Positron annihilation spectroscopy (PAS)Positron ... · Positron annihilation spectroscopy (PAS) is a nondestructive nuclear physics method allowing the study of condensed matter

Positron annihilation spectroscopy (PAS)Positron annihilation spectroscopy (PAS)

What is PAS?What is PAS?

How PAS works in amorphous matter?Pick-off annihilationTao-Eldrup model

How PAS works in amorphous matter?Pick-off annihilationTao-Eldrup model

How we do PAS?Doppler broadeningLifetime measurementsAMOC measurements

How we do PAS?Doppler broadeningLifetime measurementsAMOC measurements

What we get from PAS?What we get from PAS?+− +−

+−

What is PAS?What is PAS?

Positron annihilation spectroscopy (PAS) is a nondestructive nuclear physics method allowing the study of condensed matter microstructure in the scale as small as few tenths of nanometers through annihilation processes of positron and electron.

Positron annihilation spectroscopy (PAS) is a nondestructive nuclear physics method allowing the study of condensed matter microstructure in the scale as small as few tenths of nanometers through annihilation processes of positron and electron.

In non-conductive amorphous matter, the positron can extract an electron from surrounding material to form a semi-stable bound state called positronium (Ps). According to the mutual spin orientation of the positron and the electron two positronium states can be formed: the orthopositronium (oPs) and the parapositronium (pPs).The laws of conservation cause the oPs annihilates into as much as three photons and thus the oPs lifetime is thousand times longer than the pPs lifetime.

In non-conductive amorphous matter, the positron can extract an electron from surrounding material to form a semi-stable bound state called positronium (Ps). According to the mutual spin orientation of the positron and the electron two positronium states can be formed: the orthopositronium (oPs) and the parapositronium (pPs).The laws of conservation cause the oPs annihilates into as much as three photons and thus the oPs lifetime is thousand times longer than the pPs lifetime.

Ps oPs

pPs

(triplet)

(singlet)

3γ

2γ

lifetime ~ 1,42.10-7s


Ps oPs

pPs

(triplet)

(singlet)

3γ

2γ



How PAS works in amorphous matter?How PAS works in amorphous matter?

In an amorphous matter, however, the long orthopositronium lifetime is strongly reduced by the "pick-off" process. This process appears when the positron bound in the orthopositronium interacts and eventually annihilates with the other electron in the surrounding material.

In an amorphous matter, however, the long orthopositronium lifetime is strongly reduced by the "pick-off" process. This process appears when the positron bound in the orthopositronium interacts and eventually annihilates with the other electron in the surrounding material.


Pick-off annihilationPick-off annihilation

2γ pick-offprocess

lifetime ~ 10-9s ~ free volume hole size

Ps oPs

pPs

(triplet)

(singlet)

3γ

2γ



Ps oPs

pPs

(triplet)

(singlet)

3γ

2γ



The probability of the pick-off annihilation process can be described by the semi-empirical Tao-Eldrup model, which allows to relate the "pick-off“ orthopositronium lifetime to the mean radius of the free volume sites.

The probability of the pick-off annihilation process can be described by the semi-empirical Tao-Eldrup model, which allows to relate the "pick-off“ orthopositronium lifetime to the mean radius of the free volume sites.

Pick-off annihilationPick-off annihilation


free volumePs

electron layer

This makes the PAS studies of amorphous matter unique and very useful, e.g. in free volume studies of polymers from glassy to liquid state.

This makes the PAS studies of amorphous matter unique and very useful, e.g. in free volume studies of polymers from glassy to liquid state. +−


Positronium resides in a spherical potential well (radius R0) with a homogenous electron layer inside the wall (thickness ∆R), where the electron and the positron densities overlap. Using the probability P of Ps in the ground state inside the electron layer

Positronium resides in a spherical potential well (radius R0) with a homogenous electron layer inside the wall (thickness ∆R), where the electron and the positron densities overlap. Using the probability P of Ps in the ground state inside the electron layer

Tao-Eldrup modelTao-Eldrup model

drr4P 22

)RR( 0 Ps∫∞

∆−ψπ= drr4P 22

)RR( 0 Ps∫∞

∆−ψπ=

and the annihilation rate of positronium inside the electron layer (2ns-1) we get the connection between the pick-off annihilation lifetime and the radius of the free volume:

and the annihilation rate of positronium inside the electron layer (2ns-1) we get the connection between the pick-off annihilation lifetime and the radius of the free volume:

