Hatano Y., Katsumura Y., Mozumder A. (Eds.) Charged Particle and Photon Interactions with Matter - Recent Advances, Applications, and Interfaces

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140 Charged Particle and Photon Interactions with Matter

where

is the depth of the potential for Ps

r is the radius of the potential

is the surface tension

p is the pressure

(U, r) is the Ps zero-point energy in the bubble. The second term is the energy of the surface, and

the third term is the volume energy. The bubble is stable at the minimum of the total energy, E.

Therefore, the bubble size is larger at smaller surface tensions, which means that it will be larger

also at higher temperatures. Figure 7.3 shows the temperature dependence of o-Ps on the positron

annihilation lifetime (PAL) in neopentane (Jacobsen et al., 1982: 71). Since, at higher temperatures,

the bubble size is larger as the surface tension is lower, the lifetime of o-Ps is also longer. Above the

critical temperature, T

, there is no effect of the surface tension, and hence there is no temperature

dependence

on the o-Ps lifetime, that is, the bubble size.

lower temperatures, Ps is squeezed out from the bubble due to large surface tension. Very

interesting phenomena were observed for one liquid and some solids (Mogensen, 1994, 377;

Goworek, 2007, 318). In liquid CS

, Ps is squeezed out from the bubble because of the large surface

tension and large electron and positron afnities of CS

. The zero-point energy of Ps elevates due

to large surface tension, and then the Ps electron and positron prefer to smear out on the molecules,

even though the positron and the electron interact with each other due to Coulomb attraction. This

is called the fourth positron state. The transition from the Ps bubble state to the fourth positron state

is indicated in Figure 7.4 (Hirade, 1996: 2153). This state was conrmed by adding 1M of methanol

to CS

. The energy level of the fourth positron state is lower in methanol, and therefore the transition

to this state appeared at higher temperatures, as shown in Figure 7.4 (Hirade, 1996: 2153). Pressure

also

affects the bubble size and Ps formation (Kobayashi, 1992: 1869).

7.3.2 ps in SolidS

The repulsion between Ps and molecules exists even in molecular solids. If there are open volumes

like vacancies or vacancy clusters, Ps will be trapped. Moreover, positrons and electrons can be

trapped by these defects, which will affect Ps formation. Probably, Ps chemistry in solids is more

complicated

than in liquids.

100

0.1 1

Radius (nm)

Annihilation lifetime (ns)

10 100

Figure 7.2 Annihilation lifetime of the o-Ps measured in various porous materials as a function of average

pore radius. The dashed line is a calculated correlation curve. (Reprinted from Ito, K. et al., J. Phys. Chem. B,

103,

4555, 1999. With permission.)

Positron Annihilation in Radiation Chemistry 141

Several very interesting effects can be observed in solids. One of them is the Ps Bloch state in

crystals. It was found only in some very brittle solids. The rst experimental evidence of the Bloch

function state for Ps was found in quartz (Brandt, 1969: 522), MnF

(Coussot, 1970), and later for

O and D

O ice (Mogensen et al., 1971: 71), and in several alkali halides at LN

and LHe tem-

peratures (Hyodo and Takahashi, 1977: 1065; Kasai et al., 1988: 329). Ice is the only molecular

crystal in which the Ps Bloch function was found, as shown in Figure 7.5 (Mogensen and Eldrup,

1978: 85). The Bloch function state can be detected by angular correlation of annihilation radia-

tions (ACAR) (see Section 7.4.4). The curve shown in Figure 7.5 is only the component of the p-Ps

0.0

20 60 100

Temperature (°C)

Lifetime (ns)

140 180T

0.2

0.4

0.6

0.8

Liquid neopentane

Figure 7.3 Temperature dependence of the positron lifetimes in liquid neopentane as obtained fromlife-

time spectra resolved into three exponential components. T

is the critical temperature. (Reprint from Jacobsen,

F.M.

et al., Chem. Phys., 69, 71, 1982. With permission.)

–120 –100 –80 –60 –40

Temperature (°C)

o-Ps intensity (%)

–20 0 20 40

Figure 7.4 Intensity of the longest-lifetime component, that is, o-Ps, versus measuring temperature.

