6.8 Di ffus i on Mechan i sm .. Flick's law in microscop ic form 1. One dimensional diffusion F I: jump frequency period T: probability of atom jumping to nearest position
§6.8 Diffusion Mechanism ◆ Ⅰ.Flick's law in microscopic form 1. One dimensional diffusion. Γ: probability of atom jumping to nearest position 1 = : jump frequency period
21 2 =J12-J21=(n 1·6 J1=(C1-C22=mB3(、c=,dC 2 dx D=-62=-la
1 2 1 2 1 2 2 1 2 1 J = n J = n = 1 1 n C 2 2 2 1 2 1 D = = a ( ) 2 1 1 1 2 2 1 1 2 J = J − J = n − n x C C C J C C d d 2 ( ) 1 2 1 ( ) 2 1 2 1 2 2 1 1 2 = − − = − =
TWo dimensional diffusion D 4 3. Three dimensional diffusion simple cubic D=6 FCC(a-Fe D A[(
simple cubic: 2. Two dimensional diffusion. 3. Three dimensional diffusion. 2 4 1 D = a FCC( − Fe ): 2 2 12 1 ) 2 ( 12 4 a a D = = 2 2 1 6 1 D = a
4. For diffusion of interstitial atoms in bcc D=aTo=aTa For tetrahedral interstitial a For octahedral interstitial a' 40—4 6 D=(=) 6224
4. For diffusion of interstitial atoms in BCC 2 2 D = =a For tetrahedral interstitial For octahedral interstitial 4 1 = 4 0 = 2 2 24 1 ) 2 ( 6 1 6 2 1 a a D a = = = =
I. Di i on mechan i sms 1. Direct exchange of neighboring atoms Atom must acquire additional energy ag called the activation energy, before they jump from normal state to activated state(the saddle point) △G"=△H-TAS=△E+P△V*-TAS* This mechanism seems to be unrealistic for large Ag
◆ Ⅱ.Diffusion Mechanisms 1. Direct exchange of neighboring atoms. Atom must acquire additional energy ,called the activation energy, before they jump from normal state to activated state (the saddle point). This mechanism seems to be unrealistic for large G G G = H −TS = E + PV −TS
100 ③0od Befo diffusion +6◎ 0 Cu Ni 90000 100 ng ②○000 diffusion 0 100 o0◎ After diffusion Is completed 0 Distance Distance
2 Interstitial mechanism to be effective for diffusion in interstitial sol sol 3. Vacancy mechanism Atoms jump directly in to nearby vacant site, AG being small Different kind of atoms has different( chemical) affinity for vacancy Motion of atom Motion of vacancy (a)Vacancy mechanism (b)Interstitial mechanism
2. Interstitial mechanism to be effective for diffusion in interstitial sol.sol. 3. Vacancy mechanism. Atoms jump directly in to nearby vacant site, being small. Different kind of atoms has different (chemical) affinity for vacancy. G
Motion of a host substitutional atom Position of interstitial Position of interstitial atom before diffusion atom after diffusion oo③③③
川. calculation of d D=ald 1.rF=R2=v∞ xp(4G/ RT D=Cavo exp(AG Pr)=aav expC(AH-TAS RT -aa vo exp(As e9x-4 RT T=PPP PI: probability of atom acquiring additional AG
◆ Ⅲ.Calculation of D 1. 2. 2 D =a ) ( ) exp( ) exp( * * 2 * 2 RT H T S a RT D a G o o − − = − = exp( ) exp( ) * * 2 RT H R S a o = − exp( ) * 1 2 RT PP G o = = − = P1 P2 P3 P1 : probability of atom acquiring additional G
△G 12v P=e RT v: eigenfrequ ency of vibration △G p=e/RT -(4G+4G1 T=ve RT=ve/RT ∠H RT ∠H D RT
RT G P e * 1 − = o v P = = 1 2 2 o : eigenfrequ ency of vibration RT Gv P e − 3 = R T H R T H R S o R T G o R T G G o D e e e e e v − − − + − = = = = ( ) ( ) * *
