Determination of track parameters by diffraction method using laser light

NUCLEAR

INSTRUMENTS

AND

METHODS

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NORTH-HOLLAND

PUBLISHING

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D E T E R M I N A T I O N OF TRACK P A R A M E T E R S BY D I F F R A C T I O N M E T H O D U S I N G LASER L I G H T M. V/~.RNAGY, J. SZABr, S. JUH/i,SZ and J. CSIKAI

Institute of Experimental Physics, Kossuth University, Debrecen, Hungary Received 17 July 1972 Measurements were performed for determining the diameter of tracks by the Fraunhofer-diffraction method. A ~ 1 mW He-Ne gas laser as a light source as well as cellulose acetate track detectors irradiated with alpha particles at different energies were

used. The diameter of tracks determined by the diffraction method as well as those measured by microscope are in good agreement with each other.

1. Introduction

with 9 the angle between the parallel and diffracted beams (see fig. 1). The intensity I(P) has its principal maximum at x = 0, the places of secondary maxima and minima can be calculated from the conditions

Although the solid dielectric track detectors have only been in use for a few years, they are applied in more and more fields owing to their advantageous properties 1-3. In our Institute especially the detection problems of light charged particles (Z ~< 2)'*-7), application of plastic track detectors for cross-section measurement of nuclear reactionsn), charged particle angular distribution from nuclear reactions a-l°) as well as separation of charged particles according to energy and type by track parameters 4'7) have been investigated. However, the measurement of track parameters (which give a lot of useful information to understand the mechanism of track formation, too) s'~2 demands difficult microscopy work. To make this work easier investigations for the determination of track parameters by the diffraction method were performed. In a former study, the diffraction method has been effectively applied to determine the average diameter of blood cells TM 14). 2. Theory If a monochromatic, parallel light beam passes perpendicularly through a circular hole in the Fraunhofer-diffraction arrangement, then at a point P of the screen, which is placed parallel to the circular hole, the intensity distribution of the so-called Airy-diffraction pattern will be /(P)

=

,

dx and

Ja(x) = O.

I f a number of N randomly distributed, monodiametric, circular holes or disks are placed in the way of the beam (according to the Babinet-principle the pattern will be the same), the places of maxima and minima can be determined similarly by eqs. (3) and (4), merely the intensity will be N 2 times higher. Solving eqs. (3) and (4), values for the places of maxima and minima are as in table 1. Let k~ be the x/Tr value corresponding to the ith minimum, D~ the diameter of ith dark ring and taking

l

I

2

(2)

Cellulose acetate deteeton

r"

lle - Ne

~

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%

"- Photo~/ocfe i r"

- - ,

"

.

"i

(1)

where d is the diameter of the circular hole, 2 the wave length of monochromatic light, J1 (x) the first order Bessel-function of first-kind and red sin 0

Screen Lens

\42)

x -

(4)

Z =/00 mm

Fig. 1. Experimental arrangement used for the track parameter measurements. 301

302

M. V , ~ R N A G Y TABLE 1

and so that of the track diameter were estimated by the maximum likelihood method. For the measurements cellulose acetate detectors (T-cellit, violet-coloured, VEB Filmfabrik, Wolfen) of 12 mg/cm 2 were used. They were irradiated with alpha particles of different energies entering the plate at right angles. The following etching reagents were used:

Maxima and minima of Jl(x).

xlrt 1.220 1.635 2.233 2.679 3.238 3.699 4.241 4.710 5.243

min. max. min. max. rain. max. min. max. rain.

solution A: 90 g H 2 0 + 13.3 g N a O H + 10.6 g K O H + +4.5 g KMnO4; solution B: 9 0 g H a O + 2 0 g NaOH+16 g KOH + +4.5 g KMnO4 ; solution C: 90 g H 2 0 + 12.5 g N a O H + 10 g K O H + + 4.5 g KMnO4 ; solution D: 90 g H 2 0 + 15 g N a O H + 12 g K O H + + 4.5 g K M n O 4 ; solution E: 90 g H 2 0 + 30 g N a O H + 30 g K O H .

into account the (fig. 1) sin ~9i =

Di

(5)

2L [1 + (OJ2L)2] ~'

we have from eqs. (2) and (5)

d - 2L2ki [1 + (DJ2L)2] ~.

et al.

(6)

Di In a given arrangement (fig. 1), by measuring the diameters of dark rings, knowing the wavelength of light and the focus distance of the lens (L), d can be determined.

