先进材料疑固实验室 Liquid/Solid interface Laboratory of Advanced Materials Solidification Am(for melting)and AF(for freezing)are the probability of atoms not bouncing back after crossing the S/L interface(normally Am≈1，A-≤1). A is affected by the number of neighbouring atoms after an atom jump from the liquid side to the solid side.The more neighbouring atoms there are,the higher Ap is. bs and bL are vibration frequencies of atoms in the solid and liquid.It can be considered that bs=b=b. T;is the temperature at the S/L interface Q and AGy take the unit of J/atom. ed Matenal 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY
Liquid/Solid interface Am (for melting) and AF (for freezing) are the probability of atoms not bouncing back after crossing the S/L interface (normally Am ≈ 1, AF≤1). AF is affected by the number of neighbouring atoms after an atom jump from the liquid side to the solid side. The more neighbouring atoms there are, the higher AF is. bS and bL are vibration frequencies of atoms in the solid and liquid. It can be considered that bS=bL=b. Ti is the temperature at the S/L interface. Q and ∆GV take the unit of J/atom
先进材料疑固实验室 Liquid/Solid interface Laboratory of Advanced Materials Solidification Only when ()()the crystal can grow and the crystal growth rate,v,is proportional to the difference between the two rates: ).-a)s-L -君ep(品)A4,-em(】 we know,AG=T andso above equation can be rewritten as: 君ap(l-em(色》 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY
Only when , the crystal can grow and the crystal growth rate, v, is proportional to the difference between the two rates: we know, , and so above equation can be rewritten as: Liquid/Solid interface
先进材料疑固实验室 Liquid/Solid interface Laboratory of Advanced Materials Solidification From above equation,we can see the only when the interfacial undercooling,,-T-T,,is sufficiently large to make Ar>exp( v>0,and the crystal can grow. This means that in order for the crystal to grow,we mush have (v>0): △Gv<kTln(Ae) The value of 4.is determined by the atomic scale roughness of the solid/liquid interface.The rougher is the S/L interface.The higher the value of 4 In addition to the thermodynamic barrier,there is also kinetic barrier related to how the atoms move from liquid to solid across the S/L interface. 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY
Liquid/Solid interface From above equation, we can see the only when the interfacial undercooling, ΔTi =Tm-Ti , is sufficiently large to make , and the crystal can grow. This means that in order for the crystal to grow, we mush have (v>0): The value of AF is determined by the atomic scale roughness of the solid/liquid interface. The rougher is the S/L interface. The higher the value of AF In addition to the thermodynamic barrier, there is also kinetic barrier related to how the atoms move from liquid to solid across the S/L interface