Byeong-Joo Lee

Transcription

1 yeg-j Lee OSECH - MSE calphad@pstech.ac.r yeg-j Lee

2 Fudametals Mcrscpc vs. Macrscpc Vew t State fuct vs. rcess varable Frst Law f hermdyamcs Specal prcesses 1. Cstat-Vlume rcess: U q v 2. Cstat-ressure rcess: H q p 3. Reversble dabatc rcess: q 0 4. Reversble Isthermal rcess: U H 0 yeg-j Lee

3 Secd Law f thermdyamcs - Reversble vs. Irreversble S measurable quatty u-measurable quatty q/ S rr q rev / yeg-j Lee

4 Secd Law f thermdyamcs - Mamum Wr U U q w δ q du system δw q ds system δ ds rr du system δw ds system ds δw ds system du system rr ds rr w w ma S system U system yeg-j Lee

5 Secd Law f thermdyamcs - Etrpy as a Crter f Equlbrum fr a slated system f cstat U ad cstat V (adabatcally ctaed system f cstat vlume) equlbrum s attaed whe the etrpy f the system s mamum. fr a clsed system whch des wr ther tha wr f vlume epas du ds dv (vald fr reversble prcess) U s thus the atural chce f depedet varable fr S ad V as the depedet varables. fr a system f cstat etrpy ad vlume equlbrum s attaed whe the teral eergy s mmzed. δw ds dv system ds system du system du 0dU system ds rr ds system rr ds rr yeg-j Lee

6 Secd Law f thermdyamcs - Cdt fr hermdyamc Equlbrum Further develpmet f Classcal hermdyamcs results frm the fact that S ad V are a cveet par f depedet varables. eed t clude cmpst varables ay equat f state ad ay crter f equlbrum eed t deal wth -V wr (e.g. electrc wr perfrmed by a galvac cell) Cdt fr hermdyamc Equlbrum f a Uary tw phase system ds α slated _ system ds ds β 1 α 1 β du α α α β β dv α µ α α µ β β d α he same cclus s btaed usg mmum teral eergy crter. yeg-j Lee

7 New hermdyamc Fucts Reas fr the ecessty Further develpmet f Classcal hermdyamcs results frm the fact that S ad V are a cveet par f depedet varables. eed t clude cmpst varables ay equat f state ad ay crter f equlbrum eed t deal wth -V wr (e.g. electrc wr perfrmed by a galvac cell) du ds dv S V are t easy t ctrl. Need t fd ew state fucts whch are easy t ctrl ad ca be used t estmate equlbrum F G yeg-j Lee

8 Helmhltz Free Eergy - Wr Fuct F U S df du ds Sd Fr a reversble prcess df [ds dv δw ] ds Sd Sd dv δw df dv δw δw.tal Mamum wr that the system ca d by chagg ts state at Cstat V - F. Fr a rreversble sthermal prcess F [q w] S S q S rr w V w w Fr cstat V F V w S rr 0 If cat d a mamum wr t s due t the creat f s rr. Uder a Cstat V a equlbrum s btaed whe the system has mamum (w s rr ) r mmum F. yeg-j Lee

9 Helmhmlz Free Eergy - Eample Equlbrum betwee cdesed phase ad gas phase. Use Helmhltz Free Eergy Crter t determe equlbrum amut f gaseus phase at a gve temperature ad hw t chages wth chagg temperature yeg-j Lee

10 Gbbs Free Eergy - Gbbs Fuct G U V S dg du dv Vd ds Sd Fr a reversble prcess dg [ds dv δw ] dv Vd ds Sd Sd Vd δw dg δw Mamum wr that the system ca d by chagg ts state at Cstat - G. Fr a rreversble sthermal prcess G [q w] V S S q S rr w V w G w S rr 0 If cat d a mamum wr t s due t the creat f s rr. Uder a Cstat a equlbrum s btaed whe the system has mamum (w s rr ) r mmum G. yeg-j Lee

11 hermdyamc Relats - Fr a clsed system du ds dv dh ds Vd df Sd dv dg Sd Vd yeg-j Lee

12 hermdyamc Relats hermdyamc Relats - Fr a multcmpet system Fr a multcmpet system ) ( L j G G L L L L L j j d G d G d G d G dg j j j G µ Chemcal tetal yeg-j Lee j µ L d Vd Sd dg 1 µ d dv w µ δ d µ s the chemcal wr de by the system Chemcal tetal