3. Experimental arrangement, results A ~ 1 mW H e - N e laser as a light source ()l= 6328 A,) and cellulose acetate track detectors as diffraction obstacles were used. The screen was set up into a Zeiss-type comparator (with accuracy of 0.001 mm), which was moving in the line perpendicular to the laser beam; the screen was placed into the focus plane of a quartz lens of L = 100 m m focus distance (fig. 1). In such a way the Fraunhofer-diffraction arrangement has been realized. A photodiode with an active surface of 0.3x3.5 m m 2 was set up on the screen and its output was fed directly to a plotter. The comparator was moved by a motor with constant velocity. In such a way the intensity distribution and the diameters of dark rings (Di) could be determined. Nevertheless, Di can be directly measured visually by the determination of minima. The latter method is faster and its accuracy proved to be about the same as that of the photodiode method, so the direct method was used in our measurements. The average track diameter was calculated by eq. (6) with the slope of the line going through the origin and fitted to the experimental points (Di, kl). The error of the slope

The temperature of the etching reagents was 50°C. Diffraction patterns with at least two well measurable dark rings have been obtained in the track-area density interval, Nd2n/(4A) from 0.015 to 0.45, where " A " is the area of the detector surface including N tracks. Using the solution A at the track-area density of 0.15 even the fifth order dark rings could be measured (the third order rings were visible in day-light), while below the value of 0.01 the intensity of the pattern was poor. The situation is the same using solution C (solutions C and A are both weak reagents) as well as the solution E + A ; i.e. etching first using solution E, then solution A. lit should be noted here, that with solution E, the ratio of the etching rate along the track and on the detector surface, VT/VB, is relatively large, but applying this reagent the track contour is undetermined and the diameter of a track can be poorly measured. This situation can be improved using KMnO4 solution after etching with solution E7).] In the case of solution B well measurable diffraction rings can be obtained in the track-area density interval of 0.045-0.45. It was found that the dark ring diameters were independent of the track density, in good agreement with the theory (fig. 7). The increase of the lower value of the track density in comparison with the plates etched in the solution A can be explained by the fact that the solution B is a very strong reagent (using that, proton track can be etched, too), thus the inhomogeneties both on the surface and in the inside of the detector appear as background pits with diameters of 0.5-1/zm after the etching. These pits give a diffuse background in the diffraction pattern. Over the track-area density of 0.45 the essential role is played by the fact that most of the tracks overlap (this fact is especially important

DETERMINATION OF TRACK PARAMETERS at the higher t r a c k density a n d smaller t r a c k diameter) a n d the diffraction p a t t e r n can n o t be evaluated. O u r results are s u m m a r i z e d in figs. 3-7. F o r c o m p a rison in fig. 3 a result for red b l o o d cells can also be seen. In fig. 3 the deviation f r o m the theoretical line calculated f r o m diameters o f t r a c k s m e a s u r e d by microscope, can be a t t r i b u t e d to the fact that particle-tracks do n o t

303

realize the ideal c o n d i t i o n s m e n t i o n e d in the theory. N a m e l y , the particle-tracks are three d i m e n s i o n a l obstacles a n d they are p a r t l y t r a n s p a r e n t . In o u r opinion, therefore, the d e p t h o f the b o t t o m o f the t r a c k has also an i m p o r t a n t role in the f o r m a t i o n o f the diffraction pattern. (Investigations on these p r o b l e m s are in progress.) T h e deviation is especially

Fig. 2. Interference fringes from the diffraction of laser light on a-particle track [(a), (b), (c)] and on red b l o o d cells (d). The rays on the photograph (c) are due to scratches on the detector surface. Insets: photomicrographs of the tracks and blood calls, respectively. One division of the scales on the photomicrographs corresponds to 1.125/~m. The measured diameters are marked with symbols O and x in fig. 3.

304

M. V I t R N A G Y

well-marked at the plate irradiated with alpha particles of energy E = 3.8 MeV and etched in the solution B. This solution - as mentioned above - is a strong reagent; its threshold of detection is low, the ratio Z,T/VB is higher for this solution than for solutions A, C and D 5' 7). For solution B - if the thickness of the layers removed is the same - the developed tracks are relatively deeper than for other solutions (see photographs in fig. 8). It

[] E ~Z~l MeV, Solubon E÷'4 A E -5,8MeV Solution D

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Fig. 3. Plot of the corrected dark ring diameters against order k~. The thicknesses of the layers removed from the detector surface and the track diameters are as follows: [] v B t = 4.9 mg/cm ~, d=31.5#m; A v B t = 4 . 1 m g / c m z, d=22.2ym; I v g t = 4 . 1 mg/cm e, d = 2 7 . 4 / x m (the photomicrographs are given in fig. 8)'; O v B t = 2.7 mg/cm ~, 2 mg/cm e, 1.6 mg/cm z, d = 15.2/xm, 10;6~m, 8.3 y m (see fig. 2); A v B t = 1.7 mg/cm z, d = 12.4/~m. The solid lines and the dashed one (belonging to symbol I ) w e ~ calculated on the basis of track diameters measured by microsi~ope. The dotted lines are least square fits to the experimental points. The ring diameters are in ram.

