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Subsections

• 2.1. Identification
• 2.2. Informative character

2. Basis for phase-transition nomenclature

Discussion of the thermodynamic phase diagram of a substance has often been facilitated by use of a simple notation assigned to each phase in the diagram. Hence, the use of Greek letters ($\alpha$, $\beta$, $\dots$, $\omega$) is widespread in identifying the various phases in metals and alloys. The $\alpha$ and $\beta$phases, for example, are commonly used to designate, respectively, the disordered (Cu-type) and the ordered (CsCl-type) phases of the Cu-Zn alloy. Such notations are immediately understandable to workers familiar with the given metal or alloy since they refer to specific experimental conditions for observing these phases and to a definite set of experimental results (twinning appearance, mechanical properties etc.). However, this compact notation has several drawbacks. It is uninformative to the reader with only a general knowledge of the field of phase transitions, since it does not summarize any specific crystallographic or physical information. In addition, it is inflexible since the discovery of a new phase within a given diagram containing phases labelled $\alpha$, $\beta$, $\gamma$, $\dots$ will usually require the introduction of more complicated symbols such as $\alpha$$^\prime$ or $\beta$$^\prime$. Further, it is not universal since different systems of labelling (e.g. I, II, $\dots$) are common in fields other than metallurgy (e.g. that of structural transitions or the phase diagram of ice).

Our aim is to define a reasonably compact nomenclature for the phases that is both free from the preceding drawbacks and clearly preferable to the many current alternatives for the various disciplines dealing with crystalline phase transitions. In deciding the content of such a nomenclature, two types of questions have to be considered.

2.1. Identification

In the first place, a rapid and intuitive identification of each phase must be possible both for an expert on a specific substance and for other users. This implies a `nickname' for each phase in the spirit of the labels currently used in the literature. Compatibility with existing notations requires the `nickname' to incorporate these labels. On the other hand, the `nickname' should also incorporate an element of intuitive identification for the general reader. We recommend that the range over which a given phase exists be used as an appropriate element of identification. In many cases, this is a temperature range. It may also be a pressure range or both thermal and pressure ranges.

The nickname of the high-temperature phase in quartz could hence be written $\beta$ $\vert$>846 K$\vert$, while the tetragonal phase of barium titanate could be nicknamed II $\vert$403-278 K$\vert$. Such a convention has the advantage of flexibility. Consider for instance a phase nicknamed I $\vert$T₁-T₂ $\vert$ (with T₁ > T₂). The discovery of a new phase transition at T₃ between T₁ and T₂ would then lead to a sequence of two phases denoted I $\vert$T₁-T₃$\vert$ and -$\vert$T₃-T₂ $\vert$ if the second phase has been assigned no label. Thus, this situation is dealt with by modifying the temperature range of the initially considered phase I. In systems that have been investigated for a long time, the most recently discovered phases may be recognized by the leading hyphen unless a label has been assigned by its discoverers.

2.2. Informative character

A fully informative description of the various phases formed by a given substance begins with the chemical formula and requires use of a large set of crystallographic and physical data, each part of which may be relevant to the expert. Hence, in addition to a knowledge of the structure type (e.g. perovskite) and space groups of the different phases (e.g. Pm$\bar 3$m$\rightarrow$P4mm), it may be necessary, in order to draw inferences concerning the properties of the substance, to have access to the relative positions of the various atoms in the unit cell of each phase, to their systematic change as a function of temperature across the transition, to the possibly singular behaviour of the anisotropic displacement ellipsoids of certain atoms etc. From the physical standpoint, a given phase may have many remarkable properties, e.g. magnetic, electric etc. Moreover, if ferroelectricity is present in a given phase, for instance, its bare mention is preferably extended by stating the magnitude of the spontaneous polarization, its temperature dependence and its structural origin (atomic displacement, electron cloud deformation, asymmetric occupation of certain sites, $\dots$)etc.

Information of this kind, however, can be found readily in the published scientific reports on the given material; a sufficient nomenclature does not have to display all this information but only an appropriate fraction in simplified form. This format should lead the worker with a general knowledge of phase transitions to a straightforward identification of the transition category. The essential crystallographic information we recommend is provided by the space group and the number (Z) of chemical formula units in the conventional unit cell, since these features are involved in a number of key aspects of phase transitions, as follows. Knowledge of the crystal symmetry on either side of a phase transition helps define the experimental methods that may be used to study the transition. A relationship of inclusion between the two space groups (i.e. if one is a subgroup of the other) of the phases surrounding a transition can suggest the possibility of a continuous transition (with zero latent heat). A change in point group across a transition indicates twinning with a definite pattern of variants. A change in the number of chemical formula units in the primitive (elementary) unit cell can denote the onset of a superstructure. In order to avoid possible ambiguity in the event of a change in unit-cell orientation from phase to phase, both space-group symbol and number, as given in International Tables for Crystallography (1996) are included. In compliance with normal crystallographic usage, we recommend giving the number of formula units in the conventional crystallographic (i.e. multiple if relevant) unit cell. Although physical information such as the appearance of a superstructure is clearly related directly to a primitive unit cell, derivation of one cell from another is a standard operation.

Secondly, the essential physical information retained in the new nomenclature is the ferroic character of the phase studied (i.e. ferromagnetic, ferroelectric, ferroelastic etc.). The main categories of ferroic materials have been defined in the IUPAC document (Clark et al., 1994) and elsewhere. This information allows inferences to be made regarding the twinning habit of the given phase and its response to external fields (magnetic, electric, mechanical stress etc.) and provides a guide to the choice of experimental techniques best suited for studying the corresponding phase transition.

Finally, it is recommended that certain specific information be added to the nomenclature in the form of a `comment field', see also §3.6.

Copyright © 1998 International Union of Crystallography