Open circles indicate the results for pure CS

and lled squares are for 1 M methanol/CS

142 Charged Particle and Photon Interactions with Matter

intrinsic annihilation, that is, the broad components of free positron and o-Ps pick-off annihilation

are subtracted. Another broad component appears at higher temperatures. It is the component of the

intrinsic

annihilation of p-Ps localized on vacancies.

Irradiated

ice was also studied using positron techniques (Eldrup, 1976: 5283). Figure 7.6

shows the measured temperature dependence on PAL for irradiated ice at −196°C. In this case,

the lifetime spectra were analyzed with four lifetime components, because there were two differ-

ent vacancies that give two different lifetimes of the o-Ps pick-off annihilation. One of these had

= 1.20 ns that was considered to be the o-Ps pick-off annihilation in mono-vacancies. The other

had τ

, that is, the o-Ps pick-off annihilation in vacancy clusters. The change of τ

can provide the

information of change of the cluster size. I

is the intensity of p-Ps, I

is the intensity of the pick-

off annihilation of o-Ps in mono-vacancies, and I

is the intensity of the pick-off annihilation of

o-Ps in vacancy clusters. There was inhibition of Ps formation below −180°C, which was caused

by hydroxyl radicals formed by irradiation. τ

was initially about 2.3ns, probably the lifetime of

the divacancies, and it increased by elevating the temperature. This indicates the increasing size

of the clusters. Then I

and I

decreased simultaneously because of the decrease in the number

density of vacancy clusters. Above 130°C, the concentration of clusters became so low that Ps

trapping could not be detected.

–10

Broad component

at –181°C

Single crystals

of ice

[0001]-direction

Counts (arb. units)

–181°C

–96°C

–80°C

–69°C

–52°C

–35°C

–26°C

–16°C

–1°C

+2°C

–5 0

Angle (mrad)

5 10

–181°C

Figure 7.5 Temperature dependence of the ACAR spectra for single crystals of H

O ice oriented

along the a-axis. The broad component was subtracted. (Reprinted from Mogensen, O.E. and Eldrup, M.,

Positronium Bloch function, and trapping of positronium in vacancies, in ice, Risø Report No. 366, 1977.

With permission.)

Positron Annihilation in Radiation Chemistry 143

7.4 experimental teChniQues

Positron methods can be one of the important tools to study radiation chemistry, as mentioned

above, because Ps formation is the result of the fast spur reactions and very short lifetime of posi-

trons in condensed matter. Hence, positron annihilation methods are very useful for radiation chem-

istry. Therefore, only the methods related to the positron annihilation techniques used for the study

radiation chemistry will be discussed here.

–200

0.0

4.0

Lifetime (ns)Relative intensity (%)

8.0

12.0

80 100 120 140

=1.20 ns

160

(K)

–180 –160

Temperature (°C)

–140 –120 –100

Figure 7.6 Lifetime results for pure H

O ice gamma-irradiated at −196°C and measured as a func-

tion of increasing temperature. (○) Polycrystalline samples (11 Mrad), (△) single crystals (4.1Mrad), and

(□) another single crystal (11 Mrad). (Reprinted from Eldrup, M., J. Chem. Phys., 64, 5283, 1976. With

permission.)

144 Charged Particle and Photon Interactions with Matter

7.4.1 poSitron Source

A positron is the antiparticle of an electron. We need to employ some special methods to obtain

positrons. The most convenient method is the use of radioisotopes. There are some radioisotopes

that emit positrons. A list of positron emitters is given in Table 7.1.

Na is the most common radio-

isotope. There are some reasons why it is often used. A γ-ray of 1.28MeV emitted almost simultane-

ously with a positron is one of the reasons. A γ-ray of 1.28MeV is very convenient because it gives

information of the time of the positron emission, and hence the time interval between the 1.28 MeV

γ-ray and 511keV annihilation γ-rays gives information of the lifetime of the positron. Another

reason why

Na is often used is its longer half-life of 2.6 years. It is possible to use the same source

for

several years.

