上海交通大学：《材料加工原理 Principles of Materials Processing》教学资源（课件讲稿）凝固和铸造 Solidification and casting_Crystal growth of single element solids 3/3（Crystal growth methods（technology））

先进材料疑固实验室 Laboratory of Advanced Materials Solidification 1896 1920 1987 2006 Crystal growth of single element solids(3) Dr.Mingxu Xia anced Mat 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY

1896 1920 1987 2006 Crystal growth of single element solids (3) Dr. Mingxu Xia

先进材料疑固实验室 OUTLINE Laboratory of Advanced Materials Solidification Liquid/solid interface Crystal growth of single element solids Types of crystal growth ·Kinetics of growth Morphology control of crystals Crystal growth methods(technology) ory of vanced Materials Solid 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY

OUTLINE Liquid/solid interface Crystal growth of single element solids • Types of crystal growth • Kinetics of growth • Morphology control of crystals Crystal growth methods (technology)

先进材料疑固实验室 Morphology control of crystals Laboratory of Advanced Materials Solidification Since during solidification of a liquid heat is released,the growth rate is very often controlled by the heat flow from the interface into the solid,liquid or both. Solid Liquid Continuous growth: R=LAT Growth based on surface nucleation: -b R2 M2 exp △T Growth based on spiral growth 4G ed Ma 3=43△T2 h△G 熟 上海充通大￥ SHANGHAI JIAO TONG UNIVERSITY

Morphology control of crystals Since during solidification of a liquid heat is released, the growth rate is very often controlled by the heat flow from the interface into the solid, liquid or both. Q         ∆ − = Tk b R2 µ2 exp 2 R3 3 ∆Tk = µ ⋅ R1 = µ1∆Tk Continuous growth: Growth based on surface nucleation: Growth based on spiral growth

先进材料疑固实验室 Morphology control of crystals Laboratory of Advanced Materials Solidification What is the mechanisms of the effect of heat flow on crystal growth? After nucleation,normally AT;is fairly large,and this causes high growth rate and rapid heat release. If the (negative)temperature gradient in the solid or the liquid is not sufficiently large,the heat cannot be transferred away quickly enough, and the residual heat is used to heat the solid and liquid near the S/L interface. This will cause an increase of Ti,and a decrease of ATi,which in turn leads to a decrease of growth rate and the rate of heat release from solidification. At some point,these two opposite effects are balanced,and ATi remains unchanged.This is called steady state for crystal growth. T;and AT;are the temperature and undercooling at the interface 上海充通大￥ SHANGHAI JIAO TONG UNIVERSITY

Morphology control of crystals What is the mechanisms of the effect of heat flow on crystal growth? • After nucleation, normally ∆Ti is fairly large, and this causes high growth rate and rapid heat release. • If the (negative) temperature gradient in the solid or the liquid is not sufficiently large, the heat cannot be transferred away quickly enough, and the residual heat is used to heat the solid and liquid near the S/L interface. • This will cause an increase of Ti , and a decrease of ∆Ti , which in turn leads to a decrease of growth rate and the rate of heat release from solidification. • At some point, these two opposite effects are balanced, and ∆Ti remains unchanged. This is called steady state for crystal growth. Ti and ∆Ti are the temperature and undercooling at the interface

先进材料疑固实验室 Morphology control of crystals Laboratory of Advanced Materials Solidification Normally,in steady state,AT;is fairly small,and less than 1K. The temperature gradient in the liquid in front of the S/L interface has a significant effect on the stability of S/L interface. Positive temperature gradient in the liquid>stable S/L interface. Negative temperature gradient in the liquid>unstable S/L interface and formation of solid dendrites. For single element solids,the morphology of the crystal depends on microstructure of the interface(surface type)and the temperature distribution in front of the interface. 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY

