Computer simulation of the etching process of the fission track

Perpmou

Nsw/. Trad~ P_-,~__~.Mere, Vol. 22, Nm 1-4, pp. 773-776, 1993 ~ Scismce Ltd h'beed m Omst llrttWm. 0969-8078/94 S6.00+.00

COMPUTER SIMULATION OF THE ETCHING PROCESS OF THE FISSION TRACK

DeNO XeaLU Depmlmont of Phymcs, Darien Umve~rmtyof Technology, 116023 Dahan, Chma

ABSTRACT

This paper |ntr_*~__~_~d m methed - - a r r a c k - b e l t " method which can simulate the etching process of the f i s s i o n track and COmpute the etching curve f o r external detector using mlcroc~puter, in a d d i t i o n , verteus dtstr|lmJtions of the Latent track, the etchebte track, the etched track and the ebeervebte track were obtained. A important conclusion that the density of the etched track is generetty tess then that of the etchabLe track was d r a m . KE'fMORDS f t s s t e n track, " t r a c k - b e l l " method, external detector, Latent track, etchabte track, etched track, observable track, d i s t r i b u t i o n , etching curve.

I NTROOu~rIOM What about the various d i s t r i b u t i o n s of the Latent track and atchabte track a f t e r • s o l i d s t a t e nuclear track detector used as the external detector ms i r r a d i a t e d with f i s s i o n fregexnts? Whet Ill)out the various d i s t r i b u t i o n s of the etched track and observable track a f t e r the detector w e etched f o r • t i m t e with sam etchant? And how does the density of the etched track change when the etching t i m increases?

ASSUI~T l Oil

A urentum-centiintng eaterteL (the source) was attached to • detector, we # ~ : e s e : (1)the f i s s i o n i n g nucleus were uniformly d i s t r i b u t e d in the source m t e r l e l . (2)the source attached to the external detector Nas t r r e d t l t e d with u n t f o m t y d i s t r i b u t e d neutron f i e l d . (3)the t u t o r i a l s of the source and the detector are t s o t r q p t c . (4)the range f o r each frslMmnt is the sam ms it s in the source and it~ in the detector. (5)the bulk etching rate Vb is I constant and the etching r i t e V , elong the Latent track ('s also ! constant, and etched track w l t t be p r o t o n p d with Vb a f t e r the Litent track has been revealed f u l l y . "TRACK'BALL M NETHG)

Ilimgtne that the source nmterlet having been i r r a d i a t e d with t h e r m t neutrons were equal Ly divided into i tot of thin Layers, there would be equal ntadmr of the f i s s i o n e v i l s in each Layer and suppose i t equsts r~r, then nT= ( a f eCue SedBedeaeC=~,; el)n ) / A. tdlere of is t h e ' e f t ' a c t i v e fissPm~ cFoss'section of the ureniunl for reactor neutrons, c u the uranium content of the source. $ the cress section of the source, dH the thickness of each thin Layer. d the density of tlt~a#ource, i Avoqadro ruIiber. C23§ the isotope abundance of the " ~ ' U in the source. ~0 the integrstad neutron f l u x and Au the average stimic weight of uranium.

41

And ilmlltne that e l l Latent tracks in each Layer were moved tegether k m t n g the same ortontattons as they have o r i g i n a l l y , then we m u t d obtain a i l o t r q ~ t c belt of latent tracks. I t is ebvteus that only p a r t i a l frmllm~ts of these Layers et I distance equal or tess then Rs f r m the interface betwasn the source and the detector can reach the detector. L e t ' s oenstder the Layer at a distance II from the interface (Fig. 1).