13 Gbbs Eergy fr a Uary System - frm dg Sd Vd Gbbs Eergy as a fuct f ad dg S d V d G( ) G( ) S d V cstat S( ) S G( ) G( C ( ) d C ( ) ) S d cstat G( ) G( ) V d yeg-j Lee

14 Gbbs Eergy fr a Uary System Gbbs Eergy fr a Uary System - frm frm G H G H S S Gbbs Eergy as a fuct f ad S H G S S S H H H G ) 1) ( ) ( ( 1)) ( ) ( ( ) ( S H S H S S H H ) cstat d C H H ) ( ) ( d C S S ) ( ) ( yeg-j Lee d C H H ) ( ) ( d S S ) ( d C d C S H G ) ( ) ( ) cstat d V V d V S d H H d V ) 1 ( α d V d V d S S α

15 Gbbs Eergy fr a Uary System - emperature Depedecy G( ) G( C ( ) ) S d d G( ) H S C ( ) d C ( ) d 서로다른출발점에서유도된위의두식은같은식인가? Emprcal Represetat f Heat Capactes c a b c 2 를이용하여위의두식이동일한것임을증명하라. yeg-j Lee

16 Gbbs Eergy fr a Uary System G( ) H S C ( ) C ( ) d d V d V() based epasvty ad cmpressblty C p () S 298 : by tegratg C p / frm 0 t 298 K ad usg 3rd law f thermdyamcs (the etrpy f ay hmgeeus substace cmplete teral equlbrum may be tae as zer at 0 K) H 298 : frm frst prcples calculats but geerally uw H 298 becmes a referece value fr G Itrduct f Stadard State yeg-j Lee

17 Crter f hermdyamc Equlbrum hermdyamc Relats Helmhltz Free Eergy Gbbs Free Eergy Crrelat btw Free eergy mmum & equlbrum Chemcal tetal vs. Gbbs eergy µ d erm as a Chemcal Wr hermdyamc Relats: Imprtace & pplcats yeg-j Lee

18 Statstcal hermdyamcs asc Ccept f Statstcal hermdyamcs pplcat f Statstcal hermdyamcs t Ideal Gas Uderstadg Etrpy thrugh the Ccept f the Statstcal hermdyamcs Heat capacty Heat capacty at lw temperature yeg-j Lee

19 pplcat f Crter 1.1 기압하 b 의 meltg pt 는 600K 이다. 1 기압하 590K 로과냉된액상 b 가응고하는것은자발적인반응이라는것을 (1) mamum-etrpy crter 과 (2) mmum-gbbs-eergy crter 을이용하여보이시오. H meltg 4810 J / mle C p ( l ) C p ( s ) J / ml K J / ml K 2. 1 번문제에서의 b 가단열된용기에보관되어있었다면용기내부는결국어떠한 ( 평형 ) 상태가될것인지예측하시오. yeg-j Lee

20 Numercal Eample quatty f supercled lqud s adabatcally ctaed at 495 K. Calculate the fract f the whch sptaeusly freezes. Gve H S m 3 C p S l J / K ( ) 7070 J at m 505 K 3 C p S( s) J / K 505 K 495 K 1 mle f lqud mles f sld (1-) mles f lqud yeg-j Lee

21 yeg-j Lee OSECH - MSE calphad@pstech.ac.r yeg-j Lee

22 hase Dagram fr H 2 O yeg-j Lee

23 hase Dagram fr Fe yeg-j Lee

24 hase Dagram fr Fe yeg-j Lee

25 Equlbrum hermal Mechacal ad Chemcal Equlbrum Ccept f Chemcal tetal I a e cmpet system G µ emperature ad ressure depedece f Gbbs free eergy G( ) H S C ( ) d C ( ) d yeg-j Lee

26 emperature Depedece f Gbbs Eergy yeg-j Lee

27 emperature Depedece f Gbbs Eergy - fr H 2 O H m H ( s l) 6008 J at 273K SH O( l)298k J / 2 SH O( s)298k J / 2 K K C J / p H O( l) / 2 K C p H O( s) 38 J / 2 K yeg-j Lee