The

maximum energy of positrons emitted from

Na is 540keV. Radioisotopes are usually

shielded by polymer or metal lms. An

Na source of about 400kBq shielded by Kapton or Mylar

lms is often used for PAL, Doppler broadening (DB), and age-momentum correlation (AMOC)

measurements. Kapton is a polyimide and has no Ps formation. It means that there is just one anni-

hilation-lifetime component of the free positron that is about 380ps. It is easy to subtract the PAL

component from the measured spectra. Kapton lms having a thickness of about 7.5μm areoften

used. It is necessary to know how many positrons will annihilate in the lm to subtract the annihila-

tion

component in

the

source lms from

the

spectra. It is possible to

estimate

this by calculation or

experiment. For example, the lifetime in well-annealed metals has just one short-lifetime component

and the fraction of positron annihilation in the lm can be estimated. There seems to be the effect

of back-scattered positrons, that is, the fraction of positron annihilation in the lm will be larger for

heavier samples. It is difcult to estimate it experimentally for samples with a free-positron lifetime

of about 400 ps. For these samples, it is necessary to assume the fraction of positron annihilation in

the

lms. Usually, a fraction of 10%–12% is used.

Recently,

it is possible to buy sources for these methods. A shielded

Na source of less than

1MBq

can be used in laboratories that are not specially installed for handling radioisotopes.

For

angular correlation measurements or mono-energetic positron beams, stronger shielded

positron sources (400–4000 MBq) are used. Pair production by high-energy radiation is also

used for creating a large amount of positrons for intense positron beams (Suzuki et al., 2000: 603;

1991: L532).

7.4.2 poSitron annihilation lifetiMe MeaSureMent

The most important and common positron annihilation method is the PAL measurement. For PAL,

Na is the most common positron source, because it emits a positron and a prompt γ-ray of 1.27MeV,

almost simultaneously. The dominant decay scheme is indicated in Figure 7.7. The detection of

table 7.1

Characteristics

of s

ome

Common p

ositron-emitting

adioisotopes

radioisotopes Fraction of e

half lifetime maximum energy (mev) prompt γ energy (mev)

C-11 99% 20months 0.97 —

Na-22 90% 2.7

years 0.54 1.28

Ti-44 (as Sc-44) 88% 47 years 1.47 1.16

Ni-57 46% 36

h 0.40 1.4

Co-58 15% 71

days 0.48 0.81

Cu-64 19% 12.8

h 0.66 —

Zn-65 1.7% 245

days 0.33 —

Ga-68 (from Ge-68) 88% 275 days 0.98 —

Positron Annihilation in Radiation Chemistry 145

a1.27MeV γ-ray indicates the emission of a positron. The annihilation of a positron with an electron

can be observed by the detection of one or two annihilation γ-rays. In condensed mater, the energy

of the annihilation γ-ray is about 511keV, as almost all of the annihilations give two γ-rays. The

detection of a 511keV γ-ray indicates the annihilation of a positron. Therefore, the time interval of a

coincident event of two γ-rays, 1.27MeV and 511keV, will be the measured PAL.

This is the gamma–gamma coincidence method. There is one more method that can be applied

for measuring the PAL. It is the beta–gamma coincidence method. A positron injecting into a sam-

ple is observed by a beta-particle detector. If the energy of the positron is very high, scintillators can

be used as the detector (Castellaz et al., 1996: 457). If radioisotopes are used, thin photodiodes

can be used as the detector (Chalermkarnnon et al., 2002: 1004). There are some advantages of

thismethod. One is that a prompt γ-ray is not necessary. The second advantage is a lower random

coincidence background on the PAL spectra. However, there are some disadvantages too. One of

them is the difculty in obtaining a good time resolution because of the time-of-ight of the posi-

tron

coming into the sample (Chalermkarnnon et al., 2002: 1004).

The

most common PAL setup is shown in Figure 7.8. Fast scintillation detectors should be used to

obtain a good time resolution. Therefore, the scintillators used should be BaF

or fast plastic scintil-

lators. The BaF

scintillators have larger efciencies but a slower luminescence component. When

the counting rate is high, piling up of fast and slow luminescence components will shift theenergy

spectra; therefore, the energy windows selected by the single-channel analyzers (SCAs) of the

2+ 1.2746

90%

EC 10%

0.05%

3 ps

2.60y

Figure 7.7 The dominant decay scheme of

Na.

