Citation
Neutron spectrum measurements in heterogeneous media

Material Information

Title:
Neutron spectrum measurements in heterogeneous media
Creator:
Salah, Sagid, 1932-
Publication Date:
Copyright Date:
1964
Language:
English
Physical Description:
xii, 132 leaves : illus. ; 28 cm.

Subjects

Subjects / Keywords:
Absorption spectra ( jstor )
Collimators ( jstor )
Crystals ( jstor )
Effective temperature ( jstor )
Fuels ( jstor )
Neutron spectra ( jstor )
Neutron spectrometers ( jstor )
Neutrons ( jstor )
Spectral energy distribution ( jstor )
Temperature measurement ( jstor )
Dissertations, Academic -- Nuclear Engineering Sciences -- UF ( lcsh )
Neutrons -- Measurement ( lcsh )
Neutrons -- Spectra ( lcsh )
Nuclear Engineering Sciences thesis Ph. D ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis - University of Florida.
Bibliography:
Bibliography: leaves 127-131.
Additional Physical Form:
Also available on World Wide Web
General Note:
Manuscript copy.
General Note:
Vita.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
022272497 ( AlephBibNum )
13579150 ( OCLC )
ACZ2176 ( NOTIS )

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NEUTRON SPECTRUM MEASUREMENTS

IN HETEROGENEOUS MEDIA



















By

SAID SALAH











A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY


UNIVERSITY OF FLORIDA

December, 1964













.,.Kr 'Jli'LElr'1Eh T3


i;,e a lthror would l il e t;, tha.- r;i i? per'i'-,sr

c:r-mittec, .pF.e:-l liv n- i' th-eri. supcr.'ii.r, lr. T. F.

Pi krirn-cr fl'or ra-i.; pat iernc, ad.'..c .i,.E ecai oura,emer.t

Jurinr, tlh c',urs: :.f the 4orl':. le 4OUI C l j al s. likae TO

c:rnvie h i1 gratitr u e t.5 .r. '1. F,. l'alton, mener r or

his 5upervi ;or,. :Cormi tte, ifr iil itn. arra-ngrmentr Itr,

Dr. 'J. ,ric_ rief o f I' ai Ridg ':arso,ar La.:Cra or',',

to V's tr the Lab..ratory ur. eCr "." pF ri.:iFpati:.n c:-n:r .ac

in order to consult .itr r tr.c e there .r-on r:,- u.3 i ,an.

cori;truct inr of tre ir.ur Erci ai f rac:i:r sp 'ctr.areter.

P-se autlh r roul 1 also li've r; .'pri3 ;-i.; cratsi-

tude to ir E. O. llan .f ia Page .A dtiorna Lar.c:r-

to.', for ris relpfij c ugge ti.n:r, and de .ron;.Lrrat :r o

rhe ope-rari: r, rl-of t a,. Piag cr.,';t-l ;-pe trometer.

Also, tre a 1 i r joul. 11i' to a :ri'.'c ,iiny tier.. tor

L'r. L. ail -.r of Brokha '.'lrti oral Lab:.ractor,, for

ris.- r ilpfaui uggest i rOn an. for sending telue print; fr

tr -C ,onstrucricn o.f tne collimator anr to Dr. '.1 J.

rrtur o*f the Irnternat onal Institute ofr 'jucl'ar 7.:i nrcc

ard Eng;ineerin., at Arianr.e Jat;ionai Latc.ratory,' for seriair.,

omea drarinaps of tre cr-,ri al spectrore:er with a cop,. of

the e'xerimrntal 'Jr!ite-up.









The aij of Dr. L. E. 'rri ter, Dean :.' Tr. Gra uate

-r.iol. l.n ,r.'e:ro t, o r Fioriao a r.j ,r. io .- rt E. lnri r1 ,

tn S i comiiL t tee ei r e an Ile. ia f Ti :'e .-epartmcar.t -.f

u: lear [ri rin e rirg,: for :* tair. r.g the r.-':e ; ;ar, f r.in s

.itr l wrcr, to -.ur':a? th'e 'mair ger arinc s iSte-n f the*

;E.:tro,-M Cere w'ia- .,er m cr a ; ira e reic a= .

Ais, .u:n ;r rit tJle ji idue [Dr. F. E. ..irnarl a;a

or J.lI, F'. Lrur-h of J a For.t ae IlenouJr' Irnc.

-aariran Piver LaLt:rator,', Ai-en, _otn Ciirolina for

imalkini the TIHEPrI : ca i"cjiat' ir. for tr.e eometrie. ise

LI-. t6 -Lcriticai riaCtir.

Tre eaitnor 4-'JlJ i1de t.o 'ar.a cr.,e D i.'s;or oft

a,1 ..1Cl r i II3at:i ari TtrairsnFin LU. .A. .- 'aslirctor,

D. c. for tre !,ar3 r:f t ri natural 'raniiYii sl.i 3 an I

b 0.r Aiso, r. 'woil lik .e to cori -,' tis gratiCtilde to

re Laarran F .'ver 'Cpe'ratt iriE ,: iffi:e, IJ. A. E. Aif err,

*i.tr, ar iina f:r the loar. of natural *rariji' sev;,?rnt r .

Tne arnthr ii jeepiv. ir*n c. tce to. Mr. L. D.

E u t erCr i id F,. actor .'upe r'.'isor, ari lr t. L. T'-w-.Cet.

for pat icrt ly rnr .r.r, thne irT marn' tinmea afrer norm-al

wcork:ir ric.ur:; to Mr. .;. w. rogie f)r ni nelp iin rne

ornstrujtriorn of tri tcnpcrature ccrtrol JInit; to Mr.

F. A. Primo and t'r. rl. H. loos anr mair, o.tners for the

C:-ri t ruction of apparatia .

Finally.', thr' autrn-r wouii ii, e to express r1is

sircer gracit;tul e ,j to fisi arara 3'.'l.a for nr sugg sionsr

ar. r, lp irn utting inro fi f ilorm in and vpirg this rhesis.










TABLE OrT .:.TE; T




.: ,ll ril JL E,'El :ilT . . . . . . . . . i

LI T -F T LL . . . . . . .

LIu T ..r F FE . . . . . . . . .

AB .TT.CT ................ ..... .




i. LCE : FTiTi- [i :F TMH Fr- bLEL- . . . .

iI. 'IfE. UF r !Mr;T Er iCilTPC i -P CTP.RA . . .

III. Ej: 1''l 0iiAl ,0 1 At'F.i Tu . . .. . . ;:

I'.'. FELJLT: ",*F I rTLJft-.L FCi:';, .'TFT
MLA.LIFErII.IT . ... . ........ .

PEt LT' .:.F C. ITFr EPCI TI L :E; T; RU'1
M1A i- i PL rL:JT . . . . . . ... '. -

'I. PLE I.LT :, "* rJ iiL .i-i 'I .N 11' t C:.: l' lll 'TI l_. L,




A. EITH'):,D OF CAL-.ILATI'-, t ,1 ""' . . 1 1

p. T LH TIHERilM. C,'DE, . . . . . . .

TH F:E iPR F' CAL LATTIi E .. ..... L

D,. PlC.: 'O T CALCULATI'I-'li . . . . .. .

E. PF ':'P f.L T': U'L L UFT' .A ;:i.iIF E _Fl'R
THE ,IECFITI'AL A.-.EI L' ..... . . .... .1

LI T Or FEVEFE.IICL'. . . . . ... . . .

ii :'i' A HI .EPTCI.L : l . .. . . . . .











I. 1 : T T'.- P,. ELL


T I: ra- f' n-r

'.1 r,.r'.a :rer ri tL: .? : r .' .t ti r
I-._t ._ .r . . . . . . 1

S. T l f : .-r" f r 'iffer-,;


S.. rr I w 1 1 t a E .It . .'


,r a l F .. . . . . . . i
' _, r L 1 e--. r I -. . . . . . . . :
'.. oi :. -a',, i =' ,r r: F :.r u rF aJ.r
L .i1" 1 ..-:.-orr-cr l -.t ir;ei . . '

.. Lu ,N',d L, ."r,, z.h : ., a T . .r
En er y -- I1 .7. .. I-

-. : i;.r 3il 3 A.:ti .'L Ci 3 tII I i -i' '
S:, l t i r, . .. . . . . . 1'

.' A 1' ,"T fadn, in A4.u- aou' -: ut i .- ;.',

... hFati: .r tr,_ At '' I AL- rer in 1:, R'm.
L.i' Liter . . . . . -. . ''r

-.' 3.t.: I',' ti .:.r, Fa-' tait r s f- : r ui.FTF ,:'r_ . ,''

:. .1 :.-,l:-ar n1 :f tr, e :lIri e t- E. ff-.:c .'-
'i-u r.,':r, T_ -LrFstlr r. a Jr, t L.:ili . 11.

.1 [r _-r '.' 'r,, fc, r I, 'I- .. C:.al:u t 'r "i ir













FLirre ase

:'.1 :,crtvi ti r, ,'ria ,ecr i.n:-n . . . . .

S a it-rat '. :ur. e -r . . . 12

p. r, of Fiflectr l . . . . .

1.1 "in g C i'r atr t . . . . i

3.1 : : .f Eff ect i.m ure . . . 31

3. biffra.ct:.or. e.:trcme-nr r in C[ r. aticr . j3

S3. DI.tc t.r .rm .- trn l cc.nJ c.llin- tor . .

3 .'. T Lle.ati r. . . .. .. . . . :

3. Top .' of t :e iit-:riti l Latr ic . u

.'" "i i:, ,f tr i r'- r ar tor .r.,. . . . :

.1 rilj' ir.jn F 2 *,,1 i 1 in. t 1 r. i ;:
r 'i . . . . . . . I.i

4L. Lu Tr .erz; i Tnrrcugh I.i- aI . . .

4. I /.1 'Can i t. tal .-te:t: r i il) r . . .

4. 'l "ormal :-. Ll, tm ,.: i t it e in .i "it
Fill- n ith j', c I M -: i2 Ir I :. o luticnr z . .

U.5 IJ)lrna lL eJ Lu'1 A.: tr t ie r AlI :ar-
FilleJ 'I tlh Aj :.u L,1:' .Oliuticn: . :

N.i'. h:-rmaiz-d l i r i rziteI ir. Al an
Fi l ,: i th A iue. !' E olut .n . .

." cr,-,a i ze J s : n lPr J'j:t .A:Mi 'iti .es
in Al C: r. 11Fil 3 ith .' P ec - C0
i uti n: 1 . . . . . . . .


Li r ,F FIr: ..1PE'








LIST OF FIGURES (continued)


Figure Page

4.8 Lu177/Lu176m Ratios in B203 Solutions . 62

4.9 Comparison of Normalized THERMOS Flux . 63

'. in Fr;. t ;.on o.f :.:tl .'tin: DO -t tors in
J.rT R ,:or . . . . . .. .. . t

.i- Tr '. r; s T rI .I,,in li FT i r '-.re . . . .

'<.1 u HC:ti. i t.' Li ;trr uti.:ri frr Marl.. '.-
Natural 'I F u.i Ui rn 1l.' c ti . .

i.' Lu Ac., ' Lie r t -r.ji.:rl for 'iar 'l-
jd At .r a 1-1 Ftu w r i ~ : i rt:. . . .

4.1" Pu Act c .' 'i St .i,'i: n for Mir, '-

I: tur i 1 Fu : .i: .:~ Fit . . .

'.1': u r i .i. Li.trat.u ".ri f.r r' r I arV-
ca r .-- '. t jrs i I Fu Fitr cu. cm. . r. .



-4. Lu ,Cti .'it L' itri ut i -r f r I i'r' I ar
r' r1 '.-I l3t.,jral F.ai il . in ~- : r.1 .

,-, i ,Lu ,:, i .' t 'L1,= trit-,t i' nr, f r r'.ar i ar l
'. i i. fuel .' r I ; i: r t r .i :.. . . .
ili.2 rk lo 'f -i l r'. -'. It . lit





'i.ir .u F: rom rt-ir r .:r-i r r, r rl. r' I an ral
,4.2' Ai F'il r I.. a I .I i ir





I.I *j Ir. .:I-; Fa *C.: ... .... .. . ......... .-.

F.. 'lot of A Al e", r .'T T ar. ':1 utF.
LDi ; t ar*-*. Fr- rTi L r.-r 'a l rirF in I ari
riar'. .- lat urai 1.1 Fuel .*i th I c. f ctcr. A4


Di 5 ar.:- Froi, C,.'er, r I.ii f r.* liar' I arl
'art. ''-b 'laturai '. Fu- 1 Jitri. c: m 'il :r, t








LI7T OF FrIGuPEE j t conrtire.j


figure Pa.e

4. 4 A* ial Cli; tribj tio.n of rlux in tr.e
T, o Foot Tank T.l=in Ha lrk I and MarP .-E
!litural IU F el i wi cr. Pi irch . . 8

.2': ai'i al Di ribujtior of Flux in rn-. T .:
Foot T i. using ar.k -R l:Iat.ral
Fuel lth r, cm Pirt n . . . . . '

.2E 4 l ['1ii rlri ,uti of Flux in tn, Tiwo
Foot a-nir r.1n= ri,ark V.-l a t.,ral '.1
Fuel Jirn i 4. cm Pit. . . .. .

?' A'ial ['istriC.'utior of Flux in. tre-
TwD FT.oot .an:. Using irt .. . . .

5.1 rletrin of Alignm-ienr of tr, Diffraction
-pqetrormeter . . . . . . .

2. Po:kin C.~rv. of :.'1 'i ( 20.I . . . .

5. Po: ing 'tar e f LiF (111 . . . .

.4 'Fein Beam li-lurron p.e rjrin From i Cenrter
of FTR Core Usinr I.iF ( 111) ,.r,'tal . *'

5.5 Pati -f Hax,. 11 ran iist riljt ion an i
t-.e ExpFerTrimntal pe.trtct l, at To
Di ffercnt Teri;eratuires . . . ... 10

i.E Experi rencta and THELF.lr-I I"pe :t a sirn;
lark .,'- Natural u Fuel itro 2 .cm, PiN r, 10.3

.' Lxpcrimen:tal ani T1"HrF.'OR r:ectra Usiriv
llarn. I and. Mark V-B Natural 1Il Fuel
With 22 :1m Pir c . . . . . .. . ..i4

x ExpF.rimen ical an, THEPI M': M peccr.a Lusi .i
Mark '.'-r natural 1- Fuel Witt j .' .:mi Pt:n l.jn

Experimrnta anrid :rrec:a.d THEPrIOL ;e :cra
l.'sing ilark I in3 larlk '/-5 sltural 1 Fuel
'i r. :: :r Pitcn . . . . . .. i

.i Unit Call -_ a Lat .:t c . . . . . 11ie


'.'I 1











Abstract of Dissertation Presented to the Graduate Council
in Partial Fulfillment of the Requirements for the
Degree of Doctor of Philosophy


NEUTRON SPECTRUM MEASUREMENTS IN HETEROGENEOUS MEDIA


By


Sagid Salah


December, 1964


Chairman: Dr. Thomas F. Parkinson
Major Department: Nuclear Engineering


In this investigation neutron spectra were

measured both integrally and differentially and then

compared with theoretical calculations. Measurements

were made in highly absorbing media in the University

of Florida Training Reactor (UFTR) thermal column, in

the UFTR core and in the subcritical assembly sitting on

top of the graphite pedestal of the UFTR. The subcritical

assembly contained some typical D20-moderated natural

uranium lattices.

Precise knowledge of the neutron spectrum in a

heterogeneous medium makes it possible to optimize the

neutron economy. This is true because fuel elements in

a reactor have varying cross sections for different energy

neutrons. By proper choice of the fuel-to-moderator ratio









and t geometry an.J composition of fuel clements, optimum

,'ie of nrciutror9 can !e attained for maximum, fuel burn-up

.,ti-t trie .a- ine t cncr.'er;iio ratio.

In tre trer-n.l column of t e ..F'TP, rernmal neutron

spectra were neasurej integraiiv usinr activation letectora

.sucl as AP.17, L'1 Lu1 Lu16 and P. i The detectors

Lil?' enJ P, ". 9 rnave icw-l ingr atvs:rption resonances,

anereas Au1 ard Lul n rave a l:v ac-sorprirn, cr.'s:- section

for neutron cr-loa L.'1 e.'. fin: dO te ccor .r, sh ar.

abstrp ion cr3os 3 _:tlon trat i steeper tnan i v. Te-,

mrcuarimenr jr ir mi d' in a atainl-ss steel rod, a n turai

uraniuri ;lat arn, in an 'i1 cr.n fiiild l it', c.orated water

and results -re inrt rpre tei u irs'iin,; J tcctC' forri ilat .rr.

In a nat rural urarniurm slar. the effective neutron

temperature cnanr,- frcn teai center to me o, uts e Doojrar;

of -he siat was or-tair.nd mv meIjsurir. the .jci'itv ratio-

of Lu1"6 ard u1 '. In stainless Teell rd, tr,?e -'r-spel al

-effect i'e neutror trmperarure crane waI mea-Icaudr-3 Uiinge

Pu' and Lu5T activaticn detectors aria trner, re rartos

of activitieE to trn- ic:l t.'iTi of 1 a ar.sorr-rc -je-re

oDAined.

The i T's t,'p of mEsasureTenTss i4re mrad:e in ar Al

can filled with different concern rat or. r '. Tnrse

results were crompares witr TIILPHE'. caiculations3 r,noever,

due to the ari i tr :, orf trh e < ir.i-,ni. our:- :nr t .ns=,

agreement was poor.









The effective neutron tempe ratur- arni tre epitr.rmal

index, rVT/To, were measured t. ..3inr activati:rion etectorc

in the UFTR core between the rtw fu.1 b*ox- in tre Nortr-

South center line. The result of tr,- effrcti'.e neutron

temperature measurement was cnr.parer l iitr. tne oC'en-Dam

differential spectrum and fou-a to in g o:-. a;rement.

A crystal diffraction 3pectromretr for differ.rnteia

spectrum measurements in the .j?:rtl:i:.i asemDrl/ wbs. dued.

For these measurements, the total fficien:, ci nce raariine

for different Bragg's angle wa3 firsr octine. t.' taKirn a

neutron beam with known spectrum o fut of the abt.:rLt-i:l

tank. The tank, 24 in, in diameter anr 66 in. lonc, was

filled with D20 and rested on to; of tne irsprit. pezscital

of the UFTR. The neutron spe:trr.. out of tri .cie lim Jas

measured at two different temp~;rtur . re ratio: of ter

two spectra were plotted with the ratioe :.f tn :aic'iatiiorn

and found to be in good agreement.

The neutron spectrum oat of the .-t.:ritrcal a;embtly

was measured for two different laric-e pI'c.e;; u3ing MarP i

and Mark V-B natural U fuel elementrs irn -. A neutron .-te

was extracted from the cell boundar/ anr from tre center of

the cell for each of the three iatt:ic arrangement. The

results were compared with the trne:retl:aJ spe:tra :alc.latec

with tre THEPRH13 code and founl to be in excellentt agreement.

irtegral measr r mert rere alc'-. i:ma inr trie ur-
tial 17 a A e ex
critical s;Ln cr1i a ru e rdetctrI. r ine experimental









.ictivation measLre-Serits were compared 'Jitn tre THiEPHi'.

calculations and 'ere also four.i to Lb ir, excellernt

agre cc nt .

Finaii, tihe cffecti'.'e neutron temperature charge

in a unit cell for four U-D.O lattice arrangements wer-

r.easurej differentiall-. ani integrall' and comrare.3 w.tr

nhe tneoreti.cal calculations. ine results ,ere in goo.j

agreement.














'uIIAPTEP I


LL.:.hIF[ I [ OJ; F Ti FFj. LEML


iJ -tror s;ictruT iT, .a iu -.r, c 'i. ero,-ne-js

n- i 3i ar. importare c fcr a ral ri It :rns: i' fior

S., a udt iari .,rf trr u tifrIal ut l :atic n factor f ar.1

rr1e r- err, a i r ro-Juj t io fa:toz r,; for ti-.- :al-

c'lirt on f r j :.aC. r f'u.l :.: le i ; (.? f cr -o' .ar i-i.:r.

.-iftlI', ,uLt L arou;- : i .u at or, of rn rneutror, ;.ec r urm;

ar.a ( '' r F r' tr. gre.ji:t. i n o f 3I-- :e rat : in a .iipL ,

rin .3:i nr c. tc-r ni rn eutra-r c r rgy i; r ric:.jE i.

Fr~r ;- ir : nc. lc 1ej cf trni rne4tron -;ectr'um itn

a .er',rc-g r-.-.; re iuh- .iI- mi- it r- iir.i c. tI Oitimiz-E

tie rn~utrc.r. c: r:.mT,. I'ris i.- tr'Ijc Li7c d jais, fue l

-.lereint it n r a recta or r.avy '.'-ryvtrg ro. ; t c or,.r for

ttfftrinr enr rg' ni--utrorn;. '3 i propF.r ic-r:.a of tne

fu.? -t--i o .-i o3ratior rat ic arna tirc geometr.,, arna ccuipo: L -

fr. cf f-1 tCene-rt, opticu- aE- of n:uEtroras caJr

,t: iLadnr,c for m.axuimm fu -uel aur r-up ai rni r.Lgi i Cl:

ccOne'Tra;i-r rat ic. Iri mry .ae e nc, ci-ntrroi ing tih

i1kdagi pe':tr4m, frTc a a : dtcr core to i 3 air-l forn'.,

tir, Taoxiiurr, coJon- ri ionr ratio in true j.lar.i -t riaterial










rill be realized. T : fol.lowi becajie 1i.3 anj In i32

w~,icn are tr.e usual fhrt ile oiarnet material for nuclear

reacrors, r.ave r rir. resonarnces for ncirrc.r *:apturc ar

3.d ev ari. 2'-2 ev, re pectiv-1y,. in oraer to pre-

dicrt tre ;~acia i and siecrral di- ribution of neutrons

trenorericaily, trie bera.v.ior 3f reutr-nsr in the rneter.-

gen-eous m~iia miust t-e wull understood.

ir. Tri i inve t, igation, the neutron spectrum -wa;

neasurIed torr integrally (1) an a ifieretntially ( and

trier :o.iipared wirrn rre:re iL.:al calcuiartions (3 S, i .

Meas remni iii -''ere carried our in a hiigr.ly

ab;orling iMela.un i1 the rUniv.'rsit ,' of Fiorida iTrininc

Paicor uL'TR) rnermal column, ir the 'rTR :ore, anr it

the iub:zri tiial asse.erLly sitting orn tp o. trne ;-.rapir

p-Jesrai of ri. UFTR. Ti;e ub:rritcal a;sermbi con-

sairi.. oe typical [.,3-moaerated natural uranium

lattices.


Uirnerlirneo nruirers in parentnesI s refer c. o he List
of Reference;.














':APTLE ii


-A !t. L I OLIiT ':F F "IL 'JT P]"':j I "E ,'T F..


rIt r: :2jCt .: ri


Ai- early at i- i, rI:utri:r. iit ffri:t ~on .

