(IUCr) Nomenclature of magnetic, incommensurate, composition-changed morphotropic, polytype, transient-structural and quasicrystalline phases undergoing phase transitions. II. Report of an IUCr Working Group on Phase Transition Nomenclature1

Volume 57
Part 5
Pages 614-626
September 2001

Received 26 February 2001
Accepted 19 April 2001

Nomenclature of magnetic, incommensurate, composition-changed morphotropic, polytype, transient-structural and quasicrystalline phases undergoing phase transitions. II. Report of an IUCr Working Group on Phase Transition Nomenclature¹

J.-C. Tolédano,^a ⁺ R. S. Berry,^b ⁺⁺ P. J. Brown,^c A. M. Glazer,^d R. Metselaar,^e ⁺⁺⁺ D. Pandey,^f J. M. Perez-Mato,^g R. S. Roth^h and S. C. Abrahamsⁱ ^*⁺⁺⁺⁺

^aLaboratoire des Solides Irradiés and Department of Physics, Ecole Polytechnique, F-91128 Palaiseau CEDEX, France,^bDepartment of Chemistry, University of Chicago, 5735 South Ellis Avenue, Chicago, IL 60637, USA,^cInstitut Laue-Langevin, BP 156X CEDEX, F-38042 Grenoble, France,^dClarendon Laboratory, University of Oxford, Parks Road, Oxford OXI 3PU, England,^eLaboratory for Solid State and Materials Chemistry, Eindhoven University of Technology, PO Box 513, NL-5600 MB Eindhoven, The Netherlands,^fSchool of Materials Science and Technology, Banaras Hindu University, Varanasi 221005, India,^gDepartamento de Física de la Materia Condensada, Universidad del País Vasco, Apdo 644, E-48080 Bilbao, Spain,^hB214, Materials Building, National Institute of Standards and Technology, Washington, DC 20234, USA, and ⁱPhysics Department, Southern Oregon University, Ashland, OR 97520, USA
Correspondence e-mail: sca@mind.net

A general nomenclature applicable to the phases that form in any sequence of transitions in the solid state has been recommended by an IUCr Working Group [Acta Cryst. (1998). A54, 1028-1033]. The six-field notation of the first Report, hereafter I, was applied to the case of structural phase transitions, i.e. to transformations resulting from temperature and/or pressure changes between two crystalline (strictly periodic) phases involving modifications to the atomic arrangement. Extensive examples that illustrate the recommendations were provided. This second Report considers, within the framework of a similar six-field notation, the more complex nomenclature of transitions involving magnetic phases, incommensurate phases and transitions that occur as a function of composition change. Extension of the nomenclature to the case of phases with less clearly established relevance to standard schemes of transition in equilibrium systems, namely polytype phases, radiation-induced and other transient phases, quasicrystalline phases and their transitions is recommended more tentatively. A uniform notation for the translational periodicity, propagation vector or wavevector for magnetic and/or incommensurate substances is specified. The notation adopted for incommensurate phases, relying partly on the existence of an average structure, is also consistent with that for commensurate phases in a sequence. The sixth field of the nomenclature is used to emphasize the special features of polytypes and transient phases. As in I, illustrative examples are provided for each category of phase sequence.

Keywords: phase transition; nomenclature.

1. Introduction

A multiplicity of terminologies for distinguishing individual members of a sequence of crystalline phases that form as a function of temperature and/or pressure may be found in the crystallographic and other literature of the condensed state. Confusion caused by the lack of a unified nomenclature led the Commission on Crystallographic Nomenclature to establish a Working Group on Phase Transition Nomenclature.² The Working Group was charged with studying the multiple nomenclature in current use for naming such sequences of phases and with making such recommendations for its improvement as may be appropriate. The term `phase-transition nomenclature', as used throughout this Report, applies to the nomenclature of phases that form as a consequence of one or more transitions; the nomenclature of materials that exist only in single phase form is adequately treated elsewhere, e.g. Leigh et al. (1998).

In I, the general purpose of the nomenclature was defined, the relevant information it should contain was specified, and a recommendation was made for the adoption of a six-field notation in the case of structural phase-transition nomenclature, i.e. of transitions between two crystalline (strictly periodic) phases that involve only a modification of the atomic arrangement. Extensive examples providing illustrative use of the nomenclature were presented for a variety of substances (metals, alloys, oxides and minerals) that undergo phase transitions as a function of temperature and/or pressure. The recommended notation is not only unambiguous; it also provides a full context for the transitions undergone by each phase.

The recommended nomenclature employs the following six-field notation for each phase with given chemical composition, each field being separated from the others by vertical bars:

$[\rm \matrix{\rm Usual\cr\rm label\ in\cr\rm literature\cr (\alpha, I,\ldots)}\left\vert\matrix{\rm Temp.\ (K)\cr\rm and\cr\rm pressure\cr\rm range \ (Pa)}\right\vert \matrix{\rm Space\hbox{-}group\cr\rm symbol\ and\cr\rm number\cr \cr }\left\vert\matrix{\rm Number\ of\cr\rm chemical\cr\rm formulas\cr\rm per\ unit\ cell}\right\vert\matrix{\rm Ferroic\cr\rm properties\cr \cr \cr }\left\vert\matrix{\rm Comments\cr \cr \cr \cr}\right.]$

Full information concerning the content of each field is available in I, see also footnotes in §§6.1, 7.1.3, 7.2.2 and 7.3.3.

This second Report considers the more complex nomenclature required for transitions involving magnetic phases, incommensurate phases and transitions occurring as a function of composition change. The case of phases with a relevance to standard schemes of transition in equilibrium systems that is not yet clearly established is considered more tentatively; such phases include polytypes, see also Guinier et al. (1984), quasicrystalline, radiation-induced and other transient phases and their transitions.

The six-field nomenclature defined in I was found to be convenient and applicable to all the new systems above, provided a suitable adaptation of the content of each field is followed as recommended below. In addition, the present analysis led the Working Group to recommend, for every category of transition (including those considered in I), where known, that the order of the phase transition be noted as a comment in the sixth field.

