An Introduction Guna Selvaduray San Jose State University

Credit for Phase Diagram Drawings: Richard Brindos Credit for scanning the phase diagrams: Brenden Croom

G. Selvaduray - SJSU - Oct 2004

Utility of Ternary Phase Diagrams

Glass compositions Refractories Aluminum alloys Stainless steels Solder metallurgy Several other applications

G. Selvaduray - SJSU - Oct 2004

References on Ternary Phase Diagrams

A. Prince, Alloy Phase Equilibria, Elsevier Publishing Company, New York, 1966 D. R. F. West, Ternary Equilibrium Diagrams, Chapman and Hall, New York, 1982 G. Masing, Ternary Systems, Reinhold Publishing Company, New York, 1944 C. G. Bergeron and S. H. Risbud, Introduction to Phase Equilibria in Ceramics, The American Ceramic Society, Ohio, 1984 M. F. Berard and D. R. Wilder, Fundamentals of Phase Equilibria in Ceramic Systems, R.A.N. Publishers, Ohio, 1990 F. N. Rhines, Phase Diagrams in Metallurgy, McGraw-Hill, New York, 1956 A. Reisman, Phase Equilibria, Academic Press, 1970

G. Selvaduray - SJSU - Oct 2004

What are Ternary Phase Diagrams?

Diagrams that represent the equilibrium between the various phases that are formed between three components, as a function of temperature. Normally, pressure is not a viable variable in ternary phase diagram construction, and is therefore held constant at 1 atm.

G. Selvaduray - SJSU - Oct 2004

The Gibbs Phase Rule for 3-Component Systems

F=C+2-P For isobaric systems: F=C+1-P For C = 3, the maximum number of phases will co-exist when F = 0 P = 4 when C = 3 and F = 0 Components are “independent components”

G. Selvaduray - SJSU - Oct 2004

Some Important Terms

Overall composition Number of phases Chemical composition of individual phases Amount of each phase Solidification sequence G. Selvaduray - SJSU - Oct 2004

Overall Composition - 1

The concentration of each of the three components Can be expressed as either “wt. %” or “molar %” Sum of the concentration of the three components must add up to 100% The Gibbs Triangle is always used to determine the overall composition The Gibbs Triangle: An equilateral triangle on which the pure components are represented by each corner

G. Selvaduray - SJSU - Oct 2004

G. Selvaduray - SJSU - Oct 2004

Overall Composition - 2

There are three ways of determining the overall composition Method 1 Refer to Figures OC1 and OC2 Let the overall composition be represented by the point X Draw lines passing through X, and parallel to each of the sides Where the line A’C’ intersects the side AB tells us the concentration of component B in X The concentrations of A and C, in X, can be determined in an identical manner

G. Selvaduray - SJSU - Oct 2004

G. Selvaduray - SJSU - Oct 2004

Overall Composition - 3

Method Two: Draw lines through X, parallel to the sides of the Gibbs Triangle A’C’ intersects AB at A’ B’C” intersects AB at B’ G. Selvaduray - SJSU - Oct 2004

Concentration of B = AA’ Concentration of C = A’B’ Concentration of A = B’B This method can be somewhat confusing, and is not recommended

G. Selvaduray - SJSU - Oct 2004

Overall Composition - 4

Method 3 Application of the Inverse Lever Rule Draw straight lines from each corner, through X %A = AX %B = BX %C = CX AM BN CL Important Note: Always determine the concentration of the components independently, then check by adding them up to obtain 100%

G. Selvaduray - SJSU - Oct 2004

G. Selvaduray - SJSU - Oct 2004

Ternary Isomorphous System

Isomorphous System: A system (ternary in this case) that has only one solid phase. All components are totally soluble in the other components. The ternary system is therefore made up of three binaries that exhibit total solid solubility G. Selvaduray - SJSU - Oct 2004

The Liquidus Surface: A plot of the temperatures above which a homogeneous liquid forms for any given overall composition The Solidus Surface: A plot of the temperatures below which a...