:r,'at ii e r At. ri r al a su 3gg. t L,-] L i- ia -er 1.L

ain experimTirii : a ily ir I on r. ra t- Lit I, iL L r, rini Preiu erK k7)

anJ i., itc li anr] .' -ers ( :. Ui -ing F.a-b e sour:, s,

triee experi r ltnt pr-.? triear r,-ijcroria .-ij r ie i fra cc ,

L it tn-y --re : no r 1-ac r ,- l to or t rain rU r.:-crir-7mdt :

rineutr.i-i: -u-ie r: .r, -r nirie:: ,.r tr,- 3ou'rc. -.

nO. r aft- the -'..-?lopm- r ir tr e .-uc 'iear rcact:.r,

rniutrori i -ere, 3,. 1 i c. li in great qiUanr i anrd ri-u ror,

1iffraccion -pe:r*: r;.- errs -ere DuLi at Arg-rinre (i, 1 .,

i'a' F.1 lg- i ', CraiK -.1'.er, *'ara.aia j ar-ell,

rngiarn (ii) ar.i i-- r-e. .1c' at. r Me t r-, t It.

:f-f ig ~: E TCrn ii' d a- re aevelopel ( 'l, L). ArOaut tr e

Sii -. vT rr;crc ri i et.cnOs cif reutro n nFI:trum dr al, 1i

-Ir iiCrlc-ti Cmy d' Jm C (r i* Cdm C L- 1 e-r al. I

ari ii I gnii ara T rrn cli ffe (18). 1 r :e (ii) and 13 e i 20

.a l co- 'ru 3 li tgr.t ri. tri- uu jcz ct.










An earl:" theoretical treatment of the spectral

nardening ess carried our n:, Plass (ii), .ho assumed

neutrons of eacr energy diffused independently without

energy interchange. Later models were develop..p to

calculate neutron -pectra cy the u e of free nyfrogen

arnd found hbydro,=n scattering kernel (2., -3).

One of the better me.ho's for calculating the

Pace and energy dependent flux in a unit cell was

developed tb HonecK (.4, ?i) for rH0 and D0-,TOioerated

syvsems; it is described in Apperdix II. Re-ently

at tAPL, GolIman (C.) constru-ted a scattering la-

based on Nelvin'- model, and agreement ith trhe

experimental results using iZI.> is excellent. At

General Atomics, Younr (27) has measured neutron spectra

using a pulse nign-currenr electron linear accelerator

in H C', C:I and C 6H6 mocerators poisoned with B, Sm, Er

Cd and also D.0 (28). Heasurea spectra were compared

with DSE (5) transport-tneory caicilations utilizing

the Dound hydrogen scattering model for water. Earlier,

Beyster (2') measure neutron spectra in pure and

poisoned H,O, iH2.n, and ZrH using the pulsing technique

and compared it with jS'l calculations.











litigrai 11ltnoa

ini r,- 3" -ur -i. lr.t of ri cutcrcr. rit. rh -, E:rt u11 nir

L.a im-c- :)f- f itt tec'.:rIn .Ie r a crystal ;i ;pec ror m ze er

rju.irs tr,'e e xtra:ti ior of a re.-'ucr .-.rI ru iam ro

recat: r i ti: icn i s i ifficu l t t. -io for ,iore

an i fei. r.epr eertat i s posite ir.. h-c.ier rE;

u. Lri, ract i E icr, 3tec .ars, ;leDctru-i cr.iriges trirougriut

cr-i cI ii mi, IL. mUippiJ Out ( gooa-i ispd:i a

r s: luE icr c O ain J -itr. mirnimai c ii p rtur.at 1 :.ri)

Tr.e u:u1i ea.ri[ertai t crir..i ue rfor o-er. ing

tr e Spe- trat :_iarge ir. 3 urit c: il of a rLa:tcr ir.i .l

apping trne itivit/ rari; of r-sonan:- ani 1 .' crIos

-?cticn IJeector For triii type of mTesureUnCr- various;

y '-i of -'t c toru arI uLImmaar l in: ? ri T it* .1. Ir

iFigure :.1 ru- .:ros q e :.ic.nr of tre i aLs3oro.er Lu1

arin re rsc-rarince ac.iorter Lul i.6 ) 3are gaon. sis.

incl-uli -i in tne figure are tin croi ;n:cioni-l fcr aLi D

i j1) ar3.1 FP ( ). tli a l li a-r ne-.utronr i istr :.zi 0or

in tnie ttnrual r-aergr; rl gicrn i t i .r. average tEitmperaura-

of 2'ii. is i ro-n in -re Bar-e figure.

by ir crt ioin of figure 2.1, it is seen trl ,

as tr.e leaxeiiiar.n 3sritj;ion shift; to rnigrer energies,

tne riti1 of r? act.'ioties of L! ard Lu 7' will

increase 3ir; trIe r.acticr, rat- is prcportrionrai to tne

integral of tne in'utrr.r, flux times; tn iL.-sorpticn *ross

-iction ( i3)






























































.10 1-


Enerr.',, ev.





Figure 2.L. Activation Cross Sections


'1'


(-I




C.


C.

iI



















- I -.


Z I j




C..-'


- '


2*



r. c .-. .

44 -

'S Z 1 I


'2 -'

E L t i
L t
i r. r
'S I








CJ


-
j


-7 ..~











j

3


--

-


- ~ J



C










in well-moderated media with low absorption,

(e.g., D.l, H,1-, C, Be) far away from neutron sources

and t.ouar3aries, me spectrum approaches a Maxsellian

diitrirution witn the. average temperature corresponding

to the temperature of tne medium. 4ren these weil-

thermalized neutron eiter a nighly at.sorbirg medium

(e.g., a fuel element nwich nas a 1/v absorption cross

sectionn, lowei energy neutrons are preferEntially

absorbed, resulting in a gardeningg" of the energy,

spectrum within trh fuel.

ine activation results were interprecea ct

using rne WeEtcotr formulations t23). Trig r.erhod applied

to .aell-moderated sy'srer aucn as tri UF.i. In a reactor

;pectrum, effective cross 3;ctions are given as


3 = Jo (g*ras) (2..)

where


0 = effective cross -ection

o = cross section at v = 2200.1 ni/ec

r = relative intensity/ of the blowing
down spectrum (or epitnermal indes'

g,s functions of the neutron temperature, T


The values of g and a are tabulated (35) fcr various

nuclides. For 1iv absoruers g = 1 and s = '. Using

this notation, the CJ ratio for a very tnin detector

is gi-.en as:











g + rs
Red rs + -2-

K To (2.2)



where 1/K is approximately the density fraction of

epithermal neutrons transmitted by the Cd (34). The

factor 1/K varies with the thickness of the Cd filter

and is tabulated in the literature (34). For 1/v

absorbers g = 1 and equation (2.2) becomes


1 + rs
Rcd = ---
rs + (2.3
K (2.3:'


Rearranging this equation gives:




1 1
o s(To/T) (Rcd-1) + Rcd/K (2.')



T',ere fore, :',, usinr ver, thr n sr terctor i, t-e factor

r ca" r. Ieasljre .

ror *ear.acora wirr appreciac-le -"lf aesorprtL:r,

eiUacrion ( 12.) :e:orme, 3 l0










z, h e-
r i-- -
S (FP -li ) r I. -R )
-,1 C'e.I ( ,.






Gth :rhnermal reutror self nshiel-irm factor,

r = resonance self snieldir,, factor,

F Cj transmission for resonance flux,

,i = fraction of resonance acti.artion belo,
Co cutoff,

h = thermal transmisr.ion of Cd filter.


In order to measure the effective temperature

of the tnermal rneurons, the activity ratio: of Lul17

and Lui 'm were measured. ihe activity ratios of tnaee

isotopes at position x wlth respect to a standard

position a is expressed as


[A17 ( r. )176 '

J L(q + rsil7 1 '.


[AImj [(g ),





SEquation (C.6' i? for ver; dilute J-tector3, Jriere
resonance anr thermal self abDorption is negligible.










F, aisu.jmirn, 1 and r 1, ana1 30ol-irg for C

r.n- following relati.ronnip ii oDtainred:






(g rsa
[ -1ra r11
x -


J*- r, ;)l (2.n



For r = : (i.e., ro epitrn rnal neutrori ) qquat.i. (2.7)

reduce; to


[E6 : F :z P[g17 )s (.


The effecrti, neutron temperature for gR.6 (teperature

ir.JeK ,of Lu17') S oDTairne. from Figure .2 ( .

If r +: m ce [(I + r E ll mux t be evalusatd.

For Lul = 1 an r. r' is a r-,measrable val.ije .it-

jilute fails.




\ 1 Io r Gso r




*' This equation takes into account tre self-shielaing
of resonance neutrons.


















Mir. iMB.64






10,








I '.





3I

CALcuA.AfTl vfLU.




CodIMrIW *T.TIFTICS i/



1.5


1 0


2000 30 4.0 00 w0. 10 %G 00 000
SPKCTIAL Ira ,*3 r



figure 2.2. Calioration Curve for 9176









is ai o Jdeterrmind exp.crim.ntall.'. Tnen using the values

1of g17 ani ', giver, bt Westcott (~ ', .orrrectej values

tf g176 and S, are obtained by trial an- error. The
effective neutron temperature It found from tre value

of Gl-6 lsee Figure 2.:).

An alternative metrCod of evalo.ating r\ T/.' is

to irr-diate two tIi.ctors and express their activation

ratio- as fcllous:





L( g,Stn r ^ '


Ab gL( G r' ra ,' )a
Srr


or rearranging




[g"h r TT 5 G i]
Sh o r x
X a R' 1 / X---
x S
th r. r'To sn s rx (2.10)



s is determined from the Cd ratio of one of tne detectors.

Solving for r, T/T0 in equation (2.10), the following is

obtained:














R' Xs(gGthb (gGth)a

r\ T T, :
(e G Ir R'. r )b
o r or .11)




Lif feren iai methodd


Time-of-FligIit

Tri time-of-flight Metrioo utilizes a mechanical

rotor with narrow slits rallea a chopper (37) or a

pulsed accelerator to produce Dur;cs of neutronr witr

a time duration depending on the speed of the rotor or

accelerator pulsing system. Tne Dursts of neutrons travel

trough an e.acarted tuDe to a Dank of detectors. The

energies of neutrons are determined o. electronically

measuring tme time it takes for neutrons to travel from

the sourcee to the detectors.

Usually cnoppers are classified as slow and

fast. Slow choppers give bursts of about 20 u sec.

duration whereas the burst of a fast cnopper is on

the order of 1 u sec. Unlike crystal spectrometers

whicn produce monoenergetic neutrons, croppers select

certain velocitv neutrons out of heterogeneous beams.










Tnre energy res slut ion of a cnoppEr ic Ja.cri'ced

t.y tl eq'jat ion ( i



3E b t :
= -0.0''- r + --
E T, ". 12 -


aJfl'C rI


LAE urcert.air.ty ir erergv,

E = enT er, of cne nutrorn,

at = ur certairat, inr flight Tlrie per m eter,

= fli r,C p.atr, meters,

.m uncertairtv ir, fi nrit patr.


For a flit c.-opper, tr-e second term i rnligule

rJ tre reoolution r-eiuCes to th.i fir.t term. Letter

energy/ r5es)litior i o-.btarn ed atn lon er flirt pacti-.

A list of re- lclt ions coletner 1ith flignt paths for

.3xfifeiar choppers is limited tb, Arnaer=.or ( '.. Multi-

creannre analysis deTrrminres tre irernsities of neijtror,

in different ererg, irnerals.

1.wi crnoppers car. ie conrstructej muc r more

sasili than tne fast cr-oppert.. Tr i; is Jue to cre fact

treat for the former, c nopping is ac:'ompiil-he.d atrn thin

layer; of Cd, whereas it takes marn irchea of pFlasci anr

steel for fast cn:ppera ( ').









An alternate methoJ for reasuring neutron energy'

spectra (40) is the tie-of-flight mertoo with a pulsed

source. The advantage cof this metnod are: (1) the

fuel elements get low irradiation, n'1 the rotor cut-

off function ,does nor have to be Jeatrmined, and (I)

Dy the use of tne chopper and pulsed source, t.e neuatraor

spectrum as a function of slowing dor.n time can be

determined.


Crystal Spectromerer

The jue of crv6til jiffractic.n spectrometer. for

detecting monochromatic neutrons has ceean investigate

Dy man'. autnors (9, 10, ul-471. ; fraction is a

scattering process. A regularly arranged series of atoms

of a cr.,stal will Ecatttr the neutron a res in all

directions, buc ordl in particular directions will

scattered waves te in phase and reinforce eacr. other to

form a diffracted beam. The atoms of a crystal are

arranged periodicaliv in parallel planes, so that in

gEneral scattered waves are out of phase except in a

few directions where reinforcement takes pla.:i.

Tr.e diffraction process applies to X-rays a;

well as to neutrons. The fundamental difference between

the two is that <-rays are scattered .'y tne orbiting

electrons, unere aE rhe neutrons are .cattere tb the

nuclei of the atom. For this reason, the X-ray











-:acttring amplitzude i proporrt.onal to ten atori.

nuririer i"f mne eie irm.nt, w ni le tr neutron scattering

arpii tuJd :-rio a relativ.el ,' small *Jr Lar. ion wi,

atomicT nurri r.

Jren neutronr frrom collimator impirnge on a

crytFl piano of a single crvstai at an angle, u, onri,

neutron: of o-nc enerp', are Jiifracte.1 in trhe 2irectior

of tren angle 2'. Tncrefore, the :cr-',-st l srd tne

ietector rust mairtrain an angle ratio of Mne-rnalf ir

orJer to trail norenergeti. nretror .

rr.e diffraction of .tre neutronr :earim penri on

tre lattice pia:ing in :r-e r, saal. Tnhi space .'aries

japn-ring on trh *:r'sal. material anil cn tre crystal

axi; along rnicrn it i.:- cr ir.e conerent :attering of

neutron from trhe ruc-?i of atomsi in a s*inpie crystal

Ic proi.duJ a morochromatic neutron betiam n is po.'erniJ

tre familiar tragg's relation:


n = 2, rin (c.1 )


anere

.3 = lattice spacirg,

n order,

I = aave lent ,

= g.glarcing angle.


In energy terms, tnis relarai nsiip becomes:











Fcv) i n .' r ; E


inere k i3 a constant for ca:h latti-:e spacing.

Tiale 2.:' glves a liis of cr-,tail with e. and the

Jetectsole energv at 1'.




TABLE 2.2


TABLE OF P AID ErjEFLP' FOF
DIFFEPL-NI CF'i'TALS AT 10


(2. I" )


Crvstals x. 10 ( ev Energ,, (evl


-u (1ll) 71 E.s:

Na Cl (200) 2.S 8.4

Al (1i 11 3.76 12.2

Ge ,111 1.?2 6.22

LiF (111) j.6L 1i .25




From equaior, (:.14) it can be seen rrat the

nigher order inrerferencr will c due to neutrons with

energy n- times trn lowest .rdier. Aleo, there 1 inter-

ference due to the mosaic spread of the cr.3tal.










Mosaic Structure


In order to know the energy of diffracted

neutrons at different angles, it is necessary to know

the distance between the atomic planes of the crystal.

The distance depends on the direction in which the

crystal is cut and also on the crystal material. If

the crystal were perfect, neutrons of a single energy

would be diffracted at any given angle. However, all

real single crystals have a mosaic structure, that is,

they possess structural imperfections which break up

the arrangement of atoms into a number of small blocks,

each slightly disoriented from one another. This

mosaic structure causes the diffracted neutrons to

have a spread of energies at any angle.


Higher Order Diffraction


Also, i-cor-jing to equation (2.14), there are

higher order neutrons diffracted at -acr, angle. The

ratio of the second order to firir order neutron

detected in the cam can De .rLtter, s (&6s :



f(!) (E. tE) S(E:)r,-E w*-',n r,(E,
'2. n.1 ni)


wr.ie-re
















E(E)







i .i )L)

Fn= .(n=-, E)


(*(E) is aa4unei to Ce 1/E
for energy greater than 0.4 e..')


(ratio of the detector efficiency"
for second ana firnt order neutrons)






1 E)3 co9[ (4fE, n=?)jAe(LE)

2 (E) .Cfoa e(E, n l)]J Le( )


2 .16)


were


w (4 E) rL r=I
ww (L1 r
w(l, nfl)


o(E) = n
r(E)n;l


(w(E) i tre fraction
of reflected Deam trans-
rittse by collimating
sysE ter)




(r(E) 5i reflectivity
of tre crystal plane
use )


In equation 2.16) cos[d(uE, nri2 ] : cos [a(E, n:l)J.

ani let a = CE) wricr red.ices the energy band
trar e to (E detector to
transmitred to the detector to


a(L) = o,
L .


. .17)


where c = 4
o










ri.e rrf'ict; i ".t" of a crvs a ri for rieutrcn. is

gi.'en I; equation i ll) of -olm ( ) for tre La.je C eia



-A tcan li*1
r.' = exrp'.-2H' '. -A r

1J (2.18)



wner-

exp(-:M' = DEcr-Wal er temperat ure
correct ion factor

r "rmiaic ipr'a of tr e cr,'stai

A = p;rDd-ct of the inr-ear dt-lorp ion
coefficient and the patr iengtn
in crvytal


E. 3 -
( 2 r, 3

t trhickne-s .f cr' tal

'i reciprocai of tr, unit cill

r = crystal trurcture factor


The [Leb,,e-,aler teimFeratjure c;rrecrion factor

a:cournt; for the reduction in intensity of the Praeg

reflecriorn dJe to tre rhermal motion of trie strci: in

tre lattice, hr, ere



M ( T,( T ( .lil
mL i, 6 J













= xdx
( J -x
0 e'x1 ( 20)


Here,

HlI L= Deobe or cnaracteristic temperature
of tne crystal

h,k Planck's and ialtzmann's constant

a r nuclear mass

T = temperature of tre cr/3tal in degrees
:e lvin


jince the factors in equation (.'.1) cannot be

calculated accuratel, it is easier to obtain an open

beam count rate of L and 4E. Tr.e ratio 13:


c:unt (rE1
f-(L) -- = o(E)E(E)o(E) U(E (r))
count (E) nl n=(E i n

(2.21)

Equation (2.21) is a good approximation obcause the

second order contamination is usually on the orier of

a few per cent, unless the first order energy is be1loi

tne Maxi-llian peak. Now, o(E)ni is




aE(n=i, 4E) 4E ''cos[( (4E, n=i)]a, (4E)
L(Ern=, E E cos--C, n-)J(- ) (2.2)
Eirn=l, E) E cos[i(E, nr l)]a> (E) (2.22)











wrc re

co* f .(L .n=i)]

.:O [,(E, n a)]



3( E)r= i -- o a r 4-.? )



.,~(E r ( fE) term in terms of f' L', .: expre:aeJ as:


r(EE) -

r F : f ( E )





: lir,.-. i ( )r, i = 1, h.-nr,
r'Fl .'wE'







r( L) .
f = f.') 1:: ------ f (E) ("L''
ruE)




Tri re f rc. u- inr tre C al :i ate i value *f F(' I f(F

car te eiTimatiJ.


i re F.rnningr .r E tfecr


whern a neutrcrn ;rpectrrurm wa: ineasiurcd usLirng a

cr-.'tal 3p:etrja.rter ar.d correct iron wer- made, manr,

large lxps were fc-nIr (2, 5j-5) insarea of trie irrootr

i'ectiruim idaracteriktic o)f a :Baxweilliar, *jistriDutic

or neutron veilocitie friac fluc tuat i.rs are due to









Eraig reiiection of nr.u-ror s from reflecting plane;

otinr inan that usel to obtain tne rmono.n romatic Deam.

Tnii rerlecttion is best .Expla;i=-j by the use orf the

reciprocal lattici ano sneare re flcti.:. conceptE (iS

and ti .,ectr)r rotation as outlined in App-n.jix III.

Figure 2 nemo3nstrates multiple reflec-icn by

miia3 of th ap3nerF off reflect ion, where tne radiLu of

tne 3phere is 1.' ; it 1i center-;: on tne cryscal at C,

arin passes thr.r u n cie origin of thii r-eciprc al l attice

at 0. For ar in.:io-er. direction CO, reflection occurs

in tr~h .ir-ectin CP 1if Eii r.e :iprc.cal iatti:e vector

', tcrmir.nates at F en rte Ftnere. iupposi a 5econr

re:iFrc:al letri:e sectorr r; terminate at :, on the

ipere trlenr re flect i.:n :.f rte same t.ave length ;.:cUrs

1t rhe drecion Co. fa:king C as tie orignL of tnr

reciprocal iieti:e an: CQ ar : he i:icidelnt direction,

firtnrer r rlectioi :orr.e;ponring to nte victor r', i

rc.si",le. Trhe dcu 'i refl-ection Dy .a.i of r' and r

giveI a re-'suiant in tie sam ie ir.crion and at tne same

wa. 'e len ith a s a re f l i i on tr, rojug in:e rl r,

* r tre 11iller indieC; of the Flanes ire related cy:


ri : r 4 1 KL 2 3' 1 i 3 ( '


irTe .jDobl reflection can occur wiErn ar. reciprocal la tice

point ', ii or t.ne sprere, wrere Q is n:r necessarily




























.1


F1

- -- -4-i~.n _Ci~cinI


F gt' E i .3. Sphere : f ReftLc:i.:n


F. ff l ct i re :t i,.rn









located coplanar .itll C, u, and P. Finally, it should

be noted trar Whern nultlple Sraeg reflection occ.rs

for firat order reflection, it also occurs for rnigner

order reflection at the same angle of inciden.e.


Feflectivitiea


:inr:e reflecrl.it ie3 for NaCi an- be have deen

c:alcuiated ('9), a iaCl :ry 3 al cut along the ( 20'L'

plan was u:-ed. Tr. 3i 3ada'.ntage of tiis .:ry'stai is

that tne seconj order contamination tec:ome: s ery large

at law energies (e.;., = S., per -ent at L = .0u cv).

In orler to rdu:e this i =Seor..: orJer contaminat,-.n,

3 cr,.:ail trn :-upFre.p ed sec rnd orfer refie.ctivit.

must L- used, LIT (1il1 is su.-n a crystal. Tn,

suppression or secor3 crrcr refiectior, : .ue to the

oppcsire sigr of acattr.rLrn frorM S.ucci ,ile plain (1:).

Thrre are sOme dJiajvantace, in u.ing LFi

:ry'tais. Tnese ar.: tih lattice. psraimters are

uncertain t55), tie .diffiu e .a.:kgrcunJ :atternln s1

fairiv nigr, single cr,'stalz are hard to ottairn aal

suppres-;ion of ;ec.rn order in n-r .,ery e r- r [F (il )'

F k2 :*:1 1.97].

Jse of Ge ani -i cr'y tals, .nuC: rie ianmond

stru:ture, i .verv favorac e iecauz-, f:.r tre (111) plane,

t-.e e-ond order ;. ) vanishmi completely, in fact,










it has been shown (56) that at 0.015 ev, the higher order

contamination of a Ge (111) crystal is only 2.5 per cent.

Use of a quartz filter also reduces the higher order

contamination considerably (57).


Transmission of Reflected Beam Through Filters


Transmission of a neutron beam through a filter

can be expressed as:


T = T1 + T2X2 + T33 + (2.


where

Ti = transmission of neutrons at
energy Ei

Xi = fraction of neutrons at energy
Ei.


