先进材料疑固实验室 Thermo performance Laboratory of Advanced Materials Solidification Phase 1:T>TL g1=-mcAT/t Phase2:T<=TLq1=-mc△T/t+△V*L △V*L<q1 △T/tK0 Phase3:T<TLq1=-mc△T/t+△V*L △V*L=q1 △T/t=0 Phase4:T<TLq1=-mc△T/t+△V*L ￥e △V*L>q1 ① △T/t>0 unjeJedwel Phase5:T=TLq1=-mc△T/t+△V*L ⑤ △V*L=q1 ③ ② △T/t=0 ④ Time(t),s 上游充通大￥ SHANGHAI JIAO TONG UNIVERSITY
Thermo performance Temperature (T), K Time (t), s Phase 1: T>TL q1=-mcΔT/t ① Phase 3: T<TL q1=-mcΔT/t+ΔV*L ΔV*L=q1 ΔT/t=0 ③ Phase 5: T=TL q1=-mcΔT/t+ΔV*L ΔV*L=q1 ΔT/t=0 ⑤ Phase 2: T<=TL q1=-mcΔT/t+ΔV*L ΔV*L<q1 ΔT/t<0 ② Phase 4: T<TL q1=-mcΔT/t+ΔV*L ΔV*L>q1 ΔT/t>0 ④
Conventional Nucleation 先进材料疑固实验室 Laboratory of Advanced Materials Solidification Theory(CNT) When T=Tm,Gs GL,both the liquid and the solid are stable phases,and there is no thermodynamic driving force for solidification of the liquid or melting of the solid. (Tm is the melting point of the solid,and Gs and GL are the free energies of the solid and the liquid respectively.) www.shutterstock.com 94316782 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY
Conventional Nucleation Theory(CNT) When T= Tm, GS = GL , both the liquid and the solid are stable phases, and there is no thermodynamic driving force for solidification of the liquid or melting of the solid. (Tm is the melting point of the solid, and GS and GL are the free energies of the solid and the liquid respectively.)
Conventional Nucleation 先进材料疑固实验室 Laboratory of Advanced Materials Solidification Theory(CNT) ·G=H-TS ·S,T positive value Gliquid ·Ssolid2 Siqud AGsolidification=Gsolid Gliquid Gsolid Then only T<T Gsolid<Gliquid G<0. △ So,4T=T-T,,is the driving force for nucleation and only T<T, Nucleation occurs.And, Tm Temperature △GY=△H-TAS At nucleation point,.△H≈-△and△s≈-ASm=-AHm/Tm △Hm·△T Tm △T=T-Taeri8 上游充通大学 SHANGHAI JIAO TONG UNIVERSITY
Conventional Nucleation Theory(CNT) • G=H-TS • S, T positive value • Ssolid>Sliquid • Then only T<Tm , Gsolid<Gliquid, ΔG<0. So, ΔT=T-Tm is the driving force for nucleation and only T<Tm, Nucleation occurs. And, At nucleation point, and Gsolid Gliquid ΔGsolidification=Gsolid-Gliquid Tm Free energy Temperature ΔT
Conventional Nucleation 先进材料疑固实验室 Laboratory of Advanced Materials Solidification Theory(CNT) Gliquid AGsolidificationGsolidGliquid Gsolid △ △Gcurvature 人 Temperature Effect of curvature: AGeurvature=VsoldApeurvatureVsold Where Vsolid is the volume of solid part,Apcurvature is the press variation due to the curvature reduction,osi is the interface energy between solid and liquid,r1 r2 is the radius of the embryo before and after and k is the curvature of the embryo. 上游文通大￥ SHANGHAI JIAO TONG UNIVERSITY
Effect of curvature: Where Vsolid is the volume of solid part, Δpcurvature is the press variation due to the curvature reduction, σsl is the interface energy between solid and liquid, r1 r2 is the radius of the embryo before and after and k is the curvature of the embryo. Conventional Nucleation Theory(CNT) r Gsolid Gliquid ΔGsolidification=Gsolid-Gliquid Tm Free energy Temperature ΔT ΔGcurvature