Nomenclature of magnetic, incommensurate, composition- changed morphotropic, polytype, transient-structural and quasicrystalline phases undergoing phase transitions. II. Report of an IUCr working group on Nomenclature

Citation for published version (APA): Toledano, J. C., Berry, R. S., Brown, P. J., Glazer, A. M., Metselaar, R., Pandey, D., Perez-Mato, J. M., Roth, R. S., & Abrahams, S. C. (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 Nomenclature. Acta Crystallographica. Section A, Foundations of Crystallography, A57, 614-626. https://doi.org/10.1107/S0108767301006821

DOI: 10.1107/S0108767301006821

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Acta Crystallographica Section A Foundations of Nomenclature of magnetic, incommensurate, Crystallography composition-changed morphotropic, polytype, ISSN 0108-7673 transient-structural and quasicrystalline phases undergoing phase transitions. II. Report of an IUCr Received 26 February 2001 1 Accepted 19 April 2001 Working Group on Phase Transition Nomenclature

² Chairman of IUCr Working Group. J.-C. ToleÂdano,a² R. S. Berry,b³ P. J. Brown,c A. M. Glazer,d R. Metselaar,e§ ³ Ex officio, International Union of Pure and D. Pandey,f J. M. Perez-Mato,g R. S. Rothh and S. C. Abrahamsi*} Applied Physics. § Ex officio, International Union of Pure and Applied Chemistry. aLaboratoire des Solides IrradieÂs and Department of Physics, Ecole Polytechnique, F-91128 } Ex officio, IUCr Commission on Crystallo- Palaiseau CEDEX, France, bDepartment of Chemistry, University of Chicago, 5735 South Ellis graphic Nomenclature. 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 FõÂsica de la Materia Condensada, Universidad del PaõÂs 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: [email protected]

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-®eld notation of the ®rst 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 modi®cations to the atomic arrangement. Extensive examples that illustrate the recommendations were provided. This second Report considers, within the framework of a similar six- ®eld 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 speci®ed. 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 ®eld of the nomenclature

# 2001 International Union of Crystallography is used to emphasize the special features of polytypes and transient phases. As in Printed in Great Britain ± all rights reserved I, illustrative examples are provided for each category of phase sequence.

1. Introduction function of temperature and/or pressure may be found in the A multiplicity of terminologies for distinguishing individual crystallographic and other literature of the condensed state. members of a sequence of crystalline phases that form as a Confusion caused by the lack of a uni®ed nomenclature led the Commission on Crystallographic Nomenclature to estab- 2 1 Established 15 February 1994 by the IUCr Commission on Crystallographic lish a Working Group on Phase Transition Nomenclature. Nomenclature; following the resignation of two members upon acceptance of The Working Group was charged with studying the multiple the ®rst Report, three new members were appointed 18 July 1998. This second nomenclature in current use for naming such sequences of Report was received by the Commission 26 February 2001 and accepted 19 April 2001. The present Report, as all other Reports of the Commission, is phases and with making such recommendations for its available online at the Commission's webpage: http://www.iucr.org/iucr-top/ comm/cnom.html. 2 See footnote to paper title.

614 ToleÂdano et al.  Phase-transition nomenclature Acta Cryst. (2001). A57, 614±626 research papers improvement as may be appropriate. The term `phase-transi- Table 1 tion nomenclature', as used throughout this Report, applies to Recommended abbreviations for various magnetic categories. the nomenclature of phases that form as a consequence of one Property Abbreviation Property Abbreviation or more transitions; the nomenclature of materials that exist Paramagnet P Exotic EX only in single phase form is adequately treated elsewhere, e.g. Ferromagnet F Amplitude modulated IC Leigh et al. (1998). Antiferromagnet AF Helical H In I, the general purpose of the nomenclature was de®ned, Spin ¯op SF Canted ferromagnet CF Weak ferromagnet WFM the relevant information it should contain was speci®ed, and a recommendation was made for the adoption of a six-®eld notation in the case of structural phase-transition nomen- clature, i.e. of transitions between two crystalline (strictly periodic) phases that involve only a modi®cation of the atomic arrangement. Extensive examples providing illustrative use of the nomenclature were presented for a variety of substances unambiguously indicated by the number Z of structural units (metals, alloys, oxides and minerals) that undergo phase in the conventional cell. transitions as a function of temperature and/or pressure. The A recommended adaptation of the six-®eld nomenclature to recommended notation is not only unambiguous; it also magnetic phase transitions is now presented. provides a full context for the transitions undergone by each phase. 2.1. First field The recommended nomenclature employs the following six- The usual name used in the literature for a magnetic phase ®eld notation for each phase with given chemical composition, tends to emphasize the magnetic behaviour of the phase. For each ®eld being separated from the others by vertical bars: instance, antiferromagnetic phases are often nicknamed AF1, Usual Temp: K Space-group Number of Ferroic Comments AF2 etc; likewise, spin ¯op phases are nicknamed SF1, SF2 etc. label in and † symbol and chemical properties In simple situations where either temperature or magnetic literature pressure number formulas ®eld is the dominant parameter controlling the phase diagram,

; I; ... range Pa per unit cell † † the numeral in the nickname commonly increases with

decreasing temperature (e.g. in antiferromagnetic phases), or

Full information concerning the content of each ®eld is commonly increases with increasing magnetic ®eld (e.g. in spin available in I, see also footnotes in 6.1, 7.1.3, 7.2.2 and 7.3.3. xx ¯op phases). It is recommended that this practice of numeral This second Report considers the more complex nomen- increase be extended to newly discovered magnetic phases. In clature required for transitions involving magnetic phases, more complex situations involving an intricate phase diagram incommensurate phases and transitions occurring as a func- as a function of temperature and ®eld, with the possibility of tion of composition change. The case of phases with a rele- con¯ict between the assignment of increasing or decreasing vance to standard schemes of transition in equilibrium systems numerals, it is recommended that the sequence due to an that is not yet clearly established is considered more tenta- increasing magnetic ®eld be given precedence. Although such tively; such phases include polytypes, see also Guinier et al. nicknames do not always describe the magnetic character of (1984), quasicrystalline, radiation-induced and other transient the substance explicitly, since `AF' for example may be phases and their transitions. mistaken for antiferroelectric, this lack is compensated for by The six-®eld nomenclature de®ned in I was found to be the ®fth and sixth ®elds (see the examples in 31±3.5). A set convenient and applicable to all the new systems above, of intuitively obvious notations for the differentxx categories of provided a suitable adaptation of the content of each ®eld is magnetic behaviour is presented in Table 1. We recommend followed as recommended below. In addition, the present the assignment of nicknames as in this table. Two ferromag- analysis led the Working Group to recommend, for every netic phases in a sequence would hence be labelled F1 and F2. category of transition (including those considered in I), where known, that the order of the phase transition be noted as a 2.2. Second field comment in the sixth ®eld. The magnetic ®eld range (H, in T) over which the phase is stable, if known, should be added to the temperature (T,inK) and pressure (P, in Pa) ranges used for structural phase 2. Magnetic phases transitions. Clearly, a summary of the detailed phase diagram Several major additional factors must be considered in the of a given material as a function of three controlling param- designation of a magnetic phase transition as compared with eters cannot be provided in a highly compact nomenclature. a structural phase transition. These include (a) the magnetic However, the present aim is to provide an immediate under- con®guration, which must be speci®ed as well as the atomic standing of the experimental stability conditions for the con®guration, (b) the magnetic ®eld, which is as relevant and material. If the phase is stable over a region bounded by all controlling a parameter as the temperature and pressure, and three variables T, P and H, then these ranges should be (c) the magnetic periodicity of the system, which is not always indicated by their end-values; in turn, the boundary conditions

