Surface Energy and Crystal Shapes

It is instructive to carry this slightly further. Let us imagine a crystal in the shape of a regular octahedron made up of (111) surfaces. The total surface energy is directly proportional to the surface area and if the octahedron is made irregular (but kept at fixed volume, keeping all (111) surfaces), the distortion will always 

Unreconstructed surfaces in a homopolar semiconductor. The crystal is viewed along a [ 110] 

Further, imagine that the corners of the octahedron arc truncalal by (100) planes as shown in Fig, 10-2, If this is done at constant volume, the total surface area will decrease, so if the surface energy were the. same on both the (100) and 

The equilibrium shape for any crystal can be obtained by an ingenious construction due to Wulff (1901) for a discussion,. see Herring (195.3, p. 5). Wulff noted that if ones makes a polar plot of surface energy and constructs planes perpendicular to the polar vector at each point on the surface, the volume con- 

The natural octahedral shape for a hoinopolar semiconductor, with a possible truncation of the corners. 

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