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SECONDARY PROCESS OF RADIATION DAMAGE IN HALIDESAn heterogeneous nucleation model for the
irradiation coloring of alkali halides
M. Aguilar, F. Jaque, F. Agulló-López
To cite this version:
M. Aguilar, F. Jaque, F. Agulló-López. SECONDARY PROCESS OF RADIATION DAMAGE IN HALIDESAn heterogeneous nucleation model for the irradiation coloring of alkali halides. Journal de Physique Colloques, 1980, 41 (C6), pp.C6-341-C6-343. �10.1051/jphyscol:1980686�. �jpa-00220124�
JOURNAL DE PHYSIQUE Colloque C6, suppkment au no 7, Tome 41, Juillet 1980, page C6-341
SECONDARY PROCESSES OF RADIATION DAMAGE IN HALIDES.
An heterogeneous nucleation model for the irradiation coloring of alkali halides
M . Aguilar, F. Jaque and F. Agullo-Lopez
Departamento de Optica y Estructura de la Materia, lnstituto de Fisica del Estado Sdlido (CSIC), Univers~dad Autonoma dc Madrld, Cantoblanco, Madrid, Spain
Resume. - On prtscnte un modele de nucleation hettrogbne pour la coloration induite par radiation dans lcs halogtnures alcalins. Lc modtle est forme par un mecanisme primaire que produit les centres F et H, suivi de reactions secondaires activees thermiquement et que incluent la recombination F-H ainsi que la capture des inter- stitiels. On considere explicitement l'existence des aggregations tres instables d'interstitiels. Le modele peut expli- quer la structure en trois etapes de la courbe de coloration F ainsi que I'inhibition de la dernitre en diminuant la dose ou en dopant avec des impuretes.
Abstract. - An heterogeneous nucleation model for the radiation-induced coloring of alkali halides is presented.
The model assumes a primary mechanism producing F and H pairs, followed by secondary thermally activated reactions including F-H recombination a s well interstitial capture. The existence of a very unstable interstitial aggregate is explicitely considered. The model is able to account for the three-stages structure of the F-coloring curve and the inhibition in the occurrence of the late-stage by lowering dose-rate or by impurity doping.
1 . Introduction. - It is now well documented that the damage to alkali halides by ionizing radiation operates v i a two basic processes [I, 21. A primary mechanism consisting in the production of well- separated F and H pairs as a consequence of some non-radiative decay of self-trapped excitons (STE), and secondary reactions involving those primary centers as well as impurities and probably other lattice defects. In accordance with this scheme a number of models have been reported to understand the kinetics of F-center growth. As far as we know, the model proposed by Agullo-Lopez and Jaque [3]
is the only one able to account for the major features of the coloring in NaCl and similar crystals (mainly KCI and KBr). In particular, it satisfactorily explained the three-stages structure of the coloring curve at near room-temperature (RT) as well as the qualita- tive effect of dose-rate and impurity doping. However, the model assumed homogeneous nucleation of interstitial clusters through interstitial-interstitial aggregation and some of its implications have not
, been supported by experiment [4].
The purpose of this paper is to present a short report on a new model of coloring, which assumes heterogeneous nucleation of interstitials on initially existing traps, mostly associated to impurities. The thermal evaporation of interstitials from the clusters (back-reactions) is explicitely considered in the sim- plest possible way.
2. The kinetic model. - The following secondary reaction channels are considered : a ) interstitia1-F-
center recombination; b) interstitial trapping to an impurity (or impurity-related defect) designed as So center to form the S , center ; c) trapping of another interstitial to the S, center, leading to the S2 center containing two interstitials and so on. Therefore, in this model, the impurities act as nucleation seeds for interstitial clustering.
A truly realistic model should take also into account the thermally-induced back reactions involv- ing the evaporation of interstitials from the various aggregates and clusters. This is a very difficult task and one should try to consider a very simplified version on the basis of some major experimental facts. It is well known that during the first-stage (stage I) of the coloring the relatively stable Vy (or D,) centers are optically observed a s counterparts for the F- centers [5]. Since after saturation of that stage a marked inhibition in the coloring-rate is observed it appears quite reasonable that a very unstable center is being formed by additional interstitial trapping This is, in fact, taken as the key point of our new model : the occurrence of a very unstable or short- lived interstitial center, once those associated to stage I have reached saturation. For simplicity, we will assume that the unstable center is the S2 center whereas the S, center, corresponding to stage I, is essentially stable. In fact, it should be more appro- priate to associate the S2 center to stage I, since the V'; centers, already mentioned, are believed to consist of two interstitials trapped into a cation vacancy or an impurity vacancy-dipole [6]. In such a case, the S j center should be the short-lived species
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980686
C6-342 M . AGUILAR, F. JAQUE A N D F. A G U L I . O - I ~ P E Z
blocking the stabilization of additional F-centers.
However, this point does not essentially influences the results of the model and complicates the kinetic equations. Finally, since large clusters are known to be stable, it will be assumed so in our model for all S, centers with n > 2.
The occurrence of an unstable aggregate before stable clusters are formed is not unreasonable since the theory of nucleation establishes that clusters are thermodynamically unstable below a critical radius, and only those reaching this radius are able to form stable precipitates.