Acta Cryst. (2001). A57, 614±626 ToleÂdano et al.  Phase-transition nomenclature 615 research papers

Table 2 onset of different superlattice re¯ections in the various phases De®nition of types. of a sequence. Note that such information is analogous to (and Paramagnet Normally the magnetically disordered phase less accurate than) the speci®cation of the wavevector de®ning stable at high temperatures these superlattice re¯ections. Ferromagnet The magnetic phase with all spins parallel Ferrimagnet A spin array intermediate between that of a It is more convenient, for magnetic phases, to specify the ferromagnet and an antiferromagnetic magnetic propagation vector which ®lls the same function by Spin ¯op A phase in which some fraction of the moment providing information on the `magnetic periodicity' of the has been forced from antiferromagnetic to ferromagnetic order by the application of a phase. A similar option is adopted below for incommensurate ®eld systems (see 5). However, as in the latter systems, an ambi- Collinear A unique magnetization direction exists guity arises sincex the components of the propagation wave- Non-collinear Antiferromagnets with no unique magnetization direction vector can be referred either to the reciprocal cell of the non- Canted ferromagnet Small (<5) non-collinearity producing weak magnetic phase in the sequence or to that of the `chemical in a basically antiferromag- structure' of the magnetic phase itself (which may differ from netic arrangement. Includes weak ferrromag- nets of the Dzyaloshinski±Moriya type that of the non-magnetic phase). It is hence recommended, for Antiferromagnet Commensurate in the strict sense that the the sake of clarity and consistency with the option chosen for propagation vector corresponds to a special incommensurate systems, see 4.4, that the reference phase be point in the Brillouin zone. Could be modi®ed x by collinear or non-collinear spins speci®ed in the fourth ®eld. Also, that the value of Z for the Amplitude modulated Structures generated by a single modulation conventional chemical cell of the magnetic phase be indicated with wave vectors incommensurate in the at the beginning of the fourth ®eld. sense given above Helical Structures generated by two orthogonal modula- tions in phase quadrature with the same 2.5. Fifth field incommensurate wave vector Exotic Cases not covered by the above descriptions The recommended information for this ®eld, in the case of Weak ferromagnet Commonly used name for a canted ferromagnet structural phase transitions, see I, is the name of the ferroic of the Dzyaloshinski±Moriya type property. For magnetic phase transitions, speci®cation of the magnetic type instead is recommended. The various magnetic types to be considered are listed in Table 2 together with their de®nitions.

2.6. Sixth field are separated by semicolons. 3.5 illustrates this notation for This ®eld may include complementary information such as the intricate case of EuAs ,x the phase diagram of which is 3 the magnetic moment, its magnitude and direction for simple reproduced in Fig. 1. Since the magnetic ®eld direction is of structures, the direction of the external magnetic ®eld relevance, this information when available should be speci®ed controlling the stability of the phases and any other infor- in the sixth ®eld. mation that contributes to the understanding of the magnetic con®guration. Recommended descriptions for this ®eld are 2.3. Third field given in Table 3. In the case of structural phase transitions, this ®eld is The content of the various ®elds is summarized as follows devoted to the speci®cation of the space-group symbol and number (to avoid ambiguities related to the setting); such Usual Temp: K ; Crystallo- Reference Magnetic Magnetic magnetic pressure † graphic phase; Z; type cf: configuration information is insuf®cient for magnetic systems since it does label as Pa and space-group and Table 2 and † † not describe the nature of the magnetic ordering. An alter- used in magnetic symbol and magnetic comments

literature field T number propagation cf: Table 3 : native might be to indicate the magnetic . † † e:g: AF1; range vector

However, the lack of a standard magnetic space-group nota- cf: Table 1 tion leads us to recommend the use of the same crystal- † lographic information (i.e. the crystallographic space-group symbol and number) in this ®eld as for sequences of structural transitions. This does not detract from the total information provided since ®elds four and six contain additional infor- mation specifying the required magnetic structure (i.e. 3. Examples of magnetic phase-transition nomenclature magnetic periodicity and spin con®guration). 3.1. Fe (Geissler et al., 1967)

P >1040 K Im3m 229 P; Z 2 Paramagnet 2.4. Fourth field † 0; 0; 0ˆ

F <1040 K Im3m 229 P; Z 2 Ferromagnet Easy magnetization The recommendation in I for this ®eld is to provide the † ˆ 0; 0; 0 direction 110 : h i number of chemical formulas per conventional unit cell, i.e. Z.

The purpose is to specify the change of lattice periodicity Columns I, II, III and V above indicate that Fe undergoes a occurring between phases or, in other terms, to indicate the transition from paramagnetic to ferromagnetic at 1040 K

