X-rays •X-ray Radiography -absorption is a function of Z and density •X-ray crystallography 'X-ray spectrometry Wilhelm K. Roentgen (1845-1923) NP in Physics 1901 ♦ Clí, Mix Au -60 kV i -30 mA A*" *h ^ -2A ^ >. X-rays Heated filament emits electrons by thermionic emission Electrons are accelerated by a high voltage, ^ Cupjjör rod lor &al dissipation Glass envelope x-rays produced when high speed electrons hit the metal targei. CuK I h High voltage source Cathode rays a X-rays E = 8.05 keV 1 «M^^^^^^l Cathode A,= 1.541Á Interaction of Electrons with Matter Emission of electromagnetic radiation: •Characteristic radiation, discrete energies •Bremsstrahlung, continuous energy distribution •Luminiscence (UV or visible region) Electron emission: •Backscattered electrons (BSE) •Auger electrons •Secondary electron emission (SE) Effects in the Target: •Electron Absorption (ABS) •Heat X-ray Tubes High vattage anode Glass wa Cathode Tungsben filament Tungsten target j / \ \ Focusing Tube He window *< \ Vvreiead Takeoff angle Center of Takeoff generated X-ray angle Filament X-ray (obe X-ray Tubes FILAMENT CATHODE \ ''■' '. JÍRAVS _ AMODF \>sss//jjj;;Z Tungsten wire at 1200-1800 °C (about 35 mA heating current) High Voltage 20-60 kV High max. power 2.2-3 kW Typical operating values Cu: 40 kV, 35 mA Mo: 45 kV, 35 mA WATER U3 C OJ Spectrum of the X-ray tube Characteristic radiation 0.5 1.0 1.5 2.0 Wavelength (a) Fig. 4.2. Characteristic spectrum of copper superimposed on the white radiation spectrum. Notice the ratio of the relative intensities of the Ka and Kß lines. Bremstrahlung (white radiation) Emax= E0 = exV0 E = (hxc)A, 4™ (A) = he _ 12.398 ^V0~V0(kV) Characteristic X-ray radiation Primary (incident) electron iilkIcíH ctai run E^viid X-ray (fluorescence) photon K Selection Rules •n = 1, 2, 3.... (principal quantum number), corresponds to K, L, M... shells •1 = 0, 1, ..., n-1 (orbital quantum number) •j =| l±s|; s = 1/2 (spin-orbit coupling) •mj = j,j-l,j-2, ...,-j •Transition only, when An>l,Al=l,Aj = 0orl Selection Rules M = 2J + 1 X-ray Quantum numbers Maximum ■ \\j i-iii t\ji i n / ; m, population K 1 Ü i ±i 2 Lt 2 0 i 2 ±1 2 L* 2 1 í ±k 2 ^ii i 2 1 3 2 ±1. ±1 4 *#, 3 0 I 2 ±k 2 Mxt 3 L 1 2 ±1 2 W..I 3 I i ±1 ±\ 4 W,v 3 2 í í ±í. ±\ 4 Mv 3 2 ? 2 *!. ±1 ±5 6 wi 0 i ±i 2 tfn 1 1 2 ±1 2 *nr 1 í ±1, ±2 4 ",v 2 2 ttí. ±i 4 "v 2 a ±í. ±í- — 6 "vi 3 •j 4 ±i. ±{ 6 "vii 3 ľ 2 ±t ±1, *1, ^2 8 Allowed Transitions Mosley's Law (for multiple electron atoms) 1 A, = ciZ-ofil/n^ - l/n22) •Z = atomic number •a = shielding constant •n = quantum number Vi3(Ka) = V3/4R(Z-l) 3 4 5 5 7 S 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 25 27 28 29 30 31 32 Atomic Number Decreasing wavelength X with increasing Z Characteristic Wavelengths Element Ka2 Kal Kß K abs. edge Cu 1.54433 1.54051 1.39217 1.38102 1.380 Mo 0.713543 0.70926 0.62099 0.61977 Ag 0.563775 0.559363 0.49701 0.48701 