphous state 18
Crystal systems 19
Unit cell 14 Bravais lattices 32 crystal classes 230 space groups 20
Miller indices 21
X-ray powder diffraction • The sample consists of infinitely large number of small crystallites, ideally randomly oriented. It is only necessary to vary the angle of incidence and the angle of diffraction. The diffractogram is obtained by counting the detected intensity as a function of the angle between incident and diffracted beam. = constant) and n=1 : Monochromatic radiation ( λ = = = • λ n ( ) = d ∆ = λ = θ s n d ( ) 2 sin i θ 2sin i i i The diffraction pattern: d i (2 θ i ) - I rel (= 100 I i /I 100% ) data. • – The diffraction pattern is characteristic for each crystalline substance. • Also, substances with same chemical composition, but different crystal structure (e.g. TiO 2 , rutile and anatase) differ in their diffractograms. • Identification of phases is achieved by comparing the diffractogram obtained from an unknown sample with patterns of a reference database. 22
X-ray powder diffraction • The main topic of XRD is qualitative and quantitative phase analysis. • The X-ray diffractometer: • X-ray tube (Cu, Cr, Mo… anode), generator; • Primary optical components: Soller slit, divergence slit; • Sample holder; • Goniometer; • Secondary optical components: receiving slit, Soller slit, anti-scatter slit; • Monochromator; • Detector (proportional, scintillation, solid-state). 23
X-ray tube, generator 24
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X-ray tube 26
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Reflection geometry 28
Detectors • Proportional counter (Xe, Kr gas) • Scintillation counter (e.g. NaI/Tl) • Solid-state detector (Si(Li), Ge(Li)) 29
Production of monochromatic radiation • β filter • Pulse height selection • Monochromator • Solid-state detector 30
Effect of β filter Unfiltered and filtered Co radiation. 31
Pulse height selection 32
Monochromator 2·d·sin θ θ θ θ = (n)· λ λ λ λ 33
Sample preparation Sample: powder, gel, liquid. Sample holder Representative sample Homogeneity Absorption Thickness and analysis depth Mounting of the specimen Flatness Particle size (1-5 � m) and crystallite size Preferred orientation 34
XRD data collection and processing Sample preparation Optimum measurement conditions (kV, mA, divergence and receiving slit) Data collection (start and end angle, step size, time per step) (e.g. 4-70° 2 θ , 0.02° 2 θ , 1 s) Data processing (smoothing, background, K α 2 stripping, peak position, 2 θ calibration ) 35
Qualitative phase analysis Determination of background, peak positions, intensities, and widths etc. Relative intensities of reflections are calculated. The strongest reflection is normalized to 100%. Editing of the peak table. Nr. Pos. (° 2 θ ) d-value ( Å) Rel. Int. (%) Intensity (cts) 1 24.4002 3.6481 1.17 53.19 2 29.4716 3.0309 4.32 196.96 3 33.7833 2.6532 21.43 977.14 4 38.1742 2.3576 100 4560.28 36
- The measured diffractogram is compared with a reference database consisting of experimentally determined d-values and intensities of calculated patterns from crystal structural data. - e.g. The PDF database (Powder Diffraction File, earlier named ASTM and JCPDS) of the ICDD (International Centre for Diffraction Data). - Identification of the main phase. - Identification of further phases using the unidentified reflections. - …. 37
A typical JCPDS powder file card 38
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Quantitative phase analysis In 1919, Hull described that the intensity of the X-rays diffracted by a certain phase is proportional to its amount in the phase mixture. Methods: 1. The spiking method (Lennox, 1957); 2. The absorption-diffraction method (Klug and Alexander, 1948); 3. The internal standard method (Klug and Alexander, 1974); 4. Full pattern methods (e.g. Rietveld method, 1969). 40 40
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