Positron Annihilation techniques for material defect studies

Transcription

1 Positron Annihilation techniques for material defect studies H. Schut Section : Neutron and Positron Methods in Materials (NPM 2 ) Department: Radiation, Radionuclides and Reactors (R 3 ) Faculty of Applied Sciences November 26,

2 The positron Prediction by Dirac (1930) theory of relativity and quantum mechanics E = ± (p 2 c 2 + m o2 c 4 ) 1/2 Hole Theory these solutions are interpreted as electrons with negative energy November 26,

3 Positron discovery: the first pictures Picture of a positron in the cloud chamber (1932) Decreased curvature C.D. Anderson (23 MeV) Lead foil Begin of track (63 MeV) November 26,

4 More recent positron-electron tracks From: Phys. Edu 34(5) september 1995, G.T. Jones November 26,

5 Recent picture of a positron as iso-surface of the positron wave function Seitsonen, Puska and Nieminen (Helsinki University of Technology, 1995) Si Si vacancy + Sb neighboring atom Free positron Trapped positron November 26,

6 Positron annihilation history Prediction Ps discovery Ps (Deutch) s 70 s 80 s 90 s 2000 Electronic structure studies Bulk defect studies, polymers Development exp. techniques ACAR, Doppler, lifetime Near surface defects thin layers, interfaces, nano precipitates New applications New techniques (PEAS, AMOC,... Theory, QM calculations Fast e+ Isotopes (weak sources) Slow e+ beams Isotopes (strong sources) accelerators reactors November 26,

7 Positron annihilation (the Science Fiction approach ) Positron gun! The comic Barbarella Jean Claude Forest 1964 The movie Barbarella Jane Fonda; Roger Vadim 1968 Antimatter + Matter complete destruction November 26, More details

8 Characteristics of the positron as the anti-particle of the electron positron electron Rest Mass kg Charge C - Spin ½ lepton ½ Magnetic moment + g q/ 2m S - (g = ) Classic radius m Lifetime stable (in vacuum) stable t > 2 x year E = mc 2 rest mass = kev / c 2 ( 1 Joule= 1/ q ev) November 26,

9 Positron Annihilation Process of transforming mass into photons e + + e - gamma quanta (photons) General Conservation law s: energy linear momentum electric charge angular momentum most probable: tw o photon parity Hence the study of the annihilation quanta will give information about the state of the annihilation positron electron pair immediately before the transition! November 26,

10 Annihilation cross section for tw o photon annihilation in the low velocity limit (free particles) 2y = r o 2 c / v With r o the classical Borh radius of the electron (positron) ~10-15 m The other annihilation rates (1, 3 photons ) scale w ith the fine structure constant 4 and, respectively = e 2 / o = 1/ 137 November 26,

11 Case 1) zero momentum both particles at rest (in lab system) or observation in the center of mass system Before annihilation: After Annihilation Total energy E = E electron + E positron = 2 m o c 2 E y1 + E y2 (1) Total momentum p = 0 E y1 / c + E y2 / c (2) (as components of p vector) tw o photons emitted in opposite directions energy of each photon = m o c 2 = 511 kev November 26,

12 Case 2 : electron momentum p = p x Before annihilation: After Annihilation Total energy E = E electron + E positron = (m o2 c 4 + p x 2 c 2 ) 1/ 2 + m o c 2 = E y1 + E y2 (1) Total momentum p = p x = E y1 / c+ E y2 / c p y = p z = 0 = p y = p z (2) in case gamma s emitted in the direcion of p tw o photons emitted in opposite directions energy of the photons = m o c 2 ± c p x / 2 (doppler broadening) November 26,

13 General solution 1 2 = 2 pc sin( ) pc cos( ) + m c m c p c E = 1 mc mc pc pc cos( ) E = 2 mc mc pc pc cos( ) p 2 1 November 26,

14 Approximation: E = m o c 2 ± ½ p c kev y-y = - p / m c radians Some values : Energy of electrons (in solids) 10 ev ½ p c = 1.5 x 10 3 ev (compare to 511 x 10 3 ev) p of the order of 1x m kg/ s p / mc = 3 mrad ( 3 mm at 1 m ) November 26,