The model can be easily translated into rate equa- tions governing the time evolution of the various defects during irradiation. Let f , i, so, s,, s,, and s, be respectively, the concentrations of F-centers, free
interstitials I, empty traps So and the corresponding interstitial centers after capturing one (center S , ) ,
two (center S2) or more (clusters
S3
halogen intersti- tials by the traps. The corresponding rate equations can be written :d i
- = 6) - oiso - cis, - cis2
+
as2-
a, is, - aifdt
where o stands for the common cross-section for all interstitial processes, except for the capture by clusters S,. For this case, the cross-section a, will be assumed to be proportional to the surface of the cluster. This implies that a, = ii:I3 a where means the average number of interstitials per cluster. This assumption is reasonable and it has been previously uscd to understand coloring kinetics in KC1 and KBr at very high doses. a is the decay constant for the thermal bleaching of the S2 centers and g represents the concentration of Frenkel pairs produced per unit time.
3. Computer simulation of coloring curves. - Rate equations have been solved by using an IBM 370 computer at the IBM-UAM research center.
T o reveal the role of the thermal stability of the S2 center on the kinetics of coloring, F-growth curves have been computer-simulated for various values of a, figure 1. In all cases the value of g has been taken g = 1016 ~ r n - ~ s-' which corresponds to a dose-rate of lo'* eV c m - 3 s-', if one assumes an energy of 100 eV required for the creation of each Frenkel pair.
The value of a = 10- l4 cm3 s-
'
is the same used in the previous model [3] for RT irradiations. The initial concentration of traps has been chosen so = 10'' ~ r n - ~ and corresponds to a very pure sample.Ttmr I s I
I - ~ g 1 . - Computer-a~mulated F-center growth curves for dllfe- rent values of the thermal dccay parameter a.
The three stages structure~of the F-coloring is readily apparent. For lower a-values, the structure is lost and a monotonous rise is obtained as observed for low-temperature or high dose-rate irradiations.
For higher values of a no stage 111 behavior is obtained for usual irradiation doses.
4. Role of dose-rate and impurity doping. - The dose-rate is proportional to the concentration y of Frenkel pairs produced per unit time. Therefore, changes in dose-rate can be simulated by altering the value of g. Figure 2 shows computer-simulated F-coloring curves for a number of dose-rates. An increase in dose-rate induces a shortening of stage I1 and therefore an earlier occurrence of stage 111. This effect is well supported by a number of experimental data in a variety of alkali halides. At very high dose- rates, the three-stages structure of the coloring curve becomes blurred (see curve for g = 1018 cm- s -
'
in figure 2) and a monotonous rise in coloring is observed.This is the situation when high-current electron radiation is performed.
1 I I I
1 10'
T~me I s 1
Rg. 2. - Computer-simulated F-growth curves for various dose- rates, a = 5 s - ' .
AN HETEROGENEOUS NUCLEATION MODEL FOR THE IRRADIATION COLORING C6-343
Fig. 3. - Computer-simulated F-growth curves for crystals with ,,06 different initial trap concentrations, a = 5 s-
'
; s = si.The simulation of the effect of different initial trap concentrations on F-coloring is illustrated in figure 3. E The increase in the height of stage I as well as the lengthening of stage I1 with increasing trap concen- tration are clearly observed in the figure, in accor- dance with the experimental data on the effect of impurity doping [ 5 ] . Now we can obtain the predic-
2003
tions of the model with regard to the effect of impu-
rities on interstitial clustering. The evolution with Fig. 4. - a ) Evolution of the average number F, of interstitials
irradiation tirne of the concentration of aggre- per duster with ~ r r a d ~ a t ~ o n time. b ) Corresponding evolution of
gates and their average size are respectively shown the number of interstitial clusters with irradiation time.
in figures 4a and 4b. It can be inferred from this
figure that increasing the doping of the crystal should size. This result is typical of an heterogeneous nuclea- cause an increase in the concentration of aggregates tion model and is in accordance with experimental observed a t high dose and a reduction in their average data by Hobbs et al. [ 4 ] .
DISCUSSION Question. - A. WINNACKER.
How would the phenomena of stress induced luminescence fit into your model. Could moving dislocations initiate an evaporation of aggregates or what would happen ?
Reply. - F . AGULLO-LOPEZ.
I think the phenomena of stress-induced lumines- cence is completely apart from the radiation-induced processes considered in our kinetic model. Anyhow, moving dislocations can possibly cause aggregation or disaggregation of pre-existing defect species.
cal nucleation and growth involves two competing terms (interface enkrgy, chemical potential) which may lead to an initial free energy barrier until a stable nucleus is formed. In the present case, considerable strain energy is involved, as well as the possibility of chemical reaction of two H centres, which are the driving forces for loop nucleation. It is likely that the energy barrier to stable aggregation is indeed the irreversible shear to form interstitial dislocation loops.
This may occur with as few as four H centre pairs.
Reply. - F . AGULLO-LOPEZ.
I agree with you that it might provide an explanation Question. - L. W. HOBBS. for the occurrence of a critical size cluster before We know that at a later stage of interstitial aggre- stable nuclei are formed and further aggregation gation dislocation loops form exothermically. Classi- proceeds. Thank you.
References
[I] SAIDOH, M. and TOWNSEND, P. D., Radiat. Ef 27 (1975) 1. [5] KOWALCZYK, J. and DAMM, J. Z., Acta Phys. Pol. A 49 (1976) [2] ITOH, N., J. Physique Colloq. 37 (1976) C7-27. 713.
[3] AGULLO-LOPEZ, F. and JAQUE, F , J. Phys. Chem. Sol~ds 34 (61 HOSHI, J., SAIDOH, M. and ITOH, N., Cryst. Laltice Defects
(1973) 1949. 6 (1975) 15.
(41 HOBBS, L. W., HUGH=, A. E. and P ~ E Y , D., Proc. R. Soc.
London A 332 (1973) 167.