616 ToleÂdano et al.  Phase-transition nomenclature Acta Cryst. (2001). A57, 614±626 research papers

Table 3 3.4. a-Fe2O3 (Shull et al., 1951; Nathans et al., 1964) Description of magnetic spin arrangements. P >945 K R3c P; Z 4 Paramagnet Screw spiral Helical structure with spins in the plane perpen- ˆ 167 0; 0; 0 dicular to the propagation vector † WFM 945 260 K R3c P; Z 4 Canted Moments in 111 Cycloidal spiral Helical structure with spins in the plane containing ˆ † 167 0; 0; 0 ferromagnet ferromagnetically the propagation vector Bunched spiral Helical structure with spin directions bunched † coupled: Nearly

about particular directions in the plane in which antiferromagnetic

they rotate coupling between

Sinusoidal modulation The amplitudes of the spins in a collinear arrange- ; adjacent planes ment follow a sine curve moment directions Square wave The amplitudes of the spins in a collinear arrange- in the planes: ment follow a square wave Three s domains: Fan A cycloidal structure with bunching  AF <206 K R3c P; Z 4 Antiferromagnet Moments in 111 Antiphase domains Regions of an antiferromagnetic structure related ˆ † 167 0; 0; 0 ferromagnetically by inversion of all spins † coupled: Exact k domains Domains corresponding to different arms of the antiferromagnetic stars of the propagation vector coupling between s domains Domains with the same propagation vector, but planes: Moments different spin directions parallel to 111 : Chirality domains Domains corresponding to oppositely directed ‰ Š propagation vectors, when these are inequiva-

lent, as for helical structures

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

P >11:1K; 0T; C2=m P; Z 4 Paramagnet 0K;>6:5T 12 0; 0; 0ˆ † IC 10:1 11:1K; C2=m P; Z 4 Amplitude  0:15 0:075; ˆ ˆ <0:83 T 12 1; 1; 1=2  modulated 11:12 10:17 K:

† Moments b;

coupling ask AF1: T without a change in crystallographic space group at c; column AF1 0 10:1K; 0T; C2=m P; Z 4 Antiferro- Moments b and

IV that both phases have two atoms in the conventional cubic 09:8K; 0:7T: 12 1; 1; 1ˆ magnet ferromagneticallyk 2 † unit cell and the reference of the k vector is the P phase. 0 10:1K;<0:3 GPa; coupled across the 5 9:8K;<0:6 GPa centre of symmetry at origin:

HP 0K;>0:3 GPa; C2=m P; Z 4 Helical Cycloid; moments ˆ 5 9:8K;>0:6 GPa 12 0:11; 1; 0:22 in ac plane; coup- † ling as AF1: Two

chirality domains:

3.2. NiO (Roth, 1958) SF1 <9:5K; 0:7T; C2=m P; Z 4 Helical Cycloid; moments ˆ <7K; 2:2T 12 0:1; 1; 0:25 in ac plane; coup- † P >523 K Fm3m P; Z 4 Paramagnet ling as AF1: Two

ˆ chirality domains: 225 0; 0; 0  † SF2 <5:8K; 2:2T; C2=m P; Z 4 Non-collinear Antiferromagnetic AF <523 K R3m P; Z 4 Antiferromagnet Moments ferromagneti- ˆ 0K; 4:8T 12 0; 1; 0ˆ:25 ferromagnet components c; 166 1 ; 1 ; 1 cally coupled in 111 2 2 2 † coupled as ink AF1: † † planes; adjacent layers Two chirality antiferromagnetically domains: coupled: Spins 112 : SF3 0K; 4:8 5:5T; C2=m P; Z 4 Exotic Fan structure with k‰ Š ˆ Four k domains each 5:8K; 2T 12 0:1; 1; 0:225 antiferromagnetic † containing three s components c; k domains: coupling as AF1:

SF4 9:6 10:8K; 0:83T; C2=m P; Z 4 Exotic As SF3 but with ˆ 0K; 5:5 6:5T 12 0:102; 1; 0:225 antiferromagnetic k domains differ in propagation vector direction, s domains in † components at 8 spin direction, cf. Table 3. The Z value refers to the conven- to c:

tional cell, hence the primitive cell in the AF phase (which is identical to the conventional cell) is quadruple that of the The P±T and H±T phase diagrams of EuAs3 are given in Fig. 1. primitive cell in the P phase (one-fourth the cubic cell). 4. Incommensurate phases A preliminary adaptation of the structural phase-transition nomenclature to the case of incommensurately modulated 3.3. K IrCl (Hutchings & Windsor, 1967) 2 6 systems was proposed in I, 5, as illustrated by the example of x P >3:05 K Fm3m 225 P; Z 4 Paramagnet K2SeO4. The requirement to keep the nomenclature as † 0; 0; 0ˆ uniform as possible for the various types of phase system leads AF <3:05 K I4=m 87 P; Z 2 Antiferromagnet Spins 001 ; † ˆ k‰ Š us to adopt the same convention in the fourth ®eld as that used 1; 0; 1 in Fm3m 6 k domains: 2 1 ; 1 ; 1 in I4=m for magnetic systems, i.e. specifying the wavevector of the 2 2 2 modulation rather than the approximate period of the

modulation, see Chapuis et al. (1997).

Acta Cryst. (2001). A57, 614±626 ToleÂdano et al.  Phase-transition nomenclature 617 research papers

Similarly, the possibility of substituting the multi- 4.2. Second field dimensional space group (Janssen et al., 1992) for the usual As in the case of magnetic materials, an additional (average) space group in the third ®eld was considered but 1 controlling parameter, namely the electric ®eld, E in V m ,is discarded for reasons similar to those for not using the often relevant. Indeed, the stability range of modulated magnetic space-group symbol (viz. the specialized nature of `ferroelectric' phases is very sensitive to the application of an the topic and the possibility of ambiguity in the case of more external electric ®eld (which can play a roÃle similar to that of than one direction of modulation). It is hence recommended the magnetic ®eld in helical or sinusoidal magnets). Here, also, that the space group of the average structure, i.e. the structure the option is taken of providing a simpli®ed phase diagram; obtained by averaging the effects of the modulation, be the approximate range of stability of the given phase, as a inserted in this ®eld. function of all three parameters T, P and E, is indicated by the We brie¯y summarize the content of each ®eld. appropriate stability intervals relative to each parameter, see also 2.2. Examples 5.1±5.6 illustrate the application of this notation.x xx

4.1. First field 4.3. Third field The common names used for incommensurate phases are This ®eld, for both the incommensurate and commensurate identical to those for ordinary crystalline phases (e.g. I, II etc.). phases in a sequence, speci®es the average space group of the The incommensurate character appears in the fourth ®eld (in structure, namely that obtained by averaging the modulated which the wavevector of the modulation is speci®ed) and, positions of the atoms. Each atom is located at the centre of more explicitly, in the sixth ®eld. 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 re¯ections and ignoring the satellite re¯ections. 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 speci®ed in the third ®eld below the average space group in order to provide more accurate information.

