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1. Course Code: MEC208 MEC208 LPU Engineering Materials Most of the images are courtesy of the book “Material Science and Engg. an Introduction” by William D. Callister, Jr. & David G. Rethwisch. Few were adopted from “ The Science and Engineering of Materials” by Donald. R. Askeland. Images collected from Wikipedia and google images were also used. 1

2. Unit 4 Fundamentals 2 Unit 4: Alloys & Phase Diagrams

3. Topics covered in last class: Revision of Unary Phase diagrams Binary Phase diagrams Different systems in Binary Phase diagrams Isomorphous Eutectic Eutectoid Peritectic Binary Isomorphous system Cu-Ni Alloy binary phase diagram Interpretation of phase diagram

4. Interpretation of Phase Diagram : (Nickel – Cu System) For a binary system of known composition and temperature that is at equilibrium, at least three kinds of information are available: (1) the phases that are present, (2) the compositions of these phases, and (3) the percentages or fractions of the phases. The procedures for making these determinations will be demonstrated using the copper–nickel system. Phase Diagrams

5. Interpretation of Phase Diagram : (Nickel – Cu System) A) Phases Present : One just locates the temperature–composition point on the diagram and notes the phase(s) with which the corresponding phase field is labeled. For example, an alloy of composition 60 wt % Ni–40 wt % Cu at 1100 deg would be located at point A ( since this is within the region, only the single phase will be present.) On the other hand, a 35 wt % Ni–65 wt % Cu alloy at 1250 deg (point B ) will consist of both and liquid phases at equilibrium. Phase Diagrams

6. Interpretation of Phase Diagram : (Nickel – Cu System) B) Determination of Phase Composition: The first step in the determination of phase compositions (in terms of the concentrations of the components ) is to locate the temperature composition point on the phase diagram. If only one phase is present, the procedure is trivial: the composition of this phase is simply the same as the overall composition of the alloy. For example, consider the 60 wt % Ni–40 wt % Cu alloy at 1100 deg (point A ). At this composition and temperature, only the phase is present, having a composition of 60 wt % Ni–40 wt % Cu. Phase Diagrams

7. Interpretation of Phase Diagram : (Nickel – Cu System) B) Determination of Phase Composition: For an alloy having composition and temperature located in a two-phase region , the situation is more complicated. In all two-phase regions, horizontal lines called tie lines are drawn as per following A tie line is constructed across the two-phase region at the temperature of the alloy. The intersections of the tie line and the phase boundaries on either side are noted. Perpendiculars are dropped from these intersections to the horizontal composition axis, from which the composition of each of the respective phases is read. Phase Diagrams

8. Interpretation of Phase Diagram : (Nickel – Cu System) B) Determination of Phase Composition: For example, consider again the 35 wt % Ni–65 wt % Cu alloy at 1250 deg located at point B in Figure and lying within the region. Problem is to determine the composition (in wt % Ni and Cu) for both the and liquid phases The tie line has been constructed across the phase region The perpendicular from the intersection of the tie line with the liquidus boundary meets the composition axis at 31.5 wt % Ni–68.5 wt % Cu, which is the composition of the liquid phase, C L Phase Diagrams Likewise, for the solidus–tie line intersection, we find a composition for the solid-solution phase, C , of 42.5 wt % Ni–57.5 wt % Cu.

9. Unit 4 27 Phase Diagrams Lever rule: Between Liquidus and Solidus lines, both phases, liquid and solid co-exist under equilibrium, and the relative amounts of both liquid and solid at given temperature and composition can be calculated by applying Lever Rule. Consider an alloy of two components A and B. At temperature, T the alloy of a given composition will consists two phases, liquid and solid.

10. Unit 4 28 Phase Diagrams Lever rule: T o o b tain the relative a m o u nts o f li q uid a n d so l id, draw a vertical li n e representing the alloy (W) and horizontal temperature line ( T ) to intersect the liquidus and solidus lines at L and S respectively. The Lever rule states that the vertical line divides the horizontal line into two parts (LO and OS) are inversely the a m o u nt of whose lengths proportional to phases present.

11. Unit 4 28 Phase Diagrams Lever rule: To determine the phase composition, locate the t e m p e ratu r e ( T ) and composition point (O) on the phase diagram. To o b tain the relative a m o u nts o f li q uid a n d so l id, draw a vertical li n e representing the alloy (W) and horizontal temperature line (T) to intersect the liquidus and solidus lines at L and S respectively. The tie line through (O) extends across the two phase region and terminates at the phase boundary lines (L&S) on either side. The perpendicular lines drawn through these points on the composition axis determine the composition in respective phases.

12. Unit 4 29 Phase Diagrams Amount of Solid Phase (%) : LS X 100 S = LO LS X 100 L = OS Amount of Liquid Phase (%) : Lever rule: The lever rule may be used to determine the relative amounts of phases at equilibrium in any two phase region for a binary alloy as below…

13. Unit 4 32 Phase Diagrams Lever rule: Weight /Mass Fractions and Volume Fractions From the figure From the figure

14. Unit 4 33 Phase Diagrams Lever rule: Weight /Mass Fractions and Volume Fractions Conversion of mass fractions of phases to volume fractions Conversion of volume fractions of phases to mass fractions

15. Unit 4 Phase Diagrams Pro b l e ms

16. Unit 4 Phase Diagrams Pro b l e ms

17. Unit 4 Phase Diagrams Pro b l e ms a) ~ 1350 o C b) ~ 59 % Ni + 41 Cu c) ~ 1390 o C d) ~ 81 % Ni + 19% Cu

18. Phase Diagrams Lever rule: (Also called Inverse Lever Rule) The tie line is constructed across the two-phase region at the temperature of the alloy. 2. The overall alloy composition is located on the tie line. 3. The fraction of one phase is computed by taking the length of tie line from the overall alloy composition to the phase boundary for the other phase, and dividing by the total tie line length. 4. The fraction of the other phase is determined in the same manner. 5. If phase percentages are desired, each phase fraction is multiplied by 100.