15 The effect of conservation of momentum and energy 2 e + + e - annihilation process : before e - e + p = 0 CM frame after E m o c o E m o c 2 = 511 kev x conservation of energy and momentum lab frame z e - e + before p p y after E m o c 2-1/2 c p 180 o - p / m o c E m o c 2 + 1/2 c p Doppler broadening 2D - ACAR November 26,

16 counts spectrum HOR spectrum HOR counts gamma energy (kev) gamma energy (kev) Electron momentum broadens the 511 kev line peak width 2.5 FWHM (kev gamma energy (kev) November 26,

17 Positronium: An electron - positron bound state e + Ps atom e - H atom physical property Ps atom atomic mass (amu) reduced mass ½ 1 a 0 (radius) size 2 a 0 (diameter) ev ionization energy ev J =0 (para) spin states S = 0 (para) J=1 (ortho) S = 1 (ortho) life time 125 ps ( 125 x s, para) 142 ns (142 x 10-9 s, ortho) November 26, a 0 = Bohr radius = A

18 Positronium annihilation modes: Para Ps self annihilates by two-gamma emission (125 ps) Ortho Ps self annihilates by three-gamma emission (142 ns) or in media: o- Ps ( ) + e - () p-ps () + e - () (spin exchange) o- Ps ( ) + e - () 2 gamma s + e - () (pick off) Para -Ps has zero internal momentum therefore Ey ~ 511 kev (only translational momentum of the atom) November 26,

19 Positron sources Isotopes nuclear reactions neutron absorption Pair production Electron accelerators Fission reactors neutron gamma conversion prompt gammas November 26,

20 Examples of positron emitters Isotope half life % e+ production application 11 C 20 min B(p,n) 11 C medical diagnostics (PET) 10 B(d,n) 11 C 14 N(p, ) 11 C 13 N 10 min C(d,n) 13 N 16 O(p, ) 13 N 15 O 2 min N(d,n) 15 O 18 F 110 min O(p,n) 18 F 22 Na 2.6 y Mg(d,) 22 Na PA accelerators 58 Co 71.3 d Ni(n,p) 58 Co nucl reactors 64 Cu 12.9 h Cu(n,y) 64 Cu nucl reactors November 26,

21 22Na 22 Na decay scheme 22Na %, EC 9.5% MeV 3.7 ps + (0.1% ) 0 22Ne + end point energy 540 kev half life year November 26,

22 Positron kinetic energy distribution 22 Na 22 Ne + e + + e (1274 kev 22 Ne * ) HOR gamma flux distribution Pair production: positron kinetic energy depends on the initial energy of the photon (Bremsstrahlung or prompt fission gamma energy MeV) Photon energy (MeV) November 26,

23 Positron - solid interaction First encounter Fast positrons entering a solid loose their kinetic energy by different ineleastic energy loss mechanisms Timescale < seconds Vacuum Solid scattering e + core exitations Secundary electron November 26,

24 Positron - solid interaction Thermalisation Timescale < seconds e + Vacuum Solid Plasmons Electron-hole pairs phonons Fast Ps Fast e + Non thermal e + November 26,

25 Positron - solid interaction equilibrium Timescale < seconds Vacuum Solid Diffusion and trapping annihilation e + Energetic Ps thermal e + Slow e + Surface trapping November 26,

26 Positron implantation profile Fast positrons ( + energy distribution) No depth resolution Implantation depth range Element density a + r (99%) [g/cm 3 ] [cm -1 ] [m] Al C Li I(x) = I(0) exp (-a + x) a + = (16±1) E m (cm 1 ) (E in MeV) Mo Si W November 26,

27 Positron implantation profile Slow positrons Mono energetic beams (~ kev) w ith m = 2 Si x o = 1.3 <x> <x> = ( / ) E n n = , ~ 4.0 P(x,E) 2 kev 5 kev 10 kev 20 kev X (nm) November 26,

28 Positron w orkfunction diffusion Implantation and stopping Beam or source annihilation Positron w ork function + vacuum solid + < 0 spontanous emission from the solid into vacuum (W, Mo, Ni, SiC,...) November 26,

29 Positron trapping diffusion Implantation and stopping Beam or source Trapping + annihilation Positron w ork function + vacuum solid E B = 1 3 ev (vacancies in metals) The attractive potential w ell (a defect) results in a confinement of the positron (collapse of the w ave function ) November 26, Trapping rate ( t ) of the order of s -1