MCACF/SCA CF/SCA

Start

Stop

Source/sample

sandwich

delay

TAC

Figure 7.8 The most common PAL setup.

146 Charged Particle and Photon Interactions with Matter

constant fraction (CF) cannot detect the objective signals. The photomultiplier (PM) tubes need

quartz windows because the fast luminescence component is ultraviolet light. The PM also should

have a fast rise time of the signal. The PM tube used most often is H3378-51 (Hamamatsu) and has a

rise time of 0.7ns. The most important module for PAL is a CF discriminator, which is supplied by

many companies. The signals from PM tubes come into CF/SCA directly without inserting preamps.

These signals should be large enough to be selected by SCA. Then, two sets of detectors and CF/SCA

supply the timing signals for positron birth and death. The time interval should be converted into

amplitude of the output using a time-to-amplitude converter (TAC). Then the lifetime spectra can

be viewed using a multi-channel analyzer. This is the conventional PAL measurement technique.

Some important information is introduced here. It is most important to reject the piling up of the

1.27MeV γ-ray and one of the annihilation γ-rays. The geometry one can obtain for a good count-

ing rate is to place the sample and the source assembly in the middle of the detectors. One of the

detectors is used for the 1.27MeV γ-ray and the other is used for one of the annihilation γ-rays. One

should not forget that there is one more annihilation γ-ray that will go in the opposite direction of

the other annihilation γ-ray. It means that it will enter the detector for the 1.27MeV γ-ray, and then

two signals will easily pile up. This will affect the lifetime spectra, and the articial short-lifetime

component will easily appear. It is also important to have enough knowledge of the interaction

between γ-rays and the materials. When one prefers to have a large counting rate, one tends to apply

the wider energy windows. If wider energy windows are applied for the 1.27 MeV γ-ray including

the Compton area, scattered γ-rays can enter the detector for the annihilation γ-rays. It means that

articial counts appear near time zero on the lifetime spectra.

Recently, it has become possible to use digital storage oscilloscopes (DSOs) to store all of the

waves from detectors. One of the advantages of applying DSOs is that several analyses with differ-

ent parameters can be performed. For example, it is possible to select the wave data by adjusting

energy windows. Moreover, when one nds something strange on the spectra, it may be possible

to nd the cause. The biggest advantage is that the triple coincidence measurement is quite easy.

This measurement has two stop detectors for both of the annihilation γ-rays. It provides better time

resolution

(Saito et al., 2002: 612).

7.4.3 doppler broadening MeaSureMent

The peak width of the whole absorption peak of annihilation γ-rays observed by Ge detectors is

wider than those of the other γ-rays. It is caused by the Doppler shift by the momenta of an electron

and a positron just before the annihilation. It means that it is possible to obtain information of elec-

tron and/or positron momenta in the materials. p-Ps annihilation is intrinsic, and the momenta of the

electron and the positron cancel out each other. And hence, the energy of the annihilation γ-rays is

very close to 511keV, which is equivalent to the rest mass of an electron (or a positron). On the other

hand, o-Ps and free positrons annihilate by picking off one of the electrons from the surrounding

molecules. This means that the energy distribution of the annihilation γ-rays is wider because of the

Doppler shift. A so-called S parameter is often used to indicate the annihilation γ-ray energy distri-

bution. The value of S is the ratio between the counts appearing in a xed central area and those in

the entire peak area. The narrower the peak, the larger is the S value.

With spin conversion reactions, p-Ps annihilation increases and the distribution of the annihila-

tion γ-ray energy becomes narrower. These reactions are difcult to detect by just the lifetime mea-

surement. There are many researches carried out using the lifetime and Doppler shift measurements

(Komuro

et al., 2007: 330).