The sum of the fractions of neutrons must add up to

one (EXi = 1). By use of absorbers such as Au, Cd,

Sm, Ag, Rh, In etc., neutrons with certain energies

can be suppressed. These absorbers ri.' a large re -nanr;

and'or a l'v cro's section. For instance, for a l'v

3Lruler, jupprfi.:3;.- i r r n- fir.r *:.r.ir o,; per crr n

si-.i.re- s Trn :E:OnrJ orl-r L ?I,) i;.r .:.- t. T ri T r ; ,

the rr,:,i-is;i3 cn ,'rC .j i s a v. ery j:2rf ore for



r-oilutin .of ae r'stnl1 sp.,:tro.re-r regie::in ; cntr

rmc.si.: s3 r-'i of cnr. :ry;ial is 3ei;r-e.sij a; ( i:










L



Tre arctul reclu:ton ;I determined v. plc.tting tnh rockir.n

curi'.? or different angle. Tne roci-ng curve is ot-

tain 0., counring 3iffractre. r neurons with a stationar.,'

j-ate:ctor and t rot r, ig or rockiing tI :r.'sal to

.JifrferenTr anfl1 Thie maximum of trhe 3i tritution

c*:rre F ;cii t. tne positior, D rnere the j.-tector and .:r,'tal

planr. are aliEned. iTn; widtn of t-e; pear at narf-

rma'imuium is= ual to al trn: .nrgy spread, of th- sy3stm.

the ain advantage of a crv.Ctal spectromiter

:rompare. to rne time-of-fllghr marni-l in rne Ic. ernrg.,

range i n tntrl te area of tne ctrm at tre ,je cctor is

quite n5mall. A diffraction spe:tromrletr car cover the

ererg:' range, from J0.0l trc e.', whereas, it is

difficult Co cover rnii energy range t.ir one cn:pper.

The *3isadJvantag-g of a crystal -spectrometer are: (1)

tin reflectri.,it varies in.'ersel as t ire neuron enrg'.y;

(2) th-e .ontrisuticn of the nigner c.rOr aiffraction

increarSe3 teid t e Maxweiiiar pea'., anl.; ( ) tie

sFectrof.ter detector i: lc;ser to the r-actor than rth

tire-:f-flight de tecors, resulting in a nigner bacgrcuiud.














.i-tiTLpl III


[ ,' C. F ii J ,: F .,-F P A e lT ,lK





*' i .lmTi .: r

in c..ll.LiT titrtr i-a Etraras tr rroir. r .a r :rar ei,

ran intren.,it Jecrea.ec very raF l.,,. Tper force it

is ie.:essar, to pri.ae srd- ral cl i Lasrt r.g ctarn1. JB id

r.,, .- ie, hr-rr cr :nar nrail ra: tc ie re 4 ired r sj mall

arguLar .iverrr -rc. Tris trYe of .-oiil tai :,r i; call e

a o.iiar coliriator i'i.

l-.llar :oLlirmator was cor.i trcte frcr, si- gr.t

: tan irlesi -r el tri '. .0. t Li. trin:, L. li. wiiJe

ar, 1 "i ir. L.:.r'g. :.ta;ile_- sitc i roa *:-.re-5igrtra of

,a icrac uar Jicre 2 sd foar scfaraii ig tn-g tri[ .

Tr'i coiiiir.atc r iwa trier, i ri i rted i.',toi a .a- 1 rei; : i-ot

1 in. x 1..5 in. x A3 in. r, a 3 ir. Jiae m eter .JaoJer,

c:.iirjr; cthe :cl Limrtcr wir ri.la 1 r, the Sl.;i t.y

friction.. I~r cc liIeratr -'a trh-n 3ipp g d int a

Dail rg L-atr of paraffin in, '-i r ,, ai;,i v.sd tr

t* ira-Z ( :i- T is procedjure gai a tr rii, coaT of

''i.- oir tri, -E urface .;f the .:ollicr.ating piste; it









order to eliminate the secornlar.', 3:atterkng from ti',

ill;. Trne a.ngular Jiv;rgen:e of this collimator ie

1..0 mnirnjte; oe -ection cf the -oiilimacor is shoin

il Figure 1.

ileutron: etraring the collimator propagpte in

four oiff.rcnt (a1',: (1) Jirect tranqsmis ,crn (2)

mirrl or reflection (.r) tranam: ion through tie

oliiimat:r .alis, arn (u) res:attering ty cne walis.

rne-e 'ffe:ts are r.owa considered in txrrn.

For dire-t transmission wiftn an isotropic

sOuirce on one ernd, ccrnier a narrow slit itr rhi-:.nIesi

T, uidth 4, and length L, as h.rown in rFiure 3.1.

Th'r rumtr of neutron em ierging from t.,e

.;ollimator rer unit widtl .i1 founr from the relation (.-"'


a 1 T
'l(neutrns .': sec) = J
o a' L3?ec- 6




S t TIJ( L tsn 6) i3.1I
0

wt ce r -

CiL tan 6) = lire aour:e eiemenr


-I T3(L tan A) m source sirergth pF2r unit
'" soliJ ais gle







U


_T -. ,
-9.
4,d


F r i I I i.01E "'-- I L r.ari.r C : 1 ,r


IT [
L.



L,

--- T


H- .


__~ _
i ------- CI


F ,z ,r ? ',. 1z -. ., r.-, E f -. -r e r.: -











L2 ec' : Jdiranr.e from emitting
elemenr a(L tan e) to the
receptor


0 = angle from the emitting
element to the receptor in
radia ns


On integratir.n equation (3.1 the following ra;ult s

obtained:



0-
rlineutr.nscc sec) = ---- a
-" L o .2)


DEividirn born sides of equation. (3.2) y th Eliicness I,

a reitriornhip between me direct inlet and outlet

3caler flux IF obtained aj folloW2a:




." L ( .)


Tne intensLt,; of rhe neutron bteam emerging from

tne collimator ouldl be a triangular functicn if the

coliiti ator were perfe-.r;


I (.) = I [1 e,a] ( )



.here

I(s) = integrity a3 a function of angle *

I = maximum intensity in the center of
tne collimator axis











a i. r tri ar gI v* .iari e fr.io -a r. *a. Lu- to

imiu rf :tr .1- rr. :-Diimar or an-1 trme fi.rit- train;-

mi lo o1 lieutr.crS errrn.ugr. trc ..all tris rri rnguiar

urti; ri r rr15 t i r c r r Er 'a3'j 5i r. rtri u iricr.

r'-. r a ir ia3arl appr ma1ii-.r or e u ti rra ( 3. : iS







.rnre




E lrt a tual *eA;'ieril tal se -up t di

sour..e i l.'Cat 3 soiTi di tar:e L.,aC, tre *:cl 1 at*ir

irliet ti-re tfori ari drpjrc*-Lcmtt rl- 1ati:ri-r must L,

jerJi C-d r : l trie -srai-r fiux *,omiri, Iout cf tr-n

:. I i TEtor a r i tr,, sr:ali r flu j-,' r;I, e c 5.u. r:-e. ghFain ,

a; :um r.e d r.?e :.ur: ,c i; itrF .'pL: a ~n c n i.JI r til'. t,-r c

ritucror.i nii:n ar; inn tea 3ir c.t ly. Firure 3 .L s j'- i

S ari i tre .. il tri iird trr r tr, rr:- c f tre scur r e

L ter-I? d N r.; E c lImator cJt l t ...r cr. ; a -pr .x im a eI

rect aIular irn hali.

re ixpr- lsoi.r: for and w a r' a; f:ciiows:


14, ,J*; C i.E


(5.0)










'o' iimagir, that t j-e .ollimaror ii of thick~neas T

4i.tr, .: air, l' rgth (Li L2). Using equatio. (3.3),

trer relate ionMhip for [r-. out ~. EC.alr fluix for this

coll niatr 15 :


r'(nsutrors'cm; sec~


T Q e
BG


Sirxce ,the act ~Ja area of the

is TI' rarner thar 7 -'.j- an

the oucletr caier flux using

as follc.s :




w *T
4( reutrors.'cm' sec) e
*.I


outlet colmiTair g s.it

approximat. expressing for

cqutic .n r i. ) is bitir] d







\f9 exp(-( Q' )J*'] d


e x p. do_


( 3. 8


whe r


l/2(T T)
Ar = rc *s n
L,



S- Arc sin L(r 'L;J


( 3.7)










Tle rc-t al refle-. tion of nclrr:.-ns L tr.< wall

cf trhe c.:.ii mat.:r can aier .:rt Tr, i.,eutr.r n ;.ectrum.j

u-icc a refl-ticn .a. first repcrt-r- t Firmi an.d "irn

( i. i'- c:ritr. ai anrgl. for su;n r f'icction t (o i-'.





I Na n)
1I S. i .1 ang Bi ,




g nutro i -at L'rc.tr.

I : cume .r of atoms ;' i in tra s.atterring
me Iajl

"a' : a rage .jnr- renrt sca trying lcngtr


l a.i. .-.r i( ". si c. tr.at there r tic. e l angl i.; .iv

funrc: .:.- ri.-iutr-r n e*n rg.,. In tHm i reljati.o r.ip f.or

trie crt.cial angle, "a' can r'e either poiti ,e -:r

n-gatrir *.penrin; orn trie -:atterurg material. For

inrtarnce rnarc.ger as, r -i i a.'c c:dattring lengTrn,

r,,iile cartocr ras a p :.ti'e .'al e. Lxplri'ert-r,3 ha'.'

Le';n 1.erfc.rmirel sing neutron mirrors irt, .,ariouls rir,.:r.-

carlc.ri (i.t ) arn] it .a3 four that -. t c *i..mes zero for

a rat ri f m 'C 1. '- i.e., trhe negari .- sc. at er ,ng

1Angtri of h i equal.ji t -: r pt ciit ive value e of C. Th rr-

f;re, if trie cc-llimat:r wilE rnave a ,alui c.f li .

larger tr.r an .'S, [.tal reiflec:t in- carrot occur.

*.:cort'ngl;, 1 ti-. s urface c.f tsr, co.lli ,Mator .alls -aS

cc'atel -itlr a trrn ioat *oa paraffin r i ni:r, d'ain, g anr









ii. ratio of approximaTs ly ahoulJ elininiat the

otcal reflection, of neutrons. 7nhi type of collimaror

has Deer. constr.uctr previously (64b with a thin film

of polyerhyince.

The probarlitty of direct transmisrn io.n through

the 'jali of tre Coilimator without absc.rption or

scattering is expressed as A where t is the

tOtai cross section of the wall materLal anJ. z is the

path length of tne neutrors through the walls. L..e

:hough the aLeorption of ateel is not rign, this

proabiliity is very;' mall since sar neutrons whicr the

steel aso.O's, will pass through it at very smial angise.

nTus, the neutrorn patr length in steel is relatively

long, and tranrmi3sion through the wall is negligile

compare.J to the iarect transmission.

Calculations have oeen maJe (:t for th. trans-

nissi:n of neutrons 'F rescattering in the walls of a

similar collimator. For this calculation, this co,-

trit'tiorn from rescatteri-ng was founi tc be less than

one-nailf per cent of the total rransnri ted intensity

witn neglLgible effect upon the angular Jistriburion.

The description above state that the neutrons

emerging from the collimator come predominantly from

Jirect transmission. A calculation -wa made for rhe

ratio of o.,o for the =cperiramntal ert-ip and was founr

t be ie uai to ".14 x 10" .













Iall a ] Li (1 r, t 3a J we ,3j

for tr,- i e ;a-er imei L lmer, or: of [, )ri c ry' t.3a

. r- 1 1 o n. < i. x in.r




Trlie ,.or.i etter Lorsi' tI 5f sad ple rKacl.-e it%

a c:r .c.t l holder, an erv, or, Ari:rli :.-, e,,C-'or,. col .at r

i,-.] :ei ector 5r, el. jre- a.t acr, s.r tr.e earir.

,:-rm Trse gearir-g .t-n i1 in a ca31 alumifilfu D;x,

ar.] K .*:i e, mo.veJ mTauaii or electr nir i Figir

3.:1 irn s ru. c r,; al ; p:tror.t.- r ir. c.O erar3i n 3r t3

or rr ijr *r i': cf Florine Trar-nr.; $--3:or (ifliP..

ITre .:r, tai rol.Jer i, mr, e from a re:tar.-ular al mi.j 'J.T.

LO i X t L t', enrji 4-e.. n i tn rsi : e .: r" ital fit .

Tr.i DOx 1 a3 a cr a 1to O n *:r', t til Ll.e rl-, r..n of

,a t ai r.i :I c- l ro 3 ir. Ji amete. r.

neir 3e or &i [ i iiel i s tt a t to 1 re i 1 r -M t'r

a *co*1i im acor aj i; ;r)o r. ,n der. ai r. Fi lure 3. Tre

r. .ov.:er r.t of the cr'/y cal r,:ijer an the ]etI.ect:r arm car,


: These :r,-. tale were otrtaned from irie tironrrw
r.Ti al ,c.-mp.an. 193' L. 'tr r tre z Cle ..iar.
t '.rio.

** Picrer Lip lar.ar i. ffra torn Ter, 11 'l :.o. 3:27.







N


FicurE i.j. 1% r r a -r i or, : er irmeer In OpF~ra t io


























'I









I U









-. I










K-<-

fte


I __________
L










ibe performed separat,.,ly or at an angle ratio of 1."'.

Trre i:.2 mo'.'ement is carried out at .'-ry nign preci iaon

Ly rmeans of Jormi gear in tne macnir,e. Taj odometer&

are attached to the box where tne angular pFosioias of

the crystal and tne detector can oe read to 1. 1).utn off

a degree.


.J:'curor De:erction ystein

Ine detector used for these measur'emrinE ia

1/3J in. diaaeter, 4r per cent e 1 enricned -F3

counter within pressure of :6 cm 1ig. The lerngn of the

tune is 1i. 3,u in. long with 1i' j3/ In. of senaiti.'e

lengt;; it nas a ceramic eni injdow." The center of

the plateau for tr.is detector was found to be u8,'0 vol~a

using tne existing cabis The length of the plateau

'4aa about 4ji v. wir.n change of siLope Co one per :ent

per 10iC' volt-.

The efficiency. of En- jeteitor for iffEtr ,nt

energy ieutrona 'as not calculated Lucause it wa:

Jeterminei experimentall/. Ineareticaiiy, efficiency

.arn Be calculated from tmh following relatior.niii ("):


E = 1 ea p -N> : 1 ) (3.1i )


n* Tio Jtector was supplied Dy Reuter-'3tokes
Electronic Components, Inc., Model Io. FPC--li5.










where

N = number of atoms per cm3 in the
counter

x = length of the counter

C = numerical constant which gives the
1/v slope of the Bl0(n,a) Li7
cross section

E = energy.


With the BF3 counter, a Radiation Counter

Laboratory (RCL) decade scaler, preamplifier and linear

amplifier (model numbers 2032, 20200 and 20100,

respectively) were used. In addition, Atomic Instru-

ment Company regulated high voltage supply, Model 319,

was used.


The Subcritical Assembly


A subcritical tank made from 6061 Al, 24 in.

diameter and 60 in. long and wrapped with .030 in.

thick Cd, was placed on top of the graphite pedestal

of the UFTR. A grid made from the same type of Al was

placed in the tank, so that the fuel eimerint could be

arranged in a hexagonal pattern with lattice pitches

of 14.7 and 22 cm.

Figure 3.5 shows the location of the tank in

the UFTR, and Figure 3.6 shows the top view of the

lattice arrangements in the subcritical assembly.






















I.






-r










U S

L TZS l


1* r

. '. .






'' '


; /


* I


II







'I


II
r, 7


1._














0


Figure 3.6. Top View of the Subcritical Lattice









The pl ane Zourc-e of th-e rnautroin3 cnrters tr -J surcr.tlca

,eml'.' from the LcottoC face of t.re ranP. There is

a proximatr:: l.4 ,n. of moderator betw6.-r the grid ana

rnre cotton of tr e tank.

Two t:.peB r-f riacurai urarniumrt fali. eierents were

useI for tr.he experiinent : Marr V-8 snd ilarr I. Iari:

V-B is anr ar ralar t.':pe of eiem-rent 2.ES ir.. c. :. anr

i. I n. 1. i anrj 6 *i .: in. long. larr I is a ;oliJ

fuIel lenert one in. in aiamater ran 3 i. ;n. long.

There were :ix fuel eilmern, in -ar, tJbLe. Tnre rcieracor-

to-fuJ volume: ri ratio ',' If( arj p. c.ne ar- li3s1

in laLte 3.1.


TAiLLC '.


:.UtehITI'CAL LATTIC.:E c:Jii.UFATI,':r



Pitcr (ci) Mark V-. F.ojs Mars I F.-.ds Vmi''f

:.0 0 : 73.?

1 i 1 ii

I1). d i 0 '. -

14.' l i. 4. '5




:c-im oif t:- pjret aier of tre IbiJcrt ical

a:-seLnly 1 latticaL us ing tth BUir'SC.'T C'o i ( b ) ier

calcul ate an art listed in ApF:rndix IV. A prop-sal











for performing experiments in the subcritical assembly

utilizing the UFTR as a plane source is outlined in

Appendix E. The critical rod position of the reactor

'was checked after the installation of the subcritical

assembly as outlined in the proposal. No coupling

between the UFTR and the subcritical assembly was found.

At. i .'iE.iO. 0 rI.-.I :tor; i -tC u;. r i rt kir- r a

,Tieasur-mr.nrt_ anrJ :r ;rai .:iffr' r. ra, *e.:. rromei t r for

i iff-renrrial ,i'i.ii ur-lii-:rit For coiipsrisnc.r f ex i-ri-

-:.-tal r.;- ilts3 Mi : t i i tr- Dr..*, t IF-P '.i.: I arJ Ci'FiP

i :.,:Od; r .s ,jW3 .

i-o fi.. k lo r.iTt rej-it re I-.re tr aerr.td into

tr. [rnk a t tr D-0 :ould [t r,atei. A :r;rstant

itmpc raure inr tir tan ii mainrair. d / f rne u,3e of a

t-ErIerat.jrt :orntrol unic -hin Jti liJed four tr,.rmo-

:o-iples. .ijo, a rtirrer rAilF T.:. p a urnfprm

te.-pe rature trrougr, ut tr,- rank. A :-il i-: -f rii

s- -up. ir. lir tar. i s sr, n r in Fir r gur- J. '.

Tr1 r,. r.ir .ge, .:.-,r.: r-,i -,f tri, [ -. w,is iE[arnrar --J t.;

u_-i of the; ili J lu: -ar ignr r.ti: Fis er,.::e i -quic.,Tert L..

:-: 'J.i r : : :r:.. ", C :-,.:c. :tr '.:; lir -,-rt .a, '-. r,-.

T:. c_= .-1.r,5' per cent,



Triri.k are i-, u r. J3 il3:e ri c-f rhrc Jr1ni eCrB t of
i;ridj tieii:tr r'eparrm-rT f-r TmaKin tpri; ietermi.-atior.










































Fiuee M of
.II









1


Frmoc.upl



aEr r. m me


re r


.- Collimator Tjioe













CHAPTER IV


RESULTS OF INTEGRAL SPECTRUM MEASUREMENTS


Introduction


The first integral measurements were made in

the UFTR core and thermal column where there were few fast

neutrons (66). The spacial hardening of the thermal

neutrons in highly absorbing media was observed.

Then, the spectral hardening in a subcritical exponential

facility which uses the graphite pedestal of the UFTR

as a neutron source was measured specially using

differential and integral methods and results were

compared with theoretical calculations (4).

For integral measurements of the neutron spectrum,

various types of activation detectors were used. All of

the detectors fell into two categories: either they

had a 1/v absorption cross section or they had a large

low-lying absorption resonance.






4


;i.easuroeenrt in th.a Thermal Coluirnn


tainlej areel z Pod

Integral iieasiuremerts *ere made in a stanie-lss

steel rod one in. Jiameter and i .; in. long and in a

urariurm slat : in. x In. x 1.'I in. fPa.ai noles

).'j)' in. diameter and 1/. in. J-eep were Jrille.1 in

tre stainices steel pin holder 6.5 in. from me en.i.

iii; -.as done by cutting the :tainiess reel roJ into

two piece;. Tnese noles -l ielJ 4ir.e .etecror;. Fr te

uranium llaL, aicrectr-D. were -,ni.al.:hed in Letrien tre TJ

f:.-is u icr.. were in. A .' in. :n .0). in. Ilea ;ure-ents

were made :4 in. from the east endc of tne thermal colurin

cf r;te UFiF. At trPi: position, the ratri of rj-ermal to

epitnermal flux is approximately- i1,1. i(ii. Therefore,

the contric ti n iof tre ep i therr.al neutrons is rie&iigiole

and e iuation( ) a im usia d,recrty to nme.au re ii- crantge

in effi-cciv;e neutron temperature.

ui7 17 i64
Fot these measurlmenti Lu L ,

.1, and P4 r d.tuctors wur e Led. TIr detecCtors

.,ere fabricated in tre form of wires J..03j0 in. diamterr

containing 10 per cent by weig .r of the activarnt in an

Al marrix, except for trn Au wires, whicr, iare 0.L00~ in.

in diameter. The fir:t miea3iremTint wer. malej in rne



SPrelainar-. res.ul; gi -en in JL-713, Vcl. II,
pages j3E -: ( 1-1 .










stainileJs :-t; ro.J u: ing nr Eural Lu-Al .ire..' A few

n.hurs after irradi at on, Lu16m an Lu ac ivit ie

.,ere co'-rtel fi.'e r.imie using s scintillatic, counterr.'

ALco.u four da,'G later, after tre Lu 1 E acti.viy rtad

3.:a;/l Cout, fi'e mcr i --t r st f counts e.sre Eta Ker of tre

LuLI acri .iti:S. Tiie total *:I rnt rate for eacn t irT

.i3 at least 1.,'00 .:ojrnt TrIe procedure for obtain-

ing the averarc normali;ze activities of trie ruo

inocopes ani tneir raieos is ou a ine irn Appenalx A.

Pu-Al wire; werr calibrated b, measuring their

nart ral gia.-ia acti.'zies h.ese res were then

Lrra3Iatej in a stailnie: artEl re] ani garrumas from

tne [issis n fragments Lwere count- 1 : ''. Tre Pul

and DL.' wires were aic. irradiated in trte stainlis

steel pin rnold-r. Tie corrected activities from all the

deti ct.--rs are l15tei in 'aLle 4.l. The activities rf

tr,e '.' atio;rLers, the Lul?? an tri-e Pu:39 fission pro-

J.:uct w-re eac.rh itftej to the BeEsell function, I i r r)

and are plotted on rigure 4.1. ire ration of fitted

c jr'e fo.,r ,Lul ? l.'% absorber) and (Pu- .'1,'. aosorLUe )




* Intural Lu contains 2.6 per cent Lu1'' rl
;7.4. per cent L.1 5

Eaird,-Atoromc, Inc., Gamma Spectr.-meCter, Model No. 810.

* '. A:tiviieC of P, -'3 m ars act ivities of ene fission
fragmrnt ; of Pu-'I















Io ll. ir)
. Aui9" act.
Lui '' art. Io(O.980r)
Lul7 act.
S Fu 33 act.


