Abstract
In these lectures we shall outline the use of the positron (e+) annihilation technique for the study of electrons (e-) in metals and, in particular, in non-dilute disordered alloys. The behavior of slow e+-s in condensed matter has been the subject of intense experimental and theoretical investigations during the last two decades, and the field has been reviewed thoroughly;1 positron annihilation has become a useful new tool in solid state physics. By studying the various properties of annihilation quanta one obtains direct information about the electrons the positrons annihilate with. In particular the 2γ angular correlation of annihilation radiation (ACAR) reflects, by momentum conservation, the momentum density of the annihilating e+-e-pair. Discontinuities in the correlation curves can be used to mea-sure the size and shape of the Fermi surface (FS) in pure metals as well as in alloys. If the behavior of the e+ is sufficiently well understood and the effect of the e+-e- Coulomb interaction sufficiently well accounted for, the ACAR measurements can lead, as we shall see, to a test of the electronic wavefunctions of the system under investigation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
a) R.N. West, Adv. Phys. 22, 263 (1973); S. Berko in “Compton Scattering” edited by B. Williams, McGraw Hill, London, 1977, Chapter 9. P.E. Mijnarends in “Positrons in Solids”, edited by P. Hauto jarvi, Springer Verlag, 1978, to be published.
See for example A.P. Cracknell and K.C. Wong, “The Fermi Surface”, Clarendon Press, Oxford, 1973.
See for example the review by L. Muldawer in “Charge Transfer Electronic Structure of Alloys”, edited by L.H. Bennett and R.H. Willens, Metallurgical Society of AIME, 1974, p. 291.
T.B. Massalski and V. Mizutani in “Progress in Materials Science”, edited by B. Chalmers, J.W. Christian and T.B. Massalski, Pergamon Press, Oxford, 1978, to be published.
See for example W.E. Spicer in “Band Structure Spectroscopy of Metals and Alloys”, edited by D. Fabian, Academic Press, NY, 1972.
G.K. Wertheim and S. Hufner in “Charge Transfer-Electronic Structure of Alloys”, edited by L.H. Bennett and R.H. Willens, Metallurgical Society of AIME, 1974, p. 69.
See for example the extensive review by H. Ehrenreich and L.M. Schwartz in “Solid State Physics”, edited by H. Ehrenreich, F. Seitz and D. Turnbull, Academic Press, NY, 1976, Vol. 31, p. 149.
W. Kohn, Phys. Rev. Letters 2, 393 (1959).
See review by S.C. Moss and R.H. Walker, J. Appl. Cryst. 8, 96 (1974).
See for example K. Ohshima and D. Watanabe, Acta Cryst. A29, 520 (1973).
See the review by E.A. Stern in “Charge Transfer-Electronic Structure of Alloys”, edited by L.H. Bennett and R.H. Willens, Metallurgical Society of AIME, 1974, p. 197.
“Compton Scattering” edited by B. Williams, McGraw-Hill, London, 1977.
V. Heine, Proc. Phys. Soc. A69, 505 (1956).
P.T. Coleridge in “Low Temperature Physics-LTI3”, edited by K.D. Timmerhaus, W.J. O’Sullivan and E.F. Hammel, Plenum Press, NY, 2. 1974, Vol. 4, p. 9; P.T. Coleridge, to be published 1979.
See for example the papers by E.A. Stern, Phys. Rev. 157, 544 (1967); 168, 730 (1968); 188, 1163 (1969); B5, 366 (1972); 7B, 1303 (1973) and references therein; see also R.S. Sorbello, Phys. Rev. B15, 3045 (1977), as well as ref. 7.
P.T. Coleridge and I.M. Templeton, Can. Journal Phys. 49, 2449 (1971).
J. Friedel, Adv. Phys. 3, 446 (1954).
A.H. Lettington, Phil. Mag. 11, 863 (1965).
R.S. Rea and A.S. DeReggi, Phys. Rev. B9, 3285 (1974).
P.T. Coleridge, N.A.W. Holzwarth and M.J.G. Lee, Phys. Rev. B10, 1213 (1974); Phys. Rev. B13, 3249 (1976).
R.G. Poulsen, D.L. Randies and M. Springford, J. Phys. F4, 981 (1974).