4.4. Fourth field This ®eld contains the modulation propagation vector (the modulation wavevector), as referred to the reciprocal lattice of the phase speci®ed 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 appropriatex clarifying comments in the sixth ®eld. 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 re¯ections, 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 ®eld, the number of units in the unit cell of the average structure. We denote this number ZA. In the present case, however, the superlattice re¯ections 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 ®eld. The ZA value relative to the average structure of the incommensurate phase should also be Figure 1 included. The latter option has the advantage of lifting the The P±T and H±T phase diagrams of EuAs3 ambiguity concerning the phase taken as reference for the

618 ToleÂdano et al.  Phase-transition nomenclature Acta Cryst. (2001). A57, 614±626 research papers

Table 4 5. Examples of incommensurate phase-transition Abbreviations used in the illustrative examples for composition-changed, nomenclature transient-structural and quasicrystalline phases. 5.1. SO2(C6H4Cl)2 (ZuÂÄniga et al., 1993; Etrillard et al., 1996) Property Abbreviation A single phase transition at T 150 K is reported; the Ferroelectric orthorhombic FO i ˆ Ferroelectric tetragonal FT incommensurate phase exists as low as 0.1 K. Ferroelectric rhombohedral (high/low temperature) FR (HT/LT) Antiferroelectric AF I >150 K I2=a Z 4 Non-ferroic Paraelectric P 15 ˆ † Quasicrystalline Q II 0:1 Ti I2=a ZA 4 Non-ferroic Icommensurate:  ˆ Approximant A 150 K 15 0;;0 referred Modulation:  0:78;  †  Radical pair RP to phase I displacive modulation:

Metastable (higher temp.) MS1

Metastable (lower temp.) MS2 Rotator phase just below melting temperature RI Non-rotator phase T Modulated quasicrystalline MQ

5.2. K2SeO4 (Iizumi et al., 1977) The succession of four phases (three commensurate and one incommensurate) is denoted as follows:

I >630 K P63=mmc Z 2 Non-ferroic 194 ˆ † II 630 130 K Pnam Z 4 Ferroelastic 3 variants modulation wavevector. It also provides a uni®ed nomen- ˆ 62 clature scheme for the incommensurate and the magnetic † III 130 93 K Pnam ZA 4 Ferroelastic Incommensurate: ˆ systems, which may also be incommensurate. 62 1=3  ; 0; 0 Modulation: † † referred to  0:05;  phase II ferroelectric

distortion of

SeO tetrahedra: 4 4.5. Fifth field IV <93 K Pnam Z 4 Ferroelectric Commensurate; A 62 1=3;ˆ0; 0 and ferroelastic 6 variants:

It is recommended that, as with ordinary structural phase Pna†2 referred to 1 transitions, the `average ferroic' properties be stated in the 33 phase II;

† ®fth ®eld whenever they exist. In most examples, the point Z 12 ˆ symmetry of the average structure is identical to that of the `high-temperature' phase and no macroscopic ferroic proper- ties exist. However, certain materials display ferroic properties in the incommensurate phase (cf. 5.2). 5.3. Ba2NaNb5O15 (ToleÂdano et al., 1986) x I >850 K P4=mbm Z 1 Non-ferroic 127 ˆ † II 850 570 K P4bm Z 1 Ferroelectric 2 variants: ˆ 4.6. Sixth field 100 Polarization † along the 4 axis: This ®eld may include complementary information such as III 570 540 K Cmm2 Z 2 Ferroelectric Incommensurate A ˆ the incommensurate character and the nature of the structural 35 1  =4; and ferroelastic modulation † ‡ † 1 1 modulation (e.g. onset of a modulated ferroelectric dipole of 1  =4;  10 : 2 referred‡ † to NbO octahedral† speci®ed orientation or the modulated deformation of a 6 phase I tilts: 4 ferro- speci®c group of atoms), as well as the possible occurrence of electric ferro- multiple k or several independent modulations. elastic variants:

The content of each nomenclature ®eld is summarized as IV 540 110 K Cmm2 ZA 2 Ferroelectric Commensurate ˆ follows: 35 1 0 =4; and ferroelastic 0 0 in certain † ‡ † 1 ˆ Bbm2 1 0 =4; 2 samples: Same ‡ † 40 referred to variants as III: † Usual Relevant Space-group ZA; Ferroic Incommen- phase I;

label in controlling symbol and modulation type surate char- Z 16 ˆ literature parameters: number for propagation acter and V <110 K P4bm ? ZA 1 Ferroelectric Re-entrant phase † ˆ I; II; ... temperature the average vector label nature of 100 1  =4; sample † † ‡ † 1 K ; structure of the the 1  =4; dependent : † Æ ‡ † 2 † pressure reference modulation: referred to Characteristics of

Pa and phase : Z for phase I; k uncertain; † † electric field commensurate Z 32 2 directions of

Vm 1 phases ˆ modulation likely: † †

Acta Cryst. (2001). A57, 614±626 ToleÂdano et al.  Phase-transition nomenclature 619 research papers

5.4. (CH ) NCH COO CaCl 2H O (Chaves & Almeida, 5.5. TaSe (Fleming et al., 1980; Bird et al., 1985) 3 3 2 Á 2 Á 2 2 1990) I >123 K P63=mmc Z 2 Non-ferroic 194 ˆ † II 123 112 K P63=mmc ZA 2 Non-ferroic Incommensurate: I >164 K Pnma Z 4 Non-ferroic ˆ 4 GPa;>230 K 62 ˆ 194 1  =3; 0; 0 Triple-k modula- † † II 164 129 K † Pnma † Z 4 Non-ferroic Incommensurate 0; 1  =3; 0 tion along three A † 4 GPa ; 230 225 K 62 0; 0;ˆ  0:29: referred hexagonal direc-

† † referred to  to phase I tions:  2 10 2: phase I   III 112 90 K Cmcm ZA 4 Ferroelastic Double-k modula- ˆ III 129 127 K Pnma ZA 4 Ferroelectric Commensurate 63 1  =3; 0; 0 tion: Commensu- ˆ † † <2 GPa 62 0; 0; 2=7 ferroelectric 0; 1  =3; 0 rate along k : † 1 † † 3 0:4MVm Pn21a referred to polarization 1=3; 1=3; 0

143 122 K 33 phase I; along b: † † referred Z 28 ˆ to phase I IV 127 117 K Pnma ZA 4 Non-ferroic Incommensurate ˆ IV <90 K Cmcm Z 4 Ferroelastic Commensurate: 4 GPa; 225 215 K 62 0; 0;  0:27: A ˆ 1 † †  63 1=3; 0; 0 The amplitude of <0:2MVm referred to † phase I 0; 1=3; 0 the modulation is

V 117 116 K Pnma ZA 4 Ferroelectric Commensurate referred equal along two ˆ 62 0; 0; 4=15 ferroelectric to phase I; directions and 1 † 0:4MVm ; Pn21a referred to polarization Z 36 unequal in the

