Coh et al. presented in [Phys. Rev. B 88, 121106(R) (2013)] a systematic search of the simplest so-called “canonical” structures allowing isotropic magnetoelectric response, and reported a total of 30 such magnetic configurations. Using magnetic symmetry we show in this Comment that this listing is severely incomplete, and 14 additional distinct cases satisfying the same conditions should be added. The complete list of these elementary magnetic arrangements is then presented in a short and efficient form as distinct Wyckoff positions of some cubic magnetic space groups.

The numerous structures that have been reported for the different phases of the lead zirconate titanate system, PbZr_1-xTi_xO₃ (PZT), are analysed by means of a systematic symmetry-mode analysis. The distortion corresponding to the order parameter has been separated out and expressed in all phases in a comparable form. The fact that the physical origin of the PZT phases is an unstable threefold degenerate polar mode, plus in some cases an unstable octahedral tilting mode, produces structural correlations between the different phases. These correlations had remained unnoticed until now but are directly observable in a mode parameterization. They can be used both to characterize the evolution of the order parameters through the phase diagram and as a stringent test of the reported structural models. It is further shown that the activity of a single polar mode yields a specific feature in the mode decomposition of the monoclinic phases. This single-mode signature can be observed in the majority of the monoclinic structures proposed, making the others questionable. In fact, this internal constraint is satisfied by PZT to such a high degree that it drastically reduces the number of effective structural degrees of freedom. It is conjectured that this type of structural constraint beyond space-group symmetry can be a rather general property of low-symmetry distorted structures. As shown here, its existence can be detected and assessed by a symmetry-mode analysis, if considered in relation to the single underlying multidimensional order parameter.

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.

MAGNEXT is a new computer program available from the Bilbao Crystallographic Server (http://www.cryst.ehu.es) that provides symmetry-forced systematic absences or extinction rules of magnetic non-polarized neutron diffraction. For any chosen Shubnikov magnetic space group, the program lists all systematic absences, and it can also be used to obtain the list of the magnetic space groups compatible with a particular set of observed systematic absences. Absences corresponding to specific ordering modes can be derived by introducing effective symmetry operations associated with them. Although systematic extinctions in neutron diffraction do not possess the strong sym- metry resolving power of those in non-magnetic crystallography, they can be important for the determination of some magnetic structures. In addition, MAGNEXT provides the symmetry-adapted form of the magnetic structure factor for different types of diffraction vectors, which can then be used to predict additional extinctions caused by some prevailing orientation of the atomic magnetic moments. This program, together with a database containing comprehensive general information on the symmetry operations and the Wyckoff positions of the 1651 magnetic space groups, is the starting point of a new section in the Bilbao Crystallographic Server devoted to magnetic symmetry and its applications.

The Bilbao Crystallographic Server is a web site with crystallographic databases and programs available online (www.cryst.ehu.es). It has been operating for more than ten years and new applications are being added regularly. The programs available on the server do not need a local installation and can be used free of charge. The server gives access to general information related to crystallographic symmetry groups (generators, general and special positions, maximal subgroups, Brillouin zones, etc.). Apart from the simple tools for retrieving the stored data, there are programs for the analysis of group-subgroup relations between space groups. There are also software package studying specific problems of solid-state physics, structural chemistry and crystallography.

Until recently, many computational materials scientists have shown little interest in materials databases. This is now changing because the amount of computational data is rapidly increasing and the potential for data mining provides unique opportunities for discovery and optimization. Here, a few examples of such opportunities are discussed relating to structural analysis and classification, discovery of correlations between materials properties, and discovery of unsuspected compounds.

New ferroelectrics can be predicted by considering the existence of pseudosymmetry with respect to a higher symmetry structure using the so-called atomic displacement method and investigating the minimal supergroups of the given structure's space group. This analysis can be performed with the new version of the computer program PSEUDO, located at the Bilbao Crystallographic Server. After defining the procedures for the detection and quantification of pseudosymmetry, we present the new program, illustrating its use with worked cases of polar structures from the literature which are either known or reported as possible ferroelectrics.

