= Solution
Both starting arrangements converge toward the same \b[chemically ordered <alloy>], exhibiting <chemical ordering in alloys>. This supports a lower <free energy> for the ordered unlike-metal neighbour pattern than for the segregated core-shell or disordered precursor at the final <temperature>. In a simple nearest-neighbour model, ordering is favoured when
$$
w=\epsilon_{AB}-\tfrac12(\epsilon_{AA}+\epsilon_{BB})<0,
$$
with consistent bond-energy conventions. Bulk mixing and ordering then compensate the loss of <configurational entropy> on cooling. Annealing alone does not supply numerical bond or surface energies, and elastic mismatch or adsorbed <ligands> can also matter.
The final morphology does not show a thick single-metal skin: the surface-energy difference is not large enough to overwhelm the bulk preference for ordering throughout the particle. Some atomic-scale surface enrichment is compatible with the drawing, so exact equality of the two surface free energies is not established.
If B has a much lower surface <free energy>, \b[<Surface segregation> of B and an A-rich interior] become favourable. A nearly continuous B shell is likely if enough B is present and the surface-energy gain exceeds the cost of disrupting favourable A-B bonds; otherwise only partial enrichment occurs.
\Image[/past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2019/paper-2-surface-segregation.png]
{title=An illustrative surface-energy preference enriches the outermost layers without fixing a universal shell thickness}
{source=paper-2-surface-segregation.py}
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