7.4.4 age–MoMentuM correlation MeaSureMent

AMOC is the combination of PAL and DB, as shown in Figure 7.9. The most important use of

AMOC in radiation chemistry is in determining the time-resolved DB. Fortunately, there are two

Positron Annihilation in Radiation Chemistry 147

annihilation γ-rays in many cases. One of them is used for PAL and the other is used for DB, and

hence the DB measurement with the annihilation time stamp is possible. Afterward, it is possible

to construct a DB spectrum at the specic range of the positron annihilation time stamps. As men-

tioned above, DB is an effective tool for the investigation of the annihilation from p-Ps. This method

can provide the information of the positron annihilation process, for example, the Ps formation

process and spin conversion reactions (Castellaz et al., 1996: 457; Komuro et al., 2007: 330). The

details

are given in Section 7.6.7.

7.4.5 other techniQueS

ACAR is also a very important method. It measures the angular correlation between two annihila-

tion γ-rays. The shift from 180° can indicate the shift on the sum of the momenta of the annihilated

electron and the annihilated positron. The obtained information is almost the same as DB, but the

resolution is much better. On the other hand, it is necessary to use much stronger sources so that

the positron irradiation effect is very large. Therefore, it may be difcult to apply ACAR in studies

of polymers.

The Ps Bloch state in crystals can be observed as shown in Figure 7.5. Many liquids are measured,

and the ACAR measurement could give very important information on the positron state in liquids.

Unfortunately,

now there may be no ACAR method that can be applied for liquid measurements.

Positrons

annihilate with one of the electrons from molecules or atoms, which means that a

positron can be used to create cations. This phenomenon was used in some methods. One of them is

the

Auger electron measurement. Usually,

Auger electrons

are

obtained

by the ionization produced

by electron irradiation. However, the background is usually very large, because many secondary

electrons also enter the detectors. Nevertheless, there exists no background for the positron Auger

method, because low-energy positrons are used instead of high-energy electrons. Sometimes oxy-

gen exists as an impurity on the surface, but it can be detected effectively by the positron Auger

method

due to its large positron afnity (Ohdaira et al., 1997: 177).

100,000

10,000

Counts

1,000

100

490

511

Energy (keV)

Time (ns)

532

–2

Figure 7.9 AMOC spectrum of water.

148 Charged Particle and Photon Interactions with Matter

7.5 positronium Formation

If a positron is placed in a material, Ps does not form. The binding energy of Ps is 6.8eV in vacuum,

which is smaller than the ionization potentials of molecules or atoms. This means that positrons in

materials cannot pick off electrons to form Ps. A fast Ps formation model, the so-called Ore model,

was proposed by Ore in 1949 (Ore, 1949). As mentioned above, extra energy is necessary to pick off

an electron from molecules or atoms; therefore, the idea of the Ore model is to supply the necessary

energy from the kinetic energy of the positron. This model can explain the Ps formation in rare gases.

However, this model cannot explain the Ps formation in condensed materials. In 1974, Mogensen

proposed the spur model (Mogensen, 1974: 998) that could explain the Ps formation in condensed

materials. In the case of the Ore model, extra kinetic energy from the positrons can make Ps forma-

tion possible, while in the case of the spur model, the production of free or quasi-free electrons makes

Ps formation possible. Injected positrons will make spurs on the track of positrons and will be ther-

malized at the end of the track. The structure is similar to that indicated in Figure 7.10 (Mogensen,

1974: 998). Therefore, it is quite possible to have free electrons near the thermalized positrons, which

allows Ps formation. This model could well explain qualitatively the experimental results.

However, in 1980s, a very large enhancement of Ps formation at low temperatures was reported

for many materials (Kindl and Reiter, 1987: 707). This enhancement could not be explained by the

spur model, which was the main reason why some people did not accept this model. Until almost

theend of the twentieth century, this Ps formation enhancement had not been explained, and so,

some people used other models. One of these models was called the free volume model of Ps forma-

tion, which was often applied to discuss polymer physics (Jean, 1993: 569). The basic idea of this

model was as follows. The measured o-Ps lifetime was always the longest and clearly identied by

the PAL measurement. The long o-Ps lifetime indicates that there were empty spaces for o-Ps in the

materials (see Figure 7.2). Hence, something like a hole (which does not mean the positively charged

species) was needed for Ps formation, and thus, more holes could produce more Ps. Some people

believed that the total free volume could be obtained by the free volume hole size observed by the

o-Ps lifetime (see Figure 7.2) and the number of holes observed by the Ps formation probability.

