Abstract
The study of defects in crystals through their interaction with thermalized positrons is usually based on the trapping model. The theoretical foundation of the trapping model, based on the theory of diffusion-limited reactions, is reviewed with particular emphasis on short-range interactions between positrons and trapping defects. For this case the analytical properties of the trapping model are developed in some detail, including the effects of the initial pair distribution on the trapping rate, the effects of detrapping, and the effects associated with more than one type of trap. The assumptions that are usually made in determinations of monovacancy formation enthalpies from positron annihilation experiments are critically discussed. The need for additional experiments capable of providing information on the temperature dependence of the various parameters involved is, stressed. As an illustration we treat in detail monovacancies with finite detrapping rate plus divacancies, both in thermal equilibrium. In the final section a few remarks are added on cases with long-range interactions between positrons and traps, such as electrically charged point-defects in insulators or semiconductors, and dislocations.
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References
R.N.West: Adv. Physics22, 263 (1973)
A.T.Stewart: In:Positron Annihilation, ed. by A.T.,Stewart and L.O.Roellig (Academic Press, New York, London 1967), p. 17
W.Schülke, O.Brümmer: In:Elektronenstruktur, ed. by H.Ringpfeil (VEB Deutscher Verlag für Grundstoffindustrie, Leipzig 1972), p. 95
P.M.Platzmann: Comm. Solid State Phys.4, 85 and 101 (1972)
V.J.Gol'danski, E.P.Prokop'ev: Fiz. Tverd. Tela6 3301 (1964);-Sov. Phys.-Solid State6, 2641 (1965)
W.Brandt: In:Positron Annihilation, ed. by A.T.Stewart and L.O.Roellig (Academic Press, New York, London 1967), p. 178 seq.
I.K.MacKenzie, T.L.Khoo, A.B.McDonald, B.T.A.McKee: Phys. Rev. Letters19, 946 (1967)
B.Bergersen, M.J.Stott: Solid State Commun.7, 1203 (1969)
D.C.Connors, R.N.West: Phys. Letters30A, 24 (1969)
A.Seeger: J. Phys. F (Metal Phys.)3, 248 (1973)
M.Doyama, R.R.Hasiguti: Cryst. Lattice Defects4, 139 (1973)
A.Seeger: Cryst. Lattice Defects4, 221 (1973)
W.Frank, A.Seeger: Appl. Phys.3, 61 (1974)
H.Reiss: J. Appl. Phys.30, 1141 (1959)
F.C.Collins, G.Kimball: J. Colloid Sci.4, 425 (1949)
L.Monchick, J.L.Magee, A.H.Samuel: J. Chem. Phys.26, 935 (1975)
T.R.Waite: Phys. Rev.107, 463 (1957)
T.R.Waite: Phys. Rev.107, 471 (1957)
T.R.Waite: J. Chem. Phys.28, 103 (1958)
T.R.Waite: J. Chem. Phys.32, 21 (1960)
M.Abramowitz, I.A.Stegun: Handbook of Mathematical Functions (Dover Publications, New York 1965)
H.Mehrer: Z. Naturforsch.24a, 358 (1969)
H.Mehrer: Z. Naturforsch.24a, 367 (1969)
K.Schröder: Rad. Effects17, 103 (1973)
E.Kamke:Differentialgleichungen, Lösungsmethoden und Lösungen, Vol. 1. “Gewöhnliche Differentialgleichungen” (Akademische Verlagsgesellschaft Geest+Portig, Leipzig 1961)
A.Seeger: In:Frontiers in Materials Science: Distinguished Lectures, ed. by L.Murr and Ch.Stein (Marcel Dekker, Inc., New York), to be published
G.E.Roberts, H.Kaufman:Table of Laplace Transforms (W.B. Saunder, Philadelphia, London 1966)
R.M.J.Cotterill, I.K.MacKenzie, L.Smedskjaer, G.Trumpy, J.H.O.L.Träff: Nature239, 99 (1972)
I.K.MacKenzie, P.C.Lichtenberger: Appl. Phys.3, 393 (1974)
D.Knapton, B.T.A.McKee: Second Intern. Conf. Positron Annihilation, Kingston, Ontario 1971, pp. 4.70–4.78
A.Seeger, H.Mehrer: In:Vacancies and Interstitials in Metals, ed. by A.Seeger, D.Schumacher, W.Schilling, and J.Diehl (North-Holland Publ. Comp., Amsterdam 1970), p. 1
H.C.Jamieson, B.T.A.McKee, A.T.Stewart: Appl. Phys.4, 79 (1974)
J.D.McGervey, W.Triftshäuser: Phys. Letters44A, 53 (1973)
R.N.West, V.H.C.Crisp, G.deBlonde, B.G.Hogg: Phys. Letters45A, 441 (1973)
B.T.A.McKee, A.G.D.Jost, I.K.MacKenzie: Canad. J. Phys.50, 415 (1972)
R.W.Siegel: 3rd Internat'l Conf. Positron Annihilation, Otaniemi, Finland (1973)
B.Bergersen, E.Pajanne: Appl. Phys.4, 25 (1974)
A.Seeger: Phys. Letters40A, 135 (1972)
A.Seeger: Phys. Letters41A, 267 (1972)
C.H.Hodges: Phys. Rev. Letters,25, 284 (1970)
B.Bergersen, D.W.Taylor: To be published
J.Cheng, C.K.Yak, S.I.Ma, C.S.Su: Phys. Rev.8, 2880 (1973)
S.Nanao, K.Kuribayashi, S.Tanigawa, M.Doyama: J. Phys. F (Metal Phys.)3, L225 (1973)
O.Sueoka: J. Phys. Soc. Japan36, 464 (1974); J. Phys. Soc. Japan, in print
A.N.Goland, T.M.Hall: Phys. Letters,45A, 397 (1973)
A.Seeger: Phys. Stat. Sol.41, 509 (1970)
A.Seeger: Phys. Letters38A, 45 (1972)
E.Kuramoto, S.Takeuchi, M.Noguchi, T.Chiba, N.Tsuda: J. Phys. Soc. Japan,34, 103 (1973)
A.Seeger: To be published
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Seeger, A. The study of defects in crystals by positron annihilation. Appl. Phys. 4, 183–199 (1974). https://doi.org/10.1007/BF00884229
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DOI: https://doi.org/10.1007/BF00884229