or PEC

BRILLO UI N SPECT RO SCO PICSTUD I ES OF TilEORIENTATIO NALLY DISORDEREDPHASEOFC2 F.

Ily

€)Cordon ToddAn(lrcwlI II.Sl~.(!lOlLlI.) ,MemorialUnive rsity

o r

Newfoundland

A THESIS SUBMITTED TO THESCHOOLOF GRADUATE STUDIESIN PARTIAL FULFILLf,f ENT OF THE

REQUIREMENTSFOR THE DEGREE OF MASTER OFSCIENCE

DEPARTMENTOF PHYSICS MEMORIALUNIVERSITYOF NEWFOUNDLAND

JULY1992

ST.JOli N'S NEW FOUNDLAND

1+1

NatiooalLibfary

ctce-ece

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"'--

=.ar.a-o

[)ifec:liondes 3CQ!jsil ioo$Cl desservicesbibliographiqu(ls

...

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~~

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natlon ale du Canada de reproduire,preter,distribu erou vendre descopl esde sa

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de quelqu e menlere et BOUS quelque for me que ce soit pour mettredes exemplai res de cette these

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L'auteur conservela prcpr fetedu droit d'auteur qui protege sa these. Nila thesenides exlraits substant iels de celle-ci ne doivent etre lmpri rnes ou autre ment reproduits sans son autorlsatlon.

Canada

Abslrncl

Theclastic ron, l1InhamidAllla.0I)lir rot-llir wnlrll.li!... urtil" t1rk'1I1aliollallJ.Iill- ord ered,a-phase orC2F,hA\'{'l)('l'll dt'lc'Tlllinc'tlllliill& LIM'1t'f'llIIiCllll'orhiF,hTl'l<l llul itlll Brillouinspectroscopy,JUMtbelowthelriplt'po in t,AtIii!)h".till'value-s

t1r

till'(,laHlic' constants(in unitsofkbl'lr )are:

(.'11 26.9!J ± 0.IO,

en

U1.32±0.IO,

C4 '1 ,\..1'\±O.OI.

The clasto-opt ic coefficientrat ioHat.IemJ\'l\rc~

1'11h 11l I.O!J± O.O!I, ,'," h' ll = 0.11±0.111.

theranr;e169h"10144.K,Gil"IulCnIIp pl'aTto have liuraTt"u1Iwralll rr .1"...·",I.'Iu·,....

withtJ.Cn!tJ.T=-0.335::1:0.010kbar!h",andtJ.Cn ! tJ.'J'=-O.1:lfi ± O.lJIOJ.-/w,r!/;'.

0.005±0.011J.·bn.r!K.

ValuesortherAtiO!!orlLCOllll1kvclodti C!linhi~h"ynull....ry.lirl'f'liollHintill'ny"' talindicatencarperfectc11111tiC isot ro pyandthat1I1I1.l,·I·IIII·lyIIlTIJII~tlJtllli"1I·1rlUlIiI/llillti couplingispresentillp·C~ Fo.TIll:exte rnof theCflup1iltlo:i~oftl,,·Oft/I'l'of1\I;d.o!lsl'rw,1 inplastic(ClhCNh.Thill ill inCOlllrlL~ttothl"!IItl'llr.lurllllylliltlila T uri" nliltio lllllly

.!i ".

ord e redphaseofS'Fo,whichbclll\w~elasticallyli k.~ararl~galol s..lie],

Acknowledgem ents

1wishto llmllkIllysli llcrvis(Jr.~,Dr. II.I,id te ami Dr.~LI.Cloutcr,for sharing withlIIellldr ,:xp l!rl iscillt.ll.lIieklof ligllLscall er ingand fortheirskilfuldirectionofmy

(would lik<'10 exprel\smygrat it ude toMr.It.Dnranowskiforhis heir intiletype- sl·Uiugoft.his1IIl~sis,Mr. W.Iiollyforproviding a con1inuous supplyofliquidnitrogen, Mr.Ii.GIll'lllfor thedrll.rlingof sevum lfiguresan dMr.R.Bradleyfor printsorseveral Ilhot.o).!,raphs.

Iwouldalso Iik('tothaukmyIamily who havealwaysencouragedme 10pursue my

Wliill!1'111;;'/!;1'11 illthis\\'orkIwassupported b)'IIMemorialUniversityGraduate I'H lowlIhipwhich1grat.dllllyackno wledge.

Table ofConte nts

Abst ract Acknowledgements List of Tables Listof Figures 1 Introduction

1.1 Orlonte tlonalDisorderandH(lt il.l ion-Trall HI I~liul\{:ulIplingin1\\(,lt,t'"lilr Solids

1.2 StructureandPhasesof C1FG. 1.3 Disorder and Dyunmlcs ofC2Fa .. . 2 Theory

2.1 nl'illuu in Scattering . 2.2 Acoust icWaves andE1a..~t icCOllSliUlls 2.3 Elesto-op ticCcefllcicntsorCubicCr)'slals

3 Experimental 3.1 Experimental Setup... 3.2 Cryostat. . .

3.3 Temperat ureSCll~jllgand Control..

iii vi

vii

III

"'

I:!

I.';

11

I.

:10

a.7 I."Sf!r. 2;

:I.!J 1)~ llj.A"flll i ~ it i oll111101SlahiJi~ a1 i fJllSy~t'~JI\ 29

a.HIOpl.i ,~nlSy~lf'll1 AJigllll ll~ lIl. • 30

a.ll HrillouillSpt!dra 31

" It es utte 35

,1.1 IIrillouill Shin smlf lllll" lI si l.if'~. .. . . .... . . 35

·1.2 1':J~~~ti(:Cnlll'itanis 38

.r.a

Elllsto.npt if!Ccctflclcnt s 43

14

,'; Discu ss ion 45

rJ.i U(' !<UltfirorC, Fo 45

1".2 (:(II11 par b ontofJt llf'rUricnt a tionallyDisord eredMolecu larSolids 46

References

51

53

Listof Tables

1.1 Ra tio s ofacousticvelocitiesillhi~hsyn m1l'I,'y direct ionsfil l'""ri'l"';lH' I!W- ular solidsnca rtlu-lrtriph-po illh..

01.1 Brillouin»cattcriug datu fnr/1-(.'1/';,atJ(j!}1\' , 4.2 Dl'illouin"clIlterin!;dntaforp-C 1/';iaI,HiOI,' . 4.3 Brillouinscattering dill-IIforil-(.'l/·;1itl,IH/\' . , 4..1Temperat uredep l'lItle'nt,1111" IorP-['l/·;"

·!. 5 Eluxto-op tic ra t iosHUl!fCK,[fki l'ulsfurfj.(,'l/·;~' 4.6 Atlia billicuulk modulus andi\UillOl,l'Opyfad,urforJ~-( '1J':1- 5.1 Tompcrat.uredepende nceofri\tio.~

or

ucnust.ir-Vl'lociti .,sinIli~l l»ymua-try

directionsfor{J-C1/'f;' .

5.2 Ratios ofacoustic velocities inhigh Hyn lllll'try,lir"('l iull!cfurSI'VC'l'illllll,l,'I"

111.'1\'solidsIIClIl'theirtrilJlf~points..

:Ii

·Hi

17

List ofFigures

:1.1 TherOHlpl,·jc·,~xrll'rill lf'lIl.ulse-lup forBrillouin~call('rillgexperime nts011

:1.2 Tile cryostat tail soctio n. . .. :l.:f L:uU'diffrac tiollphotograph ofcr)'!ital#:1..

:u

Alh illollill sl,ic'kspectrumsJlowingtheHa.rl {·ighpeaks(U)<Iudthevarious HrilloninC'llll lpOlWIIl!c(1'.,'12andJ..)•••

'1.1 Atypical Brillouin»pcerrurnoffi-C2F'o.•.

-1.2 AJiabllt ic clas uclTIllSll\lIbof jJ·G'2f:1AS1\functi onoftcrnp cret ur e. The 11lll'l'r l ain l i,..s MI'approximately the sizeofthesymbols. . ..

vii

II

'I

'"

3·1 36

Cha pte r 1

Int r od uction

1.1 Or-ientetioual Disor de r andRotnt.ion-Trnnalnt.i c nCoup ling in Molecular Solids

In thepast Iewyl'nrHthen-IWH heeu lilliI'll1,IIt~ll'l'liC'alHIIIIt'Xpl'l'illl" 1I11l1illll 'n·s!.ill orluntationallydlsordercdsolids[1\,12].SII.;:!LsolidsHI'I'rh llrlH'h'riz"'1

" r

ltlll~nUlAI'lm lls' lntionalorder[nlthoughindividuelruok'rnlaro-uterofIlliWS,lis p lilf·"IlWII(.sllll"u tfix,',]

la tt icesitesmaybelarge ) alltlllloll'(;ularori"llln l.ilJllnl ,lisflnlt ,r.orpllrlirula ri\ll t,rt'lll,ill thesesolidsisthe couplingbctwrenthcrolaliullltlnUt[lnlllslllli tl IW] IIlUI" I'llIM111l11iulls.

