Positron theoretical prediction

Positron theoretical prediction Schrödinger equation: ˆ 2 p x, t Vx, t x, t i 22 m tt non-relativistic equation of motion for electron Erwin Schrödinger 1933 Nobel prize

Positron theoretical prediction 2 x, t ˆ i tt Dirac equation: αpc mc x, t relativistic equation of motion for electron solutions with positive energy: normal electrons Paul Adrien Maurice Dirac 1933 Nobel prize P.A.M. Dirac, Proc. R. Soc. Lond. A 117, 610-624624 (1928) P.A.M. Dirac, Proc. R. Soc. Lond. A 133, 60-72 (1931)

Positron theoretical prediction 2 x, t ˆ i tt Dirac equation: αpc mc x, t relativistic equation of motion for electron solutions with positive energy: normal electrons solutions with negative energy energy of a free particle E 1 mv 2 2 2 p 2m (classical) Paul Adrien Maurice Dirac 1933 Nobel prize P.A.M. Dirac, Proc. R. Soc. Lond. A 117, 610-624624 (1928) P.A.M. Dirac, Proc. R. Soc. Lond. A 133, 60-72 (1931)

Positron theoretical prediction 2 x, t ˆ i tt Dirac equation: αpc mc x, t relativistic equation of motion for electron solutions with positive energy: normal electrons solutions with negative energy relativistic energy E 2 m 2 c 4 p 2 c 2 E m 2 c 4 p 2 c 2 Paul Adrien Maurice Dirac 1933 Nobel prize P.A.M. Dirac, Proc. R. Soc. Lond. A 117, 610-624624 (1928) P.A.M. Dirac, Proc. R. Soc. Lond. A 133, 60-72 (1931)

Positron theoretical prediction 2 x, t ˆ i tt Dirac equation: αpc mc x, t relativistic equation of motion for electron solutions with positive energy: normal electrons vacuum is a see of electrons with negative energy E > 0 mc 2 E = 0 -mc 2 E < 0 ray Paul Adrien Maurice Dirac 1933 Nobel prize P.A.M. Dirac, Proc. R. Soc. Lond. A 117, 610-624624 (1928) P.A.M. Dirac, Proc. R. Soc. Lond. A 133, 60-72 (1931)

Positron theoretical prediction 2 x, t ˆ i tt Dirac equation: αpc mc x, t relativistic equation of motion for electron solutions with positive energy: normal electrons vacuum is a see of electrons with negative energy positron is a hole in vacuum E > 0 mc 2 E = 0 -mc 2 E < 0 + electron Paul Adrien Maurice Dirac 1933 Nobel prize pair production positron P.A.M. Dirac, Proc. R. Soc. Lond. A 117, 610-624624 (1928) P.A.M. Dirac, Proc. R. Soc. Lond. A 133, 60-72 (1931)

Positron theoretical prediction 2 x, t ˆ i tt Dirac equation: αpc mc x, t relativistic equation of motion for electron solutions with positive energy: normal electrons vacuum is a see of electrons with negative energy positron is a hole in vacuum E > 0 mc 2 E = 0 -mc 2 + E < 0 ray ray anihilation Paul Adrien Maurice Dirac 1933 Nobel prize P.A.M. Dirac, Proc. R. Soc. Lond. A 117, 610-624624 (1928) P.A.M. Dirac, Proc. R. Soc. Lond. A 133, 60-72 (1931)

Discovery of positron discovery of positron 1932 Lorentz force F ev B B e + 23 MeV 6 mm Pb foil e + 63 MeV Carl David Anderson 1936 Nobel prize

Discovery of positron discovery of positron 1932 B = 1.7 T P = 425 kw m >3 t

Positron positron positron = antiparticle of electron rest mass: m e charge: +e spin: 1/2

Positron sources Cosmic rays 90 % protons 9 % -particles 1 % heavier nuclei & other particles (e -, e +, p - ) interaction with atmosphere p + NO N,

Positron sources Cosmic rays 90 % protons 9 % -particles 1 % heavier nuclei & other particles (e -, e +, p - ) interaction with atmosphere p + NO N,