I.M. Templeton and P.T. Coleridge, J. Phys. F5, 1307 (1975); P.T. Coleridge, J. Phys. F5, 1317 (1975).
L.J. Hornbeck, W.K. Fung and W.L. Gordon, Phys. Rev. B15, 4750 (1977)
W.K. Fung and W.L. Gordon, Phys. Rev. B15, 4762 (1977).
“Electron Lifetimes in Metals”, edited by D.H. Lowndes and F.M. Mueller, Physics of Condensed Matter, Vol. 19 (1975).
See for example J.M. Ziman, “Principles of the Theory of Solids”, second edition, University Press, Cambridge, 1972, p. 155.
E.J. Woll, Jr. and W. Kohn, Phys. Rev. 126, 1693 (1962); P.L. Taylor, Phys. Rev. 131, 1995 (1963); S.H. Vosko, R. Taylor and G.H. Keech, Can. J. Phys. 43, 1187 (1965); M.I. Kaganov and A.I. Semenenko, Soviet Phys. JETP 23, 419 (1966);L.M. Roth, H.J. Zeiger and T.A. Kaplan, Phys. Rev. 149, 519 (1966).
B.N. Brockhouse, K.R. Rao and A.D.B. Woods, Phys. Rev. Lett. 7 ,93 (1961).
A. Paskin and R.J. Weiss, Phys. Rev. Lett. 9, 199 (1962).
J.W. Weymouth and R. Stedman, Phys. Rev. B2, 4743 (1970).
A.D.B. Woods and B.M. Powell, Phys. Rev. Lett. 15, 778 (1965); B.M. Powell, P. Martel and A.D.B. Woods, Phys. Rev. 171, 272 (1968).
G. Nilsson and S. Rolandson, Phys. Rev. B9, 3278 (1974).
S.C. Ng and B.N. Brockhouse, S.S. Comm. 5, 79 (1967).
H.G. Smith, N. Wakabayashi and M. Mostoller in “Superconductivity in dand f-band Metals”, edited by D.H. Douglass, Plenum Press, NY, 1976, p. 223.
See for example the review by R. Comes and G. Shirane in “Highly Conducting One-Dimensional Solids”, edited by J.T. DeVreese, Plenum Press, NY, 1978, to be published.
G. Shirane, S.M. Shapiro, R. Comes, A.F. Garito and A.J. Heeger, Phys. Rev. B14, 2325 (1976).
D.E. Moncton, J.D. Axe and F.J. DiSalvo, Phys. Rev. B16, 801 (1977).
P.C. Clapp and S.C. Moss, Phys. Rev. 142, 418 (1966); Phys. Rev. 171, 754 (1968); Phys. Rev. 171, 764 (1968).
M.A. Krivoglaz, “Theory of x ray and Thermal Neutron Scattering by Real Crystals”, Plenum Press, NY, 1969.
S.C. Moss and R.H. Walker, J. Appl. Cryst. 8 ,96 (1975).
R.O. Scattergood, S.C. Moss and M.B. Bever, Acta Met. 18, 1087 (1970).
See Fig. 13 in S. Berko and J. Mader, Appl. Phys. 5, 287 (1975).
K. Ohshima and D. Watanabe, Acta Cryst. A29, 520 (1973).
Y. Yamada, J.C. Tsang, G.V. Subba-Rao, Phys. Rev. Letters 34, 1389 (1975).
W,A. Kamitakahara, B.N. Harmon, J.G. Taylor, L. Kopp, H.R. Shanks and J. Rath, Phys. Rev. Lett. 36, 1393 (1976).
J.C. McGroddy, A.J. McAlister and E.A. Stern, Phys. Rev. 139, A1844 (1965); Phys. Rev. 140, A2105 (1965).
J.M. Tracy and E.A. Stern, Phys. Rev. B8, 582 (1973).
W.B. Vail, III, and E.A. Stern, to be published.
C.S. Kumar and E.A. Stern, to be published.
M.R. Halse, Phil. Trans. R. Soc. London A265, 507 (1969).
N.E. Christensen, Phys. Stat. Sol. B54, 551 (1972).
H. Jones, Proc. Phys. Soc. London 49, 250 (1937); W. Hume-Rothery and D.J. Roaf, Phil. Mag. 6, 55 (1961).
C.J. Flaten and E.A. Stern, Phys. Rev. Bll, 638 (1975); see also G.P. Pells and H. Montgomery, J. Phys. C3, Suppl., S330 (1970).
