90 Nuclear Instruments and Methods in Physics Research B44 (1989) 90-96

North-Holland

ANNEALING KINETICS OF HEAW ION PRODUCED DEFECTS IN CRYSTALLINE MINERALS

Lakbwant SINGH and Surinder SINGH

Department of Physics, Guru Nanak Dev University, Amritsar-143005, India

Received 12 May 1989

The annealing kinetics of Pb*“(13.8 MeV/n) ion produced defects in crystalline minerals, viz muscovite mica, garnet and quartz are discussed. On the basis of annealing behaviour, we have proposed two annealing processes one at a lower temperature and the

other at a higher temperature. These annealing stages are described by two newly proposed empirical relations based on the change in

track etch rate and track retention rate. The results for the two activation energies corresponding to two annealing stages are determined for each mineral.

1. Introduction

When crystalline minerals are bombarded with heavy ions of sufficient energy, they create a linear damage (latent tracks) along their path and leave behind much physics to be investigated, viz the physical and chemical properties of the damaged and undamaged material and the etching and annealing phenomenon of latent tracks. Chemical etching and annealing studies play an im- portant role in the field of solid state nuclear track detectors (SSNTDs). Although etching of heavy ion tracks destroys almost all the radiation damage physics which is stored as energy and is characteristic signature of latent trails, yet these etched tracks become the basis of well known numerous applications in diverse fields [l-5].

There are various physical processes taking place during the passage of heavy ions through solids. How- ever a complete and satisfactory description of heavy ion spikes is not yet available [6]. The phenomenon of thermal annealing of radiation damage tracks in miner- als has been studied now for over two decades by various authors [7-111. Most of the previous studies of thermal annealing have been done on fission fragment tracks in crystalline minerals, glasses [12-141 and plas- tics [15,16]. It is obvious that these studies do not reveal the reaction kinetics to predict the annealing behaviour for arbitrary initial damage. Most recent studies [17,18] have been attempted to elucidate the contribution of various reaction mechanisms. But still the existing theo- ries of track fading in glasses and minerals are being questioned.

In the present work an attempt is made to under- stand the annealing kinetics of heavy ion latent tracks as a function of time and temperature, which as a consequence determines the microscopic spatial distri-

0168-583X/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holland)

bution of various defects produced along the environs of heavy ion trails. Before proceeding towards this, we would like to give some recent studies about the energy loss, defect production and their investigation through different annealing experiments.

2. Energy loss and defect production

It is assumed that the crystal structure is anisotropic and its characteristic molecular layers are separated by planar channels. During the passage of swift heavy ions in the crystal lattice, the distribution of the energy to its environment is essentially given in three ways [19].

-dE

+dx ( I radmtion (1)

The major part of the energy lost per unit length of its range is accounted for, by the ionization of the atoms in its way. Some of the energy is imparted to displace the atoms in the planar channels and to create the interstitial-vacancy pairs known as point defects, while the remaining part is accounted for, by relaxation of stresses and strains due to mechanical as well as Coulombic forces, which in turn are known as stable defects. To investigate such defects, X-ray scattering experiments have been carried out on four silicates (viz muscovite mica, Labradorite Pyroxen and olivine-pre irradiated with Ne, Ar, Fe, Cu, Kr and Xe ions [20]). These authors propose a new model of nuclear particle tracks in SSNTDs referred to as the “Gap Model”. They concluded that the latent tracks consist of ex- tended defects, separated by “gap zones” loaded with point defects. The size of the extended defects depends

L. Singh, S. Singh / Annealing of heavy-ion tracks in minerals 91

upon the mass, energy and charge of the ion as well as

the type of the crystal. A later independent series of experiments was also

employed to investigate the heavy ion produced defects in various dielectrics [21]. These experiments include X-ray small angle scattering along with the scattering of cold neutrons from the irradiated foils of the dielectrics. They observed that the average radius of Kr tracks in mica is compatible with that calculated by Dartyge et al. [20]. However they were not able to observe the agglomeration of point defects predicted by her model. Moreover they did not observe any “diluted” case men- tioned in her paper even for the lightest ion. However none of authors of the two papers [20,21] have tried to interpret the defects from the microscopic etching and annealing parameters of the latent tracks.

3. Analysis of previous annealing models

Almost all the previous annealing models are based on the annealing kinetics of fission fragment tracks (spontaneous or induced) in minerals and glasses.