1I1 0(6.8r i


- c


1.11 '


--_ I .' i r


c






.od



0. 1.0 1.5
Pa'Jiu c m
Figure .1. Flux grr'.' erei and Ratio of Lu1
Lul .ann3 Pu 3j .'Au 'I in i in.
Ttanirc CSteei Rca



































S


- -, S














* -'~~r-- - S S


3
-T ~
~_C

-


~ -














- - - -~

~~~,,,,


L.-


Tr .' T
J
-. .-. r -f









are rabulaste in Tdarl 4. togeCrier r.wh the cianre

in affecti.,e neutron tr,-.perature from the outer surface.

to tr, c *nter line of rhr. stainl~sa steal ro J using

taiuJated' g factor:. TreF ratios show trat rnt

actii'.'t ratio 'Lui'/ I/Iv adcsorerL is more sernsitive

t c Th j- aect rT, i 5nift in igil,'gr an3 ort -igng gmdia than

the (Pu23:'-, ao.-or-.mr) ratio.


Llrarnium :las

Lu wiri- werei placed terwesrc uJraniun foils as

sri.~ri in Figure t.'.anr the uraniiuu foils l ere posI iionl .J

.n a slot in a graprl.ite Diocki Tr.e corrcied, arct i.i e-

.f Lu I' at Lu 1 ttoget-i r.r ,' th ir, i r ratio ar- p ot1t F.

orn tr c.' ottom of TEurc 4.. and tabuiatre. ir Table 4. ).

Trie djta in. t-hi mdi3 umT jere i terpret .- it t rrn of

f fe :riv- rineutron t perature using p: 'iat on (.'.d

C'- ratios ..r-rr measured irnide andi oursiJe of Lie iJ

las arr, it as3 found tr-at trrie ;orricution of epi-

irn rmal rneutrrion to tre Lu a:tiv.itie- ai i neglipible.

Trhe effctv.'e rneutrcr, terampi nature crrarnga in trie s.ian

"ja foun-d to b 'j.4 0 1 u-ing tabulated g

factor:.







___ ___ ___ ___ /


't~ilrls il
I' 'fl I~
' ~ J ....~.cc.


I:


-F-

K ; .


---

J--a


I a .j a .


rig.re 4.. L. TraveraI, IhrOUgn U-Sl1dD


,I ,

I 1

[ai


'""I--


j, i










T4ELL 4.2


RAi'IIO F LPu2 .'v AB;OFBLP) AD

[Lu 77 .,'v Ab'OPiEi ] A:TI'.'ITI[L'


(Pu2j33,j, absorber)
Radius i ( 30rrI (1.0lj r)'
(cr,)


fLull7 ,l.'v a: e orDer)
I (. 8Cr) I ( l.L10 ,r)'


j. 0' 1. 30 1.0 '


0. 0 '" 0. 9 7

,-I .1 .', ? 9 t 9 t -




1. U 0. 7,, 1 93 2

1, ".'0 0,. 96'* 0, '-1 "
1 7 ,0.-' 7 .t 770.
7~9:


S Trie
are

S TreI
tuJO


Srand.ar.J aevii. onr :.f Tret3e value e
les& tran 1'.

cnarge in neutron temperature using
'ifferen ratio- were:

"TLuli ~ 26.4 f J .[C


p,.2j :3 '0.)1 lu. C











TABE.LE '


Lu 1 AND Lu176 A "" .. ril 1: A il TiHEIf.
RATIO. IrN UFAJll.iM LA,


Pc Itio: (cmJ A A17A" A1 .'A


0' 5 1.1300 1.l. 0u.95'

0. 1' i.0 a 1i.0 69 0.9 0 6
.i1. i .. 'i. 00 '0J
-0. i' 1 i i. 00 1 ' i4 ." 0.9 3'rj
J.5' 15 1.1 ) 1.15 4 '.91
-0.:55 l.IiJ60 1.160 1.93


s" rim.atea2 tarniarJ aelviation is
less itar.n 1 *r *:crEt.



A: rivat ions in U 1 i' -o urion

Tne sp.etral hardenrng in an Ai *:ai filled with

s.i c Icus scl.jiion of r ., asi measureJ using activation

-litectors. T.ne IJ taii l f the Al can iI 3r.c.un in

figure ..

The. Al can, fille wuicr aqueous E -0 solutions,

was pia-eJ :14 a frc rim ti east -idJ o-f the thermal

columni anr irra-iatwil for ten minutes. Thn flux at tne

centerr of trie an ai.4 approximately 4 A i) neurror;.'crm

sec. Trirei .ilffer-s r 503 solutiois were use. as

follows: orainar.r tap water, I grams s 03.'1 iter, ani

11' grams 3 0, 'ilter. Tr e Maxwillian. averaged absorption






















Section AA\

3.5" S
3' -



'4 11.1 I.

9',j A P rod






















Figi


riRi~re 4.3. Al I~n Ui~h r.1,e De~aectr HlOlder










cross sections for these concentrations Jrr-e u.tl Darrn,

2.609 barns and 4.496 barns, respectively Tre jc~d .EorP

used for these measurements were Dy164, Lu', Lui

Au197 and Pu239

Normalized activities of the five Jerector: are

listed in Table 4.4 and plotted in Figure- "..-'.'. Ti.e

ratios of Al77/A176m are listed in Table .5: aniJ .Lttr.

in Figure 4.8.

In order to compare the measured a:t.'irie 'Jitri

theoretical values, calculations were male using rti,

THERMOS Code (4). The results of the cal.uiaronea gave

the neutron density and flux per unit volu-me for tnirrt;

energy groups at different space positions n.ar- aiio tr,

activities of Dy164, Pu239, Lu176, Au197 ein L1 i-. Tih

calculated activities of 1/v absorbers ?ere found. to et

almost identical to the calculated neutioro flu,; tnere-

fore, experimentally measured activities fr;m trae 1,.

absorvers were compared with the calculars. neutron

fluxes. The results are plotted on Figure ". Tnr.e

is some difference between the two which ,. arrricut-l

to the inability to mock-up the axial feei of cner -odjr:ei

in the THERMOS code.* The axial feed of r.- ;ourceB

makes it anisotropic wheres; the THERMOE *:,ee sseum;-

isotropic scattering of tr,- sources. The trnecrerical

fi, < -alk. ir the H 0 medium a few mm. n ir,.i e tii. Al



















I

1.1-













r r
















Sarar
0.i" i, g thd n i) e
.




l.u g- -- -n- lt











AI Po. B2,, bi s.ion uAi cani:
. L ..-.. .__ ,___ .. L. .. . ..... 4.....- ... c :--_,u i -... .



DL'itance Fr--m Center of Can inm)

Figure 4.<. iNormali:ed Luit'n ActLvir I in
Al Can i.lled d.irr Aqueous B.33 Sol.. lon.;
































II
1.-





1.i





I :-'








0" -- --.










0,4



-.C---" fi(tandard Leviation
les6m tnan it)






AL R.. E.." sEolut L ---U Al car,
, I .. .. .

1 : 3 4 5

instancee Frcm Center :ci Car (cm|

Figure '.:.. tJcrmalizeiJ Lu 17' Activities ir Al Can
Filled With Arueou- B.O3, Solutions











r








1.0-



















gm -a l r
I!. i-
L









i.or 3' '
M /
o a I









10 gm B., 3'liter








u ..
(Standiara 'eviati n
1e tha an lb1




alJ o ..------. iO. solution ----. Al Can

u.. -----. ... .-...
1 2 3 .

ristarce From Center of Car, (cm)

Figure 4.. N. f;rmralized Tr,164 A.ctivities in Al Can
Fill-J Withn Aqueous b C'. Solutilcri
















i4*-


11:1 gnm b ., la ter





i -arn.Jara Die li.a3t 1on
1..53 thin 1)


" --- ----0 soutior _--..Al Carn
-1


lirt anc frr m Ci-r er of -'rn ..-m

Figure 4.7. tJorrm lized Fission F'r:.odu Acti/ities
ir. Al :an Fill-d. with; Aquec.u 8; ,
Solutions


i -


u .0














































** l1ter
- ted curve
f.tted curve


Al +.. VI* 'G a d B 2 .1 + A L + C.r- C.
,, A I+ H, a i i r.c I 4 A t





r cLI1 7 LU1 7. Rat L 1.
6 7 ;ol~tions
2 3


L1 '





63






1. 4





1. 2



,'4
1.0




SH20-
.oo-

< 0.8

-'0
:a I


0.6r 5 gm B203/liter

O L
S210 gm B 2O3/1iter



i O(Standard Deviation
1 less than 1%)

0.24



r.0 / less than Can1
0 Ro -------3 solution AI CanI

1 2 3
Distance From Center of -:an (cm)

Figure '. .*mg ril .n of Nornmaii:ze. IHLPMi'." Flux











i.lr LL 4.4


IOPME\Li:ED Ai-CI'ITIEs IJl P i,.'E'OUS 'OjLU7IOrlS


B E Detector6

Grams' s m) Lu ?" .u1 r,,,I"* ul?7 Pu1 3'
Liter

: .6 0.5 0 7 0. 5955 0.,636 0. 386 0.. I2
S 1 .6 '.ijt9 '."066 ------ .t 73 u.t. ii
7 ;. 4. . 7 4 I) ~, 76 :< 0, 741 0 7 3 74
3.1 0.i')6 0. 8 3 1 0 910: 0.8)1
i 4 -.45 1. l ?nl j i l0 0l 0. 67 l. 74.1 0.73l

5.0') 0.2774 O 9 .2743 : 0.; 6 'l. 3ob8
5.0 ]O l i2 : 1 7 .l 3 17 0. 16i 3
.0 2.6 u l.] i j 3 5. It. 1 i ) 3.' 1
..' 3. i]. '8i u. 7 0, 4i 0. 7229 '. 83.3
5.1 i 1 l. ) 0 1 j. I i-10 0 I .00'.') l 0 0u00

1l .' 0.6 0.1S 8 .i 78 0.157 8. j C. i .1714
1J.)i 1.E :I 1. 1 21) 4 .; 7 0. o .,; '
10.i' .6 i. 372~5 23t, i 3t 6 0. 39 :
i0.0 j.i l.7171 0. 4j) I i.7u0t 1 0.6E 0- U.'33 8
10.0 4 5 1 .00 1j0 1.000) 1.11) J0 1.0u



LatimateJ stani.ari deviartia r less than ii..

















TAiLE A4.


s' ''is1 7E .rIpL: I: A:'iuEc'LIS L'I.*


Ditrince from
,'entf.r (cm) LIg,: Water '.gm'liter i'igm literal



r) (, 1 .. 6 'l 4 .'. I ,,'l'. :

l.t i. 0 i{ ,liil5 i l 9

.1 1 1 7: 1.0 1.0

3. 1.' : 8 1.0 1 i d

4. 5 1. 0 1 s.r 00i 1. 00 )0



Estimated staralar. deviation less than I .










can, ana trhs is --lie.ed to t- due to tre external

sour-e conjitionr. Ine rarios of A1',','v at2orber for

exp-rimentai ani theoretical calculations are listed

rn Tabie 4.o. The theoretical spectra are softer than

the experimnntai valueS and again, thiS is due to the

THEPRM, source :onadtions.


-A L.'EL 4.6

1"
FATI:' 'r A 1 'v AB:, IFnT.P I N 10 gm. b-,. LI .LR



Distan:e ( cr m i teore t i a i Experimeirtal

0.6 1i.0 63 1.1191
16 1. 3:U0 i.i05
".6 1.0> 1., i 3
3.0 0. 99i 1i.0331

*, .50 i. 00'i1 i, 0


: standardd ieviat ion less thrn 1 p r cent.


in order to duplicate tne source conditions

imposed t the TIILPWI' Co3-, an atrrtept aas made to

perfor.i, an experiment L', placing the Ai caan filled with

c.orated watrr in rne center of tne UFT-i. However, with

.nnl one gram of ;j'.OIliter, te exce-ss reactivity of

the reactor was not *nr.,ugh to override rne poisoning

effect. Therefore, tr e onlr way this experiment :an re

performed properly. is to provide sufficient reactci.it.

ro override tnt B. 3 aLsorptlon.









Measurements n tr,.e Ur'F Coic


In order to measure tne 3picii d-p:rn.-rce -f

the effective neutron temperature .-.r tr, r'. 'T,

factor in the UFTR core, Lu -r:i ani ver: tnhin Au

foils were irradiated. The Au f(cls .wer mia-e u~ril,

Au resinate solution,' which oa appiil tEc Ine -urfi:e

of an Al foil and then baked Ilo.l; in an electric cv-er

for about 45 minutes until tre tcimpirature ra.crine

9000 C. The baking process vlarllii:j tr.e crgani-:

material in the film of resinate -.ltlr: n ar lifrt a

thin film of Au on the surfac- of r't .,i f.il. TI-

maximum thickness of the Au film a.i nrr .ore train

0.5 microns. This was determane t,. cimiaring tln

activities of Au foils of kn.:. an r. s nrjr.nr tr icne;s.e

in a known flux. Since the iif-aL-orption i:

negligible for a Au foil wi-' t'i-;i re ;f u.S micron;

(68), it was correct to assjme tinat titii- oils ir

infinitely dilute. Activities: frcim rru~ mpiJrite 3 r

found to be negligible. Ac.:jr-at-e *eir n of tr.le

thin Au foils was practical. i.ipc .Li e; tnr f.re,

the same foils were used to mreaure rnme bre and tre

Cd covered activities. This pr'-?e ::.rre:re foir Jacinr



* Supplied by the Hanovia Cnimi.:ai and :1arfacturrn
Company, East Newark, Ne. J-r=~c.









.'ariatior. A:ti.'ir.v from the first irradiation 'was

au.tracted from the. acord using crue same foil for

L, rn irradiation;, cirn:e tr,- naif-life of Au i well

i.nown. iner LJ wires were 30) 'ils in dii mei r and Crn-

mained 1I] per *:nrt by ieinr of Lu.:,. The positions

where Lu wire; ina Au foila 3ere irrdiat-ej is showrn

Ir rFliure 4.i1. COn na:surement wa. made i r nrs-

nerntr of tnn fuiel cox.

Frcm r;,e result of r-e Au foil act ivations,

Jalue4 of r T'T were :alculate uSinrg qcijitior (. ''.

Ir tlis r ]i uatl. n, ao for Aj is kno.rn i, (E ani is

&pproximiaely u ual to 1 .5. From these caiijiated

.'al-e of r", I,; ther effective neutrc,' rsmperar ejr irn

the center of tre UTTFP. :cre was calcul atea ov trial and

error using equation (2.;). For these calculations

tatulatEd values of g an. 3' ere ue;i for L176. nhe

factor g for Lui isIs appr.oxiatii:/ one arnd the factor

SG'r ~as djeteriined exprim.nrtall .y cy rne use of Ca

ratios of Lul'', and by using r '. -cotained from

cne Au foil activator, togeth cr tri equatio (:.).

Ihe effective neutron temperature .as calculate to ce

-'.0 ;.9- C in tne center of ti e UIrNf uwen compared

to the reference point in the thermal column.

Ine numerical rereult for r'. T. T A'

A17Al9m 175 and (, s C are taculatcd
r. :1 .:a o r







69








































Ie. /LL rltr I
ol wret restriew




Figure 4.10. Position of Activation Detectors
in UFTR Core










ir, Ta.le 4.7. In Figure 4.11, A 7?'7 '7 Fi3 and
Cd
r"' T';; are plo ted.


iHe:asurments in rte ;uD:rirnal Asssmbti


Integral mctauremenits .erE onae rJaiall.' 12.5

in. from tre bot torm 3f rre central fuie tuce because the

aiot in tie special llark. V-E fuel elemenci was locate.t

at ciis position. At T.ti ri ;rig t the axial Cd rario

nis reacrie.j a constant vala~ indicating spectral tequilir-

rium. An At foil nC.i.Jer was attnacri to i;ne tuDe at

t.i- heigr so trmat racial traverses co'iid :e Tak=dn to

the cell boundary ard Dc'.:r..

Bare a.nd co'.ereJ Lu anJ A.i frc s -ere irrad.i-

aced i- four different arranigeinmrt. using to lattice

Firches as 1_ l4stLc in 1 i:i J.l. Also, TlEF.I1103 anr

CEPTF. calculia.iona -ere nadl for nhese arranremirirs

ar, all n~e C~perienrtal anrJ heoretical results are

plotted ira Figuras .12 to .i9 for rthermal and epi-

thermal activities All the experi':.c atl results were

norrmaliied at tre cell ;Drdar.', ard tre dir.ectior. of

:ne traverse uwa equidistant ctctweer Seo fuel tuL.e3.

Au foils 0.001 in. tnis:K na 0.2 in. iameter werre u:ed

together 'itr. foils containing a 10 weight pr cent


pec.i.al unclal Mark V-5 and Mar,. i fel elements
wirrt sl:.ta for ictivatirzr detectors were LborrowJc
from tr, ie savannra Fiver uperat ions Office, Aliern,
Soutn Carolina.






















































15 10 5 0 5 10 1i 20
9-p) 1 4.4


Figure 4.11. Traverse Through UFTR Core






7-


I


1. '




1.:


1



i


Epicadnmi u
(s.d. 1 1


m


.Al Al' Al
AI Al' Al
E. u I'l )


H 1 -! -_ Ii,
: 6 F 10 12

Distance From Center i cm

Figure .1. A Au A:tit'.itr Disrruutiion for rlark: V-B
Natural U Fuel Jitri 14.7 cm Pitclh


Thermos Curve
Norma.iized at
Cell Edge

C.- 11


.ub.ca Jnium


0. .4


1 I
1"<


j -J






























*:r; i r ur. e-1
,r-' r 1 1',.ge




,11 Cell







.,dur.:Jriu


A, 1 A! %I
-. ':. ,j-- i ` li ij


__ II L _l.._u i ..
S 6 I : 1;
Cis Tranrc From *rnter (:m)
Figure '. iJ. Lu Acti .i.,' Di trirutiorn f.cr Marar V-B
Natural U Fuel Wi -. 1w.7 c Fitc:h


ij 6


1"






















1.81 -




1.b






1.2l


*uc U Smi 2 Ti


PaC 1i
PaiusIs


- r'- .,


Ai
T.I;


Epicadmium
( .d. 1 6 i)





I" D;.C

_ 1 1 ... .


Distance From Center (cm)

Figure 4.14. Au Activity Distribation for Marb.
V-P rNtural U 'itrh 2; cm Pitcn


Trermo, 'Jirve
.crml i e 3 at
Cell Elge


1 i) 4


,., Lzi'






















Tre rr.:' L C r' e
',rnal ie d at
Ce11 EL3ge


1.c.admi u
(9.a. : .711


dielu
R dis


D0.


1 --o- .. i-


Al -Al
Ai ,'


Epica.lmium x 10
(3.d. 3.S)


8 10 1: 14


List-nce From Center (-:mi
Figure ".15. Lu ActivLEt DistriSurtonr for MarK V-B
Natural U Fuel Witn 22 m Pitch





















Trnermro Cur'.r .
NIrcrmalized i







Cel l
PaJius

I

z jut..4adriiuirT





3. . 71)






E Epica miu rri x 1'






Al Al Ai *Al
i C0
.1 ECi0 u (J-. -.

6 11 1


14


EDistance From Cnerer (cm.'
Figure 4. 1. Au Actr .'itr Di trijburion for Marn I and.
HarK V-B Jarurai uj jael L tir 14.?7 cm Pitcn
























Sri.rt|: ur u i






: l:l : 1





raliu;

L u 3 l ui
*k' J. : ii


1 x F:'i: JTiurm


41 4 11i

.i "iI I
,! "-0 i2 i .


,st rance FrcirT. .enter .c -i

FipJr-. u.17. Lu .ct "i t',' LI'c riut C r, t c. r rarp: I
arl 'lark V'-3 IJa jrai 1I FIel JitrI
lu.' .m F tic r


































.1


Ihermos Cur.'e
Normalizel at
Cell Edge


Cell
Radi'js


s'jca miu
(...j. .


Ep
I;


LI
Al Al Al Al

Li h 0r[


m
ILI







7c








,cadmium
. 3. 1.6't


.__ _-_ L..L .
S 4 6 A 10U 1 2

Cistance From Center (cm)
Fig 're ". 18. Au Ac.ti'.'it Distribuuornr for MarK I
and :lark V-R Narural IJ iT4n ;2 cm PLtch


--I--

























-4--
-- -- r


i r rTTr,? ur
liorm asize.- at
Cell Ej,-e


dCll
Fadius


ut'caJir~iu


1.0 h


E pi c almi u- m


Al Al Al
U E' -.1' i


6 10 12 14


Distance Trom Cente r (cml
Fimire .19. Lu Activit: [Listritut ion for Mar. I
and MarK V-B tlatural IU Witn :2 cm Pitch


S. C r










8-




-






r-- I




i -, I
2 3


r J









*. r. ,









O I
=*-E




a r~ C = -




















oi 0 & C. *















N I








o











di:p-ril.on cf LJ..,' ini Ai. Tr1 latter were trie 0.01:.i

rh. rni, i .. r. a m. ans ret r. E*k[ i TE we re

:c.rr -e K-. f-ir E. r 3iatal .o ri f u x i i r5 t r n if.r cr,

iui-rit ii .s:cuor-ir fg to the relation:




S P r r ---



S = r.c c.rr. ct. j flu


i' = :orre ri flux


EL aTi r-..a 1 a K i 'iriec -cr- A eeAurmd u;rg 1.U.' 3i in.

a cov.r-s. Iiirefor a cur-off .:f .' :.' as- us3e for

'.ri THELJP : ;al:ui.atioiC..

;r. ai3itior, car- ansd Cd cojerei. traverses Fcre

milr as rlr l nfii it 3ilute Au foil tc. .'alujdare rhe

-r.ttr: irnai ir, e.J r in the unr t z l il for e cr. lattie.:

arranc.T eant ijing n ir. iJ~. rdat i:c of Lu a ri

Au effecci;v rieutrorT r:mpr uare at J Jffererr cell

po itr iton. wiere :alc.jiaced .L Iu in g equa'r.r (2.1 icr

a refererc:e tr.e neuct rcrn r-mprature at tre cill Dour,..ar/

*- e detr.eriLned y a i fferenclal nmetro.l in oraer to

d' err;,irs. trei efficti.- tenlf.:rature change in nte unir

c li. Tre results of treese aasaure.Ten t are plo cei on

Figure' 4. ". to L.:1. Also nrown ori Figurse '".2 to

.27 arc cre s
tne corresp lring -J ratios .






























i'j















-


P

0 -
1 1


Ai Ai' Al
., : u D :'J

O I i 5 4 7 f ) 10 11
Distan,: From ,:erter (cm)

Figure 4. Flot of Al" 'A19i r'. To ar .:p
With Distance Fror, Center Using Marl: V''-
Natural U Fuel dirn 14.7 cm Pit.ct





















I, IA1


S---












i
1K _____ (___




Y


S I A Ai


E a 9 10l


Figure ".21.


Di['scan -.c romri C rncer (cri.)

Flst of A ,i r I.T arin Cnp With
E'i- stance From C.rter Ulling Mark: '-B
iatural I.I i. n 1--' cii ,'itl h


1.0 L0





.9 .09


-.08 r


3.0










r-


'






L14


-- A177, "
A ~~


L






i-


;1 Al Al' Ai

'j D i- "

I0 i 'i F
Distancrce from


D- j

L 7 6
centerr ( cm


10


Figure u. 2. Flot of A"' A19cl, r ".'r, and CdR Wri
Distance rrom C-;nte-r .iinrg Mark I and
Mark V- nJatural IU Fuei With 14. 7 cm Pitch


r 'i










I l I






















I I





:II


S; r .1'4. -


- .1 **'1


r I .


Hrm n. 1 Ai .z1



i- I t i.r. Frc-cm sncter '.cm'
ict cf nir m '' ,- r 1T ,i-i C-3; 'Jitiri
ir ta r. i Frcrrn .- r.t-r i. i-. lIar 1 3rand
;ar -v ; ,tj r.31 1., Fu-: 1 w t:r c.. Pitchr


Ir











i
I













10 0
Fii
S7-rire 4erl Act Fvation
I-


1
























root lank Usin-g rak I an- Mar .'-B
I- iural Fe .itr ?? :m Pit r
--- ,:,i Pl ic, x ICo'-'






L


105 1 :- t








rigire i.2". Ax Foot ]ank l' sing rMark I ani Mark '.'-B
ltiiural U J uel r Jitr, 4,? .: P Pit.:r























S.TI- T r.a~ : i rc. r










j


*:, . I 0-r 1


[:1 [r r,-it l
'. -t1i 'at r -


'J


F jrc .. .


1i 11 i lij
b n i r L) t i .:|T T
An. i D'i-,tribujt :'n tf fIux i tricn TIJ.
F.-c i ariI 1. Mair, '-E[ iJd urral I
Fu uli rt1 .- m F 1 t :ri





3 S


Thermal Act '.'at .ro


f i


1' Epittrermai
SActu Jat io'r











----- --


1 l







rF.;ure ;'c. 4i
Fiie


- Ci Hai: 1'?


Ii


Sr, '* 1 t .

Height ( :r,.
ii f'liriblbj10i1 oif Frui ir. tree Two
ot Tanr: TJ;ir.A '"ria V-B Nratural U
l Wicr 14.' cm Pitch


I




Full Text

PAGE 1

NEUTRON SPECTRUM MEASUREMENTS IN HETEROGENEOUS MEDIA By SAGID SALAH A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA December, 1964

PAGE 2

ACKNOWLEDGMENTS The author would like to thank his supervisory committee, especially his thesis supervisor, Dr. T. F. Parkinson, for his patience, advice and encouragement during the course of the work. He would also like to convey his gratitude to Dr. G. R. Dalton, member of his supervisory committee, for making arrangements with Dr. W. W. Grigorieff of Oak Ridge National Laboratory, to visit the Laboratory under "S" participation contract in order to consult with those there on the use and construction of the neutron diffraction spectrometer. The author would also like to express his gratitude to Dr. E. 0. Wollan of Oak Ridge National Laboratory for his helpful suggestions and demonstration of the operation of the Oak Ridge crystal spectrometer. Also, the author would like to convey many thanks to Dr. V. L. Sailor of Brookhaven National Laboratory for his helpful suggestions and for sending blue prints for the construction of the collimator and to Dr. W. J. Sturm of the International Institute of Nuclear Science and Engineering at Argonne National Laboratory for sending some drawings of the crystal spectrometer with a copy of the experimental write-up.

PAGE 3

The aid of Dr. L. E. Grinter, Dean of The Graduate School, University of Florida and Dr. Robert E. Uhrig, thesis committee member and Head of the Department of Nuclear Engineering, for obtaining the necessary funds with which to purchase the main gearing system of the spectrometer was very much appreciated. Also, much gratitude is due Dr. F. E. Kinard and Dr. John P. Church of E. I. duPont de Nemours, Inc. Savannah River Laboratory, Aiken, South Carolina for making the THERM0S calculations for the geometries used in the subcritical reactor. The author would like to thank the Division of Nuclear Education and Training, U.S.A.E.C, Washington, D. C. for the loan of the natural uranium slugs and D2O. Also, he would like to convey his gratitude to the Savannah River Operations Office, U.S.A.E.C, Aiken, South Carolina for the loan of natural uranium segments. The author is deeply indebted to Mr. L. D. Butterfield, Reactor Supervisor, and Mr. K. L. Fawcett for patiently running the UFTR many times after normal working hours; to Mr. G. W. Fogle for his help in the construction of the temperature control unit; to Mr. F. A. Primo and Mr. H. H. Moos and many others for the construction of apparatus. Finally, the author would like to express his sincere gratitude to Miss Barbara Gyles for her suggestions and help in putting into final form and typing this thesis.

PAGE 4

TABLE OF CONTENTS Page ACKNOWLEDGMENTS ii LIST OF TABLES v LIST OF FIGURES v £ ABSTRACT i x Chapter I. DESCRIPTION OF THE PROBLEM 1 II. MEASUREMENT OF NEUTRON SPECTRA 3 III. DESCRIPTION OF APPARATUS 29 IV. RESULTS OF INTEGRAL SPECTRUM MEASUREMENTS . 4 7 V. RESULTS OF DIFFERENTIAL SPECTRUM MEASUREMENTS 9 VI. RESULTS, CONCLUSIONS AND RECOMMENDATIONS . 10 7 Appendices A. METHOD OF CALCULATING A 177 /A 176m 112 B. THE THERM0S CODE 115 C. THE RECIPROCAL LATTICE 117 D. BUCKSH0T CALCULATIONS 120 E. PROPOSAL TO USE UFTR AS A SOURCE FOR THE SUBCRITICAL ASSEMBLY 121 LIST OF REFERENCES 127 BIOGRAPHICAL SKETCH , 132

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LIST OF TABLES Table Page 2.1 Characteristics of Activation Detectors 2.2 Table of k and Energy for Different Crystals at 1° 18 3.1 Subcritical Lattice Configurations ... 44 4.1 Lu, Au, Dy and Pu Activations in Stainless Steel Rod 51 4.2 Ratios of [Pu 239 /i/ v Absorber] and [Lu l77 /l/v Absorber] Activities 54 4.3 Lul" 77 and Lul 76 m Activities and Their Ratios in Uranium Slab 55 4.4 Normalized Activities in Aqueous Solutions 64 4.5 A 177 /A 176m Ratios in Aqueous Solutions . 65 4.6 Ratio of the Al 77 /l/v Absorber in 10 gm. B 2 3 /Liter 66 4.7 Activation Parameters For UFTR Core ... 80 6.1 Comparisons of the Change in Effective Neutron Temperatures in a Unit Cell . . . 110 B.l Energy Groups for THERM0S Calculations . 116

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Page LIST OF FIGURES Figure 2.1 Activation Cross Sections 6 2.2 Calibration Curve for g-*76 12 2.3 Sphere of Reflection 25 3.1 Single Collimator Slit 31 3.2 Size of Effective Source 31 3.3 Diffraction Spectrometer in Operation . . 38 3.4 Detector Arm with Second Collimator ... 39 3.5 UFTR Elevation 42 3.6 Top View of the Subcritical Lattice ... 43 3.7 Side View of the Moderator Tank 46 4.1 Flux Traverses and Ratio of Lu 177 /Lu 176m and Pu239 /Au i97 in x in# stainless Steel Rod 50 4.2 Lu Traverses Through U-Slab 5 3 4.3 Al Can With the Detector Holder 56 4.4 Normalized Lu 176 m Activities in Al Can Filled With Aqueous B 2 3 Solutions ... 58 4.5 Normalized Lul?7 Activities in Al Can Filled With Aqueous B 2 3 Solutions ... 59 4.6 Normalized Dyl64 Activities in Al Can Filled With Aqueous B 2 3 Solutions ... 60 4.7 Normalized Fission Product Activities in Al Can Filled With Aqueous B 2 3 Solutions 61

