Unit II Crystal Structure and X-ray diffraction Engineering Physics

Transcription

1 Unit II Cyst Stutue nd X-y difftion Engineeing Pysis Intodution It is we nown ft tt mtte onsists of toms nd moeues. Te popeties of mtte depend on te ngement of toms inside mtte wi depends on te emi onding etween te toms. To undestnd te onding in soids, it is neessy to now te eetoni stutue of toms. Mtte in te univese is miny ssified into tee inds; tey e soids, iquids nd gses. In soids, te toms nd moeues e nged in fixed mnne. Soids ve definite spe nd size, wee s in iquids nd gses toms o moeues e not fixed nd nnot fom ny spe nd size. Tese mteis gin te spe nd size of te vesse in wi tey e ten. On te sis of ngement of toms o moeues, soids e ody ssified into two tegoies; tey e ystine soids nd non ystine (o mopous soids) Cystine soids In ystine soids, te toms o moeues e nged in egu nd peiodi mnne. If yst es, te oen piees so ve egu in spe. Tese soids ve dietion popeties nd e teefoe ed nisotopi sustnes. Te ystine soids ve sp meting point. Exmpes Meti soids - Cu, Ag, Au, A Non - Meti soids NC, MgO, CO, Dimond, Si, Ge. Amopous soids (non-ystine soids) In mopous soids te toms o moeues e nged in n iegu mnne. If n mopous soid es, te oen piees ve iegu in spe Tese soids ve no dietion popeties nd e teefoe ed isotopi sustnes. Te mopous soids ve wide nge meting point. Exmpes Gss, psti, wood. Spe ttie A yst is tee dimension ody. Cysts e mde up of egu nd peiodi tee dimension pttens of toms e moeues in spe. Te yst stutue my e desied in tems of ideized geometi onept ed spe ttie. Let us onside te se of two dimension ys of points s sown in te figue. It is ovious fom te figue tt envionment out ny two points is te sme nd ene it epesents spe ttie. Te spe ttie my e defined s An y of points in spe su tt te envionment out e point is te sme.

2 Unit II Cyst Stutue nd X-y difftion Engineeing Pysis If we oose ttie point t distne fom te oigin te tnstion veto n e witten s Wee, e integes. In figue Te tee dimension tnstion veto n e witten s Two dimension spe ttie: Two dimension spe ttie n e defined s An y of points in two dimension spe in wi evey point s te sme envionment wit espet to ote points. Tee dimension spe ttie: Tee dimension spe ttie n e defined s An y of points in tee dimension spe in wi evey point s te sme envionment wit espet to ote points.. Bsis: A goup of toms o moeues is tted identiy to e ttie point ten it gives te yst stutue, tis goup of toms o moeues is ed sis. Te sis is identi in omposition, nd ngement, wi is epeted peiodiy in spe to fom te yst stutue.. Unit e: In ode to onside te ide of unit e, et us onside two dimension yst in wi te toms e nged s sown in te figue. If we onside peogm su s ABCD wit side AB nd AD ten y otting tis peogm in dimensions, te woe yst ttie my e otined. In tis wy tis fundment unit ABCD is ed unit e. Tus unit e is defined s A smest geometi voume te epetition wi gives te tu yst stutue

3 Unit II Cyst Stutue nd X-y difftion Engineeing Pysis. B A A D C. Lttie pmetes Te ines dwn pe to te ines of intetion of ny tee fes of te unit e wi do not ie in te sme pne e ed ystogpi xes. Te nges etween te ystogpi xes epesented yα, β nd γ e ed intefi nges. Te inteepts,, nd on te espetive ystogpi xes, e ed pimitives of te unit e. Z Y α β γ X Te omintion of pimitives, nd nd tee intefi nges α, β nd γ e nown s ttie pmetes of te unit e. Wi detemine te tu size nd spe of te unit e. 5. Cyst systems On te sis of ttie pmetes (o engt nd dietions), te yst systems my e ssified into te foowing seven systems.. Cui. Tetgon. Otoomi. Monoini 5. Tiini 6. Tigon (o) Romoed 7. Hexgon D. P.Seenivsuu Reddy M.S, PD

