Positron Methods for the Study of Defects in Bulk Materials

The basic principles of positron annihilation physics are briefly discussed and the three most important experimental techniques used for bulk studies are described (i.e. positron lifetime, angular correlation, Doppler broadening). Several examples of the use of the positron methods are discussed for metals, ceramics and molecular materials, which illustrate the sensitivity of the positron annihilation techniques to vacancy type defects. For example it is shown how information can be obtained about vacancy formation energies, vacancy migration and clustering, vacancy-impurity interactions, densities of rare gasses in bubbles in metals, and about free volume in molecular materials. 1.INTRODUCTION The positron is the antiparticle to the electron. This means that the positron has the same mass and spin as the electron, but has the opposite charge, viz. one positive elementary charge. Furthermore, if a positron is surrounded by one or more electrons the positron may annihilate with one of the electrons, i.e. both particles disappear and their masses are transformed into energy which is emitted as y-quanta, normally two or three. The properties of these y-quanta, such as their energies, emission directions, and time of emission which can all be measured, provide useful information about the material in which the positrons annihilate. Very briefly, this is the principle of the Positron Annihilation Spectroscopy. Positron Annihilation research is a very wide field as can be judged from the proceedings of the most recent international conferences [I-51 and other recent publications [6-101. In the present paper we shall concentrate on a discussion of the possibilities to study defects in solids, by giving exampIes for metals, ceramics and molecular materials. First, however, let us discuss some of the basic physical principles of positron annihilation and then describe the most important experimental techniques used in positron annihilation studies of defects in bulk materials. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1995111 C1-94 JOURNAL DE PHYSIQUE IV 2. POSITRONS IN SOLIDS In conventional positron annihilation experiments the positrons are injected into a solid with a mean energy of the order of 200 keV. They slow down to thermal energies in about 10-12-10-1' sec (1-10 psec) by ionisation and excitation of the solid. During this time they penetrate a distance of 10-1000 pm depending on the density of the solid (the penetration depth is roughly inversely proportional to the density). Hence, the positrons probe bulk material in such experiments. In recent years a rapid development of a new technique has taken place, viz. of low-energy-positron beams. This technique will be discussed by others at this workshop [Ill. 2.1. Annihilation of Positrons A positron that has been injected into a solid and has slowed down, in most cases annihilates with the emission of 2 y-quanta, since for free positrons the cross-section for emission of 3y is only 1/379 of the 2y cross-section. The two annihilation quanta have a total energy of E = 2m0c2 = 2x511 keV (mo is the electron or positron rest mass, c the velocity of light) and are emitted in almost opposite directions as sketched in Fig. 1. The angle O is usually very small, typically < 20 milliradian (mrad) (20 mrad = lo). This is so, because the total momentum of the annihilating positron-electron pair has to be conserved in the momentum of the two quanta. If this momentum deviates from zero, the directions of emission of the two quanta will deviate from co-linearity (Fig.1). In a good approximation the angle between them is given by: where p, is the total momentum of the y-quanta. Fig.1. Emission of two annihilation y-quanta in almost opposite directions. The vectors represent the momenta of the two quanta and F2) and the total momentum of the pair . The angle Q is usually very small,