Positrons in Solids

265 Pages·1979·5.69 MB·English

by  P. Hautojärvi

12
Topics in
Current Physics
Topics in Current Physics
Founded by Helmut K. V. Lotsch
Volume 1 Beam-Foil Spectroscopy
Editor: S. Bashkin
Volume 2 Modern Three-Hadron Physics
Editor: A. W. Thomas
Volume 3 Dynamics of Solids and Liquids by Neutron Scattering
Editors: S. W. Lovesey and T. Springer
Volume 4 Electron Spectroscopy for Surface Analysis
Editor: H. Ibach
Volume 5 Structure and Collisions of Ions and Atoms
Editor: I. A. Sellin
Volume 6 Neutron Diffraction
Editor: H. Dachs
Volume 7 Monte Carlo Methods in Statistical Physics
Editor: K. Binder
Volume 8 Ocean Acoustics
Editor: J. A. DeSanto
Volume 9 Inverse Source Problems in Optics
Editor: H. P. Baltes
Volume 10 Synchrotron Radiation Techniques and Applications
Editor: C. Kunz
Volume 11 Raman Spectroscopy of Gases and Liquids
Editor: A. Weber
Volume 12 Positrons in Solids
Editor: P. Hautojarvi
Volume 13 Computer Processing of Electron Microscope Images
Editor: P. W. Hawkes
Volume 14 Excitons
Editor: K. Cho
Volume 15 Physics of Superionic Conductors
Editor: M. B. Salamon
Positrons in Solids
Edited by P. Hautojarvi
With Contributions by
A. Dupasquier P. Hautojarvi M. J. Manninen
P. E. Mijnarends R. M. Nieminen A.Vehanen
R. N. West
With 66 Figures
Springer-Verlag Berlin Heidelberg New York 1979
Professor Dr. Pekka Hautojarvi
Department of Technical Physics, Helsinki University of Technology.
SF-Q2150 Espoo 15, Finland
ISBN-13: 978-3-642-81318-4 e-ISBN-13: 978-3-642-81316-0
001: 10.1007/978-3-642-81316-0
Library of Congress Cataloging in Publication Data. Main entry under title: Positrons in solids.
(Topics in current physics; v. 12), Includes bibliographical references and index.
1. Positrons. 2. Positron annihilation. 3. Solids. I. Hautojiirvi, Pekka. II. Dupasquier, Alfredo E.
III. Series. QC793.5.P622P67 539.7'214 79-1191
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Softcover reprint of the hardcover 1st edition 1979
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2153/3130-543210
Preface
In condensed matter initially fast positrons annihilate after having reached equi
librium with the surroundings. The interaction of positrons with matter is governed
by the laws of ordinary quantum mechanics. Field theory and antiparticle properties
enter only in the annihilation process leading to the emergence of energetic photons.
The monitoring of annihilation radiation by nuclear spectroscopic methods provides
valuable information on the electron-positron system which can directly be related
to the electronic structure of the medium. Since the positron is a positive electron
its behavior in matter is especially interesting to solid-state and atomic physi
cists. The small mass quarantees that the positron is really a quantum mechanical
particle and completely different from any other particles and atoms. Positron
physics started about 25 years ago but discoveries of new features in its interac
tion with matter have maintained continuous interest and increasing activity in the
field. Nowadays it is becoming part of the "stock-in-trade" of experimental physics.
A striking feature is the great diversity of fields in which positron annihil
ation is applied. In addition to solid-state physics, which is the topic of this
book, there are intensive activities in atomic physics, and positronium chemistry
is the traditional name for the chemical applications. There exists plenty of
earlier reference material in the form of review monographs and conference pro
ceedings. However, the recent development and achievements especially in momentum
density and defect studies have rapidly attracted the interest of a wider scienti
fic community outside of the traditional positron physics thus providing justifi
cation for the publication of this topical volume.
The first chapter is an introduction devoted to readers who have no former
familiarity with positron annihilation. It gives a short account of annihilation
processes and of conventional experimental techniques. Also some recent topics of
positron studies are very briefly discussed.
Chapter 2 is concerned with electron momentum density studies by means of an
gular correlation of 2y-annihilation radiation. It discusses the state-of-the-art
in the application of independent-particle theory and describes the recent deve
lopment of two-dimensional detector geometries which have greatly increased the re
solution and efficiency of the positron method. The latest results on metals and
alloys are thoroughly reviewed.
VI
The extreme sensitivity of positrons to crystal imperfections in metals is re
flected through positron trapping. This makes the positron annihilation method
capable of yielding unique information on the concentration, configuration and
internal structure of lattice defects in solids. Positrons have within a few years
proved to be a new microscopic tool the use of which has produced significant
achievements in the physics of lattice defects. The new experimental results and
progress in theoretical understanding are reviewed in Chaps.3 and 4, respectively.