Thiscouplingisa. wellknown phenomenoninl1ln[t'f:Uhlr litill i lis\:11, hutinlJl"II~'1I1ar solidsitseflcctsarconlyrecentlyheing uuderstood.Uolat iu lH l'llll stnl.iuliI'CJllplillP;, liSil is known,maybe thought

or

asarisi ng{romthl'rllllllW'illnrit'lIt llt io nnlput ,'nli;ll,hwtil tilelocal straininducedby1\pho non

1'1]

or,allc'rllflt ivdy,liS 11 nmplilll;Iw l.wl "'1Itilt'hy- drcdynamicanisot ro pyt11~n~ityandthostrain~dll[!'ilorsil1lply,till 'illt,'rad,i " n1,,'I..v'~'l1 therot ation alandtra nslat ionaldegreesofffl'('(]CIlI.(lualila lil'd y,ii, isc',lsytoil wl ~irw lhat anychango inmolecularl'ul,an ollallllol.inllwillpPrllll'hmill,illIIIHUy niSI'S, II,IIIII"'U (or softe n)thetraualution al mot.ionof the1lIoll'Cll lc.'S,COIISf'IIIlI'nl,ly,ti lis f'llll jlJill .l;is"rt l'lI strongenoughtoalterthell1\l ureorthet'ollf:diw',':uili ,l.illlls

u r

1111's"lirl.

An ext e nsiverevie wofthelit l'r alul'(!1l11ro uuiou- tr nuslationClI lljJl i llgtnayIIf'rrlllll,1ill refe renc e[G].Manylc clmiq ul,'shavehl,('UlIsc~l losludyrot atill1l,l.rlLllslllt11111ill1l1l,!f'('rI!M

soli,kTIll'llIustrcnununilldllllf~nmh-rular-dynamic scomputer simulationsandthe 1.I:dlll iqll'~(If1I"ul UJIINI'1l11 1~rillK'IIIitd dit ion,110WI'VI'l",lightscatteringhas alsobeenIIS1.'d toiltVI"Sl.i~i1tl't.hixi'llI~nUIllI'lIfJllinoril'lItalio !iilllydisordered solids.Brillou in scatteri ng

"lq ...riuu'ulllIJIl lJlI'11i.~onll'l'(~1pltases ofSf,:,[i),ClJr.l[8J,CC/~I!I].cyclooctaneand ()~[tu]ill til isInl",ral,ory aswellas11",Jliolll~'ringwork ofBan dand Sl.oichelfonCII~

111,,1

c n

_l[I 1]IUlvl.'1~lJl llril)llt,'(1signilkillllirto au1I1L1lerstllll(lingofthisronpllnginthese soli,k

IIIuri,'nl,al.iullall yIlisurl ll'f(~1solil!.",rotution-trnnslatiou coupling maybe' observed asu Ih'ffl'iL"C 'ill(or snftl'lling

00

aeousticphcuou frl'flul' l1ck'S.'I'he transversee.coustlc IlhollOliS111"1'1,.~PI '(' i illlyslIsl"'pl ihletot'Ollplillgtorolil1iulialmotions. A quantltatlve 1I11'aSlll1~orthel'xll'lltorthis coupling is providedbythedensity-Independentratiosor a(,()lIstil~V/'Iu.itil'llillhighs)'I11111l'lrydirectionsilltile crysta l, nam elyVi./VT,andVL/VTl [wher eI"'f'l iUIlI'I'::correspond 10I.hl~longitud ina l,theslowand thefllsltransve rse ar ollst klILolll'S,rl'Spl~~th'dy),whichmaybecalcu lated ouco thec1a.stic constantsofthe solidlm\'c l)l'f'llIld l' r milll-<1 \11).These acoust ic velocit y ratios for various molecular t'r)'s1.al!!llrt·gh'l'll illTahle1.1.along with thoseforthe raregas solids. Thevalu es for 1I11'raregas solidsSt'r\'(' ;,sitzerorot ation-translat joncouplingreferen cebeca usetheyare lI1(lI1l\lumiraudt!lllSillII1111'lIdl'ul or rol at ious .Therefore,ratios for a simplemolecu lar sulid(urcubic S,\'I1l11l('l.ry)whicharc significauHygreater thanthe corresponding ra tios fortlu- 1',,1'('/o\llS solilillronldludkatoIhat soure degree ofrotation-translationcoupli ng

'l'hc[irstHrllloulnsr'ltkrilLgcvktcucc of acoustic modesofteningwas notedbyHand

ll1111}ituid lt'!rII

II

\\'110 I1lt'lISIIIl'<10111anomalously largemineof~·i.IVTIillthe<110

>

directionin bothClJ~andCD~(Sl.'CTable1.1)1I11dCOll~l'II\U'llllrnttrihnh'llittorotutlon- translat ioncou pling. Theth('Owlir al cak ullliiolillofWOHllt'lwrgl'f~u\llllii llt'f[121,whil'h assumed a Leonard -Jones type Inrcrncnonbotwoeumclrc ulrs,lnterronfh-nn-rltln-roh-o[

rotation-t ra nsla t ioncouplinginreducing trans verse arcust k-phcuourl'l~IIl"IWil'llill ('Il.., In addition, this theo ryalsoyieldedvtlhlt'llfo tthedaslit'fOllstllll!,Sl\m!.'!lll<tit"illlisulttl[J)' whichwereingoodagreem ent withthoseobtainedIroruexpeeiuu-ut[151.

Table1.1:Ratiosof acou sticvelocitiesinhighayunuc l.ry tlil'toctiollsfurImi llusmohx-ulur solids near thei r triple points.

SOLID <100> <III> <IIII> <110>

Vt./V1',1' VdVl' ,l' Vdl"/" Vt./VT Nc,A,',

u-»:«

(13] 1.014 2,:H l,fi:, ~.71

CJI..,CD4[II } 1..17 2.,1(j 1.70 :1.2:1

cn-,

(8] ].66 2.7-1 Ui7 :\.'i"l

CCI, [.} 1.7!) a.07 2.111 4.10

(C/l ,C N ), [J'1 2,7!1 2.60 2.71i 2.M

C!1f16(ClJdoor./fIllC)[10) :t~ !J 3,:15 :1.-18 :I,2!>

0, 1;01'

a.07 :I.Oll :I,ll7 :1.111

crelorientationallydisorderedvan tierWaals solids. Brillouin!!m ll"r ill/l;"lI l't~rilllt~lIl,!I ontheoricntatiouallydisorderedphaseof(.'/J I·.1IS]h~IV"Iouuds;gl!iliralltly sIIft.'m"'!

transversephonons illthe<111>uut]t'speciall yt1w<110>dil"td iUII111';11"'f'"='0, indica tiveof rota tio n- t ransla lio/lcoupling.Neutron,';(~lil,1.t~rillgexpel'ill~'lIL"lOil (.'11,'"[l

ti l

also suggesteda strongrctatlon-trausla tlouCOIlI,lillgnearIf

=

^Il,Tltf,Sf~r<~1l1tsW('I"tlIIllt consist ent whhmolec ular dynamics Silll1l1a!i o lls oftill'ol'i'~lll.lLl;flllllltydistlnl'~rI",1I,ll;,st·

ofCBr4{17}wherenoro t at lon-tmnslatkm cOlJpliug was]If('flidf~dill Ibisrl'~iwl.

0...:.. f 111':lIw,sl"x l l1:lIl'!I:XiLlIIJ1Ie;,lodate,01ancrientetiouallydisorderedsolid

"xllil,ili n,ll; sofl"]I'<I tr" nsvc fS('phononIrcqncneics,iiithecuhie phMCIa ofCCI4•Liglu ,....';luI:ringeXl'f:rimellL'lI!J]allthill phase yielded eeeust!c \"Ciocilyratioswhich were 40%

lOlI.1 10%l.iglJl:rlimn lhr torrt'5fJOllding ral iosfor the fluegas solidsinthe<111>

illlIl<110>di!"f.-OC l io lill. tclfllcc l.ivd y.Ro t at ion-transla t ion coupling,infact.isSOstrong ill(.'(;[41Iial ilishdil~\'I'f110be f"e;fJOllsihlcfor the metastabililyofphaseIa, This

iu..lltslJflJilily was alsoIJrNlid ,l:(1 in till' ruolccul ardynamics lIimu la li onsofMc Do n~1rld ul.[IHIallliwlt..'1IlU rihnt f'fl loII.st mng da1nllillgof'IIow<110>transverse phc n one.

Hrllluuin lIfill.ll'l"illginvestlgntlons

o r

theorlcntatlonallydisordered phasesof cyclooc- Inlll'[ llIl.O2[lu],fllldlightllcnll cl"ing expe riments011(CI/2CNh[19)have foundnear I'I~rfl!f:'lr-lwdici.o;u1.rflI'Yll('ilrtheir respectivetriplepoints and highra tiosofacousticvcloc- iti.'!I innllthn"l 'high symm et ry dlrecucus<100>,<III>and<110>.In the case of (")"("1(1'..-1.<11.1' alltlO2,lhe above fea t ul'CSwereconsist entwithstron/; rota t ion-tr an sla t ion mllplillt!:. A lhro ry developedbyCourtcllll[5) for(CIl_2CNh,whichincludedcouplingof mul,oclliarn'Orit'1I1at toUl\lmotiolilotransverseacoustic phono ns ,WI\Sin excellentagree- 11...111.withtlll't·xpc rin ll"l1laII'Cll LlII.lf.

