84540 - THERMODYNAMICS AND KINETICS OF SOLIDS, SURFACES AND NANOSTRUCTURES

Learning outcomes

At the end of the course, the students learn the rules that govern thermodynamic equilibrium in condensed phases, from 3-dimensional bulk solids down to nanostructures and 2-dimensional systems. Moreover, they are able to analyze non-equilibrium processes both in the frame of a general thermodynamic description and within the microscopic theory of mass transport via atomic diffusion. The students understand important phase transformations such as nucleation and growth, spinodal decomposition, order-disorder transitions, as well as microstructural evolution phenomena like coarsening, surface evolution, and mechanical plasticity. Particular emphasis is given to microstructural features such as structural defects, surfaces, dimensionality, and small-size effects, which lie at the very heart of contemporary materials physics and nanoscience.

Course contents

Equilibrium Thermodynamics
Equilibrium physical properties and their symmetry. Conditions for equilibrium in an isolated system. Heterogeneous systems with one component (pure substances): Clapeyron equation, vapor pressure, and construction of the phase diagram.

Multi-component homogeneous systems: partial thermodynamic quantities. Gibbs-Duhem equation. Solid solutions: ideal, diluted and regular solutions.

Multi-component heterogeneous systems: equilibrium conditions. Microscopic model of a binary system: long-range order and miscibility gap versus temperature.  The chemical potential. Construction of binary phase diagrams: the common tangent method and the lever rule. The Gibbs phase rule.  Basic features of phase diagrams: invariant points, liquidus, solidus, and solvus lines. Examples of binary phase diagrams. Introduction to ternary phase diagrams.

Multi-component heterogeneous reacting systems: affinity and van 't Hoff equation. Richardson-Ellingham diagrams for oxidation.

Kinetic Mechanisms
Entropy and entropy production. Basic postulate of irreversible thermodynamics. The Onsager reciprocity relations: symmetry of transport properties. Thermoelectric effects. Driving forces and fluxes in atomic diffusion: the diffusion potential. The diffusion equation. Link between the macro-and microscopic viewpoints: thermally activated jumps, random walk and diffusion coefficient. Atomistic diffusion mechanisms in solids: vacancies, interstitials, diffusion in a concentration gradient (Kirkendall effect). Defects and diffusion in ionic solids.

Structure of  interfaces and surfaces in materials. Driving forces for interface motion. Curvature and diffusion potential. Morphological evolution due to capillary forces. Surface smoothing via surface diffusion or vapour transport. Anisotropic surface free energy and faceting. Wulff constructoin for the equilibrium crystal shape. Coarsening of microstructures (Ostwald ripening): mean-field theory in source-limited and diffusion-limited cases. Morphological evolution due to applied stress.

Introduction to phase transformations: conserved vs non-conserved order parameter. Continuous transformations: spinodal decomposition and order-disorder transition. Cahn-Hilliard and Allen-Cahn equations.

Discontinuous transformations: the classical nucleation theory. Heterogeneous nucleation. Nucleation and growth: Johnson-Mehl-Avrami kinetics and time-temperature- transformation (TTT) diagrams. Precipitation in the Cu-Co and Al-Cu systems: effects of elastic strains on nucleation. Martensitic transformations and shape-memory alloys.

Readings/Bibliography

· R.W. Balluffi, S.M. Allen, W.C. Carter, Kinetics of Materials, Wiley

· R. DeHoff, Thermodynamics in Materials Science, Taylor and Francis

Teaching methods

Frontal lectures, both at the blackboard and with the aid of a videoprojector

Assessment methods

Oral examination. The student is allowed to start the exam illustrating a topic of his/her choice among the ones treated during the course.

Teaching tools

The course teaching material is available on AMS Campus.

Office hours

See the website of Luca Pasquini

See the website of Vittorio Morandi