MECH6661 lectures 10/1 Dr. M. Medraj Mech. Eng. Dept. - Concordia University

Transcription

1 Outle Revew ublattce Mdel Example ublattce Mdel Thermdyamc Mdelg Itrduct Example lly Desg Terary Phase Dagrams Gbbs Phase Rule Thermdyamcs f Multcmpet ystems Mech. Eg. Dept. - crda Uversty Revew: ublattce Mdel Fr rdered termedate sld sluts, t s better t use a mdel that ca descrbe the structure mre specfcally. I the sublattce mdel the elemets f the phase are dvded t separate lattces accrdg t the crystallgraphc structure f the phase. Fr example, a smple structure stes at the bdy s cetre ad crer psts ca be descrbed as dfferet sublattces, as llustrated the accmpaed fgure. structure I the sublattce mdel, stead f the verall cmpst x, the ste-fract y s used as a ceffcet whe defg the Gbbs eergy f the phase. The ste-fract s defed as the fractal ste ccupat y f each f the cmpets the specfc sublattce. MEH666 lectures 0/ Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/ y Revew: ublattce Mdel where s the umber f atms f cmpet sublattce s perfrmed fr all cmpets sublattce If there are vacaces the sublattce they are tae t accut as cmpets. The verall cmpst gve mle fracts s drectly related t ste fracts by the fllwg relatshp: where N s the ttal umber f stes sublattce ad y Va s the umber f vacaces sublattce The deal etrpy f mxg s made up f the cfguratal ctrbuts by cmpets mxg each f the sublattces. The umber f permutats that are pssble, assumg deal terchages wth each sublattce, s gve by: Mech. Eg. Dept. - crda Uversty x W N P N y ( y Va N )!! Example: ublattce Mdel d the mlar Gbbs eergy f deal mxg s: d G T RT N The ed members geerated whe ly pure cmpets exst the sublattce, effectvely defe the Gbbs eergy referece state. Fr a sublattce phase wth the fllwg frmula (,) (,D), t s pssble fr fur pts f cmplete ccupat t exst where pure exsts sublattce ad ether pure r D sublattce r, cversely, pure exsts sublattce wth ether r D sublattce. MEH666 lectures 0/3 Mech. Eg. Dept. - crda Uversty d y l y MEH666 lectures 0/4

2 Example: ublattce Mdel - The cmpst space f the phase ca the be csdered the fgure abve as csstg f fur cmpuds, the s-called... (at the crers f the square). - The cmpst f the phase s the ecmpassed the space betwee the fur ed-member cmpuds ad the wll l as shw the abve fgure. Ths surface ca be represeted by: Why Thermdyamc Mdellg? s we all w s far, thermdyamcs prvde relats betwee may dfferet materals prpertes le amut f phases ad ther cmpsts, heat f trasfrmat, partal pressures etc. Expermetal thermdyamcs has prved ts value fr materals research fr mre tha 00 years. Mder multcmpet materals wuld requre very extesve expermetal wr rder t establsh the relevat data fr phase equlbra ad thermdyamc prpertes. Mdellg s the ly pssble techque t reduce expermetal wr ad t crease the value f each ew expermet by allwg accurate extraplat. Thermdyamcs prvde the mst mprtat frmat fr a phase trasfrmat: the fal equlbrum state Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/5 Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/6 Example: lly Desg Usg Thermdyamc Mdelg lly Desg t d Z Z l l l-z exp. Phase dagram, after H. ag et. al Z9 (9 wt% l, wt% Z) qud wt% l T = 400 (heat treatmet ) Temperature Z9 (9 wt% l, wt% Z) q+ + qud q Mass fract l Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/7 Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/8

3 - ystem supercductvty at 39 K (hghest T c fr -xde) Thermdyamcs prvde helpful sght t the apprprate prcessg cdts fr Temperature Example: Prcess Develpmet y Thermdyamc Mdelg Gas+ + Gas P= Trr Gas+ 7 Gas+ 4 ld (s) tmc Fract f r Temperature - calculated phase dagram, after X. X et. al. (00) Mech. Eg. Dept. - crda Uversty Gas+ Gas+ 7 Gas+ 4 + Gas ld+ P= mtrr (s) tmc Fract f r Isuffcet supply wll lead t 4, 7 r sld phases. Gas+ 4 - ystem The pressure temperature phase dagram fr the -, after Z.-K u et. al. (00) MEH666 lectures 0/9 Mech. Eg. Dept. - crda Uversty Prcess Develpmet t d uldg a thermdyamc database fr ths system helps t develp a prcess t depst the supercductg phase MEH666 lectures 0/0 Terary Phase Dagrams Terary PD ct d T:% =..%; % = %; % =..% R: % =..%; % =.%; % =..% :% =..%; % =. %; % =.% R T % % X +X + X = 00 Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/ Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/

