Modeling the fission track etching process in apatite: Segmentation or crystallography influence

Radiation Measurements, Vol. 25, Nos 1--4,pp. 137-140, 1995

Pergamon

Copyright© 1995 ElsevierScienceLtd Prin~l in ~ m

Britain. All rights rese~v~l 1350-4487/95 $9.50 + .00

13~4,187(95)00098-4

MODELING THE FISSION TRACK ETCHING PROCESS IN APATITE: SEGMENTATION OR CRYSTALLOGRAPHY INFLUENCE

F. VILLA, M. GRIVET, M. REBETEZ, C. DUBOIS and A. CHAMBAUDET Laboratoire de Microanalyses Nucldaires, UFR des Sciences et Techniques, 16 route de Gray, 25030 Besangon cedex, France

ABSTRACT In this study, two factors which can influence fission track etching in apatite are considered: track segmentation (induced by thermal annealing) and variable radial etching speed (due to the reagent diffusion during the etching process). During the latent track annealing, two distinguishable steps can be identified by measuring track lengths or diameters. A length reduction is firstly observed, followed by a segmentation process which leads to the emergence of disrupted regions (gaps). At present time, electron microscopy studies on fission tracks in apatite show profiles which lead to hypotheses of a variable radial etching speed versus depth. These variations can be interpreted in terms of acid diffusion along the track. Moreover, the existence of several bulk etching speeds related to crystallographic orientation is approached. Taking into account these different points, a software program, integrating parameters as original track orientation and depth, number of gaps, etc., is developed in order to model the track profile evolution during the etching process. Comparison with experiments in Durango apatite (Mexico) are also undertaken.

KEYWORDS Fission track; etching; segmentation; simulation; crystallography; annealing.

INTRODUCTION The latent fission track registration in Solid-State Nuclear Track Detectors (SSNTD) has many applications, especially with apatite for oil prospecting: the analysis of track densities in a mineral may allow to determine its age, and the employment of the track length distributions may allow the reconstitution of its thermochronological history (with confined and surface tracks). However, the reduced dimensions of the latent tracks prevent a direct measure of their lengths. Their observation with a microscope is possible only after etching by an acid solution. The parameters then measured and used in the models depend on the characteristics of the reagent. Indeed, etching generates a difference between the measured etched track lengths and the latent ones, because of the under- or over-etching phenomena. In the goal of establishing the optimal etching conditions, i.e. to get a minimal deviation between latent and etched track lengths, we realised a simulation of etching in apatite. Two parts will be separately treated in this paper: first, the influence of track segmentation on the etching process and second, the introduction of crystallographic parameters.

INFLUENCE OF TRACK SEGMENTATION ON THE ETCHING PROCESS Track segmentation The fission tracks are very sensitive to a thermal effect: it produces an annealing, resulting in a reduction of their initial lengths. Carlson (1990) has established that a very high annealing may generate gaps and may result in a random segmentation. This segmentation do have some effects on the length distribution, and consequently it is important to understand the etching mechanism of a segmented track. 2s:l/4-t

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138

F. VILLA et al.

Etchinl~ simulation: Drincinle The principle of the etching simulation is as follows: * Only the surface tracks are considered and the simulation is developed in two dimensions. * The etching is simulated by applying a Vg vector normal to the surface, in each point of the mineral in contact with the acid, and a Vt vector applied into the direction of the track (Vt>Vg) (Somogyi & Szalay, 1973). * For a non-segmented track the algorithm includes several steps (Fig. 1) : Firstly, (x0,z0) is defined as the point of intersection between the track and the surface. The reagent enters into the track at a rate V t. During a time At, it has covered a distance of Vt.At along the track from (x0,z0), and Vg.At perpendicular to the both sides of the track. During this time, the surface has regressed of Vg.At, too. There are two intersections between the surface and the track opening, called (Xl,Zl) and (x2,z2). The point reached by the acid along the track is called (x3,z3). The next step is the attack of the three points (Xl,Zl), (x2,z2) and (x3,z3) up to the deeper point of the latent track. These three points are sufficient to define a track during this under-etching stage. Finally, the bottom of the track is developed circularly with a radius of Vg.At. The limit of the circular part is defined by two other points: (x4,z4) and (x5,z5). So, for a non-segmented track, an etched figure can be described by the evolution of only 5 points. * A segmented track is etched according to the precedent algorithm but the etching rate along the track is alternatively V t when the acid is in a segment and Vg when the acid is in a gap. So, the beginning of the etching process is similar to a non-segmented track. When the etching front encounters the second segment, two other rectilinear slopes are developed. When the acid reaches the bottom of the second segment a new circle appears.

vgAt

,~0,z0 ) (x,,z,)

::::::::::::::::::::::::::::

" //

IVg ./it

! i i ixiz//i..f

/~

xi!

!

Initial step Final step Fig. 1. Simulation of the etching process without segmentation. Finally, if the track has n segments, an over-etched segmented track is described by 4n+l points. For example, on the Fig. 2 the latent track has 2 segments and the etched figure is described by 9 points. Track Segment n°l (over-etched)

i Vg.At

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/

/~£2;4):

(X1,Zl )

!

::::::~7

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i! iT:ra:~e~e~,in:~ iiiiOio~tdh~d) il iii Initial step

!

i

i i iii

i i iii

~

/

~

z

2

7

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ii Final step

Fig. 2. Etching process of a segmented track.