TI••'lIOfl.l:·llillp;ofaruulIlk I,ho llon fl'('(jueuc"icsmayalso l'Cltu ltin decreasedrnedlan ical lIl.111i1il)'oflht' ,;ol idand a("orn'lfpon d ingdecreaseinthehlJrnrc1;u;lic constant slISan Mclt'r-disurdt'" phaserrnn-drionisapproached .Thereleva ntthl.'Oryforio nicruoleculer

"n lills haslnx-ndt,\,d opt'c1 ma inlyby~Ikhdand Nnuclls[20),[21),[221.The inter- mohvuhn- inll 'l'1lf' t ion isIlf":l('ri bClI hya Born-M ayerre puls ive overla p poten ti al andthe 1I11ll1il1011irU1illd ll(!('s ho lh1,1"1I!1lflllt ion nl androtationaldegreesoffree domaswellasn.

l'ollplil1~ht'll\'('I'1IIlwsl'motions.11(,1'('.IIvnuishlng valueofshea rela st icconst a ntC~~

was predictednca r thest.ruct.ur al phnsetrunsh.ions oflht'sl' solids.Thiswasillngrt't'llll'Il1 withbuthne ut ron[23JandBrillo uinsCIlUt'ring(:z-Ijstwlit'Sus\\",,11 asultrnsonir- uwa- surcrncnt s 125/.IIIparticular , softening of t'1<lst,icroustnntC_I_.wnsUhSl't\-I,d illBrillou in [26J andinelasticneutronscettcriug[23)ofKGNilSil,Il IJltasl'f.nmsitlouwusillJpn'jldw<l fromabove.

1.2 Str uc t u re andPhasesofC2FIl

The hcxasubsti tuted cth aucs(C2.\1i'whoreX isu.Illllngt' n)I"ompri!«·udll.~sufl<ol ids allof whichexhibit an oricntationallyIlisor<!c'rcilplustlcph asl' ll('t,\\'l't'tIthe-irtlldLill~

point sandlow temperatureIJha!ll'~ 'Que ofLht' llll'lIllll'rsof thisdaslIislIH'hi~llt,'I1\- perat ure phaseofhexafluorcct hnne«(.'2/'6)'

The oricntntlonelly diso rde red~-lI lli1seofU2/;"exists1It'IIIIVllw tripll'point,uf17:1.1 J([2i},The crystalstruct ureis body-centered cubic wlthIltOlts:ll lt'soflIynlllll 'l.r y

;j ,,,

occupying sit e'S of symmetry111:1111illthecubicIlalliC(~ [2~J.'I'h{~I'xistt!lII'(' ofIItmllsil.io lt toalow temperaturea-ph ase at 10-1K was iudientc dlJyheat c'll[Jad l,y(Jilt"(27)IlSWI,II

a.:'Imeasurementsof NMR lincwldt h[2!lj anllllie litvibrnj.iouulspI~rtl'a[:lOI. X-ray

diffractiondataat8.1J([30Jindicate tlmtthc low tempern l.urepltiIS" 1t00S ttllUllwli/lic' st ru cturewithspacegroupP2a/m.TheX-raydilfrflct ioll rl'SultsalsosllgW'lillhat then'

is disorderin the a-phaseofthe stalistiraltypcsilll':c'only afe w(li~cn'1.,~,Jilfrlld iulls]lo ts

wereobserved. Thiswassubstantlatnd hyKolde r.l«f. [alJ whoul~,sll,l;w·s!A·dtb'll.

the re remainsdisorderconcerning1II0]cI:11]at'erieuta tionillI.IwluI\'tl;tltJ H' mt11 Tt ~pI11lSI"

Neutron diffraction experiments conductedbyPowell(./«i. {2fi],!l(jW{~\-('l',sllowlila!.

powder profilesobtained at9.jJ(lindIJOKan!qualitativelysimllnriIlIIJtl'i,'_llClll,1-;11'

1.11';IUlo"'f'd011tl"~I)/I."i~flra body-centeredcubic~truct'lr"_Thelowtemperature profiles O.lJrlfltIICimlf'xr.1011thehllSisofthelIIonoclinic spacegoUf.lsuggest.edbytheX-ray

~tudic:l.IIIadJir.ioll, thcyJcuud thaL"sluMi:-hstructuraltralI5ition hqins.t70Kand

IM:l1Ii~lII lo40Kand.Ullthoth0andfJplJaSC!llcoexistinthistemperaturerange.

More recent.neutronJIClI.ttl!rin«experiments[321indicatethallistructural phaserren- .~iti(JndOl'MoccurIwtWl!("u91gllucll 17K.Thelowtemperat uredataarecurrently!>dn g llllalyzl.·d in11Ildrorttcdeterminetilestructureof thelowtemperaturec-phese. There i~dearlyKlillSOllll~confusionaboutthephasetrau5itionlempcraturc(s).

1.3 Disord erandDynami csof C2Fll

Arnmliug toIUok:culardynamicssimulationscalculALions,theoriginofthe disorder ill(#-C,F.illtll"ofold1:131.[3-1).ThemolcculllrlIYmmetryislowerthanthesite symme- try whichJeatlftt.o sl.,tiliLicaldisorderin tile orienlltionsoftheC-Cbonds.Since, IlOlI'ever,the

f .

franlcw1)rkisnearlyoctahedral, themolecularsymmetry is almost lhl t

lJr

lire ftite.andprtolirllillo\rysimulationsofdifferenlmodelsofC,F,{:J3l,[:WI indicate Lllat oril.'1IWiollalrn.~lrMwnexistsASinSF,\a5I.(36],[3iJ,The molecularstructureof Ctf.isshowninFigure1.1.InSF"whentheS - Fbondsarc ali!Dedalongthecubic

ill( £'!t,t1wOCill'5tIlrighbollrinkrac1.ionsarcaUrACth"ewhilethenextnearest neighbour

inLctactiOllSAll'repulsive.Thisgi\'('!1risetorompeLinl; intermolecularorienLationaiin·

k'radiall sknown Morirnlllliolllll frustration.Thesimulationssuggesttbat omnt ational frustrationisi\siglliliCIIlltrl~lltlln'illC1Foandlha.Lmanypropertiesofthe orientationally llisnnlt·u·t! pllllS('^fIl'f'rcl;lh~110thedyuarnlcs oftheapproximateFeoctahedra (ra.ther thantIll'di-onh-ruflhl'C -Coou(15) lindarethusverysimilartothe ccrreeponding

Infllrmhtionl:OlJc(~rlliugthe singlemoleculeIllotion!!'inC2F"lias been obta inedfrom theC-f' hone!IIri("lIla tiondistrihulioufunction dclcrnlincdbyPowell d61.[281al U:IIIJHTl lutefof110Kand951\.Thisfund ionindicatr&thatalthoughtheftuorinC!l ere predomina ntly locali1.l-donthe crysllli axes,thedistributio naboutthese directionsis Vt~ry1,1'0<...11 withaliigllilic'.Antprohahilityforthe Jluorinestobeoff axis.Thisdistribution is Cjualilativelyliirnilnr (0dlatforSF/I(381.wllichalsoexhibitsbroadmaxima in the

<100 >dirceLiuns.In(11I~r.JlSCoCSFa^.11.(!lG.5K,the overallCormofthebond orlentatlo n distribution Iuuct louIYIUIIIttrilm t<,dtolargeamplitude molecularlibrationsAbout the cllhicillU'lIamIsuhslnlltialth(:rn",1reorientation.Thismay11.)50be the caseCorC2Fa nllhollgh motionsmore akin torot atlonaldlflnsion1\II(I/ orlowfrequencyreorientation

Molcculardyuamicllsimulations also predictthatthecollective dynamicsofC2FGarc verysimihu1.0thO!lCofplilllt icSF.(33]. \301].Inpar ticula r.itissuggested tbat rotation- trAnlllAtionCOUI)lingillC2F.willbest rongest atq=0and droptoeero atthe Brillouin

1.0 11('boundary.parAllcltingthe simulationresultsCorSF•.Neutron diffract ionexperi- mentllIlavcshownthAtcorrela tio ns betweentranslationaland rota.tional displacements illG', Poareillllwrlallt(281.nrillouinscatla- ingcxperi mmlsonSFe(71.however.show

110(allomalous modesoCtening) evidence for strong rotation·translation coupling near q=O.

Ith.'UI)n 'CllsuggestedhyKokletIal.[31)thatdisordercall be:acquiredat the:0 ....{J

pIHlSI~transitio nby internalrct ntlouof oneCF3group withrespectto the other.They

nlsallt.lll(' thCltillthehigh tem peratur e phasethemolcculneaxis (the centra lC - C bond]euus paralleltoth('Iour bcdy-diegcneleinII.randomC...ehion and thattheinternal

axis begintobeIullyexcited.Intht'lowh'llI lK'1'atUrt'l'h a1l<'tllt'...•IIIUliUlli'lart·I 'i'I-....nlla ll,.

frozen-in[3 l).

In orderto(,XI'II11111(' 1I1crutAliull·trall~Ialillllruuplilljl;1II,'C'h"n ismill("1f~;\11,1.ill particular,lomakea,\uallt ilAti w oolllpnr illolltoSf';,.itillillillOrltl1llllmliii'!,·jili'!lil·

constantsbe dctcnnlncd.'rhisIla.~bl'l.·11dOlle , ill lh,'Pfl'l'Clilwork,usillgIh"I" d lllillllC' or highresolution Drillouinspectroscopy,1\ lIowkdgcoftill'1'1;U\lk('(JUllt"IIIK"lIl1wKfor calculationofthe,1'·ll111ty·in<1C'pl'u<!Clltratiosorn('{lll11l,k\'l'!uc1ti,'sill highsyllll11l'1,r)' directionsintheerystal.Comparoouorthc~(.','lll,iosforCl f-;\withthllS!'

