材料热力学与动力学 3.pptVIP

Dr. Lu Li Basic Interface Types 3.1 Interfacial Free Energy 3.2 Solid / Vapour Interfaces High-indexed surface g - plot Surface Equilibrium Equilibrium crystalline shapes 3.3 Boundaries in Single-Phase Solids Tilt boundaries Low-angle tilt boundaries Twist boundaries Twin boundaries (large-angle) Large-angle grain boundaries Large- low-angle boundaries Misorientation and boundary energy measured grain boundary free energies Various grain boundaries grains and grain boundaries Equilibrium of GBs Boundary curvatures Grain Shapes in 3D Topological considerations Grain topology dislocation 3.4 Grain Growth Basic comprehensions about GG Qualitative considerations Neumann’s 2D grain growth equation Hillert’s statistical grain growth model Zhao’s model considering textures Summary End of Chapter 3 0.5 0.4 0.3 0.2 0.1 0 0.2 0.4 0.6 0.8 1.0 relative temperature, T/Tm kinetic exponent, h Zr Ti Pb Cd + 1ppm Pb Sn brass Pb Al + 400ppm Cu b-brass Al + 0.12% Cu Cd + 20ppm Pd Al a-iron g-steel n (A, n) grain n, area A, side n s f(s) x r(s) T if m, g are constants Neumann’s 2D grain growth equation n (A, n) for a circle grain x x T f1 f2 x T p/3 A jump of p/3 at every triple point should be leaved out of account from the integral. For a n-sided 2D grain, smaller grains: shrinking, larger grains: growing, convex, r 0 concave, r 0 statistically, R: radius of the equal-volume sphere n [H,i] m [K,j] Snm ds O O’ q b dq df ds migrates in direction for Dz at time Dt the distance between ds and O increases from r(s) to r(s) + Dr Dz = Dr(s) cos b (1) if the grain geometric profile keeps unchanged during Dt, Dr(s) = C0 r(s), hence: Dz = C0 r(s) cos b (2) Snm ds O O’ q b dq df let: Znm and rnm be the average of Dz and r(s)cosb over Snm respectively in time Dt C0 = Znm / rnm (3) area of ds: r r sinq in dt: (4) n [H, i] Dr Dz b Snm DSR total energy change: work done by the driving force: work = - energy change, i.e. migration rate of the boundary section Snm: su