Iron has \( B C C \) structure below \( 910^{\circ} \mathrm{C} \) and FCC structure above this temperature. Assume the same atomic radius in both structures. Find the percentage change in volume, when the mel undergoes the structural change at \( 910^{\circ} \mathrm{C} \). (a) Volume is contract by \( 8.14 \% \) (b) Volume is increases by \( 10.24 \% \) (c) Volume is contract by \( 83.12 \% \) (d) Volume is increases by \( 23.14 \% \)
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For BCC (Body-Centered Cubic) structure: The volume of the unit cell \( V_{\text{BCC}} \) can be expressed in terms of the atomic radius \( r \) as: \[ a_{\text{BCC}} = \frac{4r}{\sqrt{3}} \] \[ V_{\text{BCC}} = a_{\text{BCC}}^3 = \left( \frac{4r}{\sqrt{3}} Show more…
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Iron (Fe) undergoes an allotropic transformation at $912^{\circ} \mathrm{C}:$ upon heating from a $\mathrm{BCC}$ ( $\alpha$ phase) to an FCC $(\gamma$ phase). Accompanying this transformation is a change in the atomic radius of $\mathrm{Fe}-$ from $R_{\mathrm{BCC}}=$ $0.12584 \mathrm{~nm}$ to $R_{\mathrm{FCC}}=0.12894 \mathrm{~nm}-$ and, in addition, a change in density (and volume). Compute the percentage volume change associated with this reaction. Does the volume increase or decrease?
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