Ilr

nllll'fotlentu- tionallydisorderedsolids(ill pa r tkulilfSJ'~I)provkle,iufonuauonrllll'·'·fIIill~till' IIlltllfl' andexten torthe roterion-translation('Quillingdft~dill/1'( .'11':,.

Chapt e r 2

Th eor y

2.1 Brilloui n Scatte r iug

ItillwdlknowlI tllatatlcmpcratum<!greater lIulil alJ!lOlutczerothemolec ul esinII.

crys t....l arc:illl:Olllll.1Ut therma l merion.Collectively,these motions resultinprop ltga t ing la ltiC'l~\\'aWlIwhlrh,forwlwdc~l1l'tthllmuchgrea ter tha n the unit cel lside,arc acoustic nKKlc'll.Till:lncl...~ticscaltcrilll'toflightby such llwrma Jly gener a ted \\'A\"CS isknow n as Ilrillouin sCfl,lkr inp;.

TIll' l!woryof Brillou inscatt ering incubiccrystalshasbeendiscussedindetailby n"u('(l('kamiI·'ritllc!l13!J].Th...yhavej;llOWIIthattheIrequcucyofthescatteredlight,w"

illslliflc'(lfromthatoftheind clentlight.^Wi,accordingto

w.=w;±w... (2.1)

wh('f(' UlI'W..= ...

{¥l

arc theangularIrcq uc nelcs orthethree acoust icmodes with 1,\'a\ ,:\,'("1or

. i

I\utlc1iffC'rcu t poll\ri7.ationscorf'l."SlJOlulingtothree modes p.

=

L,TI,Tr-

!'illlongwa\'l'ic'np;lhIlfOulllk modes,WI'islinearinqtol\very go odApproxi ma t io n.

Thc·c lilllll·rllicm rl,llltifll1isthon

(2.2) 10

scatteringprecess1.11('1"('isvery lltt]odilfl'rl'IlCt'1>('1.11'1'\.'111111' l1Hll\llillltl('llftlw\\"lI\'('Wdut oftheincide ntlight,~'iandtILlltof tlH.'M'illicrt'(llight,~'. ,Th i~illIlt'nlllt<t'tlu- phllllllll (i1COllsticwave)e-nergy ismuchkssthanthat of lh,'photon. 11" 111'"1111'wnvevertor

Figure2.1:HrllloulnSClllt('rillggmll\f'I,I'Y.

triangle inFigure 2,1is no...rlyisoscl'!<'1I1\1Idit is evidl'utUliLl

wherenis the index ofrefraction oflh(~mediumIwing pru!J(·tlllnl! n ist.l",st·a1.tt,till~

angle.

Substitutionof equations(2.2)and(2.:1) intoequatlou(~.l)1I11'1Iyid /ls

(2.'11

wherek..has been replacedby w;/candcistlu-"(1('\.·(1ofligllL.E'llJlllic/Il(2..1)i"thewI,1I

11

COUSf'fjucntl y,Ior~illgrf~eeystnls,thf('CBriJIouiucompone ntscorrespond ing toII=L ((IIIIu~ilc)llJ;illlflill1lll,'Ii(slllwqnasitrnnaver sc],and'/~(fast(IUasitr,IlIS\'CfSC) arc generally l!)CPp(:t.f~d .TIlf'Yarc fJl,Sf'f \'Cc!asilpamldowlllShi rlf~dpeakslo catedsymmetricallyabout UI'~Illlyl,·ighIJI'I,kattill!incidentlasf'rFrequency .

2.2 Acou s ti c'wav esnndElasticConsta nts

'1'111' ilf:O(Jsl kW,lW':!whichpropa g a tein erystalliucsolidshave wavelengthsmuch gn'alt'rthan tilt!illlcl'IllOlecuh\rspacingsalit! tucrcforc,illdescribingthemotionofthese waves,U,CcrYlflallllaybetreated M all clasticcontinu um .Accordingly,theequations or motlouofthesowavosnro [·10]

(2.5) wlwtl~Jlislilt'density,Iiisthedisplacementvector ,

r =

Xiiiisthe positionvectorand the C,jklart-the ('Instil'constants.TheCijklforma tensor of rank Iour. Symmetryproperties oflilt'I,(!IISOI'reduce tilenumber or independentclementsfrcm81 to21. Thetensor may tlu-uhe \\,rlU(' 1Iill ma t rixCon n lIyred ucingthenumberorsubscrip tsfrom 4 to 2 using tllf' etendnrd notationofVoigt, Inthe case of a systemwithcubicsymmet ry,such as Ill('lI-phllSt·

o r

hexalluoroctham-,thehighsymmetry

or

thelattice furthe rreduces the 1I11l 1l!l('r(Ift'lal'lticronstnntsto three,nRlIK·I}'CII,Cl2 andC4..,and thematrixof clastic

12

ronsteurebecomes[oJIJ:

C'1lC_{Il Cl~} 0

en

('" Cl 2 0

en c.., ell

0

0 (.'u II

0 ('~~ II

(2.6)

o

(.'~I

To solvethe equation of nmtlon,(2..':il.11111111'wnwlIu\uliuliliofII..•fo r m

12·7)

lire assumed where ".,;i~t1U! lllllllli11l1l1-·. Suhst illllillg (2.;)illlu "' IHaliull(2.!1)111111 per fo rming thellec~Si\ryclilfl·t elllill i io lls yi"\l lliIllC1If'CIlI"r('(l" atioll

wavele ngth acousticwav es .Forllonl rh'i,,1 MJlulicJlil'l i1 illIIC'nx si.rylhal

(2.!1)

wherefor cuhiccrystals,

(2.111)

t;xI'Jid1.ly,e(1l1alilJll(2.9)t]WII bec omes,

I

(ell-CH )(JI+,\ (e12

+

GU)(Jif/2

(en+(.'4·J)(MI (Cll- (,'44 M + ,\

((:12

+

(,'H)((:II/l (G'n

+

(44)'t"r/~

(C"+C,,I'I,'I.,

I

((,'n

+

(.'411'12(/3 =0, ((,'ll-C.I-I}r/~+ '\

(2.11)

wlwl"e',\=G'H,l-pV 2andpisth,:el'~lIllilyofthesolid.The'I,arcthe dlrcctloncoslnca

ThisillitcubiccquntlonillpV2RIHIhall been eelvedanalytically byEvery [·121to yit'l,I,

wlu-n-,

(2.12)

ljI

= ~ I

^{arccos]I-jaB:-}

~J, (/ =

3C₃(2_C_{3 ),}

,,= ~CJ(3

^-2C3 ).

. (l-Cl,s), 2

'l'heindexj

=

Il,I,2111111 COTrl'llllondstoII= L,'1'1and1

1,

respecuv cly,

Int.!l{'<100».<110>and<III>direct ions equation(2.12) is considerab ly sil1lplifil'tlandran('lIsilr1.('1I01\"l.'dtogivethefollowingacoul>t icwave velocit ies in the

1·1

<tOil>direction

(~. t ,l)

<I [0>dlrecf.lon

<111>directio n

Knowledge ofthe clasticrcnstants thercforonllowlIformkuln1.iull ufL11l'l1I·UIlSt.irwludlY ratioswhichcallprovldea measureoftill'extenteft11(~"lliit ioll·l nlllllllll,iun(:ulIp liuA mechanism.

2.3 Blast o- c p tlcCoefficientsofCubicCr -yst nls

The coup ling between thestr nin(Ifilcryst al,f:kl (f~.I),utnltill'rli,.)(·(·tri.:h~ll llnl' , f;j(r,I), isknowna.sthepllotocla.~ticclfl'Ctandis d('S(:rilwt!II)'lilt,('(IUIIUOlI

\-11 1

(:1.17)

'.\

1';1/'cuhiccr)"ital~UKTr.f\Jl'only three indeJK'fldcntelMto-op ticcoefficientsPII,PI2 11I1111'41'III'IIt'l', ''''IUilLio ll(:!.J7)~imJlliIjC!lLa

Fromthil!itIollowsthattheratio ofhncnsltlcsoftwoDrillouin compo ne ntsis[131,

!:! _ [w, .(;)It' I]'

h -

",,(;)11"1 '

wl.f're'w~istil...i111F;ula r f('('(llIeuc)'ofacoustic mode p. and.f~is giVC1lby (2.19)

C' =

ijx(,)(Ul~ «"Eo)i~+{i~·f:.l'}

+(PII

-1'12-21'...)

L W,(E.Mr' ), i,+pl2 (t".q)E .1J

, (2.20)

tut cubie(rYlltaL~.llcrc,

q

an d

i;.

arcunit vectorsinthedirection of

q

andtheincident ligh t",1\\''''respectivelyamii"lstilt'unitpolarizationvector ofmodep.The quan tities (i")j,(f;..)/and(4),arctheJt.beempo nems of unitvectorsi,

E .

andti,respectiv ely,

i,

(1

=

1.:!,3)1l1't.·unit vectorsalonp;thl'cuhc exes.Thevect or

to'

sp-ciflesthe polariza tion uf lilt' eadintlonIIra U('rl'l'l fromaroll~tiemodeI',

111'111'(',thl.'illtt'lHtitil~ofthelldJloui nccnrp c ucnteyiel dinformation abouttheclesto- 11111it-inlt'rllrt iollthruug lllIl1.' elasto-opt lecoefficients,

10

2.4 Der ivedQmmtities

Many physicalquantitiesranbedet cnnlnod onceI,ll(' ('omp l\'l l'Sl'tofI'lastil'nJllstll1lh is known for apa rt icul ar so lid.Twooftill' moreim port an tlind ('asilr !'" lfl lla tl'd l'lnsl,ir propertiesarc the anisotropyfactor,A,andthendiab<1lirhulkJlIt1dl1l11.~,II.Explkit.ly, in terms oftheelasticconstants,these qnulltit iesareg1\'('llII)'[l:J1

and

for cubic systems.