120 110 K 33 phase I; along b; electric ˆ third: There are † † Z 60 field applied three orientation ˆ along b: domains each VI 116 80 K; 5GPa Pnma Z 4 Ferroelectric Commensurate A containing 9 trans-  62 0; 0;ˆ1=4 ferroelectric

† lation domains: P21ca referred to polarization

29 phase I along a: † Z 16 ˆ VII 4 GPa; 210 180 K Pnma ZA 4 Ferroelectric Commensurate 5.6. Bi2 xPbxSr2CaCu2O8 (ToleÂdano et al., 1990)  ˆ X111 62 0; 0; m=n for m even; phases with † referred to n odd n 7; 9; 11; 14; Bi2 xPbxSr2CaCu2O8 is an example of a material exhibiting ˆ phase I; or m odd; 17; 19; the incommensurate phases with two unusual characteristics: the Z 4n n even existence of ˆ ®rst a compositional dependence of the wavevector, the some of these

phases is second the presence of two modulations along the same

uncertain: direction. XIV 78 57 K; 5 GPa; Pnma ZA 4 Commensurate:  1 ˆ 0:2MVm 62 0; 0; 1=5 Electric field I x 0 Bbmb ZA 1 Twinned Incommensurate:  P 2 †2 2 referred to along b: ˆ ˆ 1 1 1 66 0;;1=2 ferroelastic? Modulation:  0:21; 19 phase I; † †  `buckling' of BiO † Z 20 planes: XV 57 50 K; Pnma Z ˆ 4 Ferroelectric Commensurate A <0:2MVm 1 62 0; 0;ˆ1 ferroelectric II 0:25 x>0:10 Bbmb ZA 1 Twinned Incommensurate: 6  ˆ P †ca 66 0;;1=2 ferroelastic? Modulation:  0:21; 21 referred to polarization † †  `buckling' of BiO 29 phase I; along a: † Z 24 Electric field planes: ˆ along b: 0:10>x 0:05 0:18>>0:10:  XVI <50 K; Pn21a Z 4 Ferroelectric Nonmodulated III x 0:10 Bbmb ZA 1 Twinned Two modulations with ˆ  ˆ 4 GPa;<180 K 33 ferroelectric 66 0;;1=2 ferroelastic? characteristics close to † polarization † 0;;0 † that of phases I and II:

along b:  0:22;  2=3  : 1 2 1  ˆ †

6. Composition-changed phases A growing number of materials are being reported for which a change in composition results in a phase change; such mate- rials are commonly referred to as morphotropic. IUPAC (Clark et al., 1994) de®nes a morphotropic phase transition as `an abrupt change in the structure of a solid solution with variation in composition'. If this de®nition 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 transi- tions, concerns the structural changes (e.g. as speci®ed by its space group) at a precisely de®ned composition. The nomenclature recommended in I and in 2 and 4 of the xx

620 ToleÂdano et al.  Phase-transition nomenclature Acta Cryst. (2001). A57, 614±626 research papers present Report is readily applicable to morphotropic phase P 0

Table 4 presents the meaning of these labels. 6.1.3. La2 xSrxCuO4 (Torrance et al., 1989; Burns, 1992). The La2 xSrxCuO4 solid solutions have been widely studied for their interest in the important ®eld of high-temperature superconductivity. Elucidation of the phase diagram by the work of many authors has revealed a rich diversity of ®elds. 6.1. Examples of composition-changed phase nomenclature3 The example given here illustrates the phases at T 300 K; superconducting and other phases form at lower temperatures.ˆ 6.1.1. PbZr1 xTixO3 phases at room temperature (Corker et al., 1998). I 0:07

octahedral tilts;

6 variants:

FR HT 0:35

FR LT 0:06

AF 0

† system: 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. The symbols aaa and aac‡ are from Glazer's (1972) However, they also raise a speci®c dif®culty since the condi- system of specifying the anion octahedral tilts in perovskite tions of phase stability (de®ned by a controlling parameter structures. The perovskite structure consists of corner-linked such as temperature and pressure) are ill-de®ned and, so far, it octahedra that can tilt about any combination of pseudocubic has not been possible to determine an acceptable phase axes, ap, bp and cp. The three letters refer to each axis in turn diagram giving stability ®elds for the known polytypes of and indicate equivalence or non-equivalence of the angle of materials such as SiC, ZnS or CdI2. The relevant parameters in tilt. Equivalence is indicated by repeating a letter. If successive this case are hence concerned with the method and conditions tilts about an axis are in the same sense, then a superscript is of phase stabilization. used; if in opposing senses, then a superscript is used. Thus‡ A similar situation is also applicable in the case of transient the symbol aaa means that all octahedra tilted about the or metastable phases obtained through the irradiation of ap axis are tilted in alternating senses. The same is true for the samples by light or particle beams. Moreover, the physical octahedra viewed down bp and down cp. All tilts are of characterization of the phases observed often leads to a equivalent magnitude; the net effect is to create a rhombo- different categorization than for the phases dealt with in the hedral structure. preceding sections (viz. ferroic properties). raise 6.1.2. KTa1 xNbxO3 (Perry et al., 1976). The end members even greater dif®culties since, in addition to the former of this solid solution undergo transitions as a function of features (metastability, speci®c characterization of the temperature (for KNbO3, Tc ~ 698 K; for KTaO3, Tc ~ 1±3 K). physical properties), the atomic structure can only be very All transitions described below are a function of composition roughly speci®ed without making use of the specialized at room temperature, except for the FR phase. nomenclature of six-dimensional crystallography; unlike the situation in incommensurate systems, it is not possible with 3 See footnotes 4 for the third and fourth, 5 for the sixth and 6 for the ®fth ®elds as de®ned in Report I. Second ®eld, Report I: If the phase is stable over a quasicrystals to `bypass' this abstract description by use of a thermal range, then the temperature limits should be given in kelvins; if over a modulation wavevector and an `average space group'. pressure range, in pascals. SI pre®xes should be used as required. If no In view of this situation, the following proposals for the pressure range is indicated, the observations correspond to atmospheric pressure; similarly, if no temperature range is indicated, the observations nomenclature of these systems must be considered as tenta- correspond to room temperature. tive.

