CHAPTER 8 Phase Diagrams 1

ISSUES TO ADDRESS... Phase B Phase A • When we combine two elements... what is the resulting equilibrium state? • In particular, if we specify... -- the composition (e.g., wt% Cu - wt% Ni), and -- the temperature (T ) then... How many phases form? What is the composition of each phase? What is the amount of each phase? Phase B Phase A Nickel atom Copper atom 2 2

Phase Diagrams. Phase : A region in a material that differs in structure and function from other regions. Phase Diagrams - graphical representation of what phases are present in a materials system at various temp Phase diagrams: Represents phases present in metal at different conditions (Temperature, pressure and composition). Indicates equilibrium solid solubility of one element in another. Indicates temperature range under which solidification occurs. Indicates temperature at which different phases start to melt. In materials science the most common phase diagrams involve temperature versus composition.

Microstructure of carbon steel

Phase Diagram of Fe 6

For pure Iron PT phase diagram, there are 3 separate and distinct solid phases: alpha (α) Fe delta (δ) Fe gamma (γ) Fe BCC crystal structure FCC crystal structure There are 3 triple points in the iron PT phase diagram where 3 different phases coexist: Liquid, vapor, and delta (δ) Fe Vapor, delta (δ) Fe, and gamma (γ)Fe Vapor, gamma (γ) Fe, alpha (α) Fe

Gibbs phase rule Gibbs Phase Rule is an equation that computes the number of phases that can coexist in equilibrium in a chosen system. P + F = C + 2 Where P= no. of phases that coexist in a chosen system C= no. of components in the system () F= degree of freedom ( no. of variables [pressure, temperature, and composition] that can be changed independently without changing the no. of phases in equilibrium in the chosen system)

Application of Gibbs phase rule to the PT phase diagram of pure water; At the triple point; 3 phases coexist in equilibrium, no. of component in the system is one (only water)C=1 Therefore; P + F = C + 2 3 + F = 1 + 2  F=0 (zero degree of freedom) None of the variables (T, P, composition) can be changed and still keep the 3 phases in balance.

Gibbs phase rule consider a point along the liquid-solid freezing curve; at any point along this line 2 phases will coexist. P + F = C + 2 2 + F = 1 + 2  F=1 (one degree of freedom) F=1 means there is one variable (T or P) can be changed independently and still maintain a system with 2 coexisting phases. Thus if a particular pressure is specified, there is only one temp. at which both liquid and solid phases can coexist

Cooling curves for Pure Metal Plots of temp. vs time acquired during solidification of a metal and alloys (the metal cools from a temp. at which it is molten through solidification and finally to room temperature). It provides phase diagram information as temperature is lowered. Thermal arrest A region of the cooling curve for a pure metal where temperature does not change with time (plateau) representing the freezing temperature. Thermal arrest : heat lost = heat supplied by solidifying metal

Fig. The cooling curve for a pure metal A to B -- cooling of liquid B– solidification begins C– solidification ends BC region of thermal arrest OR plateau, the metal in the form of a mixture of solid and liquid phases. The latent heat keeps the mixture at freezing temp. until complete solidification is achieved. C to D – cooling of solid A B C D Pouring temp Temp (T) Time (t) Freezing temp (melting point) Liquid Liquid+solid Solid Cooling under the freezing temp. is required for the formation of solid nuclei

Cooling curve for pure iron at a Pressure of 1 atm

Binary Isomorphous Alloy Systems Mixture of two systems Two component system Binary alloy Isomorphous system: Two elements completely soluble in each other in liquid and solid state. Example: Cu-Ni solution. Composition at liquid and solid phases at any temperature can be determined by drawing a tie line. Isomorphous - only single type of crystal structure exists for all compositions of the components 14

Phase Diagram of Solid Solution Cu-Ni CO : overall composition, CS: composition of solid phase, CL: composition of liquid phase

Phase Diagram from Cooling Curves Series of cooling curves at different metal composition are first constructed. Points of change of slope of cooling curves (thermal arrests) are noted and phase diagram is constructed. More the number of cooling curves, more accurate is the phase diagram. Alloys solidify over a range of temperature (no thermal arrest) Figure 8.4 16

