M ODERATED

10'\

10' \

E M IT T E D P O SITR O N SPEC TRU M FOR C o -5 8

10'":

TTttr

ln [E (e V )]

Figure 1.8. Comparison of the slow positron yield from a W(IOO) moderator with the P spectrum from a ^®Co source.

The p o s s i b i l i t y that positrons with near thermal energies could be o b t a i n e d by implanting part i c l e s from a r a d i oactive source into a solid was first s u ggested by Ma d a n s k y and Rasetti (1950). They e s timated that the e f f iciency of such a m o derator w o u l d be deter m i n e d by the ratio between the positron d i f f u s i o n length and the m e a n implantation d e p t h of the incident (3'^ particles. This they calculated to be of the order of 1 0^ for the samples used in their experiment. Here, a ^ C u p o s i t r o n source w i t h an a ctivity of (10-3 0)mCi was used to irradiate various samples including Pt, g l ass and mica. The slow posit r o n s w ere to be confined by a m a g n e t i c field and detected by o b serving 7-rays from their a n n i h i l a t i o n on an Al foil, arou n d 80cm from the sample. Unfortunately, M a d a n s k y and Rasetti (1950) were unable to d e tect any low energy positrons, prob a b l y due to the low s e n s itivity of their apparatus and defective samples. They did however, attribute the zero y i e l d to p o s i t r o n trapping in the samples and Ps formation; two processes that have s ubsequently been shown to be of great importance.

The first observation of slow p o s i t r o n emission from a metal surface was made by Cherry (1958) . Positrons were found to be emitted w i t h energies of less than lOeV from Cr plat e d mica when irradiated with 13'^ p articles from a ^Na source. The ratio between the number of slow positrons to fast 0+ particles was found to be around 1 0*.

The importance of this result was largely u n a p p r e c i a t e d until 1969, w h e n M a d e y (1969) p e r f o r m e d a similar experiment with p o l y e t h y l e n e and Groce et al (1969) r eported that a slow posit r o n flux w i t h energies of a few eV h a d been o btained from Au. Here an A u surface was b o m b a r d e d w i t h fast p ositrons obtained from p a i r produ c t i o n in a Ta converter by the br e m s s t r a h l u n g r a diation p r o d u c e d by a 55MeV b e a m of electrons from a linear accelerator. This w o r k was e xtended by Costello at al (1972) who m e a s u r e d the energy d i stributions of slow positrons emitted from an appro x i m a t e l y 2 00Â thick layer of Au, depos i t e d on mica, CsBr and Al substrates. The energy d i stributions w ere m e a s u r e d u s i n g a

time of flight technique and were found to p e a k between 0.75 and 2.90eV. It was proposed for the first time that this energy was due to a negative p ositron w o r k function of the surface. Costello et al (1972a) went on to use this flux of slow positrons to make the first p o s i t r o n - a t o m total scattering cross section measurements. This w o r k is d iscu s s e d in § 1.5.

A positron work function (#+) m a y be defined, in an analogous way to the electron work funct i o n (0.) as the m i n i m u m energy required to move a p o s i t r o n from a p oint well inside the surface to a point well outside. If 0+ is negative, positrons are ejected from the surface w ith kinetic energies approximately equal to 0+.

Lang and Kohn (1971) defined 0. as

<|)_ = A(p - \ i _ (1.7)

wh ere jii. is the bulk chemical p o tential of the electrons, relative to the mean electrostatic p o t e n t i a l in the metal interior and Acp is the rise in mean e l e c t r o s t a t i c potential across the surface. The surface dipole, A<p, is caused by the electron gas from the metal interior, spill i n g out beyo n d the last atomic layer and into the vacuum. This is shown in figure 1.9. Here the ion-core potential is r e p r e s e n t e d by a u n i f o r m background, equal to the a v e rage interstitial potential, according to the jellium model. The combined effect of this and the electron gas, w h i c h as already mentioned, spills out of the surface, creates a dipole m o ment across the surface and tends to bind elec t r o n s to the solid.