28 emperature & ressure Depedece f Gbbs Eergy Clausus-Clapeyr equat d d eq S V H V Fr equlbrum betwee the vapr phase ad a cdesed phase d H H V Vvapr Vcdesed phase Vvapr 2 d eq V Vv R d S H H d d l d H l 2 2 R R R cstat H H C 298) [ H 298 C ] C 298 ( C H C l l cstat R R yeg-j Lee

29 hase Dagram - fr H 2 O C p H O v J / K 2 ( ) C p H O( l) J / K C p ( l v) J / K H evap H evap373 H R 373 d l 2 C d p( l v) d lg ( atm) 5.465lg lg ( atm) 4.65lg fr S/L equlbrum d d eq S V H V yeg-j Lee

30 Equlbrum vapr pressures vs. emperature yeg-j Lee

31 Equlbrum vapr pressures vs. emperature yeg-j Lee

32 Gbbs hase Rule Degree f Freedm umber f varables whch ca be depedetly vared wthut upsettg the equlbrum F p(1c) (p-1)(2c) c p 2 yeg-j Lee

33 Eample - hase rasfrmat f Graphte t Damd Calculate graphte damd trasfrmat pressure at 298 K gve H 298gra H 298da J S 298gra 5.74 J/K S 298da 2.37 J/K desty f graphte at 298 K 2.22 g/cm 3 desty f damd at 298 K g/cm 3 G H S 1 V graphte damd d yeg-j Lee

34 yeg-j Lee OSECH - MSE calphad@pstech.ac.r yeg-j Lee

35 hermdyamc rpertes f Gases - mture f deal gases 1 mle f deal cstat : G ( 2 ) G( 1 ) R l 2 1 dg Vd R d Rd l G( ) G( ) R l G G R l Mture f Ideal Gases Deft f Mle fract: Deft f partal pressure: p p artal mlar quattes: Q Q' j K G µ Q' Q G cmp V yeg-j Lee

36 hermdyamc rpertes f Gases - mture f deal gases G G R l R l Heat f Mg f Ideal Gases ( G / ) ( G / ) m H ' H H 0 H Gbbs Free Eergy f Mg f Ideal Gases G' m G G H R l Etrpy f Mg f Ideal Gases G ' m H ' m S ' m S' m R l yeg-j Lee

37 hermdyamc rpertes f Gases - reatmet f deal gases Itrduct f fugacty f dg Rd l f f 1 as 0 G G R l f Fr Equat f state V R α Vd f α Rd l f d l d R l f l f 0 α R f R R e α / α 1 V R d actual pressure f the gas s the gemetrc mea f the fugacty ad the deal he percetage errr vlved assumg the fugacty t be equal t the pressure s the same as the percetage departure frm the deal gas law yeg-j Lee

38 hermdyamc rpertes f Gases - reatmet f deal gases lteratvely f α V 1 d l d d R R Z V R d l f Z1 d l f 0 Z1 d dg f Rd l f R d l R d l Eample) Dfferece betwee the Gbbs eergy at 150 atm ad 1 atm fr 1 mle f trge at 0 C f G R l R l J yeg-j Lee

39 Slut hermdyamcs - Mture f Cdesed hases Vaper : Vaper : Vaper : Cdesed hase Cdesed hase Cdesed hase G vapr G cdesed G vapr G cdesed vapr G G cdesed G' m G G vapr G p R l p G cdesed fr gas yeg-j Lee

40 Slut hermdyamcs - deal vs. -deal slut Ideal Slut r e ( ) p r e( ) p p p Ndeal Slut r ' e( ) p p r' e( ) r e ( ) p p p yeg-j Lee

41 Slut hermdyamcs - hermdyamc ctvty G ( hermdyamc ctvty f a Cmpet Slut a 2 ) G( 1 ) R l f f a p p 2 1 fr deal slut Draw a cmpst-actvty curve fr a deal ad deal slut Hera vs. Raulta yeg-j Lee

42 ) '( ' 2 1 c Q Q L c d Q d Q d Q dq j j j 1 ' ' ' ' L L artal Mlar Quatty j Q Q ' c d Q dq ' Slut hermdyamcs Slut hermdyamcs - artal Mlar rperty artal Mlar rperty yeg-j Lee 1 c Q Q 1 ' 0 1 c dq 0 1 c dq Gbbs Gbbs-Duhem Equat Duhem Equat Mlar rpertes f Mture c dx Q dq 1 c Q X Q 1

43 ' ' ' Q Q Q m c Q Q 1 ' Slut hermdyamcs Slut hermdyamcs - artal Mlar Quatty f Mg artal Mlar Quatty f Mg deft f slut ad mechacal mg yeg-j Lee Q c c m Q Q Q Q 1 1 ) ( ' s a pure state value per mle where 왜 partal mlar quatty 를사용해야하는가?

