questions:

5. CMSX-4 is a nickel superalloy with composition Ni-6.4Cr-9.7Co-0.6Mo-1.0Ti-5.6Al-6.5Ta-6.4W- 0.1Hf-3.ORe (wt.%). It is composed of two phases, an fee y-Ni phase and a primitive cubic y phase of nominal composition NigAl, where the Al atoms are placed on the cube face centres and the Ni atoms are placed on the cube corners. You may assume that the solubility of Al, Ta and Ti in the is nil and that these atoms are only found on the Al site in the y' phase. Further, assume that Re has no solubility in the y' and that all the remaining atomic species have complete solubility and partition evenly in the y phase and on the Ni site in the y'. Therefore, calculate the volume fraction of y and the compositions of each phase in at.%.4. You are provided below with a partial phase diagram for the TIO,-Nbgo, system. (a) Designate each of the single phase fields (some have very limited solid solubility) and determine the nominal compositions of the phases. (b) Label the two phase fields and note the compositions and temperatures of the eutectic points. (e) Draw a schematic diagram of the variation of Gibbs Energy against Composition for all the phases at a temperature of 1466"C, that is, between the lower two eutectic temperatures. Label the known compositions of the phases and draw common tangents where appropriate [hint: draw the liquid first].3. The MgO-FOO system shows complete solubility in both the solid and liquid phases. Values for the d420 interplanar spacing of the solid phase obtained by X-ray diffraction are given below. (a) MgO and FeO are cubic with a = 4.213 A and 4.307 A, respectively. Using dau = a/ VR + + 1. calculate digg for the end-member (0 and 100) compositions. (b) Vegard postulated that the lattice parameter (unit cell size) of a material varies linearly with composition. Thereby determine the unknown compositions of the solid phase in the Table (ignore the possible effect of thermal expansion). (e) Hence plot the equilibrium phase diagram for the system. (d) The Figure below shows the Gibbs energy curves of the solid and liquid phases for the sys- tem. By comparison with your equilibrium diagram, determine the temperature to which it corresponds. Liquid Composition Temp. Solid Solution G mol% MgO . C dago A mol% MgO solid 0 1350 0 20 1900 0.951 Liquid 40 2200 0.947 60 2500 0.944 80 2700 0.943 100 2800 100 FeO mol % Mgo Mgo2. The Snog-Tio, system shows complete solid solution at high temperatures and a solvus at lower temperatures. Thermodynamic data indicate that the value of Ww is 28.3 kJmol" in the expression for the enthalpy of mixing AHmix = rryWw, where rs is the mole fraction Sno, and ry is the mole fraction Ti02. (a) Calculate AHmix at as = 0, 0.1, 0.3, 0.5, 0.7, 0.9 and 1 and plot your values on a graph of AHmix against composition. (b) Calculate the entropy of mixing at the same compositions and add a curve for -ASmix to your graph (ASmix = -R(as Ines + er Inry) for random mixing of Sn and Ti on their sites). (c) Calculate the Gibbs energy of mixing for these compositions at temperatures 7 of 1550-C, 1300'C and 1000"C. Make another graph of these values. (d) From this graph, estimate the compositions of the co-existing phases in the two-phase region and hence plot the solvus on a binary phase diagram.Presented below is the aluminium-rich end of the Al-Cu binary phase diagram, which is the basis of many high-strength aluminium alloys. You may assume that all the phase boundaries may be described by straight lines (not necessarily the case in reality). 700 660 .C L L+0 BOO L+a 548 9C 500 5.5 wt 9% Cu 33 wt %% Cu 400 Temperature PC) 300 0+0 200 100 1 wt.M Cu 10 20 30 40 50 Al Composition (wt.% Cu) 0 - Al-Cu 1. For an alloy containing 4wt.% Cu, (a) Calculate, assuming slow cooling, the volume fraction and composition of the solid at 600 C. (b) Repeat the calculation for rapid cooling conditions (Scheil). (e) For slow cooling, at what temperature does solidification complete? (d) For fast cooling, what is the fraction eutectic? (e) Sketch the solidified microstructure you would expect to observe for each assumption