Positron sources Cosmic rays 90 % protons 9 % -particles 1 % heavier nuclei & other particles (e -, e +, p - ) interaction with atmosphere p + NO N, e e e e

Positron sources Cosmic rays 90 % protons 9 % -particles 1 % heavier nuclei & other particles (e -, e +, p - ) interaction with atmosphere p + NO N, e e e e

Positron sources Cosmic rays 90 % protons 9 % -particles 1 % heavier nuclei & other particles (e -, e +, p - ) interaction with atmosphere p + NO N, e e e e

Positron sources Cosmic rays 90 % protons 9 % -particles 1 % heavier nuclei & other particles (e -, e +, p - ) interaction with atmosphere p + NO N, e e e e e e

Positron sources - decay - decay: e A Z A Z e X X ' 1 e e p n e u d e e Ba Cs 137 56 137 55 + decay: e A Z A Z e X X ' 1 e e u d e e n p N 22 N 22 e e Ne Na 22 10 22 11

Positron sources - decay - decay: A Z 137 55 X n Cs p A Z 1 137 56 X' e e e Bae e e + decay: A Z X p A Z 1 ne X' e e e Na 22 Nee 22 22 11 10 e

Interaction of e + with solid 0.035 Positron implantation profile 0.030 0.025 Mg Cu E ~ 250 kev 0.020 p 0.015 1274 kev 0.010 0.005 0.000 0 100 200 300 400 500 depth (m) + mean Free positron lifetimes penetration depth Mg Cu 154 114 m ps Al Nb 126 99 m ps Cu Al 163 30 m ps Nb Mg 233 31 m ps Thermalization 22 22 t < 1110 Na ps 10Ne e l ~ 50 m E kt (0.03 03 ev) 1/2 = 3.7 ps 22 10 Ne Difusion t Na ~ 100 ps l ~ 100 nm 22 11 T 1/2 = 2.6 year 90.4 %, EC 9.5 % 1274 kev 0.06 % + - 511 kev 511 kev Anihilation start signal

Positron lifetime N(t) - probability that e + is alive at time t : dn( t) N ( t) N ( 0) 1 dt positron annihilation rate: r 0 c n ( r) n ( r) dr N ( t) e t positron lifetime spectrum: - d N ( t ) dt e t mean time of positron life: dn( t) dt t d t 0 free positron lifetime: t t t 1 1 t te dt te 0 e dt 0 0 e 0 t 1

Positron lifetime spectrum positron lifetime spectrum: S id - dn ( t ) t e t 0.010 0.008 Cu 114 ps Mg 233 ps intensity 0.006 0.004004 0.002 0.000 0 200 400 600 800 1000 1200 1400 time (ps)

Positron lifetime spectrum positron lifetime spectrum: S id - dn ( t) t e t 1e-2 Cu 114 ps Mg 233 ps 1e-3 slope: 1 inten nsity 1e-4 1e-5 1e-6 0 200 400 600 800 1000 1200 1400 background time (ps) real positron lifetime spectrum: S real ( t) S id ( t ) R( )d B resolution function of spectrometer

Positron trapping Cu: fcc lifetime B = 114 ps 2.0 (001) plane 10] [0 1.5 1e-5 2e-5 3e-5 4e-5 5e-5 6e-5 7e-5 8e-5 (001) plane y (a) 1.0 1e-4 8e-5 0.5 n + (a.u.) 6e-5 4e-5 2.0 0.0 0.0 0.5 1.0 1.5 2.0 x (a) [100] 2e-5 0 2.0 1.5 [010] 1.0 y (a) 0.5 0.0 0.0 0.5 1.0 1.5 x (a) [100]

Positron trapping Cu: fcc vacancy in [1/2,1/2,0] position lifetime 1v = 180 ps 2.0 (001) plane [010 0] 1.5 2e-3 4e-3 6e-3 8e-3 1e-2 (001) plane y (a) 1.0 0.014 0.012 0.010 0.5 n + (a.u.) 0.008 0.006 2.0 0.0 0.0 0.5 1.0 1.5 2.0 x (a) [100] 0.004 0.002 0.000 20 2.0 1.5 [010] 1.0 y (a) 0.5 0.0 0.0 0.5 1.0 1.5 x (a) [100]