2. Magnetic phases

Several major additional factors must be considered in the designation of a magnetic phase transition as compared with a structural phase transition. These include (a) the magnetic configuration, which must be specified as well as the atomic configuration, (b) the magnetic field, which is as relevant and controlling a parameter as the temperature and pressure, and (c) the magnetic periodicity of the system, which is not always unambiguously indicated by the number Z of structural units in the conventional cell.

A recommended adaptation of the six-field nomenclature to magnetic phase transitions is now presented.

2.1. First field

The usual name used in the literature for a magnetic phase tends to emphasize the magnetic behaviour of the phase. For instance, antiferromagnetic phases are often nicknamed AF1, AF2 etc; likewise, spin flop phases are nicknamed SF1, SF2 etc. In simple situations where either temperature or magnetic field is the dominant parameter controlling the phase diagram, the numeral in the nickname commonly increases with decreasing temperature (e.g. in antiferromagnetic phases), or commonly increases with increasing magnetic field (e.g. in spin flop phases). It is recommended that this practice of numeral increase be extended to newly discovered magnetic phases. In more complex situations involving an intricate phase diagram as a function of temperature and field, with the possibility of conflict between the assignment of increasing or decreasing numerals, it is recommended that the sequence due to an increasing magnetic field be given precedence. Although such nicknames do not always describe the magnetic character of the substance explicitly, since `AF' for example may be mistaken for antiferroelectric, this lack is compensated for by the fifth and sixth fields (see the examples in §§31-3.5 ). A set of intuitively obvious notations for the different categories of magnetic behaviour is presented in Table 1. We recommend the assignment of nicknames as in this table. Two ferromagnetic phases in a sequence would hence be labelled F1 and F2.

Table 1
Recommended abbreviations for various magnetic categories

Property	Abbreviation	Property	Abbreviation
Paramagnet	P	Exotic	EX
Ferromagnet	F	Amplitude modulated	IC
Antiferromagnet	AF	Helical	H
Spin flop	SF	Canted ferromagnet	CF
		Weak ferromagnet	WFM

2.2. Second field

The magnetic field range (H, in T) over which the phase is stable, if known, should be added to the temperature (T, in K) and pressure (P, in Pa) ranges used for structural phase transitions. Clearly, a summary of the detailed phase diagram of a given material as a function of three controlling parameters cannot be provided in a highly compact nomenclature. However, the present aim is to provide an immediate understanding of the experimental stability conditions for the material. If the phase is stable over a region bounded by all three variables T, P and H, then these ranges should be indicated by their end-values; in turn, the boundary conditions are separated by semicolons. §3.5 illustrates this notation for the intricate case of EuAs₃, the phase diagram of which is reproduced in Fig. 1. Since the magnetic field direction is of relevance, this information when available should be specified in the sixth field.

2.3. Third field

In the case of structural phase transitions, this field is devoted to the specification of the space-group symbol and number (to avoid ambiguities related to the setting); such information is insufficient for magnetic systems since it does not describe the nature of the magnetic ordering. An alternative might be to indicate the magnetic space group. However, the lack of a standard magnetic space-group notation leads us to recommend the use of the same crystallographic information (i.e. the crystallographic space-group symbol and number) in this field as for sequences of structural transitions. This does not detract from the total information provided since fields four and six contain additional information specifying the required magnetic structure (i.e. magnetic periodicity and spin configuration).

2.4. Fourth field

The recommendation in I for this field is to provide the number of chemical formulas per conventional unit cell, i.e. Z. The purpose is to specify the change of lattice periodicity occurring between phases or, in other terms, to indicate the onset of different superlattice reflections in the various phases of a sequence. Note that such information is analogous to (and less accurate than) the specification of the wavevector defining these superlattice reflections.

It is more convenient, for magnetic phases, to specify the magnetic propagation vector which fills the same function by providing information on the `magnetic periodicity' of the phase. A similar option is adopted below for incommensurate systems (see §5). However, as in the latter systems, an ambiguity arises since the components of the propagation wavevector can be referred either to the reciprocal cell of the non-magnetic phase in the sequence or to that of the `chemical structure' of the magnetic phase itself (which may differ from that of the non-magnetic phase). It is hence recommended, for the sake of clarity and consistency with the option chosen for incommensurate systems, see §4.4, that the reference phase be specified in the fourth field. Also, that the value of Z for the conventional chemical cell of the magnetic phase be indicated at the beginning of the fourth field.

2.5. Fifth field

The recommended information for this field, in the case of structural phase transitions, see I, is the name of the ferroic property. For magnetic phase transitions, specification of the magnetic type instead is recommended. The various magnetic types to be considered are listed in Table 2 together with their definitions.

Table 2
Definition of magnetic structure types

Paramagnet	Normally the magnetically disordered phase stable at high temperatures
Ferromagnet	The magnetic phase with all spins parallel
Ferrimagnet	A spin array intermediate between that of a ferromagnet and an antiferromagnetic
Spin flop	A phase in which some fraction of the moment has been forced from antiferromagnetic to ferromagnetic order by the application of a field
Collinear	A unique magnetization direction exists
Non-collinear	Antiferromagnets with no unique magnetization direction
Canted ferromagnet	Small (<5°) non-collinearity producing weak ferromagnetism in a basically antiferromagnetic arrangement. Includes weak ferrromagnets of the Dzyaloshinski-Moriya type
Antiferromagnet	Commensurate in the strict sense that the propagation vector corresponds to a special point in the Brillouin zone. Could be modified by collinear or non-collinear spins
Amplitude modulated	Structures generated by a single modulation with wave vectors incommensurate in the sense given above
Helical	Structures generated by two orthogonal modulations in phase quadrature with the same incommensurate wave vector
Exotic	Cases not covered by the above descriptions
Weak ferromagnet	Commonly used name for a canted ferromagnet of the Dzyaloshinski-Moriya type

2.6. Sixth field

This field may include complementary information such as the magnetic moment, its magnitude and direction for simple structures, the direction of the external magnetic field controlling the stability of the phases and any other information that contributes to the understanding of the magnetic configuration. Recommended descriptions for this field are given in Table 3.