Tong (1972) p roposed that the surface dipole

c o ntribution to 0+ should have an equal m a g n i t u d e but opposite sign to A<p and hence

4)+ = -Acp - (1.8)

where is the bulk chemical poten t i a l of a positron, relative to the mean electrostatic p o t e n t i a l in the metal interior. Since the surface dipole has the o pposite sign for a positron, this will tend to make p o s i t r o n s escape from the

surface. It is the cancellation between and A<p that causes 0+ to be close to zero, or negative in many cases. The potentials a p ositron or electron sees close to a metal surface are repr e s e n t e d in figure 1.9. This shows that for a p o s i t r o n there is an attractive poten t i a l well just outside the surface. This is due to the image p o tential seen by the posi t r o n at large distances and the c o r r elation w ith the electron gas spilling out of the metal surface at small distances.

Tong (1972) predicted negative values of 0+ of a few electron-Volts for Al, Mg, Cu and Au. The w o r k function of Au has since been experimentally m e a s u r e d to be positive

(Nieminen and Hodges 1976, Lynn 1980 [unpublished]). The

e Jellium b ackground z electrons vacuum e -e n e rg y vacuum Level L<p e *e n e rg y vacuum Level

Figure 1.9. The potentials seen by a positron and an electron near the surface of a metal.

results of Costello et al (1972) may t h e r e f o r e be ascr i b e d to epithermal p ositron emission or sample impurities causing (f>+ to become negative.

A 300-fold improvement in m o d e r a t i o n e f f i c i e n c y was achieved by Canter et al (1972) from an Au m o d e r a t o r c o nsisting of vanes arranged in the form of a V e n e t i a n blind coated with MgO. This was bombarded w i t h fast posit r o n s from ^^Na to obtain a flux of slow positrons. The e n ergy spread of the slow positrons was around 3eV and the m o d e r a t i o n e f f iciency was approximately 3x10^. This was u s e d to meas u r e the total cross-section of He as d i s c u s s e d in § 1.5.

An alternative method of slow p o s i t r o n beam produ c t i o n was developed by Stein at al (1974) . A B t a rget was b o mbarded w i t h 4.75MeV protons from a Van de Graff g e n e r a t o r to produce positrons from the decay of "c, p r o d u c e d by the reaction ^^B(p,n)'*C. The B target also acted as the m o d e r a t o r and

positrons emitted from the surface w e r e extracted

electrostatically, with an energy spread of around O.leV. The efficiency of this type of moderator was e s t i m a t e d to be around 10^. These slow positrons were u s e d to m a k e the first observation of a R a msauer-Townsend m i n i m u m in p ositron elastic scattering cross-sections, as d i s c u s s e d in § 1.5.

Further study of the moderation p r o p e r t i e s of various p oly- c r y s t a l l i n e moderators was carried out by P endyala et al (1976). An increase in slow posit r o n y i elds after heat treatment was reported, with the h i g hest y i e l d o btained from Cu after baking at 4 50K for several hours.

Until the work of Mills et al (1978) , all investigations had been p e rformed with samples of u n k n o w n structure and purity. This had h indered progress in the u n d e r s t a n d i n g of the m o d e r a t i o n process. Mills et al (1978) investigated p o s i t r o n emission from clean single crystal surfaces of Al, Cr and Si, w i t h known crystal orientations, b o m b a r d e d w ith positrons of known energies. A ^Co source and Pt m o d e r a t o r was u sed to produce a flux of slow p o s i t r o n s of v a r i a b l e mean energy, which were used to bombard targets w i t h energies from (0.1-3.0)keV. The annihilation of p o s i t r o n s at the target was

me a s u r e d by detection of the a n n i h ilation 7-rays and the energy spectrum of the slow positrons was d e t e r m i n e d by recording the annihilation rate as a function of a negative potential applied to the target. The energy d i s t r i butions were measu r e d for different target tempe r a t u r e s up to 500°C. Mills et al (1978) p roposed the following m e c h a n i s m for the thermalisation, diffusion and emission of p o sitrons from m e t a l s .