Positron lifetime spectrum 1e+6 Intensity 1e+5 1e+4 Cu: c 1v = 2.7 10-3 at% 1 = 84 ps I 1 = 48% 2 = 180 ps I 2 = 62% 1e+3 1e+2-2000 -1000 0 1000 2000 3000 4000 5000 6000 t (ps) decomposition of PL spectrum: lifetimes i type of defects present intensities I i defect densities

Simple positron trapping model: Cu with vacancies E free positron N f ( t ) f thermalization annihilation rate B = 1/ B binding energy ~ 1 ev trapping rate K 1V K 1v 1v c trapped positron N 1v ( t) 1v annihilation rate 1v = 1/ 1v Cu vacancy: 1v annihilation B = 114 ps 1.4 10 14 s -1 at. 1v = 180 ps two-component spectrum: 1 K 1 I 1 1 I 2 B 1v 2 S 1 K1v I2 K 1v B 1v id 1 I 1 1 e t 1 1 free positrons 1v 2 I 2 e t 2 positrons trapped at vacancies

Positronium hydrogen-like bound state of positron and electron parapositronium p-ps 1 S 0, singlet state, antiparallel spins, lifetime p-ps = 125 ps, 2- orthopositronium o-ps 3 S 1, triplet state, parallel spins, lifetime o-ps = 142 ns, 3- formed in large open volumes: e.g. in polymers in solids pick-off annihilation of o-ps o-ps reduced to several ns polycarbonate iron

Positron lifetime spectrometer 511 kev STOP detector START detector 511 kev 1274 kev Detector photomultiplier p BaF 2 scintillator

Positron lifetime spectrometer 511 kev STOP detector START detector 511 kev 1274 kev Detector BaF 2 scintillator Fast component: 1 = 220 nm, = 0.6 ns Slow component: 2 = 310 nm, = 630 ns

Positron lifetime spectrometer 511 kev STOP detector START detector 511 kev 1274 kev Detector Linearly focused PMT

Positron lifetime spectrometer 511 kev STOP detector START detector 511 kev 1274 kev CFD constant-fraction discrimination inversion+attenuation crossover CFD delay sum amplitude selection lower level upper level

Positron lifetime spectrometer STOP detector 511 kev START detector 511 kev 1274 kev CFD CFD START STOP delay STOP TAC START ADC PC

Positron lifetime spectrometer detectors t fast-fast PL spectrometer timing resolution 160 ps (FWHM 22 Na) coincidence count rate 100 s -1 10 7 counts in spectrum F. Bečvář et al., Nucl. Instr. Meth. A 443, 557 (2000) source-sample sandwich

Hydrogen in Niobium Nb: bcc structure t a = 3.3033(1) 3033(1) Å [PDF-2] H in Nb interstitial solid solution size (r Nb ): 0.155 0.291 N i /cell 6 12 N i /M 3 6 H 0.35 035 x H = N H /M number of hydrogen atoms per metal atoms

Hydrogen in Niobium Equilibrium phase diagram of Nb-H system two-phase field ( + ) x H = 0-0.06 (atom ratio H/Nb): single phase solid solution (-phase), bcc H fills tetrahedral interstitial positions

Hydrogen in Niobium Equilibrium phase diagram of Nb-H system two-phase field ( + ) -phase (NbH) orthorhombic a = 4.859 Å b = 4.878 Å c = 3.453 Å c z y x x H = 0-0.06 (atom ratio H/Nb): single phase solid solution (-phase), bcc H fills tetrahedral interstitial positions b a

Samples defect-free Nb - bulk Nb (99.9%) - annealing 1000 o C / 1h to anneal out all existing defects electron irradiated Nb - bulk Nb (99.9%) 9%) - annealing 1000 o C / 1h to anneal out all existing defects - 10 MeV electron irradiation, F = 2 10 21 m -2, T irr 100 o C all samples: Pd cap (thickness 30 nm) prevent oxidation facilitate H absorption R. Kircheim et al., Acta Metall. 30, 1059 (1982)

