Solute Mass Balances: Macrosegregation

Solute rejection and its redistribution during freezing and melting are basic topics introduced by the Dutch physical chemist H.W.B. Roozeboom more than a century ago [1, 2] to explain the influence of phase equilibria on the solidification behavior of alloys. Solute redistribution occurs at a moving solid–liquid interface when limited—or so-called local—thermodynamic equilibrium prevails, often aided by transport processes (diffusion and convective mixing) acting primarily within the melt phase ahead of the advancing interface. In this chapter several important settings are explored involving the rejection and redistribution of solutes under differing conditions of solidification. Specifically, during alloy freezing it will be shown that the condition of local thermodynamic equilibrium usually holds, whereas total—or so-called global—equilibrium seldom, if ever, occurs. Nevertheless, both local and global equilibria represent useful idealizations as thermodynamic limits, between which operate most solidification and single crystal growth processes encountered in practice. Local equilibria at solid–liquid interfaces are also exploited in several solidification-based ultrapurification methods, such as repeated unidirectional freezing and multipass zone melting, both of which processes will be explored in detail in this chapter.