4 Unit II Cyst Stutue nd X-y difftion Engineeing Pysis. Cui Lttie pmetes A tee sides e equ :- A nges e igt nges :- α β γ 90 Bvis tties : -, & Exmpes : - NC, po, N, W, Ag, Au, P, α Fe. Tetgon Lttie pmetes Two sides e equ :- A nges e igt nges :- α β γ 90 Bvis tties :- & Exmpes :- NiSO, SnO, TiO, KH PO et. Otoomi Lttie pmetes A tee sides e diffeent :- A nges e igt nges :- α β γ 90 Bvis tties : -,, & Exmpes: KNO, BSO, PCO, K SO, α S et. Monoini Lttie pmetes A tee sides e diffeent :- Two nges e igt nges :- α β 90 Bvis tties : - & γ Exmpes: CSO. H O, N SO, FeSO, gypsum, et 5. Tiini Lttie pmetes A tee sides e diffeent :- A nges e diffeent :- α β γ 90 Bvis tties : - Exmpes: CuSO. 5H O, K CO7 et 6. Tigon (o Romoed) Lttie pmetes A tee sides e equ :- A nges e equ ut not igt nges :- α β γ 90 Bvis tties : - Exmpes: CSO, ite, As, S, Bi et 7. Hexgon Lttie pmetes two sides e equ :- two nges e igt nges α β 90 nd tid is γ 0 Bvis tties : - Exmpes: qutz, Zn, Cd, SiO, AgI et

5 Unit II Cyst Stutue nd X-y difftion Engineeing Pysis S.No. Nme of te Lttie pmetes Exmpes yst system Cui : α β γ 90 po, N, W, Ag, CF, Tetgon : α β γ 90 NiSO, SnO, TiO, Otoomi : α β γ 90 KNO, BSO, PCO, Monoini : α β 90 γ CSO. H O, N SO 5 Tiini : α β γ 90 CuSO. 5H O, K CO7 6 Tigon : α β γ 90 CSO, As, S, Bi 7 Hexgon : α β 90 ; γ 0 qutz, Zn, Cd, SiO 6. Bvis tties Bvis sowed te inds of spe tties, on te sis of symmety. Tese inds of spe tties e wys eonging to te seven yst systems. Tese e ed s Bvis tties. Cui Lttie pmetes A tee sides e equ :- A nges e igt nges :- α β γ 90 Bvis tties :-, & P I F Tetgon Lttie pmetes Two sides e equ :- A nges e igt nges :- α β γ 90 Bvis tties :- & P I Otoomi Lttie pmetes A tee sides e diffeent :- A nges e igt nges :- α β γ 90 Bvis tties : -,, & D. P.Seenivsuu Reddy M.S, PD 5

6 Unit II Cyst Stutue nd X-y difftion Engineeing Pysis P I F B Monoini Lttie pmetes A tee sides e diffeent :- Two nges e igt nges :- α β 90 γ Bvis tties : - & P B Tiini Lttie pmetes A tee sides e diffeent :- A nges e diffeent :- α β γ 90 Bvis tties : - P Tigon Lttie pmetes A tee sides e equ :- A nges e equ ut not igt nges :- α β γ 90 Bvis tties : - P D. P.Seenivsuu Reddy M.S, PD 6

7 Unit II Cyst Stutue nd X-y difftion Engineeing Pysis Hexgon Lttie pmetes two sides e equ :- two nges e igt nges α β 90 nd tid is γ 0 Bvis tties : - P Hee P pimitive ttie FFe enteed ttie 7. Bsi definitions I Body enteed ttie BBse enteed ttie Neest neigoing distne ( ) Te distne etween te entes of two neest neigoing toms is ed neest neigoing distne. If is te dius of te tom, neest neigoing distne is. Atomi dius ( ) Atomi dius is defined s f te distne etween te neest neigoing toms in te yst. Coodintion nume (N) Coodintion nume is defined s te nume of equidistne neest neigos tt n tom s in given stutue. Atomi ping fto o ping fto o ping density: Atomi ping fto is te tio of voume oupied y te toms in unit e to te tot voume of te unit e. voume of toms in unit e ping fto voume of te unit e Lttie points Lttie points denote te positions of toms o moeues of te yst. Effetive nume of toms Te tot nume of toms ppeed in unit e i.e., one, enteed nd fe enteed is ed Effetive nume of toms. Void spe o intestiti spe Te empty spe vie in yst ttie wit toms oupying tei espetive positions is ed void spe D. P.Seenivsuu Reddy M.S, PD 7