Jj=C^ll~J:K't~ (:!.:!:!)

For an elasticallyisot rop ic solid ,A=I.Approximateeliu/tieisoll'OpyWM OhSNVI'd inlight scatteri ngexperiments011thecricutatiouallydisordered plm.'i<'l\uf(Cl/~(.'Nh (19),eyclooctaneandO2[101,Her eA=0.8S,

o.so

an dL1I2(Il r('iu'hIIfthl'!1('snlills, respectively,near their trip lepoints.Thisisot ro pyalsoresultsintlwIWM('q ll;,lit.yuf theacousticvelocityratiosill allhighaymmotry directionsfor lIH:setl11"1,(~solids, I1Srun be seenfromTable 1.1.Ncarperfect elnstlcisotropy,infad,1l.1s(Jtlll'U!1Ullt t.tlhl~a significantfeatur eoff3-C2F6(1\8discussedill Chapter 5),It !11111Uldalsohf~llot.('(lthat/I characteristic

or

orle ntatio uallydisorderod crystals is11slll il lihulkmodulus (lypif"ll lly..., 30kbar).

17

Chapter3

Exp er im en ta l

a.1 Exp es-lmen t nlSe t up

Thec' xpe rill1"nl ill...r.t llPilltill'Jlwscntworkisthestand ardone used(orBrillouin sn,t,Ie'rill';t~XJlf'riIlWlll14illtlti14II\IIor1110l"Yand hasbeendescribe dind('ta ilelsewhere [431.

II.i14sllmY Ii inFigure:U,

lucldcnt ralliat iollat5101.5flmlVasprovidedbyasingle-mode Ar+laser(Spect ra I'hJli in ).ThiNlightIVlIlIdirected.. long the x-axlsorthela brefe ren ce frame and focused at tln-scattering o-ute rhyle ns1.1[foca l length

=

40cm).A Ircut eurfa ce mirror(M) S!.·f\,t<tlto rellecttheincidentb(>1\1II alon g thea-axlsandupintuthecryostal(CR ).Asa rr-"ull1I1~ind d Mltllo hni 7A'll ioll WI\lIin thex-dircctlon.

Thl'J<t'ilU.t'rI.'Illi;lltwa~rollected at1M)- by collimatin g lensL2 {focallength

=

^{20 em)}

lind eflll'n, 1atripk-- I)II~'l,pit"I'.ockdrica llysca nnedFebry-P crctintcrlercmeter(FP),The cli;llllC'h 'for aportun-J\:JwaHlIetill 0.i5 em rcaultlngill1\collect ionangleorH.bout~, 'I'll('lightIrlmllmith"llJythl'illtt'rfc'romt'lcrWallfocusedIIylensL3(focallength=80 f'l1I) out<lpinho l.,'\,1[eliauu't.er=8001'111) andsube-squent lyIoe nsedontothecathode til'IIII'uh'r'l'\lOlf'(lphototunhiplicrI.lIb<:, (ITTFW130)h~'1(,1l~IA. Theoutputfromthe I'htllll lHUllipl i"rII'n"feeltOlldatil arqulsitiou andstabilizationsystem (BurleighDAS-I)

\'iii<111 1l1llplili('I'llis"l'il11hliltol'(AD),Ot her componentsincluded11temperat urecontrol

IS

, '"

~o

N

~x

~-:- ~

"'=

I

-' I

I I

'"

-- - -- - = -

---~

_:_4

1

9 -

",D_ ^1-'

In

x[===:J

^I

f1~ ~il _{lJ ~}

19

lluit(TCMI, dl<1rtrecorder (HEC)nudLaue X-raydiffractionapparatus(X R,COand PC).Tllest:will1mdiscussed illmoredetail insub sequent sections.

3.2 Cr yo st a t

Tile singll:Cl"ystlllsofG'~/'nusedinthese experimentswere grown andma inta ined in

11liqui dllitl"Ogl:1Inyos l'lt(SulfrianCryogenicsInc .] whichwas consi derablymodified for thepreslmt work.The illodifiedla ilsection of thiscryosta tisshownin FigUl'e3,2.

Till:slImplt,cell, whichis housedinthecryosta t ,consistsof a (3 mrlli.d.,5mmo.d.) glllsStubeandi,~about 7cmlong. Thelower end issca ledwitha polishedglass plu gand sil.~illa springlcl1ldcuBeCu jacket which is connecte dto a brassheat sinkviatwoflexible copper braills,This assemblyprovidesthe necessarythermalcontactto the cell while not restrictingits rotation.At thetop of thecell isaglass-to-kovargrad edsealwhich allcwa thefelltohe connectedto a hrASSplate wit hlow-rneltlng-pointsolde r,Crystals or eylindricnlshapewithJiallll'{el' 3111manclheight I -2emwe regrowninthiscell.

Ccllrotntiou wusuchie vedbyturninga rotary-scaledknurledknobwhichwas connected tothocell hytwo rigidstelulesssteeltub esandabr-ass plate.One of thestainlesssteel illlll'~wasused forga.~entryliScallheSCI.' I!in Figure3,2.

Luscrlig ht, enteredtill'bo t tom orthecryostatalongthea-axis or thelabfra me illrlmghafusedqll1lti~windowand\\'/I Sscattered ill all direct ionsby thesample.Only light,sl'aUI'n'c\nt. 900 in l,h{'y-directionwas collected throu gh ala rgeplexiglasswindow,

' 0

- CAPIl.LARY TUBE - HEATER

- RADIATIONSHIELD

LARGE PL(XIGLASS WINDOW

1f-ff-h , -ff--SAIoIPLE

SITE

Figure3.2:Thecryostattailscctlcn.

21

A~lIlalJNplcxlgluss windowallowed X-raysto cute rthecryosta t and thusbe diffracted l1ythesantplotlltfmgh the la rge plexiglasswindow, Plexiglas s was chosen for these windowsllf'cnll~f~it isverytra1JSra rl~lltto X-rays.

Cooli ngto1.I :lIJp f'ratu ff~illthe viclnity of thetriplepoint ofC2F6wasaccomplished by allowiug nitrogenfromtheinne r reservoir,located in thema inbody ofthe cryostat, tonowthroughItth incnpillatytubewhichwas thermallylinked to the bott om ofthe

!lamp l!!rdlvia 111l' hra."slu:at sinklindcopper hraid/Beeu jacket assembly mentioned ahove.Theflow of nitrogenthrough thistubewas cont rolled by a Ilne needle valveat t11f~topof rhocryostat,

Topart.iullycompensa teIorthecoolingand to controlthetem pera ture, threerceis- tancowireheatcrawen! strategically placed in closeproximity1.0tim cell ,The first,wit h a resistnnceof5111,WlISlocat eddirectl ybenea ththecapillarytubeand allowedfor the 'smooth ingout'oftempe ra ture Ilnct uat.ionsbeforethey reached the sample. The second helll,t'r (Il=:16 U) was epoxiedverynear the bott om of the celland perm itted finead- jus tllll'llt orthellamllk,tl:m per alure,Athirdheater withresistance51

n

wasplaced near

~hctopofth(~cellandcouldbe usedfor contro llingthe temperaturegrad ient bet ween thetop,mil bottomorthe cell.

3,3 TemperatureSen sin gnndControl

Tomoulterthetomperntureucnrthetopandbot tom of thecell,two GaAsdiodes withIIrnnstnnt-curreut(10,rA)supplywereused. The diodes were calibra ted using the

trip lepoint ofC1F;,and apointai,roo mtell1pl'r il l.ur l'(tlt' h ,ntti llt'l!Frotua Il1C'l't·nrrtlu-r- rncmctcr].Alinea r dopendonce of voltngeoutcmpernt.urewnsaS~1l\l1('I1.TIll'l(lpI11H~1 diode andhea lerwere usedillronjuur-tjouwitha proportlonnlfl'('lllwc ktt'l1lpt'rill. nr ,·

contro ller. ThisdeviceIlwmm fl'tlthe \·ol!ag(·ll(TOS~tilt'clioll\'and t'lJIlLpar l',1itwithu set-pointvoltage. IftheIliod l' voUilg\,\\'i'I~highorthan1I11'sc·I.-p(linl.v(lltn!!:I'(irulit'ut- ing a temperatu reslight ly \m1'1'1"llmll,(I('l'ire<l)Ilu' cout.rcllr-rwould1'11111[' 1.\'rnrrenl,tll the h('atl"l'towarm the areaulltilthe dlodc\'Oltllll;t, 1'l1111l11l'dtill'sl'l _pui lll.voll11W'. II shouldbenotedhereIhat in ilin l1y tIlt'R'Illl1rl.·dtemperutu re\\'<111renelu-dapp l'Hxillwto'I)' by controllinglIlI'no wofliquldnitrcgcu throughtimrapillMYlulu'with tile'Ill'!·tllt·vnlw- (secprevious sectlon} .Qnly11£1('1'this wasdOIWccuhltil ..11l'al,t~rprm'idpI' lltluglllWl1l lu maintainthetemperaturewitholl~hei ng~alllr11 ted("lIl1~ lnllt.lyIlu l'ttl(·x("I!."~i\'t' 1"'lClli ll~

from the uit rogcu.Usingthissystem.the temperature (011M bc:l'olllrull (..:ltu111.0 tlt±O..'i 1\'.

