Discontinuous fission tracks in crystalline detectors

0191-278X/89$3.00 + .00 PergamonPressplc

Nucl. Tracks Radiat. Meas., Vol. 15, Nos.1--4,pp. 31--40,1988 Int. J. Radiat. Appl. lnstrum., Part D

Printed in Great Britain

DISCONTINUOUS FISSION TRACKS IN CRYSTALLINE DETECTORS LEWIS T. CHADDERTON # Institute for Advanced Studies, Research School of Physical Sciences, Australian National University, GPO Box 4, Canberra, ACT 2601, Australia. JOCHEN P. BIERSACK Hahn-Meitner Institute, Dept. C-2, Glienickerstrasse 1130, D-1000 Berlin, 39, FRG. and SOHAN L. KOUL CSIRO Division of Materials Science and Technology, Locked Bag 33, Clayton, Victoria 3168, Australia. Abstract - It is widely recognized that a key to the more complete exploitation of solid state nuclear track detectors lies in knowledge of the ways in which a particle is brought to rest, and how its energy is stored as lattice defects. One indirect way of looking at latent tracks - in an effort to bridge the micro/macro - has been small angle X-ray scattering, and the subsequent, multi-parameter model has spawned others for different solids. This work led to the so-called "gap model", in which intermittent extended defects are separated by point defect rich regions. Latent intermittent fission fragment tracks were seen as long ago as 1962, using direct transmission electron microscopy (TEM). It is shown, in more detail, that the intermittency arises from periodic bursts of electronic energy loss along the panicle trajectory, and that this makes it possible to measure the thickness of a crystal, using TEM, to an accuracy of one atomic (or molecular) layer. In other words anisotropy of the basic crystal lattice is responsible also for the latent track structure, as it is for the well-known angular variations in particle ranges evidenced in etched track polar plots, for which "channelling" and "quasi-channelling" arc responsible. Simple probability theory, isotropic fragment emission, and the lattice structures of muscovite mica and molybdenite are used to predict the most probable extended defect length for at least an order of magnitude comparison with the X-ray work, since crystal orientations are not specified. Speculation is made on the consequences of this work for the etching of latent tracks. I.

INTRODUCTION

It is norrnal to make certain simplifying assumptions in all theoretical treatments of the interaction of radiation with matter, especially condensed matter. We often consider, for example, two-body collisions of an ion with an atom, independent of collective effects - including phonons and potential continua, In addition the collision itself is frequently simplified by adopting a screened-Coulomb potendai which, despite its limited validity, has distinct advantages in that the Bohr parameters ~: = {Zl7_,ze2/hv} and

~ = {b/a}, where the symbols have their usual meaning,

degree the quantum and classical mechanical regimes 1, and the relative significance of screening. It is also normal, in the first instance, to consider that the scattering medium is essentially structureless, that there is no space lattice, and that collisions are determined by probabilistic 'Also: Chief Re~xrch Scientist, CSIRO,Australia 31

32

L . T . C H A D D E R T O N et al. concepts in which impact parameters are drawn from a range of values determined heuristically by the average atomic density no, and collision diameters from the energy dependent collision dynamics. In other words the medium is 'random' and, by implication, isotropic. It follows that in classical mechanics (e.g. with charged ions) there will be no channelling, and in quantum mechanics (e.g. with X-rays) there will be no anomalous transmission (the well-known Bormann effect). Neither will there be any quasi-channelling2 and scattering greater than random, nor any anomalous absorption. What all this means is that the approximations are a reductio ad absurdem carried out for the purpose of asking what the solid does to the radiation.

II.

