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An Investigation of the Bragg-Gray Principle with Fluorescent X-Rays

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An Investigation of the Bragg-Gray Principle with Fluorescent X-Rays AN IIM:3~GA'ltON aF :mE JU\AGG-GBAY PRINCIPLE WI~ P'LlJORESCEN';J.* X-RAYS by JIAROU) VINCmJ' .I.A.RJ()lf A~IS subnitted to ill. partf.al tultillment ot tbe requ:L~ts tor tbe degree or MAS~ OF SCIENCE June 1957 lillWt Redacted for Privacy Redacted for Privacy IllrrcL farfrmr eil.$elrm Io ercilr of hrl Redacted for Privacy &.t d lnrrtxt of W.or Redacted for Privacy &im of fahf {&re*t; fFililtttr Redacted for Privacy Srm d iBratr*r l&a[ ffr thai,r i,r lmntri T ',nut,A{r,,,(,1,*. nn* tr lu{rl.ry frilfir !lbe. author desires: to ~retts hie gratitude to Dr. w. c. Boesch tor e:u.ggestilla this problem e:nc1 to I. ~. M1ers 'for advice on ~bnt.. ques. AN DM$~00 OF 1HE BRAG<.J-GRAX PRINCJ:'PLE tttZ!..FLtJORESC!E:Nlr x...RAYS s.-~. ~: !!4t Introcluct1on l Ob,leetive 3 Method. ·5 ~tion Cllam.'bers 9 Val.i\U:ty of the ~...G~ Pz1n.ciple 20 B1bl1~ 26 t?able No. 'atle !!I! l. !rheorettw Values of JAJ/Jair 10 2 ~rt:tical VaJ:.ue of Jcu/Ja.tr 10 3 ~~ ot ~tical tm4 Ex.Perl.Diental. Ve.lues o~ JAliJ'IJ.'Lr · leu/~a.J:r 23 4 Com.p.arison ot 'l!heo:retical. 8lld B:l(perimental Value ot J au/JAl 23 &1;.tle 1 ~son v.tt.b Attix's lata 4 2 Extre.:polation CUrves 2l 3 Extrapolation CUrves 22 a'=J:tle ~ IOllizat:ton Chamber AssemblY 2 ~ Vaeuurn Chamber .and tbe Iomzat:LQ!l ~ber :1u Relation to the Fluol'f:sc:ent X·Rau Source 15 1.f.tle 1 13 2 17 AN DM.S~GA1!0lf OF !l'fiE BRAGG-GRAY PRINCIPLE WI~ FLUORESCEN7,' X-RAYS IN):'RODlTC').'ION '-'he primary standard tor low energy X-ray dosimetry measurements is the tree a.1r ionization chamber . For some measurements, such as that o~ surface dOse,. the free air ionization cbam.ber is difficult or iDg?ossible to use. For these measurements the Bragg-Gray chamber (12, pp.6oo-612), (13, PP·721-742)., and (14, pp.578-596) is a valu... able instrument. A compa.r:Lscn o:t tree air ionization chamber measurements with Bragg-Gray chamber data using lov energy x..ra.ys is needed to verti'y the Bragg•Gra.y principle and establis the lim:it• ations on a Bragg-Gray cbamber in this energy region. ~e Bragg-Gray principle has been the subject of numerous 1nvest1&f.t1ons (22, pp.l94·195). 1~ derivations of this principle are tound in the literature (ll, P.P·259-295), (19, pp.68-74), and (24, pp.581-589). A rigorous der·ivation ot the principle was made by Cormack and Johns (6, PP·7-9) and (7, pp.l34-l39) · For the mediUirl soft x..ray energy region, !artnelli (20, p.251) expresses the Bragg-Gray principle in tbe tolloWing torm: l) =S W ;r ::: h lrP.;11 q (l) D • dose rate 1n tbe walls ot the chamber in ergs per gram per second 3'" a ion current per gram ot gas in the cavity W • energy in ergs necessa.'1.'7 to form an ion pair in the cas 2 S : ratio ot the mass stopping power of tbe va.U materla.l to that of the eas for the ionizine ;particles associated W1 th tb.e inci·dent radiation 11 : number of incident photons of energy h-v · per em?- per seconcl hv• eJ.>ergy of the photon in ergs ,11•=mass energy abso~on eoeftie:f.ent Of the wall materi-al in cm2 p~r gam :the mass energ;r absorption coetncient :ts det'ined by: ~<£>=/"It-s/ (2) .tN • mass absorption coefficient in em2 per gram <E) = the a:verage energy- ot the electrons a.t the t:J.me of production in erss At low photon energies the mass energy absorption coefflc.:t.ent. ba.$ two cam,ponen~s . .MIt = £G:.. .,. (1- ~,.,.. )Jll /-· . r... lt"V tl (3) <Pi• Calp:pton absorption ooeffic'ient per electron in em2 7; c photoelectric a..bsorptiou coefficl.ent per elect'l"'n in wall of atooti..c number Z in cm2 f- • fluorescent yield tor the K level. ~ =btM:In& energy ot tbe K level ~=¥= nUDber of electrons per gram of wall materieJ. ~ · Avogadro's number A • atomic weight Wilson and his co-workers (1, pp .243-254), (16, PP·509-510), a.nd (17, pp .57-68) tried to establish tbe validity of equation {1) tor C, Al . e.nd CU walled ionization chambers end f'or X..ra.ys with '' e~ective 11 3 energies fran 25 to 125 Kev by ustns an extrapolation chamber {8, pp.2Q2...2i5) technique. 