Table 3
Description of magnetic spin arrangements

Screw spiral	Helical structure with spins in the plane perpendicular to the propagation vector
Cycloidal spiral	Helical structure with spins in the plane containing the propagation vector
Bunched spiral	Helical structure with spin directions bunched about particular directions in the plane in which they rotate
Sinusoidal modulation	The amplitudes of the spins in a collinear arrangement follow a sine curve
Square wave	The amplitudes of the spins in a collinear arrangement follow a square wave
Fan	A cycloidal structure with bunching
Antiphase domains	Regions of an antiferromagnetic structure related by inversion of all spins
k domains	Domains corresponding to different arms of the stars of the propagation vector
s domains	Domains with the same propagation vector, but different spin directions
Chirality domains	Domains corresponding to oppositely directed propagation vectors, when these are inequivalent, as for helical structures

The content of the various fields is summarized as follows

$[\matrix{\rm Usual\cr\rm magnetic\cr\rm label\ as\cr\rm used\ in\cr\rm literature\cr (e.g.\rm\ AF1,\cr cf.\rm\ Table\ 1)\cr}\left\vert\matrix{\rm Temp. \ (K),\cr\rm pressure\cr\rm (Pa)\ and\cr\rm magnetic\cr\rm field\ (T)\cr\rm range\cr \cr }\right\vert\matrix{\rm Crystallo\hbox{-}\cr\rm graphic\cr\rm space\hbox{-}group\cr\rm symbol\ and\cr\rm number\cr \cr \cr }\left\vert\matrix{\rm Reference\cr\rm phase, \it Z,\cr\rm and\cr\rm magnetic\cr\rm propagation\cr\rm vector\cr \cr }\right\vert\matrix{\rm Magnetic\cr\rm type\ (\it cf.\cr\rm Table\ 2)\cr \cr \cr \cr \cr}\left\vert\matrix{\rm Magnetic\cr\rm configuration\cr\rm and\cr\rm comments\cr (cf.\rm\ Table\ 3).\cr \cr \cr }\right.]$

3. Examples of magnetic phase-transition nomenclature

3.1. Fe (Geissler et al., 1967)

$[\matrix{\rm P\cr\cr\rm F\cr \cr}\left\vert\matrix{\gt 1040\,\rm K\cr\cr\lt 1040\, \rm K\cr\cr}\right\vert \matrix{ Im3m \ (229)\cr\cr Im3m\ (229)\cr\cr}\left\vert\matrix{{\rm P}, Z = 2\cr 0, 0, 0\hfill\cr {\rm P}, Z = 2\cr 0, 0, 0\hfill}\right\vert\matrix{\rm Paramagnet\hfill\cr\cr \rm Ferromagnet\cr\cr}\left\vert\matrix{-\hfill\cr\cr\rm Easy\ magnetization\hfill\cr\rm direction\ \langle110\rangle.\hfill}\right.]$

Columns I, II, III and V above indicate that Fe undergoes a transition from paramagnetic to ferromagnetic at 1040 K without a change in crystallographic space group at T_c; column IV that both phases have two atoms in the conventional cubic unit cell and the reference of the k vector is the P phase.

3.2. NiO (Roth, 1958)

$[ \matrix{\rm P\hfill\cr\cr \rm AF\cr\cr\cr\cr\cr\cr\cr\cr}\left\vert\matrix{\gt 523\,\rm K\cr\cr \lt 523\, K\cr\cr\cr\cr\cr\cr\cr\cr}\right\vert \matrix{ Fm3m\cr (225)\hfill\cr R{\bar3}m\hfill\cr (166)\hfill\cr\cr\cr\cr\cr\cr\cr}\left\vert\matrix{{\rm P}, Z = 4\cr 0, 0, 0\hfill\cr {\rm P}, Z = 4\cr \textstyle{1\over2},\textstyle{1\over2}, \textstyle{1\over2}\hfill\cr\cr\cr\cr\cr\cr\cr }\right\vert\matrix{\rm Paramagnet\hfill \cr\cr \rm Antiferromagnet\hfill\cr\cr\cr\cr\cr\cr\cr\cr}\left\vert\matrix{-\hfill\cr\cr\rm Moments\ ferromagneti\hbox{-}\hfill\cr\rm cally\ coupled\ in\ (111)\hfill\cr\rm planes,\ adjacent\ layers\hfill\cr\rm antiferromagnetically\hfill\cr{\rm coupled.\ Spins}\, \Vert\, [11\bar{2}].\hfill\cr{\rm Four}\ k\ {\rm domains\ each}\hfill\cr{\rm containing\ three}\ s\hfill\cr \rm domains.\hfill}\right.]$

k domains differ in propagation vector direction, s domains in spin direction, cf. Table 3. The Z value refers to the conventional cell, hence the primitive cell in the AF phase (which is identical to the conventional cell) is quadruple that of the primitive cell in the P phase (one-fourth the cubic cell).