8 Unit II Cyst Stutue nd X-y difftion Engineeing Pysis 8. Simpe ui (SC) stutue o Pimitive In simpe ui stutue, te toms e pesent t te ones of te ue. E one tom is sed y eigt suounding ues. Hene in e tom, ony /8 potion eonging to te ue. In SC stutue, e tom is suounded y six toms; ene its oodintion nume is six. A B Te nume of toms pesent in simpe ue 8 8 Voume oupied y te tom π Voume of unit e If is te dius of te tom nd is te side of te ue ten In simpe stutue ( fom fig AB ) voume of toms in unit e ping fto voume of te unit e π ping fto π π Q () 8 π 0.5 o 5 % 6 Tus, te ping ftion fo simpe ui stutue is 5% i.e., te toms oupy ony 5% of te spe nd te est 8% is void spe. D. P.Seenivsuu Reddy M.S, PD 8

9 Unit II Cyst Stutue nd X-y difftion Engineeing Pysis 9. Body enteed ui (BCC) stutue In ody enteed ui stutue te toms e pesent t te ones of te ue nd one tom is pesent t te ente of te ue. E one tom is sed y eigt suounding ues. Hene in e tom, ony /8 potion eonging to te ue nd te enteed tom is ompetey eonging to te ue. In BCC stutue e tom is suounded y eigt toms; ene its oodintion nume is eigt. A A B C C Te tot nume of toms pesent in BCC 8 8 Voume oupied y te toms π Voume of unit e If is te dius of te tom nd is te side of te ue ten In ody enteed ui stutue ( ) Fom fig AC AB BC voume of toms in unit e ping fto voume of te unit e 8 8 π π π ping fto Q 6 π 0.68 o 68% 8 Tus, te ping ftion fo BCC stutue is 68% i.e., te toms oupy ony 68% of te spe nd te est % is void spe. D. P.Seenivsuu Reddy M.S, PD 9

10 Unit II Cyst Stutue nd X-y difftion Engineeing Pysis 0. Fe enteed ui (FCC) stutue In FCC stutue, te toms e pesent t te ones of te ue nd s so te toms e pesent t te ente of its six fes. E one tom is sed y eigt suounding ues. Hene in e tom ony /8 potion eonging to te ue. E fe enteed tom is sed y two suounding ues; ene in e fe enteed tom, ony / potion is eonging to te ue. In FCC stutue e tom is suounded y toms; ene its oodintion nume is. A B C Tot nume of toms pesent in FCC Voume oupied y te tom π Voume of unit e If is te dius of te tom nd is te side of te ue ten In simpe stutue ( Fom fig AC AB BC ) ; ( ) voume of toms in unit e ping fto voume of te unit e 6 6 π π π π ping fto 0.7 o 7% ( ) 6 Tus, te ping ftion vue fo FCC stutue is 0.7 i.e., te toms oupy ony 7% of te spe nd te est 6% is void spe. Te ping fto is moe fo FCC stutue. Hene it is poved tt, FCC stutue is osey ped tn te simpe stutue nd ody enteed ui stutue. D. P.Seenivsuu Reddy M.S, PD 0