~I.?L]

~//~

~

o E = 2 5 MeV ~ Solution o E = 3.1 HeV

Fig. 5. D - d relation. The diameters D were calculated from the 1st and 2nd dark rings (see text), the d values were measured by microscope. The error bar of d gives the halfwidth of the track diameter distributions.

A

~ E = ~ I MeV 70

n E - 3,8 MeV ] Solut/on

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E = ~8 HeY ) Solution

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~b ' . . . . . 2o. . . . Troth dio~neter measured by mmroscope

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Fig. 4. The diameters of the 1st and 2nd corrected dark rings (in ram) as a function of track diameter. The solid curves were calculated using eq. (6).

Fig. 6, Track diameter particle energy relations for a-particles entering cellulose acetate detectors at right angles. The diameters d marked with symbols • and • were measured by microscope; the diameters D marked with symbols © a n d / k were determined by diffraction method.

DETERMINATION OF TRACK PARAMETERS was f o u n d that the deviations f r o m the theoretical line were significant at t r a c k diameters over 2 0 / l m a p p l y i n g solution B (fig. 4). In o u r experience the values o f t r a c k diameters deterrnined by the diffraction m e t h o d , and m e a s u r e d with a m i c r o s c o p e are in g o o d a g r e e m e n t if only two d a r k rings were considered. T a k i n g into a c c o u n t higher o r d e r d a r k rings, too, the deviations are a b o u t 5 - 1 0 % . T h e d i a m e t e r o f a track, d e t e r m i n e d by the diffraction m e t h o d , decreases with the increase o f the n u m b e r o f rings. Fig. 5 shows the d i a m e t e r o f tracks using the diffraction m e t h o d p l o t t e d against d i a m e t e r values measured by microscope. M e a s u r e m e n t s were also p e r f o r m e d with the diffraction m e t h o d at different a l p h a energies to investigate the change o f t r a c k diameters as a function o f etching

So/uL/on

r..

°o

o

°°

o

o o

o

B. I - = 5 0 ° 0

VB t

-

Z25mg/cm ~

t = [90 mg/crn 2 o

VBt-[35 mp/cm ~

E~3.2SNe7

T?QCk <~enslty

Fig. 7. Track diameters D as a function of the track density.

305

o f the surface. Results are illustrated in fig. 6. F o r c o m p a r i s o n , o u r earlier results, m e a s u r e d b y microscopeT), are also plotted. The a g r e e m e n t is fairly good. M e a s u r e m e n t s on the s e p a r a t i o n o f tracks with different diameters (i.e. particles with different er~ergies) as well as on the d e t e r m i n a t i o n o f p a r a m e t e r s for n o n c i r c u l a r tracks are in progress. The p r e l i m i n a r y results are encouraging.

References 1) Proc. Intern. Conf. N u c l e a r t r a c k r e g i s t r a t i o n (ClermontFerrand, 1969). 2) Proc. 7th Intern. Colloq. C o r p u s c u l a r p h o t o g r , v i s u a l s o l i d d e t e c t o r s (Barcelona, 1970). 3) p. B. Price and R. L. Fleischer, Ann. Rev. Nucl. Sci. 21 (1971) 295. 4) G. Somogyi, M. Vfixnagy and G. Pet0, Nucl. Instr. and Meth. 59 (1968) 299. 5) G. Somogyi, M. V~trnagy and L. Medveczky, Radiation Effects 5 (1970) 111. 6) M. V~irnagy, J. Csikai, S. Szegedi and S. Nagy, Nucl. Instr. and Meth. 89 (1970) 27. 7) M. Vfirnagy, Thesis (Kossuth University, Debrecen, 1970). 8) G. Somogyi, B. Schlenk, M. V~.rnagy, L. Mesk6 and A. Valek, Nucl. Instr. and Meth. 63 (1968) 189. 9) S. Szegedi, Thesis (Kossuth University, Debrecen, 1970). :o) E. Baratcugil, S. Juh~lsz, M. Vfi.rnagy, S. Nagy and J. Csikai, Nucl. Phys. A173 (1971) 571. 11) J. Szab6, Thesis (Kossuth University, Debrecen, 1971). :2) E. V. Benton, Nucl. Instr. and Meth. 97 (1971) 483. :8) E. Ponder, Med. Phys./Chicago:Year Book (1947)p. 301. :4) C. Bowlt, Phys. Education 6 (1971) 13.

Fig. 8. Photomicrographs of 0r-particle tracks (see fig. 3). One division of the scale corresponds to 1.125/zm for (a) and 0.925 ym for (b) and (c).