3.3. K₂IrCl₆ (Hutchings & Windsor, 1967)

$[ \matrix {\rm P\hfill\cr\cr \rm AF\cr\cr\cr}\left\vert\matrix{\gt 3.05\,\rm K\cr\cr\lt 3.05\,\rm K\cr\cr\cr}\right\vert \matrix{Fm3m\ (225)\cr\cr I4/m\ (87)\hfill\cr\cr\cr}\left\vert\matrix{{\rm P}, Z = 4\hfill\cr 0, 0, 0\hfill\cr {\rm P}, Z = 2\hfill\cr 1,0,\textstyle{1\over2}\ {\rm in}\ Fm3m\hfill\cr \textstyle{1\over2},{1\over2},{1\over2}\ {\rm in}\ I4/m\hfill\cr}\right\vert\matrix{\rm Paramagnet\hfill\cr\cr \rm Antiferromagnet\cr\cr\cr}\left\vert\matrix{-\hfill\cr\cr \rm Spins\, \Vert\, [001],\hfill\cr 6\ k\ {\rm domains}.\cr\cr}\right.]$

3.4. -Fe₂O₃ (Shull et al., 1951; Nathans et al., 1964)

3.5. EuAs₃ (Chattopadhyay & Brown (1987, 1988a,b,c)

$[ \matrix {\rm P\hfill\cr\cr\rm IC\hfill\cr\cr\cr\cr\rm AF1\hfill\cr\cr\cr\cr\cr\rm HP\hfill\cr\cr\cr\cr\rm SF1\hfill\cr\cr\cr\cr\rm SF2\hfill\cr\cr\cr\cr\cr\rm SF3\hfill\cr\cr\cr\cr\rm SF4\hfill\cr\cr\cr\cr}\left\vert\matrix{\rm \gt 11.1\, K, 0\, T\semi\hfill\cr\rm 0\, K,\gt 6.5\, T\hfill\cr\rm 10.1\! -\!11.1\, K,\hfill\cr\rm\lt 0.83\, T\hfill\cr\cr\cr\rm 0\!-\!10.1\, K, 0 \, T\semi\hfill\cr\rm 0\!-\!9.8\, K, 0.7\, T.\hfill\cr\rm 0\!-\!10.1\, K, \lt 0.3\, GPa\semi\hfill\cr\rm 5\!-\!9.8\, K, \lt 0.6\, GPa\hfill\cr\cr\rm 0\, K, \gt 0.3\, GPa\semi \hfill\cr\rm 5\! -\!9.8 \,K, \gt 0.6\,GPa\hfill\cr\cr\cr\rm \lt 9.5\, K, 0.7\, T\semi \hfill\cr\rm\lt 7\, K, 2.2\, T\hfill\cr\cr\cr\rm \lt 5.8\, K, 2.2\,T\semi\hfill\cr\rm 0\, K, 4.8\, T\hfill\cr\cr\cr\cr\rm 0\, K, 4.8\!-\!5.5\, T\semi\hfill\cr\rm 5.8\, K, 2\, T\hfill\cr\cr\cr\rm 9.6\!-\!10.8\, K, 0.83 T\semi\hfill\cr\rm 0\, K, 5.5\!-\!6.5\, T \hfill\cr\cr\cr}\right\vert \matrix{C2/m \hfill\cr(12)\hfill\cr C2/m\hfill\cr (12)\hfill\cr\cr\cr C2/m\hfill\cr (12)\hfill\cr\cr\cr\cr C2/m\hfill\cr (12)\hfill\cr\cr\cr C2/m\hfill\cr (12)\hfill\cr\cr\cr C2/m\hfill\cr (12)\hfill\cr\cr\cr\cr C2/m\hfill\cr (12)\hfill\cr\cr\cr C2/m\hfill\cr (12)\hfill\cr\cr\cr }\left\vert\matrix{{\rm P}, Z = 4\hfill\cr 0, 0, 0\hfill\cr {\rm P}, Z = 4\hfill\cr 1,1, 1/2- \delta\hfill\cr\cr\cr {\rm P}, Z = 4\hfill\cr 1,1, \textstyle{1\over2}\hfill\cr\cr\cr\cr {\rm P}, Z = 4\hfill\cr 0.11, 1, 0.22\hfill\cr\cr\cr {\rm P}, Z = 4\hfill\cr 0.1, 1, 0.25\hfill\cr\cr\cr {\rm P}, Z = 4\hfill\cr 0, 1, 0.25\hfill\cr\cr\cr\cr {\rm P}, Z = 4\hfill\cr 0.1, 1, 0.225\hfill\cr \cr\cr {\rm P}, Z = 4\hfill\cr 0.102, 1, 0.225\hfill\cr\cr\cr}\right\vert\matrix{\rm Paramagnet \hfill\cr\cr\rm Amplitude\hfill\cr\rm modulated\hfill\cr\cr\cr\rm Antiferro\hbox{-}\hfill\cr\rm magnet\hfill\cr\cr\cr\cr\rm Helical\hfill\cr\cr\cr\cr\rm Helical\hfill\cr\cr\cr\cr\rm Non\hbox{-}collinear\hfill\cr\rm ferromagnet\hfill\cr\cr\cr\cr\rm Exotic\hfill\cr\cr\cr\cr\rm Exotic\hfill\cr\cr\cr\cr}\left\vert\matrix{-\hfill\cr \cr\delta = 0.15-0.075,\hfill\cr\rm 11.12 - 10.17 \, K.\hfill\cr{\rm Moments} \ \Vert\ b,\hfill\cr\rm coupling\ as\ AF1.\hfill\cr{\rm Moments}\ \Vert\ b \rm\ and\hfill\cr\rm ferromagnetically\hfill\cr\rm coupled\ across\ the \hfill\cr\rm centre\ of\ symmetry\hfill\cr\rm at\ origin.\hfill\cr \rm Cycloid,\ moments\hfill\cr{\rm in}\ ac\ \rm plane,\ coup\hbox{-}\hfill\cr\rm ling\ as\ AF1.\ Two\hfill\cr\rm chirality\ domains.\hfill\cr \rm Cycloid,\ moments\hfill\cr{\rm in}\ ac\ \rm plane,\ coup\hbox{-}\hfill\cr\rm ling\ as\ AF1.\ Two\hfill\cr\rm chirality\ domains.\hfill\cr \rm Antiferromagnetic\hfill\cr{\rm components}\ \Vert\ c,\hfill\cr\rm coupled\ as\ in\ AF1.\hfill\cr\rm Two\ chirality\hfill\cr\rm domains.\hfill\cr\rm Fan\ structure\ with\hfill\cr\rm antiferromagnetic\hfill\cr{\rm components}\ \Vert\ c,\hfill\cr\rm coupling\ as\ AF1.\hfill\cr\rm As\ SF3\ but\ with\hfill\cr\rm antiferromagnetic\hfill\cr\rm components\ at\ 8^\circ\hfill\cr\rm to\ \it c. \hfill}\right.]$

The P-T and H-T phase diagrams of EuAs₃ are given in Fig. 1.