The Lever Rule The Lever rule determines the amount of each phase The Lever rule gives the weight % of phases in any two phase regions. Wt fraction of solid phase = Xs = w0 – w1 ws – w1 Tie line Wt fraction of liquid phase = X1 = ws – w0 ws – w1 wO : overall composition, wS: composition of solid phase, wL: composition of liquid phase 17

The lever rule The lever-rule equations state that to calculate the wt fraction of one phase of a 2 phase mixture (alloy), one must use the segment of the tie line that is on the opposite side of the alloy of the interest and is farthest away from the phase for which the wt fraction is being calculated.

8.10 page 352 Consider an alloy containing 70 wt% Ni and 30 wt % Cu. a. At 13500C make a phase analysis assuming equilibrium conditions. In the phase analysis include the following: (i) What phases are present ? (ii) What is the chemical composition of each phases ? (iii) What amount of each phase is present ? Make a similar phase analysis at 15000C. Sketch the microstructure of the alloys at each of these temperatures by using circular microscopic field

Sample Problem on Lever rule Example 1. A copper-nickel alloy contains 47% Cu and 53% Ni and is at 1300 C. What is the weight percent of copper in the liquid and the solid phases at this temperature? What weight percent of this alloy is liquid and what weight percent is solid?

Example 2. Calculate the percent liquid and solid for the Ag-Pd phase diagram shown in Fig. at 12000C and 70 wt % Ag.

Example 3 Do a complete phase analysis (phases present, their amounts, and their compositions) for the lead-tin alloy. (Fig 1) With 10wt% Sn at 3500C, 2750C, 2250C and 500C. With 30wt% Sn at 3500C, 2750C, 2250C and 1840C

Phase Diagram of Immiscible System (Pb-Sn) Fig 1. Colored fields show two-phase regions.

Microstructures in Eutectic Alloy

Ternary Phase Diagram Ternary Phase diagrams are diagrams that represent the equilibrium between the various phases that are formed between three components as a function of temperature

Ternary Phase Diagrams Three components Constructed by using a equilateral triangle as base. Pure components at each end of triangle. Binary alloy composition represented on edges. Temperature can be represented as uniform throughout the Whole Diagram Isothermal section. 26

Ternary Phase Diagram (Cont..) Example:- Iron-Chromium-Nickel phase diagrams. Isothermal reaction at 6500C for this system Composition of any metal at any point on the phase diagram can be found by drawing perpendicular from pure metal corner to apposite side and calculating the % length of line at that point 27

Three Dimensional Ternary Phasee

Ternary phase diagram using Gibbs Triangle

Sample Problem on Ternary Phase Diagram : What are the compositions of point y and z in the figure ? X y z

Binary Eutectic alloy system Eutectic reaction (in a binary phase diagram):- A phase transformation in which all the liquid phase transforms on cooling into two solid phase isothermally. Eutectic temperature:- The lowest temperature at which the liquid phase can exist when cooled slowly Eutectic composition:- The composition of the liquid phase that reacts to form two new solid phases at the eutectic temperature. Eutectic point:- The point determined by the eutectic composition and temperature.

Binary Peritectic alloy system Peritectic reaction (in a binary phase diagram):- A phase transformation in which, upon cooling, a liquid phase combines with a solid phase to produce a new solid phase.

Binary Monotectic alloy system Monotectic reaction (in a binary phase diagram):- A phase transformation in which, upon cooling, a liquid phase transforms into a solid phase and a new liquid phase (of different composition than the first liquid phase). L1 L2

Summary • Phase diagrams are useful tools to determine: -- the number and types of phases present, -- the composition of each phase, -- and the weight fraction of each phase given the temperature and composition of the system. • The microstructure of an alloy depends on -- its composition, and -- whether or not cooling rate allows for maintenance of equilibrium. • Important phase diagram phase transformations include eutectic, eutectoid, and peritectic. 34 34