[PDF] Diamond Monochromator for High Heat Flux Synchrotron X-ray

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Diamon

d Monochromato r fo r Hig h Hea t Flu x

Synchrotro

n X-ra y Beams. * A.M . Khounsary , R.K . Smithe r an d S . Dave yAdvanced Photon SourceArgonne National Laboratory9700 South Cass AvenueArgonne, IL 60439

December

, 199
2 Th e submitte d manuscrip t ha s bee n authore d b y a contracto r o f th e U . S . Governmen t unde r contrac t No . W-31-109-ENG-38 .

Accordingly

, th e U . S . Governmen t retain s anonexclusive, royalty-free license to publish o r reproduc e th e publishe d for m o f thi s contribution , o r allo w other s t o d o so , fo r U . S . Governmsn t purpons . c zF"3 - 3 1S93 ijTl *Thi s wor k supporte d b y th e U.S . Departmen t o f Energy , BES-Material s Sciences ,under contract no. W-31-109-ENG-38

DISCLAIME

R Thi s repor t wa s prepare d a s a n accoun t o f wor k sponsore d b y a n agenc y o f th e Unite d State sGovernment. Neither the United States Government nor any agency thereof, nor any of their employees , make s an y warranty , expres s o r implied , o r assume s an y lega l liabilit y o r responsi -bility for the accuracy, completeness, or usefulness of any information, apparatus, product, or proces s disclosed , o r represent s tha t it s us e woul d no t infring e privatel y owne d rights . Refer - enc e herei n t o an y specifi c commercia l product , process , o r servic e b y trad e name , trademark ,manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom- mendation , o r favorin g b y th e Unite d State s Governmen t o r an y agenc y thereof . Th e view sand opinions of authors expressed herein do not necessarily state or reflect those of the Unite d State s Governmen t o r an y agenc y thereof .IER

DISTRIBUTIO

N O F THI S DOCUMEN T I S UNLIMITE D

Diamond Monochrotnator for High Heat Flux

Synchrotro

n X-ra y Beam s A.M . Khounsary , R.K . Smither , an d S . Davey ,

Advance

d Photo n Sourc e A . Purohit , Engineerin g Physic s Divisio n

Argonn

e Nationa l Laborator y

Argonne

, I L 6043
9

ABSTRAC

T Singl e crysta l silico n ha s bee n th e materia l o f choic e fo r x-ra y monochromator s fo r th e pas t severa l decades . However , th e nee d fo r suitabl e monochromator s t o handl e th e hig h hea t loa d o f th e nex t generatio n synchrotro n x-ra y beam s o n th e on e han d an d th e rapi d an d on-goin g advance s i n syntheti c diamon d technolog y o n th e othe r mak e a compellin g cas e fo r th e consideratio n o f a diamon d monochromato r system . I n thi s paper , w e conside r variou s aspects , advantage s an d disadvantages , an d promise s an d pitfall s o f suc h a syste m an d evaluat e th e comparativ e performanc e o f a diamon d monochromato r subjecte d t o th e hig h hea t loa d o f th e mos t powerfu l x-ra y bea m tha t wil l becom e availabl e i n th e nex t fe w years . Th e result s o f experiment s performe d t o evaluat e th e diffractio n propertie s o f a currentl y availabl e syntheti c singl e crysta l diamon d ar e als o presented . Fabricatio n o f a diamond-base d monochromato r i s withi n presen t technica l means . 1 . INTRODUCTIO N Th e combinatio n o f hig h powe r an d hig h powe r densit y associate d wit h th e x-ra y beam s generate d b y insertio n device s a t th e thir d generatio n synchrotro n radiatio n facilitie s ha s create d ne w challenge s i n th e desig n o f th e beamlin e component s tha t intercep t th e x-ra y beams . Th e challeng e i s nowher e greate r tha n i n th e desig n o f th e firs t optica l components , notabl y monochromator s an d mirrors , whic h mus t provid e acceptabl e performanc e unde r th e merma l loa d o f th e x-ra y beams . A resurgenc e o f researc h activitie s i n th e developmen t o f monochromator s fo r hig h hea t loa d beamliik s ha s le d t o examinatio n o f man y aspect s o f th e problem . Muc h attentio n ha s bee n concentrate d o n th e coolin g o f monochromator s wit h th e ai m t o reduc e th e temperatur e gradien t an d thu s th e therma l distortio n i n th e system . 1 Nove l monochromato r design s suc h a s th e inclined ^ o r asymmetric ^ monochromato r hav e als o bee n suggested . Th e combine d effor t ha s resulte d i n th e desig n o f monochromator s tha t ca n adequatel y handl e th e need s o f th e synchrotro n communit y fo r th e nea r future . Fo r th e x-ra y beam s tha t com e o n lin e i n th e secon d hal f o f th e decade , th e currentl y availabl e design s ma y no t b e adequate . On e are a wit h substantia l potentia l i n th e desig n o f hig h performanc e monochromator s i s th e monochromato r materia l selection . I n thi s paper , w e conside r thi s aspec t o f th e proble m an d specificall y sugges t diamon d a s a materia l o f choice . Whil e diamon d ha s previousl y bee n use d i n diffractio n work , i n thi s pape r w e conside r it s applicatio n i n hig h hea t loa d monochromator s an d provid e a preliminar y stud y o f th e design , fabrication , analysis , an d characterizatio n aspect s o f a diamon d monochromato r system . Th t submitte d manuscrip t ha s bee n authore d toy a contracto r o f th e U . S . Governmen t unde r contrac t No . W-31-109-ENG-38 .

Accordingly

, th e U . S . Governmen t retain s a nonexclusive , royalty-fre e licens e t o publis h o r reproduc e th e publishe d for m o f this - contribution , o r allo w other s t o d o so , fo r U . S . Governmen t purposes .