Figure 1
The P-T and H-T phase diagrams of EuAs₃

4. Incommensurate phases

A preliminary adaptation of the structural phase-transition nomenclature to the case of incommensurately modulated systems was proposed in I, §5, as illustrated by the example of K₂SeO₄. The requirement to keep the nomenclature as uniform as possible for the various types of phase system leads us to adopt the same convention in the fourth field as that used for magnetic systems, i.e. specifying the wavevector of the modulation rather than the approximate period of the modulation, see Chapuis et al. (1997).

Similarly, the possibility of substituting the multidimensional space group (Janssen et al., 1992) for the usual (average) space group in the third field was considered but discarded for reasons similar to those for not using the magnetic space-group symbol (viz. the specialized nature of the topic and the possibility of ambiguity in the case of more than one direction of modulation). It is hence recommended that the space group of the average structure, i.e. the structure obtained by averaging the effects of the modulation, be inserted in this field.

We briefly summarize the content of each field.

4.1. First field

The common names used for incommensurate phases are identical to those for ordinary crystalline phases (e.g. I, II etc.). The incommensurate character appears in the fourth field (in which the wavevector of the modulation is specified) and, more explicitly, in the sixth field.

4.2. Second field

As in the case of magnetic materials, an additional controlling parameter, namely the electric field, E in V m^-1, is often relevant. Indeed, the stability range of modulated `ferroelectric' phases is very sensitive to the application of an external electric field (which can play a rôle similar to that of the magnetic field in helical or sinusoidal magnets). Here, also, the option is taken of providing a simplified phase diagram; the approximate range of stability of the given phase, as a function of all three parameters T, P and E, is indicated by the appropriate stability intervals relative to each parameter, see also §2.2. Examples §§5.1-5.6 illustrate the application of this notation.

4.3. Third field

This field, for both the incommensurate and commensurate phases in a sequence, specifies the average space group of the structure, namely that obtained by averaging the modulated positions of the atoms. Each atom is located at the centre of the `cloud' of positions determined by the modulation. In practice, this structure can be determined in many cases (if the modulation is not very large and not very anharmonic) by taking into account only the main reflections and ignoring the satellite reflections. If an incommensurate phase undergoes a transition to a commensurate phase on reducing the temperature, the exact space group of the latter, if known, should also be specified in the third field below the average space group in order to provide more accurate information.

4.4. Fourth field

This field contains the modulation propagation vector (the modulation wavevector), as referred to the reciprocal lattice of the phase specified therein (either the nonmodulated phase or the average structure of the modulated phase), following the nomenclature for magnetic phases. In the case of materials with a phase in which more than one modulation exists, cf. §5.5, the individual propagation vectors must be indicated with appropriate clarifying comments in the sixth field. On the other hand, it may be noted that, in a sequence involving one or several incommensurate phases, there may also exist phases that are strictly periodic, i.e. commensurate. These phases involve superlattice reflections, denoting a change in the unit cell. A comparable circumstance is taken into account for ordinary structural transitions in I by specifying, in the fourth field, the number of units in the unit cell of the average structure. We denote this number Z_A.

In the present case, however, the superlattice reflections in these commensurate phases are generally analogous to those observed in the incommensurate phase except for their commensurate location in reciprocal space. It is therefore recommended, for consistency in a sequence of phases, that, in addition to Z, the commensurate propagation vector be included in the fourth field. The Z_A value relative to the average structure of the incommensurate phase should also be included. The latter option has the advantage of lifting the ambiguity concerning the phase taken as reference for the modulation wavevector. It also provides a unified nomenclature scheme for the incommensurate and the magnetic systems, which may also be incommensurate.

4.5. Fifth field

It is recommended that, as with ordinary structural phase transitions, the `average ferroic' properties be stated in the fifth field whenever they exist. In most examples, the point symmetry of the average structure is identical to that of the `high-temperature' phase and no macroscopic ferroic properties exist. However, certain materials display ferroic properties in the incommensurate phase (cf. §5.2).

4.6. Sixth field

This field may include complementary information such as the incommensurate character and the nature of the structural modulation (e.g. onset of a modulated ferroelectric dipole of specified orientation or the modulated deformation of a specific group of atoms), as well as the possible occurrence of multiple k or several independent modulations.

The content of each nomenclature field is summarized as follows:

$[\matrix {\rm Usual\cr\rm label\ in\cr\rm literature\cr\rm (I, II,\ldots)\cr\cr\cr\cr\cr\cr}\left\vert\matrix{\rm Relevant\cr\rm controlling\cr\rm parameters\!\!:\cr\rm temperature\cr\rm (K),\cr\rm pressure\cr\rm (Pa)\ and\cr\rm electric\ field\cr\rm (Vm^{-1})}\right\vert \matrix{\rm Space\hbox{-}group\cr\rm symbol\ and\cr\rm number\ for\cr\rm the\ average\cr \rm structure\cr\cr\cr\cr\cr}\left\vert\matrix{Z_A \semi\cr\rm modulation\cr\rm propagation\cr\rm vector\ (label\cr\rm of\ the\cr\rm reference\cr{\rm phase}).\ Z\ (\rm for\cr\rm commensurate\cr\rm phases)}\right\vert\matrix{\rm Ferroic\cr\rm type\cr\cr\cr\cr\cr\cr\cr\cr}\left\vert\matrix{\rm Incommen\hbox{-}\cr\rm surate\ char\hbox{-}\cr\rm acter\ and\cr\rm nature\ of\cr\rm the\cr\rm modulation.\cr\cr\cr\cr}\right.]$

6. Composition-changed phases

A growing number of materials are being reported for which a change in composition results in a phase change; such materials are commonly referred to as morphotropic. IUPAC (Clark et al., 1994) defines a morphotropic phase transition as `an abrupt change in the structure of a solid solution with variation in composition'. If this definition is adopted, it is necessary to point out, however, that the boundary between phases in the examples below need not be `thermodynamically abrupt' (i.e. involve a latent heat and discontinuities in the physical quantities). The abruptness, as in most phase transitions, concerns the structural changes (e.g. as specified by its space group) at a precisely defined composition. The nomenclature recommended in I and in §§2 and 4 of the present Report is readily applicable to morphotropic phase transitions.

