Massachusetts Institute of Technology Department of Materials Science and Engineering 77 Massachusetts Avenue, Cambridge MA 02139-4307 3.21 Kinetics of Materials Lecture 2: Irreversible thermodynamics: entropy production; conjugate driving forces and ﬂuxes; basic postulates; linear irreversible thermodynamics; the diffusion potential; Onsager’s symmetry principle. References 1. Ballufﬁ, Allen, and Carter, Kinetics of Materials, Chapter 2. 2. Christian, J.W., Phase Transformations in Metals and Alloys—Part I, Pergamon Press, 1975, Chapter on Irreversible Thermodynamics. Key Concepts • The local entropy production can be expressed as a sum of terms, each of which is a product of a ﬂux and a conjugate “force” (see KoM Eq. 2.15). • Familiar empirical laws are linear relationships between ﬂuxes and their conjugate forces: Fourier’s law of heat conduction, Fick’s law for diffusion, and Ohm’s law for electrical conduction (see KoM Table 2.1). • The basic postulate of irreversible thermodynamics is that, near equilibrium, the local entropy pro duction is non-negative (see KoM Eq. 2.16). • When more than one force is active, each force will generally cause a ﬂux of its corresponding quan tity. There are both direct couplings between forces and conjugate ﬂuxes, and cross terms that may also contribute to ﬂuxes. • When several forces are active and a system is “near” equilibrlum, the ﬂux of a given quantity is postulated to be linearly related to all of the forces (see KoM Eqs. 2.20–21). • The potential which appears in the total conjugate force acting on a component in a material is called the diffusion potential, Φ (see KoM Eqs. 2.40–41). • According to Onsager’s symmetry principle, the matrix of coupling coefﬁcients Lαβ in the system of linear equations Jα = Lαβ Xβ is postulated to be symmetric, that is, Lαβ = Lβα . Related Exercises in Kinetics of Materials Review Exercises 2.1–2.4, pp. 36–38.

Lecture 2 Notes: Irreversible Thermodynamics

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