2. MONOCHROMATOR MATERIAL

Currently

, silico n i s almos t universall y use d i n th e desig n o f monochromalo r system s fo r hig h energ y (ove r 2- 3 keV ) x-ra y beams . Th e choic e arise s fro m th e availabilit y o f low-cost , large-size , an d extremel y hig h qualit y singl e crysta l silico n develope d primaril y fo r th e semiconducto r industry . Singl e crysta l diamond s hav e no t bee n use d fo r thi s applicatio n fo r a numbe r o f reasons . Th e tw o mai n (an d mutuall y reinforcing ) reason s hav e bee n a genera l lac k o f nee d for , an d unavailabilit y of , suitabl e singl e crysta l diamond s fo r x-ra y optic s applications . Ther e ar e no w som e compellin g reason s wh y th e subjec t o f a diamon d monochromato r shoul d b e reassessed . T o begi n with , th e x-ra y beam s produce d b y undulator s a t moder n synchrotro n facilitie s ar e s o intens e tha t the y caus e unacceptabl y hig h therma l distortio n i n th e coole d optica l element s o n whic h the y impinge . Thus , a n opticall y suitabl e singl e crysta l wit h hig h therma l conductivit y an d lo w therma l expansio n coefficien t i s highl y desirable . Singl e crysta l diamon d at room temperature fits thi s descriptio n rathe r wel l a s doe s silico n at cryogenic temperatures.^'^ A t temperature s belo w 2 0 K , singl e crysta l silico n ha s a negligibl e therma l expansio n coefficient , an d it s therma l conductivit y i s abou t 5 0 W/cm- K (i.e. , abou t 1 2 time s bette r tha n tha t o f coppe r a t roo m temperature). ^ I t ha s a negativ e therma l expansio n coefficien t belo w 12 5 K (i.e. , i t contract s upo n heating) . Th e therma l expansio n coefficien t i s zer o a t abou t 12 5 K wher e th e therma l conductivit y i s abou t 6 W/cm- K (o r 50
% bette r tha n tha t o f coppe r a t roo m temperature) . Thus , a cryogenicall y coole d silico n monochromato r system , operate d fo r exampl e a t liqui d nitroge n temperature , i s conceptuall y attractive . I n practice , however , th e desig n o f a syste m capabl e o f removin g severa l k W o f hea t wit h on-the-surfac e pea k hea t fluxe s i n exces s o f 5 0 W/mm ^ (expecte d fro m AP S Undulato r A , fo r example ) i s a rathe r formidabl e task , th e mos t obviou s complication s o f whic h ar e th e critica l hea t flux issue , th e require d larg e coolin g are a tha t necessitate s a multi-laye r hea t exchanger , an d a robus t desig n fo r maintainin g th e integrit y an d th e figur e unde r therma l cycling . I t i s mor e realisti c t o conside r a cryogenicall y coole d silico n monochromato r syste m wit h a n incline d o r asymmetri c geometr y i n whic h th e inciden t hea t flu x i s sprea d ou t ove r a muc h large r are a tha n i n a conventiona l monochromator. 2

Diamon

d a t roo m temperatur e offer s a mor e manageabl e an d ye t competitiv e alternativ e t o silico n a t cryogeni c temperatures . Singl e crysta l diamon d ca n hav e a therma l conductivit y i n exces s o f 2 1 W/cm-K . Thi s i s fiv e time s bette r tha n coppe r a t roo m temperature , an d th e rati o i s accentuate d a t lowe r temperatures , t o som e 2 5 time s a t liqui d ai r temperatur e (Typ e H a diamon d ha s a fantasti c therma l conductivit y o f abou t 10 0 W/cm- K a t abou t 100K)
. Thus , i t i s apparen t that , a t leas t fro m a therma l poin t o f view , a diamond-base d monochromato r syste m ca n provid e a n optio n fo r dealin g wit h hig h therma l loa d x-ra y beams . I n usin g diamon d fo r th e desig n o f a n x-ra y monochromato r system , however , a numbe r o f issue s mus t first b e resolved . Thes e concer n th e availability , quality , an d suitabilit y o f diamond s fo r synchrotro n applications . Thes e issue s ar e discusse d nex t 3 . SINGL E CRYSTA L DIAMOND S

Diamonds

^ a r e classifie d (base d o n thei r I R an d U V absorptions ) a s Typ e I o r I I dependin g o n whethe r nitrogen , a commo n impurity , i s presen t o r not . Eac h Typ e i s furthe r subdivide d int o a o r b , t o indicat e th e specifi c for m i n whic h impuritie s ar e presen t A majorit y o f natura l diamond s ar e Typ e I , wit h hig h concentration s o f nitrogen , whil e Typ e I I diamond s (whic h mak e u p abou t 2 % o f diamonds ) hav e little or no nitrogen. Type II diamonds contain impurities with concentrations of about 10 parts per millio n an d a s ge m stone s ar c considere d t o b e nearl y '"perfect " an d fre e fro m "defects. " Mos t o f thes e ar c Typ e Ila , havin g a hig h electrica l resistivit y (-5xlf)' < + ohm-m) , an d ar e essentiall y insulators . Typ e H b diamonds , o n th e othe r hand , ar e semiconductor s wit h a resistivit y o f 10 0 ohm- m o r less , du e t o th e presenc e o f boro n a s a n impurity . Hig h qualit y natura l diamond s ar e availabl e i n size s u p t o 1 0 x 1 0 x 1 mm ^ o r larger.10-1 1 Th e price ^ fo r a 1 0 x 1 0 x 0.2 5 mtn ^ Typ e Il a diamon d i s unde r $8000 . Large r are a diamond s ca n b e availabl e a t substantiall y highe r costs . Typ e li b crysta l price s ar e abou t twic e thos e o f Typ e H a diamonds . Typ e la diamond s ar e no t suitabl e fo r th e presen t application , whil e Typ e I b diamonds , whic h ar e availabl e i n size s u p t o 6 m m x 6 m m x 0.2 5 m m (o r thicker) , ar e price d a t abou t $200 0 o r roughl y abou t 20 % highe r tha n Typ e H a diamond s o f th e sam e size . * 0 Fo r x-ra y diffractio n applications , on e ma y ideall y wan t t o us e a perfec t diamon d crystal , tha t i s a diamon d fre e o f al l impuritie s an d lattic e defect s & dislocations . Suc h crystal s ar e rare , an d extensiv e testin g o f man y crystal s i s necessar y t o selec t a suitabl e specimen . W e note , however , tha t certai n imperfection s i n singl e crysta l diamond s ma y eve n b e desirabl e i n certai n x-ra y diffractio n applications . A hig h qualit y diamond , i n th e aestheti c sense , wit h n o "impurities " ma y stil l b e (an d ofte n is ) imperfect , i n th e diffractio n sense . Thi s i s du e t o lattic e defect s an d lattic e deformations . Th e forme r includ e missin g o r displace d atom s fro m th e point s o f thei r geometri c locatio n an d loca l elasti c deformation s whic h alte r th e inte r atomi c spacin g an d th e bon d length s Lattic e deformation s ar e du e t o th e presenc e o f a fe w o r a larg e numbe r o f elasticall y staine d region s i n th e crysta l leadin g t o a crysta l tha t i s divide d int o man y smal l region s wit h slightl y differen t lattic e orientations . Thi s i s th e mosaicit y o f th e singl e crysta l diamon d tha t broaden s th e rockin g curve .

