Positron trapping in some metals

Materials Chemistry and Physics, 27 (1991)

POSITRON

TRAPPING

IN SOME

55-60

55

METALS

A. BELAIDI Departement 31000 H.

de physique,

Oran

( Algeria

AOURAG,

B. KHELIFA,

Laboratoire

d’optique,

3 I 100 Es-senia

Received

Ecole

Normale

M. ELIAS

Departement

( Algeria

d’Enseignement

Technique

d’Oran,

and

M. OUBADI

de physique,

Universite

d’Oran

Es-senia

)

I, 1990 ; accepted

August

Superieure

I

September

25,

1990

ABSTRACT In this

work,

ments.

A good

curves.

Some

a three linear

state

trend

indication

was

trapping

model

found

in both

of positron

trapping

has been applied F F Elv vs. Tc, Elv in divacancies

to several 2

Tm

is also

metal

and

ele-

Tc vs.

reported

Tm

in some

elements.

INTRODUCTION Since

its

discovery

physics

and

chemistry

by the

strong

ion

state

energy

voids

are

The proved defects

and

where

For

and

three [7]

has

-state

been

model

model

its of

has

positive the

positron

extensively

charge,

the This

positron

such

as vacancies, it can

by

the

used

increases

wherein

energies

is a plethora

been

crystal.

defects

the

in the

is repelled its

ground

dislocations

be

positron

of positron-derived

or

trapped. technique

has

information

about

.

may

sometimes

by various

trapping

and

three

Positron

be appropriate

authors

model

we consider

divacancies.

of

formation

there

used

positron

volume for

[I - 43

positron

. In this and

open

monovacancy

alloys

the

interstices

sites

Today

trapping

its

application

positron

detrapping

for

trapping

to gold

formalism

is reported

: the bulk or metal

states by

a defect

. A full theoretical

[5 - 7]

monovacancies

has

been

elsematrix, neglected

model. a modest

temperature, dence

that

of

in metals

and

the

favorable

successful.

monovacancies in this

it follows

ago,

Because

matter. to

measurement very

A three-state

the

of

60 years

potentials

potentially

phenomenon of

some

the

attributable

0254-0584/91/$3.50

temperature

range

(0.4

S-parameter

shows

a relatively

to

the

effect

of

thermal

Tm

to 0.6

Tm ), where

modest

and

linear

expansion

and

lattice

0 Elsevier

Sequoia/Printed

Tm

is the

melting

temperature vibrations

in The

point

depen[8]

on the

Netherlands

56

positron

which

suggested strongly tice

is generally

believed

an alternative interacts

with

dilatation.

momentum

evidence

reflect

is a strong

and hence

be trapped. centration

essentially

close

all positrons

compared

to their

the electronic borhood

increases, fraction

type

wavefunction

[lo]

trapping

[9]

has

lat-

non-existent

of lifetime

or

of the metal.

concentration

range

increases

can find a vacancy

trapping

made

where

the vacancy

is then directly

defect.

0.6

accor-

in which they

related

may

to the con-

in fee

ttvmax

represents

however,

both

and/or

important

the prevacancy

weak due to

by divacancies

[ 11.

and de-

Some investigations

effects effect

neigh.

with the ion electron

trapping

detrapping

reflects the

were

considered

and positron

detrapping

( after

entering

for a given

the metal ) at which

temperature

can find a monovacancy,

positron

[7] . Thus, the shorter

get trapped

and annihilate

trapping

by

tlvmax , the

therein.

AND DISCUSSION vs.

temperature

2 shows

temperature Figure

both positron

short

rate about

is usually

wavefunction

high that

in a time

the annihilation

dependence

positron

metals ) may become

the time

is maximum

a positron

tlvmax

In this region,

This temperature

trapping

is sufficiently

can be trapped

and divacancies.

monovacancies

RESULTS

they

and this may give information

of the trapped

divacancy

concentration

wherein

the vacancy

[.5] . In this work we have neglected by mono-

the

for

fraction

these

1 curves

curves

monovacancies curves

in Figl.

for different

annihilating

metal

in different

elements.

states

against

elements. lineshape

are reported different

to those

to the lineshapes

( Fig. 2 ) , The critical

ned via a somewhat

route

corresponding

corresponding

temperature

in Table

[7] . The Tc temperatures works.

are depicted

of positrons

show similar

in the bulk but are opposite

curves

of positrons

is either

results

over the appropriate

the vacancy

in the bulk metal.

. Near melting,

( less probable

have been

to melting,

around

of the overlap

other

time

Seeger

the positron

in a transient

trapped

properties

dependence

of such positron

lifetime

structure

of a vacancy

perature

self-

the observed

electronic

can find a vacancy

the reduction

Figure

becomes

whereby

of traps.

For temperatures

quicker

Bloch state.

region,

for this at the present

temperature

an increasing

The probability

and

in this region,

the non-local

non-linear

Tm to Tm. As the temperature dingly

potential

cl] . Consequently,

density

There

for this prevacancy

the lattice

Nevertheless,

or contradictory

in a delocalized

to exist

mechanism

to positron

to positron

Tc deduced

from

the ttvmax

I. In this work, the Tc temperatures

from obtained

those

usually

obtained

are in good agreement

annihilation

annihilation

from

in

vs. tem-

are obtai-

the S-parameter

with those

reported

in

2.29

1.14

t , vmax vs. teirqerature.

Fit;. 1. Table

I.