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SIMULATION OF ETCHING IN APATITE

139

First simulations Figure 3 presents the simulation obtained by the etching of two tracks oriented with the same angle, but which have two different segmentation degrees. The first one has 3 segments and the second one 10 segments. The etching conditions are identical in the two cases (Vt/Vg = 20, tetching -- 40, Vt = 0.5, arbitrarily chosen). We can see that the shape depends strongly on the degree of segmentation. Indeed, the depth and the opening dimension of a track are much more important with a low segmentation than with a higher one. The etched track length varies on the same way. st

2,..i

,x..,-J~

/ / /

3 segments, Vt/Vg = 20

10 segments, Vt/Vg = 20

Fig. 3. Comparison of the etching for two degrees of segmentation.

The degree of segmentation of a track can be described by the ratio between the gap length sum and the entire track length. For a given degree of segmentation, there is an infinity of possible gap distributions along a track. Indeed, gaps may be numerous with reduced dimensions or fewer with more important dimensions, with the same degree of segmentation. Moreover, gap length can be the same or not for all the gaps, and the gaps can be distributed homogeneously or randomly along a track. Carlson (1990) indicates that an annealing results first in a track shortening by its extremities. Then a random segmentation occurs. In order to determine which kind of gap distribution leads to projected length histograms consistent with the experimental ones, we have assumed to simulate the etching of tracks which are segmented according to different ways. Thus, a first simulation was realised on a population of homogeneously segmented tracks. These tracks have an initial length of 16 ~m and they contain 10 gaps of 0.08 I.tm each. The angle and the intersection of each track with the plane of cut are randomly chosen in the conditions defined by the 'porcupine' geometric model (Dakowski, 1978). If we define a horizontal reference plane as the plane intersecting the upper point of a track, the etching one is randomly chosen between the two depths -Vg.tetching and +Vt.tetching in order to simulate the probability of intercepting a track. Etching conditions are: Vg = 0.05, Vt = 1.00, tetching = 16. First results show that hypotheses defined on the segmentation are not realistic because the projected length distribution doesn't agree with the experimental data. The deviation can be due to a wrong distribution of gaps, or to the combination of the gap number with their lengths. In conclusion of this part, the major axis for the development of this work is to define a realistic gap distribution along the track, and then to link it with the annealing degree, by comparison between simulation and experiments.

CRYSTALLOGRAPHIC ASPECT If we look at the tracks on a prismatic plane, we obtain sometimes figures such as those presented on Fig. 4. It represents a prismatic plane of a Durango apatite which has been exposed to a normal Krypton ion beam of 1.29 MeV/nucleon, and then etched by nitric acid 1%. The track intersection with the surface presents a geometrical figure that we can explain by the hexagonal crystallography of the apatite. A simulation has been realised and a good agreement was attained with the integration of a diffusive term into the crystallographic routine. * For the crystallographic aspect, the apatite belongs to an hexagonal group of symmetry. The norm of an attack vector is taken to be proportional to the crystallographic parameters. The value of this norm depends on two angles which are necessary to indicate the direction of the attack vector in a crystal bulk. This calculation required a mathematical development which is not detailed in this paper.

140

F. VILLA et al.

* To integrate the diffusive term, we used the second Fick's law.

C i = concentration at Az and t given (mol.1-1) t = time (s) The solution is given by :

Di

32Ci

~C i

~Az2

~t

= 0

(1)

Az = depth (txm) D i = coefficient of diffusion (I.tm2.s-1)

C = Cs + ( C O - C s ) . e r f ( x )

C = concentration at Az and t given (mol.1-1) CO = concentration at the bottom of the track (tool.1-1)

with

X - 2~D~.t

(2)(3)

C s = concentration of the reagent (mol.1-1) eft(X) = error function of Z

The main parameters are D i and Az. A good combination of these two parameters produces an important etching rate at the top and a low etching rate at the bottom of the track and produces a similar figure to this obtained by TEM (Fig. 4) (Grivet et al., 1993).

Simulation

TEM picture

Fig. 4. Crystallographic simulation compared with carbon track replica observed by TEM. CONCLUSION Two etching simulations are presented in this paper: on one hand, the influence of the segmentation on the etching parameters is studied. A segmentation leads to an important deviation in the projected track length distributions. The quantification of this deviation necessitates a better knowledge of the gap distribution along a track. On the other hand, a preliminary approach of the crystallographic influence shows the necessity to integrate a diffusive term, at the very least for the weakly concentrated reagents. Comparisons with experiment on the Durango apatite are under development in order to determine relations between annealing and projected length distributions, including crystallographic parameters. REFERENCES Carlson W. D., 1990. Mechanics and kinetics of apatite fission track annealing. Am. Mineralogist, 75, pp. 11201139. Grivet M., Rebetez M., Chambaudet A. et Ben Ghouma N., 1993. Electron microscopy analysis of Krypton ion tracks induced in Durango apatite. Nucl. Track Rad. Meas, .22, n ° 1-4, pp. 779-782. Somogyi G. et Szalay S. A., 1973. Track diameter kinetics in dielectric track detector. Nucl. Instr. Meth., 109, pp. 211-232. Dakowski M., 1978. Length distributions of fission tracks in thick crystals. Nucl. Track Detection, 2, pp 181190