FISSION FRAGMENT TRACKS AND THE ANISOTROPY OF TARGETS If a fission fragment leaves an observable track in a detector it is because the remanent

radiation damage is localized on the transient particle trajectory. What may be a fuzzy image of a track seen in the transmission electron microscope (TEM), due to the wave nature of the scattered electroia beam, can become a very clear image in the optical microscope (OM) after a chemical etching of the solid state detector. For crystalline detectors the etchant seeks the line of least chemical resistance, as when dislocations are present, and the etch-rate also varies with direction. For most amorphous solids and polymers the tracks are usually predictably featureless along their length, and the approximations made in first order theories are adequate at least:

Amorphous Solid + Fission Fragment => Continuous Track

(1)

There is little doubt that excited electrons, or 3-particles, are most frequentiy the primary agents responsible for radiation damage by fission fragments, and with absolute certainty when tracks are seen, either by TEM or OM, notwithstanding the complexities of the slowing-down process3. Note that in metallic solids, however, the energy carried off in the electronic stopping power Se can be fruitlessly dissipated in electrordelectron collisions, and remanent damage then often consists of randomly aggregated point defects and dislocation loops due to Frenkel pairs generated by the nuclear stopping component Sn. There is no demarcation of the trajectory - and no track. So, to a first approximation, for the case of metallic solids:

Metallic Solid + Fission Fragment => Random Damage

(2)

and nQ track, which is why metals find little application as detectors of the kind which concern us here. In the face of these two extremes - the metal and the crudely isotropic properties of its Fermi (surface) electrons, and the polymer or dielectric with such readily destroyed bonds - it is useful to ask what lies between. The rules of crystallography are such that, using the theory of groups one may describe all known crystals, both natural and synthetic including, inter alia, all minerals. It is not surprising, therefore, that a great deal of interest has focused on tracks in minerals as a consequence of the chemical etching techniques used for natural crystals in fission track (b-T) methods. Nor is it surprising that attention should also be focused on crystalline detectors generally, because of their unique physical properties. Quer~ and his colleagues 4 have used the anisotropy of the crystal lattice and the sensitivity of plastic detectors to study canaligraphie- or channelling imaging - of fission fragments

D I S C O N T I N U O U S FISSION T R A C K S to great effect. This beautiful example of how an aggregate of many fission tracks can display both easy and difficult paths through a crystal tells us at once the Sn and Se are spatially anisotropic and differently so, and may even to a degree be complementary. This brief paper addresses the question of intermittent fission fragment tracks in crystalline solids.

III.

INTERMITrENT TRACKS Small angle X-ray scattering experiments have been carried out on four silicates -

muscovite mica, labradorite, pyroxene and olivine - preirradiated with Ne, Ar, Fe, Cu, Kr and Xe ions from accelerator beams, crudely simulating fission fragments5. As a consequence the authors propose a 'new' model of nuclear particle tracks in dielectrical minerals, referred to as the "gap model", since it is concluded that latent tracks comprise extended defects (ED), separated by gap zones loaded with point defects (PD). The 'size' d of extended defects scales as it should with particle properties - energy E and charge Z 1 - and with crystal type. It would seem that d - in the interval 15/~ (muscovite mica) to >40]k(Olivine) - is to be considered as a track width, whilst another parameter ~ is described as the effective length of the core zone, ranging from 700/~ in muscovite, down to 60/~ in olivine. According to Dartyge et al.5 each extended defect represents the microscopic scar of an "ionization" spike. There is no explanation of the repeated discontinuities, however, and it must be assumed that the mineral samples are each, in their turn, automatically considered to be random, isotropic scattering media. We read, for example, "as the mean ionization potential is nearly constant in all silicates, the linear density of the spikes should be similar in these minerals", which would seem to exclude influences of crystal structure. A later independent series of experiments6 also employed small angle scattering of cold neutrons. The widths of tracks in mica were essentially conf'trrned, but the "diluted" model of Dartyge et al. was not.

