Problem 4: (15 marks) Pure iron goes through a polymorphic change from BCC to FCC upon heating at 912°C. 4.1) Calculate the volume change associated with the change in crystal structure from BCC to FCC if at 912°C the BCC unit cell had a lattice constant a = 0.293 nm and the FCC unit cell a lattice constant a' = 0.363 nm. Make sure to explain clearly the different steps you have undertaken to come up with the solution. 4.2) What consequences this change of volume could have? Give an example where this change of volume is important to consider.
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The volume \( V_{\text{BCC}} \) of a BCC unit cell is given by: \[ V_{\text{BCC}} = a^3 \] where \( a = 0.293 \, \text{nm} \). \[ V_{\text{BCC}} = (0.293 \, \text{nm})^3 = 0.0251 \, \text{nm}^3 \] Show more…
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2. What is the lattice constant for pure iron in the FCC configuration? (Atomic radius of Iron is 0.1241 nm). Show your work. 3. What is the lattice constant for pure iron in the BCC configuration? (use the same atomic radius as for Q2) Show your work. 4. Pure iron goes through a polymorphic change from BCC to FCC upon heating through 912°C. Calculate the volume change associated with the change in crystal structure from BCC to FCC using the results of Q2 and Q3 above.
Assume that a pure metal changes its structure from a simple-cubic (SC) to a face-centered-cubic (FCC) and then to a body-centered-cubic (BCC). If the relations between the atomic radius (r) and lattice parameter (ao) are given by the equations: ao = 2r (for SC), ao = 4r/sqrt(2) (for FCC), and ao = 4r/sqrt(3) (for BCC), calculate: i) The theoretical volume change accompanying a polymorphic transformation in a pure metal from the SC to FCC ii) The theoretical volume change accompanying a polymorphic transformation in a pure metal from the BCC to FCC.
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