773

774

DENG XINLU

Not|rig t h a t t h e r e a r e tMo fraglmnt8 coming from each f i s s | o r l event e the ntad~r of t h e Letent t r i c k 0|vM1 mJt from • u n i t 8oLtd IngLe is nT/2W, SO the ~ r of the Latent t r i c k g | v ~ l out from the s o t | d angle dO wiLL be: d n ( I , q))=(nT/21) ado-(nTI2V) 08 i nlodlodll. Cons|daring that t h e L a t e n t t r i c k of the beLL are syemetr|c in respect to the imis of the beLL, Me have ¢In(1)- ~ d n ( l In the Latent t r i c k baLL of the Layer at a distance H from the | n t e r f i c e , only those Latent t r i c k M|th a dip angle # from 0 to erccos(H/R.) can reach the detector. For d i f f e r e n t values of D, the f o n a U l N used f o r computing the t o t a l Length (rP, the hor|zontaL p r o j e c t i o n (L), the vert|caL p r o j e c t i o n (h) and the mJIlber of the Latent t r i c k are as foLLows: Pn(Rs'H/cos| )oRd/Rs , Lures|n#, h=recosO+ rle un~-sinOedO. Hiving r, L and h arranged |n Length order and added up for d i f f e r e n t 0 of every Layer, Me tiiLL o b t a i n the d | s t r i b u t t o n s of r , L , h lad ( I / 2 - 0 ) in the externaL detector. Here the c r | t i c a L angle ( | c ) MIlS not cons|deled, the COleputed d | s t r i b u t | o n s Mere for the Latent tracks. In order to obtain the distr|bl~t|ons of the etchabLe track Me must add 8 s t a t e | a n t |nto the program as 8 R~e (1) or r ' ur -+ReeUe| nD/coM+(Re- I-),s | nOc for r (2)

,

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Fill, I r ~ P r ) I b

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I m m =

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as •holm in FI9. 2 lad FI9. 3. I t is obvious that i f ~l>:(w/2-#p) then r'<:O Wh|ch means that those Latent t r a c k • t i | t h a incidlmt angle Len then I~. miLL be etched away. F-or formula (2), •inca r can take the values from 0 to Rd, i t t • p o u | b L e that r'o, Me conqgute t ' ,h* and n ' as foLlous: L ° s t **•|rlO hOurlocol~ nil °=nTo•inlod then Me can o b t a i n the d|str|lxltiOnS of the etched track using the same procedure as for the Latent t r i c k . To obta|n the dtstrll3ut|ons of the observable track Me need to add 8 c r | t e r l o n of L*>=Lmtn i n t o the program. To o b t l | n the etching curve, we can colapute the density of the etched t r i c k for d | f f e r e n t etching t i m t .The program chert Which cim he used for computing various d t • t r | b u t i o r l s of the Latent t r i c k , the etchabte teicke the etched t r i c k ~ the obeer~abLe track using d i f f e r e n t inputs as in TabLe 1 Mes choun |n F|g. 4. Where the subroutine S tills used f o r arranging r, L and h (or r', L' and h ' ) |n order and add|ng them up f o r d | f f e r o n t of evar~/ Layer. RESULTS Fig.5 ~ the various d | a t r | h u t | o n s of the Latent track, etchabLe track, etched t r i c k and OtmlervabLe t r i c k for T>=R_. Fig.6 sh~t~s the etching curve for T)~it s. F i t t i n g the etching curve Me heve~9ot a etching formula for the external detector as foLLows 68 ~ . E X P ( - ( O..(T/R.)%cos' ItceVt*te)/R d) (3) Wh•re 7e t • ~he-~llnslty o~ the ~tched t r i c k , T the thickness of the source, Joe the d l m s | t y of the e t c i t l b | e trick: J;t = n , * T ( l " • i n L ) for O
ETCHING COMPUTER SIMULATION