0.4858 W 0.213813 0.208992 0.17950 0.17837 X-ray Absorption At the absorption edge, the incident X-ray quantum is energetic enough to knock an electron out of the orbital jLX = absorption coefficient Absorption edge x Monochromatisation of X-rays •Filters (Ni filter for Cu Ka) •Crystal Monochromators Sample Holders Capillary Transmission Reflection Detection of X-rays Detectors •convert energies of individual photons to electric current •convert current into voltage pulses that are counted •Film (in the linear range, Guinier, Debye-Scherrer, precession cameras) •Gas Proportional Counter •Si(Li) solid state detector (powder diffractometers) •Scintillation counter (photocathode, dynodes, 4-circle diffractometer, Stoe powder diffractometer) •Position Sensitive Detectors (ID or 2D, Stoe powder diffractometer) •Image Plate Detectors (2D detection, Stoe IPDS) •CCD Detectors (Bruker SMART system) Image plate detectors •Metal plate, 18 cm diameter, coated with Eu2+doped BaFBr •X-rays ionize Eu2+ to Eu3+ and the electrons are trapped in color centers •Read out process with red laser leads to emission of blue light, when electrons return to ground state •The blue light is amplified by a photomultiplier and recorded as a pixel image Detector properties •quantum-counting efficiency •linearity •energy proportionality •resolution Resolution 10000.0 9000.0 8000.0 70000 6000.0 5000.0 4000.0 3000.0 2000.0 1000.0 0.0 SOOO.O 4ÖOO.O 2MDÜ FWHM = 0.34 deg. FWHM =0.13 deg. 24.0 26 D •»a^^wwJ^jaAa-í^^XJ^. 5.0 25.0 45.0 65.0 85.0 X-ray Powder Diffraction William Bragg (1912) n.A, = 2 d sin 0 ^^ tncicf&nt J^ľi "N. p'ane wave —• • # 7*> • • 2d sin e Constructive interference d sin 6 when nX = 2d sin 0 Bragg's Law Laue method —► Single crystals Debye-Scherrer, diffractometers — poiycrystaiiine Different Geometries of Powder Diffractometers • Debye-Scherrer • Bragg-Brentano • Guinier Film Powder sample Debye-Scherrer v-:::;';.x:;::::-:■::■::::::::■■■:■■■ Debyegram práškového stříbra (A = 1,54 . 10 í0 m) Debye-Scherrer Bragg-Brentano Information Extracted from Diffraction Experiments • Determination of known phases • Crystallinity • Determination of lattice constants • Structure solution Crystalline and Amorphous Phases E nnfei QTrnroDn .-fcrvt.- tt-Vxrtt- Pp. Hi I HUM. TU* f Inj >i. u - ľj ■ h | h U.Ľ H iMif] s**—.L^^ X-ray powder diffraction pattern of Fe 3 PDF tt 060696,1.54056 06-0696 Quality. CAS Number: 7439-39-G Molecular Wetghl: 5585 Volume[CD|: 23.55 Dx: 7 375 Dm: S,G.: Irn3* (229) Cell Parameters a 2.866 b a_________ß SS/FOM: F 6=225(.GD44, S) UlcQt: Rad: CuKal Lambda: 1.5405 Filter: Ni d-sp:___________________ Mineral Name: Iron, syn J (110) Fe Iron Ref: Swanson et at Natl Bur Stand. [U.S.]. Circ. 533,4, 3 [1355) dA int h k I 2.0268 100 1 1 O 1.4332 20 2 O O dA int h k I 1.1702 30 1.0134 10 2 1 1 2 2 0 dA int h k I .90640 12 3 10 82750 6 2 2 2 xW^l o> ^ >- ^C^l v_ ■ I ■■ ■ ■ ■!