Physical metallurgy principles. Chap 7 Vacancies

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1 Physicl metllurgy priciples Chp 7 Vccies

2 Iterl eergy & etrpy Iterl eergy (U): ttl kietic d ptetil eergy f ll the tms i mteril bdy. Temperture mplitudes f the elstic wes iterl eergy The itesity f the lttice ibrtis is therefre fucti f temperture. etrpy (S): fr reersible pth S S T dq dq S S S ] re; ds T etrpy i stte etrpy i stte bslute temperture elemet f het dded t system fr irreersible pth: S S dq S ] irre; ds T dq T dq T Etrpy is fucti f stte; it depeds ly the stte f the system. The etrpy differece (S - S ) is idepedet f the wy.

3 Spteus rectis & Gibbs free eergy Rectis tht ccur spteusly re lwys irreersible. Gibbs free eergy is the imprtt t kw the cditis tht brig but spteus rectis. G U PV TS G : Gibbs free eergy U : iterl eergy P : pressure V : lume T : bslute S : etrpy temperture ethlpy : H U PV G H TS G G2 G1 H TS ( H 2 TS 2 ) ( H 1 TS 1 )

4 Reersible recti: free-eergy chge is zer t cstt temperture d pressure. dq Q S T e Te Q : the ltet het f freezig fr wter H U PV deritie f H dh du PdV VdP pressureis cstt VdP 0 the chge f lume is eglected PdV dh du Q Q dg Q Te Q Q 0 T If irreersible recti: TS > Q G < 0, the free eergy chge fr this spteus recti is egtie. G H TS While the free eergy tells us whether r t spteus recti is pssible, it ct predict the speed f the recti. Ex. Dimd d grphite e Q TS 0 0

5 H: H -

6 Sttisticl mechicl defiiti f etrpy * the mixig f gses is spteus (irreersible) recti free- eergy equti : dg dh TdS dh 0 dg TdS (t cstt P & T, iterl eergy chge) free- eergy decrese ds 0 Etrpy f the system hs icresed by the mixig f the gses. (system becmes mre disrdered) * reltish ip betwee etrpy d prbbilit y ltzm equti : S k l WP WP : the prbbilit y f stte k : ltzm' s cstt

7 the chge i mixig etrpy: S S S k l PW 2 k l PW 1 P S kl P S S W2 2 W1 1 1 etrpy f umixed gses P W 1 etrpy f mixed gses 2 W 2 prbbility f umixed stte prbbility f mixed stte * The prbbility f fidig the tms i the umixed (ll tms f gs i V ; ll tms f gs i V ) V V P, : umber f d tms V V W 1 V V P 1 S k l P k l V V V V kl kl V V k l k(1 )l(1 ) W2 2 W1 1 V V ( d 1 ) V V R k, k kn R N mixig-etrpy equti:(fr e mle f gs) P S R[ l (1 )l(1 )]

9 相變態 Idel Slutis Idel slutis - Whe H mix = 0, the resultt sluti is sid t be idel. - I sttisticl thermdymics, etrpy is qutittiely relted t rdmess by the ltzm equti, i.e. k: ltzm s cstt, W: mesure f rdmess. - There re tw ctributis t the etrpy f slid sluti- therml ctributi S th d cfigurtil ctributi S cfig. If there is lume chge r het chge durig mixig the the ly ctributi t S mix is the chge i cfigurtil etrpy. efre mixig, the d tms re held seprtely i the system d there is ly e distiguishble wy i which the tms c be rrged. - Stirlig s pprximti If N G mix S k lw S H 1 k l1 0 S mix S 2 mix ln! NlN N TS mix G TS (1.22) mix mix 9 (1.23)

10 lw lw lw lw lw lw lw S cfig cfig cfig cfig cfig cfig cfig k lw ( N l N N N ln N N N N l N N N l N N N N N N R = N k: uiersl gs cstt. N l N l N l N l N N N )! l( N! N! l k N Nl l N Nl l N N l l N l N N l l N l N l l l R l l 2 cfig l N N )! l N S R l l ) (1.25) mix ( N l! l N N! 1 l 1 l S 0 mix 0 0 G T mix S mix Fig. 1.9 Free eergy f mixig10 fr idel sluti.

Higher the temperture mre itese the therml ibrtis mre frequetly re the eergy brriers ercme.