1'bis work is sul)jeet to crtt1~sm since heterogeneous X-rays were used ,as the source ot radiation. Siuce these X-~s were J;l.Ot monoenergetic, the average mass energy absor,p.. t.ian eoettioient used in the eal..eula.tions does not nece:ss:arily con-espond to the average elierSf in the X-ra.r spectrum. !lbe extra.. polatton teehnique used 1n ·tbelr e:lq)erinlents vas to vary the electrode spaeUJg betwetm o. 5 and 5 an ot air. As Will be shoVtl below, :for a go.od extrapole.tioli, eJ(l)erlmen'\;al data should. have been obtained for eleetr<xle spacillgs be.lov 0.5 mm. Also, the fluorescent yield t was ignored in their cow;pu.tations. Atttx (2, pp.1...9) a.:r¥1 (3, pp.1...27) recentl:Y testeG. the Bl'ags· Gray pnDc1ple ill the· energr region h'otll 38 to 670 Kev using C, Al, cu, sn, aDd Pb wa.Ued extrapolation Clmmbers. His method 'lila$ to vaey tbe dlam~r spacing between o •.5 and l2 •· A curve ot current per .arum ot Ur ill B~·Gl"&Y ebamber (J.z) relative to the current per gram of air as meas~ \w a free atr ton cbam~ (Jatr> ve~au chamber spae1ll8. 'W'aS extr&pole;te4 to zero clumiber .spaetug.. ·J:be Oasbe4 line in Figure 1 represents Attix•s Clata., For a sood extra• pola.tiou the chamber spacing shoUld have been reduced another order of JDqllituae. Also~ the, radiation W'!ed in tlUs ~~t w.a fllterecl x...~. De.epite the heavy fUtrat1ou, .there rema:tne a. oonsiderable spread 1n energy ot these x...~s. ~e present 'W'OJ:'k was undertaken to establish tl1e W:U.di.ty or l.aek 4 cu 0 LARSON, 34.3 KEV ATTIX, 38 KEV AL -----.......­..... ---­ --.... -- ....... ...... FIGURE I COMPARISON WITH ATTIX'S OA TA THE CURRENT PER GRAM OF AIR IN A BRAGG-GRAY CHAMBER (Jz) RELATIVE TO THE CURRENT PER GRAM OF AIR AS . MEASURED BY A FREE AIR ION CHAMBER (JAIR) 5 ot valiclity ot the Bragg-G~ princ;1ple in the energy- r&r~&e f'1"0IIl 8.16 to 34.3 Kev tor copper 8.Dd allllliDUDl val.lecl ionization chambers. MEtl'.HOD • For low eDerQ' work the above method ot extrapola.tin& is ~tiw. NO't anJ.y would the plate sepe.n:tion measurements be :lDAOcmr&te1 but also a small vriDkl.e 1n the vall material voul.d eauae electrical ditf'iculties aDd talst17 volUme ~ts. Another method ot extrapolating is to hold the volume ot the chaaber constant and vary the pressure. ~ a. curve ot the current per sram of a.ir in a. l3ra.gg-Grq cbanlber rel.e.tive to the current per sram of air as· measured by a. tree air ion cbember versus pressure could. be extra,... polated to z~o pressure. ~s latter e~ra.polation technique all.ows the pressure of the gas between tlle electrodes and thus the distance between the electrodes to be reduced by at least another order of m88Jlitude as shown in Figure 1. Equation (4) expresses the relationslU.p betveen the current (in amperes) per unit pressure (J') and the ion current per gram of the detecting ,gas. (4) 8 V =~..2"/;2 X/0/ J / (~) ( .:z:.) ~-'it ?.: J; = 76o mm-bs Itt • volume of the Braeg-.G~ chamber in cm3 .r • 273 .20Jc ~ • <lensity ot gas at 0°C end 76 Ci;ll.•ha in grams per cm3 'r• absolute tell;pera.ture of the air in 01( 6 Equation (4) is a conversion of ox.perlmenta:J. data according to the pertect gas la.vs. For a tree air ion chamber: .. (5) J;;,. = ~. 24.1 ~ ID ISf:.Z:•'~) ( ~';.) ( p':-- ) ~~~ 70 pd,,.. ~,. .. ion current per gram of gas in the collecting volume of the tree air 1oni2:at1on chamber r.,.,. =current in amperes as read by tbe vibrating :reed electro­ meter V.ir .. eollectiDg volume of the tree a.i.r ion chamber in cm3 7J;, ~; absolute temperature of the a.:l.r in the free air ion chamber in OK P.;,. • atmospheric pressure in Dlll-hg D1vi41ng equation (4) by equation (5) results in: I .r;7: - J" ( ,tl,;. >( 7' ) (6) /" .,.,. -.r.,j../"'' Vc, "/ r.;: Also, for chambers With different vall materials, but the ssme detecting gas: (7) ~- /JAt =;c.'k', Kt1I J;/'1A1 vc~ One ot the purposes ot tbis work is to compare equation (6) to its tbetretica.l counterpart, equation (10},~ in the energ,y region. from 8.16 to 34·3 Kev. A nearly monoenergetic photon source (18, pp.l00-102} proViding energi.es han 8.16 to 109 Kev was developed by Larson, et eJ.., wbich uses the K :fluorescence ra41ation trom targets of different atanic numbers.
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