J.W.M. DuMond, Rev. Mod. Phys. 5, 1 (1933).
See review paper by P. Platzman and N. Tzoar in “Compton Scattering” edited by B. Williams, McGraw-Hill, London, 1977, p. 28.
For experimental details see discussion by R.J. Wein, W.A. Reed and P. Pattison in “Compton Scattering” edited by B. Williams, McGraw Hill, London, 1977, p. 43; see also R.M. Singru, Phys. Stat. Sol. (a) 30, 11 (1975).
For a review see R.A. Bonham and H.F. Wellenstein in “Compton Scattering”, edited by B. Williams, McGraw-Hill, London, 1977, p. 234.
See for example the review by A.P. Mills, Jr., S. Berko, K.F. Canter in “Atomic Physics”, 5, edited by R. Marrus, M. Prior and H. Shugart, Plenum Press, NY, 1977, p. 103.
See the review by H.S.W. Massey, E.H.S. Burhop and H.B. Gilbody in “Electronic and Ionic Impact Phenomena”, V, University Press, Oxford, 1975.
See for example V.I. GoldanskiLand V.P. Shantarovich, Appl. Phys. 3, 335 (1974).
A. Seeger, Appl. Phys. 4, 183 (1974).
K. Fujiwara and O. Sueoka, J. Phys. Soc, Japan 21, 1947 (1966).
S. Berko, M. Haghgooie and J.J. Mader, Phys. Letters 63A, 335 (1977)
A.P. Jeavons, G. Charpak, and R.J. Stubbs, Nucl. Inst. Methods 124, 491 (1975); A.A. Manuel, G.H. Bongi, O. Fischer, and M. Peter, Helv. Phys. Acta M), 166 (1977); R.J. Douglas and A.T. Stewart in H14 IV Int. Conf. on Positron Annihilation, Helsingr (1976).
R.N. West, private communication.
W. Triftshauser in IInd Int. Conf. on Positron Annihilation, Kingstron, 4.77–86 (1971).
R.A. Ferrell, Rev. Mod. Phys. 28, 308 (1956).
Chang Lee, J. Exptl. Theor. Phys. (USSR) 33, 365 (1957).
See the review by L. Hedin and S. Lundqvist in “Solid State Physics” 23, edited by F. Seitz, D. Turnbull and H. Ehrenreich, Academic Press, NY, 1969, p. 1.
D.J.W. Geldart, A. Houghton, and S.H. Vosko, Can. J. Phys. 42, 1939 (1964).
S. Kahana, Phys. Rev. 117, 123 (1960); Phys. Rev. 129, 1622 (1963); J.P. Carbotte and S. Kahana, Phys. Rev. 139, A213 (1965). See also other references quoted in e+ reviews (Ref. 1).
H. Weisberg and S. Berko, Phys. Rev. 154, 249 (1967).
C.K. Majumdar, Phys. Rev. 140, A227 (1965).
J.J. Donaghy and A.T. Stewart, Phys. Rev. 164, 396 (1967).
W.C. Phillips and R.J. Weiss, Phys. Rev. 171, 790 (1968); P. Eisenberger, L. Lam, P.M. Platzman and P. Schmidt, Phys. Rev. B6, 3671 (1972); see also the discussion of K.F. Berggren, et al. in “Compton Scattering” edited by B. Williams, McGraw-Hill, London, 1977, p. 138.
K. Fujiwara, T. Hyodo and J. Ohyama, J. Phys. Soc. Japan 33, 1047 (1972).
S. De Benedetti, C.E. Cowan, W.R. Konneker and H. Primakoff, Phys. Rev. 77 ,205 (1950).
S. Berko and J.S. Plaskett, Phys. Rev. 112, 1877 (1958).
P. Kubica and M.J. Stott, J. Phys. F4, 1969 (1974).
P.E. Mijnarends, Physica 63, 235 (1973).
R. Harthoorn and P.E. Mijnarends, J. Phys. F., to be published.
P.E. Mijnarends, Phys. Rev. 160, 512 (1967); Phys. Rev. 178, 622 (1969) .
M.J.G. Lee, CRC Crit. Rev. in Solid State Sci. 2, 85 (1971).
J.J. Paciga and D.L. Williams, Can. J. Phys. 49, 3227 (1971).
