Mass Transport and Nonequilibrium Thermodynamics

Nothing in Section 2.3 concerning the thermodynamics and energetics of solid-state reactions, was different in principle from gas- or solution-phase systems. Indeed, thermodynamics is universal. The significance and respect of thermodynamics within the scientific community is well established. Albert Einstein once said (Klein, 1967)  

Other examples of transport properties include electrical and thermal conductivity. Transport of a physical quantity along a determined direction due to a gradient is an irreversible process by which a system transitions from a nonequilibrium state to an equilibrium state (e.g., compositional or thermal homogeneity). Therefore, it is outside the realm of equilibrium thermodynamics. (For this reason, equilibrium thermodynamics is more appropriately termed thermostatics.) Transport processes must be studied by irreversible thermodynamics. 

In this book we are concerned only with mass transport, or diffusion, in solids. Self-diffusion refers to atoms diffusing among others of the same type (e.g., in pure metals). Interdiffusion is the diffusion of two dissimilar substances (a diffusion couple) into one another. Impurity diffusion refers to the transport of dilute solute atoms in a host solvent. In solids, diffusion is several orders of magnitude slower than in liquids or gases. Nonetheless, diffusional processes are important to study because they are basic to our understanding of how solid-liquid, solid-vapor, and solid-solid reactions proceed, as well as [solid-solid] phase transformations in single-phase materials. 

Diffusion is a concentration gradient-induced process that follows Fick s laws of diffusion—macroscopic, or continuum-level, empirical relations—derived by the German physiologist Adolf Eugen Fick (1829-1901) in 1855 (Fick, 1855). Fick s first law is written as 

Fick s first law represents steady-state diffusion. The concentration profile (the concentration as a function of location) is assumed constant with respect to time. In general, however, concentration profiles do change with time. To describe these non-steady-state diffusion processes use is made of Fick s second law, which is derived from the first law by combining it with the continuity equation [dni/dt = -(Jin - /out) = — VJ,] 

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