1oPs )]

RRR2sin(

21

RRR1[

21 −

∆+π

π+

∆+−=τ 1

oPs )]RR

R2sin(21

RRR1[

21 −

∆+π

π+

∆+−=τ

How PAS works in amorphous matter?How PAS works in amorphous matter?Tao-Eldrup modelTao-Eldrup model

0 1 2 3 4 5

1

10

100

RPs

lifet

ime

(ns)

radius [nm]

0.1 0.2 0.3 0.4 0.5

1

2

3

4

5

R [< 0.5nm]

How we do PAS?How we do PAS?

time difference −> positron lifetime

positron source (22Na)

511keV+ ∆ E

511keV

1274,5keV

γ1

γ2’γ2’’

*

sample

Doppler broadening −> momentum of the e+e− pair

start

stop

energy

e+



Positron annihilation spectroscopy measures the distribution of positron lifetimes, which is related to the electron density of the material at the positron-electron annihilation site, and, in the case of positronium formation in the material, the orthopositronium lifetime is related to the free volume size. The lifetime is measured as the time difference between the detection of the 'start' gamma quantum (1274,5keV) emitted with positron from the positron source (22Na) and the detection of the 'stop' gamma quantum (511keV) from the annihilation event.

Positron annihilation spectroscopy measures the distribution of positron lifetimes, which is related to the electron density of the material at the positron-electron annihilation site, and, in the case of positronium formation in the material, the orthopositronium lifetime is related to the free volume size. The lifetime is measured as the time difference between the detection of the 'start' gamma quantum (1274,5keV) emitted with positron from the positron source (22Na) and the detection of the 'stop' gamma quantum (511keV) from the annihilation event.

Lifetime measurementsLifetime measurements


Lifetime measurementsLifetime measurements

0 5 10 15 200.01

0.1

1

10

100

1000

10000

cou

nts

positronium formation no positronium formation

time [ns]

This picture shows a histogram of detected time differences (∆t) between the ‘start’ (γ1) and the ‘stop’ (γ2’) signal. It can be described by an exponential decay function. By fitting this function to the spectrum the positron lifetime may be determined.

This picture shows a histogram of detected time differences (∆t) between the ‘start’ (γ1) and the ‘stop’ (γ2’) signal. It can be described by an exponential decay function. By fitting this function to the spectrum the positron lifetime may be determined.


Doppler broadeningDoppler broadening

The information on the electron momentum density is obtained from the measurements of the Doppler broadening of the annihilation 511-keV-line and is expressed via the "S_parameter" and “W_parameter”. The annihilation spectrum is deconvoluted using the modified van Cittert's algorithm (Gold) and the 1274-keV-line as the system response function.

The information on the electron momentum density is obtained from the measurements of the Doppler broadening of the annihilation 511-keV-line and is expressed via the "S_parameter" and “W_parameter”. The annihilation spectrum is deconvoluted using the modified van Cittert's algorithm (Gold) and the 1274-keV-line as the system response function.


Doppler broadeningDoppler broadening

506 511 516102

103

104

cou

nts

experimental data

W2

resolution function

W1

S

energy [keV]

S parameter is defined by the annihilation events recorded in the central part of the annihilation line –area S (small doppler shift) and is calculated as a ratio of the area S to the total area A. Again, the W parameter is defined by events on the ‘wings’ of the annihilation line – areas W1, W2 (larger doppler shift) and is calculated as a ratio of the areas W1+W2 to the total area A.

S parameter is defined by the annihilation events recorded in the central part of the annihilation line –area S (small doppler shift) and is calculated as a ratio of the area S to the total area A. Again, the W parameter is defined by events on the ‘wings’ of the annihilation line – areas W1, W2 (larger doppler shift) and is calculated as a ratio of the areas W1+W2 to the total area A.


AMOC measurementsAMOC measurements

AMOC - age-momentum correlation measurements take advantage in collecting all three gamma quanta (γ1, γ2’, γ2’’) referring to one single positron. The coincidence of the lifetime and the doppler parameters has been formed by the CAMAC multidetector system and specially designed software developed at the IP SAS. This unique system has been put to operation in Bratislava in 1992.