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LIST OF FIGURES (continued) Figure Page Lu 177 /Lu 176m Ratios in B,0o Solutions ... 62 2 U 3 4.9 Comparison of Normalized THERM0S Flux ... 63 4.10 Position of Activation Detectors in UFTR Core 69 4.11 Traverse Through UFTR Core 71 4.12 Au Activity Distribution for Mark V-B Natural U Fuel With 14.7 cm Pitch 72 4.13 Lu Activity Distribution for Mark V-B Natural U Fuel With 14.7 cm Pitch 73 4.14 Au Activity Distribution for Mark V-B Natural U With 2 2 cm Pitch 74 4.15 Lu Activity Distribution for Mark V-B Natural U Fuel With 2 2 cm Pitch 7 5 4.16 Au Activity Distribution for Mark I and Mark V-B Natural U Fuel With 14.7 cm Pitch. 76 4.17 Lu Activity Distribution for Mark I and Mark V-B Natural U Fuel With 14.7 cm Pitch. 77 4.18 Au Activity Distribution for Mark I and Mark V-B Natural U With 2 2 cm Pitch .... 78 4.19 Lu Activity Distribution for Mark I and Mark V-B Natural U With 22 cm Pitch .... 79 4.20 Plot of A 177 /A 198 , rVT/T and Cd R With Distance From Center Using Mark V-B Natural U Fuel With 14.7 cm Pitch 82 4.21 Plot of Al 77 /Al98, rVlvT and Cd R With Distance From Center Using Mark V-B Natural U With 22 cm Pitch 83 4.22 Plot of Al 77 /Al98, rVT/T Q and Cd R With Distance From Center Using Mark I and Mark V-B Natural U Fuel With 14.7 cm Pitch. 84 4.23 Plot of Al 77 /Al98 f rV^7T and Cd R with Distance From Center Using Mark I and Mark V-B Natural U Fuel With 22 cm Pitch . 85

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LIST OF FIGURES (continued) Figure Page 4.24 Axial Distribution of Flux in the Two Foot Tank Using Mark I and Mark V-B Natural U Fuel With 22 cm Pitch 86 4.2 5 Axial Distribution of Flux in the Two Foot Tank Using Mark V-B Natural U Fuel With 22 cm Pitch 87 4.26 Axial Distribution of Flux in the Two Foot Tank Using Mark V-B Natural U Fuel With 14.7 cm Pitch 88 4.27 Axial Distribution of Flux in the Two Foot Tank Using D 2 89 5.1 Method of Alignment of the Diffraction Spectrometer 93 5.2 Rocking Curve of NaCl (200) 94 5.3 Rocking Curve of LiF (111) 94 5.4 Open Beam Neutron Spectrum From Center of UFTR Core Using LiF (111) Crystal ... 95 5.5 Ratio of Maxwellian Distribution and the Experimental Spectrum at Two Different Temperatures 101 5.6 Experimental and THERM0S Spectra Using Mark V-B Natural U Fuel With 22 cm Pitch . 103 5.7 Experimental and THERM0S Spectra Using Mark I and Mark V-B Natural U Fuel With 22 cm Pitch 104 5.8 Experimental and THERM0S Spectra Using Mark V-B Natural U Fuel With 14.7 cm Pitch 105 5.9 Experimental and Corrected THERM0S Spectra Using Mark I and Mark V-B Natural U Fuel With 22 cm Pitch 106 CI Unit Cell of a Lattice 118

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Abstract of Dissertation Presented to the Graduate Council in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy NEUTRON SPECTRUM MEASUREMENTS IN HETEROGENEOUS MEDIA By Sagid Salah December, 1964 Chairman: Dr. Thomas F. Parkinson Major Department: Nuclear Engineering In this investigation neutron spectra were measured both integrally and differentially and then compared with theoretical calculations. Measurements were made in highly absorbing media in the University of Florida Training Reactor (UFTR) thermal column, in the UFTR core and in the subcritical assembly sitting on top of the graphite pedestal of the UFTR. The subcritical assembly contained some typical D 2 0-moderated natural uranium lattices. Precise knowledge of the neutron spectrum in a heterogeneous medium makes it possible to optimize the neutron economy. This is true because fuel elements in a reactor have varying cross sections for different energy neutrons. By proper choice of the fuel-to-moderator ratio ix

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and the geometry and composition of fuel elements, optimum use of neutrons can be attained for maximum fuel burn-up with the highest conversion ratio. In the thermal column of the UFTR, thermal neutron spectra were measured integrally using activation detectors such as Au 197 , Dy 164 , Lu 175 , Lu 176 and Pu 239 . The detectors Lu and Pu have lowlying absorption resonances, 1P7 175 whereas Au and Lu have a 1/v absorption cross section for neutrons below 1.0 ev. The detector Dy has an absorption cross section that is steeper than 1/v. The measurements were made in a stainless steel rod, a natural uranium slab and in an Al can filled with borated water and results were interpreted using Westcott's formulation. In a natural uranium slab the effective neutron temperature change from the center to the outside boundary of the slab was obtained by measuring the activity ratios of Lu 176 and Lu 1 . In a stainless steel rod, the spacial effective neutron temperature change was measured using Pu 239 and Lu 176 activation detectors and then the ratios of activities to the activities of 1/v absorbers were obtained. The same type of measurements were made in an Al can filled with different concentrations B 2 3# These results were compared with THERM0S calculations; however, due to the anisotropy of the experimental source conditions, agreement was poor.

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The effective neutron temperature and the epithermal index, Wt/T 0| were measured by using activation detectors in the UFTR core between the two fuel boxes in the NorthSouth center line. The result of the effective neutron temperature measurement was compared with the open-beam differential spectrum and found to be in good agreement. A crystal diffraction spectrometer for differential spectrum measurements in the subcritical assembly was used. For these measurements, the total efficiency of the machine for different Bragg' 3 angle was first obtained by taking a neutron beam with known spectrum out of the subcritical tank. The tank, 24 in. in diameter and 60 in. long, was filled with D 2 and rested on top of the graphite pedestal of the UFTR. The neutron spectrum out of this medium was measured at two different temperatures. The ratios of the two spectra were plotted with the ratios of the calculations and found to be in good agreement. The neutron spectrum out of the subcritical assembly was measured for two different lattice pitches using Mark I and Mark V-B natural U fuel elements in D 2 0. A neutron beam was extracted from the cell boundary and from the center of the cell for each of the three lattice arrangements. The results were compared with the theoretical spectra calculated with the THERM0S code and found to be in excellent agreement. Integral measurements were also made in the subcritical using Lu 176 and Au 197 detectors. The experimental

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activation measurements were compared with the THERM0S calculations and were also found to be in excellent agreement. Finally, the effective neutron temperature change in a unit cell for four U-D 2 lattice arrangements were measured differentially and integrally and compared with the theoretical calculations. The results were in good agreement.

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CHAPTER I DESCRIPTION OF THE PROBLEM Neutron spectrum measurements in heterogeneous media are important for several reasons: (1) for evaluation of the thermal utilization factor f and the thermal reproduction factor n; (2) for the calculation of reactor fuel cycles; (3) for comparison with multigroup calculations of the neutron spectrum; and (4) for the prediction of dose rates in a sample, which depends on the neutron energy distribution. Precise knowledge of the neutron spectrum in a heterogeneous medium makes it possible to optimize the neutron economy. This is true because fuel elements in a reactor have varying cross sections for different energy neutrons. By proper choice of the fuel-to-moderator ratio and the geometry and composition of fuel elements, optimum use of neutrons can be attained for maximum fuel burn-up with the highest conversion ratio. In many cases, by controlling the leakage spectrum from a reactor core to a desired form, the maximum conversion ratio in the blanket material

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will be realized. This follows because U 238 a nd Th 232 which are the usual fertile blanket material for nuclear reactors, have high resonances for neutron capture at 6.8 ev and 22-24 ev, respectively. In order to predict the spacial and spectral distribution of neutrons theoretically, the behavior of neutrons in the heterogeneous media must be well understood. In this investigation, the neutron spectrum was measured both integrally (1) and differentially ( 2_) , and then compared with theoretical calculations (3, 4, 5). Measurements were carried out in a highly absorbing medium in the University of Florida Training Reactor (UFTR) thermal column, in the UFTR core, and in the subcritical assembly sitting on top of the graphite pedestal of the UFTR. The subcritical assembly contained some typical D 2 0-moderated natural uranium lattices. Underlined numbers in parentheses refer to the List of References.

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CHAPTER II MEASUREMENT OF NEUTRON SPECTRA Introduction As early as 19 36, neutron diffraction by crystalline material was suggested by Elsasser (6_) and experimentally demonstrated by Halban and Preiswerk (.7) and by Mitchell and Powers (£) . Using Ra-Be sources, these experiments proved that neutrons were diffracted, but they were by no means able to obtain monochromatic neutrons due to the weakness of the sources. Soon after the development of the nuclear reactor, neutrons were available in great quantity, and neutron diffraction spectrometers were built at Argonne (9_, ICO , Oak Ridge (11), Chalk River, Canada ( 12) , Harwell, England (13_) and elsewhere. Also, at the same time, timeof-flight techniques were developed (14, 15). About the same time integral methods of neutron spectrum analysis were described by Westcott ( 16_) , Campbell, et al. (17) and Bigham and Tunnicliffe (18). Trice (19) and Nisle (^0) also shed light on this subject.

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An early theoretical treatment of the spectral hardening was carried out by Plass ( 2JL) , who assumed neutrons of each energy diffused independently without energy interchange. Later models were developed to calculate neutron spectra by the use of free hydrogen and bound hydrogen scattering kernels (22, 23 ). One of the better methods for calculating the space and energy dependent flux in a unit cell was developed by Honeck (24, 2£) for H 2 and D 2 0-moderated systems; it is described in Appendix II. Recently at KAPL, Goldman (26) constructed a scattering law based on Nelkin's model, and agreement with the experimental results using (CH^ i a excellent. At General Atomics, Young C 2_7_) has measured neutron spectra using a pulsed high-current electron linear accelerator in H 2 0, CH 2 , and C g Hg moderators poisoned with B, Sm, Er Gd and also D 2 ( 2_8) . Measured spectra were compared with DSN (5) transport-theory calculations utilizing the bound hydrogen scattering model for water. Earlier, Beyster (2£) measured neutron spectra in pure and poisoned H 2 0, < CH 2 > n » and ZrH using the pulsing technique and compared it with DSN calculations.

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Integral Method The measurement of neutron energy spectra using the time-of-flight technique or a crystal spectrometer requires the extraction of a neutron beam from a reactor lattice, which is difficult to do for more than a few representative positions. However, by using activation detectors, spectrum changes throughout the cell may be mapped out (i.e., good spacial resolution is obtained with minimal cell perturbation). The usual experimental technique for observing the spectral change in a unit cell of a reactor involves mapping the activity ratio of resonance and 1/v cross section detectors. For this type of measurement, various types of detectors are summarized in Table 2.1. In Figure 2.1 the cross sections of the 1/v absorber Lu 1 t and the resonance absorber Lu 176 (30) are shown. Also included in the figure are the cross sections for Dy ( 31) and Pu 2 (32). A Maxwellian neutron distribution in the thermal energy region with an average temperature of 29 3°K is also shown in the same figure. By inspection of Figure 2.1, it is seen that, as the Maxwellian distribution shifts to higher energies, the ratio of the activities of Lu 176 and Lu 175 will increase since the reaction rate is proportional to the integral of the neutron flux times the absorption cross section ( 3 3) l

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Figure 2.1. Activation Cross Sections

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In well-moderated media with low absorption, (e.g., D 2 0, H 2 0, C, Be) far away from neutron sources and boundaries, the spectrum approaches a Maxwellian distribution with the average temperature corresponding to the temperature of the medium. When these wellthermalized neutrons enter a highly absorbing medium (e.g., a fuel element which has a 1/v absorption cross section), lower energy neutrons are preferentially absorbed, resulting in a "hardening" of the energy spectrum within the fuel. The activation results were interpreted by using the Westcott formulation (34.) . This method applies to well-moderated systems such as the UFTR. In a reactor spectrum, effective cross sections are given as: wh< o 8 = a o (g+rs) (2.1) effective cross section cross section at v = 2200 m/sec r relative intensity of the slowing down spectrum (or epithermal index) g,s = functions of the neutron temperature, T The values of g and s are tabulated ( 35_) for various nuclides. For 1/v absorbers g = 1 and.s = 0. Using this notation, the Cd ratio for a very thin detector is given as:

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'cd g + rs . gr / T rs + — A/ — (2.2) where 1/K is approximately the density fraction of epithermal neutrons transmitted by the Cd (,3k). The factor 1/K varies with the thickness of the Cd filter and is tabulated in the literature ( 3»Q . For 1/v absorbers g = 1 and equation (2.2) becomes 1 rs
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10 'th (1 R cd (FR -1) cd G r 8q R . (1/K -W) cd (2.5) where ! th = thermal neutron self shielding factor, G = resonance self shielding factor, F Cd transmission for resonance flux, W = fraction of resonance activation below Cd cutoff, h a thermal transmission of Cd filter. In order to measure the effective temperature of the thermal neutrons, the activity ratios of Lu and Lu 176m were measured. The activity ratios of these isotopes at position x with respect to a standard position s is expressed as A 177

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11 By assuming G th = 1 and G s 1, and solving for Y , the following relationship is obtained: (g + rs G r ) 176 Y = RY x s (g + rs G^) 175 (2.7) For r = (i.e., no epithermal neutrons) equation (2.7) reduces to 176 Y x = [g ] x = RY S = R[gi76^ (2.8) The effective neutron temperature for K 176 (temperature index of Lu 176 ) is obtained from Figure 2.2 (36). If r = the [(g + rs) 176 ]^ must be evaluated. For Lu 175 , g r 1 and rVT/T i s a measurable value with dilute foils. sVT / T G r I Jx a„ G, 175 '* This equation takes into account the self-shielding of resonance neutrons.

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12 Mrt HW-«4««« 4.0

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13 is also determined experimentally. Then using the values °^ ^176 anc * s i+ given by Westcott ( 3_5^ , corrected values °^ ^176 and s 4 are obtained by trial and error. The effective neutron temperature is found from the value of 8176 (see Figure 2.2). An alternative method of evaluating r"VT/T i s to irradiate two detectors and express their activation ratios as follows : gG th rs G r )' _(gG th + rs G r ) ] UA E (gG th rs G ) a 1 (gG t , rs G ) ] (2.9) or rearranging CgG th + WtTt^ s^ Gj' o o r x X a R' X X £ Cg6 1 . h rV T/T J th g r o o r x (2.10) X s is determined from the Cd ratio of one of the detectors, Solving for r"V T/T Q in equation (2.10), the following is obtained:

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11 R' X s (gG th ) b (gG th )'
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' 15 The energy resolution of a chopper is described by the equation ( 38) & = -0.0279^ E 2±» E mm (2.12) where AE = uncertainty in energy, E = energy of the neutron, At = uncertainty in flight time per meter, m = flight path, meters, Am = uncertainty in flight path. For a fast chopper, the second term is negligible and the resolution reduces to the first term. Better energy resolution is obtained with longer flight paths. A list of resolutions together with flight paths for different choppers is listed by Anderson ( 38) . Multichannel analysis determines the intensities of neutrons in different energy intervals. Slow choppers can be constructed much more easily than the fast choppers. This is due to the fact that for the former, chopping is accomplished with thin layers of Cd, whereas it takes many inches of plastic and steel for fast choppers ( 39 ) .

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16 An alternate method for measuring neutron energy spectra (40) is the time-of-flight method with a pulsed source. The advantages of this method are: (1) the fuel elements get low irradiation, (2) the rotor cutoff function does not have to be determined, and (3) by the use of the chopper and pulsed source, the neutron spectrum as a function of slowing down time can be determined. Crystal Spectrometer The use of crystal diffraction spectrometers for detecting monochromatic neutrons has been investigated by many authors (9^, 1£, •1-47). Diffraction is a scattering process. A regularly arranged series of atoms of a crystal will scatter the neutron waves in all directions, but only in particular directions will scattered waves be in phase and reinforce each other to form a diffracted beam. The atoms of a crystal are arranged periodically in parallel planes, so that in general scattered waves are out of phase except in a few directions where reinforcement takes place. The diffraction process applies to X-rays as well as to neutrons. The fundamental difference between the two is that X-rays are scattered by the orbiting electrons, where as the neutrons are scattered by the nuclei of the atom. For this reason, the X-ray

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17 scattering amplitude is proportional to the atomic number of the element, while the neutron scattering amplitude shows a relatively srilall variation with atomic number. When neutrons from a collimator impinge on a crystal plane of a single crystal at an angle, 9, only neutrons of one energy are diffracted in the direction of the angle 26. Therefore, the crystal and the detector must maintain an angle ratio of one-half in order to obtain monoenergetic neutrons. The diffraction of the neutron beam depends on the lattice spacing in the crystal. This space varies depending on the crystal material and on the crystal axis along which it is cut. The coherent scattering of neutrons from the nuclei of atoms in a single crystal to produce a monochromatic neutron beam is governed by the familiar Bragg' s relation: n X = 2d sin 6 (2.13) where d = lattice spacing, n = order, A = wave length, 9 = glancing angle. In energy terms, this relationship becomes:

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18 E(ev) = kn 2 /sin 2 9 where k is a constant for each lattice spacing. Table 2.2 gives a list of crystals with k and the detectable energy at 1° . (2.14) TABLE 2.2 TABLE OF k AND ENERGY FOR DIFFERENT CRYSTALS AT 1° Crystals k x 10° (ev) Enerj

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19 Mosaic Structure In order to know the energy of diffracted neutrons at different angles, it is necessary to know the distance between the atomic planes of the crystal. The distance depends on the direction in which the crystal is cut and also on the crystal material. If the crystal were perfect, neutrons of a single energy would be diffracted at any given angle. However, all real single crystals have a mosaic structure, that is, they possess structural imperfections which break up the arrangement of atoms into a number of small blocks , each slightly disoriented from one another. This mosaic structure causes the diffracted neutrons to have a spread of energies at any angle. Higher Order Diffraction Also, according to equation (2.14), there are higher order neutrons diffracted at each angle. The ratio of the second order to first order neutrons detected in the beam can be written as (^jO : f(E) = 4(E) e(E) «5(E) ns2 w(E) n=2 p(E) n=2 where (2.15)

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6(E) 20 $(E) = lilEl U(E) is assumed to be 1/E *(E) for energy greater than 0.4 ev) , n e(4E) c^l; (ratio of the detector efficiency e(E) for second and first order neutrons) AE(n=2, HE) 1 (4E) 3/2 cos[9(4E, n=2)]A8(4E) n=2 A E(n=l, E) 2 (E) 3/2 cosC6(E, n=l)] A6(E) where (2.16) w(HE),n=2) w(E) n = 2 = sl (w(E) is the fraction w(E, n=l) of reflected beam transmitted by collimating system) r(4E) n _ ? p(E) _ = 2-i (r(E) is reflectivity n=2 of the crystal plane used) In equation (2.16) cos[6(4E, n=2)] = cos [8(E, n=l)]. and let o = f which reduces the energy band A6(E) transmitted to the detector to °
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21 The reflectivity of a crystal for neutrons is given by equation (11) of Holm (^9.) for the Laue Case _A tan 2 e (-lP* 1 r(E) = exp(-2M) v/2 ne £ Y where W j 3 exp(-2M) Debye-Waller temperature correction factor n = "mosaic spread" of the crystal A = product of the linear abosrption coefficient and the path length in crystal (0 > in n 3 (2.18) t = thickness of crystal N = reciprocal of the unit cell F = crystal structure factor The Debye-Waller temperature correction factor accounts for the reduction in intensity of the Bragg reflection due to the thermal motion of the atoms in the lattice, where M = ^T^ (~) 2 [1/4 + (T/®) 2 Q((H)/T)] (2.19)

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22 with .z xdx Q(Z) = / o e x _i (2.20) Here, (h) = Debye or characteristic temperature of the crystal h,k s Planck's and Boltzmann's constants m * nuclear mass T s temperature of the crystal in degrees Kelvin Since the factors in equation (2.15) cannot be calculated accurately, it is easier to obtain an open beam count rate of E and HE. The ratio is: count (HE) f*(E) = — count — . ( E )e(E),(E) nrlM(E , n=ip(E)n=i (2.21) Equation (2.21) is a good approximation because the second order contamination is usually on the order of a few per cent, unless the first order energy is below the Maxwellian peak. Now, o(E) nsl is A E(n*l, HE) HE 3/2 cos[ 6 (HE, nsl)] A9 (HE) o(E) nsl = . AE(n=l, E) E cos[9(E, n»l)]Ae(E) (2.22)