See the reconstruction of p(p) for Li from CP measurements by W. Schulke, Phys. Stat. Sol.b80, K67 (1977), and references therein.
J.J. Mader, S. Berko, H. Krakauer, and A. Bansil, Phys. Rev. Letters 37, 1232 (1976).
A.T. Stewart, private communication.
S. Cushner, J.C. Erskine and S. Berko, Phys. Rev. B1, 2852 (1970).
H. Bross and H. Stohr, Appl, Phys. 3, 307 (1974).
N. Shiotani, T. Okada, T. Mizoguchi and H. Sekizawa, J. Phys. Soc. Japan 38, 423 (1975) .
S. Wakoh, Y. Kubo and J. Yamashita, J. Phys. Soc. Japan 38, 416 (1975).
O. Terasaki, T. Fukamachi, S. Hosoya and D. Watanabe, Phys. Letters 43A, 123 (1973); T. Paakkari, S. Manninen, O. Jukinen and E. Liokkonen, Phys. Rev. B(6, 361 (1972); W.C. Phillips, Phys. Rev. B7, 1047 (1973).
S. Wakoh and J. Yamashita, J. Phys. Soc. Japan, 35, 1406 (1973).
R.W. Williams and A.R. MacKintosh, Phys. Rev. 168, 679 (1968).
R.P. Gupta and T.L. Loucks, Phys. Rev. 176, 848 (1968).
S. Berko, Positron Annihilation, eds. A.T. Stewart and L.O. Roellig (Academic Press, NY, 1967) pp. 61–79.
a) P.E. Mijnarends, Physica 63, 248 (1973); b) S. Berko and A.P. Mills, Jr., J. Physique J32, C1–287 (1971).
N. Shiotani, T. Okada, H. Sekizawa, T. Mizoguchi and T. Karasawa, J. Phys. Soc. Japan 35, 456 (1973); see also Ref. 96b.
C. Hohenemser, J.M. Weingart and S. Berko, Phys. Lett. 28A, 41 (1968).
N. Sakai and K. Ono, J. Phys. Soc. Japan 42, 770 (1977).
S. Wakoh and Y. Kubo, J. Magnetism Magn. Mat. 5, 202 (1977).
J.P. Carbotte and A. Salvadori, Phys. Rev. 162, 290 (1967);
T. Chiba, G.B. Dürr and W. Brandt, Phys. Stat. Sol. (b) 81, 609 (1977).
A. Bansil, H. Ehrenreich, L. Schwartz and R.E. Watson, Phys. Rev. B9., 445 (1974)
L. Schwartz and A. Bansil, Phys. Rev. B10, 3261 (1974)
A. Bansil, L. Schwartz and H. Ehrenreich, Phys. Rev. B12, 2893 (1975).
G.M. Stocks, B.L. Györffy, E.S. Giuliano and R. Ruggeri, J. Phys. F., 7 ,1859 (1977)
B. Gordon, W.M. Temmerman, B.L. Györffy and G.M. Stocks, Inst. Phys. Conf. Ser. 39, 402 (1978),
G.M. Stocks, W.M. Temmerman and B.L. Györffy, Phys. Rev. Letters 41, 339 (1978).
P.E. Mijnarends and A. Bansil, Phys. Rev. B13, 2381 (1976).
P.E. Mijnarends, private communication.
K.M. Hong and J.P. Carbotte, Can. J. Phys. 55, 1335 (1977).
M.J. Stott and P. Kubica, Phys. Rev. Bll, 1 (1975).
D.G. Lock and R.N. West, J. Phys. F4, 2179 (1974).
A.T. Stewart, Phys. Rev. 133, A1651 (1964).
P. Kubica, B.T.A. McKee, A.T. Stewart and M.J. Stott, Phys. Rev. Bll, 11 (1975).
C. Koening in “IVth Int. Conf. on Positron Annihilation,” Helsingor, 1976, Paper D6, also, to be published.
Y. Tsuchiya and S. Tamaki, J. Phys. F8, L29 (1978).
A.G. Mathewson and H.P. Myers, J. Phys. 3 ,623 (1973).
