Face-Centered Cubic Versus Hexagonal Close-Packed Structures

1 Face-Centered Cubic Versus Hexagonal Close-Packed Structures 

Periodic table of the metals that form fee, hep, and bee structures. The transition metals tend to go from hep — bee — hep — fee except for Mn, Fe, and Co whose magnetic properties apparently influence their structures. Mn has a complex cubic structure with a space group I34m. 

Both fee and hep stmetures have the same coordination number (number of nearest neighbors) of 12 and the same atomic packing fraction of 0.74 (ratio of the volume of oranges to the container volume), but metals that form the fee stmeture are generally more ductile than hep metals because there are more planes with high area fraction which provide slip systems in the fee structure. This will be discussed in more detail in Chapter 9. 

Note that the space group for the hep structure is PSs/mme. The point group is 6/mmm, but the subscript 3 next to the 6 signifies additional symmetry in the space group in the form of a threefold screw axis parallel to the sixfold rotational axis. Similarly, the c in place of the last m signifies a glide plane parallel to the c-axis. 

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Fig. 1. The total electronic energy versus the atomic volume for several Si structures diamond, hexagonal diamond, white tin ( -Sn), hexagonal close-packed (hep) body-centered cubic (bcc), and face-centered cubic (fee). The volume is normalized by the experimental value. The dashed line is the common tangent of the energy versus volume curves and gives the transition pressure between the diamond and white tin structures (see the title paper)...

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