Acta Cryst. (2001). A57, 614±626 ToleÂdano et al.  Phase-transition nomenclature 621 research papers

7.1. Polytypic phases specify stacking sequences have not been widely used in the Polytypic transitions are de®ned by IUPAC (Clark et al., literature. Instead, a simple notation in which `c' is taken for 1994) as transitions from `a crystalline structure into one or cubic and `h' for hexagonal packing appears to be in common more forms which differ in the way identical layers of atoms use and is adopted here. The sixth ®eld should contain the are stacked'. preparation conditions and structure type or related infor- 7.1.1. First field. The IUCr (Guinier et al., 1984) has mation. Six examples illustrating the recommended nomen- recommended two kinds of symbolism for use with either clature for polytypic phases follow. simple or complicated polytypic structures. The ®rst consists of `indicative symbols' in a modi®ed Gard notation, the second of 7.2. Examples of polytypic phase nomenclature `descriptive symbols' based on earlier proposals by Dorn- 7.2.1. Ca2Ta2O7 (Grey et al., 1999; Grey & Roth, 2000). Ï berger-Schiff, DurovicÏ and Zvyagin. Use of the term `nN', 7M >1673 K C2 Z 28 hccccchccccccc Stable high-temperature commonly used to designate the stacking sequence of layers 5 ˆ polytype: † 3T <1673 K P3121 Z 6 Unknown Metastable low-temperature (n) and the crystal system (N), is recommended for the ®rst ˆ 152 form: Not reversible from ®eld. Guinier et al. (1984) recommend the upper-case letters † higher temperature: that follow for the crystal system. Note that the common 6M Unknown Cc Z 24 hccccchcccch Obtainable with either a ˆ meaning of n, i.e. the number of layers, may depend on the 9 Ca V O or a Ca B O 2 2 7 2 2 5 † flux: system. Thus, as in the examples below, n is either the smallest

number of layers necessary to describe a sequence or is the 5 entire number of layers required to de®ne the unit cell. The 7.2.2. Ca2 xMgxTa2 yNbyO7 (Grey & Roth, 2000) . intent of the convention used becomes apparent in the ®fth 7M 0

Tetragonal (quadratic) Q

Orthorhombic O Monoclinic M 7.2.3. Ca2 xSmxTa2 yTiyO7 (Grey & Roth, 2000). Triclinic (anorthic) A 6T 0:11297 K P63mc Z 2 All hexagonal May exist metastably 7.1.4. Fifth and sixth fields. In principle, the ®fth ®eld of the 186 ˆ packing at room temperature and † nomenclature should specify the ferroic properties of the transform irreversibly to

3C above 673 K: phase but this is likely to be blank for most polytypes; it is 3C <1297 K F43 m Z 4 All cubic packing Transforms into 2H ˆ hence recommended that this ®eld should instead provide 216 martensitically: the essential stacking sequence information. The detailed † descriptive symbols recommended by Guinier et al. (1984) to

4 See footnotes 3 for the second, 5 for the sixth and 6 for the ®fth ®elds as de®ned in Report I. Third ®eld, Report I: The space-group symbol and number of the phase, as used in International Tables for Crystallography (1996), should 5 See footnotes 3 for the second, 4 for the third and fourth, and 6 for the ®fth be given. When incomplete crystallographic information is available, these ®elds as de®ned in Report I. Sixth ®eld, Report I: If the phase crystallizes with data may be replaced by specifying the point group (e.g. 4mm) or the crystal a standard structure type, then the sixth ®eld should begin with an entry in the system (e.g. tetragonal). Fourth ®eld, Report I: The number of chemical format | Type = XXXX. Typical structure type names are, for instance, XXXX formula units per conventional cell should be entered; if undetermined, the = NaCl, pyrite, sphalerite, etc., with the name in italics or, alternatively, ®eld should contain only a dash. The (tripled) hexagonal unit-cell setting in structure-type formulas such as XXXX = GXX 0, T3(T0/L)X4 etc. with the rhombohedral systems should be used. formula in italics.

622 ToleÂdano et al.  Phase-transition nomenclature Acta Cryst. (2001). A57, 614±626 research papers

7.2.6. SiC (Ramsdell, 1947; Pandey & Krishna, 1982).The 7.3.4. Sixth field. A brief description of each transient SiC family is probably the best known of all polytypes. No phase in the system should be given. Comments should temperature, pressure or compositional differences have been include an indication of the experimental conditions used for proven for long-period modi®cations of SiC. Shaffer (1969) phase onset, phase lifetime and preparation. reports 74 different polytypes. Pandey & Krishna (1982) have listed 60 polytypes, with complete stacking sequences of 7.4. Examples of transient-structural phase-transition layers, the more common of which are listed below. nomenclature

7.4.1. Na2[Fe(CN)5NO] 2H2O (Carducci et al., 1997). 2H <1673 K P63mc Z 2 11 h Transforms irreversibly above Á ˆ 186 1673 K to 3C and above GS Zero irradiation Pnnm Z 4 Ground-state structure: † ˆ 2273 K to 6H: at 50 K 58 Crystallized from aqueous  † 3C <2273 K F43m Z 4 c Transforms irreversibly above solution: ˆ 1 216 2273 K to 6H: MS1 488 nm; Pnnm Z 4 Metastable state I: Laser- † 2 ˆ 6H >2273 K P63mc Z 6 33 cchcch 2H and 3C transform 1 kWm at 50 K 58 excited: Heated to 165 K for ˆ † 186 irreversibly to 6H above 5 min; recooled to 50 K: † 2273 K: Most common form MS 1064 nm; Pnnm Z 4 Metastable state II: Longer 2 in -SiC: 0:7kWm 2 at 50 K 58 ˆ wavelength laser-excited: 15R Unknown R3m Z 15 32 cchch Second most common form in † ˆ †3 160 -SiC:

4H Unknown P 6 mc† Z 4 22 chch Third most common form in 3 7.4.2. n-Hexadecane, C16H34 (Sirota & Herhold, 1999). 186 ˆ -SiC: Can occur in melt-

† R 289:66 K Fmmm Z 4 Transient <10 s rotator phase: Forms grown crystals below 2273 K: I 69 ˆ on slow cooling † from the melt: † T <289:66 K P1 Z 1 Non-rotator phase: Transforms from R ˆ I 2 phase; melts at 291:5K: †

7.3. Transient-structural phases 7.4.3. 2,2 -Di(orthochlorophenyl)-4,4 ,5,5 -tetraphenylbi- It has recently become possible to study a range of photo- 000 000 000 imidazole (o-Cl-HABI) (Kawano et al., 1999). induced and other transient phases with lifetimes of order ranging from picoseconds to hours. Studies of short-duration GS >103 K Pbca Z 16 Ground state; two independent 61 ˆ molecules; A and B: Pale phases by use of synchrotron radiation, see e.g. Helliwell & † yellow: Irradiated as for RP;

Rentzepis (1997), are being reported with increasing warmed to 300 K giving GS; frequency in the current literature. The lower limit is likely then cooled to 103 K:

RP High-pressure Pbca Z 16 0% A molecules; 10% B mol- to be reduced further by the introduction of femtosecond ˆ Hg lamp; 20 min 61 ecules converted into radical synchrotron radiation (see e.g. Schoenlein et al., 2000). On the † irradiation at 103 K pairs at 103 K: Reddish-brown: other hand, phases can be stabilized outside their ordinary Cleavage of the C N bond stability range by irradiation with various types of beams, e.g. gives two planar radicals in an

RP: 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 7.4.4. Titanium under high-energy ion irradiation require revision. The usage recommended in I, as modi®ed in (Dammak et al., 1996). 2 and 4 of the present Report, is readily adapted to radia- xx T P mmc Z tion-induced phases as follows. <1200 K; 63= 2 Twinned p<500 MPa 194 ˆ 7.3.1. First field.AsinI(3.1) and in 4.1 of the present 13 2 † ! >2 10 ions cm ; P6=mmm Z 3 Twinned Phase stable at high x x  ˆ Report. The signi®cance of the labels used is indicated in 1 GeV; 80 K; 191 pressure; stabilized at  † Table 4. p>500 MPa room pressure by

irradiation with high- 7.3.2. Second field. In addition to the temperature/pressure energy lead ions: 3 stability range of each phase in the system, the wavelength twin orientations 2 (nm) and radiant ¯ux (W m ) necessary to obtain the irra- c along a : ! T>1200 K Im3m Z 2 † diated phase should be given. In the case of other types of 229 ˆ irradiation, equivalent speci®cations for the radiation used † should be given. 7.3.3. Third, fourth and fifth fields.AsinI( 3.3±3.5).6 In xx most examples below, information pertaining to the ®fth ®eld 7.5. Quasicrystalline phases (ferroic property) is unavailable. Reversible phase transitions have been observed between 6 See footnotes 3 for the second, 4 for the third and fourth, and 5 for the sixth ordered and disordered quasicrystals, also between quasi- ®elds as de®ned in Report I. Fifth ®eld, Report I: Contains the name of the crystalline phases and either orientationally twinned crystal- ferroic property exhibited by the phase, see Clark et al. (1994). If this property line approximant phases or modulated quasicrystals (Fettweis has not actually been observed experimentally but is nevertheless probable on crystallographic grounds, a comment indicating this situation should be added et al., 1995; Steurer, 2000; Zurkirch et al.1998). A rigorous in the sixth ®eld. An unknown property is denoted by a dash (see e.g. 7.4.1). de®nition of any of these phase categories has not yet been x

Acta Cryst. (2001). A57, 614±626 ToleÂdano et al.  Phase-transition nomenclature 623 research papers achieved (cf. Launois, 1999, and references therein). The basic spacings allow the reproduction of an entire set of present tentative adaptation of the nomenclature in I to these reciprocal positions. These basic spacings are derived from a systems hence uses the simplest pragmatic de®nitions avail- `hypercell' in the n-dimensional (n = 4, 5 or 6) description of able even if these do not adequately explain all the complex the structure. The fourth ®eld should contain an indication of situations observed. A quasicrystalline phase is thus consid- the hypercell parameters, if available. Such information is ered to be characterized by the absence of an average Bravais analogous to the speci®cation of Z for a crystalline phase. lattice and/or the observation of `forbidden' crystallographic The third ®eld, for modulated quasicrystalline phases as for symmetry (e.g. decagonal). incommensurate phases in 4.3, should specify the average An approximant phase is a crystalline phase with large unit (corresponding tox the main re¯ections). Field four cell and diffraction pattern closely resembling that of a should provide the propagation wavevector of the modulation, quasicrystalline phase in the sequence. In practice, approxi- either as a fraction of the `hypercell' reciprocal-lattice vectors, 1 mant phases of different coherent or incoherent orientations or in absolute units (AÊ ). For approximant phases, the coexist, forming twinned structures. Such twinning can normal space group should be given in the third ®eld, while produce a diffraction pattern that exhibits `forbidden the fourth ®eld should contain the dimensions of the large cell symmetry'. Modulated quasicrystals are systems with a or the number of formulas in the large cell. diffraction pattern that displays two sets of re¯ections: the ®rst 7.5.4. Fifth field. The recommendations of I are applicable, is a set of strong `main' re¯ections, characteristic of a quasi- if relevant, see footnote 5; if not, as is generally the case for crystal. The second is a set of weaker `satellite' re¯ections that this class of phases, the ®eld contains only a dash. symmetrically surround the main re¯ections. The two sets are 7.5.5. Sixth field. Phases in alloys that display quasicrys- interpreted as the presence of a periodic modulation of atomic talline phases are often characterized by small changes in the positions in the quasicrystal. We consider hereunder the measured composition, with respect to that of the average adaptation of each nomenclature ®eld to the speci®c features composition. Whenever available, this information should be of these systems. stated. In addition, the type of twinning in approximant phases 7.5.1. First field. Unless a label has been applied previously should be indicated, including the forbidden symmetry thus to the phase, we suggest the abbreviations given in Table 4. generated. If the phase transition is irreversible, this should be Additional numbering is used, e.g. Q1, if phases of the same noted here, see 7.5.2. type in a sequence are to be distinguished. If more complex x phases are involved in a given sequence, then an appropriate 7.6. Examples of quasicrystalline phase nomenclature label may be similarly de®ned. 7.6.1. Al63Cu17.5Co17.5Si2 (Fettweis et al., 1995). 7.5.2. Second field. Temperature appears to be the relevant Q1 >1070 K Two-dimensional Reversible transition controlling parameter in all transitions observed hitherto decagonal with 100 K hysteresis: between quasicrystalline and other phases. The standard P10 =mmc 5 conventions in I hence remain applicable. However, since A1 <1000 K Orthorhombic a b 51:5; 5 variants rotated by  Ê base-centred c 4:1A 72: phase-transition irreversibility may be of importance in 

considering these systems, it is recommended that this be speci®ed, if present, in ®eld six. 7.6.2. Al69Pd22Mn9 (de Boissieu et al., 1998; Boudard et 7.5.3. Third and fourth fields. It is recommended, for al., 1992). quasicrystalline phases, that these ®elds provide only an Q1 >1013 K 3-dimensional Composition elementary description of the structural geometry. Both the icosahedral Al Pd Mn : 68:8 22 9:2 Fm35or F235 dimensionality and type of the system point symmetry Q2=F2 <1013 K 3-dimensional 6d hypercubic Twinned Composition (crystallographic or noncrystallographic) should be speci®ed M hypercubic cell Al Pd Mn : 69:3 22 8:7 in ®eld three. This information immediately distinguishes F lattice a 12:90 AÊ 5 variants related