Naeser et al. [22] and Wagner et al. [23] have found an empirical relation based on the laboratory annealing data of fission tracks in apatite.

p(t) =A -B(T)p(O) In t, (2)

where p(O) and p(t) are the densities of the tracks before and after annealing, while A and B are the annealing constants.

Dakowski et al. [24] tried to establish an equation to represent their isothermal annealing data for a variety of minerals and glasses on the basis of track reduction density as

In(t)-ln(i,)=(~-~i(,,l+~~+y), (3)

where r = p( t)/p(O), (Y, p and y are the coefficients which can be fitted using the data found from an Arrhenius plot. (ln(t,), T,) is a point common to all track retention levels. However the authors proceed to show that the second order term in eq. (3) is vanishingly small and can thus be reduced to

~(f)/p(O)=a--6 In t, (4)

which is similar to eq. (2) and becomes the logarithmic model. Laslett et al. [25] show that this model is in- compatible with their annealing data. Montavani [26] gave a linear relationship between the track retention rate and annealing time

P(f)/P(O) = a - bt, (5)

which was also supported by Burchart et al. [27] for fission fragment tracks in muscovite mica. On the other

hand Bertel and Mark [17] suggested that the annealing behaviour of etchable fission tracks in minerals is, in practice, represented by an equation of the form

p(t) = P(O) exp(-at), (6)

where (Y is the annealing coefficient depending upon the temperature and is given by the sum of two exponential decays

(7)

where a,, and ao2 are annealing constants and k is the Boltzmann’s constant. The authors found that the two values of activation energies E,, and E,, correspond to two different processes for the annealing of fission tracks.

Green et al. [28] tried to explain the annealing be- haviour in inorganic solids particularly in apatite using a different approach. The authors claimed to described their data as a best fit by the expression

ln f - C,{ln[l -/(t)//(O)]} = C, + C,/T, (8)

where I(t) and I(O) are the annealed and unannealed track lengths, respectively, and C,, C, and C, are the annealing constants, that can be determined from the experimental data. The authors of this model examined whether the annealing behaviour of fission tracks can be described by a single annealing process.

Modgil and Virk [29] postulated a three step anneal- ing model relating the annealing rate, VI, with activa- tion energy, E,, as,

v, = At-” e-E.Jkr, (9)

where A is the proportionality constant, n, the expo- nent of annealing time, k, the Boltzmann’s constant and T is the absolute temperature. The annealing rate, V,, is defined as the rate of change of track length at given annealing temperature. This model also predicts the single annealing process. The activation energy, E,

for annealing can be determined from the slope of the plot of In V, versus l/T.

Despite the existence of numerous investigations about the annealing behaviour of fission fragment tracks in minerals, there is no generally accepted description of the annealing kinetics and as a consequence the applica- tion of these models to age correction methods is still being questioned [17]. Moreover, since the fission frag- ments are undefined and the tracks produced by them yield more statistical and personal errors, this creates ambiguities in understanding the annealing mechanism. Thus an attempt has been made to understand the annealing mechanism of the defects produced by defined heavy ions in crystalline minerals.

92 L. Singh, S. Szngh / Annealing of heavy-ion tracks in minerals

4. Heavy ion track structure and annealing mechanism

The heavy ion irradiation of the crystal lattice causes the production of different types of defects along the environs of its trajectory, viz (i) ionic defects, (ii) inter- stitial-vacancy pairs and (iii) extended defects.

It is assumed that the main part of the heavy ion energy is imparted to ionize the atoms in its way [30] and produces ionic defects. Some part of the heavy ion energy is used to displace the atoms from their normal lattice sites into the interstitial positions and create interstitial-vacancy pairs. Both types of defects are generally known as point defects. The main type of defect which plays a special role in the formation of etchable heavy ion trails are known as extended defects. They involve Coulomb repulsive forces as well as the relaxation of the elastic and mechanical strains between ionic defects and the bulk of the solid. So it is proposed that heavy ion latent tracks consist of all of the above types of defects, in particular of extended defects which are separated from zones of loaded point defects. A schematic representation of heavy ion track formation is shown in fig. 1.

It is believed that the different defects return to their original positions particularly when the crystal is heated. To understand the systematic annealing mechanism of such defects, two annealing models are postulated to govern the corresponding two annealing stages of the defects. These models are formulated on the basis of different etching and annealing parameters, which are determined from the laboratory annealing data.

Fletcher and Brown [31] proposed three annealing stages of the point defects on the basis of the electrical parameters: (i) monomolecular recombination of Fran- kel defects, (ii) transient diffusion of point defects to the defect sinks as dislocation or the sample surface, and (iii) bimolecular recombination of complementary defects.