Hydrogen loading Electrochemical H loading R. Kircheim, Prog. Mat. Sci. 32 (1988), p. 261 hydrogen concentration ti Faraday s law i = 0.3 ma/cm 2 V impedance changer timer + current source + Ag/AgCl electrode - Evolution of defects was studied as a function of gradually increased hydrogen concentration in sample. Pt electrolyte: sample H 3 PO 4 (85%) + glycerin (85%) 1 : 2

H-induced lattice expansion: X-ray diffraction relative lattice expansion: a a 0 x a 0 H a 0 a lattice constant for virgin sample lattice constant t for hydrogen-loaded d d sample for Nb : 0.058 H. Peisl, in:. Hydrogen in Metals I, Springer-Verlag, g, Berlin (1978), p. 53 0.0022 0.0020 0.00180018 0.0016 0.0014 a / a 0 0.0012 0.0010 0.0008 = 0.058(1) 0.0006 0.0004 0.0002 0.0000-0.0002 0.00 0.01 0.02 0.03 0.04 0.05 x H

Hydrogen-induced vacancies well annealed Nb (1000 o C / 1h): single component PL spectrum 1 = (128.3 0.4) ps calculated l dbulk lknblif lifetime (ATSUP): B = (126 1) ps defect-free material TEM no dislocations observed, grain size > 10 m

Hydrogen-induced vacancies well annealed Nb (1000 o C / 1h) hydrogen loading hydrogen induced defects 2 = (150 0.5) ps hydrogen-induced volume expansion elastic process dislocations calculated lifetime for Nb vacancy (ATSUP): V = (222 1) ps vacancies surrounded by hydrogen shortening of positron lifetime 160 80 140 2 60 lifetime (ps s) 120 100 I 2 (%) 40 80 1 20 60 0.00 0.01 0.02 0.03 0.04 0.05 0 0.00 0.01 0.02 0.03 0.04 0.05 x H x H

1e+0 e+71e+ 1e+0 Hydrogen-induced vacancies Effective medium theory J. Nørskov, Phys. Rev. B 26, 2875 (1982) 2.00 1.75 E hom (r) in (001) plane vacancy in 1,1,0 1e+6 1e+7 1e+8 1e+5 1e+5 1e+4 1e+4 1e+3 1e+6 1e+7 1e+8 1e+3 1e+4 1e+5 1e+6 1e+3 1e+2 1e+2 1e+1 1e+2 1e+1 10 1e+1 1 1e+0 1e+0 n 1.50 0.1 1e-1 1e-1 1.25 0.01 +31e+1e+6+8 1e +4 1e+1 1e+0 100 1.00 0.75 e+51e1e+6 175 1.75 1.50 1.25 [010] 1e +2 1e+0 +2 +1 1e 1e-1 1e 1e 1e+3 1e+4 1e+ e+5 1e+ e+6 1e-1 1e-1 0.50 1.00 [010] 1e+0 1e+1 0.25 1e+2 1e+1 1e+2 1e+0 1e+5 1e+4 1e+3 1e+3 1e+4 1e+1 1e+5 1e+6 1e+2 1e+6 1e+3 0.00 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 0.75 0.50 175 200 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 [100] 1e+4 [100] 0.25 0.00 H positions: [0.64,1,0],, [1,0.64,0],, [1,1,0.36], [1.36,1,0], [1,1.36,0], [1,1,-0.36]

