75 In general, the slow e+ yield has been observed to increase with the workfunction

value of the surface (Murray and Mills, 1980, Gullikson et al 1988) for a particular metal. In the study of Murray and Mills (1980), samples of single-crystal Cu and Al of different face orientations were coated with impurities and raised in temperature to achieve a change in the workfunction value. A magnetically guided variable energy (0-3keV) beam of positrons bombarded the samples in UHV conditions and the re-emitted e+ were detected with a Nal(Tl) detector. They found that the variation of the observed slow e+ yield with the <j>+ value was accountable using the simple picture described above. By considering the time, At, spent by the positrons in a region of thickness Az from where they are accelerated out with a final energy -<J)+ and the capture rate, C, then the probability of e+ emission, exp(-CAt) is given by

y0= exp(-<y<j)+)1/2 2.16

<J>0= l/2m £2Az2 and is constant if C is constant. Figure 2.8 shows this data for Cu fitted with Equation 2.16.

With some relevance to the present study, Wilson and Mills (1983a) observed a change in the <}>+ value of single crystal W ( lll) from -(2.59±0.1)eV for a clean surface to -(3.3±0.1)ev and -(5.0±0.1)eV for C and O coverage respectively. Fischer

et al (1986) also found similar values of -(2.95±0.1)ev and -(4.1±0.2)eV for C and

O coated W(110) samples; the differences may be due to the thickness of coverage and the face orientation of the crystals. An oxygen coverage, however, was noted to decrease size of the workfunction of Ni(100) from the clean surface value of -1.4eV to -0.95eV in the study of Fischer et al (1986).

An increase in the workfunction by adsorbate coverage has been used to enhance slow e+ yields by Mills (1979a,b). A coverage of S on C u ( lll) of the order of a monolayer was found to increase the efficiency of the moderator by 30% above the pure sample, with a full width at half maximum (FWHM) energy width of 0.2eV. Overlayers greater than a few monolayers can result in the domination of the adsorbate workfunction. Lynn and Lutz (1980) employed this effect in the proposal of a hybrid W+Cu moderator which would incorporate the superior stopping power of W but, due to the small <I>+ of Cu (=0.4eV), produce e+ with an energy distribution smaller than from W.

Wilson and Mills (1983a) and Vehanen et al (1983) and Schultz et al (1983) and found to emit a narrow energy beam of e+. However trapping at interface defects substantially reduced the efficiency from the single crystal W value. Vehanen et al

(1983) noted that the B+- e + conversion efficiency of the hybrid moderator was 3X10"4 compared to 3.2xl0“3 for W(110) and 1.3xl0'3 for C u (lll)+ S in the backscattering mode. The FWHM energy spread obtained, 0.4eV, was similar to that from a pure Cu sample. Annealing to below 850°C improved the efficiency to 1.2x1 O'3, however, heating to 850°C resulted in islanding of the Cu on the W surface. Thus, the interfacial defects could not be annealed out without evaporation or rearrangement of the overlayer.

2.3.2 Ps emission, trapping and reflection

The main processes which can occur at the surface in competition with the e+ emission are briefly discussed below. The first is the formation of Ps with energies much greater than the thermal values. Although Hasegawa et al (1985), from angular .correlation studies, have obtained evidence of the formation of Ps in the voids of

neutron-irradiated vanadium, in pure crystalline metals Ps has not been observed to form in the solid bulk. Rather, e" pick-up by the outgoing e+ occurs at the surface where the electron density falls to =1/1 Oth of the bulk values (Held and Kahana, 1964, Lowy and Jackson, 1975). From conservation of energy, the Ps energy Eps, can be calculated from

Ep, = <1>_+<J>+—Eb 2.17

where E*, is the binding energy of positronium. Ps formation is always a favourable process in metals with negative <j)+ since the energy required to remove the electron is compensated by Eb thus making Epf negative.

A non-adiabatic model of Ps formation at the surface has been proposed by Mills et al (1983) in which the removal of the electron leaves the metal in an excited state. The resulting Ps energy has a maximum value of Epf and a spread corresponding to the density of states of the electrons at the surface. In their investigation, the energy spread of the normal component of the energy of the Ps emitted from an Al(100) surface was measured (Figure 2.9) and found to be in accord with the above model

7 7

(represented by the solid line). An adequate explanation for the discrepancy at energies <leV has yet to be offered.

Ps emitted with energies greater than Epf have been observed by Howell et al (1986) from LiF samples and have been attributed to the formation of Ps by backscattered epithermal positrons. This process is discussed in Section 4.2.1.

The trapping of positrons at the surface in wells created by the attraction from the image induced potential with the correlation potential was first predicted by Hodges and Stott (1973a). Positrons at the surface were estimated to be bound with energies of l-3eV by Nieminen and Hodges (1978) and possess a lifetime against annihilation of 2-3 times of that in the bulk. Evidence of e+ trapping was obtained by Mills and Pfeiffer (1979) when the energy distribution of the Ps emitted from a C u ( lll) surface was observed to be temperature dependent. In this study, a time-of-flight technique was used to measure the Ps velocity by detecting the Ps annihilation y-rays in coincidence with the pulsed incident e+ beam. They observed that at 30°C Ps was formed with energies corresponding to those relating to the workfunction process described above. However, at a sample temperature of 790°C, an additional delayed component was found which correlated to Ps of mean energy 0.14eV and a non- Maxwellian thermal distribution. The authors attribute this to desorption of surface trapped e* as Ps. This effect is illustrated in Figure 2.10 from Mills (1981a).

Lastly, the e+ can undergo reflection at the surface potential. Nieminen and Oliva (1980) have shown this process to be temperature dependent, predicting a decrease in the emission rate of e+ and Ps to zero at OK. Trapping of e+ was calculated to be temperature independent. Subsequent studies did not provide support but indicated a weak temperature dependence (Lynn et al, 1981, Schultz and Lynn, 1982). However, the recent study of Britton et al (1989) has demonstrated a temperature related variation of the e+ and Ps yields from C u ( lll) and Al(110) surfaces which can be described in terms of quantum mechanical reflection at the surface potential. They demonstrated that the elastically transmitted thermal e+ flux would vanish at OK for a negative <J)+ surface and attributed the discrepancies with the earlier studies to insufficient separation of the thermal and epithermal contributions.

o Experimental data Calculated data 2 CLEAN SURFACE Ui _J < m tc 1 H