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23 where cosCeC+E, n=l)] 6 . cos[e(E, n*l)] o(E) n=1 = 2o o aS (2.23) Now the f(E) term in terms of f*(E) is expressed as: r(UE) n=2 f(E) r f*(E) r(4E) nsl 2Bw(E) nsl (2>24) Since Bw(E) nsl j, f then r( «'„=2 f(E) = f*(E) 1/2 = f*(E) R(4E) r(4E) n=l (2.25) Therefore, by using the calculated value of R(HE), f(E) can be estimated. The Renninger Effect When a neutron spectrum was measured using a crystal spectrometer and corrections were made, many large dips were found (2_. 50-53) instead of the smooth spectrum characteristic of a Maxwellian distribution of neutron velocities. These fluctuations are due to

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24 Bragg reflection of neutrons from reflecting planes other than that used to obtain the monochromatic beam. This reflection is best explained by the use of the reciprocal lattice and sphere reflection concepts (54) and the vector notation as outlined in Appendix III. Figure 2.3 demonstrates multiple reflection by means of the sphere of reflection, where the radius of the sphere is 1/X; it is centered on the crystal at C, and passes through the origin of the reciprocal lattice at 0. For an incident direction CO, reflection occurs in the direction CP if the reciprocal lattice vector r' , terminates at P on the sphere. Suppose a second reciprocal lattice vector r^ terminates at Q on the sphere, then reflection of the same wave length occurs in the direction CQ. Taking Q as the origin of the reciprocal lattice and CQ as the incident direction, further reflection corresponding to the vector r' i 8 possible. The double reflection by way of r' an d r' gives a resultant in the same direction and at the same wave length as a reflection through r' . Since r' = r' + r^ the Miller indices of the planes are related by: h x = h 2 + h 3 , k 1 = k 2 + k 3 , i ± = * 2 + a (2.26) The double reflection can occur when any reciprocal lattice point Q is on the sphere, where Q is not necessarily

PAGE 37

25 Reflected Direction q Incident Direction < Figure 2.3. Sphere of Reflection

PAGE 38

26 located coplanar with C, 0, and P. Finally, it should be noted that when multiple Bragg reflection occurs for first order reflection, it also occurs for higher order reflections at the same angle of incidence. Reflectivities Since reflectivities for NaCl and Be have been calculated ( 4_9) , a NaCl crystal cut along the (200) plane was used. The disadvantage of this crystal is that the second order contamination becomes very large at low energies (e.g., = 50 per cent at E = .025 ev) . In order to reduce this second order contamination, a crystal with suppressed second order reflectivity must be used; LiF (111) is such a crystal. The suppression of second order reflection is due to the opposite sign of scattering from successive planes (12) . There are some disadvantages in using LiF crystals. These are: the lattice parameters are uncertain (_55) , the diffuse background scattering is fairly high, single crystals are hard to obtain and suppression of second order is not very great [F (111)/ F (222) = 1.97]. Use of Ge and Si crystals , which have diamond structure, is very favorable because, for the (111) plane, the second order (222) vanishes completely. In fact,

PAGE 39

27 it has been shown (SO) that at 0.015 ev, the higher order contamination of a Ge (111) crystal is only 2.5 per cent. Use of a quartz filter also reduces the higher order contamination considerably (57). Transmission of Reflected Beam Through Filters Transmission of a neutron beam through a filter can be expressed as: t = i A V2 t 3 x 3 ... (2>27) where transmission of neutrons at energy E. fraction of neutrons at energy The sum of the fractions of neutrons must add up to one (EX^ =1). By use of absorbers such as Au, Cd, Sm, Ag, Rh, In etc., neutrons with certain energies can be suppressed. These absorbers have a large resonance and/or a 1/v cross section. For instance, for a 1/v absorber, suppression of the first order by 99 per cent suppresses the second order by 90 per cent. Therefore, the transmission method is a very useful one for estimating higher order contamination. The energy resolution of a crystal spectrometer neglecting the mosaic spread of the crystal is expressed as C+4):

PAGE 40

28 R = — = 2 Ae cot e E (2.28) The actual resolution is determined by plotting the rocking curve for different angles. The rocking curve is obtained by counting diffracted neutrons with a stationary detector and by rotating or rocking the crystal to different angles. The maximum of the distribution corresponds to the position where the detector and crystal plane are aligned. The width of the peak at halfmaximum is equal to AE, the energy spread, of the system. The main advantage of a crystal spectrometer compared to the time-of-f light method in the low energy range is that the area of the beam at the detector is quite small. A diffraction spectrometer can cover the energy range from 0.01 to 10 ev, whereas, it is difficult to cover this energy range with one chopper. The disadvantages of a crystal spectrometer are: (1) the reflectivity varies inversely as the neutron energy; (2) the contribution of the higher order diffraction increases below the Maxwellian peak, and; (3) the spectrometer detector is closer to the reactor than the time-of-f light detectors, resulting in a higher background.

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CHAPTER III DESCRIPTION OF APPARATUS Crystal Spectrometer Collimator In collimating neutrons through a narrow channel, the intensity decreases very rapidly. Therefore, it is necessary to place several collimating channels side by side, where each channel has the required small angular divergence. This type of collimator is called a Sollar collimator (58) . A Sollar collimator was constructed from eight stainless steel strips 0.010 in. thick, 1.50 in. wide, and 33 in. long. Stainless steel rods one-eighth of an inch square were used for separating the strips. This collimator was then inserted into a Cd-lined slot 1 in. x 1.50 in. x 33 in. in a 3 in. diameter wooden cylinder; the collimator was held in the slot by friction. The collimator was then dipped into a boiling bath of paraffin wax, (CH 2 ) n , dissolved in benzene, (CgHg). This procedure gave a thin coat of (CH 2 ) n on the surface of the collimating plates in 29

PAGE 42

30 order to eliminate the secondary scattering from the walls. The angular divergence of this collimator is 13.0 minutes; one section of the collimator is shown in Figure 3.1. Neutrons entering the collimator propagate in four different ways: (1) direct transmission (2) mirror reflection (3) transmission through the collimator walls, and (4) rescattering by the walls. These effects are now considered in turn. For direct transmission with an isotropic source on one end, consider a narrow slit with thickness T, width W, and length L, as shown in Figure 3.1. The number of neutrons emerging from the collimator per unit width .is found from the relation (59) 9 1 T N(neutrons/cm sec) = / o 2* L,2 S ec2 e x <|> o TdlL tan 6) (3.1) where d(L tan 9) = line. source element o ~ Td(L tan 9) = source strength per unit solid angle

PAGE 43

31 Figure 3.1. Single Collimator Slit T } hw

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32 distance from emitting element d(L tan 8) to the receptor angle from the emitting element to the receptor in radians On integrating equation (3.1), the following result is obtained: T 2 N(neutrons/cm sec) = — — <•> e 2 » L ° (3.2) Dividing both sides of equation (3.2) by thickness T, a relationship between the direct inlet and outlet scaler flux is obtained as follows: o ^* 9 * (neutrons/cm^ sec) = ° 2ff L (3.3) The intensity of the neutron beam emerging from the collimator would be a triangular function if the collimator were perfect: I <) = I Cl " /o] C3.«0 where K*) = intensity as a function of angle $ I = maximum intensity in the center of the collimator axis

PAGE 45

33 and the angle $ varies from -a to +o. Due to imperfections in the collimator and the finite transmission of neutrons through the wall, this triangular function tends to be closer to Gaussian distribution (60). The Gaussian approximation of equation (3.4) is I <) = I Q exp -U/ a ') 2 (3.5) where 1/2 a = a/(ln2) In the actual experimental set-up, the disk source is located some distance below the collimator inlet; therefore, an approximate relationship must be derived between the scaler flux coming out of the collimator and the scaler flux of the source. Again, assume the source is isotropic and consider only those neutrons which are emitted directly. Figure 3.2 shows T g and T w , the width and the thickness of the source subtended by the collimator outlet which is approximately rectangular in shape. The expressions for T and W are as follows: T s = T+JIJLj/lJt W g = W+2 [l 2 /lJ W (3.6)

PAGE 46

Now imagine that the collimator is of thickness T s » width W g a nd length (L^L^. Uging equation (3.3), the relationship for the outlet scaler flux for thii collimator is: T ( o s ° '(neutrons/cm^ se c) = 2L' (3.7) Since the actual area of the outlet collimating slit is T-W rather than T^, a n approximate expression for the outlet scaler flux using equation (3.5) is obtained as follows : v T s J ,W-c*/«v 2] d * (neutrons /cm 2 sec) = $' " i . / s exp[-(*/ a » ) 2 ] d* (3.8) where . 1/2(T + T) '1 „ = Arc sin tT s /L s J

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35 The total reflection of neutrons by the wall of the collimator can distort the neutron spectrum. Such a reflection was first reported by Fermi and Zinn (61). The critical angle for such reflection is (62). , ,1/2 MNa/») (3.9) where X = neutron wave length N = number of atoms /cm 3 in the scattering medium "a" = average coherent scattering length Equation (3.9) shows that the critical angle is a function of neutron energy. In the relationship for the critical angle, "a" can be either positive or negative, depending on the scattering material. For instance, hydrogen has a negative scattering length, while carbon has a positive value. Experiments have been performed using neutron mirrors with various hydrocarbons (&y> and it was found that 6 becomes zero for a ratio of H/C 1.748, i.e., the negative scattering length of H is equal to the positive value of C. Therefore, if the collimator walls have a value of H/C larger than 1.748, total reflection cannot occur. Accordingly, the surface of the collimator walls was coated with a thin coat of paraffin which, having an

PAGE 48

36 H/C ratio of approximately 2, should eliminate the total reflection of neutrons. This type of collimator has been constructed previously (6JO with a thin film of polyethylene. The probability of direct transmission through the wall of the collimator without absorption or scattering is expressed as e" t z ( W here E i 3 the total cross section of the wall material and z is the path length of the neutrons through the walls. Even though the absorption of steel is not high, this probability is very small since any neutrons which the steel absorbs will pass through it at very small angles Thus, the neutron path length in steel is relatively long, and transmission through the wall is negligible compared to the direct transmission. Calculations have been made (2) for the transmission of neutrons by rescattering in the walls of a similar collimator. For this calculation, this contribution from rescattering was found to be less than one-half per cent of the total transmitted intensity with negligible effect upon the angular distribution. The description above states that the neutrons emerging from the collimator come predominantly from direct transmission. A calculation was made for the ratio of /* for the experimental set-up and was found to be equal to 7.14 x 10" 5 .

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37 Crystals NaCl (200)* and LiF (111)* crystals were used for these experiments. Dimensions of both crystals were 1/2 in. x 2 in. x 2 in. Goniometer** The goniometer consists of a sample table with a crystal holder, an arm on which the second collimator and detector shield are attached, and the gearing system. The gearing system is in a cast aluminum box, and they can be moved manually or electrically. Figure 3.3 shows the crystal spectrometer in operation on top of the University of Florida Training Reactor (UFTR). The crystal holder is made from a rectangular aluminum box with both ends open in which the crystal fits. This box is attached to the crystal table by means of a stainless steel rod 3/4 in. diameter. The detector shield is attached to an arm with a collimator and is shown in detail in Figure 3.4. The movement of the crystal holder and the detector arm can * These crystals were obtained from The Harshaw Chemical Company, 1915 E. 97th Street, Cleveland 6, Ohio. ** Picker Diplanar Diffractometer, Model No. 3527.

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Figure 3.3. Diffraction Spectrometer in Operation

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39 u

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40 be performed separately or at an angle ratio of 1:2. The 1:2 movement is carried out at very high precision by means of worm gears in the machine. Two odometers are attached to the box where the angular positions of the crystal and the detector can be read to l/100th of a degree. Neutron Detection System The detector used for these measurements is 2 1/32 in. diameter, 96 per cent B 10 enriched BF 3 counter with a pressure of 76 cm Hg. The length of the tube is 15 3/4 in. long with 12 3/4 in. of sensitive length; it has a ceramic end window.* The center of the plateau for this detector was found to be 2 800 volts using the existing cables. The length of the plateau was about 400 v. with change of slope of one per cent per 100 volts. The efficiency of the detector for different energy neutrons was not calculated because it was determined experimentally. Theoretically, efficiency can be calculated from the following relationship (44): E = 1 exp (-N X CE1/2 ) (3 . 10) * This detector was supplied by Reuter-Stokes Electronic Components, Inc., Model No. RSN-108S.

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41 where N = number of atoms per cm 3 in the counter x = length of the counter C = numerical constant which gives the 1/v slope of the BlO( n a ) L ^7 cross section E = energy. With the BF counter, a Radiation Counter Laboratory (RCL) decade scaler, preamplifier and linear amplifier (model numbers 2032, 20200 and 20100, respectively) were used. In addition, Atomic Instrument Company regulated high voltage supply, Model 319, was used. The Subcritical Assembly A subcritical tank made from 6061 Al , 24 in. diameter and 60 in. long and wrapped with .030 in. thick Cd, was placed on top of the graphite pedestal of the UFTR. A grid made from the same type of Al was placed in the tank, so that the fuel elements could be arranged in a hexagonal pattern with lattice pitches of 14.7 and 22 cm. Figure 3.5 shows the location of the tank in the UFTR, and Figure 3.6 shows the top view of the lattice arrangements in the subcritical assembly.

PAGE 54

12 <>.

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i*3 Figure 3.6. Top View of the Subcritical Lattice

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44 The plane source of the neutrons entered the subcritical assembly from the bottom face of the tank. There is approximately 4 in. of moderator between the grid and the bottom of the tank. Two types of natural uranium fuel elements were used for these experiments: Mark V-B and Mark I. Mark V-B is an annular type of element 2.684 in. o.d. and 1.970 in. i.d. and 8 9/32 in. long. Mark I is a solid fuel element one in. in diameter and 8 3/8 in. long. There were six fuel elements in each tube. The moderatorto-fuel volumetric ratio V m /V f and pitches are listed in Table 3.1. TABLE 3.1 SUBCRITICAL^ LATTICE CONFIGURATIONS Pitch (cm)

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45 for performing experiments in the subcritical assembly utilizing the UFTR as a plane source is outlined in Appendix E. 'The critical rod position of the reactor 'was checked after the installation of the subcritical assembly as outlined in the proposal. No coupling between the UFTR and the subcritical assembly was found. Activation detectors were used for the integral measurements and a crystal diffraction spectrometer for differential measurements. For comparisons of experimental results with the theory, THERM0S (4_) and CEPTR (3) codes were used. Two five kilowatt heaters were inserted into the tank so that the D 2 could be heated, A constant temperature in the tank was maintained by the use of a temperature control unit which utilized four thermocouples. Also, a stirrer helps to keep a uniform temperature throughout the tank. A side view of this set-up in the tank is shown in Figure 3.7. The hydrogen content of the D 2 was determined by use of the NMR (Nuclear Magnetic Resonance) equipment in the University of Florida Chemistry Department* a nd found to be 0.661.05 per cent. * Thanks are due Dr. Wallace Brey of the University of Florida Chemistry Department for making this determination

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46 60" A. W Collimator Tube C^O w* — Thermocouple Heating Element Stirrer — Moderator 24" Figure 3.7. Side View of the Moderator Tank

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CHAPTER IV RESULTS OF INTEGRAL SPECTRUM MEASUREMENTS Introduction The first integral measurements were made in the UFTR core and thermal column where there jere few fast neutrons (66_) . The spacial hardening of the thermal neutrons in highly absorbing media was observed. Then, the spectral hardening in a subcritical exponential facility which uses the graphite pedestal of the UFTR as a neutron source was measured spacially using differential and integral methods and results were compared with theoretical calculations (4). For integral measurements of the neutron spectrum, various types of activation detectors were used. All of the detectors fell into two categories: either they had a 1/v absorption cross section or they had a large low-lying absorption resonance. 4 7

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48 Measurements in the Thermal Column* Stainless Steel Rod Integral measurements were made in a stainless steel rod one in. diameter and 12.5 in. long and in a uranium slab 2 in. x 2 in. x 1/2 in. Radial holes 0.050 in. diameter and 1/2 in. deep were drilled in the stainless steel pin holder 6.5 in. from the end. This was done by cutting the stainless steel rod into two pieces. These holes held wire detectors. For the uranium slab, detectors were sandwiched in between the U foils which were 2 in. x 2 in. x .005 in. Measurements were made 2 4 in. from the east end of the thermal column of the UFTR. At this position, the ratio of thermal to epithermal flux is approximately 100 (66). Therefore, the contribution of the epithermal neutrons is negligible and equations. 8) is used directly to measure the change in effective neutron temperature. For these measurements, Lu 175 , Lu 176 , Dy 16 \ .19 7 2 39 Au , and Pu detectors were used. The detectors were fabricated in the form of wires 0.0 30 in. diameter containing 10 per cent by weight of the activant in an Al matrix, except for the Au wires, which were 0.005 in. in diameter. The first measurements were made in the * Preliminary results given in BNL-719, Vol. II. pages 336-58 (1962).

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4 9 stainless steel rod using natural Lu-Al wires.* a few hours after irradiation, Lu 1 m and Lu 177 activities were counted five times using a scintillation counter.** About four days later, after the Lu activity had decayed out, five more sets of counts were taken of the 177 Lu activities. The total count rate for each time was at least 10,000 counts. The procedure for obtaining the average normalized activities of the two isotopes and their ratios is outlined in Appendix A. Pu-Al wires were calibrated by measuring their natural gamma activities. These wires were then irradiated in a stainless steel rod and gammas from 19 7 the fission fragments were counted (67). The Au and Dy wires were also irradiated in the stainless steel pin holder. The corrected activities from all the detectors are listed in Table 4.1. The activities of the 1/v abosrbers, the Lu 1 an d the Pu 239 fission products were each fitted to the Bessell function, I (
PAGE 62

O Au 198 act. A Lu 176m act * Lul77 act# ° Pu239 act> /l o (1.045r) I o (0.980r) I o (0.880r)

PAGE 63

51 J o H < > H < C 0) g* bOcn
PAGE 64

52 are tabulated in Table H.2 together with the change in effective neutron temperature from the outer surface to the center line of the stainless steel rod using tabulated g factors. The ratios show that the activity ratio (Lu 177 /1/ V absorber) is more sensitive to the spectrum shift in highly absorbing media than the (Pu 23 9/i/ v absorber) ratio. Uranium Slab Lu wires were placed between uranium foils as shown in Figure 4 . 2 . and the uranium foils were positioned in a slot in a graphite block. The corrected activities of Lu 77 and Lu 1 ™* together with their ratios are plotted on the bottom of Figure 4.2 and tabulated in Table 4.3. The data in this medium were interpreted in terms of effective neutron temperature using equation (2.8). Cd ratios were measured inside and outside of the U slab and it was found that the contribution of epithermal neutrons to the Lu activities was negligible. The effective neutron temperature change in the slab was found to be 9 . 4° C + 3. 4° C using tabulated g factors.

PAGE 65

bJ .» .6 .i .2 .4 Figure H.2. Lu Traverses Through U-Slab

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54 TABLE 4.2 RATIOS OF [Pu 239 /l/v ABSORBER] AND [Lu 177 /l/v ABSORBER] ACTIVITIES* (Pu 239 /l/v absorber) (Lu 177 /l/v absorber) 5r) + I C.880r)/I (1.045r) + 1.000 0.997 0.987 0.973 0.948 0.932 0.915 0.8977 * The standard deviations of these values are less than 1%. t The change in neutron temperature using two different ratios were: Radius

PAGE 67

5 5 TABLE it. 3 Lu 177 AND Lu 176m ACTIVITIES AND THEIR RATIOS IN URANIUM SLAB Position (cm) A 177* A 176m* A 177 /A 176m * 0.8255

PAGE 68

Figure 4.3. Al Can With the Detector Holder

PAGE 69

57 cross sections for these concentrations were 0.66 barns, 2.609 barns and 4.496 barns, respectively. The detectors used for these measurements were Dy 16 \ Lu 175 , Lu 176 , Au 197 and Pu 239 . Normalized activities of the five detectors are listed in Table 4.4 and plotted in Figures 4.4-4.7. The ratios of A 177 /A 176m are listed in Table 4.5 and plotted in Figure 4.8. In order to compare the measured activities with theoretical values, calculations were made using the THERM0S Code (4). The results of the calculations gave the neutron density and flux per unit volume for thirty energy groups at different space positions and also the activities of Dy 164 , Pu 239 , Lu 176 , Au 197 and Eu 151 . The calculated activities of 1/v absorbers were found to be almost identical to the calculated neutron flux; therefore, experimentally measured activities from the 1/v absorvers were compared with the calculated neutron fluxes. The results are plotted on Figure 4.9 . There is some difference between the two which is attributed to the inability to mock-up the axial feed of the sources in the THERMOS code.* The axial feed of the sources makes it anisotropic whereas the THERMOS code assumes isotropic scattering of the sources. The theoretical flux peaks in the HO medium a few mm. inside the Al * Kinard, F. E. , Private Communication.