AMOC - age-momentum correlation measurements take advantage in collecting all three gamma quanta (γ1, γ2’, γ2’’) referring to one single positron. The coincidence of the lifetime and the doppler parameters has been formed by the CAMAC multidetector system and specially designed software developed at the IP SAS. This unique system has been put to operation in Bratislava in 1992.

How we do PAS?How we do PAS?AMOC measurementsAMOC measurements

lifetimeenergy

∆ t

∆E

What we get from PAS?What we get from PAS?

The combined use of positron annihilation spectroscopy (microscopic volume measurements using free volume expansion coefficients) and dilatometric techniques (macroscopic volume measurements using bulk volume expansion coefficients) provides the temperature dependence of the absolute value of free volume fraction f(T)

The combined use of positron annihilation spectroscopy (microscopic volume measurements using free volume expansion coefficients) and dilatometric techniques (macroscopic volume measurements using bulk volume expansion coefficients) provides the temperature dependence of the absolute value of free volume fraction f(T)

1 - glassy state 2 - liquid state1 - glassy state 2 - liquid state

)TT(1)TT(1

)T(f)T(fg0

g1Fg −α−

−α+= )TT(1

)TT(1)T(f)T(f

g0

g1Fg −α−

−α+=

for T>Tgfor T>Tg

for T<Tgfor T<Tg

)TT(1)TT(1

)T(f)T(fg0

g2Fg −α−

−α+= )TT(1

)TT(1)T(f)T(f

g0

g2Fg −α−

−α+=( ) ( )121F2F

12g)T(fα−α−α−α

α−α= ( ) ( )121F2F

12g)T(fα−α−α−α

α−α=

( ) ( )121F2F

1F22F10

..α−α−α−α

αα−αα=α ( ) ( )121F2F

1F22F10

..α−α−α−α

αα−αα=α


The combined use of positron annihilation spectroscopy (microscopic volume measurements using free volume expansion coefficients) and dilatometric techniques (macroscopic volume measurements using bulk volume expansion coefficients) provides an unique information on the thermal expansion coefficient of occupied volume α0

The combined use of positron annihilation spectroscopy (microscopic volume measurements using free volume expansion coefficients) and dilatometric techniques (macroscopic volume measurements using bulk volume expansion coefficients) provides an unique information on the thermal expansion coefficient of occupied volume α0

using the free volume expansion coefficients αFi and α0 we can express the Vogel temperature T0, the WLF coefficient c2g, and the ratio c1g/B, where c1g is the WLF coefficient and B is the Doolittle constant.

)T(felog)1(Bcg

2F0g1 αα−=)T(f

elog)1(Bcg

2F0g1 αα−=2F

g21c

α=

2Fg2

1cα

=2F

g01TT

α−=

2Fg0

1TTα

−=


PAS provides the possibility to quantify the total free volumeand hence to test the free volume theories of transport and relaxation processes in amorphous matter

(e.g. the description of viscosity η(T) based on the free volume concept given by the Doolittle equation η(T)=A.exp(B/f(T)), where A and B are coefficients and f(T) is the fraction of free volume)

PAS provides the possibility to quantify the total free volumeand hence to test the free volume theories of transport and relaxation processes in amorphous matter

(e.g. the description of viscosity η(T) based on the free volume concept given by the Doolittle equation η(T)=A.exp(B/f(T)), where A and B are coefficients and f(T) is the fraction of free volume)

200 220 240 260 280 3006789

101112131415 Polyisobutylene

experimental data fit from PAS data

visc

osity

[log

η]

Temperature [K]

This picture shows the comparison of experimental data on the viscosity of PIB sample (based on macroscopic measurement) and the fitted curve from PAS data (basically microscopic technique)

This picture shows the comparison of experimental data on the viscosity of PIB sample (based on macroscopic measurement) and the fitted curve from PAS data (basically microscopic technique)

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Positron annihilation spectroscopy (PAS)Positron ... · Positron annihilation spectroscopy (PAS) is a nondestructive nuclear physics method allowing the study of condensed matter