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Grading guide: 10 points maximum, 2 pts format, 3 pts noted below in red: l t 5c t 1. The primary difference between an isomorphic phase relationship and eutectic phase relationship is whether or not the two end-member solids are completely miscible (mixable) in each other. In an isomorphic situation, they are and the solid at the bottom of the diagram is a single-phase region. The melting point of the solid is approximately the weighted average of the two end-members. In a eutectic situation, the solid at the bottom of the diagram is a two-phase region, and the melting point of the solid is depressed in the middle of the diagram because the components have to phase-separate when they solidify, each component depressing the freezing point of the other. 2. Using Cd-Bi phase diagram provided below, interpret it by (i) naming the phases, (ii) the composition of each phase, and (iii) relative mass fractions of the phases at the following coordinates: a. 50 wt% Bi at 160 °C (i) 2 phases; (ii) L, 58%Bi; solid, 0%Bi (pure Cd), (iii) L, 50/58 = 0.86; S, 0.14 Note: just supplying the L fraction is sufficient because the S 1 point for part iii fraction is simply 1-x; also the liquid/solid ratio is also a valid response L/S = 50/8 or equivalent; or S/L ratio 8/50 is fine too; but it is essential that it is clear what is being presented b. 90 at% Bi at 240 °C This is given as atomic percent, which corresponds to 94 wt%Bi (i) 2 phase; (ii) L, 91.5%Bi; solid, 100%Bi, (iii) L, (100-94)/100-91.5) = 0.71; solid, 0.29; or L/S = 3. Use the following data to create a binary phase diagram using either graph paper or software capable of generating a graph with axes. Data: component A pure melting temperature, 1052 °C; component B pure melting temperature, 1863 °C; eutectic temperature and composition, 70 wt% A, 700 °C. Label axes with units, and label all regions in terms of phases present, for example, one region will be labeled 'liquid plus pure solid A' or 'L + A(s)'. You may assume that given just the data provided, that this is a simple eutectic (meaning completely immiscible solid phases), and you may use straight lines for liquidus lines. Hand sketching without graph paper is only acceptable if you have no reasonable alternative – and in that case you must still make an effort to have linear x, y scales.

Note: if units on x-axis are wt% A, as shown, then the melting point for component A (1052 °C) must be on the right side (100% A) – and vice-versa, if you use wt% B for the composition axis. Diagram created using MS Excel

4. Using Ag-Cu phase diagram provided below, interpret the phase diagram by (i) naming the phases, (ii) the composition of each phase, and (iii) relative mass fractions of the phases at the following coordinates: a. 15 wt% Ag, 600 °C (i) 2 phases; (ii) solid α, 2 wt%Ag; solid β, 96 wt%Ag, (iii) fraction of total mass that is solid α, (96−15)/(96-2) = 0.86; solid β, 0.14 1 point 1point b. 15 wt% Ag, 900 °C (i) 2 phases; (ii) α, 8 wt%Ag; L, 43 wt%Ag, (iii) fraction of total mass that is solid α, (43−15)/(43-8) = 0.80; fraction that is liquid, 0.20 c. 71.9 wt% Ag, 779 °C, after sufficient heat to melt exactly half the mass (i) 3 phases, one liquid phase and 2 solid phases; (ii) L, 71.9 wt%Ag; solid α, 8.0 wt%Ag; solid β, 91.2 wt%Ag, (iii) L = 0.50 (as stated in problem description); solid α, 0.50×(91.2−71.9)/(91.2-8.0) = 0.50×0.23 = 0.12; solid β, 1 – 0.50 − 0.12 = 0.38

1 pt

5. At 700 °C, what is the maximum solubility of (a) Cu in Ag, (b) Ag in Cu. (phase diagram below) (a) 6 wt%Cu in Ag (or 94 wt%Ag) [when worded as Cu in Ag, then Ag is the solvent and we are looking on the right side of the phase diagram as presented, (b) 5.0 wt%Ag (see diagram below) for part b only 6. Briefly explain why upon solidification, an alloy of eutectic composition forms a microstructure consisting of alternating layers of two solid phases. Both solid phases must form simultaneously from the liquid phase. The 2 components therefore preferentially diffuse to appropriate regions so that the 2 phases can form with their respective compositions (see figure 9.13 in Callister) – this ends up being a layered – or lamellar - structure 7. For a Pb-Mg alloy at 75 wt% Pb (phase diagram provided in Callister (Fig. 9.20), also available in HO from March-1 class posted on moodle), make schematic microstructure sketches that predict what would be observed for very slow cooling conditions at the following temperatures: 600 °C, 500 °C, 450 °C, and 300 °C. Label all phases and indicate their approximate compositions. You are making sketches similar to those shown in Fig 9.16 (Callister 8/e)

600

1 point --- In this sketch at 450ºC, I want to see the roundish domains of primary, labeled as Mg2Pb, and the lamellar alternating layers labeled as Mg2Pb (same color as the primary domains, and the other layers labeled as alpha, ~40%. (1/2 pt partial credit if lamellar layering is shown)

8. On the NiTi phase diagram provided below, clearly identify the following: (Note: the ‘memory’ metal phase transition occurs at temperatures below 100 °C and is not shown in this phase diagram) a) label the liquidus line in three different places b) label one of the solidus lines (there are several) c) label one of the solvus lines (there are several) d) circle the eutectoid point, label it ‘D’ e) circle any peritectic points, label it/them ‘P’ f) circle all eutectic points, label them ‘E’ g) identify a congruent transformation, label it ‘C’ h) identify an intermetallic compound, label it ‘M’

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