Natura

l diamond s ar e generall y stressed . Sometime s a par t o f thi s stres s ma y b e anneale d b y heatin g th e diamon d i n vacuu m (t o preven t oxidation ) o r b y heatin g i t t o ver y hig h temperature s fo r a shor t perio d o f tim e (t o preven t graphitization. ) i n a n iner t environmen t A rathe r unexpecte d resul t o f a limite d numbe r o f studie s o n th e diffractio n propertie s o f natura l diamond s i s tha t becaus e o f a typ e o f dislocatio n commonl y foun d i n an d characteristi c o f th e mor e "perfect " Typ e Il a diamonds , Typ e I b diamond s ar e actuall y mor e suitabl e fo r x-ra y monochromators . ^ T o ou r knowledge , th e onl y reporte d confirmatio n o f thi s b y precis e rockin g curv e measurement s i s du e t o

Jackso

n 1 3 w h o obtaine d a doubl e crysta l rockin g curv e widt h (apparentl y th e ful l widt h a t hal f maximum , o r FWHM ) o f abou t 15 0 ar c second s fo r a Typ e Il a diamon d an d onl y 1 0 ar c second s fo r a Typ e I b diamond , bot h fro m (022 ) crysta l planes . Th e photo n energ y i s no t specified , bu t th e theoretica l FWH M o f th e doubl e crysta l rockin g curv e calculated ^ fo r thes e specime n range s fro m 1. 5 ar c second s fo r 2 0 ke V t o 3 2 ar c second s fo r 5 ke V photons . Jackso n 1 3 als o note s tha t th e annealin g o f th e Typ e H a crystal s t o 1000°
C faile d t o affec t th e rockin g curv e width .

Becaus

e o f th e recen t availabilit y o f syntheti c singl e crysta l diamond s an d ou r belie f tha t th e rapi d advance s i n diamon d technolog y ma y soo n resul t i n large r are a diamond s o f hig h consistenc y an d quality , w e hav e examine d Typ e I b syntheti c crystal s produce d b y Sumitom o Electric . 1 5 Thes e crystal s know n a s

Sumicrystals™

, ar e abou t 5 x 5 x 0. 3 mm ^ i n siz e an d ar e develope d primaril y a s a hea t sin k material . The y hav e a yello w color , indicativ e o f nitroge n impurity , whic h i s reporte d b y th e manufacture r t o b e o n th e orde r o f ten s o f part s pe r million . Th e crystal s ar e cut , usin g a Ya g lase r beam , fro m large r crystal s tha t ar e synthesize d i n a hig h pressur e (abou t 50,00
0 atmospheres ) an d hig h temperatur e (ove r 1300°C
) process . Th e Sumicrystals ™ hav e not , t o ou r knowledge , bee n adequatel y characterize d fo r x-ra y

applications, although there are indications that they may be better than most natural diamonds incrystalline quality and in consistency.

Th e hig h pressure-hig h temperatur e techniqu e t o produc e syntheti c diamon d crystal s (firs t announce d b y th e Genera l Electri c (GE ) researcher s i n 195
5 an d detaile d later , 16 ) ha s bee n modifie d an d refine d t o produc e large r an d highe r qualit y singl e crysta l diamonds . Th e onl y singl e crysta l diamond s tha t Genera l

Electri

c no w supplie s ar e th e isotropicall y pur e (99.99% ) C ^ crystals . 1 7 Owin g t o th e muc h reduce d irregularitie s i n th e crysta l lattic e vibration s presen t i n diamond s wit h natura l isotropi c composition , th e G E crystal s hav e a roo m temperatur e therma l conductivit y o f 3 3 W/cm^-K , o r 50
% abov e tha t o f th e bes t natura l diamonds . Tw o (400 ) G E sample s ( 4 m m x 4 m m i n area ) evaluate d o n th e X-2 5 beamlin e a t

