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The two commonly used systems of magnetic space-group (MSG) symbols, with accompanying numbers and settings, are those of Belov-Neronova-Smirnova (BNS) and Opechowski-Guccione (OG). The symbols from both systems have been used for several decades now. Both have advantages and disadvantages. Both present challenges of interpretation to novice and expert users alike, which can inhibit understanding and lead to errors in published magnetic structures. To address each of these challenges going forward, a new unified (UNI) MSG symbol is introduced, which combines a modified BNS symbol with essential information from the OG symbol.
Assuntos
Fenômenos MagnéticosRESUMO
The high-temperature phase behaviour of the ferroelectric layered perovskite Bi4Ti3O12 has been re-examined by high-resolution powder neutron diffraction. Previous studies, both experimental and theoretical, had suggested conflicting structural models and phase transition sequences, exacerbated by the complex interplay of several competing structural instabilities. This study confirms that Bi4Ti3O12 undergoes two separate structural transitions from the aristotype tetragonal phase (space group I4/mmm) to the ambient-temperature ferroelectric phase (confirmed as monoclinic, B1a1). An unusual, and previously unconsidered, intermediate paraelectric phase is suggested to exist above T C with tetragonal symmetry, space group P4/mbm. This phase is peculiar in displaying a unique type of octahedral tilting, in which the triple perovskite blocks of the layered structure alternate between tilted and untilted. This is rationalized in terms of the bonding requirements of the Bi3+ cations within the perovskite blocks.
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Two new programs, MTENSOR and TENSOR, hosted on the open-access website known as the Bilbao Crystallographic Server, are presented. The programs provide automatically the symmetry-adapted form of tensor properties for any magnetic or non-magnetic point group or space group. The tensor is chosen from a list of 144 known tensor properties gathered from the scientific literature or, alternatively, the user can also build a tensor that possesses an arbitrary intrinsic symmetry. Four different tensor types are considered: equilibrium, transport, optical and nonlinear optical susceptibility tensors. For magnetically ordered structures, special attention is devoted to a detailed discussion of the transformation rules of the tensors under the time-reversal operation 1'. It is emphasized that for non-equilibrium properties it is the Onsager theorem, and not the constitutive relationships, that indicates how these tensors transform under 1'. In this way it is not necessary to restrict the validity of Neumann's principle. New Jahn symbols describing the intrinsic symmetry of the tensors are introduced for several transport and optical properties. In the case of some nonlinear optical susceptibilities of practical interest, an intuitive method is proposed based on simple diagrams, which allows easy deduction of the action of 1' on the susceptibilities. This topic has not received sufficient attention in the literature and, in fact, it is usual to find published results where the symmetry restrictions for such tensors are incomplete.
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We report here on the characterization of the vacancy-ordered perovskite-type structure of BaFeO2.5 by means of combined Rietveld analysis of powder X-ray and neutron diffraction data. The compound crystallizes in the monoclinic space group P2(1)/c [a = 6.9753(1) Å, b = 11.7281(2) Å, c = 23.4507(4) Å, ß = 98.813(1)°, and Z = 28] containing seven crystallographically different iron atoms. The coordination scheme is determined to be Ba7(FeO4/2)1(FeO3/2O1/1)3(FeO5/2)2(FeO6/2)1 = Ba7Fe([6])1Fe([5])2Fe([4])4O17.5 and is in agreement with the (57)Fe Mössbauer spectra and density functional theory based calculations. To our knowledge, the structure of BaFeO2.5 is the most complicated perovskite-type superstructure reported so far (largest primitive cell, number of ABX2.5 units per unit cell, and number of different crystallographic sites). The magnetic structure was determined from the powder neutron diffraction data and can be understood in terms of "G-type" antiferromagnetic ordering between connected iron-containing polyhedra, in agreement with field-sweep and zero-field-cooled/field-cooled measurements.
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The Brillouin-zone database of the Bilbao Crystallographic Server (http://www.cryst.ehu.es) offers k-vector tables and figures which form the background of a classification of the irreducible representations of all 230 space groups. The symmetry properties of the wavevectors are described by the so-called reciprocal-space groups and this classification scheme is compared with the classification of Cracknell et al. [Kronecker Product Tables, Vol. 1, General Introduction and Tables of Irreducible Representations of Space Groups (1979). New York: IFI/Plenum]. The compilation provides a solution to the problems of uniqueness and completeness of space-group representations by specifying the independent parameter ranges of general and special k vectors. Guides to the k-vector tables and figures explain the content and arrangement of the data. Recent improvements and modifications of the Brillouin-zone database, including new tables and figures for the trigonal, hexagonal and monoclinic space groups, are discussed in detail and illustrated by several examples.
