More than two decades have passed since the previous edition of ASM Handbook, Volume 3, Alloy Phase Diagrams was published in 1992. Metallurgical & Materials Transactions E.Metallurgical & Materials Transactions B.Metallurgical & Materials Transactions A.Metallography, Microstructure & Analysis.Journal of Phase Equilibria & Diffusion.Journal of Materials Engineering & Performance.Journal of Failure Analysis & Prevention.ASM Materials Platform for Data Science.This can lead to premature mechanical failure. Upon heating grain boundaries will melt first.⇒Solidus line is shifted to the right (higher Ni contents), solidification is complete at lower T, the outer part of the grains are richer in the low-melting component (Cu). ⇒ Application of the lever rule gives us a greater proportion of liquid phase as compared to the one for equilibrium cooling at the same T. Average Ni content of solid grains is higher. The tie-line method still works for the liquid phase, where diffusion is fast.⇒Formation of layered (cored) grains and the invalidity of the tie-line method to determine the composition of the solid phase. ⇒ The new layers that solidify on top of the existing grains have the equilibrium composition at that temperature but once they are solid their composition does not change.

Diffusion in the solid state is very slow.Compositional changes require diffusion in solid and liquid phases.A system at a metastable state is trapped in a local minimum of free energy that is not the global one.Ģ1MSE 2090: Introduction to Materials Science Chapter 9, Phase Diagramsĭevelopment of microstructure in isomorphous alloysFast (non-equilibrium) cooling.The state of stable thermodynamic equilibrium is the one with minimum free energy.Under conditions of a constant temperature and pressure and composition, the direction of any spontaneous change is toward a lower free energy.In thermodynamics the equilibrium is described as a state of a system that corresponds to the minimum of thermodynamic function called the free energy. But the time to achieve equilibrium may be very long (the kinetics can be slow) that a state along the path to the equilibrium may appear to be stable. 5MSE 2090: Introduction to Materials Science Chapter 9, Phase DiagramsĪ system is at equilibrium if at constant temperature, pressure and composition the system is stable, not changing with time.Įquilibrium is the state that is achieved given sufficient time.

Materials cha pter ten phase diagrams