Question -
A) Begin with the 2D atom cluster assigned to you following {{AA,ZB,AB,JC},{TD,JH,IO,MV}} in the collection (in attached file). Imagine for your cluster that the shape has been determined by minimizing the "edge-energy" cost, where the energy-cost per unit length of diagonal (110) edges is different from the energy-cost per unit length of the square (100) edges. Do your best to estimate the ratio between diagonal/square-edge energy-costs per unit length.
B) Next imagine a regular cuboctahedral crystal like 3D, with 6 square {100}-type facets and 8 triangular {111}-type facets. this is an intermediate step in the shape transformation from cube to octahedron which might be similarly parameterized by an octahedral area-fraction which runs from 0 to 1 as the {100}-type facets shrink and the {111}-type facets expand for constant volume of 1. If we were to give you such an intermediate 3D structure, discuss how you would approach determining the ratio between (111) and (200) facet energies per unit area for it.
Attachment:- Assignment File.rar