EMA5001 Lecture 13 Solidification via Heterogeneous Nucleation, Growth of Pure Solid from Liquid by Zhe Cheng

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1 EMA5001 Lecture 1 ification ia Heterogeneous Nucleation, Growth of Pure from 016 by Zhe Cheng

2 EMA 5001 Physical Properties of Materials Zhe Cheng (016) 1 Heterogeneous Nucleation Heterogeneous Nucleation (1) Actual solidification often inoles mold wall, insoluble oxides, etc., which become substrates for heterogeneous nucleation Assuming ML is isotropic Mold wall flat ML Cos Mold r ML Free energy change in heterogeneous nucleation G het Therefore, G S het V S G r A G r A Cos 1 Cos S A ML Assuming sphere-cap geometry V S A r Cos 1 Cos r 1 Cos A r Sin

3 EMA 5001 Physical Properties of Materials Zhe Cheng (016) 1 Heterogeneous Nucleation Heterogeneous Nucleation () Continue from p. Ghet r G r S Remember for homogeneous nucleation Ghom r G r We hae G het G hom S G G het G hom r 0 S Critical nucleus size r het Cos 1 Cos r hom G 1 Heterogeneous nucleation has the same critical nucleus size as for homogeneous nucleation, but lower nucleation barrier (energy)

4 EMA 5001 Physical Properties of Materials Zhe Cheng (016) 1 Heterogeneous Nucleation Heterogeneous Nucleation () Continue from p. rhet rhom G Critical nucleation energy G het G hom S Examples = 10 o, S() = = 0 o, S() = 0.01 = 60 o, S() = 0.16 = 90 o, S() = 0.50 ML S Cos 1 Cos Cos 1 S() Heterogeneous nucleation, especially on mold wall that is similar to solid (small γ ), has much lower nucleation energy than homogeneous nucleation

5 EMA 5001 Physical Properties of Materials Zhe Cheng (016) 1 Heterogeneous Nucleation 5 Heterogeneous Nucleation Rate Define C 1 G het f 1 Number of atoms contacting heterogeneous nucleation sites per unit liquid olume Heterogeneous nucleation energy Frequency of adding one atom to a heterogeneous nucleus with critical size Heterogeneous nucleation rate (m - s -1 ) Since We hae N het G het G N het G f 1C1 exp kt G hom hom 16 L f1c1 exp S T m het 1 T A S T Phase Transformations in Metals & Alloys, Porter, rd Ed, 008, p. 199 Heterogeneous nucleation occurs at much smaller undercooling

6 Other Considerations on Heterogeneous Nucleation Rate EMA 5001 Physical Properties of Materials Zhe Cheng (016) 1 Heterogeneous Nucleation 6 Surface tension & contact angle Small solid-mold (or impurity) interfacial energy small Faster nucleation Mold surface microstructure In general, nucleation energy 1 G V G Concae mold (or impurity) surface and certain micro-cracks facilitate nucleation by decreasing V and nucleation energy Impurity density Added seeds or inoculants to increase nucleation rate to decrease grain size S Cos Cos 1 Cos ML Concae Flat Conex Oer mold or impurity surface 1 In micro-cracks

7 EMA 5001 Physical Properties of Materials Zhe Cheng (016) 1 Heterogeneous Nucleation 7 Growth of Pure from Growth of pure solid from liquid for different types of solid-liquid interfaces Diffuse L f R S R Tm Microscopically diffuse Macroscopically flat or branch-like Most metals: Ni: T m =155 o C L=98 kj/kg=17. kj/mol Lower energy for broken bonds Continuous growth Microscopically, growth occurs by adding indiidual atoms Flat L f ~ R S ~ Tm Microscopically flat With stepped or zig-zagged Features Si, Ge, and nonmetals Si: T m =11 o C L=1790 kj/kg=50.6 kj/mol Higher energy for broken bonds Lateral growth Microscopically, growth occurs along the solid-liquid interface R

8 Continuous Growth If broken bonds hae lower energy High acancy concentration at the solid-liquid interface Fast interface reaction or S L conersion Actiation energy ΔG a diffusion actiation energy in liquid (ery small) Driing force for solidification (solid growth) L G Ti T L m Latent heat of the melting T i Undercooling at the solid-liquid interface Velocity of the solid-liquid interface (growth rate of solid) G T i Mobility of diffuse solid-liquid interface is extremely high For normal rate of metal solidification, T i < 1 o C -liquid diffuse interface at close to equilibrium T m in solidification EMA 5001 Physical Properties of Materials Zhe Cheng (016) 1 Heterogeneous Nucleation G ΔG a ΔG x 8

9 Growth rate Lateral Growth If broken bonds hae higher energy (e.g. for Si) A single atom attached to a flat surface creates multiple broken bonds and tend to dissole back, leading to limited perpendicular growth Atoms prefer to attach to solid at existing ledge or jog positions, leading to lateral growth Possible growth geometries Surface Nucleation Spiral Growth Continuous growth (diffuse interface) Spiral growth Surface nucleation T i Lateral growth kinetically slower due to fewer geometric locations EMA 5001 Physical Properties of Materials Zhe Cheng (016) 1 Heterogeneous Nucleation 9

10 Temperate Profile & Growth of a Pure (1) EMA 5001 Physical Properties of Materials Zhe Cheng (016) 1 Heterogeneous Nucleation 10 Rate of solidification of pure solid determined by heat conduction grows into superheated liquid (T S < T L ) Example ification of liquid in a mold and mold wall colder is than liquid Balance of heat flow S Thermal conductiity of solid L Thermal conductiity of liquid T S Temperature gradient in solid T L Temperature gradient in liquid L Latent heat of melting growth rate STS ' LTL ' L Shape Planar (macroscopically) solid-liquid interface is stable T i T i =T m Heat Heat T S T L

11 Temperate Profile & Growth of a Pure () EMA 5001 Physical Properties of Materials Zhe Cheng (016) 1 Heterogeneous Nucleation 11 grows into supercooled liquid (T S > T L ) Example Beginning stage of solidification of supercooled liquid Balance of heat flow ' ' STS L LTL Shape Planar solid-liquid interface is unstable Form dendrite (branch-like) structures (Tip) growth rate increases as tip radius decreases generally. Growth rate approaches zero as r decreases towards r r increases towards T i T i =T m Heat Heat T S T L