M. Ide, J. Phys. Soc. Japan 30, 1352 (1971).
K. Berndt and O. Brümmer, Phys. Stat. Sol. (b) 78, 659 (1976) and references therein.
O. Sueoka, J. Phys. Soc. Japan 23, 1246 (1967)
D.L1. Williams, E. H. Becker, P. Petijevick and G. Jones, Phys. Rev. Lett. 20, 448 (1968).
S. Berko, M. Haghgooie and J. J. Mader, Inst. Phys. Conf. 39, 94 (1978).
M. Haghgooie, S. Berko and U. Mizutani, to be published.
S. Berko and J.J. Mader, Phys. Cond. Matter 19, 405 (1975).
W. Triftshäuser and A.T. Stewart, Phys. Chem. Solids 32, 2717 (1971).
B.W. Murray and J.D. McGervey, Phys. Rev. Lett. 24, 9 (1970).
A. Thompson, B.W. Murray and S. Berko, Phys. Lett. 37A, 461 (1971).
K. Fujiwara, O. Sueoka and T. Imura, J. Phys. Soc. Japan 24, 467 (1968).
J.J. Mader, PhD Thesis, Brandeis University, 1975.
T. Akahane, O. Sueoka, H. Morinara, K. Fujiwara, J. Phys. Soc. Japan 36, 135 (1974).
J.G. McLarnon and D.Ll. Williams, Sol. St. Commun. 13, 1469 (1973).
J.G. McLarnon and D, Ll. Williams, J. Phys. Soc. Japan 43, 1244 (1977).
M. Hasegawa, T. Suzuki, M. Hirabayashi and S. Yajima, Acta Cryst. A28, S102 (1972).
T. Suzuki, M. Hasegawa and M. Hirabayashi, Appl. Phys. 5, 269 (1974).
A. Bansil, H. Ehrenreich, L. Schwartz and R.E. Watson, Phys. Rev. B9, 445 (1974).
L. Hodges, R.E. Watson, and H. Ehrenreich, Phys. Rev. B5, 3953 (1972).
M. Hasegawa, T. Suzuki and M. Hirabayashi, J. Phys. Soc. Japan 37, 85 (1974).
E.C. Snow, J.T. Waber and A.C. Switendick, J. Appl. Phys. 37, 1342 (1966).
D.C. Tsui, Phys. Rev. 164, 669 (1967).
M. Hasegawa, T. Suzuki and M. Hirabayashi, J. Phys. Soc. Japan 43, 89 (1977).
T. Suzuki, M. Hasegawa and M. Hirabayashi, J. Phys. F6, 779 (1976).
T.B. Massalski and B. Cockayne, Acta Mat. 7, 762 (1959).
R. Harthoorn and P.E. Mijnarends, to be published.
See list of references in Ref. lc and Ref. 41.
A. Bansil, S. Bessendorf and L. Schwartz, Inst. Phys. Conf. 39, 493 (1978).
R. Griessen, W.J. Venema, J.K. Jacobs and F.D. Manchester, Inst. Phys. Conf. 39, 490 (1978).
See for example the reviews by H.S.W. Massey in Physics Today _29, 42–51 (1976)
H.S.W. Massey, E.H.S. Burhop, and H.B. Gilbody in “Electronic and Ionic Impact Phenomena,” Vol. 5, Oxford U. Press (1975).
See the review by W. Brandt in “Advances in Chemistry Series 158,” edited by M. Kaminsky, Am. Chem. Soc., 1976, and references therein.
K.F. Canter, A.P. Mills, Jr., and S. Berko, Phys. Rev. Lett. 33, 7 (1974).
A.P. Mills, Jr., to be published, Phys. Rev. Lett. 1973.
S. Pendayala, D. Barteil, F.E. Girouard and J.W. McGowan, Phys. Rev. Lett. 33, 1031 (1974)
A.P. Mills, Jr., to be published 1978.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1979 Plenum Press, New York
About this chapter
Cite this chapter
Berko, S. (1979). Fermi Surface Studies in Disordered Alloys: Positron Annihilation Experiments. In: Phariseau, P., Györffy, B.L., Scheire, L. (eds) Electrons in Disordered Metals and at Metallic Surfaces. NATO Advanced Study Institutes Series, vol 42. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-3500-9_7
Download citation
DOI: https://doi.org/10.1007/978-1-4684-3500-9_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-3502-3
Online ISBN: 978-1-4684-3500-9
eBook Packages: Springer Book Archive