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12.11: Questions

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    Quick questions

    You should be able to answer these questions without too much difficulty after studying this TLP. If not, then you should go through it again!

    What is the effect on the shape of the free-energy curve for a solution if its interaction parameter is positive?

    a Produces a curve which has one minimum
    b Produces a curve with no minimum and one maximum
    c Produces a curve which contains a maximum at low T
    d Produces a curve which contains a maximum at high T

    In terms of interatomic bonding, what does a negative interaction parameter represent?

    a That A-A and B-B bonds are more favoured
    b That A-B bonds are more favoured
    c That A-A bonds are more favourable than B-B bonds

    Cooling curve for a binary system:

    Cooling curve for a binary system

    a One phase
    b Two phases
    c Three phases
    d Four phases

    What is a hypoeutectic alloy?

    a An alloy which has solute content greater than that of the eutectic.
    b An alloy which has a solute content lower than that of the eutectic.
    c An alloy whose solute content is such that it contains no eutectic.
    d An alloy whose final microstructure is wholly eutectic.

    Look at the following Al-Si phase diagram. (Place the mouse over the diagram to determine the temperature and composition at any point.)

    For an Al 5 wt% Si alloy what will be the composition of the solid in equilibrium with the liquid at 600�C?

    a 1 wt%
    b 2 wt%
    c 9 wt%
    d 13 wt%

    Look at the following Cu-Al phase diagram. (Place the mouse over the diagram to determine the temperature and composition at any point.)

    What will be the relative weight fraction of CuAl2 (θ) in a Al 15wt% Cu alloy at its eutectic temperature?

    a 66.6%
    b 33.3%
    c 50%
    d 75%

    Deeper questions

    The following questions require some thought and reaching the answer may require you to think beyond the contents of this TLP.

    Using the following data, calculate the volume fraction of the beta phase and eutectic at the eutectic temperature, for an alloy of composition 75 wt% Ag. Assume equilibrium conditions.

    At eutectic temp:

    eutectic composition = 71.9 wt% Ag
    maximum solid solubility of Cu in Ag = 8.8 wt% Cu
    density Ag = 10 490 kg/m3
    density Cu = 8 920 kg/m3


    Using the lever rule, fraction of beta

    = (C - C1) / (C2 - C1) = (75 - 71.9) / (91.2 - 71.9) = 16 wt%.

    So fraction of eutectic

    = 84 wt%.

    To convert to volume fractions, we need to calculate densities of beta and eutectic.

    Density of eutectic

    = 0.719 x 10 490 + 0.281 x 8 920 = 10 049 kg/m3.

    Density of beta

    = 0.912 x 10 490 + 0.088 x 8 920 = 10 352 kg/m3.

    Therefore, volume fraction of beta

    = (10 049/10 352) x 16 = 15.53 vol%.

    Hence volume fraction of eutectic

    = 84.47 vol%.

    Composition vs temperature phase diagrams exist for the combinations of three elements A, B and C (i.e. the three phase diagrams A-B, A-C and B-C). How might they be arranged in three-dimensional space to construct a "ternary" phase diagram for a system containing A, B and C?

    Hint: Consider the possible extreme compositions.


    The phase diagrams must be constructed into a triangular prism:

    Diagram illustrating construction of a ternary phase diagram

    The rectangular faces of the prism represent binary states. The corners represent 100% pure states of A, B and C. Inside the prism details the phases of the system with varying compositions of the three elements. The phase boundary lines of each binary phase diagram extend into the prism.

    Open-ended questions

    The following questions are not provided with answers, but intended to provide food for thought and points for further discussion with other students and teachers.

    Under what conditions could the compositions of the phases present differ from that predicted in the phase diagram?

    This page titled 12.11: Questions is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Dissemination of IT for the Promotion of Materials Science (DoITPoMS) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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