Asimilar dio de-heat er-controller circ uitwas initiallyIIscllill.theboucmoft,IH~n·ll.

Itwas.however, found lhal theresult ingIHna ll-lIfnl'lit lldl'()~dllalio llsilltl~tllJ}I' rn 1. llrt · close tothenuclea t ionsiteoftheso lid invariab lyresultedinapolyn"yl'tallilu~1Ia1111'11·.

Thusthe heal er andcont roller weredisconnecte damitho diml(:voU,llg/'\Wlllltloll il.on' d todeterminethe sam pletompcrat ure.

3.4 GasHandlingSy stem

Initiall y,tile entiregasha ndl ing syst e mwasleak testedwlth1I1l1~I1Siti Vl~lu-liuruIt'ak detector , Pe riod ica lly [be twe en1'1ll11l)it\\'1111 evacuate dtonpres s ureofarl~wmilT/IIIK wit ha mechanicalvacuu m putnpandIdtIcr apc'riollofllI~vI!ralcll' YIiIIrl ':rwhichtill:

l.r''lI-~ ll r.~Walla.r;a iucheckedlo ensurelhill nok-a k~t"Xislcd inthe system. Once it wal IId.f~nnill(·(1thlllUle!IYlilf~lIlWlL~Ir.ak·t ighl.it"'Mfhrshcdfourtimes withhighpurit y .c;ll....~)ll!lImxllnuoroclllllllcto removelISuruchdustandforeign part iclesaspossible.Fol- luwiulltthis1Iloroughnusl,iugprocedure,thesamplegas WASadmittedinlothecelluntil a11I'C:K!l I,"~ofal.oo lll730'I'•.rrWiL'IIlllllinooa'iIudicared on tlit!presaur egaugt!.

3.5 Gro wthofCrystala

FeueIn-,'g"cry!lI'IlL!IWf~rcgrownin thellOOVCsyslemby IlclllJiUiug9!>.6%pure gaeccue

C1Jo';,(M itl h~son)intothecell where il wascooleduntil itcondensed.Thesampletern-

peratureWll.!1thenIlab ili1.l'([ to about1j{above andtheuabruptly lowered belowthe triplflpoi nl. l'hi!lrelil,ltl'dillIl.Holid2-311Imin llCighl whichwas usually leftfor several

!Iannilo anneal .Thequalilyofthis'seed'wasdetermined by usingLaueX-r aydiffree- lio!l(asdiscussedbelow),Iftheseed was polycryst allineit.WASmel tedandthegrowth procedurerepeated.IfitWASa single cryst al,it was grownto aheightof1emby slow ('oolillg l'lll'lrl'lU!of aholll0,1

K I'"

LAuepho tograph s were t.alen at'..erioustimesduring thecoolingprecess.Itwasnoted thatlISthecrystal,,"'asgrown it invariablybecame 'twinned'. 'rhi"\\' <,-'1probablydueloacombinatio nofa largrtempera turegradientand theCl')lItalsticking tothewallsofU",cell,Tominimi7~theadherin g ofthecrystal to thc'n.·11wallll.a11ll1allC'OllsLIUltcurrentwaspassedthroughtilt"healer locatedonthe IlcCu jacketal thebottomofthe cell. Th is warmedthewalls o( thecellpriortoJlU- d"lllionorlIlf'!I<III1[1lcam is~'('m('dtc helpsomewhat alucethequalityofcryst als grown illthi!lmanner was slightly better.'I'll(' diffract ion5110l8,in!Ill cryst alskep t(orthe light. !I('1\Ucri ngexpcritucuta,remainedfairly sharpandellipticalindica t ing little internal st raiu,Oril'lllaliowlwithrcsperttothelab Irn mc couldbeobtainedusing the standard

2,1

technique (secnextsection].AI#'II\C'dilfl,,,diollpicture of rrystnl#:1i~showll illFi~urt, 3.3.

3.6 CrystalOrienta tion and X·r nyApparatu s

The X-raysnecessary for thelI\l't hollofLa ue (1\"a11Nlll issiul1)phulnp;raphy\\,,·rt'pro- videdby/l.Philips (M U IOl)X-raySOIUTI'oper an-d .11$0 H' .TIll'pil'l.lI n'.~WI'rt·taken with aPol ar oid(XR-'i') La ud call1i'ra Ioea t r-d 10.7em aw,\yfro m1,11<'st'llttl'r i ll~ccutcr, Alead collimatorrodneeddiver ge nc eofth['beaml)(Ofon'il,reachedlilt"sHln pll'.Init,illl alignm ent,of the collimatoralongtil('opt,it-axis.d('lin<'11byIIIII'-NI'I 1\.~I 'rln-nrn,.'llSlIt l't!

lhatthe X-ril)"sprobedthe scalteringvolume.TotI1ak.~rertniulhat1I,,'i!lI'idl'l1LX-ray beamwas perpen dic ula rtotheplane oftherHl11,tilehack \"I'{ll'diotlof the lI('· Nt,brnru, pro du cedby a mirrortempcrnrtly fixed to the cnmcru1lf>ldl'l'IVn..~nllu l l ~to.'Oilldrl('wit h theincidentbeambyadj ustmentof the holder.Oncl~lidto\.111'prop l'rpus il illll,itwas leftforthe remai nderoftheexpcr tmcnts.

Thecrystalorientati on withrespect totileInl,ornlOl'yrnllneflfrl!r('I"I'm:l![xyaehowuill Figure 3.1)wasdefinedintermsof theus ualEulerallgll~(0,,p.xl.'I'lldl' I,l' r lllili clhl'lil!

anglesLaueX-mydiffractionphotogra phsweretukcnIl~lIl1'I~rystillWliSr()tlll.!iI I,hrl)ll~11 intervalsor7..')0asmeasuredfrom1.1graduatedscali:lixf~d1IJ1lIwnyflslll L,/lslumt.l be noted tha tthecha nge in rotationangleofthe crytJstlltrAJlTl 's JllllLdl ~1toadl h ll~l~ill Eulerangle¢only.Usingtill:center

or

tile lIudilftili:lf!llX-ray11('111tl1I.~1I1.~orlgln,th.·

x-z coordinates ofallthe diffracti on spot!!all(\Ilchpictur eW('l"l \lIl"ils\lfl', 1with aIiuely ruled recta ngulargridtoan accuracymuch bt:\ll'!'t1HI1I±I min, Tlu'fieCIJUI·l l i natl~.

alongwiththe crysta l-filmdislance, thenservedns input IIl\ta

r<lt

11('Olllp ll t l\rpNl~rlUll 2,'j

-(0 01) (112) -(112)

(111) -(110) -(01 3)

Figure 3.3: Laue diffractionphotograph of crystal #3.

26

which utili zedtheme thod ofstcroograph!rprojcctlcu to t'lIku!'lIt'!Jossihlt,SC'!S(J(Eult'f anglos for each photograph. 'I'll" actua lr-rystalorlentnt jon wasfoundlIyt"<lmpafil1~Itds ofEulerang lesforvariouspiclurt'll111l1illwo~t'ls""l'rt 'romulin \\'llio'h0011111 ,rt'lI1iliru'tl cons t a nt(withinedegrel' or twodiu-toslight.rcllwobblo];11l1!tht'c1i1fl'f,'Ut't'itllll1~lt, ~~

betweenthetwoequal1l'dth et'oU"<'sllOlHli ng dWlIgt,int'l".\'llll l,llt'1l1Alt",hilIiualdlt~'k , alea st squ arescrystalor k'nla tionprog r a mwnsruuOilc,;It'lipid,un'withtilt'l'UOrtliI11ILt'lI of the spots andthe chosenElIlt't1I11g ll'1Iasinput. TIll' clunlit;\,(IfIIll'IIIwm.t'XlllllillPtl andonly orientat ionswhichgavelllLavc'm gt'errorilll1wns1ll1~1andt'" k ula t.l'dc'u urtli llHtt, dista ncesof<1millforallpici.lll't'slI'(,fl'ronsldcrcd'11:('('p1.01111."

3,7 Laser

A Spect r a-Ph ysicsModd2020arg onion lase r ser veda.~theliglltsonrrefortht~SI' expe riments ,Aprisminthelasercavity1I11olVl~dsoloctionof the111-1.1111111lineilltill' Ar+sped- ru in whileallint racav ityFabry-Perot ot alonsdedt'll11lIillgh! "xilllmnclt'llf this line.Theresultantlinewidthwasof theorderof10- l!i Alii:antiW'l,~duemainlyIn freque nc y jit.ter ,Tomaximizemecha nical sta bilit ylilt'll\.~crlVa~:;1'1.(Illa lloa til1/l;gfllllill' blockwh ichrestedupo na steeltable.

3,8 Fa b ry-Pe rotInt erfer om et er

Thesca tt eredlight was an aly zed with a plcaoclcctricnlly lIGUlllf'1llriJllf~Jl!lllllFahry·

Perotinterferom eter,'l'hisiustrumcutcouslst edor twohighlyfd[t~divl'Ilaralldl1lil'l'lIfli separa tedby adistan ced,Therear mirrorortheinterfN ullll'll:r1V1lSmcuuu-dOillliH~' piezolclectric elementswhichfacilitated continuouslIeltimingt1rtIle ,,11111: 1I1!pilfa l,iu lI. TIlt'

27

'l'11(~Ircquenoy uf tim Jiglll,v,Pl~~Sf:dby theFa bry-Perot for a given plateseparation is.Id" rln illf'dI.)'l.h (~H'SUlIIIIWI'r:ollflitioll

Tile

2d

=-;;- .