Brookhave

n Nationa l Laborator y 1 8 usin g a (440 ) silico n analyze r gav e rockin g curv e FWHM s o f 2. 5 an d 8 ar c seconds , confirmin g tha t a t leas t on e o f th e tw o i s a n extremel y goo d crystal . Othe r investigation s sho w tha t th e rockin g curv e width s fo r thes e crystal s ar e no t perceptivel y dependen t o n th e isotropi c composition . 1 9 Th e siz e o f G E crystals , accordin g t o th e supplier , doe s no t excee d 5 m m x 5 m m i n area , l ^ Durin g th e cours e o f th e presen t study , i t ha s becom e obviou s tha t th e potentia l x-ra y optica l application s o f syntheti c diamond s hav e no t bee n communicate d t o th e respectiv e manufactures . I n fact , th e Sumicrystals ™ diamond s tha t w e hav e examine d ar e mostl y use d fo r hea t sin k applications , an d hav e no t benefite d fro m an y specia l handlin g (i n cutting , polishing , etc. ) appropriat e fo r optica l applications . W e hav e measure d th e RM S surfac e roughnes s o f thes e diamon d crystal s t o b e abou t 10 A wit h a radiu s o f curvatur e o f abou t 1 0 m . Th e larges t syntheti c diamon d crystal s currentl y available ^ fro m Sumitom o i s abou t 1 2 x 1 2 x 0. 3 mm 3 an d cost s abou t $32,000 . A n 8 x 1 2 x 0. 3 mm 3 wil l cos t abou t $19,000 . A s w e shal l shortl y see , thes e size s ar e adequat e fo r th e presen t application . 4 . ROCKIN G CURV E MEASUREMENT S Tw o Sumicrystal ™ diamon d specimens , 5 x 5 x 0. 3 mm 3 i n size , wer e firs t teste d usin g a Lau e camer a t o determin e th e crysta l planes . Th e larg e surfac e are a o f th e crystal s wer e foun d t o b e nearl y paralle l t o th e (400 ) planes . Thes e plane s wer e use d i n th e Brag g diffractio n experiment s t o determin e th e qualit y o f th e syntheti c crystals . Th e experimenta l setu p fo r thes e experiment s i s show n i n Fig . 1 . Th e radiatio n fro m a Mo- K x-ra y sourc e (o n th e right) passe s throug h a se t o f doubl e (vertica l an d horizontal ) slit s an d impinge s o n th e firs t diamon d crystal . Th e diffracte d bea m fro m thi s crysta l passe s throug h a secon d se t o f doubl e slit s an d impinge s o n th e secon d crysta l wher e th e radiatio n i s diffracte d fo r a secon d time . Th e intensit y o f thi s diffracte d bea m i s recorde d wit h th e x-ra y detecto r o n th e left . Thi s i s th e standar d non-dispersiv e geometr y use d t o determin e th e averag e qualit y o f tw o crystals . Th e horizonta l width s o f th e first an d secon d slit s ar e 0.02 5 m m an d 0.1 5 mm , respectively . Thes e ar e sufficien t t o limi t th e diffractio n t o on e o f th e K x-ra y line s (K-LIII ) i n th e M o spectrum . Th e footprin t o f th e bea m o n th e secon d crysta l i s abou t 0. 6 m m horizontall y an d 3. 0 m m vertically . Th e doubl e crysta l rockin g curv e (photo n coun t rat e a s a functio n o f Brag g angle ) i s obtaine d b y rotatin g th e secon d crysta l an d recordin g th e photo n coun t rate . Th e se t u p show n i n Fig . 1 wa s first teste d b y measurin g th e doubl e crysta l rockin g curv e FWHM s o f nearl y perfec t silico n (111 ) an d (333 ) crystals . Value s o f 4. 8 an d 0.9 6 ar c seconds , respectively , wer e obtained , whic h whe n divide d b y V 2 giv e th e correspondin g averag e width s o f individua l crystal s a s 3.3 8 an d 0.6 8 ar c seconds . Thes e value s ar e accurat e t o bette r tha n 3 % whe n compare d t o th e theoretica l value s (Darwi n widths ) o f 3.3 2 an d 0.6 6 ar c seconds , respectively . The double crystal rocking curve of diamond (400) crystals was then obtained as shown in Fig. 2. Als o show n i n Fig . 2 fo r compariso n i s th e rockin g curv e obtaine d b y replacin g th e diamond s wit h silico n (111 ) crystal s without changin g th e photo n sourc e o r th e sli t sizes . Th e measure d doubl e crysta l rockin g curv e FWH M fo r diamon d (400 ) i s 6. 2 ar c second s an d fo r silico n (II1 ) i s 4. 8 ar c seconds . I f th e diamon d crystal s wer e perfect , on e woul d expec t t o obtai n ^ a rockin g curv e wit h a FWH M o f 0.9 7 ar c second s a s show n i n Fig . 3 . Thus , mos t o f th e measure d lin e widt h i n th e diamon d i s relate d t o th e crysta l imperfections . Th e measure d averag e widt h o f a Sumicrystal ™ i s the n 6.2 / -v/2=4. 4 ar c seconds , whil e a perfec t diamon d (400 ) woul d hav e a FWH M (Darwi n width ) o f 0.97/-\/2=0.6 9 ar c seconds . Wit h th e abov e information , i t i s possibl e t o estimat e th e averag e mosai c widt h o f th e diamon d crystals . Assumin g tha t th e mosai c widt h add s t o th e Darwi n widt h a s th e squar e roo t o f th e su m o f th e squares , th e mosai c widt h wil l b e give n b y th e squar e roo t o f th e differenc e betwee n th e square s o f th e measure d an d theoretica l (Darwin ) widths , tha t is , Mosai c widt h = [4.4^-0.69^ 1 =4.3 5 ar c second s

Assumin

g tha t th e mosaicit y i s isotropic , on e ca n no w us e thi s valu e o f th e mosai c widt h t o estimat e th e FWH M o f th e thes e diamon d crystal s wher ; the y ar e use d t o diffrac t x-rays , fo r example , fro m th e (111 ) planes . On e combine s th e theoretica l diamon d (400 ) widt h o f 3. 1 ar c second s wit h th e mosai c widt h o f 4.3 5 ar c second s t o obtai n th e valu e o f 5. 3 ar c second s fo r thi s width . Thu s a tw o crysta l monochromato r syste m usin g thes e diamon d crystal s wit h th e (111 ) plane s shoul d generat e a rockin g curv e wit h a FWH M o f 5. 3 V2 , o r 7. 5 ar c seconds . Th e result s o f th e rockin g curv e experiment s ar e summarize d i n Tabl e I . Tabl e I . Result s o f th e rockin g curv e experiment s wit h diamon d an d silico n crystals . Al

lexperiments were performed with the Mo K-LIII x-ray. Given widths are all for onecrystal.Description

