Applications of positron-lifetime measurements to the study of defects in metals

Abstract

We describe in detail the data-analysis techniques which we have developed for obtaining information about defect properties from positron-lifetime measurements. These techniques eliminate many of the incorrect assumptions usually made in analyzing positron-lifetime data to obtain defect parameters. Some specific features of the data analysis are the use of an improved form for the instrumental resolution function, the use of a model which allows for the presence of several types of defect traps, and the inclusion of the possibility of temperature dependence in the specific positron trapping rate (defined as the positron trapping rate per unit defect concentration). These techniques were used to analyze data from heated specimens of pure aluminum, pure gold, and aluminum-1.7-at.%-zinc, in which the equilibrium concentration of vacancies was high enough to alter positron lifetimes. Analysis of data from lifetime measurements on pure aluminum at temperatures between 200 and 400 °C, and on pure gold at temperatures between 360 and 760 °C yielded monovacancy formation energies of $E_{1V}^F=0.62\mathrm{}\pm 0.02$ eV for aluminum and $E_{1V}^F=0.98\mathrm{}\pm 0.03$ eV for gold assuming no temperature dependence in the specific positron trapping rate. The fit to the data was significantly improved by assuming a temperature dependence in the specific trapping rate of $T^{1.2\pm 0.3}$ for aluminum and $T^{0.5\pm 0.2}$ for gold. The best-fit formation energies corresponding to these temperature dependences were $E_{1V}^F=0.69\mathrm{}\pm 0.03$ eV for aluminum and $E_{1V}^F=1.00\mathrm{}\pm 0.03$ eV for gold. Equilibrium measurements between 200 and 400 °C in aluminum-1.7-at.%-zinc yielded a value for the binding energy of vacancies to impurities $E_{\mathrm{VP}}^B=-0.09\mathrm{}\pm 0.03$ eV assuming no temperature dependence in the specific trapping rate. The fit was improved by assuming a temperature dependence in the specific trapping rate of $T^{1.1\pm 0.2}$, corresponding to a best-fit value for the binding energy of $E_{\mathrm{VP}}^B=+0.04\mathrm{}\pm 0.07$ eV. From our results we conclude that there is a positive temperature dependence in the specific positron trapping rate and that vacancies are not strongly bound to zinc impurity atoms in aluminum.