Past exam of the materials science course of the University of Cambridge / 2018 / Paper 1 / 7

In a displacive change, neighboring atoms move cooperatively without the long-range compositional redistribution characteristic of diffusion-controlled precipitation. The change can preserve many near-neighbor relationships and can occur rapidly when its kinetic conditions are met.

A reconstructive change requires breaking and re-forming the relevant structural connections to establish a different arrangement, often with a larger activation barrier and slower nucleation and growth. It may consequently show substantial kinetic persistence of a metastable phase. The distinction concerns the atomic mechanism, not merely whether the final phase has a different symmetry; neither label by itself supplies a universal transformation rate.

For two phases of the same pure substance at equilibrium, their chemical potentials are equal. Along their coexistence boundary,Differentiating the equality givesTherefore the Clapeyron equation isMolar or mass-specific quantities give the same slope if a consistent basis is used. $L=T\Delta s$ follows from equal Gibbs free energies at coexistence.

Solid phases are relatively incompressible and have modest thermal expansion over many intervals. If their entropy and volume differences vary slowly enough that $\Delta s/\Delta v$ is approximately constant, the boundary is approximately straight. Straightness is an approximation, not a thermodynamic requirement. Heat-capacity differences, pressure dependence of volume, other transitions and proximity to special points can curve the boundary. The ideal-vapor integrated Clausius-Clapeyron approximation is not appropriate for these two solid phases.

Read the coesite–stishovite boundary at approximately $(400{}^{\circ }\mathrm{C},7.2\mathrm{GPa})$ and $(2800{}^{\circ }\mathrm{C},13.5\mathrm{GPa})$. The slope is thereforeA Celsius temperature difference equals the corresponding kelvin difference. The graph does not justify treating the endpoints as exact measurements.

For stishovite, the tetragonal cell volume divided by two givesFor monoclinic coesite the cell volume is $abc\sin \beta$, soUsing $M_{\mathrm{Si}{\mathrm{O}}_2}\simeq 0.060084\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$ and Avogadro's constant, the mass-specific volumes areFor the direction stishovite to coesite,For the reverse, coesite to stishovite, the entropy change is about $-288\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$. Stishovite is the denser phase: a positive boundary slope and its smaller volume imply a lower entropy on the high-pressure side. Stating the direction prevents an otherwise avoidable sign ambiguity.