Measure

d averag e widt h o f th e syntheti c (400 ) diamon d specimen s

Theoretica

l (Darwin ) widt h o f a perfec t (400 ) diamon d crysta l

Estimate

d mosai c widt h o f th e syntheti c diamon d specimen s

Estimate

d widt h o f th e syntheti c (111 ) diamon d crystal *width(arc seconds) 4. 4 0.6 9 4.3 5 5. 3 *denote s inferre d value s base d o n th e compute d mosaicity . Th e compariso n o f th e rockin g curve s o f th e diamon d (400 ) an d perfec t silico n (111 ) show n i n Fig . 2 i s o f specia l interes t becaus e no t onl y th e width s bu t als o th e pea k intensitie s ar e quit e similar . I f diamon d crystal s o f thi s qualit y wer e use d i n a tw o crysta l monochromator , bot h th e angula r resolutio n (whic h i s a functio n o f th e rockin g curv e widt h an d th e synchrotro n bea m openin g angle ) an d th e pea k coun t rat e i n th e diffracte d bea m (whic h i s a functio n o f th e integrate d are a unde r th e rockin g curv e an d thu s i s sensitiv e t o bot h th e heigh t an d widt h i f th e curve ) woul d b e quit e similar . Ou r limite d test s indicat e tha t th e syntheti c singl e crysta l diamond s produce d a t thi s tim e ar e alread y o f sufficien t qualit y t o mak e usabl e doubl e crysta l monochromato r systems . Th e mai n differenc e betwee n a doubl e crysta l monochromato r usin g thes e (400 ) diamond s an d perfec t silico n (111 ) i s tha t th e Brag g angl e i n th e diamon d cas e i s a facto r o f 3. 6 larger . Thi s wil l improv e th e energ y resolutio n b y a simila r faclor since AE/E is proportional to A8/8. Here, A6 is the angular resolution of the monochromator, whic h i s simila r fo r bot h cases , an d 9 i s th e Brag g angle , whic h fo r diamon d (400 ) i s 3. 6 time s large r tha n fo r silico n (111) . Th e integra l diffractio n efficienc y fo r th e (111 ) plane s i n diamon d i s expecte d t o b e large r tha n fo r th e (400 ) planes , s o th e diamon d (111 ) plane s wil l produc e monochromalor s wit h eve n highe r efficiencies . 5 . FABRICATIO N O F A DIAMON D MONOCHROMATO R

Althoug

h singl e crysta l diamond s currentl y availabl e ar e rathe r modes t i n size , the y ar e adequat e fo r th e collimate d hig h powe r densit y x-ra y beam s generate d b y undulators . A 1 2 x 8 mm ^ diamon d i s larg e enoug h t o intercep t th e centra l con e o f th e AP S Undulato r A.2.2 0 A t 3 0 m fro m th e source , th e centra l con e o f th e x-ra y bea m a t close d ga p (a t whic h th e powe r loadin g i s maximum ) i s abou t 3. 6 m m horizontall y an d 1. 2 m m verticall y (ful l widt h a t zer o height) . Thi s mean s tha t a (111 ) diamon d crystal , 1 2 m m long , ca n intercep t an d diffrac t th e entir e centra l con e radiatio n a t Brag g angle s o f 5.7 * o r larger . Thi s cover s th e entir e 4-3 0 ke V tunin g rang e o f Undulato r A . Small(er ) Brag g angle s correspondin g t o high(er ) diffracte d photo n energie s requir e tunin g th e undulato r t o highe r harmoni c energie s a t whic h th e powe r loadin g o f th e bea m i s substantiall y reduce d an d therefor e a silico n monochromato r ca n b e used .

Becaus

e o f it s lo w atomi c number , diamon d absorb s les s x-ra y radiatio n tha n doe s silico n o f identica l thickness . Th e PHOTON^ l progra m wa s use d t o calculat e th e absorbe d values . Th e result s ar e show n i n Fig . 4 fo r AP S Undulato r A (se e specification s i n Tabl e II) . Th e thicknes s o f th e diffractin g diamon d ca n b e a s smal l a s ten s o f microns . Th e thinne r th e diamond , th e les s th e absorbe d radiation , an d therefor e th e smalle r th e therma l loa d o n it . I t i s thu s advantageou s t o us e a thi n diamon d monochromato r i f th e crysta l ca n b e convectivel y surface-cooled , fo r example , b y a heliu m o r nitroge n jet . I f th e crysta l i s edg e cooled , the n th e thinne r th e crystal , th e smalle r i s th e conductio n are a fo r th e transfe r o f th e hea t fro m th e cente r o f th e crysta l t o it s coole d periphery , an d th e ne t effec t o n th e temperatur e an d strai n i n th e crysta l is , i n general , insignificant . Th e importan t paramete r i n edg e coolin g i s th e effectiv e hea t transfe r coefficien t a t th e crysta l boundaries . Becaus e o f th e hig h conductivit y o f diamond , a doublin g o f th e effectiv e hea t transfe r coefficien t a t th e crysta l edge s wil l reduc e th e maximu m temperatur e i n th e crysta l nearl y b y half . Thus , a thi n crysta l wit h edg e coolin g ma y b e a n optio n dependin g o n th e absorbe d hea t loa d an d th e edg e coolin g efficiency . Fo r th e AP S Undulato r A bea m considere d i n thi s study , w e assum e tha t th e diffractin g singl e crysta l diamon d i s bonde d t o a substrat e mad e o f polycrystallin e diamon d t o buil d wha t w e cal l a n integra l diamon d crystal . Polycrystallin e diamond s ca n hav e hig h therma l conductivities ^ approachin g tha t o f singl e crysta l diamond s and , mor e importantly , the y ca n b e produce d i n larg e size s usin g chemica l vapo r depositio n (CVD ) o r associate d techniques . Th e diamon d (o r possibl y silicon ) diffractin g elemen t ca n b e bonded ^ t o a CV D substrat e wit h appropriatel y configure d coolin g channel s Wit h a carefull y selecte d bondin g procedure , on e ma y b e abl e t o produc e strain-fre e diamon d t o diamon d bonding . W e ar e unawar e o f an y wor k i n whic h th e stres s level s i n suc h bondin g wer e measured . A n alternativ e techniqu e woul d involv e depositio n o f CV D diamon d directl y o n th e diffractin g diamon d element . Again , w e ar e unawar e o f an y wor k t o produc e o r tes t stain-fre e bondin g usin g thi s techniqu e bu t believ e ma t thi s ma y no t b e a n insurmountabl e problem . 6 . THERMA L AN D STRUCTURA L ASPECT S O F A N INTEGRA L

DIAMON

D MONOCHROMATO R I n orde r t o determin e th e relativ e performanc e o f a diamond-base d versu s a silicon-base d monochromato r system , th e slop e error s resultin g fro m th e therma l distortio n o f th e monochromator s unde r th e hig h hea t loa d o f a n x-ra y bea m ar e required . A s a rul e o f thumb , a figur e o f meri t fo r th e

performance is given by llie ratio k/a, where k is the thermal conductivity and a is the thermal expansion

coefficient . A s see n fro m th e propert y dat a i n Tabl e II , singl e crysta l diamon d ca n hav e a figure o f meri t 4 0 t o 5 0 lime s highe r tha n silico n a t roo m temperature . Th e therma l conductivit y o f polycrystallin e diamon d i s i n th e 7-2 1 W/cm^- K rang e (an d possibl y highcr).^ 2 it s therma l expansio n coefficien t i s simila r t o tha t o f singl e crysta l diamond . Tabl e H Propertie s o f singl e crysta l diamon d an d silico n a t room temperature.6~9