A f t e r implantation in a m o derator material, p a rticles with energies less than a few MeV m a y initially lose kinetic energy to electrons in the bulk of the solid by inelastic processes such as core excitation, p l a s m o n emission and electron-hole pair creation. Niem i n e n and Oliva (1980) e stimated that such positrons w ould have reac h e d energies of

a few eV after around lO'^s. After this, near-thermal

equilibrium with the lattice is achieved, p r e d o m i n a n t l y by p honon scattering in around 10‘^^s (Perkins and Carbotte 1970) . A typical non-thermal p ositron will diffuse about 30Â in this

time. Therefore, positrons impacting the surface w ith

energies in the keV range, will t h e rmalise before r eaching the surface, since the mean implantation depth will be of the order of 100Â (Mills et al 1978) . At the surface the surviving positrons may form Ps, become t r a p p e d in a surface state, be reflected or, if the surface has a n egative be ejected into the vacuum.

M u r r a y and Mills (1980) m e a s u r e d the m o d e r a t i o n efficiency of Cu and Al as a function of 0 + by v a r y i n g the crystal orientation and the amount of S on the surface. The result for Cu is shown in figure 1.10, showing an increase in efficiency as 0+ is m a d e more negative.

D ale et al (1980) then m easured the slow p o s i t r o n y ield from a variety of samples with d i f f e r e n t structural characteristics. The highest mode r a t i o n e f f i c i e n c y was around 7x10^ from p o l y - crystalline W vanes that had been chemi c a l l y etched and heated to 2200°C. Dale et al (1980) showed that the h eat treatment was a more important factor than surface cleanliness in determining moder a t o r efficiency, since

2 0.4

1.2

0 0.4 0.6

p *(e V )

e. A, ■ Experimental

----, --- Theoretical

Figure 1.10. The slow positron yield from a Cu surface as a function of

<p+ (Murray and Mills 1980) .

annealing increases the degree of atomic order in the moderator. This causes there to be fewer defects w hich may act as positron traps (as ment i o n e d in § 1.3).

Using a clean, single crystal W sample, V e h a n e n at al (1983) obtained a m o d e r a t i o n effi c i e n c y of around 3x10^, which is around 75% the m a x imum p o s s i b l e efficiency, as calculated by V e h a n e n and M a k i n e n (1985).

Some of the diffe r e n t s o u r c e-moderator geometries that have been employed are shown in figure 1.11. Figure 1.11a) shows the back-sca t t e r i n g conf i g u r a t i o n in w h i c h particles are implanted onto a flat, usually single crystal, m aterial and slow positrons are extracted from the same surface. If this is clean, p o sitrons are emitted a l m o s t n ormally with

e*

>

X / . _

/

(a)

_(b)

(c)

(d)

Figure 1.11. Typical source/moderator arrangements showing a)

backscattering b) vane c) grid and d) transmission configurations.

only a small transverse component due to thermal energies. A d i sadvantage of this arrangement is that the source obscures p art of the moderator and so this geome t r y is only suitable for small sources with high specific activities e.g. ^Co depos i t e d on a needle or ribbon. Figures 1.11b) and c) show vane and grid arrangements. Here the posit r o n s emerge from the same surface as that entered by the parti c l e s but are ex tracted from the side opposite the source. W i t h this geome t r y the size of the source hold e r is u n i m p o r t a n t and commercially obtained ^^Na sources may be employed. The vane arrangement m a y be arranged to intercept the m a j o r i t y of the incident flux emitted in its direction, h o w ever the grid system has the advantage of ease of fabrication, alth o u g h the partial transparency m a y result in the t r a n s m i s s i o n of some

of the flux. Figure l.lld) shows the trans m i s s i o n m ode g e o m e t r y in w h ich positrons diffuse t h r o u g h moder a t o r s of thickness of a few thousand Â. This confi g u r a t i o n results in na r r o w energy and angular distributions and simplifies e lec t r o n optics since the input and output may be e lectrically screened.

All the m o deration techniques descr i b e d above use

negative work function materials. However, new high

e f f iciency moderators have been deve l o p e d based on mater i a l s p o s s e s s i n g positive values of these are the solid rare gas (RGS) and field assisted (FA) RGS moderators.

Mills and Gullikson (1986) c o ndensed Ne, Ar, Kr and Xe