Bertal and Mark [17] describe the reduction of defect concentration in an isothermal experiment by the sum

000000000 oeooo~o,go 0 0 000 0 e 0.0 4 2: I 00 a

/ O 7’ r,:::

@ Q/o “0 : ‘0 :O: : 000000000

Fig. 1. Schematic representation of track formation mecha-

nism. (i) Production of ionic defects and interstitialLvacancy pairs. (ii) Production of extended defects by relaxation of

elastic and mechanical strains and also due to Coulomb repul- sive forces between positive cores of ionic defects.

of exponential decay functions

n(t) =n(O) exp(-t/7,), (IO)

where n (0) and n(t) are the point defect concentrations before and after annealing respectively, and 7, is the mean time for monomolecular recombination of inter- stitial-vacancy pairs and is given by

T = 710 exp( K&T) 3 (11)

where E,,, is the effective activation energy. It is experi- mentally impossible to calculate the effective energy using the above relation. So we propose an empirical relation between the measurable physical quantity, i.e. etching rate as function of annealing time and tempera- ture, and the effective activation energy for recombina- tion of the ionic defects. The relation is based on the decrease of track etch rate, V, with time and tempera- ture and is given by

VT(O) - V,(t) t

= At-” e-EedkT, (12)

where I/,(O) and VT(t) are the etching rates before and after annealing, k, the Boltzmann’s constant and n is the exponent of annealing time. The etching rates used here are the instantaneous etching rates, and are de- termined from the linear portion of the graph (figs. 2, 5 and 8). The experimental data involving the etching rate as the physical parameter is found to be a best fit in the empirical relation [eq. (12)] only up to a certain range of time and temperature, however at higher temperature the fitting diminishes gradually. The annealing process for the first stage i.e. the stage of monomolecular re- combination of the ionic defects and interstitial-vacancy pairs is described by the above empirical relation and corresponds to a single effective activation energy. For calculating the effective activation energy of this stage eq. (12) can be written as

ln VT(O) - VT(f) t

= In A - n In t - E,,,/kT. (13)

The slope of the graph (figs. 3, 6 and 9) between the left hand side and T-’ gives the effective activation energy for the monomolecular recombination. As dis- cussed earlier at higher temperatures the experimental data is found to be a worse fit in eq. (12) and conse- quently involves the second stage of annealing. It is proposed that this stage is given by the transient diffu- sion of the atoms after monomolecular recombination towards defect sinks. This is similar to that proposed by Fletcher and Brown [31]. The well established theory governed by the diffusion of the defects in the defect sinks is related to the gradient of the defect concentra- tion by a phenomenological relation known as Fick’s Law,

J,, = -D grad N, (14)

where J, is the number of atoms crossing unit area in

L. Singh, S. Singh / Annealing of heauy-ion tracks in minerals 93

unit time, D is the diffusion constant or diffusivity. The minus sign means that diffusion occurs from high con- centration towards the defect sinks. The diffusion con- stant depends upon the annealing temperature and is given by

D=D, exp(-Q/kT), (15)

where Q is the activation energy for the second stage of annealing i.e. the diffusion of atoms. However it is impossible to calculate the value of the activation en- ergy using this equation from the annealing data of etchable heavy ion tracks. So it is proposed that the activation energy for the second stage of annealing must be related to the track retention rate as a function of time and temperature. Moreover at higher temperature the track retention rate plays a predominant role over the track etch rate for explaining the second single annealing process. The experimental data at higher tem- perature can be described by modified empirical rela- tion of Modgil and Virk [29] as follows

1 --r=At’-” exp(-Q/kT), (16)

where r = I(t)/l(O), the ratio of the annealed and unan- nealed track length and is known as the track retention rate. A is the annealing constant depending upon the nature of the ion and the detector. To determine the activation energy, we rewrite the above eq. as

ln(1 -r) = In A + (1 - n) In t - Q/kT. (17)

The slope of the graph (figs. 4, 7 and 10) between ln(1 - r) versus the inverse of temperature will give the activation energy for the second stage of annealing. The value of r is experimentally found at each annealing interval for different minerals.

5. Experimental procedure:

The experimental part involves the (i) irradiation, (ii) annealing and (iii) etching of the samples.