Propert

y Atomi c number , Z•3

Densit

y (g/c m )Thermal conductivity (W/cm-K)

Therma

l expansio n coefficien t ( K x 10 " )

Specifi

c hea t (J/Kg-K )Thermal diffusivity (cm^/s)

Young'

s module s (GPa )

Poison

s rati o

Meltin

g poin t (°C )

Tensil

e strengt h (GPa ) Yiel d strengt h (MPa )

Lattic

e spacin g (A )Diamond 6 3.51 6 2 1 0. 8 52
011.5 1,05 0

0.1-0.2

9 430
0 > 3 N A 3.567

0Silicon

1 4 2.33 0 1.2 5 2.3 3 75
00.72 16 7 0. 3 142
0 N A

1240-206

0 5.430 5 Fo r a mor e detaile d compariso n o f th e performances , w e evaluat e th e temperatur e fields an d th e resultin g slop e error s i n th e tw o monochromnto r systems , on e silico n an d th e othe r diamond . Th e radiatio n sourc e i s assume d t o b e Undulato r A a t close d ga p (11. 5 mm ) o n th e 7-Ge V AP S storag e ring wit h a positro n curren t o f 10 0 mA . Th e tota l powe r o f th e sourc e i s 3. 8 kW , an d th e pea k norma l incidenc e hea t flux a t th e monochromato r 3 0 m fro m th e cente r o f th e undulato r i s abou t 15 0 W/mm2 . Th e FWHM s o f th e bea m i n th e horizonta l an d vertica l direction s ar e 8. 2 an d 2. 9 mm , respectively . Th e centra l con e o f th e beam , whic h contain s mos t o f th e desire d (harmonic ) photons , ha s a muc h smalle r footprint . Fo r AP S Undulato r A a t 3 0 m fro m th e source , th e entir e (ful l widt h a t zer o height ) centra l con e ha s a footprin t o f 3. 6 m m horizontall y an d 1. 2 m m vertically . I n th e computation s tha t follow , i t i s assume d tha t a n apertur e wit h a n openin g o f 3. 6 m m an d 1. 8 m m i n th e horizonta l an d vertica l directions , respectively , i s place d upstrea m o f ?h e monochromator . Not e tha t th e vertica l dimensio n o f thi s sli t i s 50
% large r tha n th e 1. 2 m m o f th e bea m centra l cone . I t i s als o assume d tha t th e entir e hea t loa d intercepte d b y th e monochromato r i s absorbe d o n th e surface , a n assumptio n tha t i s mor e appropriat e fo r silico n tha n fo r diamond . I n fact , a s show n i n Fig . 4 , fo r AP S Undulato r A wit h a characteristi c energ y o f 23.
5 keV , abou t 30
% o f th e powe r i s absorbe d i n a 1 m m thic k diamond . Thi s figur e fo r silico n i s abou t 50%
. In-dept h absorptio n o f hea t wil l generall y lea d t o reduce d temperature s an d strains . A s mentione d previously , th e lo w absorptio n o f har d x-ray s i n diamon d favor s th e possibl e us e o f a thi n singl e crysta l diamon d i n Brag g o r Lau e geometries . Fo r example , fo r typica l inciden t angle s greate r tha n 5° , a 0. 2 m m diamon d se t t o diffrac t Undulato r A bea m wil l absor b n o mor e tha n 35
% o f th e inciden t bea m power . Not e tha t th e actua l bea m pat h lengt h i n th e 0. 2 m m thic k foi l i s 2. 2 mm . I t ma y b e possibl e t o edg e coo l th e thi n diamond . Th e cooling , a s w e hav e noted , woul d hav e t o b e exceptionall y goo d t o maintai n moderat e temperature s an d strain s i n th e diamond . In the present study, the total power intercepted by the monochromator through the aforementioned apertur e i s 86
0 W . W e se t th e monochromator s t o diffrac t thir d harmoni c radiatio n (12. 6 keV ) fro m

Undulato

r A a t close d gap . Th e crystal s ar e assume d t o b e 1 c m thick . Th e width s an d length s ar e eac h 2 c m large r tha n th e correspondin g dimension s o f th e bea m footprint . Th e thicknes s o f 1 c m i s arbitraril y chose n for comparison only, and , i n fact , i t i s neithe r necessar y no r optima l t o hav e suc h thic k substrates . Th e substrate s ar e assume d t o b e coole d o n th e bac k surfac e b y liqui d gallium . Th e hea l transfe r coefficien t use d i s 5 W/cm 2 -K . Again , thi s valu e i s somewha t arbitrar y bu t sufficien t fo r th e presen t comparativ e study . Tabl e II I summarize s thes e inpu t data . Table III . Parameter s an d dat a use d i n therma l an d structura l analyses .

Paramete

r

Radiatio

n Sourc e Bea m curren tTotal power Powe r densit y Bea m V-FWH M @3 0 m Bea m H-FWH M @3 0 m

Therma

l Sli t Locatio n Sli t openin g ( v x h ) Bea m footprin t ( v x h )

Absorbe

d radiatio n

Monochromato

rMonochromator location

Coolin

g (o n bac k surface ) Hea t transfe r coefficien t Tota l powe r intercepte d Pea k norma l inciden t hea t flu x