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i.41.2l.oiI r i 0.8b 0.6 0.4j 0.2 H 2 oo 5 gm BO /liter ' / 1 J / / er o10 gm B 2 3 /liter A (Standard Deviation less than 1%) Al Rod* . q' '//h/ mi/ in B 2 3 solution __ J Al canl 12 3 4 5 Distance From Center of Can (cm) Figure 4.4. Normalized Lu 176m Activities in Al Can Filled With Aqueous B 2 3 Solutions

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59 1.4 1.2 +J 1.0 -h 0.8 0) N 0.6 0."+ 0.2 0.0 10 gm B 2 3 /liter (Standard Deviation less than 1%) Al RocL_ B 2^3 solu " t i° n -hAI can, \/u.yc">;-i\ 12 3 4 5 Distance From Center of Can (cm) Figure 4.5. Normalized Lu 177 Activities in Al Can Filled With Aqueous BjCU Solutions t

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60 1.4'" 1.2 +j 1.0" > Q Q) N o 0.4 0.2 0.0 H 2 .©• 5 gm B 2 3 /liter 10 gm B 2 3 /liter (Standard Deviation less than 1%) AL RodnB 2 0o solutionAl Cani -.iUJJ 12 3 4 Distance From Center of Can (cm) Figure 4.6. Normalized Dy 164 Activities in Al Can Filled With Aqueous B 3 Solutions

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61 1.4 1.2 •H 1.0 +J <*> . s °' 6 u o 0.4 0.2 0.0 H„0 5 gm B 2 3 /liter / liter ^* (Standard Deviation less than 1%) Al Ro Rod, ...J L ~B 2 °3 solution ->«A1 Can | \ii \ uinti\ 12 3 4 5 Distance From Center of Can (cm) Figure 4.7. Normalized Fission Product Activities in Al Can Filled With Aqueous B„0 3 Solutions

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62 t o gn/Ut«t I 5 qnv/llter O 10 gm/llter fitted curve .0 2.0 3.0 4.0 x 5.0 I*A1+ H 2° and B 2°3 + A1 { Graphite Figure 4.8. Lu 177 /Lu 176m Ratios in BO Solutions

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63 l.tf 1.2" O.OL 12 3 4 Distance From Center of Can (cm) Figure 4.9. Comparison of Normalized THERM0S Flux

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64 TABLE 4.4 NORMALIZED ACTIVITIES IN AQUEOUS SOLUTIONS B 2 3 Cone .

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65 TABLE 4.5 A 177 /A 176ra RATIOS IN AQUEOUS SOLUTIONS Distance Center (

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66 can, and this is believed to be due to the external source conditions. The ratios of A* 77 ' /1/v absorber for experimental and theoretical calculations are listed in Table 4.6. The theoretical spectra are softer than the experimental values and again, this is due to the THERM0S source conditions. TABLE 4.6 177 RATIO OF A /1/v ABSORBER IN 10 gm. B„C q /LITER Distance (cm) Theoretical Experimental' 0.6 1.0469 1.1191 i6 1.0320 1.1058 2.6 1.0256 1.0699 3 6 0.9991 1.0321 4 l+5 1.0000 1.0000 * Standard deviation less than 1 per cent. In order to duplicate the source conditions imposed by the THERM0S Code, an attempt was made to perform an experiment by placing the Al can filled with borated water in the center of the UFTR. However, with only one gram of B^/liter, the excess reactivity of the reactor was not enough to override the poisoning effect. Therefore, the only way this experiment can be performed properly is to provide sufficient reactivity to override the B 2 3 absorption.

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67 Measurements in the UFTR Core In order to measure the spacial dependence of the effective neutron temperature and the rvT/T factor in the UFTR core, Lu wires and very thin Au foils were irradiated. The Au foils were made using Au resinate solution,* which was applied to the surface of an Al foil and then baked slowly in an electric oven for about H5 minutes until the temperature reached 900° C. The baking process volatilized the organic material in the film of resinate solution and left a thin film of Au on the surface of the Al foil. The maximum thickness of the Au film was not more than 0.5 microns. This was determined by comparing the activities of Au foils of known and unknown thicknesses in a known flux. Since the self-absorption is negligible for a Au foil with thickness of . 5 microns (68), it was correct to assume that these foils were infinitely dilute. Activities from the impurities were found to be negligible. Accurate weighing of these thin Au foils was practically impossible; therefore, the same foils were used to measure the bare and the Cd covered activities. This process corrected for weight * Supplied by the Hanovia Chemical and Manufacturing Company, East Newark, New Jersey.

PAGE 80

6 8 variations. Activity from the first irradiation was subtracted from the second using the same foil for both irradiations, since the half-life of Au is well known. The Lu wires were 30 mils in diameter and contained 10 per cent by weight of Lu . The positions where Lu wires and Au foils were irradiated is shown in Figure 4.10. One measurement was made in the center of the fuel box. From the result of the Au foil activations, values of rVT/T were calculated using equation (2.4). In this equation, s Q for Au is known (6_9) and is approximately equal to 17.5. From these calculated values of r~V T/T Q the effective neutron temperature in the center of the UFTR core was calculated by trial and error using equation (2.7). For these calculations tabulated values of g and s 4 were used for Lu 176 . The factor g for Lu 5 is approximately one and the factor s Q G r was determined experimentally by the use of Cd ratios of Lu 175 , and by using rVT/T obtained from the Au foil activation together with equation (2.5). The effective neutron temperature was calculated to be 76.0 t 2.9° C in the center of the UFTR when compared to the reference point in the thermal column. The numerical results for rVT/T A 177 A 176m A 177 /A 176m , T , R 175 , R 1 ^ 7 and (s G ) 175 are tabulated n cd cd or

PAGE 81

69

PAGE 82

70 in Table 4.7. In Figure 4.11, A 177 /A 176m R 197 a ' cd ana rvT/T are plotted. Measurements in the Subcritical Assembly Integral measurements were made radially 12. S in. from the bottom of the central fuel tube because the slot in the special Mark V-B fuel elements* was located at this position. At this height, the axial Cd ratio has reached a constant value indicating spectral equilibrium. An Al foil holder was attached to the tube at this height so that radial traverses could be taken to the cell boundary and beyond. Bare and Cd covered Lu and Au foils were irradiated in four different arrangements using two lattice pitches as is listed in Table 3.1. Also, THERM0S and CEPTR calculations were made for these arrangements and all the experimental and theoretical results are plotted in Figures 4.12 to 4.19 for thermal and epithermal activities. All the experimental results were normalized at the cell boundary, and the direction of the traverse was equidistant between two fuel tubes. Au foils 0.001 in. thick and 0.25 in. diameter were used together with foils containing a 10 weight per cent * Special unclad Mark V-B and Mark I fuel elements with slots for activation detectors were borrowed from the Savannah River Operations Office, Aiken, South Carolina.

PAGE 83

71 2.0 1.9 ru«i I 08 Ion*! Figure 4.11. Traverse Through UFTR Core

PAGE 84

72 2.0 f 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 4 6 8 10 Distance From Center (cm) Figure 4.12. Au Activity Distribution for Mark V-B Natural U Fuel With 14.7 cm Pitch

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73 2.0 1.8 1.6 1.4 0.8 0.6 0.4 0.2 0.3 Thermos Curve Normalized at Cell Edge Subcadmium (s.d. ± .7%) Cell Radius -o— O Epicadmium (s.d. i 3%) D 2 D 2 Al Al/Al 12 14 2 4 6 8 10 Distance From Center (cm) Figure 4.13. Lu Activity Distribution for Mark V-B Natural U Fuel With 14.7 cm Pitch

PAGE 86

74 2.0 h 1.8 1.6 1.4 3 i, o < > • H 1, D © 0.8 0.6 0.4 0.2 0.0 XT Thermos Curve Normalized at Cell Edge O _____JC£r-0DoO Al Al Al Subcadmium (s.d. i .5%) — O Epicadmium (s.d. i .6%) D 2 j< U | | D 2 4 6 8 10 Distance From Center (cm) Cell Radius 12 14 Figure 4.14 Au Activity Distribution for Mark V-B Natural U With 2 2 cm Pitch

PAGE 87

75 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 Thermos Curve Normalized at q^ Cell Edge / / Sub cadmium / (s.d. i .7%) N I Cell Radius Al D 2 U Al/Al 'I X— Epicadmium x 10 (s.d. ± 3.5%) DoO 12 Figure 4.15, 4 6 8 10 Distance From Center (cm) Lu Activity Distribution for Mark VNatural U Fuel With 2 2 cm Pitch 14

PAGE 88

76 4.CT 3.C Thermos Curve Normalized at Cell Edge 2.01.0 0.4 Subcadmxum (s.d. t ,7%) QO / SX^-W" — ° — "O — X -o— ^
PAGE 89

77 2.2 2.0 1.8h 1.6 1.4 1.2 1.0 0.8 0.6 0.4 Thermos Curve Normalized at/ Cell Edge Cell Radius / GU Subcadmium (s.d. ± .8%) 10 x Epicadmium (s.d. i 4%) Al Sd 2 o| Al Al/ Al h D 9 4 6 8 10 Distance From Center (cm) 12 14 Figure 4.17. Lu Activity Distribution for Mark I and Mark V-B Natural U Fuel With 14.7 cm Pitch

PAGE 90

78 4.0 3.0 O < 0/ Thermos Curve Normalized at Cell Edge Cell Radius Subcadmium (s.d. i .7%) 1.0 0.4 < G /O' DoO oEpicadmium (s.d. i.5%) -0Al Al Al/Al D 9 4 6 8 10 Distance From Center (cm) 12 14 Figure 4.18. Au Activity Distribution for Mark I and Mark V-B Natural U With 2 2 cm Pitch

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79 «+.o 3.0 2.0 1.0 Thermos Curve Normalized at Cell Edge O ®—-&—\Figure U.19. «+ 6 8 10 Distance From Center (cm) Lu Activity Distribution for Mark I and Mark V-B Natural U With 22 cm Pitch

PAGE 92

80 r-\ O OS en 13

PAGE 93

31 dispersion of Lu 2 3 in Al. The latter were the 0.0 30 in. thick and 0.25 in. diameter. Activities were corrected for the radial J Q (Br) flux distribution in the subcritical according to the relation: *!(R) *(R) = where -.(R) = uncorrected flux *(R) = corrected flux Epithermal activities were measured using 0.0 30 in. Cd covers. Therefore, a Cd cut-off of 0.5 ev was used for the THERM0S calculations. In addition, bare and Cd covered traverses were made with infinitely dilute Au foils to evaluate the epithermal index r in the unit cell for each lattice arrangement. Using the activity ratios of Lu 177 and 19 8 Au t effective neutron temperatures at different cell positions were calculated using equation (2.10). For a reference the neutron temperature at the cell boundary was determined by a differential method in order to determine the effective temperature change in the unit cell. The results of these measurements are plotted on Figures 4.20 to 4.23. Also shown on Figures 4.24 to 4.2 7 are the axial thermal and epithermal fluxes with the corresponding Cd ratios.

PAGE 94

82 1.0

PAGE 95

8 2 1.0 ^ 07 OS 5.0 ^O D 2 Al Al Al I u B*'H D 2 23 • 5 6 7 89 10 Distance From Center (cm) Figure 4.21. Plot of A 177 /A 198 , rV T/T Q and Cd R With Distance From Center Using Mark V-B Natural U With 22 cm Pitch

PAGE 96

84 -.2 5 t ? -2.0 M>8 07 06 1.1 Al Al Al Al f4D 2 0fj U " D o 01231+5678910 Distance From Center (cm) Figure 4.22. Plot of A 177 /Al9 8 , r T/T Q and Cd R With Distance From Center Using Mark I and Mark V-B Natural U Fuel With 14. 7 cm Pitch

PAGE 97

2.6 h2.5 D 2 Aim Al Al/ Al u MDoO U u i OD 2 01234 56 789 10 Distance From Center (cm) Figure 4.23. Plot of A 177 /A 198 , r T/T Q an d Cd R With Distance From Center Using Mark I and Mark V-B Natural U Fuel With 22 cm Pitch

PAGE 98

86 Figure 4.24. 100 Height (cm) Axial Distribution of Flux in the Two Foot Tank Using Mark I and Mark V-B Natural U Fuel With 22 cm Pitch

PAGE 99

Thermal Activation 20 Figure 4.2 5 un 100 60 80 Height (cm) Axial Distribution of Flux in the Two Foot Tank Using Mark V-B Natural U Fuel With 22 cm Pitch

PAGE 100

Thermal Activation 2 Figure 4.26 HQ 100 60 80 Height (cm) Axial Distribution of Flux in the Two Foot Tank Using Mark V-B Natural U Fuel With 14.7 cm Pitch

PAGE 101

8 9 Thermal Activation Cd Ratio x 10' Epithermal Activation 20 HO 60 80 Height (cm) Figure 4.27. Axial Distribution of Flux in the Two Foot Tank Using D 2

PAGE 102

CHAPTER V RESULTS OF DIFFERENTIAL SPECTRUM MEASUREMENTS Introduction Differential spectrum measurements were made using the crystal diffraction spectrometer described previously. A beam of neutrons was extracted from the subcritical assembly for this purpose. This choice of instrument was made because the crystal spectrometer is simpler, cheaper and less space-consuming than a chopper (70). The details of the crystal spectrometer and the description of the subcritical assembly are given in Chapter III. Analysis of the crystal spectrometer data is complicated due to the following effects: (1) secondaryand multiple scattering in the walls of the collimator (2) the Renninger effect (71)* (3 ) imperfections of the crystal, i.e., mosaic structure (H) variations in detector efficiency, and (5) higher order contamination. In order to simplify these corrections, the instrument The Renninger effect is explained in detail in Chapter III. 90

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91 was calibrated experimentally by using a beam of neutrons with a known energy spectrum. More detailed discussion of this method is given in the later sections of this chapter. For calibration purposes, a well-moderated neutron beam was extracted from the subcritical tank filled with D 2 0. Following this calibration experiment, beams from the D 2 0-moderated subcritical wer e extracted from the center of the fuel element, from the fuel-D 2 interface and from the moderator surrounding the fuel elements. A similar work was performed by V. I. Mostovoi, et al. (7^) in uranium-water and uranium monoisopropyldiphenyl lattices using the time-offlight technique. For theoretical comparisons, the THERM0S code developed by Honeck <»0 was used. THERM0S is a multigroup code which solves the integral form of the transport equation; it is described in Appendix B . Alignment and Calibration Alignment Several different methods of aligning were tried. First, the bore-sight method of aligning the detector and the first collimator was tried. Then, an optical method was attempted. Finally, it was decided that the easiest way to align the spectrometer was to set the detector shield in the vertical position and then to

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92 insert an Al rod 1 3/8 in. diameter through the detector shield opening with guides attached to the bottom and top of the shield. Then, a guide to the top of the collimator was attached so that when the detector hole and the collimator were aligned very accurately, the Al rod would fit into the guide on top of the collimator. The Al rod was within ±0.001 in. from being straight. In fact, a deviation of ±0.001 in. in the Al rod will cause an uncertainty in 6 by ± one minute. The final method of aligning is shown in Figure 5.1. Spectrum From the UFTR Core In order to measure the differential neutron spectrum in the center of the UFTR core the central vertical plugs above the reactor were replaced with a collimator plug. The diffraction spectrometer was then aligned with the collimator. Rocking curves obtained with NaCl (200) and LiF (111) crystals are plotted on Figures 5.2 and 5.3. Half maximum angles, A 6, of the NaCl and LiF were 1.7° and 0.5 2 5° respectively. Using the LiF crystal, the neutron spectrum coming out of the central vertical access was measured from 3° < e i 27°. Data obtained from this measurement, after correcting for the background, were plotted as E versus count rate as shown in Figure 5.H. It can be seen from the figure that the results fitted a

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9 3 t y Guide Detector Shield ^ N« Guide Collimator Top of Shield \ i Aluminum Rod — Guide M Figure 5.1. Method of Alignment of the Diffraction Spectrometer

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-2° -1° o° 1° 2< Figure 5.2. Rocking Curve of NaCl (200)

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! J5 20.0 10.0 5.0 h 2.0 1.0 0.5 0.2 0.1 .01 .02 Maxwellian O Experimental 05 .1 E(ev) P X Q .5 Figure 5.4. Open Beam Neutron Spectrum From Center of UFTR Core Using LiF (111) Crystal

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96 Maxwellian distribution very well. Therefore, the neutron temperature was calculated for the Maxwellian distribution. According to the kinetic theory of gasses (73), the average kinetic energy of thermal neutrons is given by: i mv 2 = 3 k T n 2 2 (5.1) The quantity v 2 is not measurable but it is related to v Q , the most probable velocity, which is measurable as shown below ( 74) . v* /v 2 dn aAv q 3 Jv" e ~ v? dv (5.2) 7 /dn H 2 v o ' The most probable velocity, v Q , of the Maxwell distribution is obtained by differentiating the flux distribution (equation (5.3)) and setting it equal to zero. d(nv) 4n _ JL, dv " -^ v 3 v 3 e v 2 ^^ or nu = 1.224 v (5.4)

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97 where v m corresponds to the velocity of the most probable flux or root mean square velocity. In a simpler manner, the neutron temperature of the core is related to the most probable velocity as follows: irav„ 2 = k T o o n (5.5) The neutron temperature for Figure 4.9 was calculated as outlined above and was found to be 115.4 t 6.0° C with the most probable velocity of 2531 t 314. 5 m/sec. Spectra From D 2 In an infinite moderator with vanishingly small absorption, the neutron spectrum takes the form of a Maxwellian distribution at the temperature of the media. If a poison with 1/v absorption cross section is added to a moderator, it can be shown (75_) that if the Maxwellian spectrum is to be retained, the source of the neutrons must itself be a Maxwellian spectrum. In this case, the source and loss rate from each energy interval must be the same. In an actual reactor, the spectrum is distorted from Maxwellian, and this is due to the slowing down distribution of the source from fission, which does not have the Maxwell distribution.

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98 A neutron beam has been extracted from scatterers such as H 2 0, D 2 and C (76^ TJ_) and the neutron spectrum analyzed with the time-of-flight method using a chopper and neutron pulser. The measurements confirmed that the neutron energies fit a Maxwellian distribution very v/ell from the^e non-abqorbina media. In order to extract a beam of neutrons from non-absorbing media, a cylindrical tank 2U in. diameter and 60 in. high was placed on top of the graphite pedestal of the UFTR and was filled with D 2 0. a more detailed description of the set-up is discussed in Chapter III. The purpose of extracting a beam of neutrons out of the D2O medium with variable temperature is to calibrate the overall efficiency of the neutron diffraction spectrometer using neutron spectra with fairly wellknown distributions. The count rate of a BF counter at different Bragg angles 6 for a single crystal can be expressed as: n=k C i< 6) = I T i f n F i.n (6) n=1 (5.6)

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99 where T^ = transmission of the n th order diffracted neutrons through a filter (eE tX) i = measurement index n = order of diffraction C^(8) count rate at the detector F. „(e) = *(n 2 E)e(n 2 E)S(n 2 E) w(n 2 E) r(n 2 E) D(n 2 E) ii" n n n n <|>(n 2 E) = neutron flux distribution in the media e(n z E) = BF 3 detector efficiency 2 S(n E) = spectrometer resolution for order n 2 W(n E) n = fraction of reflected beam transmitted by the collimating system for order n r(n E) n = reflectivity of the crystal plane used for order n D(n E) n = correction factor due to the multiple diffraction for order n The evaluation of F. _(8) in equation (5.6) was x ,n carried out for up to two sets of T^ n 's, by solving simultaneous equations. Since the $(n2E) is known for large D 2 media, the combined efficiency for different energies for first order can be evaluated. Instead of evaluating the combined efficiency, ratios of F. (e) l ,n

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100 of unknown and known spectra were taken and, when multiplied by the known spectrum, gave the unknown energy spectrum: ^ Q S x » n s (5.7) The neutron spectrum was extracted 7 in. from the bottom of the tank with D 2 temperatures of 25° and 75°C. The axial Cd ratio for this system is plotted on Figure 4.27. By inspection of the data it was found that the neutron temperature was 10° C higher than the moderator temperature. The ratio of the two sets of measurements are plotted on Figure 5.5 with the theoretically calculated Maxwellian distribution ratios at two different temperatur This was done to check if the spectrometer could see the change in neutron spectrum due to the change in medium temperature. Spectra from Subcritical Assembly For the differential spectrum measurements, the first three lattice arrangements listed in Table 3.1 were used. The first collimator described earlier was inserted vertically into the subcritical assembly first at the center and then at the boundary of the central unit cell. The LiF (111) crystal was used for these measurements.

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101

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102 The experimental neutron density distributions were calculated at two locations by the use of equation (5.7) for each arrangement and are plotted on Figures 5.6 5.8. In Figure 5.7 the lower experimental spectrum is much softer than the THERM0S spectrum. However, the THERM0S spectrum is at the center of the Mark I fuel element, while the extracted beam of neutrons had a diameter of approximately 5 cm. Therefore, the experimental results were plotted again in Figure 5.9 with THERM0S spectrum . 2 cm outside of the Mark I fuel element.

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103 8.0 4.0 2.0 1.0 0.8 0.4 0.2 0.1 0.08 0.04 0.02 0.01 Cell Boundary .04 .08 .1 .2 Energy (ev) Figure 5.6. Experimental and THERM0S Spectra Using Mark V-B Natural U Fuel With 2 2 cm Pitch

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104 4.0 0.04 0.02 0.01 -Cell Boundary .01 .02 04 .08 .1 Energy (ev) .2 ,4 Figure 5.7. Experimental and THERM0S Spectra Using Mark I and Mark V-B Natural U Fuel With 22 cm Pitch

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105 4.0 0.4 0.2 0.1 0.08 0.04 0.02 0.01 Cell Boundary Center of Cell *-\ \ 01 .02 .04 .08 .1 .2 Energy (ev) .4 Figure 5.8. Experimental and THERM0S Spectra Using Mark V-B Natural U Fuel With 14.7 cm Pitch

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106 4.0 2.0 1.0 0.8 0.4 0.2 0.1 0.08h 0.04 0.02 0.01 .01 .02 Center of Cell 04 .08 .1 .2 Energy (ev) Figure 5.9. Experimental and Corrected THERM0S Spectra Using Mark I and Mark V-B Natural U Fuel With 22 cm Pitch