Composition limits for each phase should be given in the second field. The remaining fields follow the recommendations presented in I for structural phase transitions. Several examples illustrating the recommended nomenclature for composition-changed phases follow. In the illustrative examples chosen, the labelling of the phases is influenced by usage. Table 4 presents the meaning of these labels.

Table 4
Abbreviations used in the illustrative examples for composition-changed, transient-structural and quasicrystalline phases

Property	Abbreviation
Ferroelectric orthorhombic	FO
Ferroelectric tetragonal	FT
Ferroelectric rhombohedral (high/low temperature)	FR (HT/LT)
Antiferroelectric	AF
Paraelectric	P
Quasicrystalline	Q
Approximant	A
Radical pair	RP
Metastable (higher temp.)	MS₁
Metastable (lower temp.)	MS₂
Rotator phase just below melting temperature	R_I
Non-rotator phase	T
Modulated quasicrystalline	MQ

6.1. Examples of composition-changed phase nomenclature³

6.1.1. PbZr_1-xTi_xO₃ phases at room temperature (Corker et al., 1998)

$[ \matrix{\rm FT\hfill\cr\cr\cr\cr\cr\rm FR(HT)\hfill\cr\cr\cr\rm FR(LT)\hfill\cr\cr\cr\rm AF\hfill\cr\cr\cr}\left\vert\matrix{0.45 \lt x \lt 1 \hfill\cr\cr\cr\cr\cr 0.35 \lt x \lt 0.45\hfill\cr\cr\cr 0.06 \lt x \lt 0.35\hfill\cr\cr\cr 0 \lt x \lt 0.06\hfill\cr\cr\cr }\right\vert \matrix{P4mm\hfill\cr (99)\hfill\cr\cr\cr\cr R3m\hfill\cr (160)\hfill\cr\cr R3c\hfill\cr (161)\hfill\cr\cr Pbam\hfill\cr (55)\hfill\cr\cr }\left\vert\matrix{ Z = 1\hfill\cr\cr\cr\cr\cr Z = 3\hfill\cr\cr\cr Z = 6\hfill\cr\cr\cr Z = 8\hfill\cr\cr\cr }\right\vert\matrix{\rm Ferroelectric\hfill\cr\rm and\ ferroelastic\hfill\cr\cr\cr\cr\rm Ferroelectric\hfill\cr\rm and\ ferroelastic\hfill\cr\cr\rm Ferroelectric\hfill\cr\rm and\ ferroelastic\hfill\cr\cr\rm Antiferroelectric\hfill\cr\rm and\ ferroelastic\hfill\cr\cr}\left\vert\matrix{\rm All\ phases\ pseudo\hbox{-}\hfill\cr\rm cubic\ perovskites.\hfill\cr\rm FT,\ no\ perovskite\hfill\cr\rm octahedral\ tilts;\hfill\cr\rm 6\ variants.\hfill\cr\rm No\ perovskite\hfill\cr\rm octahedral\ tilts;\hfill\cr\rm 8\ variants.\hfill\cr\rm a^-a^-a^-\ perovskite\hfill\cr\rm octahedral\ tilt\hfill\cr\rm system.\ 8\ variants.\hfill\cr\rm a^-a^-c^+\ perovskite\hfill\cr\rm octahedral\ tilt\hfill\cr\rm system.\hfill}\right.]$

The symbols a^-a^-a^- and a^-a^-c⁺ are from Glazer's (1972) system of specifying the anion octahedral tilts in perovskite structures. The perovskite structure consists of corner-linked octahedra that can tilt about any combination of pseudocubic axes, a_p, b_p and c_p. The three letters refer to each axis in turn and indicate equivalence or non-equivalence of the angle of tilt. Equivalence is indicated by repeating a letter. If successive tilts about an axis are in the same sense, then a superscript + is used; if in opposing senses, then a superscript - is used. Thus the symbol a^-a^-a^- means that all octahedra tilted about the a_p axis are tilted in alternating senses. The same is true for the octahedra viewed down b_p and down c_p. All tilts are of equivalent magnitude; the net effect is to create a rhombohedral structure.

6.1.2. KTa_1-xNb_xO₃ (Perry et al., 1976)

The end members of this solid solution undergo transitions as a function of temperature (for KNbO₃, T_c ~ 698 K; for KTaO₃, T_c ~ 1-3 K). All transitions described below are a function of composition at room temperature, except for the FR phase.

$[ \matrix{\rm P\hfill\cr\cr\rm FT\hfill\cr\cr\rm FO\hfill\cr\cr\rm FR\hfill\cr\cr\cr }\left\vert\matrix{0 \lt x \lt 0.37\hfill\cr\cr 0.37 \lt x \lt 0.54\hfill\cr\cr 0.54 \lt x \lt 1\hfill\cr\cr 0.45\lt x \lt 1\hfill\cr\cr\cr }\right\vert \matrix{Pm3m\hfill\cr (55)\hfill\cr P4mm\hfill\cr (99)\hfill\cr Bmm2\hfill\cr (38)\hfill\cr R3m\hfill\cr (160)\hfill\cr\cr }\left\vert\matrix{Z = 1\hfill\cr\cr Z = 1\hfill\cr\cr Z = 2\hfill\cr\cr Z = 1\hfill\cr\cr\cr }\right\vert\matrix{\rm Paraelectric\hfill\cr\cr\rm Ferroelectric\hfill\cr\rm and\ ferroelastic\hfill\cr\rm Ferroelectric\hfill\cr\rm and\ ferroelastic\hfill\cr\rm Ferroelectric\hfill\cr\rm and\ ferroelastic\hfill\cr\cr }\left\vert\matrix{-\hfill\cr\cr P_s\rm\ along\ [001]\ of\ phase\hfill\cr\rm P,\ 6\ variants.\hfill\cr P_s\rm\ along\ [110]\ of\ phase\hfill\cr\rm P,\ 6\ variants. \hfill\cr P_s\rm\ along\ [111]\ of\ phase\hfill\cr{\rm P\ at}\ T = 200\,\rm K;\ 6\hfill\cr\rm variants.\hfill}\right.]$

