Problem solving session for physical metallurgy
WS 2016 / 201705.12.201
Section A:Mostly theoretical so try to find them in the book and do it yourself.
Section B:To be solved during the tutorials. (Complete solutions)
Section C:Similar to Section B that you need to practice at home
A1Describe the cooling of a peritecticalalloywith the concentration c0 and sketch the microstructure during solidification.
A2Calculate the valence electron concentration for the alloys, each with the maximal solubility of Zn, Ga, Ge and As in Cu (use phase diagrams 4.31).
(Answer: VEC (Cu/Zn)=1.38; VEC (Cu/Ga)=1.42; VEC (Cu/Ge)=1.36;
VEC (Cu/As)=1.28)
A3a) What is the lattice structure of the intermetallic phase NiAl called? What does it have in common with the body-centred cubic structure, what are the differences?
b)In an ordered cubic alloy, which is the lowest-indexed plane that, according to the Bragg law, reflects? Give an explanation!
A4Draw aunit cell of the ordered alloys-CuZn, NiAl, Cu3Au, Ni3Al, FeAl and CuAu. Which lattice structures are existent?
A5Calculate and draw the long range order parameter (s) as a function of the temperature for the ordered bcc AB-alloy (-brass) (see sample solution).
A6a)How are Zintl-phases characterised? (1 example)
b) How are Laves-phases characterised? (1 example)
c)How are Hägg-phases characterised? (1 example)
d)How are Hume-Rothery-phases characterised? (1 example)
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B1Sketch the following binary systems:
a)with complete solubility in the solid and the liquid state
b)without solubility in the solid and the liquid state
c)an eutectic system
d) and a peritectic system.
B2Sketch the molar free enthalpy G of a regular mixture of a binary system as well as theenthalpy of mixing Hm(c) and the entropy of mixingSm(c) for a fixed temperature as a function of H0.
B3a) Determine the Gibbs free energy of a phase mixture under the assumption that it isproportionatelycomposed of the Gibbs free energy of the individual phases (tangential law).
b) Discuss the construction of a phase diagram from the G(c)-curves by the use of the tangential law.
B4Discuss the Hume-Rothery rules for the formation of primary solid solutions. What is your expectation for the phase diagrams Au-Cu, Au-Ag and Cu-Ag (aAu=4.0786Å, aAg=4.0863Å, aCu=3.6148Å)?
B5The crystal of a CuZn-alloy if given.
a)Explain the term long range order parameter. Determine the limits, within this limits the parameter is defined for an AB-alloy. Calculate the parameter for the given unit cell.
b)Explain the term short range order parameter and calculate it for the centered Zn atom pictured below.
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C1Explain the terms “congruent melting” and “incongruent melting”.
C2Calculate thefraction of the phases α und β directly after finishing the eutectic reaction for a silver-copper alloy (figure 4.6., “Physical Foundations of Material science”, G. Gottstein) with a starting concentration c0 = 50 wt.-% Cu.
C3a) Explain the following terms and name possible technical applications: solid solution, substitutional solid solution and interstitial solid solution.
b) Explain the following terms and give examples for each: “intermetallic phase”, “primary solid solution” and “intermediate solid solution”.
C4Explain, according to the long distance order, the term “antiphase boundaries”. How do they occur? Which influence do they have?
for exercise B3 b)
Mehran AfsharE-mail:
Institut für Metallkunde und Metallphysik
Kopernikusstr. 14Weekly doubt session: By appointment
Room E01, Tel.: 0241-80 – 26892Venue: Room E01
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