Heavy Ion Radiation Damage Annealing in SSNTDs and Single

Activation Energy Model

H.S. Virk

Visiting Professor, SGGS World University, Fatehgarh Sahib (Punjab)

Historical Review of SSNTD

Nuclear Track Society of India is organizing SSNTD-15 at HNB Garhwal University at Tehri with RK Ramola as its Convener; the first meeting was held in BARC, Trombay in 1979 by RH Iyer as Convener.

INTS will organize 24th Int. Conference at Bologna in Italy in 2008; starting with first meeting in Strasbourg, France in 1957.

RL Fleischer, one of the founding fathers, predicted a Plateau for SSNTD research in one of his Reports; but he has been proved wrong!

SSNTD Plateau

SSNTD Trends in Report

Average global rate of production of research papers in SSNTD during 1970-90 = 280+- 60

SSNTD applications in Nuclear, Space and FT Dating research are showing a downward trend.

Applications in Radon Monitoring and Heavy Ion Materials research are showing an upward trend.

History of SSNTD Research in Guru Nanak Dev University, Amritsar

Starting in 1979, almost all areas of SSNTD applications have been covered.

FT Dating, Inclusion Dating, Annealing. Uranium estimation, and its exploration. Radon monitoring in soil, air and homes. Earthquake monitoring using radon/helium

in soil and groundwater. Ion Track Applications in diverse fields. Heavy Ion effects in a variety of Polymers.

Radon Survey in Groundwater at Palampur (Virk, Randhawa & Ramola)

INTRODUCTION

Passage of a heavy ion in an SSNTD creates intense radiation damage which results in a series of point defects and extended defects along the latent track. Various Models have been proposed to explain track formation in SSNTDs. An equally cumbersome explanation has been given for track removal in SSNTDs, better known as radiation damage annealing of tracks.

ANNEALING of LATENT TRACKS

Track annealing is dominantly a diffusive process in which interstitially displaced atoms thermally penetrate an activation barrier to recover their initial lattice positions. Thus one is led to an Arrhenius type relation based on Boltzmann equation.

NATURE of DEFECTS

Tombrello et al. suggest that extended defects are generated by atomic K-shell excitations in the heavier elements of the SSNTD. HREM reveals that latent tracks are constituted of extended defects, separated by gap zones loaded with point defects.

Annealing of Defects in a Solid

Annealing rate or mobility of point defects increases rapidly with rise of temperature. It may occur by three different mechanisms:

Random diffusion to sinks. Recombination of vacancies and

interstitials. Annealing of defects by interaction

with impurities.

Single Activation Energy Concept

If the annealing of a defect occurs by a single activated process with a constant activation energy Ea, then rate of change of concentration of the defect is describable by the equation:dn/dt = -F(n)K = -F(n)Ko exp(-Ea /kT ), (1)

Where n is the fractional concentration of the defect, F(n) is any continuous function of n, and K is the rate constant involving a Boltzmann factor, exp(-Ea/kT), for its dependence on annealing temperature T.

It is implicitly implied by equation (1) that activation energy Ea is independent of n.

Determination of Ea

There are several methods for determination of activation energy from annealing-data curves: (i) method of cross-cut, (ii) ratio of slopes, (iii) constant rate of heating, and (iv) combination of isochronal and isothermal anneal. We discuss here only the method of cross-cut because of its simplicity and ease of performance compared with the other methods.

TRACK ANNEALING MODELS

Track annealing models are classified into three categories according to their mathematical formulation, viz., logarithmic model, linear model and exponential model.

Most of the earlier authors used logarithmic model for annealing of fission tracks in minerals and glasses using the Arrhenius equation:

t exp(- Ea /kT ) = constant,

Where is Ea effective activation energy, k is Boltzmann constant, t and T represent annealing time and temperature, respectively. This model gives a spectrum of activation energies at different annealing temperatures.

Limitations of Arrhenius Equation

(i) The Arrhenius equation is applicable under constant temperature conditions. It necessitates approximations as soon as the fading temperature varies with time.

(ii) Most models are based on an 'a priori' assumption that the latent track anneals as a whole. . Hence it is not justifiable to correlate the residual lengths or diameters of the partially annealed tracks with annealing temperature and time.

(iii) The activation energy is a function of the degree of track loss in a given temperature-time plane which results in fanning of the Arrhenius plots.

Single Activation Energy (SAE) Model: Conceptual Formulation

Ionisation rate or energy loss dE/dx in a material varies continuously along the track profile.

As a consequence, etching rate also varies along the track profile.

Annealing rate must also vary along the track profile.

Chemical etching destroys much of useful information (physics).

Bimolecular Reaction Model

To resolve the contradictions of Arrhenius approach, Modgil and Virk proposed the Single Activation Energy Model on the assumption that the activation energy is a material dependent property. The empirical formulation of this model relates the instantaneous annealing velocity

Va = dl/dt or dD/dt, explicitly with time and temperature, a

crude justification for which has been provided by the assumption of a bimolecular reaction model.

Author’s group studied radiation damage annealing kinetics in SSNTDs, viz., minerals, polymers and glasses, in great details and proposed an empirical formulation:

Va = At-n exp (-Ea / kT),

Where Va is annealing rate, Ea is activation energy, k is Boltzmznn constant, t and T are annealing time and temperature, A is proportionality constant and n is exponent of annealing time, t.

The advantage of this new approach is that it yields single activation energy of annealing which is an intrinsic property of a given SSNTD, independent of the ion beam used and annealing time and temperature.

Experimental Approach to SAE Model

Two sets of experiments are performed to test this model:

Isothermal Experiments: Annealing rate, Va, is studied by varying t and keeping T constant. Plot of log Va versus log t will yield the value of n.

Isochronal Experiments: Keeping t constant and varying T, Va is determined. Plot of log Va versus 103/T yield the value of Ea, the activation energy of SSNTD.

Determination of annealing rate,Va

Determination of power n

Determination of Ea

Modification of SAE by Price Group

Salamon et al. replaced the annealing velocity by the etch rate reduction of annealed latent tracks and found that the activation energy, Ea and other parameters, i.e. n and A, are also constants. Price et al. have found an application of our model in their annealing experiments using phosphate glass detectors for recording of relativistic cosmic ray nuclei tracks in Space Shuttle ‘IONS Experiment’.

Modification : A Final Version of SAE

To overcome the shortcomings of our earlier formulation and that proposed by Salamon et al., Bhatia & Virk proposed the new formulation replacing the instantaneous annealing velocity, Va, by the instantaneous track etch velocity, Vt: d/dta(Vt) = At-n exp (-Ea / kT),

which gives a better fit to annealing data in SSNTDs

Special features of SAE model

(i) It predicts a single activation energy of annealing for all heavy ions as required by the Arrhenius equation.

(ii) It may be used for revealing the thermal history of track recording SSNTDs (minerals, meteorites and lunar rocks).

(iii) It explains the partial fading of tracks due to environmental annealing.

(iv) It has a universal application for all SSNTDs (both crystalline and amorphous) using a variety of heavy ion beams and fission fragments.

Missed Opportunities & Lessons

Experimental work need to be supplemented by Theoretical analysis of data.

Publish the data in top rank journals otherwise your work may be ignored by peers.

Our SAE model lost its IMPACT because of the above reasons and we felt almost cheated!