In 1968 a series of TEM observations of fission fragment irradiated semiconducting layer structures were described7 which established a dependence of track registration on electrical conductivity of the crystal, when other factors such as structure, point defect mobility, and melting temperature did not differ appreciably. About a dozen transition metal dichalcogenides including that best known, molybdenite (MoS2), were examined. Those showing fission fragment tracks had a low electrical conductivity and, by way of a bonus, all the tracks were intermittent. Assuming that the anisotropic crystal structure, with its characteristic molecular layers separated by planar "channels", will impose a strong spatially variable identity on the electronic energy loss vector for the fragment, then it is clear that the stopping power in the molecular layers will greatly exceed that in the channels. Since it is rather straightforward to calculate a critical stopping power for registration of fission fragments in molybdenite, based on 'free' and 'resonance collisions', it also follows that the condition for producing intermittent tracks by marrying the structure of the lattice with the properties of the fragment is Se(layer) > Se(crit) > Se(channel). The hypothesis that intermittent tracks are due to 'spikes' or bursts of electronic energy loss when a fragment passed through successive molecular layers was tested in two quite simple ways. On the one hand counts were made of intermittent segments on individual tracks in the same crystal. Within two or three molecular sandwiches the number count was constant on the one crystal - track to track - and different but constant again on another. Also the counting method along a track was used to 'measure' crystal thicknesses which had been determined in another quite

33

34

L . T . C H A D D E R T O N et al. independent way. Apart from a minor correction due to uncertainties at the entry and exit points of the fragment the agreement was complete. Accordingly it was concluded that the intermittent tracks observed must be ascribed to the reduced energy loss when the fission fragment travels in the interplanar channel. Analysis of the free structure of the tracks indicated the presence of one defect aggregate per sandwich plane. In the case of muscovite mica, at the very least, it is hard to avoid the conclusion that the 'gap' - in the gap model5 - is anything more than an 'interplanar channer! In the present context:

AnisotropicOrystal + Fission Fragment - > Intermittent Track IV.

(3)

THE GEOMETRY Ideally, since we arc concerned with two separate experiments in which particle tracks

are investigated by the scattering of radiation, we would like to compare the predictions and results in each case. On the other hand the matter of deconvolution for small angle X-ray scattering is not a trivial task. Furthermore, although a coUimated beam of particles was employed by the French workers, strong sample orientation effects were markedly lackings. It is also to be noted that since a conventional smaU angle camera was used ion doses of such magnitude were needed - with 90% of the tracks overlapping - that it cannot be concluded that single tracks were being observed in the usual way. Conversely, T E M

methods are admittedly m o r e direct - one °sees°individual tracks. In

the limit of small sizes, however, there are problems of resolution, and of the scattering of Bloch waves at radiation induced strain fields. The geometry, too, is different in the TEM case. The fission fragments emerge into 2~ solid angle from a semi-infinite enriched uranium source placed in contact with the crystal target, which they penetrate. At birth therefore, to all intents and purposes, the fission fragment trajectory is randomly chosen, and the spatial arrangement of atoms in the target held fixed. Excluding large angle scattering events the fission fragment strikes successive molecular layers at approximately the same randomly chosen angle. Thus the target is randomly irradiated with fission fragments, rather than with a collimated beam, as though "sunburst" events - which occur when there is locally a high uranium concentration as in an inclusion - were smeared throughout the target. Indeed a random three-dimensional pattern of uranium impurities in the form of single atoms would give the same effect; quite predictable on the basis of the well-known principle of reversibility (reciprocity). Consider, then, a model for the intermittent track based on molecular layers of thickness a, in the x-y plane, separated by van der Waals gaps of thickness b (Figure 1). The vertical axis

,Z" I (the z-coordinate) is defined also to be both a polar axis and the axis of the column of the electron microscope. Passage of a fission fragment at a given angle (x to the polar axis gives track

DISCONTINUOUS FISSION TRACKS

35

intersections of layer lengths 1, and 'anti-track' intersections of 'gap' lengths m, corresponding to a and b respectively. Assuming isotropic and random emission of fission fragments from a point source, and that all register in crystal layers, but not in gaps, then we seek a solution for the projected electron microscope image, transmitted through the crystal as an x-y projection, perpendicular to the z-coordinate. Since the length 1 of an intermittent track segment is defined by the fixed length a and the randomly chosen angle t~, the basic triangle for our probabilities argument is simply the following (Figure 2): x

Figure 2. Therefore, proceeding in the normal fashion, with a on the polar axis, we define a sphere with origin on the a.1 intersect and thence a cap of that sphere through the angular element 8¢t. Hence we may write:

(i)

The probability that the track segment lies in the angular interval ~, (x+8(x is given by: 8P = 27rsinct.Stx/2rc so that we can write:

(ii)

...........