Morphology control of crystals Normally, in steady state, ∆Ti is fairly small, and less than 1K. The temperature gradient in the liquid in front of the S/L interface has a significant effect on the stability of S/L interface. • Positive temperature gradient in the liquid  stable S/L interface. • Negative temperature gradient in the liquid  unstable S/L interface and formation of solid dendrites. For single element solids, the morphology of the crystal depends on microstructure of the interface (surface type) and the temperature distribution in front of the interface

先进材料疑固实验室 Morphology control of crystals Laboratory of Advanced Materials Solidification Undercooling variation with different temperature gradient With positive temperature gradient Interface dT >0 dT/dx>0,with the crystal growth, dx x1,T↓，Tt Undercooling SIL x Positive temperature gradient Interface With negative temperature gradient dT/dx<0,with the crystal growth, 如 +∠0 xt,△Tt,Tl。 SjL Undercooling ed Ma 2 Negative temperature gradient 上浒充通大 SHANGHAI JIAO TONG UNIVERSITY

Morphology control of crystals Undercooling variation with different temperature gradient Negative temperature gradient Positive temperature gradient With positive temperature gradient dT/dx>0, with the crystal growth, x,ΔT, T With negative temperature gradient dT/dx<0, with the crystal growth, x，ΔT， T

先进材料疑固实验室 Morphology control of crystals Laboratory of Advanced Materials Solidification Positive gradient Interface 70 dx >Latent heat is extracted from solid part. Undercooling >Moving of S/L interface (growth) manipulated by the heat conducting of solid. For substance with sharp interface Interface growth (facted morphololgy):crystal grows Growth of crystal through ledges extension.With x 1, Interface mnd AT,l,and grows as facted morphology with regular shape. 熟 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY

Morphology control of crystals Positive gradient Latent heat is extracted from solid part. Moving of S/L interface (growth) manipulated by the heat conducting of solid. Interface growth Interface For substance with sharp interface (facted morphololgy)：crystal grows through ledges extension. With x , △Tk , υ，and grows as facted morphology with regular shape

先进材料疑固实验室 Morphology control of crystals Laboratory of Advanced Materials Solidification Positive gradient Interface 1lm 70 dx For substance with rough interface(non- facted morphololgy):crystal grows as Undercooling continuous growth.With x t,△Tk↓，vl,the humps on the interface will turned into flat. Solid Liquid Solid Liquid heat 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY

Morphology control of crystals Positive gradient For substance with rough interface (non￾facted morphololgy)：crystal grows as continuous growth. With x , △Tk , υ，the humps on the interface will turned into flat

先进材料疑固实验室 Morphology control of crystals Laboratory of Advanced Materials Solidification Negative gradient Interface >Latent heat can be released from both solid and liquid. >Moving of S/L interface (growth)not only relies on the heat conducting of solid. Undercooling 2 For substance with sharp interface(facted morphology):with the increase of x,AT 1,o1,the morphology is affected by a (Jackson factor): >With smaller a,crystal grows as dendrites with facted surface. >With larger a,crystal grows as lateral growth also with facted surface but keep a regular sharp shape. Pure Sb(antimony）) 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY

Morphology control of crystals Negative gradient Latent heat can be released from both solid and liquid. Moving of S/L interface (growth) not only relies on the heat conducting of solid. For substance with sharp interface (facted morphology)：with the increase of x, △Tk , υ  ，the morphology is affected by α (Jackson factor): With smaller α, crystal grows as dendrites with facted surface. With larger α, crystal grows as lateral growth also with facted surface but keep a regular sharp shape. Pure Sb (antimony)

先进材料疑固实验室 Morphology control of crystals Laboratory of Advanced Materials Solidification Negative gradient Interface For substance with rough interface(non- 正∠0 facted morphology):with the increase of x, AT1,t,the crystal grows as dendrites. SjL Undercooling (a)Succinonitrile in free growth (b)Ni dendrites in superalloy spotweld Materials Sollc 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY

Morphology control of crystals Negative gradient For substance with rough interface (non￾facted morphology)：with the increase of x, △Tk , υ  ，the crystal grows as dendrites