First stage F-centre production in irradiated alkali halides

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First stage F-centre production in irradiated alkali halides

J. Comins, B. Carragher

To cite this version:

J. Comins, B. Carragher. First stage F-centre production in irradiated alkali halides. Journal de Physique Colloques, 1980, 41 (C6), pp.C6-166-C6-169. �10.1051/jphyscol:1980643�. �jpa-00220081�

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First stage F-centre production in irradiated alkali halides

J. D. Comins and B. O. Carragher

Department of Physics, University of the Witwatersrand, Johannesburg, South Africa

Résumé. — Dans cette communication un système d'équations cinétiques décrivent la formation de centres-F pendant l'irradiation d'halogériures d'alcoyle dopés d'impuretés cationiques divalentes est développé. Ces équa- tions tiennent compte de la stabilisation des centres-H et des halogènes di-interstitiels aux dipôles impureté- lacune isolés ou entassés, ainsi que du dépiègement d'interstitiels provenant de l'irradiation. Les solutions ana- lytiques numériques et approximatives des équations révèlent, en accord avec l'expérience, l'existence d'une dépendance de la température et d'effets de saturation dynamique dans la première étape du processus de croissance des centres-F. Elles expliquent aussi d'une façon nouvelle la formule empirique que relie la concentration des centres-F pendant la première étape de croissance à la racine carrée de la concentration d'impuretés cationiques.

Abstract. — Kinetic equations describing the formation of F-centres during irradiation of alkali halides doped with divalent cation impurities have been developed. These incorporate the stabilization of H-centres and di- interstitial halogens at impurity-vacancy dipoles or dipole aggregates as well as radiation-induced interstitial detrapping processes. Numerical and approximate analytical solutions of the equations show the first stage of F-centre growth to be a dynamic, temperature-dependent process in agreement with experiment. They also pro- vide a new explanation of the experimentally observed relation between the first stage F-centre concentration and the square root of the divalent cation impurity concentration.

1. Introduction. — Substitutional divalent cation impurities in the alkali halides alter F-centre production rates during colouration with ionizing radiation near room temperature. There is enhancement of the first, rapid stage of defect growth, while the second, slow stage is suppressed [1, 2].

Most models have assumed the exhaustion of pre- existing defects to explain the saturation of the first stage [1, 2]. An apparently successful model [3] in which isolated cation vacancies act as saturable traps for halogen interstitials was based on the experimentally observed relation

To °c J~rh- (1) Here f0 is the concentration of F-centres in the first

stage and n^x is the divalent cation impurity concentration. The association reaction between isolated cation vacancies («^v) and divalent cations to form impurity- vacancy (IV) dipoles («^D) shows that near room temperature «^v °c \f*h provided n^D p n^Y. Thus relation (1) might be expected if the isolated cation vacancies but not the IV dipoles are efficient interstitial traps.

Recent work [4-10] has shown that although isolated cation vacancies do act as interstitial traps, it is the IV dipoles and dipole aggregates which play the major role. Furthermore, the transition from first to second stage F-centre production does not involve the exhaustion of these dipole traps [5-10]. Thus a new explanation of relation (1) is required in which the

first stage saturation is viewed as a dynamic rather than as an exhaustion process, and which incorporates the present understanding of the structure of the

stabilized halogen interstitials [4, 8].

2. Theoretical model. — For the simple situation where either IV dipoles or a dominant type of dipole aggregate exists prior to irradiation in concentration n^D, the kinetic equations are

% = P-°tf (2)

— = p - aif - <*! i(nD - n2 - nt)

— a2 /«! + Kt «! + 2 K2 n2 (3) d«!

— = aj i(n^D - n² - n^t) - a² «"i - ^ i «i (4) d«2

— = a2 int - i^2 «2 (5)

/ = ! + « ! + 2 B2 . (6)

Our model incorporates the mechanism of Hoshi e/ a/. [4] : an H-centre is trapped at an IV dipole or dipole aggregate to form an HD-centre («i), followed by the trapping of another H-centre to form a trapped di-interstitial (n2) known as a V^-centre [8] or D3- centre [4]. The mechanism explains the square law relation which exists between the HD- and V™ centres [4,