Diffractin

g photo n Energ y

Undulato

r harmoni cData 2. 5 m Undulato r A (close d gap ) 10 0 m

A3.8 kW

13 5 kW/mrad 2 2. 9 m m 8. 1 m m 3 0 m fro m th e sourc e 1. 8 x 3. 6 m m 7. 5 m m x 3. 6 m m surfac e absorptio n assume d diamon d o r silico n30 m from the source galliu m 5 W/cm 2 - K 86
0 W 15 0 W/mm 2 12. 6 ke V 3r d Th e mode l use d i n th e thermal-structura l analyse s o f th e diamon d monochromato r i s show n i n Fig . 5 . Th e dimension s o f th e bea m footprint s an d th e monochromato r component s ar e give n i n Tabl e III . Th e thicknes s o f th e singl e crysta l diamon d (assume d t o hav e bee n bonde d ont o th e substrate ) i s 0. 5 mm , whic h i s mor e tha n sufficien t fo r diffractio n purposes . I n th e cas e o f silicon , th e substrat e i s als o th e diffractin g element . Becaus e silico n ha s a relativel y lo w therma l conductivity , w e hav e als o considere d a silico n crystal , 0. 1 c m thick , t o sho w th e effec t o f reducin g substrat e thickness . Th e temperatur e profile s alon g th e AA'-axi s (Fig . 5 ) fo r th e diamon d an d silico n monochromator s wit h 1-c m substrate s ar e show n i n Fi g 6 . I n th e cas e o f diamond , th e temperatur e o n th e to p surfac e o f th e diffractin g elemen t (th e heav y line ) i s slightl y abov e th e to p surfac e o f th e substrat e (th e ligh t line) . Fo r th e silico n case , the y ar e th e sam e surfac e an d thu s th e sam e temperature . Th e footprin t region , whic h i s smalle r fo r th e diamon d monochromato r (large r Brag g angle) , i s highlighte d b y th e thicke r lin e i n Fig . 6 . Th e maximu m temperatur e ris e i n th e silico n monochromato r i s abou t 660°C
, whil e i n th e diamon d monochromato r i t i s abou t 55°C
. A reductio n i n th e thicknes s o f th e silico n monochromato r fro m 1. 0 c m t o 0. 1 c m wil l no t lowe r th e temperature s substantiall y (se e Tabl e IV) . Figure 7 shows the corresponding thermal distortions for the two monochromators. It plots the displacemen t i n th e plan e o f scatterin g alon g th e lengt h (A-A ' i n Fig . 5 ) o f th e crysta l monochromators . Th e maximu m displacement s fo r silico n an d diamon d crystal s ar e 0.2 7 fi m an d 1 4 jim , respectively . Th e displacemen t i n a 0. 1 -cm-thic k silico n crysta l i s no t significantl y differen t fro m tha t i n a 1.0-cm-thic k crystal . I t shoul d b e noted , however , tha t thi s displacemen t woul d b e substantiall y les s i f (a s i s normall y th e case ) di e crysta l wer e restrained . Th e maximu m temperatur e i n th e crysta l i s reduce d b y mor e efficien t cooling , whil e th e temperatur e gradien t acros s th e thickness , t o a first approximation , remain s unaffected . Tabl e IV . Simulatio n dat a an d result s fo r diamon d an d silico n monochromators .

Materia

l

Diffractin

g plane s Photo n energ y (keV ) Brag g angl e (° )

Monochromato

r siz e (c m x cm ) Bea m footprint , v x h (c m x cm )

Diffractin

g elemen t siz e (c m x cm )

Diffractin

g elemen t thicknes s (cm ) Pea k inciden t hea t flu x (W/mm^ )

Monochromato

r substrat e thicknes s (cm )Max. temperature rise above gallium temperature (°C) Max . temp , rise a t wall-G a interfac e (°C )Max. temp, rise across the crystal (°C) Max . compressiv e stres s (MPa ) Max . tensil e stres s (MPa )Max. displacement in the scattering plane (p.m) Max . slop e erro r i n th e scatterin g plan e (ar c second )Diamond (111 ) 12. 6 13. 8 4. 7 x 2. 2 0.7 5 x 0.3 6 0.7 5 x 0.3 6 0.0 5 3 5 1. 0 5 51837
2 1 80.27

5Silicon

(HI ) 12. 6 8.9 9 6. 6 x 2. 2 1. 2 x 0.3 6 N A N A 2 3 1. 0 66

027633

15 4 4 614
18 00.1 50

6280226

13 6 3 318
20 0 Th e slop e error s alon g th e AA'-axi s fo r th e tw o 1-c m thic k monochromator s ar e show n i n Fig . 8 , wher e again , th e footprin t region s ar e highlighted . Th e maximu m slop e errors , whic h occu r nea r peripher y o f th e footprints , ar e abou t 5 ar c secon d fo r diamon d an d 18 0 ar c second s fo r silicon . Sinc e th e photo n beam s hav e typicall y Gaussia n profile s wit h thei r peak s wher e slop e erro r i s negligibl e an d thei r nadi r wher e th e slop e erro r i s maximum , th e effective slope error s ar e somewha t smaller . 7 . SUMMAR Y AN D CONCLUSION S W e hav e propose d a diamond-base d monochromato r fo r ver y hig h hea t loa d beamlines . Th e monochromato r consist s o f a smal l singl e crysta l diamon d bonde d t o a polycrystallin e diamon d substrat e i n whic h th e necessar y coolin g channel s ar e configured . A preliminar y stud y o f th e subjec t examine s th e potentia l o f suc h a monochromator . Fro m a thermal - structura l poin t o f view , a diamon d monochromato r i s vastl y superio r t o a silico n monochromator . A simulate d compariso n o f a silico n versu s a diamon d monochromato r subjecte d t o th e AP S Undulato r A bea m a t close d ga p indicate s slop e error s o f 18 0 an d 5 ar c seconds , respectively . Whil e th e incline d monochromator2> 3 provide s a solutio n t o th e hig h hea t loa d monochromato r problem , a diamon d monochromato r allow s conventiona l (non-inclined ) operatio n o f a monochromator . I n addition , a diamon d monochromato r ca n b e devise d t o operat e i n a n incline d mode , i n whic h cas e ther e i s potentia l t o

be able to handle heat fluxes an order of magnitude higher than those generated by undulators in the hear

future . Thi s las t statemen t assume s tha i on e ca n obtai n large r (2- 4 c m size ) singl e crysta l diamonds .

