Tham khảo tài liệu 'modern physical metallurgy and materials engineering part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Structural phases their formation and transitions 81 this mechanism of transformation the factors which determine the rate of phase change are 1 the rate of nucleation N . the number of nuclei formed in unit volume in unit time and 2 the rate of growth G . the rate of increase in radius with time . Both processes require activation energies which in general are not equal but the values are much smaller than that needed to change the whole structure from a to p in one operation. Even with such an economical process as nucleation and growth transformation difficulties occur and it is common to find that the transformation temperature even under the best experimental conditions is slightly higher on heating than on cooling. This sluggishness of the transformation is known as hysteresis and is attributed to the difficulties of nucleation since diffusion which controls the growth process is usually high at temperatures near the transformation temperature and is therefore not rate-controlling. Perhaps the simplest phase change to indicate this is the solidification of a liquid metal. The transformation temperature as shown on the equilibrium diagram represents the point at which the free energy of the solid phase is equal to that of the liquid phase. Thus we may consider the transition as given in a phase diagram to occur when the bulk or chemical free energy change AGv is infinitesimally small and negative . when a small but positive driving force exists. However such a definition ignores the process whereby the bulk liquid is transformed to bulk solid . nucleation and growth. When the nucleus is formed the atoms which make up the interface between the new and old phase occupy positions of compromise between the old and new structure and as a result these atoms have rather higher energies than the other atoms. Thus there will always be a positive free energy term opposing the transformation as a result of the energy required to create the surface of .