The surprising role of magnetism on the phase stability of Fe (Ferro)

Abstract:

We discuss the phase stability of the important element Fe in terms of the contributions to stability from the various forms of magnetism that exist in Fe. We point out that the ferromagnetic Fe is not cubic and that it is reasonable to return the beta phase of Fe to the phase diagrams based on Fe to designate paramagnetic BCC form of iron. We give a working definition of a phase, which includes the term ‘‘order parameter’’ following the insights of Landau.

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 1. Introduction

The phase stability of many elements shows the following pattern:

 1. A low enthalpy is mainly responsible for the choice of structure at low temperatures. 

2. At higher temperatures, structures (phases) are stable which have higher entropies.

 This often translates into the low temperature phase being a close packed one and the high temperature phase having a more open structure, that is, a less close packed structure. For example, the low temperature phase of Ti is close packed hexagonal (HCP) while the high temperature phase is BCC. Fe does not follow this pattern. In fact, there are several interesting aspects of the phase stability of Fe which is the topic of this paper.

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The definitions listed above are not complete, in that no explicit mention of order parameter is included, though that of Christian [9] does use the phrase ‘‘common set of parameters’’. The order parameter is a concept that was developed by Landau in the 1930s [16]. 

Including it, we suggest the following definition of a phase:

 A phase is a physically distinct region of a system which has attained thermodynamic equilibrium, and which has a specific set of order parameters (η1, η2, . . .) which specify its physical properties. Such parameters include composition, structure, atomic order, magnetic order, ferroelectric order, etc. 

Therefore, a change of phase occurs when one or more of its order parameters changes discontinuously from one value to another or from zero to a non-zero value (or vice versa). Thus, when a ferromagnetic phase changes to a paramagnetic phase, a phase change has occurred, since the magnetic order parameter, the magnetization of the material, changes from a nonzero value to zero on passing through the Curie temperature on heating. There really is a β Fe phase, which is the paramagnetic BCC α!