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980643

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FIRST STAGE F-CENTRE PRODUCTION IN IRRADIATED ALKALI HALIDES C6-167

81. Equation (2) gives the growth of F-centres

(f)

which is limited by recombination with free interstitial halogens (i). Equation (3) expresses the produc- tion, recombination and trapping of free interstitials and includes radiation-induced detrapping terms Kl n1 and Kz n2 [ll, 121. The rate constants K , and KZ have the form Bj exp(- Ej/kT). 0 , a, and az are rate coefficients which can be estimated using (Zv/Ni) where Z is the number of sites surrounding a defect for certain annihilation or trapping of an interstitial and Ni is the interstitial site concentration.

v = v, exp(- Em/kT) where Em is the migration energy of the H-centre. Equations (4) and (5) repre- sent the production and destruction of the n1 and n , defects. Equation (6) equates the total interstitial concentration to the F-centre concentration and ignores F-aggregate centres.

The equations have been solved numerically sub- ject to the condition that the free interstitial concentration rapidly attains a small quasi-stationary value is found by setting dildt = 0 in equation (3).

The growth of F-centres, HD-centres (nl) and the Vy-centres (n2) follows the experimentally observed pattern [4, 51. For very short irradiation times, F- and HD-centres form predominantly, but the latter defects soon saturate at a low concentration and then decrease slowly, as observed [5]. The V$-centres (n,) except for the very early region grow in parallel with the F-centres again in agreement with observation [5- 8, 131.

The numerical solution of the equations provides a guide to an approximate analytical approach.

Since the HD-centres rapidly reach a small quasi- stationary state 1 2 ~ , we may set dn,/dt = 0 and use the value for

4

to calculate n,,. On substitution of is and nl, into equation (2) we obtain for the F-centre growth rate

where a = 2 a, a2/(al

+

^{az). We} assume that (al

+

^a2)^is^%^K1^;^{K1 n1}

<

K 2 n2 for nl 6 n,; and f, 2. 2 n2 for (is

+

^nl)⁴n, from equation (6). We have checked the growth curves of F-centres predict- ed by equation (7) against those from the numerical solution of equations (2)-(6) and find excellent agreement for choices of the parameters within the approximations used.

The termination of the first stage occurs when (dfldt)f,f, = 0. This gives a quadratic equation in fo which has a physically meaningful solution

for ('a/2)' ^G4paoK2 n,. For irradiations at cons- tant temperature, .f, cc

&

which leads directly to relation (1) since 12,

-

n,near room temperature.

3. Comparison with experiment. - 3.1 THE SQUARE ROOT RELATION (I). - Relation (1) will be expected if the parameters for a particular crystal-impurity system are within certain limits and there is close to proportionality between F-, Vt-centres and destroyed IV dipoles (or aggregates). We have tested the approximations used in deriving the square root relation (1) by means of the full set of rate equations and indeed find deviations from this relation when the parameters are substantially outside the limits specified.

3.2 DYNAMIC SATURATION EFFECTS. - We have measured growth curves for Korth KC1 without deliberate doping. The relatively low impurity concentration allows the accurate measurement of f, at temperatures significantly lower than room temperature.

The crystals were irradiated in an optical cryostat using X-rays from a W-target tube operated at 80 kV and 16 mA. The X-rays were filtered by 0.5 mm Al, 0.4 rnm Fe and 1 mm amorphous silica. Defect concen- trations were determined by optical absorption.

IRRADIATION T I M E (hf

Fig. 1. - Experimental and theoretical growth curves for defects in KC1 crystals. Open circles ^:F-centre growth and decay in crystal A irradiated sequentially at 293 K, 273 K , 253 K, 233 K and 293 K.

Open squares : F-centre growth for crystal B irradiated a t 273 K.

Crosses : F-centre growth for crystal C irradiated at 253 K . The dashed, full and dot-dash curves are the corresponding theoretical growth curves for F- and Vn'-centres for crystals A, B, and C respectively. Values of the theoretical parameters : p=6.3x l O I 3 cm-3 s - ' ; n D = I . 4 x lo1' ~ m - ~ ; E,,,=0.075 eV 1151;

a = 8.6 x exp(- E,,,/kT) cm3 s-

'

; a, = 0.03 a ; a, = 1.5 U ;

K , = K , = 50.1 exp(- E,,!kT) s-'; E, = 0.32 eV.

