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
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
Document status and date: Published: 01/01/2001
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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 magnetic structure 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 ferromagnetism 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 space group. 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; 0
F <1040 K Im3m 229 P; Z 2 Ferromagnet Easy magnetization The recommendation in I for this ®eld is to provide the 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- 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 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 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 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; 0 IC 10:1 11:1K; C2=m P; Z 4 Amplitude 0:15 0:075; <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 0 9:8K; 0:7T: 12 1; 1; 1 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 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 <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
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- 0K; 4:8T 12 0; 1; 0:25 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 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 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; 0 uniform as possible for the various types of phase system leads AF <3:05 K I4=m 87 P; Z 2 Antiferromagnet Spins 001 ; k 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 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 Quasicrystalline Q II 0:1 Ti I2=a ZA 4 Non-ferroic Icommensurate: 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 II 630 130 K Pnam Z 4 Ferroelastic 3 variants modulation wavevector. It also provides a uni®ed nomen- 62 clature scheme for the incommensurate and the magnetic III 130 93 K Pnam ZA 4 Ferroelastic Incommensurate: 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;0; 0 and ferroelastic 6 variants:
It is recommended that, as with ordinary structural phase Pna2 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 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 II 850 570 K P4bm Z 1 Ferroelectric 2 variants: 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 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 follows: 35 1 0 =4; and ferroelastic 0 0 in certain 1 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 literature parameters: number for propagation acter and V <110 K P4bm ? ZA 1 Ferroelectric Re-entrant phase 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 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 II 123 112 K P63=mmc ZA 2 Non-ferroic Incommensurate: I >164 K Pnma Z 4 Non-ferroic 4 GPa;>230 K 62 194 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; 0:29: referred hexagonal direc-