^(3.1)

'1'111'frl'(IIll:lI(~ydlllerenm between two consecutiveorder s of interference isalsodeter- minedhythe plnte sepal-ationlindis knownasthe freespect ral rangeofthein ter fc ro m- der.Ma t hcllllllin tlly,itb given by

rsn

=

iJ.

^(3.2)

'I'11l~fn~~.~pl)ctralrangeforthepresent experiments was 10.99GIl::.Thisvaluewas dotenuiuedusing a procisinu(luartzsamp le forwhich the longitudinaland transverse BrillouinIruquo ncy!<hiftsWCI"<'wellknown[44],[45}.

Allothcr iutp orteut chnractcrlatic of the Fabry-P erot interferometeris the finesse,:F, whkhisdcllncdby

(3.3)

WhNl',..IV11AIisthefull widthat half-maximum oftheintensitymaximum, High fill('ll!\{.'valu es wore crit icillinthes e experimen tsas closelyspaced spectrallines hadto Ill'1'(,,.01\"(·(1.Wilh optimumaligllll1eolof aJlopticalcomponentsand theinterferometer

28

switchedto triplepass,fin~nlu('!'lIidw' ''''!150.11lt1t iO wl·""llhl" in....l.

The triplepIlSlioptionoftheFAl>r)'-I~('f"Otabo (";1""0('(111...('tllllr"" l[i.•-,II... r"till uf ma ximumtominimumtrilll5l1li5$iollint.cu"itYlluI,,·('1\lJcl.Th.·n"'lll~ill':n·j ....·liulllIlli", of....1:1()'3 or moreallowedveryw('l!.kKiglll!.b10Iw·.IC'I-tr...1.'1'1...lrilll"\"'r.;l'Brill..uln componentswereveryweakinmOlll!l1)('('trllofj1-C11-rii\llIllw\lC't·trilll.,1..1:o<.'CiIlAcorIIIl"

scatte redligh~bytheinterferometerIViI." lIC'C'{':'llilryluolll'iC'n1'IllI'lH.

3.0 Dat aAcquisitionandSta biliza tionSyst em

Thedat a ecqueitlcnImdsta biliUllio llsystemper rurlllf'(l!I('\'f'ra l illlpurlalllr!lllf'lillll~.

Themostimportantorthl'SClire listedhclcw.

(i)TheDAS e m ploYl-d^II.IO:!-Ichanllelmul1idlallllcl llJllllyl"A'r foraf'U IIIlIlI,ltiulI/tlllifl,(lOn l·

ing of spectra.The:OUII\.8AndcDrrellpondingr!laUllt-l...w('r.~flispl a)'('(l1>1\/I(:In'1'1,'(1"'1 1 anda cursorwasusedtoaddff"S!lII.pa rti culiU'channel,

eter.Thisra mprcH'mblCla.taircallCwhereeae lldt'fIcor"""IKlllflstoill r:Wl II,,"t in~till' cha nneladdressscal a r ofthenlllltid \a n lldana1)'z~rbyOlll'. Th.'1.lat .. ilIf,.araUulli!l"

linear functi onoframpvollll.ge endhence(',,("hchaum-lufthl!IIllllt idl <lllllc,I,1Ilalyzc'f"mr·

responds toIIpartic ularfrer:llll'l1("ypassedbytill!(-'"h rY-P"r" tinb·rff·rnll1d .l'T.

(iii )Frequencydrift causedbycha nge illlasercavitylell~lhorilltf'l'rl'rulllf~ll'rplall 'lII'p'"

rationdueto tem peraturechangesWIl~automaticallyWJlljll.·II!1/llf'd(fIrliytill'DAi;,'l'his WIlSaccomplishedbylocatingIIdata window~ymllldrir/lllyllhunt1\p",~sl:lf~lf,,1rI-rI'I'C~1lC1~

chan ne l. Ast ro ngspl'Ctrll.lfeat ure(usu/lllytheHllyld glllilll~JIVII!!11Ic:/.;,,,1totilL"dla nud.

'1'1..,OJIIIIL'i 011either !lid,'ofHImreferencechanneland with inthe window wer estore d illtWfIfI-,;istt'tS.Fc,llu\Yill~each MWI'l'p of the ra.mpt.henumber of counts in. the registt'R werecompilfCIl.Iftill")'wereunequal,inclicatiwooffreq uency drift.,it.smallcorrection VOhil~'!WitSalllllllli'llically apl)lil..1to the ramp~(".Iartobringthe IK·akback loward,the

(iv)TheHASfOlltinuulI!llyopthnlze..1 tile interfero meterfinesse.Adata windowwas Ilgaillloqlu,.1llyllllllC'trirAllya"olltthe referencechannelwithinthe drift stabilizatio n wiudew.The counts in thiswindowwere storedinl\f'llgis h!l andmaximizedduring a fflllr IlWC'ClJlnyck-,During!IWI.'C1Jonethecountswere accumulated andstoredin the reg- isll'I',IIIsweeptwo of therallli'"test voltagewasapplied tothe piezoelect ricclements whk'htilk d therr'nr mirror oftheFabry-PerotaboutAvertica l l'lxis,At theend ofSWl'<'P two,thl!numberofcountsaccumulated duringsweepsoueAnd twowascompared and IteorrectlcnvoltageWIISappliedtoincrease the number ofcoun ts, The secondhllifof thepTOC1-'tlnre.involving'W('('j)'three androur. wasthesame as thefirst halfexceptthe mirrorwastiltedabcuta horiwnWAXis,

(v) Anolht'r imllOrl lllltfea t.ureof theHASwasthesegmented timebase.Thisallowed moreLimetobespent in specifl('(!r~iollsofthespect rumandwasusedin thepresent workto ohLainslIllicientint(,l1siL}'ofthcRayleig hcompouent(ordriftstabilisationand furmore accurate dM.('r minAtion ofthefrequencyshiftsofthetransverseBrillouin com-

3,10 Optical Syst emAlign ment

Priortoft("(·lllllUllltiollofspcctra ,allcomponentsoftheoptic-al s)'stem were carefully nlign l..ltoensnre maxiuunutr'llIlirnillll ion ofthelightscatteredbythecrystal.Thelirs t

30

step inthis[>rOC('S8wastheremovalof1111lcusos uudtheFabry-Per ot ;nll'r f"-'fo llll'l l'f leavin gonly twop;llhol ('S -A'Incarthephotomultlplk-r and:\:1Ut' ilrthl'lorntionofUII' crystalMshowninFigure3,1.,\Ik '-N('laser111'illU Willi1U1l. 11'topa ~~IlLru ughI,ul lt these pinholesandconsequently ddi lH'<.ltheopticnxls. TIll'illl,'rrl'roll ll'lt'l'Wlllltlu-u putinplacebetween the setwopinholes andits positiouMlj us1.t'lluntilitsIla r krt-lII'l'l iIHl coi ncidedwith the incide ntbeamLaensure nonunliucldeucc TtlcluainIlrt'<.'i~t'ali1tlllll"Il1.

of the Fa bry-Per o t the bea mFromtlwargon laserWllllsra~ tt'n'llIrourIIwhitecardinto theinterferomete r. A collimati nglenswa~theupltH'l't! infl'tmtnrtilt'ill 1.t'" rt'f()lll('!.t'l' andmovedalong the opticaxisuntilllarallcllig htWilHobtained.TIi,'fnllllmirroror1.11"

Fa b ry-Perot was manually adjusted1l1iLil ll l'OlIIIpsiligclrculnrfl'ingt ~pllt tl'ruWIlS OhSI'I' VI'll, Goodmanualalignmentatthis steg oWil~ludicntedbya~i np,lcI1n~h i ll gspol.1'1'11(1(1(:1'11 bythe Fabry-Pero t as itwas scanned repeate dly. Ast·coullk-nswa...tlmuill.~('rllXIh~'hilld the Fabry-Perotand focusedtheanalysedliglltontopinholeA'lnurl!H1l1sl'll'lt'ul1yontu thecathodeof thephotomultipl ierlube, FurtherfinelldjllSLllll:lIb

o r

theiUb,rrcl'OlIw1.cr mirrors,usingtheDAS·}pie zo elect riciJii\.l:lcontrols, were ilcclllll l,JisIK't1bylllilJdm il'.inK thesignalon the DAS· }CRT screen,Thecorner culml{r.\Lro l'dltdo rs)uftil"1')II,l'y' Pe rot were thenrotatedtothe triplepass position audfinal adj IlHtlllf'nl ,sW('"''UHu f.,to maximize the signa l.

3,11 BrillouinSpectra

The Brill oui nspectrawerecollected overplJ1'imls fimgillJ;Ircm al>flill '.!lo~a'IOlirs with a laserpowe rof50ml\land a fret!spectralrange

or

W.rm(,'/lz.

