The intrinsic diffusion coefficients: Darken analysis and the van Loo relation

Transcription

1 The inrinsic diffusion coefficiens: arken analysis and he an Loo relaion Fro irkendall s eperien i was clear ha one has o deerine he diffusion paraeers of boh he species. We hae seen before ha inerdiffusion coefficien (or flu) is easured wih respec o fied iniial conac plane, o. Howeer, inrinsic diffusion coefficien (flu) should be easured on he coninuously oing arker plane, only, since arker plane easures he relaie oeen of flu of he species and.

2 In he eaple gien in he preious slide, is rich and is rich alloys in he syse of -. irkendall arkers oeen indicaes ha is faser diffusing species han hrough he produc layer. Marker plane oes parabolically wih ie, fro he iniial conac plane. We can easure he inrinsic diffusion coefficiens only a he plane corresponding o he irkendall arkers, because, his is he only plane which gies he idea on he relaie obiliies of he species. Following he Fick s firs law he inrinsic flu and he inrinsic diffusion coefficiens a he arker plane can be epressed as arken deeloped epirical relaion beween he inerdiffusion and inrinsic flues as Here is he elociy wih which he arker plane oes.

3 Following olzann ariable, we can wrie o λ λ d d d d λ λ So he elociy of he irkendall arker plane can be calculaed using he aboe enioned relaion fro he known annealing ie. Inerdiffusion flu of and can be relaed as 0 0 d d Since following he sandard herodynaic relaion ) ( Fro he relaions beween he inerdiffusion and inrinsic flues as shown in he preious slide

4 Relaion deried in he preious slide is anoher way o relae he arker plane shif o he inrinsic diffusion coefficiens. ow we shall derie he relaion beween he inerdiffusion and he inrinsic diffusion coefficiens. Fro he epression of he arker elociy For Furher So we can wrie The las relaion was deried by arken

5 I can be seen ha inerdiffusion coefficien is a kind of aerage (no direc) of inrinsic diffusion coefficiens. Furher, when when This indicaes ha inerdiffusion coefficien near pure depends on he inrinsic diffusion of. This sounds reasonable because inerdiffusion depends on he ineriing of he eleens.

6 d d * * * * * ) ( P Q d d P Q eerinaion of inrinsic diffusion coefficiens by an Loo relaion d d d d P Q

7 In he preious slide, he relaion for he raio of diffusiiy deried by an Loo is shown. Following, he inerdiffusion coefficien should be calculaed a he sae irkendall arker plane. Then inrinsic diffusion coefficiens can be calculaed relaes he inrinsic and he inerdiffusion coefficiens. using he relaion ha s eplained in he preious slide, coposiion profile easured is conered o s., / s. and (-)/ s. plo.

8 For eaple i/ diffusion couple is annealed a 00 o for 96 hrs. The ariaion of olar olue is calculaed fro he laice paraeer daa aailable. oposiion profile is easured afer he annealing.

9 The arker plane coposiion was deeced by he presence of horia powder (a 40.3 a.%i) ( ) i d i d d i i P i i ( ) ( ) Q d d d since i 0,,, i 0 So afer calculaing he parial olar olue, he raio of diffusiiies can be calculaed using he aboe relaion. fer calculaing he inerdiffusion coefficien, using he raio of diffusiiies and he inerdiffusion coefficien, he inrinsic diffusion coefficiens are calculaed as i /s /s