1e+0 Hydrogen-induced vacancies Effective medium theory Stott, Zaremba, Nørskov, Lang 1980 1e+6 1e+7 1e+8 2.00 1e+5 1e+5 1e+4 1e+4 1e+3 1e+6 1e+7 1e+8 1e+3 1e+4 1e+6 1e+5 1e+3 1e+2 1e+2 1e+1 1.75 1e+2 1e+1 Nb 1e+1 1e+0 1e+0 1.50 1e-1 1e-1 1.25 1e+6+8 +4 1e+3 1e 1e+1 1e+0 100 1.00 0.75 e+51e1e+6 octahedral position [0,1,0.5] H e+71e+ [010] 1e +2 1e+0 +2 +1 1e 1e-1 1e 1e 1e+3 1e+4 1e+ e+5 1e+ e+6 1e-1 1e-1 0.50 0.25 0.00 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 [0.64,1,0], 1e+0 1e+0 1e+1 1e+2 1e+1 1e+2 1e+0 1e+5 1e+6 1e+4 1e+3 1e+3 1e+4 1e+1 1e+5 1e+2 1e+6 1e+3 1e+4 [100] H positions: [0.64,1,0],, [1,0.64,0],, [1,1,0.36], [1.36,1,0], [1,1.36,0], [1,1,-0.36] displacement = 0.46(7) Å

ATSUP calculations Nb vacancy in [1,1,0] and H in [0.64,1,0] electron density in (001) plane positron density in (001) plane n 1.75 0.016 0.014 1.50 0.012 0.010 2.00 100 10 1 1.25 0.008 0006 0.006 [010] 0.1 1000 10 1 01 0.1 0.01 0.1 1000 10 1 0.004 1.00 100 10 1 0.1 0.1 0.1 1 101000100 0.002 0.000 0.75 2.00 0.01 1.75 0.50 1.50 2.00 1.25 1.75 1.00 0.1 1.50 0.25 0.1 1.25 0.1 0.75 1 1.00 1 1 10 0.50 10 10100 100 0.75 0.00 050 0.50 0.00 0.25 0.50 0.25 0.75 1.00 1.25 1.50 1.75 2.00 0.25 0.00 0.00 [100] [010] [100] [010] 2.00 1.75 1.50 0.002 1.25 1.00 0.75 0.50 0.25 0.006 0.008 0.004 0.0040.010 0.012 0.002 0.004 0.008 0.006 0.002 000 0.00 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 [100] positron lifetime v-h = 204(1) ps

ATSUP calculations complexes (vacancy H) 2.00 1.75 vacancy + 2H 2.00 1.75 vacancy + 3H 1.50 1.25 0.002 0.006 0.008 0.004 1.50 1.25 0.004 0.006 0.002 0.008 [010] 1.00 0.010 0.012 0.008 0.004004 [010] 1.00 0.002 0.012 0.010 0.008 0.0060.002 0.75 0.0020.004 0.006 0.002 0.75 0.004 0.50 0.50 0.25 = 182(1) ps 0.00 000 0.00 025 0.25 050 0.50 075 0.75 100 1.00 125 1.25 150 1.50 175 1.75 200 2.00 [100] 0.25 = 169(1) ps 0.00 000 0.00 025 0.25 050 0.50 075 0.75 100 1.00 125 1.25 150 1.50 175 1.75 200 2.00 [100]

ATSUP calculations complexes (vacancy H) 2.00 1.75 vacancy + 4H 2.00 1.75 vacancy + 5H 1.50 1.25 1.50 0.002 0.004 1.25 0.001 0.001 0.003 0.002 0.004 0.001 [010] 1.00 0.75 050 0.50 0.002 0.008 0.006 0.004 0.002 [010] 1.00 0.001 0.001 0.001 0.007 0.006 0.004 0.002 0.005 0.75 050 0.50 0.002 0.001 0.001 0.003 0.25 = 151(1) ps 0.00 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 [100] 0.25 = 142(1) ps 0.00 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 [100]

ATSUP calculations complexes (vacancy H) 2.00 vacancy + 6H 175 1.75 1.50 0.0005 0.0025 0.0005 0.0020 1.25 0.0005 0.0010 0.0015 0.0015 [010] 1.00 0.0005 0.0020 0.0005 0.0015 0.0010 0.0005 n 0.0010 0.0005 0.75 050 0.50 0.25 0.0010 0.0005 0.0005 0.00 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 [100] 0.0000 2.00 1.75 150 1.50 1.25 1.00 [010] 0.75 0.50 0.25 000 0.00 0.50 0.25 000 0.00 2.00 1.75 1.50 1.25 1.00 0.75 [100] = 127(1) ps