(i) Irradiation of samples: The muscovite mica after cleaving a thin section (thickness 200 pm) from a tightbook was irradiated with *08Pb (13.8 MeV/n) ion at 15” angle of incidence. The other crystalline miner- als viz: garnet and quartz after cutting, and polishing the most frequent face of each were irradiated with the same ion. The ion irradiation facility was supplied by the UNILAC heavy ion accelerator at GSI Darmstadt, which is characterized by a small emittance, a well defined mass, charge and energy of the ions and their stochastical distribution in phase space. The irradiated samples were then cut into a large number of small pieces for the comprehensive study of annealing be- haviour.

(ii) Annealing of samples: The different irradiated samples were heated in a temperature controlled Muffle

furnace with an accuracy f 3” C at the temperature range from 400 o C to 950 o C for times of 10 to 50 min. Both isochronal as well as isothermal annealing experi- ments were carried out for each type of sample.

(iii) Etching procedure: The muscovite samples (un- annealed and annealed) were etched in 48% HF at constant temperatures of 27 o C for time intervals rang- ing from 20 to 80 min [32]. The mean length of the tracks at each etching interval was measured under an optical microscope. The garnet and quartz samples were etched using suitable etchants [30]. However the etching conditions are changed for the better revelation of heavy ion tracks. The boiled 15N KOH is used for etching of the quartz samples while the garnet samples were etched in 25N NaOH at 150” C of temperature. The etched samples were washed in distilled water and then dried in a dust free atmosphere. These samples are then scanned under an optical microscope at magnification of 400 x . In the present measurements, we have used the mean track length after applying the correction due to dip.

6. Results and discussion

To understand the annealing behaviour of various defects along the environs of heavy ion trails we have developed the two expressions. These are based on the change in track etch rate and track retention rate as a function of time and temperature. Fig. 2 shows the variation of track length with etching time for irradia- ted, annealed and unannealed samples of muscovite mica. No change is observed in the maximum track length up to the annealing temperature (723 K), how- ever a systematic variation occurs in the track etch rate

120

1

-.- -e-

-I-

-s-

-A-

-A-

-o-

--c

Unonneaied Annoeoling at

623 K

673’K

723’K

773’K

823’K

848’K

873’K

g23k

I I I I J

0 20 40 60 80 100

Etching time (mtn )

Fig. 2. Variation of track length with etching time of unan- nealed and annealed (for 30 min) *‘*Pb (13.8 MeV/n) ion

tracks in muscovite mica.

94 L Singh, S. Singh / Annealing of heavy-ion Iracks in minerals

-2.Or

- -3.o- L

F

+I0 min

*30min

s -4.0

: y\

+ 50min

F +

z -5.0

-6.01 , , , t r 1.2 1.3 1.4 1.5 1.6 1.7

103/T (K-l)

Fig. 3. Plot of In [V*(O)- Vr(t)/t] vs l/T for different annealing time intervals in muscovite mica.

at lower temperatures (< 823 K) of muscovite mica (fig. 2). The track etch rate decreases with increase of the annealing temperature. The experimental data of de- crease in track etch rate in the lower temperature range help us to propose a first stage for the annealing pro- cess. To describe this stage of the annealing process quantitatively, the data is found to be fitted best by the the proposed empirical relation [eq. (12)]. However at the higher temperature range (823-923 K), the eq. (12) does not satisfy the data of etching rates for muscovite mica. At the same time the other parameter i.e. the track length reduction rate gives more information about the annealing of heavy ion tracks at higher tempera- tures. This parameter is used to describe the second stage of the annealing process. In this annealing stage, we propose the transient diffusion of the atoms towards the defect sinks which supports the phenomenon, as observed by Fletcher and Brown [31] in the case of an electron irradiated crystal. To describe this stage of the annealing process quantitatively, the experimental data of track retention rate as a function of time and temper- ature is found to fit best according to eq. (16). Thus the two annealing stages, one in the lower temperature range and the other in the higher temperature range,

-l.O-

; -z.o-

c 5

-3.o-

-a- 10 mm

-o-30mm

-*- 50mtn

I I I I I I !

1.00 I .lO 1.20 1.30 l-40 1.1 1.2 1.3 14 1.5

103/T (K-‘) 103/T(K-‘)

Fig. 4. Plot of In (1 - r) vs l/T for different annealing time intervals in muscovite mica.

Fig. 6. Plot of In [V,(O)- Vr(t)/t] vs l/T for different annealing time intervals in garnet.

Table 1

Activation energy of 2osPb (13.8 MeV/n) ion tracks in musco- vite mica for different annealing intervals

Annealing

time (mm) Activation energy (ev)

1st stage (I?,,,) 2nd stage (Q)

10 0.43 1.02 30 0.46 1.01 50 0.45 0.99

correspond to two activation energies. The values of the activation energies are different for different minerals.