4 Terary PD ct d Terary PD ct d I rder t have the same frmat that we had fr bary dagrams (cmpst plus T), we wuld eed a 3D represetat wth the cmpst tragle as bass. Hwever, except fr relatvely smple cases, t s dffcult t depct clearly by meas f perspectve dagrams the cmplete terary space mdel wth ts csttuet spaces, curves, ad pts. Therefre, t s cveet t use: prected vews (e.g., a prect f the lqudus r the sldus surface t the base f the space mdel) plae sects, tae hrztally (.e. sthermally) r vertcally (smlar t the bary dagrams) thrugh the 3D space mdel. I ctrast t bares, t s mpssble t mae a cveet graphcal represetat f the cmplete terary phase dagram that ca be utlzed all practcally mprtat cases. lut: emplyg a cmputer prgram whch wll cmpute the equlbrum cmpst the terary system at ay gve temperature ad cmpst. Temperature T = value Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/3 Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/4 Terary Isthermal ects Terary Eutectc qudus prect Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/5 Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/6

5 Terary Eutectc Terary Eutectc sder the three bary systems..,, ad. We ca arrage the three dagrams three dmess as shw here. The space sde the tragular prsm represets systems wth all three cmpets preset. There wll be a feld where crystallzes frst, a feld where crystallzes frst, ad e where crystallzes frst. I realty, there s a lqudus surface cverg the tragle ad as the system cls, t wll slde dw the surface Ths dagram shws the relatshp betwee temperature the bary systems ad temperature the tragle dagram. Very fte, temperature cturs are mtted. If the system s smple, ths s t a prblem. Hwever, f there are maxma r mma the lqudus surface, the dagram becmes less useful wthut cturs Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/7 Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/8 Phase Evlut f Terary Eutectcs Phase Evlut f Terary Eutectcs The frst thg that wll happe s that e cmpet wll beg t crystallze. I ths case, t s. s we remve frm the melt, the melt cmpst wll mgrate straght away frm the crer as shw. Evetually the melt wll ht a feld budary ad the a secd cmpet wll beg t frm. I ths case, t s. The cmpst f the melt wll mgrate away frm bth ad the geeral drect f. The path f the melt s shw mageta. ce s w frmg alg wth, the sld cmpst mgrates the drect f. The melt, system, ad sld cmpsts always le a straght le as shw. Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/9 Mech. Eg. Dept. - crda Uversty Fally the melt reaches the terary eutectc ad all three cmpets beg t frm. The eutectc s usually a temperature mmum s the melt des t mve ce t reaches the eutectc. ce all three cmpets are w frmg, the sld cmpst mves t the terr f the tragle. The melt, system, ad sld cmpsts always le a straght le as shw. ce the melt stays at the eutectc, the sld mgrates tward the system cmpst as shw gree. Oce t reaches the system cmpst, the etre system s sldfed. Gve the rules abve, we ca dvde the tragle t sx felds wth crystallzat rders as shw. Nte that ay rder s.. MEH666 lectures 0/0

6 Revew: Partal Mlar Free Eergy 0 mutes rea G G ls: G bslute Mlar Gbbs Free Eergy T, P, X Partal Gbbs eergy r.. X + X G mxg ad G X Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/ X chematc plt f Gbbs free eergy vs. mle fract fr a bary system Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/ Revew: Thermdyamcs wth mpstal hages The Master equats that we develped prevusly are: It ca als be shw that: du Td PdV dh Td VdP dg dt VdP d dt PdV U, V, T, V, d d d d H, P, Thermdyamcs f Multcmpet ystems sder a system wth cmpets,,, l, dstrbuted amg phases,,,, t equlbrum t must be true that: = = = = = = = =... = = = =... l = l = l = l =... etc. hemcal ptetals represet the slpe f the Gbbs free eergy surface cmpstal space. Thus, a cmpet wll mve frm a phase whch t has a. chemcal ptetal, t e whch t has a chemcal ptetal, utl ts chemcal ptetal all phases s the... pecfc example: sder a - l-a melt equlbrum wth tw slds ad t equlbrum: melt = = l melt = l = l a melt = a = a Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/3 Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/4

