Anomalous structures due to magnetism

The presence of magnetism amongst the 3d transition elements causes magnanese, iron, and cobalt not to obey the structural trend that is observed across the nonmagnetic 4d and 5d series. Manganese takes the a-Mn 

Expanding eqn (8.34) to second order and using eqn (8.28), the nonmagnetic state is found to be unstable to antiferromagnetism if 

This is the rectangular d-band model criterion equivalent to the exact second-order result, namely 

The first term in eqn (8.38) represents the change in kinetic energy, ST. The value of the moment given by eqn (8.37) is identical to that obtained by filling the up and down spin bands in Fig. 8.12(c) and solving eqn (8.28) self-consistently. 

In fact, iron exhibits all three common metallic crystal structures bcc, fee, and hep within its pressure-temperature phase diagram, as is shown by the inset of Fig. 8.14. The transition from the bcc a phase to the hep e phase 

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Anomalous structures due to magnetism 231 Table 8.1 Coordination polyhedra of the a-Mn structure type... 

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