~x • (0,~/2)

p(oQ = dP/do~ = sin 0c

if

tx • (0,~/2).

The probability that the track segment lies in the length interval 1, 1+81is given by: p(1) = dP/dl = (dP/dct), (do./dl) whence, since:

1 = a/costx, and using the distribution from (i), we obtain: p(1) = a/12

(iii)

if

1 • (a,,,*).

The probability that the track segment projected onto the x-coordinate in the x-y (molecular plane) lies in the length interval x, x +dx is given by: p(x) -- dP/dx = dP/do~" do./dx whence, since: x = a ' tana, and using the distribution from (i), we obtain: p(x) =

x/a

if x •

(0,R)

a .3q {1+(x/a) 2 } where R is the maximum projected fragment range in the x-y plane.

(iv)

The raostprobable value o f x will be x, when p(x) is maximised, which is to say that the relationship dp(x)/dx = 0 should be evaluated for the expression in (iii). After some trivial algebra we obtain the result:

~" = a/,/2

36

L . T . C H A D D E R T O N e t al.

(v)

The m e a n value of x will be ~, when the following integral is solved: R R/a ~ = I x.p(x) dx = I a . ~ 2 / { 1 + ~ 2 } 3 / 2 " d ~ , 0 0

where ~ = x/a

Accordingly: x = a . o[ln (~ + "4(I+~2))- (~I,/(I+~2))]R/a.

V.

EXPERIMENT, RESULTS AND DISCUSSION

The outline of probabilities in the previous section is that which is based on pure geometry, and is therefore idealized in every sense. Clearly, for example, the most probable value of~ given by equation (7) is in every case a simple transformation of a by "42. For MoS2, since a = 3.13/~, "~ is 2.21/~ and this is substantially less than the resolving power, of most electron microscopes used in this kind of work. It follows that a majority of the tracks observed will be intermittent as defined by the geometry but that property cannot be detected and measured. The minority of the tracks, showing clearly intermittent segments must, by chance, have drawn a high value of the angle a. Indeed, implicit in equation (6) is a projected track length distribution which peaks at very low lengths, but which has a small component of the population in the form of long tracks, frequently intermittent, up to and including the mean projected range of the fragment.

Figure 3 Fission tracks in molybdenite: a general area showing both continuous and intermittent tracks - diameter - 10nm.

This clearly suggests a fruitful experimental approach for the future, in which identified tracks (Figure 3) are observed as the crystal is tilted through high angles, which can be measured in the electron microscope, and their images systematically recorded. Dark and bright field images, and weak beam methods could well be rich with information.