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The systematic use of symmetry arguments, with inclusion of magnetic symmetry, is scarce in the investigation of magnetic materials. This is an unfortunate situation particularly when multiferroics are being studied. The lack of a consistent complete symmetry framework often prevents the distinction of what is the signature of a specific atomic mechanism and what is symmetry-forced and therefore common to any possible underlying microscopic model. Here the recently reported magnetoelectric properties of Ba(2)CoGe(2)O(7) [Murakawa et al. (2010). Phys. Rev. Lett. 105, 137202] are discussed as an extreme example of this situation, and it is shown how three of the four magnetoelectric responses that have been reported for this compound can be predicted by symmetry considerations without appealing to any specific atomic mechanism.
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The structure of the compound Ba(1 + x)Ni(x)Rh(1 - x)O3 [x = 0.1170 (5)] has been analyzed at room temperature within the (3 + 1)-dimensional superspace approach using single-crystal X-ray diffraction data. Two different models are presented, the compound is refined as modulated composite as well as modulated-layer structure. In both models discontinuous atomic domains are applied to describe the structural modulations. While the first approach stresses the pseudo-one-dimensional constitution, the latter highlights the layered character of these structures.
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The recently determined structure of NaCa(4)Nb(5)O(17) is reanalyzed within the superspace framework. The material follows the general features of the superspace model proposed for the perovskite-related compounds of the general formula A(n)B(n)O(3n+2) [Elcoro et al. (2001). Acta Cryst. B57, 471-484]. It can be described as a commensurate modulated structure with discontinuous atomic domains given by occupational crenel functions. These atomic domains automatically introduce the layered configuration of the actual structure in real space. However, the displacive modulations follow a quite different pattern from that observed in the Sr(n)(Nb,Ti)(n)O(3n+2) series, discussed in the above-mentioned reference. The superspace group relevant in this new case has been identified through a systematic search of all the possible groups and a comparison of the resulting superspace embeddings of the experimental three-dimensional structure. Being a commensurate structure, the fundamental ambiguity of the superspace description was broken by choosing the highest possible symmetry that yields smooth displacive atomic modulations and hence minimizes the number of parameters. The efficiency of the proposed superspace model is demonstrated with a new refinement of the structure. Assuming the model's general relevance, symmetry properties for the whole [Ca,Na](n)Nb(n)O(3n+2) series are predicted.
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The structures of the trigonal compounds A(1+x)A(x')B(1-x)O(3) are described, to a first approximation, as a hexagonal close-packed stacking of A(3)O(9) and A(3)A'O(6) layers. However, quantitative analyses are usually performed in superspace, with the structures considered as modulated composites made of two subsystems: chains of A cations, and columns of trigonal prisms, A'O(6), and octahedra, BO(6). It is demonstrated that an alternative superspace description as a single modulated structure can be found in terms of the aforementioned layers, with a composition-dependent modulation parameter and discontinuous atomic domains. In this approach, these compounds fulfill layer-stacking rules analogous to those observed in other layered compounds. These rules translate into a so-called closeness condition for the discontinuous atomic domains in superspace; this condition is analogous to that postulated in quasicrystals. Both superspace models, the composite and the layered model, when considered without displacive modulations, can be taken as two limiting idealized paradigms and can be used as the starting point of a structure refinement. As an example, the structure of the trigonal phase Sr(6)Rh(5)O(15), which was previously refined as a modulated composite [Stitzer, El Abed et al. (2001), J. Am. Chem. Soc. 123, 8790-8796], has been refined anew, with equivalent results, as a single modulated structure taking as reference the ideal layered structure. A similar superspace layer description is applied to the recently reported orthorhombic family A(4m+4n)A(n')B(4m+2n)O(12m+9n). This description allows the a priori derivation of a refineable superspace model that includes the superspace symmetry and crenel functions and is valid for the whole family. This model has been successfully applied to the refinement of the compound Ba(12)Co(11)O(33) [Darriet et al. (2002), Chem. Mater. 14, 3349-3363].
