On the basis of modern knowledge of Material Science and Thermodynamics the analysis of multicomponent phase diagrams is considered, particularly, as applied to real materials and processes. Special attention is paid to computational methods (including Thermo-Calc software). Original methods based on popular software EXCEL are also considered. The program “Phase diagrams of multi-component systems” is created for undergraduate students that studied the basic courses of Material Science cycle.
Learning of proposed program will enable the student to conduct the following routines:
to analyze the phase composition of multicomponent materials at various temperatures,
to estimate by graphical method and calculate liquidus, solidus and other critical temperatures of phase transformations;
to build isothermal and vertical sections in ternary, quaternary and quinary systems both by graphical and computational methods;
to calculate mass and volume fractions of phases in multicomponent materials;
to investigate the acceptable information on phase diagrams, particularly looking for mistakes;
to predict the phase equilibria in unknown multicomponent systems.
Hours of lecture
Hours of discussion
Hours of independent study
Please note that students are expected to study outside of class for three hours for every hour in class.
The plan is to work through the following topics:
Visualization of ternary alloys on concentration triangle
Classification of ternary phase diagrams
Phase transformations in alloys during cooling and heating.
Isothermal (horizontal) and polythermal (vertical) sections
Ternary system with monovariant eutectic equilibrium
Ternary system with nonvariant eutectic equilibrium at low solubilities in solid state
Ternary system with nonvariant eutectic equilibrium at variable solubilities in solid state
Ternary system with binary congruent melting compound
Quasybinary sections and their properties
Ternary system with nonvariant peritectic equilibrium at variable solubilities in solid state
Ternary system with binary incongruent melting compound and nonvariant peritectic equilibrium at low solubilities in solid state
Ternary system with monovariant monotectic equilibrium
Ternary system with monovariant peritectic equilibrium
Examples of real phase diagrams.
Quaternary and more component systems
Visualization of quaternary alloys on concentration triangle in the corner of main component
Quasyternary sections and their properties
Polythermal diagram of quaternary systems with nonvariant eutectic equilibrium
Polythermal diagram of quaternary systems with nonvariant peritectic equilibrium
Five and more component systems
Analysis of reactions during solidification
Examples of real phase diagrams
Quantitative methods of analysis of multicomponent systems
Construction of mathematical model of liquidus and solidus by the use simplex plans
Calculation of mass and vokume fractions of phases in multicomponent alloys
Calculation of isothermal and polythermal sections
Fundamentals of thermodynamic calculations
Calculation of multicomponent systems and alloys using the Thermo-Calc software
Hans Lukas, Suzana G. Fries, and Bo Sundman. Computational Thermodynamics: The Calphad Method. Cambridge University Press, Cambridge ; New York, 1 edition edition, August 2007.
David A. Porter, Kenneth E. Easterling, and Mohamed Sherif. Phase Transformations in Metals and Alloys, Third Edition. CRC Press, Boca Raton, FL, 3 edition edition, February 2009.
David R. Gaskell. Introduction to the Thermodynamics of Materials, Fifth Edition. CRC Press, New York, 5 edition edition, March 2008.
Nikolay A. Belov, Dmitry G. Eskin, and Andrey A. Aksenov. Multicomponent Phase Diagrams: Applications for Commercial Aluminum Alloys. Elsevier Science, Amsterdam ; Boston, July 2005.
N. Saunders and A. P. Miodownik. CALPHAD. Pergamon, Oxford ; New York, 1 edition edition, June 1998.
Weekly, 12 problem sets in total, due at the beginning of the lecture. You may also submit via e-mail before the due date/time. It is of outmost importance that you invest your own effort into solving problems. Should you consult any sources, please provide references. Homework assignments should be typed. Legible handwritten assignments are acceptable.