Study of C centres in NaCl by positron angular correlation

Volume 64A, number 1 PHYSICS LETTERS 28 November 1977

STUDY OF C CENTRES IN NaCl BY POSITRON ANGULAR CORRELATION*

T. NAGARAJAN and S. RAMASAMY Department of Nuclear Physics, University of Madras, A.C. College of Technology Campus, Madras 600 025, India

and

Y.V.G.S. MURTI and N. SUCHETA Department of Physics, Indian Institute of Technology, Madras 600 036, India

Received 30 August 1977

The nature of C centres in NaCl has been experimentally studied by the positron annihilation technique. The re-

sults are in support of a previously proposed model for the C centres [I]. The approximate size of C centres has been

estimated to be of the order 6.3 + d.7 A.

The positron annihilation technique has been used effectively by various authors in the study of both

point and extended defects in solids. Positron annihilation at electron excess centres has been studied by Nagarajan et al. [2]. This paper reports positron an-

nihilation studies of C centres of a colloidal nature produced in heavily irradiated NaCl crystals [ 11. The main aim of this paper is to investigate whether the C centre in NaCl is in metallic phase or in the form of isolated alkali atoms.

The angular correlation of the annihilation photons was measured using the conventional long-slit arrange- ment [3] with angular resolution of 0.7 mrad. The data was corrected for the finite slit length following the method of Mogensen [4]. Harshaw NaCl crystals of typical sizes 3 X 1.5 X 0.1 cm3 are irradiated with y-rays to a dose of 3.4 X 108R under Co6’ source and subjected to isothermal heating in the temperature range 18O”C-200°C which leads to the growth of only C centres to the exclusion of other electron excess centres [l].

Fig. 1 (a, b) shows the folded angular correlation curves for a pure crystal and the crystal containing exclusively C centre to a concentration of =I 017

cm -3. The curves are matched at high angles and the resulting difference at low angles gives the contribu- tion of the C centres to the annihilation (fig. lc). The full width at half maximum (FWHM) of the narrow

l Work partly supported by UGC, India.

component is 2.0 mrad. The percentage of positrons annihilating with C centres is 11. The corresponding

FWHM for F centres is 2.86 mrad and the percentage of positrons annihilating with F centres is 10.6 [2]. Angular correlation measurements on additively coloured KC1 crystals and on y-irradiated NaCl and KBr crystals show that a large narrow component of annihilation is associated with F centres [2]. Although the crystals contain other defects such as the hole centres, the electronic centres alone lead to the dominant annihilation corresponding to low electron momenta.

If the C centres represent a normal alkali metal phase embedded in the crystal one may expect to find the angular correlation to have the shape of an inverted

parabola. However, the Fermi gas model of sodium metal does not give satisfactory fit with the experimental curve as seen in fig. 2a. The experimental results closely resemble the momentum distribution calculated from free atom wavefunctions. Quantum elec- trodynamically the positron annihilation and Compton line shape profile are equivalent. Thus N(P,) = J(P,) where J(P,) is the Compton line shape profile. Weiss et al. [5] have calculated J(P,) values for all the valence and core electrons of the sodium atom. These values were added to give a total momentum distribution due to free sodium atom wavefunctions. There is a consider- able deviation at large momenta but this discrepancy can be partly because of the subtraction procedure adopted for obtaining the narrow component due to C centres. Thus it may be concluded that the angular

141


250v 230

t 21oc

1

0 2.0 4.0 6.0 8.0 10.0 12.0 IL.0 e (mrodl

Fig. 1. Folded angular distribution of (a) Harshaw NaCl unirra-

diated (b) Harshaw NaCl with C centres and (c) narrow component due to annihilation in C centres.

correlation of positron annihilation at C centres is in- consistent with a model of an alkali metal phase but may be more consistent with a small cluster of sodium atoms.

In order to determine the size of the C centres at- tention may be drawn to the fact that dislocation sites are essential for the formation of C centres [6]. While the alkali atoms form clusters near the dislocation where excess electrons are present the positrons probe the average electron density in the bulk of the cluster. The overlap density of annihilating positron and elec-

x- Exper,mentol points

A- No metal

-tto 3tcm

0 0.2 0.L 0.6 0.8 1.0 12

pz - Fig. 2. Experimental and theoretical angular correlation curves

for narrow component: X - Experimental points. a - Fermi

gas model of sodium metal. b - Deduced from Compton pro-

file of a free sodium atom. Here Pa is in atomic units (2nme2/h)

tron is convoluted by the size of the cluster. Thus we

may write for the momentum distribution function in positron angular correlation

F(k) = /p(r) S(r) e-ik’r dr ,

where p(r) is the overlap density, S(r) is the size distribution of the cluster and k is the wave vector. If the colloidal centres are considered as spherical clusters of radius R the above expression reduces to

F2(k) = const. a2 (kR),

where

@(kR) = 3(sin kR - kR cos kR)

(kR)3

Fig. 3 shows the fit of ip2 (kR) for R = 6.3 + 0.7 a with the experimental momentum distribution p(k) deter-

142


I

k Ii-‘, -

Fig. 3. Fit of Q2 (kR) for R = 6.3 A with experimental mo-

mentum density distribution.

mined following the prescription of Stewart [7] :

1 WkJ ___ p(k) = const. c dkz .

Fit for 6.3 A is quite good but the deviation at large

moment can be considered to be due to subtraction procedure. Thus our results substantiate the previous

findings on C centres [ 11. Positron angular correlation technique proves to be

an effective non-destructive method to determine the cluster sizes of the order 10 8. The above analysis has been extended by us to determine the grain sizes in substances like CaF,, SrF,, BaF, and MgF, and the results will be communicated later.

The authors are grateful to Prof. V. Devanathan for his constant encouragement to carry out this investiga- tion.

References

[II

[21

131

[41 [51

[61 [71

Y.V.G.S. Murti and N. Sucheta, Phys. Lett. 56A (1976)

119. T. Nagarajan, P. Ramasamy and S. Ramasamy, Phys. Stat.

Solidi B81 (1977) 719.

T. Nagarajan, P. Ramasamy, K. iyakutti and V. Devanathan,

J. Phys. F: Metal Phys. 5 (1975) 880.

O.E. Mogensen, Nucl. Inst. Meth. 84 (1970) 295.

R.J. Weiss, A. Harvely and W.C. Phillips, Phil. Mag. 17

(1968) 241.

N. Sucheta, Ph.D. Thesis (1976) I.I.T., Madras (India).

A.T. Stewart, in: Positron annihilation, eds. A.T. Stewart

and L.O. Roellig (1965) p. 28.

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Study of C centres in NaCl by positron angular correlation