Metal

Threshold

works

Refs.

cu

842

876

L’l

hi

533

520

[‘I

Ag AU

793 782

775 755

;:;

Zn

405

395

[‘I [&I

Cd

305

377

Pb Sn

412 382

415 465

In

325

330

has been IV

Tc (K) Other

This work

This Tc method

EF

temperatures

suggested

is particularly by several

and the characteristic

C’5l

simple

authors.

or threshold

-

SOm

for deriving

Erv

[I I] have

temperature

from

experimental

proposed

a correlation

Tc at which

the onset

data

and

between of vacancy

58

Fig. 2. Positron annihilation in : 1 bulk ; 2 monovacancies ; 3 divacancies.

trapping is detected.

Kim and Buyers [ 121 have established the analytical relationship

between Eyv and Tc for the case of the two-state

model. A simple linear correlation

F between E,v and Tc, namely Ex = 14 KTc$ is thus obtained. West [l ] showed that the prevacancy and saturation region temperature dependences play little part in the determmat!on of Elv F from Tc. This Tc method is a useful route to E:v and particularly so in cases where the alternative curve fitting procedures are made difficult by a lack of clear saturation at high temperature (e.g.

low melting point metals ) as shown in Fig.

2 f Pb, Sn, In 1, or when, as is often the case for refactory

materials, the measurements

are restricted to only lower temperature parts of the curves. F F Figures 3(a) to 3(c) depict Elv -vs Tc, Tc vs. Tm and E 1v z best straight line fitted to data of Figs. 3(a) and 3(b) give Tc = 0.57 Tm, respectively.

Tm, respectively.

The

E(ev) = 1.4 10-3Tc and

These values are to be compared to

E(ev) = 1.2 10m3Tc and

Tc = 0.63 Tm as deduced by Hood and McKee [? 31. The best line fitted to Eyv -vs. Tm

59

O.l>f

,

,

,

,

,

,

1 , , , _Tc(K) IOU0

600

200 T&K) t 1000”

Tm(K)

UTmCK) 850

0

1400

300 Fig.

3.

curve

a) Efv

Rives

with

good

the

vs_

correlation of

coefficients.

the

Generalization to

the

presence

nature

random

concentrated

Some at

temperatures monovacancies

pears

of

in Fig. in Fig.

the and,

relation

methods

was

of positron near

melting.

and 2 for 2 for

. The three

The

data

to

alloys

delocalized most for

alloy

indication

by

probable.

these

of disorder A simple

vs_

scatter

.

Tm

relations

were

about

the

obtained

most

probable

line

reflects

method.

of

energy.

shown

F E ,v = 7.8 10e4 Tm

a relation

limitation

pect

; b) Tc vs. Tm ; c) Ef,

Tc

Cd

positron

the put

This

and

The Zn.

the

determination forward

trapping

same For

by

the

the

Doyama

by divacancies

increase effect, other

but

potential mobility

definition of

is characterized

the

various

state,

particularly,

a corresponding

gold.

raises

of

[ 141

of

elements,

the

positron

in the

energy

In i

. to

trapped

to a lesser

in res-

formation

formation

by a decrease in positrons

the

monovacancy

apparent

seems

difficulties

extent effect

occur

in some

in positron

metals trapping

in divacancies

( note seems

the

scale

to be

as

) , apless

60

CONCLUSION The correlations encouraging.

A three-state

is tempting.

However,

rimental

spectra

nalysis tainly

problem

the large

generally

in terms

Eyv and Tc, Tc and Tm and Ey,, and Tm, respectively,

between

number

makes

of a trapping

taking

into account

of parameters

the validity

positron required

of the model

mode1 involving

more

than

detrapping

three

by vacancies

in the analysis

difficult

of expe-

to establish.

different

are

states

An ais cer-

more hazardous.

REFERENCES 1 R.N. West, 2 A. Belaidi

in solids , Hautoyarvi

Positrons

and R.N. West,

3 A. Belaidi,

H.P. Leighly,

3. Phys.

Berlin : Springer , 1979 , pp. 89 - 145

F : Met. Phys. , -18 (1988) 1001. and R.N. West, Phys. Stat. %I; (a), 102

P.G. Coleman

(1987) 127. 4 A. Belaidi,

H. Aourag

and B. Khelifa,

5 G. Dlubeck,

0. Brummer

6 M. Doyama,

S. Tanigawa,

J. Phys. : Condensed

Matter

,2 (1990) 2929.

and N. Meyendorf, K. Kuribayashi

Appl. Phys; , - 13 (1977) 67. and S. Nanao, Cryst. Lattice Defects,

i

(1973) 225. 7 A. Belaidi,

H. Aourag

8 M.3.

and R.N.

Scott

9 A. Seeger, IO R.P.

J. Phys.

Gupta

and B. Khelifa, 3. Phys.

West,

Chem.

Phys. ) -25 (1990) 523.

F , _Z (1975) 85.

and A.R. Siegel,

11 K. Kuribayashi,

Mater.

F, 2 (1978) 635.

Phys. Rev.

Letts., -39 (I 977) 1212. S. Nanao and M. Doyama, SoIid St. Comm. , - 12 (1973)

S. Tanigawa,

1179. 12 W. Kim and W.J.L. 13 GM.

Buyers,

Hood and B.T.A.

14 M. Doyama, 15 A. Belaidi,

Proc.

Conf,

PhD Thesis,

5. Phys.

McKee,

F,s

3. Phys.

on Positron University

(1978) L 103. F, 5 (1978) 1457.

Annihilation of East

An&a,

, Helsingor, 1980.

1976.