Chapter 5 deals with ionic solids and serves as an example of problems in non
metals. It offers a solution to the origin of the complex annihilation charac
teristics in alkali halides and reviews the interaction of positrons with various
kind of defect centers.
I want to thank the authors who have not only contributed to this book but in
fact created it. The very fluent cooperation has kept the editorial work at a
minimum. In addition, I am especially indebted to Risto Nieminen for his comments
and suggestions which have largely influenced the content of the book.
Helsinki, December 1978 Pekka Hautojorvi
Contents
1. Introduction to Positron Annihilation
By P. Hautojarvi and A. Vehanen (With 15 Figures) .. ................ ...... 1
1.1 Positron Method..................................................... 2
1.2 Annihilation of Free Positrons...................................... 3
1.3 Experimental Techniques............................................. 5
1.3.1 Lifetime t>1easurements .......... ................. ............. 5
1.3.2 Angular Correlation Measurements ............................. 7
1.3.3 Line-Shape Measurements ...................................... 9
1.3.4 Correlation Between Lifetime and Momentum .................... 11
1.4 Positronium Formation and Annihilation .............................. 11
1. 5 Topi cs of Pos it ron Studi es .......................................... 14
1.5.1 r1etals ....................................................... 14
1. 5.2 Metal Defects ................................................ 14
1.5.3 Ionic Crystals............................................... 15
1.5.4 Slow Positrons and Positronium ............................... 15
1. 5.5 Gases and Low-Temperature Phenomena .......................... 17
1.5.6 r10lecular Solids............................................. 18
1.5.7 Positronium Chemistry........................................ 20
1.6 SulTlllary............................................................. 21
References ............................................................... 22
2. Electron Momentwn Densities in Metals and Alloys
By P.E. Mijnarends (With 15 Figures) ..................................... 25
2.1 Theory........... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.1.1 Momentum Dens i ty ............................................. 27
2.1. 2 Many-Body Effects ............................................ 30
2.1.3 Positron Thermalization, Effective Mass and Other Thermal
Effects ...................................................... 33
a) Thermal ization ............................................ 33
b) Effecti ve Mass ............................................ 35
c) Other Thermal Effects ..................................... 35
VIII
2.2 Wave Functi ons .................................................... 37
2.2.1 Positron Wave Function .............................. ....... 37
2.2.2 Electron Band Structure and Wave Functions ................. 39
a) OPW Method .............................................. 40
b) APW Method .............................................. 42
c) KKR and Related Methods................................. 44
d) Other Methods ........................................... 45
2.2.3 Symmetry Properties of Aj(E'~) ............................. 45
a) Radial Behavior......................................... 46
b) Directional Symmetry.................................... 47
2.3 Experimental Techniques........................................... 47
2.3.1 2y Angular Correlation Measurements............ ............ 47
2.3.2 Rotating Specimen Method................................... 51
2.3.3 Doppler Broadening......................................... 51
2.3.4 Specimen Preparation....................................... 52
2.3.5 Corrections................................................ 52
a) "Beam Profile" Correction............................... 52
b) Di ffracti on Effect ..................•................... 53
c) Angular Resolution and Positron Thermal Motion .........• 53
d) Finite Slit Length .......... ............................ 54
2.3.6 Analysis .......................... ......................... 54
2.4 Momentum Dens ity Work in Meta 1s ................................... 58
2.4.1 A1 k a 1i t1eta 1s .............................................. 58
2.4.2 Other Simple Metals........................................ 61
2.4.3 Oriented Graphite, Diamond, Silicon, and Germanium ....•.... 64
2.4.4 Noble Metals............................................... 66
2.4.5 Transition Metals and Rare Earths .......................... 70
2.5 Disordered Alloys and Ordered Metallic Compounds ...........•...•.• 74
2.5.1 Disordered Alloys.......................................... 74
2.5.2 Metal 1i c Compounds ......................................... 79
2.6 Conclusion........................................................ 80
References ..........•.•............................••.................. 81
3. Positron Studies of Lattice Defects in MetaZs
By R.N. West (With 12 Figures) ......................................... 89
3.1 Annihilation Parameters for Defect Studies ..•.....•...........•... 90
3.1.1 The Defect Trapping Phenomenon and Its Effect .............• 90
3.1.2 Positron States and Lifetime Spectra....................... 91
3.1.3 Momentum Density Parameters .......•.............•.......... 96
3.2 Monovacancies in Equilibrium...................................... 98
3.2.1 The Naive Approach to Temperature Effects ......•........... 98
IX
3.2.2 Prevacancy Effects......................................... 100