11 Unit II Cyst Stutue nd X-y difftion Engineeing Pysis. Mie indies yst pnes A yst onsists of ge nume of ttie points. Te pne wi is pssing toug te ttie points is ed yst pne o ttie pne. Te pe equidistne ttie pnes n e osen in vious nume of wys s epesented in te figue. Te poem is tt ow to designte pne in te yst. Mie evoved metod to designte pne in yst y tee smest integes ( ) nown s mie indies. Definition Mie indies e tee smest integes wi ve sme tio s te eipos of inteepts of te yst pne wit te oodinte xis. Te poedue fo finding Mie indies I. Fist of detemine te inteepts of te pne on te tee oodinte xes. II. Seondy te te eipos of te inteepts. III. Lsty edue te eipos into woe numes. Tis n e done y mutipying e eipo y nume otined fte ting te L.C.M of denominto. Exmpe Let us onside pne ABC, its inteepts ong tee xes e,, nd. Mie indies of te pne ABC n e otined s foows (i) inteepts e,, (ii) eipos of tese e,, (iii) L,C.M of denomintos, i.e.,, nd is.ene mutipying y, we ve 6,, Tus te mie indies of te pne is (6 ) Impotnt fetues of mie indies yst pnes (i) (i) (ii) (iii) Wen pne is pe to ny xis, te inteepts of te pne on tt xis is infinity. Hene its mie index fo tt xis is zeo. Wen te inteept of pne on ny ystogpi xis is negtive ten soud e ept on te oesponding mie index. A equy sped pe pnes of yst ve te sme mie indies. A pne psses toug oigin is defined in tems of pe pne ving nonzeo inteepts. (iv) If nom dwn to pne ( ), te dietion of nom is [ ] D. P.Seenivsuu Reddy M.S, PD

12 Unit II Cyst Stutue nd X-y difftion Engineeing Pysis (v) Mie indies epesent te oienttion of yst pne in yst ttie. (vi) If ( ) is te mie indies of yst pne, ten te inteepts mde y te pne wit te oodinte xis is /, / nd / wee, nd e pimitives... Mie indies yst dietions In yst system, te ine joining te oigin nd ttie point pesents te dietion of ttie point. To find te mie indies of yst dietion of ttie point fist note down te oodintes of ttie points nd enose tem in igge pentesis s [ ]. Y D C H G A B X Z E F Fo te unit e, te dietions of ttie points e AB-[00] AC-[0] AD-[00] AE-[00] AF-[0] AG-[] AH-[0] Te ine joining te oigin to te yst pne epesents te dietion of yst pne. Te mie indies of te yst pne enosed witin te igge pentesis i.e., [ ].. Seption etween suessive ( ) pnes Let us onside pne ABC ving mie indies ( ). Let e te nom to te pne pssing toug te oigin O. Let mes nges α, β nd γ Wit X, Y nd Z xes espetivey. Let, nd is te inteepts of te unit e. Te inteepts of OA, OB nd OC of te pne ABC ong X, Y nd Z xes e OA ; OB nd OC / Z B Y C / o N / A X D. P.Seenivsuu Reddy M.S, PD

13 Unit II Cyst Stutue nd X-y difftion Engineeing Pysis D. P.Seenivsuu Reddy M.S, PD Te dietion osines of te pependiu e OA α os OB β os OC γ os Fom osine w os os os γ β α Hene 0 N Let te next pne is pe to pne nd pssing toug te oigin O. Ten te distne etween te nd pnes is equ to. Hene, te intepn distne (d) etween te djent pnes is equ i.e.,. so d Fo ui ttie Ten ( ) d Fo tetgon system Ten d Fo otoomi system d Note: - Tis etion is ony ppie fo te yst systems wi systems ve nges e igt nges i.e., ui, tetgon nd otoomi.

14 Unit II Cyst Stutue nd X-y difftion Engineeing Pysis. X- Ry Difftion: Difftion of visie igt ys n podued fom difftion gting. If te gting onsists of 6000 ines/m; te sping etween ny two suessive ines in te gting in te ode of wveengt of visie igt so it podue difftion. Te wveengt of X-ys is in te ode of n ngstom, so X-ys e une to podue difftion wit difftion gting. To podue difftion wit X-ys, te sping etween te onseutive ines of gting soud e of te ode of few ngstoms. Ptiy, it is not possie to onstutive su gting. In te ye 9, Lue suggested tt te yst n e seve s tee dimension gting due to te tee dimension ngement of toms in yst. Tee e tee min difftion metods y wi te yst stutues n e nyzed.. Lue metod : ppie to singe ysts. Powde metod : ppie to finey divided ystine o Poyystine speimen powde. Rotting yst metod : ppie to singe ysts. 5. Bgg s w Sttement Bgg s w sttes tt te pt diffeene etween te two efeted X- ys y te yst pnes soud e n integ mutipe of wve engt of inident X-ys fo poduing mximum o onstutive intefeene. Pt diffeene n λ Let us onside set of pe ttie pnes I nd II of yst septed y distne d pt. Suppose now em of X-ys of wve engt λ e inident upon tese pnes t n nge θ s sown in te figue. Conside y PA efeted t te tom A in te dietion AR fom pne nd note y QB efeted t note tom B in te dietion of BS fom pne II. Te pt diffeene etween te two ys is (CBBD). Wen te pt diffeene etween te two ys is n integ mutipe of X-ys wveengt, te onstutive intefeene penomenon wi ou. Tus te ondition fo onstutive intefeene is ( CB BD) nλ C θ θ θ Fom ABC CB CB sin θ AB d CB d sinθ