Preliminar

y testin g o f Sumitom o syntheti c singl e crysta l diamonds , 5 m m x 5 m m x 0. 3 mm , gav e a doubl e crysta l rockin g curv e (fo r M o K-LIH ) o f abou t 6 ar c secon d compare d t o th e theoretica l valu e o f abou t 1 ar c second . Thes e measurement s mus t b e carefull y repeated . Furthe r stud y an d characterizatio n o f thes e crystal s i s necessar y t o evaluat e thei r suitabilit y a s monochromato r material.2 4 u shoul d als o b e realize d that , unlik e silicon , commerciall y availabl e diamond s ar e restricte d t o a limite d numbe r o f crysta l orientations . A numbe r o f additiona l issue s mus t b e investigate d t o determin e th e suitabilit y o f diamon d a s th e monochromato r materia l fo r routin e us e o n hig h hea t loa d synchrotro n beamlines.2 5 Thes e includ e (a ) strain-fre e bondin g o f diamon d t o diamond , o r depositio n o f CV D diamon d o n th e singl e crysta l diffractin g element , (b ) dimensiona l stabilit y o f a composit e diamon d monochromator , (c ) radiatio n damag e stud y fo r diamond,26-2 8 an d (Diamon dCrystal B

Detecto

r Doubl e Slit s Doubl e Slit s . Sourc e

Diamon

d

Crysta

l A Figur e 1 . Experimenta l setu p (viewe d fro m th e top ) fo r th e rockin g curv e measurements . Th e x-ra y bea m fro m th e M o x-ra y sourc e o n th e right passe s throug h a se t o f doubl e slit s an d i s inciden t o n th e Crysta l A .

Crysta

l A diffract s th e K-LII I x-ra y line , whic h passe s throug h th e secon d se t o f doubl e slit s an d i s diffracte d a secon d tim e b y th e Crysta l B . Th e final intensit y i s detecte d i n th e detecto r o n th e left . IDVI aso700 60
0 50
0 40
0 30
0 20 0 10

0Diamond (400)

•Silico n (111 ) -1

5-103-5 0 5

9 (arcsec )4.8 arcsec 6. 2 arcse c 1 015 Figur e 2 . Doubl e crysta l rockin g curve s fo r th e syntheti c diamon d (400 ) an d silico n (111 ) crystal s wit h th e M o K-LII I x-ray . Th e countin g rat e i n th e detecto r i s plotte d versu s th e Brag g diffractio n angl e o f th e secon d crysta l usin g a n arbitrar y zer o locate d nea r th e cente r o f th e peak . 1. 0 0. 8 a ais* 0.6 *5 >0.4 £ 0. 2 0.

0Theoretical(FWHM=0.97|arc secon

. t,t- fExperimental (FWHMM6. 2 aircsec ) -1 0 - 8 -6 -4- 2 0 2

6(arcsec

)4 6 8 10 Figur e 3 . Compariso n o f th e measure d an d theoretica l doubl e crysta l rockin g curve s o f diamon d (400 ) usin g photon s fro m M o K-LIII . 1.0 1 0 1 5 2 0 2 5 3 0 Dept h (mm ) Figur e 4 . Th e absorptio n o f th e AP S Undulato r A bea m i n diamon d an d silico n compute d fro m a bendin g magne t approximatio n fo r th e sourc e wit h a characteristi c energ y o f 23.
5 keV . Figur e S . Th e monochromato r mode l use d i n th e analysi s o f th e diamon d monochromator . Th e substrat e i s CV D diamon d whil e th e diffractin g elemen t bonde d t o i t i s singl e crysta l diamon d show n i n heav y lines . 1000
diffractin gclement -3. 0 -2.

0-1.0 0.0 1.0

Distanc

e (cm )2.0 3,0 Figur e 6 . Temperatur e rise i n th e 1-cm-thic k silico n an d diamon d crystal s alon g th e AA'-axi s o f Fig . 5 . 10 1 q 5 i o- A/ -Silicon |

ADiamond•diffractingelement-1 !

substrat e |\ -3. 0 -2.

0-1.0 0.0 1.0 2.0 3.0

Distanc

e (cm ) Figur e 7 . Th e displacemen t alon g th e AA'-axi s o f Figur e 5 i n th e 1-cm-thic k silico n an d diamon d crystal s unde r th e AP S undulato r bea m a t close d gap .

1000 I-

50
0 " = 1 U ouW a 3 3 -50 0 -100

0| Sil

| Di .icon imon c1 1\ \I V \/ / 1 •-3.0 -2.0 -1.0 0.0 1.0 2.0

Distanc

e (cm )3.0 Figur e 8 . Slop e error s alon g th e AA'-axi s o f Figur e 5 fo r th e silico n an d diamon d crystal s unde r th e AP S

Undulato

r bea m a t close d gap . 8 . ACKNOWLEDGMENT S Thi s wor k wa s supporte d i n par t b y th e U . S . Departmen t o f Energ y BE S Material s Scienc e unde r

Contrac

t No . W-31-109-ENG-38 . W e woul d lik e t o than k Denni s Mill s fo r hi s helpfu l comment s an d Davi d Lun t fo r obtainin g surfac e profile s o f th e syntheti c diamon d crystals . Th e crystal s wer e kindl y provide d b y Mr . I . Nakamur a o f Sumitom o Electri c USA . W e woul d lik e t o than k Patrici a Fernande z fo r he r assistan t i n rockin g curv e measurement s an d S . Picologlo u fo r editin g thi s manuscript . 9 . REFERENCE S 1 . R. K Smithe r an d A.K . Freund , editors , Worksho p o n Hig h Hea t Loa d X-Ra y Optics , Worksho p Repor t No . ANL/APS/TM-6 , Advance d Photo n Source , Argonn e Nationa l Laboratory , Argonne , Illinois , USA , 1989
. 2 . A.M . Khounsary , " A Nove l Monochromato r fo r Hig h Hea t Loa d Synchrotro n X-Ra y Radiation, " Rev. Sci. Instrum. 63
, 461-464
, 1992
. 3 . A.T . Macrander , W.K . Lee , R.K . Smither , an d D.M . Mills , C.S . Rogers , an d A.M . Khounsary , "Hig h Hea t Loa d Performanc e o f a n Incline d Crysta l Monochromato r wit h Liqui d Galliu m Coolin g o n th e

CHESS-AN

L Undulator," , Nucl. Instrum. Meth. A319 , 181-196
, 1992
. 4 . R.C . Evans , P.B . Hirsch , an d J.N . Keller, " A Paralle l Bea m Concentratin g Monochromato r fo r

X-Rays,

" Ada Cryst. 1 , pp . 124-129
, 1948
.

5. Y.S. Touloukian and E.H. Buyco, editors, Thcrmophysical Properties of Matter. IFI/Plenum

Pub. , Ne w York , 1970
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