30 Probing Local electron density w ith positrons 22 Na 1274 kev + 22 Ne 22 Na Decay (START) Annihilation (STOP) November 26,

31 Observables (1) Doppler broadening S(hape) and W (ing) detecting one 511 kev gamma and determing the width of the photo peak counts gamma energy (kev) Low momentum Valence, conduction electrons P(ara) Positronium Open volume (vacancies, voids...) S parameter W parameter High momentum Core electrons Local chemical surroundnig Nano precipitates, sub-latice defects November 26,

32 Doppler broadening setup The Variable Energy Positron beam (VEP) 22 Na source sample chamber Coincidence setup (2 detectors) November 26,

33 Some examples (beam exp t)? Model? S parameter micron depth positron energy (kev) depth November 26,

34 1 x H + cm mean implantation depth (nm) o C cavities H implantation (1x10 16 cm -2 ) 800 o C anneal 350 o C anneal S o C 1.00 Si cavity layer 0.95 Si Si e + beam nm positron implantation energy (kev) H + implantation Cavities Virgin Si November 26,

35 Observables (2) Angular Correlation measument of the angle between the two 511 kev gammas NaI detector Photomultipliers Fast e + ( 22 Na) NaI detector p x p y sample 4 x 10 8 e + /s Intense Low-energy Positron Beam POSH November 26,

36 The Delft POSH 2D-ACAR setup Anger cameras source ( 22 Na) chamber POSH e + beam line Accelerator Target chamber November 26,

37 Example of 1 D ACAR Measurement of the Fermi level of electrons in Al k z free electron gas model k f k y Highest energy level occupied E f Maximum momentum p f = ( 2 m E f ) 1/ 2 Maximum angle angular correlation ( f ) k x Uniform k- distribution show November 26,

38 Example of a 2D ACAR application Li nanoclusters are FCC and in simple epitaxy with the MgO host matrix. Li nano cluster e + MgO matrix Depth November 26,

39 Li nanoclusters are FCC and in simple epitaxy with the MgO host matrix. MgO(100):Li POSH (4 kev) MgO(100) fast e + ( 22 Na) MgO(100):Li nanocrystals Mg Li Li Mg Mg Mg O Mg [010] [100] [001] Mg O Li Li [010] [100] [001] Li O Mg [010] [100] [001] Mg O Mg Mg O O Li Li Mg Mg MgO(100) November 26, In MgO Li nano clusters have FCC structure!

40 X W Typical FS surface of an fcc alkali like metal L K Projection on p x -p y plane November 26,

41 Observables (3) positron lifetime (PALS) measurement of the time elapsed between positron injection and annihilation start 22 Na stop resolution 260 ps HV CFD CFD TAC ADC PC MCA November 26,

42 Counts 1e+6 1e+5 1e+4 1e+3 1e+2 1e+1 1e+0 Typical PALS spectra D( t) k 1 i1 I i t exp( ) i Positron Lifetimes in dense solids (metals and semiconductors) e + + e - 2 Tungsten (100 ps) Silicon (220 ps) Positron lifetimes in polymer 1e-1 1e-2 ortho - Ps formation (140 ns) 1e-3 1e Channel (t) PolyEthyleen (PE) (2-3 ns) November 26,

43 Calculated positron lifetimes in vacancy clusters ( r 0 ne ) 2 o cn vacancy e Lifetime (psec) Cu Radius (nm) Jensen et al. (1987) Tang (2003) Number of Vacancies Vacancy cluster November 26,

44 Positron lifetimes in polymers Semi empirical relation betw een volume size (R) and o-ps decay rate Usually the third long lifetime component sin(2 / 0) Ro 2 R 1 R R 1 2 R Spherical potental w ell 2 R o R = nm November 26,

45 Annealing of Fe deformed at low temperature D( t) k 1 i1 I i exp( t i ) Vacancies migrate and cluster above ~200 K November 26, Vehanen et al. (1982)

46 sensitivity range for measuring defect concentration (Al and Mo) at.fr. November 26,

47 examples of systems studied with positrons Vacancies nano precipitates interfaces polymers (free volume) Voids nano precipitates surfaces nano-colloids internally decorated voids dislocations Metals, Alloys Semiconductors (Si, GaAs,... Polymers Colloids, Ceramics, Metaloxides... November 26,