6.1.3. La_2-xSr_xCuO₄ (Torrance et al., 1989; Burns, 1992)

The La_2-xSr_xCuO₄ solid solutions have been widely studied for their interest in the important field of high-temperature superconductivity. Elucidation of the phase diagram by the work of many authors has revealed a rich diversity of fields. The example given here illustrates the phases at T = 300 K; superconducting and other phases form at lower temperatures.

$[ \matrix{\rm I\hfill\cr\cr\rm II\hfill\cr\cr }\left\vert\matrix{0.07 \lt x\hfill\cr\cr 0 \lt x \lt 0.07\hfill\cr\cr }\right\vert \matrix{I4/mmm\hfill\cr(139)\hfill\cr Abma\hfill\cr (64)\hfill\cr }\left\vert\matrix{Z = 2\hfill\cr\cr Z = 4\hfill\cr\cr }\right\vert\matrix{\rm Prototype\hfill\cr\cr\rm Ferroelastic\hfill\cr\cr }\left\vert\matrix{{\rm At}\ T = 300\,\rm K,\ metallic\hfill\cr\rm conductor. \hfill\cr{\rm At}\ T = 300\,\rm K,\ metallic\hfill\cr\rm conductor.\hfill}\right.]$

7. Tentative nomenclature for other systems

Each of the systems considered in this section have aspects that can lead to an adequate description within the framework of a six-field nomenclature. Thus, polytypes form sequences of phases that can be crystallographically and physically defined in the same way as commensurate and incommensurate phases. Further, the existence of large sequences of phases in these systems is an essential feature and therefore particularly relevant to the objectives of the present nomenclature. However, they also raise a specific difficulty since the conditions of phase stability (defined by a controlling parameter such as temperature and pressure) are ill-defined and, so far, it has not been possible to determine an acceptable phase diagram giving stability fields for the known polytypes of materials such as SiC, ZnS or CdI₂. The relevant parameters in this case are hence concerned with the method and conditions of phase stabilization.

A similar situation is also applicable in the case of transient or metastable phases obtained through the irradiation of samples by light or particle beams. Moreover, the physical characterization of the phases observed often leads to a different categorization than for the phases dealt with in the preceding sections (viz. ferroic properties). Quasicrystals raise even greater difficulties since, in addition to the former features (metastability, specific characterization of the physical properties), the atomic structure can only be very roughly specified without making use of the specialized nomenclature of six-dimensional crystallography; unlike the situation in incommensurate systems, it is not possible with quasicrystals to `bypass' this abstract description by use of a modulation wavevector and an `average space group'.

In view of this situation, the following proposals for the nomenclature of these systems must be considered as tentative.

7.1. Polytypic phases

Polytypic transitions are defined by IUPAC (Clark et al., 1994) as transitions from `a crystalline structure into one or more forms which differ in the way identical layers of atoms are stacked'.

7.1.1. First field

The IUCr (Guinier et al., 1984) has recommended two kinds of symbolism for use with either simple or complicated polytypic structures. The first consists of `indicative symbols' in a modified Gard notation, the second of `descriptive symbols' based on earlier proposals by Dornberger-Schiff, Durovic and Zvyagin. Use of the term `nN', commonly used to designate the stacking sequence of layers (n) and the crystal system (N), is recommended for the first field. Guinier et al. (1984) recommend the upper-case letters that follow for the crystal system. Note that the common meaning of n, i.e. the number of layers, may depend on the system. Thus, as in the examples below, n is either the smallest number of layers necessary to describe a sequence or is the entire number of layers required to define the unit cell. The intent of the convention used becomes apparent in the fifth field:

Cubic	C
Hexagonal	H
Trigonal (with hexagonal Bravais lattice)	T
Trigonal (with rhombohedral Bravais lattice)	R
Tetragonal (quadratic)	Q
Orthorhombic	O
Monoclinic	M
Triclinic (anorthic)	A

7.1.2. Second field

As stated in the introduction to §7, these systems do not have a generally established stability range. Hence, the second field can indicate either a temperature and/or a composition range that corresponds to the conditions for practical stabilization of the individual phase. Certain metastable phases in these systems transform on annealing above a threshold temperature that provides a sufficient activation energy. It is recommended that a comment be inserted in the sixth field in order to clarify the content of the second field.

7.1.3. Third and fourth fields

These two fields follow the recommendations presented in I for structural phase transitions by providing the crystallographic characteristics of the phases.⁴

7.1.4. Fifth and sixth fields

In principle, the fifth field of the nomenclature should specify the ferroic properties of the phase but this is likely to be blank for most polytypes; it is hence recommended that this field should instead provide the essential stacking sequence information. The detailed descriptive symbols recommended by Guinier et al. (1984) to specify stacking sequences have not been widely used in the literature. Instead, a simple notation in which `c' is taken for cubic and `h' for hexagonal packing appears to be in common use and is adopted here. The sixth field should contain the preparation conditions and structure type or related information. Six examples illustrating the recommended nomenclature for polytypic phases follow.

