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1、Lecture 2 Crystallization:thermodynamics1.Driving force of crystallization GT,P 0 G HT S HT0 S0 GHTS 0 S H/T0 G=0 G 0 H,S are constant with T)(000TTTHTHTHG Result:a.Exothermic,H 0,T 0,T T0,overheating结论：结论：Driving force of crystallization is the undercooling(T)。0TTH 2.The formation of stable nucleiA
2、.Nucleation:embryos growth or disappearance?Critical radius of the nucleus rK:a stable nucleus with the smallest sizeB.Calculation of rKAssuming at temperature T:liquid crystalGibbs energy change G G1 G2V GVA Assuming spherical embryo 4/3 r3n GV4 r2n Surface areaSurficial energy nrTTHnrGGGTTHGV20321
3、04340)(krrrG08402 nrTTHnrVKGTHTr 220rKr G0 G2 G1 GT3T2T1 G2-G1+0-rKrK rConclusion:It is easier to form stable crystal nuclei when the system has smaller rK.The undercooling is necessary in order to transform new phase.The value of rKis larger when the undercooling is smaller and the phase transforma
4、tion is more difficult.Besides the undercooling,the internal factors of the system,such as interfacial energy and melting point temperature,also affect rK.022 rTHTGKV3.Potential barrier of nucleation GKVKGTHTr 22022321131)16(31TGAGnGGGKKVKKK The provided energy must be the 1/3 of interfacial energy
5、of the liquid-solid interface in order to form the stable nuclei with the critical radius.The energy barrier is smaller when the undercooling is larger,and the liquid transform more easily to the crystal.How many stable nuclei exist in the system?)exp(RTGnnKK If the Gk of the system is smaller,the number of stable nuclei is larger and the phase transformation is easier.