15 Unit II Cyst Stutue nd X-y difftion Engineeing Pysis Fom ABD BD d sin θ ( CB BD) d sin θ d sin θ nλ BD sin θ AB Fite BD d Wee n,,... et we otin fist, seond, tid...et ode difftion spots. Sine mximum possie vue of θ is. We get d nλ λ d Tus, te wveengt λ soud not e exeed twie te intepn sping fo difftion to ou. 6. Powde metod Te powde metod ws deveoped y Deye nd See in Gemny nd y i in Amei simutneousy. Tis metod is used to study te stutue of ysts wi nnot e otined in te fom of pefet ysts of ppeie size. Tis metod n e used fo pue mets, ompounds nd oys. Bsi Pinipe Te si pinipe undeying tis powde tenique is tt, te speimen ontins ge nume of mio ysts (~ 0 in mm of powde smpe) wit ndom oienttions, most te possie θ nd d vues e vie. Te difftion tes pe fo tese vues of θ nd d wi stisfy Bgg s ondition, i.e., d sinθ nλ. Expeiment ngement:- Te expeiment ngement is sown in figue. Te finey powdeed smpe is fied in tin piy tue nd mounted t te ente of te dum sped ssette wit potogpi fim t te inne iumfeene. Coet te X-ys (non-monoomti) fom n X-y tue. We otin te monoomti X-y dition y pssing toug te fite. Tis monoomti X-y dition n e onveted into fine peni em y pssing toug te ed dipgms o oimtos. Te peni em of X-ys is owed to f on te tin wed piy tue P ontining te powdeed yst. X-ys Led Dipgm Powde Speimen D. P.Seenivsuu Reddy M.S, PD 5

16 Unit II Cyst Stutue nd X-y difftion Engineeing Pysis Teoy Te si pinipe undeying tis powde tenique is tt, te speimen ontins ge nume of mio ysts (~ 0 in mm of powde smpe) wit ndom oienttions, most te possie θ nd d vues e vie. Te difftion tes pe fo tese vues of θ nd d wi stisfy Bgg s ondition, i.e., d sinθ nλ.. Fo te vue ofθ, te em ppes t te oesponding θ devition. Te ptten eoded on te potogpi fim is sown in te figue wen te fim is id ft. Due to te now widt of te fim, ony pts of iu ings e egiste on 0 it. Te uvtue of s eveses wen te nge of difftion exeeds90. S s Knowing te distnes etween te pi of s, vious difftion nges θ s n e uted y using te fomu. S 80 S θ R π R Wee, is te dius of te me. By nowing te vue of θ fom te ove eqution, te intepn sping (d) n e uted fo fist ode difftion fom Bgg s eqution. nλ d sin θ Knowing pmetes, te yst stutue n e studied. Meits:- Using fite, we get monoomti x-ys A ystites e exposed to x-ys nd difftion tes pe wit vie pnes. Tis metod is used fo detemintion of yst stutue, impuities, disotion density et., 7. Lue metod Te Lue metod is one of te X.y difftion tenique used fo yst stutue studies. Bsi pinipe Te si Pinipe undeying tis Lue tenique is tt, e efeting pne seets wve engt oding wit te Bgg s etion, i.e., d sinθ nλ. Te esuting difftion is eoded on te potogpi pte. Expeiment ngement Te expeiment ngement of te Lue tenique is sown in te figue D. P.Seenivsuu Reddy M.S, PD 6