7.3. Transient-structural phases

It has recently become possible to study a range of photoinduced and other transient phases with lifetimes of order ranging from picoseconds to hours. Studies of short-duration phases by use of synchrotron radiation, see e.g. Helliwell & Rentzepis (1997 $[Helliwell, J. R. & Rentzepis, P. M. (1997). Time-Resolved Diffraction. Oxford: Clarendon Press.]$ ), are being reported with increasing frequency in the current literature. The lower limit is likely to be reduced further by the introduction of femtosecond synchrotron radiation (see e.g. Schoenlein et al., 2000). On the other hand, phases can be stabilized outside their ordinary stability range by irradiation with various types of beams, e.g. high-energy ions (Dammak et al., 1996). For these categories of transitions, not all variables have yet been fully explored, hence the recommended nomenclature that follows may later require revision. The usage recommended in I, as modified in §§2 and 4 of the present Report, is readily adapted to radiation-induced phases as follows.

7.3.1. First field

As in I (§3.1) and in §4.1 of the present Report. The significance of the labels used is indicated in Table 4.

7.3.2. Second field

In addition to the temperature/pressure stability range of each phase in the system, the wavelength (nm) and radiant flux (W m^-2) necessary to obtain the irradiated phase should be given. In the case of other types of irradiation, equivalent specifications for the radiation used should be given.

7.3.3. Third, fourth and fifth fields

As in I

research papers

Nomenclature of magnetic, incommensurate, composition-changed morphotropic, polytype, transient-structural and quasicrystalline phases undergoing phase transitions. II. Report of an IUCr Working Group on Phase Transition Nomenclature1

1. Introduction

2. Magnetic phases

2.1. First field

2.2. Second field

2.3. Third field

2.4. Fourth field

2.5. Fifth field

2.6. Sixth field

3. Examples of magnetic phase-transition nomenclature

3.1. Fe (Geissler et al., 1967)

3.2. NiO (Roth, 1958)

3.3. K2IrCl6 (Hutchings & Windsor, 1967)

3.4. -Fe2O3 (Shull et al., 1951; Nathans et al., 1964)

3.5. EuAs3 (Chattopadhyay & Brown (1987, 1988a,b,c)

4. Incommensurate phases

4.1. First field

4.2. Second field

4.3. Third field

4.4. Fourth field

4.5. Fifth field

4.6. Sixth field

5. Examples of incommensurate phase-transition nomenclature

5.1. SO2(C6H4Cl)2 (Zúñiga et al., 1993; Etrillard et al., 1996)

5.2. K2SeO4 (Iizumi et al., 1977)

5.3. Ba2NaNb5O15 (Tolédano et al., 1986)

5.4. (CH3)3NCH2COO·CaCl2·2H2O (Chaves & Almeida, 1990)

5.5. TaSe2 (Fleming et al., 1980; Bird et al., 1985)

5.6. Bi2-xPbxSr2CaCu2O8 (Tolédano et al., 1990)

6. Composition-changed phases

6.1. Examples of composition-changed phase nomenclature3

6.1.1. PbZr1-xTixO3 phases at room temperature (Corker et al., 1998)

6.1.2. KTa1-xNbxO3 (Perry et al., 1976)

6.1.3. La2-xSrxCuO4 (Torrance et al., 1989; Burns, 1992)

7. Tentative nomenclature for other systems

7.1. Polytypic phases

7.1.1. First field

7.1.2. Second field

7.1.3. Third and fourth fields

7.1.4. Fifth and sixth fields

7.2. Examples of polytypic phase nomenclature

7.2.1. Ca2Ta2O7 (Grey et al., 1999; Grey & Roth, 2000)

7.2.2. Ca2-xMgxTa2-yNbyO7 (Grey & Roth, 2000)5

7.2.3. Ca2-xSmxTa2-yTiyO7 (Grey & Roth, 2000)

7.2.4. Ca2-xNdxTa2-yZryO7 (Grey & Roth, 2000)

7.2.5. ZnS (Pandey et al., 1994)

7.2.6. SiC (Ramsdell, 1947; Pandey & Krishna, 1982)

7.3. Transient-structural phases

7.3.1. First field

7.3.2. Second field

7.3.3. Third, fourth and fifth fields

Nomenclature of magnetic, incommensurate, composition-changed morphotropic, polytype, transient-structural and quasicrystalline phases undergoing phase transitions. II. Report of an IUCr Working Group on Phase Transition Nomenclature¹

3.3. K₂IrCl₆ (Hutchings & Windsor, 1967)

3.4. -Fe₂O₃ (Shull et al., 1951; Nathans et al., 1964)

3.5. EuAs₃ (Chattopadhyay & Brown (1987, 1988a,b,c)

5.1. SO₂(C₆H₄Cl)₂ (Zúñiga et al., 1993; Etrillard et al., 1996)

5.2. K₂SeO₄ (Iizumi et al., 1977)

5.3. Ba₂NaNb₅O₁₅ (Tolédano et al., 1986)

5.4. (CH₃)₃NCH₂COO·CaCl₂·2H₂O (Chaves & Almeida, 1990)

5.5. TaSe₂ (Fleming et al., 1980; Bird et al., 1985)

5.6. Bi_2-_xPb_xSr₂CaCu₂O₈ (Tolédano et al., 1990)

6.1. Examples of composition-changed phase nomenclature³

6.1.1. PbZr_1-xTi_xO₃ phases at room temperature (Corker et al., 1998)

6.1.2. KTa_1-xNb_xO₃ (Perry et al., 1976)

6.1.3. La_2-xSr_xCuO₄ (Torrance et al., 1989; Burns, 1992)

7.2.1. Ca₂Ta₂O₇ (Grey et al., 1999; Grey & Roth, 2000)

7.2.2. Ca_2-_xMg_xTa_2-_yNb_yO₇ (Grey & Roth, 2000)⁵

7.2.3. Ca_2-_xSm_xTa_2-_yTi_yO₇ (Grey & Roth, 2000)

7.2.4. Ca_2-_xNd_xTa_2-_yZr_yO₇ (Grey & Roth, 2000)