Hydrogen-induced vacancies calculated positron lifetime for vacancy is surrounded by several H atoms 240 220 200 v-nh (ps) 180 experiment 150 ps 160 140 Nb bulk 120 0 1 2 3 4 5 6 number of H Hydrogen loading creation of vacancies surrounded for 4 hydrogen atoms

Hydrogen-induced vacancies well annealed Nb (1000 o C / 1h) hydrogen loading hydrogen induced defects 2 = (150 0.5) ps hydrogen-induced volume expansion elastic process dislocations calculated lifetime for Nb vacancy (ATSUP): V = (222 1) ps vacancies surrounded by hydrogen shortening of positron lifetime c v 3 10-3 at.% T 1850 o C (0.8 Tm) 160 80 4.0x10-3 140 2 60 3.0x10-3 lifetime (ps s) 120 100 I 2 (%) 40 2.0x10-3 C v-4h (at.% %) 80 1 20 1.0x10-3 60 0.00 0.01 0.02 0.03 0.04 0.05 0 0.0 0.00 0.01 0.02 0.03 0.04 0.05 x H x H

H-induced defects bulk Nb mechanism of formation effective medium theory: H v E b 0.50 ev vacancy formation energy: E f 2.32 ev P. Korzhavyi et al. PRB 59, 11693 (1999) vacancy 4H: H v E f 4E b 0.32 ev equilibrium concentration of vacancy 4H complexes: c p e S / k k e E f 4E H v b / kt 4.0x10-3 experiment 3.0x10-3 4 H in nearest neighbor positions required p at.% 4 99 ~ c H c 710.%) C v-4h (at. 20x10 2.0x10-3 theory 4 H in active volume V 0 3 V0 2.9 nm 80 unit cells of Nb 1.0x10-3 0.0 J. Čížek et al. PRB 69, 224106 (2004) 0.00 0.01 0.02 0.03 0.04 0.05 x H

Hydrogen-induced vacancies 2 = 150 ps Loading unloading experiment 60 60 loading: constant current 0.3 ma unloading: constant t voltage 0.8 V I 2 (%) 50 40 30 50 40 30 20 20 PL intensity of trapped positrons 10 loading unloading 10 0 0.000 0.005 0.010 0.015 0.020 0 0 50 100 150 200 250 x H unloading time (h) 3.307 3.306 loading unloading 3.307 3.306 3.305 3.305 (10-10 m) a ( 3.304 3.303 3.304 3303 3.303 3.302 3.302 XRD lattice constant 3.301 Nb PDF2 3.301 3.300 0.000 0.005 0.010 0.015 0.020 x H 3.300 0 50 100 150 200 250 unloading time (h)

Electron irradiated bulk Nb sample 1 bare Nb electron irradiated (10 MeV e -, F = 2 10 21 m -2, T irr 100 o C) Pd cap sputtered after irradiation sample 2 Nb with Pd cap electron irradiated (10 MeV e -, F = 2 10 21 m -2, T irr 100 o C) Sample 1 (ps) I 1 (%) 2 (ps) I 2 (%) bare Nb 47 6 15 1 190.6 0.5 85 1 electron eecto irradiated adated. + Pd cap 47 9 15 2 190.0 0.8 85 2 Nb electron irradiated 57 7 17.0 08 0.8 185.88 08 0.8 83.0 08 0.8 with Pd cap vacancy-h complexes mixture of v-h ( v-h = 204 ps) and v-2h ( v-2h = 182 ps) complexes

Electron irradiated bulk Nb 3-component fit Sample 1 (ps) I 1 (%) 2 (ps) I 2 (%) 3 (ps) I 3 (%) bare Nb 43 8 14 2 182 Fix 61 2 204 Fix 25 3 electron irradiated. + Pd cap 44 9 14 2 182 Fix 57 2 204 Fix 29 4 Nb electron irradiated with Pd cap 48 5 15 2 182 Fix 74 1 204 Fix 11 3 v-2h complexes v-h complexes