3.2.3 Other Complications .. ........ .... ...... ............. .... ... 102
3.2.4 Vacancy Formation Enthalpy Measurements.................... 108
3.2.5 Characteristic or Threshold Temperatures................... 115
3.2.6 Pressure Experiments....................................... 118
3.3 Nonequilibrium Studies .............. .............................. 119
3.3.1 The "~4any Defects" Problem .... ... .... ...................... 119
3.3.2 Deformation, Quenching, and Irradiation Experiments ........ 121
3.3.3 Anneal i ng Studi es .......................................... 124
3.3.4 Pos itron Studi es of Voi ds .................................. 126
3.4 Defect Studi es inA 11 oys .......................................... 129
3.4.1 Defect vs Impurity Problems................................ 129
3.4.2 Vacancy Studi es ............................................ 131
3.4.3 Phase Transitions and Boundary Effects..................... 134
3.5 Liquid and Amorphous ~1etals .. , ............. ....... ............ .... 136
References ............................................................. 139
4. Positrons in Imperfect solids: Theory
By RJ4. Nieminen and M.J. Manninen (With 16 Figures) ................... 145
4.1 Positron Distribution, Mobility, and Trapping. .............. ...... 146
4.1.1 Positron Implantation, Slowing Down, and Thermalization .... 146
4.1.2 Mobility and Diffusion..................................... 147
4.1.3 Positron Distribution in Solids .......... .................. 149
4.1.4 Annihilation Characteristics and Electron-Positron Corre-
lation in Pure Metals...................................... 152
4.1.5 Effect of Temperature on Annihilation Characteristics ...... 157
4.1.6 Trapping at Defects............ ..... ........... ............ 158
4.1.7 Se 1 f-t rappi ng .............................................. 162
4.2 Defects in Metals................................................. 164
4.2.1 Electronic Structure of Defects ..................... ....... 164
4.2.2 Positron-Defect Interaction................................ 168
4.2.3 Annihilation Characteristics............................... 272
4.2.4 Applications .............................................. 174
a) Vacancies .............................................. 175
b) Dislocations ........................................... 179
c) Impurities and Alloys .................................. 181
d) Vacancy Cl usters .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
e) Surfaces .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
4.3 Nonmetals......................................................... 191
4.4 Conclusions....................................................... 192
References ............................................................. 192
x
5. Positrons in Ionia Solids. By A. Dupasquier (With 8 Figures) .......... 197
5.1 Experimental Methods.............................................. 198
5.1.1 Standard Experimental Techniques .•. ........................ 198
5.1.2 Special Experimental Techniques .... ........................ 199
a) Two-Parameter Age-Momentum Measurements. ................ 199
b) Magnetic Quenching Measurements ......................... 200
5.1.3 Experimental Difficulties.................................. 201
a) Analysis of Multicomponent Lifetime Spectra ............. 201
b) Analysis of Multicomponent Momentum Distributions ....... 203
c) Source and Surface Contributions to Lifetime Spectra .... 203
d) Radiation Damage Due to the Positron Source .•........•.. 204
5.2 Annihilation Characteristics in Alkali Halides .................... 204
5.2.1 Room Temperature Measurements on Crystals with Low Defect
Concentration.............................................. 204
a) Lifetime Spectra........................................ 204
b) Angular Correlation Curves .............................. 206
c) Doppler-Broadened Annihilation Line Shape ............... 209
d) Three-Quantum Annhilation ............................... 210
5.2.2 Temperature Effects........................................ 210
5.2.3 Annihilation in Crystals with High Defect Concentration .... 212
a) Thermal Defect Generation ............................... 213
b) Thermal Quenching....................................... 213
c) Additive Coloration..................................... 215
d) F:+ F- Conversion....................................... 217
e) Aggregation of F Centers ................................ 217
f) Doping with Divalent Impurities ......................... 217
9) Defect Creation by Ionizing Radiation.. .................. 218
h) Plastic Deformation ................................... :. 221
i) Mixed Crystals .... .......... ........ ........... ......... 221
5.2.4 Magnetic Field Effects..................................... 221
a) Crystals with Low Defect Concentration .................. 222
b) Additively Colored Crystals ............................. 224
c) Doped Crystals.......................................... 224
5.3 Positron States in Alkali Halides .. .....................•......... 225
5.3.1 Intrinsic States........................................... 225
a) Nearly Free Positrons in a Perfect Lattice .............. 225
b) Quasi-Positronium in Perfect Crystals ................... 228
5.3.2 Annihilation Centers....................................... 231
a) cA Center............................................... 231
b) aA+ Center .•............................................ 232
c - c - 2+
c) A and A (Ca ) Centers ............................... 233