The {111} planes in face-centered cubic (FCC) structures are the most densely packed, or “close-packed,” planes, characterized by a hexagonal atomic arrangement. These diagonal planes intersect the x, y, and z axes at equal distances, featuring a high planar density and serving as the primary slip planes for deformation. 

Key Characteristics of {111} Planes in FCC:

• Close-Packed Structure: Atoms are arranged in a hexagonal pattern, which is the most efficient, dense packing method.
• Location: The (111) plane cuts diagonally through the unit cell, passing through the face-centered atoms and corners, specifically connecting points $$, $$, and $$.
• Planar Density: It has a high atomic density, typically calculated as $$ atoms/$$ or 90.7% of the surface area covered, which is the highest possible packing density.
• Slip Planes: Due to their close-packed nature, these planes are the primary slip planes for dislocation movement during plastic deformation.
• Family of Planes: The {111} family includes four unique diagonal planes within the cube, providing high symmetry to the FCC lattice. 

Atomic Arrangement:
When viewing the (111) plane directly, each atom is surrounded by six neighbors in a hexagonal pattern (6-fold symmetry). The plane is formed by three corner atoms and the atoms on the faces. 

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