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CHAPTER VI RESULTS, CONCLUSIONS AND RECOMMENDATIONS Comparisons of Experimental and Theoretical Spectra in the UFTR Thermal Column and Core Comparisons of the theoretical activities with the experimental results in the thermal column using an Al can filled with borated water are plotted on Figure 4.9. The differences in the two fluxes were as much as 2 5 per cent and this is due to the THERM0S source conditions. It would be interesting to perform this experiment with isotropic source conditions in a reactor which has enough excess reactivity to override the poisoning effect of the sample. The ratio of the activities of a resonance and a 1/v absorber for borated water was found to be somewhat higher than the theoretical calculations as can be seen in Table 4.6. The discrepancy is again due to the THERM0S source conditions. No theoretical calculations were made for the natural U slab and the stainless steel rod. Again, anisotropy of the source conditions would apply here and there would probably be large discrepancies between THERM0S calculations and experimental results as with the borated water data. 107

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108 From the experimental results a good comparison was made between the integral and the differential measurements in the center of the UFTR core. The effective neutron temperature determined by the differential measurement was 115±6°C compared to 76±2.9°C using integral measurements with Westcott's formulations (3H_). Thus, the difference between the two methods of measurements was 39° C. The effective temperature of the integral measurement in the UFTR core is relative to the effective temperature of the thermal column which was assumed to be equal to the temperature of the media. Johansson (]J>) nas measured the effective neutron temperature in graphite media using the time-of-f light method and found it to be 29±10°C higher than the medium temperature. If this result applies to the UFTR thermal column, then the comparison of effective temperature using the two methods will be within the experimental error. The experimental effective neutron temperature in the UFTR was compared with theoretical calculations made by C. A. Thompson (7jO who has made a multigroup-multiregion calculation for one dimension going from South to North in the reactor core. However, his calculations showed a much lower neutron temperature in the UFTR core. It is also hard to make a detailed comparison with Thompson's calculations because his energy groups in the thermal region are wide.

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109 Comparisons of Experimental and Theoretical Spectra in the Subcritical Assembly Intracell activation measurements were made using resonance and 1/v absorbers in each of the lattice arrangements in Table 3.1, and comparisons were made with THERM0S calculations for each detector. In general, the results are in good agreement except for a few points like the one in Figure 4.14. These few points are very probably due to inaccurate positioning of the activation detectors in the horizontal plane. This conclusion was verified by repeating some of the measurements. Also, CEPTR calculations for the flux distribution were made, but were found to be almost identical to the THERM0S flux. For the differential measurements , experimental calibration of the equipment proved to be successful and gave excellent results, as can be seen in Figures 5.6 5.9. The temperature calibration curve was also satisfactory which can be seen in Figure 5.5. The comparisons of the change in effective neutron temperature from cell boundary to cell center for three different methods (THERM0S calculation, integral and differential) are listed in Table 6.1. The temperature change in a unit cell for the differential measurements was estimated by fitting the experimental 3pectrum to a Maxwellian distribution using a least square fit with the IBM 704 computer ( 81) .

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110 W H J CD W W O In Eh U M < w 21 M < CJ w w s

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Ill It would be of interest to extend the data to other fuel element configurations (e.g., large clusters of U0 2 rods) in order to test the validity of the THERM0S calculations.

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APPENDIX A METHOD OF CALCULATING A 177 /A 176m Natural Lu contains 2.6 per cent Lu 176 and 97.4 per cent La* 7 *. Activities of irradiated natural Lu comes from Lu 175m and t,,177 . .. ... . . ana lu X n the fxrst two days. After four days the activity of Lu 176m decays out completely, and only the activity of Lu 177 i s left. Normally, each foil or wire was counted ten times to get better statistics. The first five counts were made for the short and long half-life activities, and then another five counts were taken for the long life activity. All the activities were corrected back to some standard time, t=0, and activities normalized to standard Cs 137 source. The average activity of Lu 177 a t t=0 is given as: A t. 5 [A* 77 ( tjL ) Background] e 2 1 A* 77 (t = 0) = I — + 5 177 i = l x where decay constant of Lu 177 time when activity of Lu 176m and 17 7 Lu was measured 112

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113 x « index for the position of the detector 5^ = standard deviation of Lu 177 activity Now the average activity of Lu 176m a t t=0 is given as A 176m Aj (t=0) 5 . . . rA 176m + 177, 177 2 j X l t j I LA X (t.)-A (t=0) e background] e j = l J x + ,176m " 6 x \ 1 decay constant of Lu 176m t. = time when the activities of ] Lu?76m and Lu 177 were measure d 6^ 76m = standard deviation of the Lu 176m activity All the activities were normalized to standard activities, A 177 (t=0) Y 177 (t = 0) = — , A 177, * ?V " ~ A x "< A^ 77 (t=0)

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114 A^ 75m (t S 0) ^ 76m (t = 0) c s Ai 76m ( t = 0) A^ 76m (t=0) x Since A^ =1 and A i/bm = 1. The normalized activity ratios become Al ?7 (t=0) r = ± . R A 176m (t=0) * 6 x

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APPENDIX B THE THERM0S CODE The THERM0S Code developed by H. C. Honeck of Brookhaven National Laboratory calculates the scaler neutron spectrum as a function of energy and position in a lattice cell. The code solves numerically the integral transport equation with isotropic scattering (4). One dimensional slab or cylindrical geometry can be used. Comparisons of the code calculations with integral measurements have been published (79, 80). THERM0S code uses 30 energy groups as given in Table B.l; it uses 20 space points and mixtures of ten nuclides. The code is used for calculations of the reaction rate of 11*33, u235 § Pu 239 ( Dy 16^ Eu 151 f and Lu 176 . Output of the THERM0S code is also used for calculating n,f (thermal utilization), £ , fQ (fraction of thermal neutrons captured in U 238 ) and D. 115

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116 TABLE B.l ENERGY GROUPS FOR THERM0S CALCULATIONS Group No.

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APPENDIX C THE RECIPROCAL LATTICE Let a-, , a 2 and a 3 represent vectors of a unit cell containing no lattice points other than those lying at its corners. Then, let b lt fc> 2 and t> 3 represent the vectors of a reciprocal lattice. The reciprocal axis b-, is perpendicular to the axis a 2 and a 3 . Also, b 2 is perpendicular to a-j^ and a 3 and t> 3 is perpendicular to a-, and a 2 . These relations are summed up in the vector equations: tH . a = bn • a^ = b . a-, = b (C.l) The magnitude of reciprocal vectors are fixed by relations: b l " d 2 ' b 2 S a 3 * b 3 = 1 (C ' 2) The length of the reciprocal lattice is given by relation: b 1 = 3(4 2 « a 3 ) (C.3) 117

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118 where B is a constant evaluated as follows : Let V be the volume of the unit cell of the lattice defined by vectors a , a , a , then: , b 2 = (a, x a-,), b, = (a, x a 2 ) (C.6) Figure C.l. Unit Cell of a Lattice

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119 The vector r(u,v,w) to any lattice point is given by vector equation: r(u,v,w) = ua, + va2 + wa(C.7) where u, v, and w are any integers, positive, negative or zero. The vector r'(h,k,i) to any point in reciprocal lattice is given by: r'(h,k,i) = hb^ + kb 2 + £b 3 (C.8) where h, k, I have the same properties as u, v, and w. Two properties of the lattice that make it of great value in treating problems of diffraction by space lattices are: (1) The vector r'(h,k,t) to the point (h,k,X.) of the reciprocal lattice is normal to the planes (h,k,£) of the crystal lattice. (2) The magnitude of the vector r'(h,k,l) is the reciprocal of the spacing of the planes (h,k,£) of the crystal lattice.

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APPENDIX D BUCKSH0T CALCULATIONS CEPTR fluxes are used as input to the BUCKSH0T calculations. It calculates the lattice parameters of natural uranium D 0moderated cylindrical heterogeneous reactors. Some of the parameters obtained for two different pitches using Mark V-B elements are listed below. •itch

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APPENDIX E PROPOSAL TO USE UFTR AS A SOURCE FOR THE SUBCRITICAL ASSEMBLY PROPOSAL August 3, 1964 TO: UFTR Subcommittee of the ENOF Committee FROM: S. Salah SUBJECT: Use of UFTR as a Source for a 2 4" D x 60" Subcritical Reactor Description of the Set-up A series of experiments is planned with a subcritical reactor sitting on top of the UFTR as shown in Figure 1. A new set of shielding blocks with heavy aggregate will be constructed which will be used as permanent shielding blocks for the top of the reactor. When the subcritical is removed from the shield structure, it will be replaced with permanent plugs with vertical access holes. The shielding plugs will be made from heavy aggregate concrete and will be lifted out with the crane whenever necessary. Object of the Experiment The purpose of these experiments is to measure the differential and integral spectrum emerging from the subcritical reactor. These measurements will comprise three parts: (1) Using submerged heaters in the subcritical filled with H-O and then with D 2 0, a calibration experiment will be done by heating the media. Following this, the same experiments with borated H 2 will be performed. 121

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122 (2) The subcritical with a lattice spacing of 5.8 in. and 8.64 in. using Mark V-B type fuel elements will be used. A beam will be extracted from the fuel element and from the D 2 moderator and hardening of the neutron spectrum in the fuel will be investigated using a crystal diffraction spectrometer and activation foils. The moderator-to-fuel ratios of the two lattice spacings are 12.1 and 24.8, respectively. Safety Measures The coupling between the subcritical and the critical reactor will be measured by noting the critical rod settings before and after the installation of the subcritical reactor. For the first reaotor run following the installation, the usual start-up procedures for a new fuel loading will be followed. At very low power level the flux level in the subcritical will be measured and compared with some reference point in the reactor. The area above the top of the subcritical will be monitored, and if the radiation level is not above the permissible limit, it is proposed to take the power level of the UFTR to the maximum level for the purpose of extracting a beam. A shielding block will be placed on top of the subcritical for 100 kw operation if it is found to be necessary. Flux levels and build up of activities in the central fuel element is estimated in Appendix A. After the experiment, the lattice of the subcritical tank will be lifted out of the reactor shield and it will be stored in the water shield tank of the UFTR until the radioacitvity of the fuel elements goes below the permissible limit. A request for performing this experiment has been approved by the Atomic Energy Commission.

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123 Appendix A I. Calculation of the flux in the center line of the subcritical assembly. The general time independent one-velocity age diffusion equation for multiplying media for cylindrical coordinates is expressed as 13 3 3 2 [r — (r, Z)] + "-S. r 3r 3r 3Z 2 m (1) [r 7(r, Z)] 7^2" * (r » Z) + B m * (r » z) = ° where „2 In k« 1/ + T The solution for the flux in the center line of the cylinder is given by (Z) = C e" aZ [1 e' 2a(H " Z) ] (2) where Z = at the reactor pedestal subcritical boundary line Pf 2 2 H = extrapolated height of the subcritical assembly. Four factors of k„ were calculated by using the method outlined in Murray, "Introduction to Nuclear Engineering,'

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124 Chapter 9 and the following values were obtained: n = 1.32 f = 0.994 P = 0.876 c = 1.003 k» = 1.152 L 2 = L 2 (1-f) = 1.346 x 10 4 (.006) = 80.74 cm 2 o t =» 12 5 cm' B m 2 = 6.9 x 104 cm2 which gives a = 0.082 cm Using Eq.(2) the flux can be calculated, II. Dose from the irradiated fuel elements in the center of the subcritical assembly. The total number of fission/sec in the fuel element can be calculated by evaluating the following integral: Z = 100 -aZ p C e A I f dZ L (3)

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X 125 where [1 e(H " Z) ] term can be neglected in the above equation. C « evaluated at Z = . A = surface of the annular part of the fuel element . At reactor power level of 100 kw, 4> Q is approximately 10l0 n /cm 2 -sec, which was extrapolated from "Guide to Irradiations in the University of Florida Training Reactor" by A. R. Boynton. The integral was evaluated in this power level and the number of fissions per sec was equal to 3.32 10H. This number corresponds to 10.1 watt-sec. Irradiation for 10 hours at this power level gives a decay rate of the fuel element of 3.03 x 10-L-L Mev/sec one hour after reactor shutdown, which was obtained from Figure 3-12 of "Fundamental Aspects of Reactor Shielding" by Goldstein. Fifteen hours after shutdown of the reactor the activity goes down to 4.55 x 10i0 Mev/sec. Since the activity of the fuel element will be hottest on the lower 20 cm of the fuel element, the dose rate of 60 cm from the lower part of the fuel element was calculated for 100 kw-10 hour operation using formula (4) out of "Reactor Shielding Design Manual" by Rockwell: S R 2 v o D(Mev/cra 2 -sec) = F(6, b 2 ) 2(a + Z) and found to be 2000 mr/hr at 15 hours after reactor shutdown, or 100 mr/hr after 26 days. (4)

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126 III. Total Pu 239 build-up. 120 cm , 239 r . « _" oZ _ 2 3 : : f
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LIST OF REFERENCES 1. T. F. Parkinson and S. Salah, Proc. of ^ Conference on Neutron Thermalization , Vol. II, 337-358 (1952). 2. R. I. Schermer, "A Crystal Monochromator for Neutron Spectrometry," Ph.D. Thesis, Massachusetts Institute of Technology (1960). 3 P. B. Daitch, et al. , "CEPTR An IBM Code to Solve the P Approximation to the One-Velocity Transport Equation in Cylindrical Geometry," TID-6940 (1959). 4. H. C. Honeck, "THERM0S," BNL-5826 (September, 1961). 5 B. Carlson, C. Lee and J. Wortton, "The DSN and TDC Neutron Transport Codes," LAMS-2346 (February, 1960). 6. W. M.Elsasser, C. P. Acad, of Sci. , Paris, 202 , 1029 (1936). 7. H. Halban and P. Preiswerk, C. R. Acad of Sci . , Paris, 203_, 73 (1936). 8. D. P. Mitchell and P. N. Powers, Phys . Rev . .50, 486 (1936). 9. W. H. Zinn, Phys. Rev. 71, 752 (1947). 10. W. J. Sturm, Phys. Rev . 71, 757 (1947). 11. E. 0. Wollan and C. G. Shull, Phys. Rev . 73, 830 (1948) 12. D. G. Hurst, A. J. Pressesky and P. R. Tunnicliffe, Rev. Sci. Instr . 2J., 705 (1950). 13. G. E. Bacon, J. A. G. Smith and C. D. Whitehead, J. Sci. Instr . 27, 330 (1950). 14. W. B. Jones, Jr., Phys. Rev . 74, 364 (1948). 15. J. Rainwater and W. W. Havens, Jr., Phys. Rev . 70, 136 (1946). 16. C. H. Westcott, AECL 352 (1956). 127

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128 17. C. G. Poole, C. G. Campbell, R. G. Freemantle, Proc. of International Conference on Peaceful U ses of Atomic Energy 16, 233 (1958). "~"~~ — 18. C. B. Bigham and P. R. Tunnicliffe, AECL 1186 (1961). 19. J. B. Trice, "Preliminary Report of an Analytical Method for Measuring Neutron Spectra," APEX-408 (April, 1957). 20. R. G. Nisle, IDO 16612 (December, 1960). 21. G. N. Plass, CP 1818 (1944). 22. M. S. Nelkin, Phys. Rev . 119 , 7m (1960). 23. H. D. Brown and D. S. St. John, DP 33 (1954). 24. H, 29. 30. C. Honek, Nuc. Sci. Eng . _8, 193-202 (1960). 25. F. E. Kinard, DP 644 (1961). 26. D. T. Goldman and F. 0. Federighi, Proc. of BNL Conferon Neutron Thermalization , Vol. I, 100-116 (1962). 27. J. C. Young, et al . , Nuc. Sci. Eng . 1£, 376-399 (1964). 28. J. C. Young, et al. , Trans. Am. Nuc. Soc . _7» (November, 1*96*4 ) . J. R. Beyster, et al,, Nuc. Sci. Eng . 9_» 168-184 (1961) J. R. Roberge and V. L. Sailor, Nuc. Sci. Eng . 7, 502-504 (1960). 31. R. Sher, BNL, Private Communication (October, 1961), 32. D. J. Hughes and J. A. Harvey, BNL 325 (1955). 33. L. C. Schmid and W. P. Stenson, HW 62777 (1959). 34. C. H. Westcott, et al. , Proc. of International Confer ence on PeaceTuT~~Uses of Atomic Energy 16, 70-76 (1958). ~ *• — 35. C. H. Westcott, AECL 1101 (1960). 36. L. C. Schmid and W. P. Stenson, HW 64866 (1960).

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129 37. T. Brill and H. Lichtenberger, Phys. Rev . 7_2_, 585 (1947) 38. C. A. Anderson, "Measurement of Neutron Energy Spectra with the MIT Fast Chopper," Ph.D. Thesis, Massachusetts Institute of Technology (1961). 39. V. V. Verbinski, ORNL 3016 (1960). 40. M. L. Yeater, Neutron Physics , Academic Press, Mew York (1962). 41. R. B. Sawyer, E. 0. Wollan, S. Bernstein and K. C. Peterson, Phys. Rev . 72 , 109 (1947). Y. Ohno, T. Asami and K. Okamoto, "The JAERI Neutron Crystal Spectrometer," Pile Neutron Research in Physics , IAEA, Vienna (1962). 43. S. Bernstein, L. B. Borst, C. P. Stanford, T. E. Stephenson and J. B. Dial, Phys. Rev . 87, 487 (1952). 44. L. B. Borst and V. L. Sailor, Rev. Pci. Inst . 24,141 (1953). 45. J. E. Evans, Phillips Petroleum Company Report, IDO 16120 (1953). 46. J. M. Auclair, P. Hubert and G. Vandryes , J. phy. rad . 16, 50s (1955). 47. Y. G. Abov, Proc. of Conference on Peaceful Uses of Atomic Energy , Academy of Sciences, U.S.^.R. (1955). 48. R. Haas and F. J. Shore, Rev. Sci. Instr . 30, 17 (1959). 49. M. W. Holm, IDO 16115 (1955). 50. R. R. Spencer and J. R. Smith, Bull. Amer. Phys. Soc . , Ser. II 4_. 245 (1959). 51. D. A. O'Connor and J. Sosnowski, Acta Cryst . 14, 292 (1961). 52. H. J. Hay, AERE Report, R 2982 (1959).

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130 53. K. Blinowski, "Neutron-Diffraction Investigations of Solids at the EWA Reactor," Pile Neutron Research in Physics , IAEA, Vienna (19"6T71 54. R. W. James, The Optical Principles of the Diffraction of X-rays , G. Bell and Sons, Ltd. (1949). 55. L. B. Borst, et al . , Phys. Rev . 70, 108 (1946). 56. B. M. Rustad, J. T. Wajima and E. Melkonian, Bull . Amer. Phys. Soc . , Ser. II 4, 245 (1959). 57. B. M. Brockhouse, Rev. Sci. Inst . 3 0, 136 (1959). 58. W. Sollar, Phys. Rev. 24, 158 (1924). 59. Theodore Rockwell III, Reactor Shielding Design Manual , McGraw-Hill Book Co., Inc. (1956). 60. V. L. Sailor, et al . , Rev. Sci. Instr . 27 (1956). 61. E. Fermi and W. H. Zinn, Phys. Rev . 71, 666 (1947). 62. D. J. Hughes, Pile Neutron Research , Addison-Wesley Publishing Co., Inc., Cambridge, Massachusetts (1953). 63. M. T. Burgy, G. R. Ringo , and D. J. Hughes, Phys. Rev . 84, 1160 (1951). 64. E. G. Joki, J. E. Evans, and J. R. Smith, IDO 16356 (1956). 65. R. B. Razminas , "Temperature Coefficients of D 2 0Moderated Systems," Unpublished University of Florida Master's Thesis (1962). 66. A. R. Boynton, "Guide for Irradiations in the University of Florida Training Reactor," Florida Engineering and Industrial Experiment Station Leaflet No. 139 (July, 1961). 67. S. Salah and B. U. B. Sarma, "Integral Spectrum Measurements," Memorandum to T. F. Parkinson, University of Florida, January 18, 1963. 68. P. S. Brown, et al,, NYO 10205 (1962).

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131 69. W. H. Walker, C. H. Wescott, and T. K. Alexander, Can. J. Phys . 3^ (1960). 70. N. J. Pattenden and A. H. Baston, AERE Report NP/R, 2251 (1957). 71. M. Renninger, Zeit. fur Phys . 106 , 141 (1937). 72. V. I. Mostovoi, et al., Proc. of BNL Conference on Neutron ThermalTzation Vol II, mi-4 36 (. ± ^ b /? > . 73. F. W. Sears, An Introduction to Thermodynamics t The Kinetic Theory of Gases, and Statistical Mechanics , Addison-Wesley Publishing Co., Cambridge, Mass., 2nd Ed. (1953). 74. W. J. Sturm, ANL 6410 (1961). 75. E. R. Cohn, Proc. of International Conference on Peaceful Uses of Atomic Energy 5. 40b (19bb). 76. E. Johansson, E. Lampa and N. G. Gjostrand, Arkiv for Fysik , Vol. 18, No. 36 (1960). 77. K. Burkhart and W. Reichardt, Proc. of B NL Conference on Neutron Thermalization, Vol. II, aia-3^29 (1962) 78. C. A. Thompson, "Neutron Flux Calculations for a Graphite Modulated Twenty Per Cent Enriched Reactor," Unpublished University of Florida Master's Thesis (1961). 79. J. C. Peak, I. Kaplan and T. J. Thompson, NYO 10204 (1962). 80. T. J. Thompson, I. Kaplan and A. E. Profio, NYO 9658 (September, 1961). 81. R. G. Cockrell, "A Description of the UF-NLLS University of Florida Non-Linear Least Squares Code," unpublished paper submitted to P. E. Uhrig, Head of the Department of Nuclear Engineering, University of Florida (August, 1963).

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BIOGRAPHICAL SKETCH Sagid Salah was born in Seoul, Korea, on September 2, 1932, of Turkish parents. He attended Seoul American School for two years, but his secondary education was interrupted by the outbreak of the Korean War in 1950, when he was captured and held prisoner in North Korea for four years. After his release from prison camp, he immigrated to the United States and attended Gainesville High School in Gainesville, Florida, for one semester, after which he entered the University of Florida in February, 19 55. On August 9, 195 8, he received the Bachelor of Chemical Engineering. Immediately after his graduation, he enrolled in the Graduate School of the University of Florida, and received the degree of Master of Science in Engineering on January 30, 1960. Following this, he pursued his studies toward the Ph.D. degree in Nuclear Engineering. He has held a graduate assistantship in the Department of Nuclear Engineering for the major portion of his graduate studies. The author became a naturalized American citizen on October 6, 1959. He is a member of Sigma Tau and the Student Branch of the American Nuclear Society. 132

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This dissertation was prepared under the direction of the chairman of the candidate's supervisory committee and has been approved by all members of that committee. It was submitted to the Dean of the College of Engineering and to the Graduate Council, and was approved as partial fulfillment of the requirements for the degree of Doctor of Philosophy. December 19, 1964 Dean, College of Engineering Dean, Graduate School Supervisory Committee: / // C^T/^vv-^, Chairman J ,g..Q^A c t^JU^. $A. (ilJLL

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