D I S C O N T I N U O U S FISSION T R A C K S The same arguments apply to the mean value of x. Equation (8) yields a value for x which is in the region of 2 or 3/~ for all layer-like compounds, simply because of the strong weighting over small values of t~ and x, and assuming that the lower limit to the integral is zero. By resorting to the means of artificially cutting-off a narrow column at the lower end of the distribution, and effectively introducing intelligent guesses for the real resolving power, for example x = 10a, we find an estimate of (the mean value of) ~ = 34.7/~. This is a clear statement that, in general, x and the resolving power are of the same order for normal electron microscopes. It should also be added that the very nature of the scattering of electron Bloch waves at fission tracks will itself produce distortions and blurring of the image. Finally, then, we are obliged to conclude that it is not possible to confirm the CBK-model for intermittent tracks and 'gaps' by experimentally establishing the length distributions (equations (6-8)) predicted on the basis of simple geometry. This is to be regretted since independent calibration of the microscope magnification, at different magnifications, would have constituted an internal normalization and absolute values for the layer thickness a, for different materials, could have been discovered from the distributions without specific knowledge of the angles t~. On the other hand the track segment lengths are totally consistent with the dimensions of the scattering objects detected by Dartyge and colleagues 4, although they prefer to assign the origin of their signal to track widths. It is fortunate, then, that the CBK-model of alternating electronic energy bursts and 'gaps '9, has two internal standard dimensions, namely the layer thickness a and the separation between those layers b (see Figure 1). Experimental values for the ratio a/b can therefore be established from electron micrographs of intermittent tracks by direct measurements of the ratio of the slice lengths 1 and m projected onto the x-y crystal plane, yielding l'/m' = 1/m anway, since the unkown angles ct disappear from the problem in each case. Accordingly, transmission electron micrographs taken by one of us (LTC) in Cambridge between 1961 and 1964 on an Elmiskop I machine and on an AEI EM6 machine, both operating at 100 keV, were carefully reexamined and track and gap length measurements made on carefully selected crystal areas. The fact that two electron microscopes were used is important since constancy of the results, independent of the machine, bear out the carefully calculated and noted corresponding magnifications for each micrograph. It has to be conceded that several of the finest electron micrographs had either no magnification recorded, or else a doubtful one. For this reason the quest for an absolute 'scattering length' - to be compared with the results of Dartyge et al.5 - was temporarily set aside - since in any case the ratio 1/m ought to uniquely relate track intermittency with anisotropic crystal structure, and calculation of the scattering lengths would then be far more attractive than the long, arduous and hesitant, multi-parameterized path of low angle X-ray scattering. Precautions in measuring values fox"1 and m were several; most of them obvious. Care was taken not to use crystals only a few molecular layers thick, because of problems of blow-out at fragment entry and exit points (frequently clearly observed). Also there were clear instances when changes in the separation of defect aggregates along the length of a track arose from a localized bending of the irradiated specimens (Figure 4(a)), or from changes of particle direction due to nuclear collision events (Figure 4(b)).

Extinction contours were avoided- the best and sharpest

measurements were made from micrographs on which kinematic conditions were clearly established. The usual rules of random observation theory were strictly adhered to and observations on every track investigated repeated on other days. The two materials investigated were molybdenite (MoS2) and muscovite mica ((OH)4K2A14(A12Si6)O20), from whose planar structures are predicted the'following (layer/gap) ratios:

37

L. T. C H A D D E R T O N et al.

38

Rmolyt~nite = (a]b)molybd~tite = 1.043 and

Rmuseovite

= (a/b)rnuseovite

= 0.857.

The experimental results are as follows: Rrnolylxl~tite = Rmuseovit e

1.09 + 0.07

=

0.89 + 0.16.

A total of 209 tracks were measured in molybdenite, and a total of 184 in muscovite mica. In each case the number of gap/layer segments was substantially in excess of a thousand.

Figure 4 (a) Micrograph (above) shows intermittent track in MoS2.Changes in segment separation can be used to measure the crystal curvature. (b) Micograph (below) showing change of character of track (continuous to intermittent) after close nuclear coUision. Track diameters - 10nm.

VI.

CONCLUSION

1.

The intermittency of fission fragment tracks, established with some difficulty using small

angle X-ray scattering5, is shown by transmission electron microscopy to be associated with bursts of electronic energy loss in anisotropic crystals. 2. There is no evidence in these studies for a zone between segments which is rich in point defects. 3.