Secondary tracks

Spurs

Terminal spur

–

Figure 7.10 Structure of terminal spur of the positron track.

Positron Annihilation in Radiation Chemistry 149

The measured slow enhancements of Ps formation at low temperatures were used for the study of

polymer physics. It was believed that the slow enhancement observed at low temperatures showed

the

physical change of polymers that could not be observed by other methods.

can be in the delocalized state in crystals. It means that the empty spaces are not needed for

Ps formation. There is no Ps formation in some polymers, such as Kapton, which is a polyimide,

even though there must exist some free volume. Indeed, any reasonable explanation has not been

obtained

by the free volume model until now.

1998, a new explanation of the appearance of Ps formation enhancement at low tempera-

tures was given by Hirade (Hirade et al., 1998: 89; 2000: 465; Wang, 1998: 4654). The Ps for-

mation enhancement, observed by the PAL measurement at low temperatures, appeared slowly.

He explained it by the accumulation of shallowly localized electrons, such as trapped electrons.

However, shallowly localized electrons are stable and live for a long time at low temperatures

because the molecular motions are frozen. Positrons in materials cannot pick off electrons from

molecules or atoms to form Ps, as mentioned above, because of the larger ionization potentials of

molecules or atoms than the Ps binding energy. The binding energy of shallowly localized electrons

is usually 0.5–3eV, which is smaller than the Ps binding energy. It means that positrons can pick off

shallowly localized electrons without the need of extra energy to form Ps. Thus, Ps can form just by

placing

positrons in the materials where many shallowly localized electrons exist.

This

Ps formation process proposed by Hirade can explain many phenomena, such as Ps formation

quenching by visible light (Hirade et al., 1998: 89; 2000: 465), relationship between the density of the

shallowly localized electrons and Ps formation enhancement (Hirade et al., 2000: 465), and delayed

Ps formation caused by the diffusion of positrons (Suzuki et al., 2003: 647; Hirade et al., 2007: 3714).

The free volume model often used for Ps formation at low temperatures cannot explain the Ps

formation quenching by visible light, while the Ps formation process proposed by Hirade and the

spur model proposed by Mogensen could explain Ps formation at any temperatures. It was accepted

that radiation chemistry processes are very important for Ps formation (Hirade, 2007: 84).

7.6 radiation Chemistry studies by positron annihilation

7.6.1 coMpariSon of the yieldS of hydrated electronS obServed by pulSe radiolySiS

Positron annihilation methods can provide some information regarding fast reactions in spurs, as

pulse radiolysis experiments can. Duplatre and Jonah tried to compare the positron and pulse radiol-

ysis experiments. The electron scavenger effects observed in aqueous solutions are studied for both

these methods. The inhibition of hydrated electron formation and Ps formation showed very similar

tendencies, as shown in Figure 7.11, and hence it was claried that the precursor of Ps was mainly

free electrons or quasi-free electrons (Duplatre, 1985: 557). As the Ps formation time is about 1ps in

common materials, the yields of Ps formation will give information of free or quasi-free electrons

similarly as the yields of hydrated electrons observed by pulse radiolysis experiments. The most

important detection method applied for pulse radiolysis is light absorption, which can make very

fast experiments possible. This implies that only the species that absorb light can be detected by the

fast pulse radiolysis experiments. On the other hand, Ps formation yields can beobtained as the

longest-lifetime component by the PAL measurement, which means that the precursor of Ps, that is,

free

or quasi-free electrons, can be detected by positrons.

7.6.2 coMpariSon of electron Mobility experiMentS

There is one more advantage of applying positron methods, which is the short lifetime of positrons.

In condensed materials, the longest lifetime is given by o-Ps, which is usually less than 4–5ns. This

means that small amounts of impurities do not affect the yields of Ps very much. Therefore, it is not

necessary to have very pure samples. In some cases, very pure samples are needed, for example