7 Terary ystems Istead f curves fr a bary system, the case f a terary system, Gbbs free eergy surfaces ca be pltted fr all the pssble phases as fucts f temp ad cmpst. The chemcal ptetals f,, ad f ay phase ths system are gve by the pts where the tagetal plae t the free eergy surfaces tersects the,, ad axs. three-phase equlbrum the terary system fr a gve temperature ca be derved by meas f the tagetal plae cstruct. Terary ystems Eutectc pt: fur-phase equlbrum betwee α, β, γ, ad lqud Fr tw phases t be equlbrum, the chemcal ptetals shuld be.., that s the cmpsts f the tw phases equlbrum must be gve by pts cected by a cmm tagetal plae (e.g. l ad m). The relatve amuts f phases are gve by the. rule. three phase tragle ca result frm a cmm tagetal plae smultaeusly tuchg the Gbbs free eerges f three phases (e.g. pts x, y, ad z). Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/5 Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/6 Thermdyamcs f Multcmpet ystems Thermdyamcs f Multcmpet ystems Fr bary systems: Partal excess Gbbs eergy Fr terary systems: x x G G 0 x G x G ( x x G ex ex x G x RT G RT l x G x G ) x x x l x x l x xx G 0 G RT l x G 0 0 Mech. Eg. Dept. - crda Uversty RT x ( x deal l x G x x Excess l x ) x x 0 ( x x ) x 0 ( x x ) l x ( x x ) ( x (( ) x x ( x ( ) x x ) where the parameters have the same values as each f the bary systems If ecessary, a terary term X X X G (T,X) ca be added rder t descrbe the ctrbut f three elemet teracts t the Gbbs eergy. ex MEH666 lectures 0/7 Mech. Eg. Dept. - crda Uversty m m G x x x x x Where = x 0 + x + x ad x + x + x = s a terary teract parameter Hgher rder teract parameters ca be usually mtted (a few excepts quaterary systems) MEH666 lectures 0/8

8 Example: Fe-N-r ystem The terary dagram f N-r-Fe cludes taless teel (wt.% f r >.5 %, wt.% f Fe > 50 %) ad Icel (Ncel based superallys). Mech. Eg. Dept. - crda Uversty The Gbbs Phase Rule: Example - Terary ystems t pt Ph = (sld & ) = 3 F = 3 Ph + as pressure s cstat F = 4 - Ph F =.. (T ad X, X r X shuld be specfed) t pt, Ph = 3 (sld, &) = 3 F = 4 - Ph = (T ly shuld be specfed) MEH666 lectures 0/9 Mech. Eg. Dept. - crda Uversty e + t E the eutectc where all three phase felds meet: P = 4 (sld,, ad ) = 3 F= 4 Ph = (T ad cmp are fxed) + E e + e 3 mple eutectc terary phase dagram at cstat pressure MEH666 lectures 0/30 Terary ystems Terary ystems wth ary gruet mpuds Nte that the eutectc pts each f the bary systems prect t the terary systems as les. These les are called budary curves, ad ay cmpst e f these curves wll crystallze the tw phases ether sde f the curve. Mech. Eg. Dept. - crda Uversty terary system that has a bary sub-system wth a cmpud that shws cgruet meltg (melts t a lqud f ts w cmpst). The result f the addt f ths termedate cmpud s essetally that the terary system XYZ s dvded t tw smaller terary systems represeted by tragles WYZ ad XWZ MEH666 lectures 0/3 Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/3

9 Terary ystems wth ary gruet mpuds Terary ystems wth ary Icgruet mpuds e The termedate cmpuds are cgruetly meltg. It s characterstc f the cgruetly meltg bary cmpud that ts cmpst pt always falls ts prmary feld f stablty the terary system. I these tw cases, ths prmary phase feld s descrbed by the les E -E ad P-e. Mech. Eg. Dept. - crda Uversty terary system ad e f the bary systems that ctas a cmpud, D, that melts cgruetly. MEH666 lectures 0/33 Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/34 Terary ystems wth ary Icgruet mpuds The termedate cmpud ths dagram s cgruetly meltg because t s t the prmary phase feld f the cmpud. gruet meltg s mprtat determg the lamade les ad the crystallzat path. Next tme: tue Terary ystems Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/35 Mech. Eg. Dept. - crda Uversty MEH666 lectures 0/36