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DENG XINLU

776 DISCUSSION

1. Our computation shows: . NobservabLa < Netched : NetchsbLe < NLatont. I t seems LoDe straflge teat Natured NetdumbLee be~lTtJ~ t h i s masse that some etchabLe tracks ware etched i may In the e t c h | n g p r o c e l a , but t~-'t~-edtt[ol~lml--]'(:[eaIwlysthmt aLL etchobte tracks c l m b e r e v e e i e d a f t a r etch|ng. .t. oonf, that the Luston that ' , trwa us,ng the the Length(r) end the incident angLe(f/2-8) o t ' ~ ' l ~ " t a t o n ~ F ~ e n d formula (2). Since r takes v a t u w from 0 to R , there always are p a r t i a l Latent track uh|ch have a t o t a l Length(r) Less then Re, so taemmd to t i e f a i l u r e (~) f o r cooq)uttng r ' . Let r'=O, ~e can solve the equation:

r-R_esing_/cos~+(R_-r)estnlL=O and f i n d v s r t c ~ solutions (ro~ for var~ous values of #. For a value of e, those Latent tracks with the t o t a l Length equal or Less then ro-wILL be etched away. TabLe 2 t i n t s some values of r 0 for m values of 8 supposing that ec.5° , R c ~ ~ Rema~.

TabLe 2 I

f/2-0

5°

6°

7°

8°

9°

100

ro(~)

8

6.54

5.50

4.72

4.12

3.63

15° 2.19

25° 1.04

35° .57

55° .17

75° .03

I f the t o t a l Length of aLL Latent tracks is equal to Rd and Re<=Rd then aLL tracks with the incident angle greater than nq: wtLt be revealed, i . e. NetchedUNetchabte . These c ~ l d i t i o n s w i l t be nearly s a t | s f l e d uhen a very very the source is used. 2. When the bulk etch|ng effect was mentioned, I t was generaLLy noted that the Latent tracks wtth the inc|dent angle equal or Less then ec w|tt be etched away in the etching process. But that is not the eLL of the bulk etching e f f e c t . Besides that there are other aspects as foLLows: (1). the distril=utions of the etched tracks are nat the same as those of the etchabLs tracks. (2). p a r t i a l Latent tracks with the Incident angle greater than (~ may be etched amy. (3). tn the etching process, some shorter Latent tracks wILL be e~ched to ones with rotalded end. (4). aLL Latent tracks wILL be etched away a f t e r a quite Long etching time. 3. L o t ' s shoe a example. For the case of T>=R_, t f the formula EsO.5eces=e_ was used for g e t t i n g the detection e f f i c i e n c y (E) we obtained Em0.499 for mica ~R~,lO.75~,Pr-3 °) and EmO.37~for glass (RdmlO/L, ~m30°); I f the .track-beLL"methodwasused, the computed dare, Lion effiCiency (E_)was (Let V.et.-Rd): EomO.kl;~for m|cemld EouO.25 for glass. The difference between the two me~hods is q~Jt~ shy|aug. Why? Becatam 0.5ecoste~=N.~k.kl./Nf Htthout const~rJng some etchabte tracks Nhich w i l t be etched away in the etching process. " H e ~ ' ~ ' f~ ' ~ s the t o t a l ~ r of the f | s s i o n event |n the source with thJckrmss of Rs . k i t Eo=NAO~o~rV~abte/Nf • . . . . . 4. b-f-experiences and our compJtatlons show that the etching condition influence the measured result s i g n i f i c a n t l y . In order to obtain a reproducible and ccxnparabte measured result i t is necessary to took f o r the optimum etching conditions for various detectors. We propose that s etching condition setJsfy|ng VteteURd ~outd be taken as o p t i u o n e . 5. The introduced "track-beLt" method in this paper has been used for c(~putJng various d t s t r | b u t l o f l of var|ous tracks and etching curves for the external surface and internal surface of the seLf-detector, results wILt be published. ACKNOWLEDGEMENTS The author is pleased to acknowledge Prof. He Zehui, Prof. Sun Hancheng, Prof. XuGeflg~a and Prof. Guo Shltun for t h e i r supports.

REFERENCES Oeng Xintu. (191~). Various d i s t r i b u t i o n s of the f | s s l o n tracks in the external detector. Proceed|rts 9f 1;hq ;~nd National Conference on NucLear Tracks in SoLids. Yantai. Dang XinLu. (1984). The etching characteristics of the external detector. Procmldlnas of the 2nd NotionaL Conference on Nuc~ur Tracks in SoLids. Yentai.