11 Vccy mechism The diffusi pheme is the mst geerlly cceptble hs bee the ccy mechism. Eergy sufficiet t ercme the brrier is furished by the therml r het ibrtis f the crystl lttice. Higher the temperture mre itese the therml ibrtis mre frequetly re the eergy brriers ercme. Vccy mti t high temperture is ery rpid the rte f diffusi icreses rpidly with icresig temperture. The equilibrium ccetrti f ccies i crystl s fucti f temperture. Vccy mti Creti ccy

12 ex. if crystlctiig tms d ct lttice sites thewrk f ccy be represeted by w crystlctiig ccies will he iterl eergy greter th tht f crystl withut ccies by w ** the free eergy f crystlctiig ccies : G H TS G : the free eergy due t ccies H : the ethlpy icrese due t the ccies S : the etrpy due t the ccies H w (iterl eergy fr ccies) G w TS

13 The etrpy f the crystl is icresed i the presece f ccies fr tw ress: 1. The tms djcet t ech hle re less restried th thse cmpletely surruded by ther tms d c ibrte i mre irregulr r rdm fshi. 2. Etrpy f mixig due t the presece f ccy. Sm S k[ l (1 )l(1 where Sm : mixig etrpy : ttl umber f tms ( ) : ccetrti f tm / (1 ) : ccetrti f tm ) /

14 ) ( ] [l 0 0] l 1 ) l( ) ( 1 ) [( 0 miimum t y gie temperture. mke ] l l ) )l( [( ccies : The free- eergy equti f ** ] l l ) )l( [( ] l l [ ) ( psitis ccupied lttice the ccetrti f : ccies the ccetrti f : ) (1 umber : ttl ccies d tms mixig csists f ex. / / kt w kt w m m m e e kt w kt w d dg G kt w T S w G k S k S

15 H f Nw d R kn Nw/ NkT H f / RT e e H f : the het f ctiti fr tfrm e mle R : gs cstt 8.31 jules/mle - K f ccies; jules/ml e ex. Cu, H f 83,700 jules/mle f ccies H f / RT 83,700/8.37T 10,000/ T e e e t T 0 e 0 10,000/ T 300K e e ,000/ T 1350K e e The strg effect f temperture the umber f ccies.

16 Temperture depedece G w TS 1 : w TS G 0 e (high temperture) e (lw temperture) ( high temp. icrese the etrpy th lw temp.)

17 ** the equilibriu m rti f ccies t tms t gie temp. T H f / RT e * the required eergy f jump f tms it ccies is supplied by the therml r het ibrti f the crystl. **fr tm jump t ccy: p cst e p : the prbbilit y f tm pssesses eergy equl t r greter th gie eergy q q : height f eergy brrier r m r e r : the umber f tm jumps per secd it H m : ctiti ethlpy fr the memet f ccies i jules per mle : cstt, depeds umber f fctrs. (the umber f tms brderig the hle; the ibrti frequecy f tms) 15 ex. Cu, 10, H m 121KJ / mle jump rte equti : 10 t 1350K r 210 jumps / sec t e 300K q H / kt / RT r q / kt 10 6 jumps / sec ccy

18 r r H H m / RT e : the umber f jumps per secd mde by tm : the umber f ccies : the umber f tms f e H f / RT : the ctiti ethlpy fr the frmti f ccies H / RT H / RT ( H )/ RT m f m f r e e e The rte t which tm jumps, r mes frm plce t plce i crystl, thus depeds tw eergies : H f : the wrk tfrm mle f ccies H m : the eergy brrier tht must be ercmei rder t me mle f tms it ccies. ** The tmic jump rte is extremely sesitie t temperture. H

19 Iterstitil tms Tw types f tms ccupy these iterstitil sites: 1. Smll sizes (C, N, H, O ) : iterstitil slid sluti. 2. Sme sizes tm (ex. Cu tm i Cu) : tm ccupy regulr lttice site, which c be redily prduced i metls s result f rditi dmge. Cllisis betwee fst eutrs d metl c result i kckig tms ut f their rml lttice sites. Oce the iterstitil defects re prduced, they re ery mbile.

20 Diccy If pir f ccies cmbie t mke sigle pit defect, diccy is sid t be creted. I metl where the ccies d diccies re equilibrium, e c pprximtely cmpute the rti f diccies t ccies usig this eq. Z: crditi., q b is the bidig eergy f diccy.

Degenerate and Non degenerate semiconductors. Nondegenerate semiconductor Degenerate and nondegenerate semiconductors

Degenerate and Non degenerate semiconductors. Nondegenerate semiconductor Degenerate and nondegenerate semiconductors 4.3.4 Degeerte egeerte semicuctrs Degeerte egeerte semicuctrs Smll mut f t tms (imurity tms) itercti betwee t tms Discrete, iterctig eergy stte. F t the bg F F r ccetr egeerte semicuctr 4.3.4 Degeerte