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# Lecture 4. Phase Diagrams ## Reading ### Required * Phase Diagrams and Their Applications, First Edition. A. Prince. Paladin Press Inc. ### Recommended * Phase Diagrams in Metallurgy. F. Rhines. McGraw-Hill Book Company, Inc. * Understanding Phase Diagrams. D. West. ## Phase ### Definit...

# Lecture 4. Phase Diagrams ## Reading ### Required * Phase Diagrams and Their Applications, First Edition. A. Prince. Paladin Press Inc. ### Recommended * Phase Diagrams in Metallurgy. F. Rhines. McGraw-Hill Book Company, Inc. * Understanding Phase Diagrams. D. West. ## Phase ### Definition A phase is a physically distinct, homogeneous portion of a system. ### Characteristics * Same structure or atomic arrangement throughout * A definite interface between the phase and any surrounding phase(s) * It is possible to mechanically separate phases ## Phase Diagram ### Definition A phase diagram is a graphical representation of the phases present in a material system as a function of temperature, pressure, and composition. ### Purpose * Show which phase or phases are stable at various temperatures, pressures, and compositions * Help in understanding and predicting the microstructure of an alloy * Phase diagrams provide valuable information about melting, casting, crystallization, and other phase transformations. ### Phase Diagram for Water * Shows the conditions under which water exists as a solid (ice), liquid, or gas (vapor). * Illustrates the concept of phase equilibrium and triple point. ### Single-Component Phase Diagram * A plot of pressure versus temperature * Used to represent the phase behavior of a single element or compound * Phase boundaries represent the equilibrium between two phases * Triple point: the point where three phases coexist in equilibrium ### Binary Phase Diagram * A plot of temperature versus composition * Used to represent the phase behavior of a mixture of two elements or compounds * Phase boundaries represent the equilibrium between two phases * Lever rule: a method for determining the amount of each phase present in a two-phase region ## Gibbs Phase Rule $$ P + F = C + N $$ Where: $P =$ Number of phases that coexist in equilibrium $F =$ Degrees of freedom (number of independently variable factors: $T, P, C$) $C =$ Number of components in the system $N =$ Number of non-compositional variables (usually 1, temperature or pressure) ## Cooling Curves ### Pure Metal or Eutectic Composition * The temperature remains constant during the phase change * The cooling curve exhibits a thermal arrest * No degrees of freedom $(F = 0)$ in the two-phase region ### Solid Solution Alloy * The temperature changes during the phase change * The cooling curve does not exhibit a thermal arrest * One degree of freedom $(F = 1)$ in the two-phase region ## Isomorphous System ### Definition A binary system in which the two components are completely soluble in each other in both the liquid and solid phases. ### Characteristics * The phase diagram consists of two single-phase regions (liquid and solid) separated by a two-phase region (liquid + solid). * Examples: Cu-Ni, Ag-Au ### Tie Line An isothermal line drawn through the two-phase region, connecting the compositions of the two phases in equilibrium. It is used to determine the amount of each phase present in a two-phase region. ### Lever Rule A method for determining the amount of each phase present in a two-phase region. * The lever rule is based on the principle of mass balance. * The amount of each phase is proportional to the length of the tie line segment on the opposite side of the overall composition. * Example: $$ \% \text{solid} = \frac{C_0 - C_L}{C_S - C_L} \times 100 $$ $$ \% \text{liquid} = \frac{C_S - C_0}{C_S - C_L} \times 100 $$ Where: $C_0 =$ Overall composition $C_L =$ Composition of the liquid phase $C_S =$ Composition of the solid phase