■■■■■ !■ ' ■ ■ ■ ■ (200) J (211) . . ■ -...... i i i ■ i -.....--.... 50.000 x : atheta y : 30414. Linear FE-FRASEK MAGNET FIELD ss: 0.0200 tu: 105.000> 3.00 CoKal+2 Quantity More complicated, volume fraction 2G.GGG 25-1047 » HC TUNGSTEN/CARBIDE 15-G8G6 * Co COBALT patrh: 2theta y : 22487. Linear PRÁSEK - OSI (HC 18COÍ ss: 0.0250 tn: 15.GG CuKal+2 ioo.ooo> Quality d = A, / 2 sin 0 Line position is given by interplanar distance d and wavelenght X Anode Wavelength [nm] Beta filter Kai [100] Ka2 [50] Kßi Cr 0.228970 0.229361 0.208487 V Fe 0.193604 0.193998 0.175661 Mn Co 0.178897 0.179285 0.162079 Fe Cu 0.154056 0.154439 0.139222 Ni Mo 0.070930 0.071359 0.063229 Zr Selecting radiation d = X12 sin 0 . longer X ... better multiplet separation shorter X ... more lines Bcc crystal, Cu radiation a=1.5nm-->20= 11.8 a= 1.2nm-->20= 14.8 a = O.9nm-->20=19.7 a = O.6nm-->20 = 29.8 a = O.3nm-->20 = 61.8 < 20.00$ 27-0997 PflTRN: Z*»02 Z] „ J^-^ PRÁSEK G<40M1KRONU; CHROM PRÁSEK G<40MIKR0Nu:CHROM SS : 0,0200 tu: S . OO CifKal + 2 ss: O.D200 tn: 3.OO CuKal+2 l^.JL -*-——' k : 2 t lie t a y ftCONIUM OKI DE J JU 1G »24. Linear l 80.GGG> 35,100 Overline x : 2t>teta si : 8366. Linear 135.OO0> 27-0997 2p02 ZIRCONIUM OXIDE PňTRN: _ LINE HEIGHT - integral intensity - quantitative analysis - texture b> LINIE POSITION - qualitative (phase) analysis t lattice macrodistortions LINIE WIDTH - size of diffracting domains lattice microdistortions A exp (-x2/a2) A exp [l+fxVsL2)]-1 A exp [l+(x2/a2)]-2 A exp [l+(x2/a2)]-n A [cL(x) + (l-c)G(x)] a ŕ o PT-ELCDE-BACK NITH MIRE ss: 0.0250 tn: 2D.DO CuKal+2 (111) ??? (400) < 37.GGG 4-G8G2 * Pt PLATINUM, SVN PATRN: _ x : 21 lie t a y :117697. Linear 1G7.GGG> a ŕ d (111) PT-ELCDE:FRONT SIDE ÍfiFT. BOMB) ss: 0.0250 tn: 20.00 CuKal+2 (222) < 37.OOO PATRN: x : 2theta y : 34811. Linear 107.000> •i/ Zr02 + Y203 T------r PRÁSEK G<4GMIKRONU:CHROM ss: G.G2GG tn: S.GG CrKal+2 30.000 135.GGG> H He Li Be B C N 0 F Ne Na Mg Al si P S Cl Ar K Ca 3c JTi V Cr Mn Fe Co Ni Cu Sn Ga Ge As 3e Br Kr Rb S r Y Sr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba La Hi Ta W Re Os Ir Pt Au Hg TI Pb Bi Po At Rn Fr Ra Ac Ce Pr Nd Pm Srn Eu Gd Tb Dy Ho Er Tm Yb Lu Th Pa U Np Pu Am Cm Bk Cf Es Fm Hd No Lw Enter Eleme nt -> _ ííb'j ali'ú ÜJ pílila 30.000 x atlieta u 4000. Linear 135.000> 37-1413 I Zr02 ZIRCONIUM OXIDE Ě7-0997 Zr02 ZIRCONIUM OXIDE PATRH: Databases • ICSD (Karlsruhe, inorganics, single crystal data) • CSD (Cambridge, organics, organometallics, sc data) • NRCC CRYSTMET (metals) •PDB (proteins, Brookhaven) •MST (NBS) •JCPDS = ICDD (PDF files, 60000 patterns) Which of these is not involved in the diffraction of X-rays through a crystal? a Electron transitions b Crystallographic planes c Nuclear interactions d Constructive interference What is the largest wavelength of radiation that will be diffracted by a lattice plane of the interplanar spacing ď! a 0.5d b d c 2d d 86