Electron irradiated bulk Nb 14 application of 3-state trapping model (trapping coefficient: = 1 10 14 at. s -1 ) 12 concentration n (10-5 at. -1 ) 10 8 6 4 bare Nb irradiated Pd cap sputtered subsequently on the irradiated Nb Nb irradiated with Pd cap catalytic ti effect of Pd cap v-h transforms into v-2h 2 v-2h v-h 0

Doppler Broadening annihilation 1 2 E mec E 1 cp e - e + E L 2 annihilation peak 207 Bi 10000 10000 2 2 E mec E 2 counts 1000 100 1000 counts 100 10 10 FWHM = 2.580(3) kev 1 490 500 510 520 530 E (kev) FWHM = 1.103(1) kev 1 550 560 570 580 590 E (kev)

Coincidence Doppler Broadening spectroscopy (CDB) 2 E mec E 1 E e cp L 2 p T HPGe detector t p p L 2 - + 1 HPGe detector CFD CFD Coincidence gate spectroscopy amplifier E 1 E 2 spectroscopy ADC amplifier

Coincidence Doppler Broadening spectroscopy (CDB) reference Fe 30 1e+0 1e+1 1e+2 1e+3 1e+4 1e+5 E1+E E2-2 x 512 ((kev) 20 10 0-10 -20-30 -30-20 -10 0 E1- E2 (kev) 10 20 30

Coincidence Doppler Broadening spectroscopy (CDB) 1e+7 reference Fe 1e+6 1e+5 resolution function annihilation peak counts 1e+4 1e+3 1e+2 1e+1 1e+0-30 -20-10 0 10 20 30 E 1 -E 2 (kev)

Coincidence Doppler Broadening spectroscopy (CDB) CDB ratio curves 2.0 1.8 1.6 Cu 1.4 ratio to Fe 1.2 1.0 0.8 0.6 0.4 Al 0.2 0.0 0 10 20 30 40 50 p (10-3 m 0 c) element sensitivity

Coincidence Doppler Broadening spectroscopy (CDB) Chemical environment of defects CDB measurements two HPGe detectors energy resolution 1.05 kev (FWHM, E = 512 kev) coincidence count rate 550 s -1 10 8 counts in spectrum J. Čížek et al., Mat. Sci. Forum. 445-446, 63 (2004)

Vacancy-H complexes calculated HMP s annihilation with core electrons 2.0 15 1.5 effect of hydrogen 1s electrons to Nb ratio 10 1.0 0.5 Nb vacancy Nb vacancy+h Nb vacancy+2h Nb vacancy+3h Nb vacancy+4h Nb vacancy+5h Nb vacancy+6h 0.0 0 10 20 30 40 50 p (10-3 m 0 c)

Electron irradiated Nb experimental high momentum profiles effect of hydrogen 1s H electrons bare Nb irradiated 1.2 1.1 1.0 ratio to Nb 0.9 0.8 0.7 06 0.6 0 10 20 30 40 50 p (10-3 m 0 c)

Electron irradiated Nb experimental high momentum profiles bare Nb irradiated effect of hydrogen 1s H electrons Nb iradiated with Pd cap 1.2 1.1 1.0 ratio to Nb 0.9 0.8 0.7 06 0.6 0 10 20 30 40 50-3 p (10 m 0 c)

Electron irradiated Nb experimental high momentum profiles bare Nb irradiated effect of hydrogen 1s H electrons Nb iradiated with Pd cap hydrogen loaded Nb 1.2 1.1 1.0 ratio to Nb 0.9 0.8 0.7 06 0.6 0 10 20 30 40 50 p (10-3 m 0 c)

Other gas impurities calculated HMP s 2.0 1.5 Nb vacancy Nb vacancy - Oxygen in center Nb vacancy - Nitrogen in center ratio to Nb 1.0 0.5 0.0 0 10 20 30 40 50 p( (10-3 m 0 c)