44 Slut hermdyamcs Slut hermdyamcs - artal Mlar Quattes artal Mlar Quattes ) l l ( ' phase ref phase ref a a R G G G ) l l ( m a a R G G G ) l l ( ' a a R G G G yeg-j Lee m ) l l ( ) l l ( m R R G G G γ γ m L R G G G ) l l (

45 Slut hermdyamcs - artal Mlar Quattes Evaluat f artal Mlar rpertes 1-2 ary System artal Mlar rpertes frm tal rpertes Q dq eample) 2 dx H ax X m 1 2 Q (1 X 2) artal mlar & Mlar Gbbs eergy 2 G G m G G R ( l a l a ) M G Gbbs eergy f mg vs. Gbbs eergy f frmat G R l a Graphcal Determat f artal Mlar rpertes: agetal Itercepts Evaluat f a M f e cmpet frm measured values f a M f the ther Q 1 X X 2 X 2 2 d Q 0 2 X 2 X X X 2 X1 d Q1 X 2d Q 2 0 d Q1 d Q 2 X X X 2 1 d Q dx 2 2 dx 2 eample) 1 yeg-j Lee 2 H 2 ax 1

46 Slut hermdyamcs - N-Ideal Slut ctvty Ceffcet R l a R lγ ( G M / ) ( R lγ ) H M 2 ( R l γ ) (1/ ) H M ehavr f Dlute Sluts lm( 1) a lm( 0) a r yeg-j Lee

47 Eample 1.Gbbs eergy f frmat 과 Gbbs eergy f mg 의차이는무엇인가? 2. Slut에서한성분이 Hera 또는 Raulta 거동을한다는것을무엇을의미하는가? Mlar Gbbs eergy 가다음과같이표현되는 - 2 원 Slut phase에서각성분은 dlute 영역에서는 Hera 거동을 rch 영역에서는 Raulta 거동을보인다는것을증명하시오. Gm G G R{ l l } L yeg-j Lee

48 Slut hermdyamcs - Quas-Chemcal Mdel Guggehem E W E W E W E W Nz W Nz W Nz E Nz 2 ( E E [2E E E ]) yeg-j Lee

49 Slut hermdyamcs - Regular Slut Mdel G s m Ω S-I S- yeg-j Lee

50 Slut hermdyamcs - Sub-Regular Slut Mdel G s m [ 0 Ω ( ) 1 Ω ] S-Z Fe-N yeg-j Lee

51 Slut hermdyamcs - Regular Slut Mdel G m G G R ( l l ) Ω Cmpst ad temperature depedece f Ω Etes t terary ad mult-cmpet system Sublattce Mdel Iheret Icsstecy yeg-j Lee

52 yeg-j Lee OSECH MSE yeg-j Lee

53 rperty f a Regular Slut G s H m Ω yeg-j Lee

54 rperty f a Regular Slut yeg-j Lee

55 Stadard States yeg-j Lee

56 Stadard States yeg-j Lee

57 Stadard States Whch stadard states shall we use? yeg-j Lee

58 yeg-j Lee

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60 yeg-j Lee

61 hase Dagrams - Relat wth Gbbs Eergy f Slut hases yeg-j Lee

62 hase Dagrams - ary Systems yeg-j Lee

63 hase Equlbrum hase Equlbrum α β β α α α β β α α α β α µ µ s sys d dv du ds ' ' 1 1 ' 2 2) 1)( ( 1) ( p c c p c p f 1. Cdts fr equlbrum 2. Gbbs hase Rule yeg-j Lee L L ε ε L L L L L f f f f f ) ( ) (1 ε ε ε ε ε ε ε ε ε f L L ε ε f L L 3. Hw t terpret ary ad erary hase Dagrams Lever-Rule

64 Drvg frce f CVD Depst - frm N.M. Hwag SNU Eample: Depst f Slc SH 4 2Cl 2 S 4HCl yeg-j Lee