The activation energy for the first stage of the an- nealing process in muscovite mica is determined from the slope of the graph (fig. 3) using eq. (13). While the slope of the graph (fig. 4) using eq. (17) gives the

go-

75 -

o Unanneoled

Annealed at

-.- 723-K

Annellng time 30 mln

-o- 773%

-x- 823’K

-*- 873’K

-A- 923’K

-A- 973’K

-o- 1023’K

-.- 1073-K

t

/. 15 , .

J 1 1

0 40 80 120 160 200 240 280

Etching time(min)

Fig. 5. Variation of track length with etching time of unan-

nealed and annealed (for 30 min) 208Pb (13.8 MeV/n) tracks in

garnet.

7 -4.0 -

2 F

1 -5.o- s

F -x- 10 mln

r _ -60. -o- 30m1n

-*- 5Omm

-7.o-

L. Singh, S. Singh / Annealing of heavy-ion tracks in minerals 95

-1 o-

_ -2.0 - L

C

= -3o-

-4.0 -

IOmln

30min

50min

I I I

-90 .95 1.00 1.05 1.10 1.15

103/T(K-‘I

Fig. 7. Plot of In [l- r] vs l/T for different annealing time

120- 0

.

loo- 0

L

2 80- :

r *

G = 2 60- 1

1

:: ; 40.

20 -

intervals in garnet.

Unannealed

Annealed at

0 2 4 6 8 10 12

Etching tlme(hrs)

Fig. 8. Variation of tracks length with etching time of unan-

nealed and annealed (for 30 min) *08Pb (13.8 MeV/n) tracks in quartz.

Table 2

Activation energy of *‘sPb (13.8 MeV/n) ion tracks in garnet

for different annealing intervals

Annealing

time (min)

10

30

50

Activation energy (eV)

1st stage (E,,,) 2nd stage(Q)

1.08 2.02 1.09 1.98

1.07 2.01

Table 3 Activation energy of P ( “a b 13.8 MeV/n) ion tracks in quartz for different annealing intervals

Annealing

time (min)

Activation energy (eV)

1st stage (I&r) 2nd stage (Q) _.. 10 1.43 2.11

30 1.42 2.10

50 1.39 2.12

-4 Or

-0.0 I , 0.0 0.9 1.0 1.1 1.2

103/T (K -‘I

-o- 10mm -.- 30mm

-x- 50mln

Fig. 9. Plot of In [V,(O)- V,(t)/t] vs l/T for different annealing time intervals in quartz.

activation energy for second stage of annealing. The results of activation energies for muscovite mica are given in table 1.

The experimental data for annealed and unannealed samples of garnet and quartz, irradiated with “‘Pb (13.8 MeV/n) ion at 30” incident angle is shown in figs. 5 and 8, respectively. Both garnet and quartz show similar annealing behaviour as in the case of muscovite mica. The lower temperature ranges for garnet and quartz, which describe the first annealing process, are 723-873 K and 873-1023 K, respectively. The second stage of annealing for garnet and quartz occurs at higher temperatures > 923 K and > 1073 K, respec- tively. The values of the activation energies for both the stages of garnet and quartz are tabulated in table 2 and 3, respectively. The effective activation energy for monomolecular recombination of defects in garnet and quartz are determined from the graph (fig. 6 and 9), while the activation energy for transient diffusion of atoms is calculated from the graph (fig. 7 and 10) for garnet and quartz, respectively. It is interesting to note that activation energies of each annealing stage for

0 5-

-0.5 -

-1.5 -

;1 L

E -2.5 -

-3.5-

10.

-4.5 I .75 80 05 90 .95 1 0

103/T~K-‘)

Plot of In [l - r] vs l/T for different annealing intervals in quartz.

time

96 L. Singh, S. Singh / Annealing of heavy-ion tracks in minerals

different minerals are nearly constant within the anneal- Insulators-3, University of Survey, Guildford, UK July

ing time range of 10 to 50 min (tables l-3). 15-19 (1985).

The authors are thankful to Dr. R. Spohr, GSI, Darmstadt, FRG for providing the heavy ion irradia- tion facility. Technical assistance rendered by Mr. Santokh Singh is also acknowledged. One of the authors (Lakhwant Singh) is grateful to the Council of Scientific and Industrial Research (CSIR) for providing financial assistance in the form of a Senior Research fellowship.

1141

[I51

P61

[I71

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u91

[201

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[221 v31

v41

v51

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