ˆ (Steurer, 1990; Launois, 1999) one-dimensional quasicrystals, to the lowering of

orientational sym- in which ordinary crystalline order is observed in two metry with respect dimensions, from two-dimensional quasicrystals, in which only to Q1: one dimension is periodic, and both from three-dimensional Q3=F2 <920 K 3-dimensional Icosahedral Metastable between icosahedral cell Q1 and Q2: quasicrystals. In the two-dimensional case, the forbidden a0 2a Composition ˆ symmetries already observed are pentagonal, octagonal, Al69:8Pd21:4Mn8:8:

Superlattice of decagonal or dodecagonal. Three-dimensional crystals gener- phase Q2: ally have icosahedral symmetry; however, examples of lower symmetries have recently been found. Since an average/ structural space group cannot be de®ned, unlike the case of incommensurate/magnetic systems, see 4 and 2, higher- dimensional space groups may be indicatedxx if available, see 8. Discussion Janssen et al. (1999). The diffraction pattern of a quasicrys- Wide acceptance of new nomenclature in any branch of talline phase displays a multiplicity of characteristic spacings science is achievable only if the clarity of communication between spots. However, by combining integer coef®cients, six within that ®eld is thereby evidently improved. The presen-

624 ToleÂdano et al.  Phase-transition nomenclature Acta Cryst. (2001). A57, 614±626 research papers tation of this second and ®nal Report offers an opportunity Further examples of the notation in other structural phase to re-emphasize the advantages of the recommended phase- transitions may be found in the ®rst Report (ToleÂdano et al., transition nomenclature. This may be illustrated by comparing 1998). As noted in I, 5, it is recommended that, following ®rst it with the typical use of earlier nomenclature found in two use of the full six-®eldx notation in a paper for identifying a recent reports of new crystal structures and their phase given phase transition, the ®rst two ®elds only need be used transitions. The ®rst, by Haile & Wuensch (2000a)on thereafter unless the phase is not associated with a label. In

-K3NdSi6O15 xH2O, with 2 x 0, appeared in the course that case, the second two ®elds suf®ce for phase identi®cation. of preparing theÁ present recommendations  and summarized Finally, it is appropriate to address the question of the the sequence of transitions in this rare-earth silicate as: potential for computer use of the nomenclature. The

400 30 K 415 25 K exchange, storage and retrieval of structural data over the last † † or 0 I and I II; decade has been greatly strengthened by the adoption of the † ! ! where the designation distinguishes the dihydrate from its Crystallographic Information File (CIF; Hall et al., 1991) as the method for submitting manuscripts electronically to the polymorphic anhydride -K3NdSi6O15 (Haile & Wuensch, 2000b). The recommended six-®eld notation for the sequence IUCr for publication. The following discussion of a possible adaptation of this approach to the nomenclature recom- in -K3NdSi6O15 2H2O, retaining the original phase labels, is: Á mended for structural phase transitions in our ®rst Report >1373 415 K Non-ferroic Anhydrous: II (ToleÂdano et al., 1998) and to that in the present Report is 11 873 K †ˆ1 based upon an analysis by I. D. Brown, Chair of the 34 M m

33 873 K Committee for the Maintenance of the Crystallographic †ˆ 1 170 M m Information File Standard (COMCIFS). 415 25 400 30 K Non-ferroic May or may not I † † All symbols used in the recommended nomenclature are insulator contain H O: 2 0 300 K>6 months Pnnm Z 8 Non-ferroic Room-temperature readily represented by ASCII characters using various text ˆ 58 insulator ordering of : conventions. However, the intent of the CIF goes beyond

<400 30 K Pbam † Z 4 Non-ferroic Hydrothermally simple text transcription by using a tag±value pair to identify † 55 ˆ insulator grown:

† particular items of information with a name that labels the

The second, by Gaudin et al. (2000) on Cu7PSe 6 in the same item and a value for that item. A dictionary de®ning these tags journal issue, summarized its sequence of phase transforma- enables the computer to relate given items to any other item in tions as at 250 (1) K and at 320 (1) K. The the CIF. The computer, for example, may thus locate other ! ! recommended six-®eld notation for the transitions in Cu7PSe6, structures with the same item value. retaining the original phase labels, is: The recommended nomenclature symbols are necessarily 320 1 K F43 m Z 4 Non-ferroic Type argyrodite: de®ned rather informally. For example, the label in the ®rst  † ˆ ˆ 216 ionic conductor ®eld is de®ned as that in common use; another user, however, † 320 25 0 K P2 3 Z 4 Non-ferroic Type argyrodite: may assign a different label. This ®eld is hence not, in general, 1 ˆ ˆ 198 unique. The alternative policy of recommending a uniform 250 1 K † Non-ferroic Type argyrodite:  † ˆ rational system for label assignment to each phase is regarded

These reports were probably submitted without knowledge as unlikely to be successful, in view of the long-established of the nomenclature recommendations in I. An obvious tradition of nickname assignment and the diversity of disci- advantage of the Working Group's notation for the ®rst case is plines in which phase transitions are studied. Similarly, the that the properties of the phase sequence are immediately numerical range(s) of the variable(s) de®ning the stability ®eld apparent, rather than dispersed over many pages (the phase is experimental, hence open to change as techniques improve; is reported to grow hydrothermally under conditions similar to thus, the second of the six nomenclature ®elds is in general the phase but not to undergo a transition to the phase). In also bound to lack uniqueness, as are the two ®nal ®elds. both cases, and quite generally, the recommended notation A consequence of the necessarily imprecise phase identi- instantly reveals the potential interest that any material ®ers is that, while the recommended nomenclature per se is exhibiting a phase transition might have for the reader, in a computer readable, its need to provide a compact identi®ca- short and standard format, without a need to search the tion for each phase that is both intuitive and informative literature. It also reveals the conditions and order under which con¯icts with the computer requirements for labels that are the sequence of phases form; in the event that a single par- unique and precise. This con¯ict represents a major problem ameter, such as temperature, is the only variable investigated, that besets the present development of computer-based it enhances the possibility that other variables might be chemical and physical crystallographic information systems. considered. Important missing information associated with the phase transition(s) is immediately revealed; in the case of -K3NdSi6O15 2H2O, the space group and structure of both It is a pleasure to thank Dr David D. Cox for discerning higher-temperatureÁ phases is unknown. In the case of comments on an early draft of the nomenclature proposed for

-Cu7PSe6, its structure has not yet been given but is to be magnetic phases, Dr Eric B. Sirota for a discussion of published. The present primary interest in both materials is n-hexadecane, Professor Y. Ohashi for discussions of photo- related to their conductance. induced structural changes, Professor I. D. Brown for

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