Course content

The course includes the theoretical basis for understanding phase transformations in metals as well as models and methods for a mathematical and numerical description of some technological important phase transformations in metals (with emphasis on aluminium) that are determining for the evolution of microstructure and properties during casting/solidification and thermal processing (heat treatments/welding). The course starts with a short description of the thermodynamical basis for phase transformations, based on the consideration of simple binary phase diagrams. It is followed by an atomistic and mathematical description of diffusion together with structural aspects of phase boundaries. After that a more detailed presentation of phase transformations by nucleation and growth is given, including homogeneous and heterogeneous solidification, precipitation, growth and dissolution of second phase particles, recrystallization and grain growth, including the concepts of Johnson-Mehl-Avrami-Kolmogorov (JMAK) kinetics, additivity and iso-kinetic reactions. The topics will be presented and analysed by means of relevant mathematical/numerical models which the students themselves should implement and use/explore through 3-4 relevant mini projects.

Learning outcome

After successfully completing the course, the students will have

Knowledge

• to derive and compare different solid solution models for binary alloys
• to derive a simple model for how solubility and vacancy concentration change with temperature
• to recognize main ingredients of a CALPHAD method for multicomponent alloys
• to account for the atomistic and continuum description of diffusion
• to describe geometrical and structural aspects of phase boundaries and explain how these relate to interfacial energies and mobilities
• to describe the theoretical basis for phase transformations by nucleation and growth
• to differentiate between homogeneous and heterogeneous solidification and precipitation
• to mathematically formulate equations for growth and dissolution of second phase particles
• to derive and discuss JMAK kinetics
• to formulate a simple heat transfer model for solidification
• to interpret iso-kinetic solutions for the secondary-phase dissolution and growth

Skills

• to compute and analyse simple binary phase diagrams by use of simple thermo-dynamical data and models
• to perform analytical and numerical calculations of a selection of relevant diffusion problems
• to solve numerically 1D diffusion problem by both explicit and implicit methods
• to appraise differences between explicit and implicit numerical schemes
• to derive the Darken's law for the inter-diffusion for a binary alloy
• to put together analytical and numerical calculations for kinetics and microstructure evolution during iso-thermal as well as non-isothermal thermal processing
• to analyse and compare how alloy composition and heat-treatment procedures influence growth and dissolution of second-phase particles in binary/quasibinary alloys during isothermal as well as non-isothermal heat treatments, including iso-kinetic solutions
• to construct coupled microstructure-heat model for solidification
• to find information from a scientific sources and make an assessment of the reliability of the information that appears
• to prepare good presentations of the project work for fellow students in plenary, as well as give feedback on others work

General competence

• to analyse and discuss limitations and validity of relevant theoretical models in relation to real life problems and industrial process conditions
• to collaborate on a project in a small team
• to prepare adequate and informative presentations of results from team work and to give oral presentations

Learning methods and activities

Lectures and computational mini-problems. Moreover 3-4 larger modelling projects, involving written reports (a presentation), plenary presentations and individual questioning. Evaluation of the computational problems and the modelling projects serve as basis for the final grade. Total work load is estimated to be about 200 hrs (incl. independent home work).

Recommended previous knowledge

Basic knowledge of materials technology/engineering is recommended, e.g. completion of the courses TMT4171 Introduction to Materials Science and TMT4178 Applied Materials Technology or TMT4185 Materials Technology or equivalent previous knowledge to be evaluated by the course responsible to be satisfactory. Moreover basic knowledge of thermodynamics and phase diagrams is required. The course will include 3-4 mini modelling projects, that requires knowledge of and experience with numerical methods as well as implementation of mathematical/numerical models in Python or similar.

Course materials

Extracts from D.A. Porter and K.E. Easterling, Phase Transformations in Metals and Alloys and selected relevant journal papers. In addition lecture notes will be made available via internet.