The result for muscovite mica conceals difficulties encountered in this case. Thus the

'gap' often still contained a faint continuous track, along which the contrast, in the best cases, varied in a symmetrical way. This must be because the 'gap '9 in fact contains the cations A1+++, Mg ++, etc., and the so-called (OH)- and free O-- layer - in other words matter available for scattering. The possible occurrence of polymorphs 1° of muscovite proper - ferrimuscovite, picrophengite, and ferrophengite should also be kept in mind. Finally there is no doubt that some annealing would have occurred. 4. During measurements of segment lengths, which were carried out in a polar fashion, 'local' angular variations in the lengths r and m' were observed. These for the most part were

DISCONTINUOUS FISSION TRACKS smeared out for MoS2, but are retained in a certain skewness in the distribution for mica. It is encouraging to note the sensitivity of the gap/segment dimensions to this effect which is undoubtedly due to crystal anistropy in the azimuth - channeling, quasichanneling etc. 5. It also follows from the CBK model, that a rather vicious particle - the fission fragment is a reasonably sensitive probe of the solid state, since at the very least it is capable of giving information at the atomic/molecular level. Clearly, studies of the interaction of collimated beams of artificial fission fragments with crystals are suggested, coupled with transmission electron microscopy. 6. Having in mind the pressing problems of geothermometry in hydrocarbon exploration it is almost certain, accepting the CBK model, that in situ studies of the annealing of latent tracks in minerals, in the TEM, will give up hard information on species annealing, activation energies, and a better definition of maximum palaeotemperatures and an understanding of their variation with time. Annealing, of course, destroys information as surely as does chemical etching. 7.

A knowledge of the real origin of intermittent tracks will tell us much about chemical

etching. It is no accident that molybdenite should be so difficult to chemically etch - the anistropic structure, the real, sharp 'gap', plays its part. By the same token the gap/segment units are highly resistant to annealing. Mica, on the other hand, has penumbral gaps - both in the real structure and when fragments have passed along. Chemical etching is more easily carried out, and latent tracks readily anneal. 8.

The qualitative features of the model by Dartyge et al5 have been eagerly seized upon as a

basis for interpretation by a number of workers, as though it were a natural corollary of that work that all tracks will be intermittent. In the CBK model the intermittency, and the gap, becomes less pronounced the less anisotropic the solid. Whilst we do not believe that profound consequences of the lattice order ever totally disappear, nor do we believe it necessary to invoke an intermittent track model of some complexity5, say, for insulators such as the alkali ha/ides 11-12, when a much simpler and proven interpretation - for the intermittent track - already exists. Acknowled~erncnt.z The authors wish to express their gratitude to Mr. Roger Lamb for the care he has taken with so many of our micrographs. One of us (PJB) appreciates support of this work from the CSIRO Division of Chemical Physics, before its transformation into a tactical materials science research laboratory. LTC is grateful to those many colleagues who supported him in his fight through those many years.

REFERENCES 1. 2. 3.

L.T. Chadderton,"Radiation DAmage in Crystals", Methuen, London (1965). L.T. Chadderton, Rad. Effects, 27, 13 (1975). L.T. Chaddcrton, this conference (1988).

4. 5.

Y. Qu6r6, J. C. Resneau, and J. Mory, C. R. Acad. Sc., 262, 1528 (1966). E. Daxtyge, J. P. Duraud, Y. Langcvin, and M. Maurette, Phys. Rev., B23, 5213 (1981).

6.

D. Albrecht, P. Armbruster, R. Spohr, M. Roth, K. Schanpert, and H. Stuhrmann, Appl. Phys., A37, 37 (1985).

7. 8.

D.V. Morgan and L. T. Chadderton, Phil. Mag., 17, 1135 (1968). Inadvertently referred to by one of our junior colleagues as the model of"bursts and gasps".

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L.T. CHADDERTON et al. 9. 10. 11. 12.

W. A. Deer, R. A. Howic, and J. Zussmann, "Rock Forming Minerals", Vol 3., Longrnans, London (1964). R. G. Wyckoff, "Crystal Structures Volume 4", Wiley, New York (1968). T. A. Tombrello, C.R. Wic, N. Itoh and T Nakayam~ Phys. Letters, 100A, 42 (1984). N. Itoh and T. Nakayama, Nucl. Instr. Moth., B13, 550 (1986).