EMA5001 Lecture 12 Solidification via Homogeneous Nucleation by Zhe Cheng

Transcription

1 EMA5001 ectue 1 olidification ia Hoogeneous Nucleation 016 by Zhe Cheng

2 EMA 5001 Physical Popeties of Mateials Zhe Cheng (016) 1 olidification - Hoogen Nucleation Phase ansfoation olid state phase tansfoation Heteogeneous tansfoation ansfoation occu at paticula locations Always inole ceation and igation of inteface Often go though nucleation & gowth Hoogeneous tansfoation ansfoation eeywhee in the ateials May o ay not inole ceation of inteface Most phase tansfoation go though nucleation & gowth Ceation of inteface nucleation Migation of inteface gowth

3 Classification of Nucleation & owth ype Phase ansfoation EMA 5001 Physical Popeties of Mateials Zhe Cheng (016) 1 olidification - Hoogen Nucleation Classification ype Militay Ciilian Effect of tepeatue Atheal Inteface type lissile Non-glissile Coposition of pecipitate and paent phase Natue of diffusion Rate liiting step Exaples ae coposition No diffusion Inteface contol Matensite, winning ae coposition hot-ange diffusion Inteface contol ain gowth, α in Fe heal actiated Inteface contol Diffeent coposition ong-ange diffusion Diffusion contol Mixed contol Bainite olidification Eutectoid

4 olidification & Cystallization Applications Casting etal pats (e.g., ion and steel, bonze, aluinu) Casting of seiconductos (e.g., i) owth of single cystals (e.g., Al O ) opics Diing foce & baie Citical conditions Rate Ipacts of Coposition Pocessing condition (e.g., ) Intefaces /ulti-cystalline-silicon /pdf/kyocea%0apphie.pdf Multi-cystalline i fo sola cells ola_panels/ apphie (Al O ) fo adanced display and lighting EMA 5001 Physical Popeties of Mateials Zhe Cheng (016) 1 olidification - Hoogen Nucleation

5 Baies in Reactions & Phase ansfoation EMA 5001 Physical Popeties of Mateials Zhe Cheng (016) 1 olidification - Hoogen Nucleation 5 Exaples of a Pocess heodynaically Faoable yet not Readily Occuing Actiated state Oxidation of cabohydates at oo tepeatue Coplete oxidation of stainless steel o aluinu iquid etal doplets undecooled below its elting point Oigins of the Baie High enegy state ow enegy state Cabohydate oxidation - plitting of oxygen olecules tainless steel o aluinu oxidation - Diffusion of oxygen o etal though the oxide shell to sustain the eaction olidification of liquid - Ceation of new suface o intefaces Nucleation of solid (o a new phase) and ceation of the inteface owth of the nucleus and oeent of the inteface

6 Hoogeneous Nucleation & Heteogeneous Nucleation EMA 5001 Physical Popeties of Mateials Zhe Cheng (016) 1 olidification - Hoogen Nucleation 6 Hoogeneous Nucleation Unifo thoughout, no special location Need lage diing foce (e.g., undecooling) ess coon Heteogeneous Nucleation Occuing at special locations (local defects: intefaces, ipuities, etc.) all diing foce (e.g., undecooling) Depend on featues and concentation of the defects (intefaces o ipuities) Coon

7 Hoogeneous Nucleation fo iquid olidification (1) EMA 5001 Physical Popeties of Mateials Zhe Cheng (016) 1 olidification - Hoogen Nucleation 7 Enegy change in hoogeneous nucleation Define V Volue fo solid nucleus V Volue fo eaining liquid ibbs fee enegy pe unit olue of liquid ibbs fee enegy pe unit olue of solid olid-liquid Intefacial enegy A olid-liquid Intefacial aea otal fee enegy of the liquid befoe nucleation V V 1 otal fee enegy of the afte nucleation V V A Fee enegy change in this pocess: 1 V A Δ otal olue V=V +V iquid etal doplet olid Added intefacial enegy Δ i =Aγ

8 Hoogeneous Nucleation fo iquid olidification () EMA 5001 Physical Popeties of Mateials Zhe Cheng (016) 1 olidification - Hoogen Nucleation 8 Continue fo p.5 We hae Define V A We hae V A is a function of tepeatue o undecooling is the latent heat of fusion pe unit olue If isotopic & the nucleus takes spheical shape Δ Δ Intefacial enegy Volue fee enegy

9 EMA 5001 Physical Popeties of Mateials Zhe Cheng (016) 1 olidification - Hoogen Nucleation Veification of Relationship between Volue Fee Enegy Change & Undecooling Poof At elting point : Which eans: At a tepeatue below elting point, Assuing enthalpy and entopy change in solidification do NO change with tepeatue 9 H 0 H H H

10 EMA 5001 Physical Popeties of Mateials Zhe Cheng (016) 1 olidification - Hoogen Nucleation 10 Citical Radius & Fee Enegy Change Continue fo p. 6 Citical nucleus size d d <, nucleus shinks; >, nucleus gows Knowing We hae Intefacial enegy Volue fee enegy When 0, 1 and both, hoogeneous nucleation will NO occu!

11 EMA 5001 Physical Popeties of Mateials Zhe Cheng (016) 1 olidification - Hoogen Nucleation Veification of Nucleation Baie

12 Citical Nucleus ize & Maxiu Cluste ize EMA 5001 Physical Popeties of Mateials Zhe Cheng (016) 1 olidification - Hoogen Nucleation 1 Continue fo p.7 1 he nube of solid clustes with size, n n n0 exp k n 0 he total nube of atos Excess enegy fo cluste of size, Fo a gien > 0 ( > 0), when < :,, n daatically hee is effectiely a axiu cluste in the liquid When, fo a gien,, n, ax < N, ax <, no hoogeneous nucleation >= N, ax >, hoogeneous nucleation occus 1 ax N

13 EMA 5001 Physical Popeties of Mateials Zhe Cheng (016) 1 olidification - Hoogen Nucleation 1 Hoogeneous Nucleation Rate Define C Nube density of nucleus with size C 0 ho f 0 Ato density Hoogeneous nucleation enegy Fequency of adding one oe ato to a nucleus Nucleation ate ( - s -1 ) ho N ho f0c0 exp k Fo hoogeneous nucleation We hae N ho ho 16 A exp f0c0 1 udden incease of nucleation ate N ~ 0. C C N ho 0 exp k ho N