Toobtainas stronga spectrum as possiblet11l~incidentlil~.!rh"lflllWillic:a rf'flllly

ell

CI'Il!c'W'! (,II lil':l,oHolll of then~1Iasdeterminedbyobservation of a backreflection ofthe-Loam.The1'l llJry-P':l'lItinterferometerwas adjustedsuchtha t theRayleigh peak Wi(S ilWdli lllilXimiz('(llisinl-;lIw linesseoptilllizatiollmodule of the ')AS-l, This gencrally rr;~ll JtediniIlill.'sseof ,"O·fiO,

With tlw lIilyldl;hIlPilks cbnly visihlein triplepessmcdc it\I'lI~possibleto maximize till'in1." llsityofL1)(~101l~it'Hlill/i1Brilloui n component.This wasdoneby adjustlngthe fmnt"" lIcdill ~lells (1..2inFignre3,1)whileobs<'I'villgthe intensityoftholongi t ud inal ecmponent011the DAf; screen, usingthe segmented ramp feature,astheinterf crcme-

tnrI....'Sr.'w',(tc.llyscanned. Whe\ltbo longltudiual compo nentwas maximizeditwas

W'Ilt'rall.rpussihl.,I,t)S(~it illOIWISscan of thelnterfcrometor,

WIWllallconditionswereoptimizedthe cent ralRayleighpeak waslocked by the DASIIIl daccumulatlon ofthespect rum bega n.Some ofthe spectra,oncecollected,were recor ded llsing " charl recorder. TheshifLsandinte nsit ies oftheBrillou in components ofmost. spcctrn,howeve r,weresim plynoted and nolia rdcopywas obtained.

TIlt'chuuucl1I11ll 1h " I'Sandintensities forpeaksR, L,T1andT'lweremeasu red direct ly fromt,11t'srrrenofthc (lata acqnisitio nsyste m.Thefrequencyshiftswerethencalculated ,H'I'01'ding10till'rnllowiug:

"I.""

F SRt .!!.

4 ; :II'i

'''1'

_I

= FSR

" ;"

t

11',

~

(3.4)

(3.5)

whereFSRis thefree spectralr.111 W'011111lIw'\ ' lllni tlill l;IIU<H1 I, it,il'~nre~htlll'l1illFi~un' 3.4{46J.Thisprocess of avcraglug ruinlmized IlwdTI'(·tof n~lip;hl ~(,lInl1inl;ll(lulill"ilrily inthcmterferomctcr.

It was noticed,earlyill the expcriurcnta,tllll l,thelh-lllouiu Spc' ltl'1Ill1of1'1-(·'11':1r-xhlb- Itod., strong barkgroulld.II was thcught thnt 1,llisumyh.1WhC'I:'lIuhsl' lIrin~lin'Sc'WIIlI transverseBrillouincomponenti1SonlyOllt'haciheeu nhSI'I'\'C'1111[1tothispuin!..'1'0 eliminatesome ofthisbackgrouu d11 £ilLcr(o f1011I/1 hillldwi!llh)was pin!1'lllJdwc'I'" 1,1[(, sample and thedetectionoptics. Nosecond LrilIISIICI"SI'couIl10IIC'1I1,WIlS"h.'« ' I"\'c'll;lll,lifllll;h the background was cut down sigllificlllltly,

Anattemptwas alsomnd« to locate the scccudll·i1n .~IIPr!lCIJd lJoll illcomponent by using the segmentedtimebase feature

o r

1I11~IJAS. Using thesPgUll'ul,c'llrallll'around the first transverse component 011sl~\leraloccasionsyielded twoIII'ill'lyfll'I-\l'IlI~rill!~JH'I,b (a small dipill intensitywaseviden t) , Tlll'SCtwopeaks were 1.111\1'111.0Ill'tln-I.rll!lSVI'r:W Brillo uin componentsinthe nine spoctraillwhichtheyWt'rf!(jhsl~rvI'd ,

~

R

II

R

t

'2~ '4

I ^I

'3

L L ¹²

+

¹³

^---j

^{L L}

¹¹⁴

T Z

14 S4

R

Figure3..1:A BrillouinstickspectrumshowingtheRayleighpeaks(R)andthevarious Brillouincomponents(Ta.T2andL).

Chapter<1

Results

4.1 BrillouinShiftsand Intensities

IIItota l, 60 BrillouinspectraW(' r!'rec o rdedforfourindl'[l(~Ilt1"lIt l'l'y~ll\l~uf,'1-C~/':1 at169, 160 and 144 R.(It should be not ed,fromTabk-'1.1,tha tl'1"y ~II,I~I,:1111I(1·1hlIV!' si mila r orient a t ions.Clearlytherewasitpreferredorioutatlonfu rgruwthal~llllllp;h1.1...

reasonforthis is unknown),Mos t Slll'Ctl'll.were oh l,air1l'dIll,

7 .r, "

inh 'rvalsofrotat ionill theanglef/J,Inallspec tr athelougitudiuulBrillouincomponent(I.)waseh-urlyvisihll' butthetra nsvers eBrillouincompo nent s ('lll\ud1

1)

^wert!VI' I")'week andin 1111 hut

n

cl thespect ra only ailewasobserved, Atypic alspectrumcollec ted Iroru r-ryatnl#1utHi!) 1<foratimeof26hours,isshow ninFigu re,1.1.Here,lilt'rountml,,~i1rl~2uml:lrl coullbjsforthe transverse(Tdandlongi t ud inal(L )Heilloulucllillponf'rr ~s ,rl'M pf'l.:ti vl'ly,

The obse rved Brillouinfrequency shirtl! nrc shown inTahlt's.1.1,-l.2aur] -l,a, As ca n besee n, theBrillouinshifts for tirecrysta lorielllati(JIt~i'llllllil~1Jrt:l"~wnrullt'lLI'ly id enticaland correspondtf)maximum varillt ious oronly 1%Ililll :I'M,fortIll''''lI~jl,l lIlilial and tra nsverseshifts,res pectively. These variati onswel'f~rrnlKI'f~lllly flifrl'rl~lIlfrom 1Ill' measurement uncerta intywhichisestimated toIn~nhout1-2 dr,uurdi'l(mrl'f'~llCIrrdill.u;lu about 0.0501/:; ).

Theratiosoftransverse IMllouincom poll entiulcIlSill(:!\lOl11ll~il\lflilllllBdllfllliu

a,'j

20

"'9

~ z

::>

8

z g 10

o J:

Q.

L

I /\R ,

I I

I

I

L

Figure<1.1:A typical Brillouin spectrum ofP-C:F6 .

36

component intensities.

hi/' t

alld

h,/it.

are allIO shownin Tahlt'll ·1.1. ·1.2IIoU<l~.:l;l.ud lireunusually small.\" f)"ingfro m0.011.01'maximumofoul)'0.10.The"",'illlt'us ityr;JtMJII arc probablysceurete onl}'1.0±15%duetolarge ,..""tioIlSinl....rkgrulI1ltliute'lIsil)'wit b channel number lindwC'al.ignals.

eu RANG l. ES 08S~;1II::Il Gil. CALC lll.An:ll«n, OH~El lnJl CAI.CIII.An:1l

. ,

141.9

. ^{.. .. ,.}

""

^{310.4 4.111}

.. ^,

^Ull

_{" .}

^{I.AU u.un I~U'l IUl:l}

141.1 " ., 310.0 •.ac o.~ 4.11 1.11-1 I.AII ".~ ^{O.(tl IWI}

UI.4 246.1 311l.8 4.20 0.00 4.11 1.!1-1 l.~7 !I.ll:! U.D2 um

141.1

,n.

31U.0 4.20 I,r" 4.17 1.').1 l.r,lI II.U4 U.Wl U."l

141.2 Wl.O 316.114.10 !.(ll! 4.17 1.0~ Ull nm ll.ll'j U.ltl

H2.2 ~., 317.1 4.1. 1.02 4.l T I.r.r, U7 IUU If,n:l e.m

142 .2 276.2 31T.I 4.16 1.71 4.W 1.G11 ,. ~ D.W llJlI

141.1 283.7 :117.1 4.15 ,.w 4.15 l.ro1 1.511 ,~

=

^\l.UI

14 \.6

""'.,

^{311.1 4.12 t.ea 4.14 1,1;7 \.Ill QAMI IU~1 11.111}

14U

"'.,

^{31T.2 4.11 ,m 4.14}

, .,

lor.2

'A'

^{lim II.UI}

141.4

...

^{31T.2 4.11 ,m 4.14 ,m}

^{,. "}

^{,~ 0.02 QJIl}

141.3 J12-ll 31T.2 4.12 ,~ W ,~ ,.~ om ,un

141A

",U,

^{311.1 4.12}

""

^{4.14 1,<;11 ,.~}

" . ^{,n ,}

, =

^~.

...

^~.

_... ...

"-'

... _n. ^=,

^271.2

_{"''' "" "',} " ... " ₌ .. .. _. ^, .. ^{, ,} _,n. ^{,n. , ,n,} ,n. 'n. ... ... ... ^" ...

^4.16w4.15_4.u^UT..r

^."

4.11

_'m

^{,m,m,~1.l'Q,mo~om}o.Y ^4.11

.., ."

^4.IT_w^4.174.184.11us ^1.';1,m^{I.. .}

^, _,

^,,n

..

on

.. ..

^~

^, :

^,~

..,

^{,~l.$7,~o.Y,~}

::

^'m,m

^'A _'" ... '" _. ,m _" ^'

^~

_'M

^.~.~~on,~

_'"

^tUII

.

^oA'

"" _'" .

'"

^,~

~.

",.

^114.1

."

^{o~ 4.17}

^,."

^{1.17 ,~}

^'A'

I4I.ll

,n, " ..

^{4.15 r.ra ,~ 4.12 ,m ,x.}

^.A'

^um

^,m

141.11 ,. .r

".,

^{<U o.~}

,..,

4.13 om 1.1'.1 IUU ,~ '00

14'U

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