Figure 1 shows the experimental growth curves for F-centres. The Vz-band due to the trapped di-interstitials behaved similarly, while HD-centre concentra- tions were too low to be measured. Crystal A was irradiated at sequentially lower temperatures between 293 K and 233 K and showed significant increases in

fo

as the temperature was reduced. When the irradiation temperature was restored to 293 K, a rapid

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reduction in defect concentration took place and the growth curve finally followed an extrapolation of the original growth curve at 293 K. The rate of reduction is considerably faster than that produced by thermal bleaching alone, confirming the presence of a radiation-induced back reaction. Crystals B and C were irradiated at 273 K and 253 K respectively yielding values of

f,

close to those produced in crystal A at the same temperature.

We have used our model to calculate growth curves for F- and Vy-centres using suitable values for the parameters (Fig. 1). The initial defect production rate p was calculated from the initial slope of the growth curve at 293 K. o was estimated from Zv,/N, exp(- E,/kT) where Z = 4 nu2 ( b ) N , ; r is the capture radius and ( b ) the average change in vacancy interstitial separation during a jump [14].

We have put K , = K 2 ⁼B2 exp(- 0.321kT) where E2 is measured from the temperature dependence of f,. B2 and a were then adjusted for a good fit. For the low values of the saturation level of the n,- centres ( n l J found experimentally, al

<<

a2. In fact the ratio a 2 / a l must reduce slowly for lower tempera- tures, since n l , increases

[a].

In the present work, this

variation makes very little difference to the growth curves for F- and Vy-centres owing to the low concentration of the HD-centres.

4. Discussion. - The model accounts successfully for several features of F-centre production in alkali halides doped with divalent cation impurities; in particular the dynamic temperature dependence of the saturation of the first stage near room temperature and the origin of relation (1). It emphasises the important role of back reactions. Changes in the forward rate by modifications of the excitonic mechanism of defect production [2, 7, 81 cannot alone explain the large decrease in the defect concentration observed when the temperature of irradiation is raised (Fig. 1).

However, we should not exclude such mechanisms completely as they may be important in some systems, e.g. NaCl(Mn) [lo] where the growth curves approach each other at a high impurity concentration and relation (1) is not obeyed.

Acknowledgments. -We thank L. A. Vermeulen and A.G. Every for valuable discussions and the C.S.I.R. (Pretoria) for financial assistance.

DISCUSSION

Comment. ^-D . SCHOEMAKER. Question. - F . AGULLO-LOPEZ.

We have performed extensive ESR measurements I think that your model could also explain the dose on H,-centres. We have detected at least five types rate dependence of the saturation level of the first but none of these involve an isolated positive ion stage, e.g. the detailed data by Mitchell et al. on vacancy. Three centres involve a simple divalent-ion- KC].

vacancy complex and the remaining two involve

dimers. One centre is a di-interstitial one. Very likely Reply. _{- .}- J . D . COMINS.

the analogous diamagnetic centres exist also and all The mode] contains which are intensity this points to a complex situation. dependent : the primary rate p and the radiation- Question. - M . GEORGIEV. induced interstitial detrapping -rate. At present the individual intensity dependences are not known but I like draw your a recent their ratio would have to be proportional to inten- paper by Watterich and Polak in Physica Status Solidi.

sity for agreement with Mitchell They have found in an ESR study that the impuritv-

vacancy complex is destroyed by the X-irradiation,

the impurity ion going to a cubic site in the lattice. Question. - E . LILLEY.

Reply. - J. D . COMINS. What is the composition of the crystal studied ? There are many mechanisms by which I.V. dipoles

might be destroyed during irradiation. There is now ^-J. D. COMINs-

considerable evidence to show that in systems such The KC1 crystals obtained from Korth were as KC1 and KBr doped with e.g. S r C + or C a + + that nominally pure but contain residual divalent impu- the major process involves trapping of interstitial rities. The absorption bands were typical of crystals halogens by I.V. dipoles and dipole aggregates. deliberately doped with such impurities.

References

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New York/London) 1 (1972) 201. (1975) 15.

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FIRST STAGE F-CENTRE PRODUCTION IN IRRADIATED ALKALI HALIDES C6-169

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[I41 KELLY, B. T., Irradiation Damage to Solids (Pergamon Press, Oxford) 1966, p. 196.

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