First-principles electronic structure calculations predict the existence of a crystalline compound in the Au-Ge system. The structure is found by matching the theoretically determined local atomic structure in the liquid state with that for experimentally known crystal structures in other alloys. Subsequently, the best matching crystalline structures were structurally optimized using first-principles methods. Surprisingly, although Au-Ge is known as a non-compound-forming system, a crystal structure was found to be more stable than the terminal phases by about 6 meV/atom at T=0K. Possibly, this structure can be prepared by a suitably chosen substrate such as Pt₅P₂.

We report the results of first-principles molecular-dynamics simulations for liquid and undercooled eutectic Au₈₁Si₁₉ alloys at various temperatures. Through comparisons between Au₈₁Si₁₉ and Au liquids, we show the strong effects of Si alloying on the atomic-scale structure, namely the occurrence of a well-defined chemical short-range order and the slowing of the formation of icosahedral local motifs as a function of temperature. Such a behavior may explain the stability of the liquid phase at the eutectic composition by an enhancement of AuSi interactions. In examining the dynamic properties of both systems, we demonstrate a strong interplay between these structural changes and the evolution of diffusivity at low temperatures. All these results yield a possible scenario for the occurrence of such an unusual deep eutectic point.

A new crystalline ground state was discovered in the Au–Si system through first-principles electronic structure calculations. The new structure was found using the experimentally and theoretically determined local atomic structure in the liquid as a guide for the solid state. Local atomic structure in the liquid was matched with that for all known crystal structures as compiled in the Pauling File structural database. The best matching crystalline structures were then explicitly calculated using first-principles methods. Most candidate crystal structures were found to be close, but above the enthalpy of a composition weighted average of the face-centered cubic Au and diamond structure Si terminal phases, but one crystal structure was more stable than the terminal phases by about 10meV/atom at T=0K. As first-principles simulations of local structure are feasible for most liquid alloys, the present methodology is applicable to other alloys lying near a eutectic composition.

A system containing two nanogears and two nanotubes acting as shafts is designed. Then, it is checked to see whether it is a stable one by means of the molecular mechanics simulation. After it was ensured that the system was suitable for consideration, molecular dynamics were applied but from the results it was observed that the selected potential was not appropriate by itself alone and reconsideration showed that improvements were to be made. This resulted in introduction of an additional potential and the simulations yielded more realistic results. As the outcome, acceleration is observed on the rotor nanogear causing the rotor nanogear to rotate faster than the motor nanogear driving it but both the snapshots of the system and the angular velocity progress showed that the rotor nanogear eventually slows down and waits until the next effective tooth of the motor nanogear comes into the vicinity, making the designed system a candidate to be used in future applications

Structural stabilities of different types of carbon nanogears have been tested against temperature by means of Molecular Dynamics procedure. Effects of periodic boundary conditions were also examined. It has been found that although the two types of nanogears (armchair and zigzag CNT yielding) investigated look similar in configuration, when tested against high temperatures, bond breakings and deformations occur at different regions.

A method for generating various forms of junctions involving armchair and zig-zag nanotubes, firstly introduced by Zsoldos et al., is developed to cover all types of armchair and zig-zag nanotubes in a systematical way. This method can also be used to produce nanogears and toothed canals. The method is explained and flowcharts are included to aid in programming into a code.

Thermal stability and molecular electronic properties of a single walled, bamboo shaped carbon naotube has been investigated. Molecular dynamics method is applied to investigate thermal stability, and the electronic properties are calculated at the Extended Hückel level. Although bamboo shaped carbon nanotubes observed in experimental literature are multi-walled, it is shown that the suggested structural model in this work, which is single-walled, is also both thermodynamically and energetically stable. Bamboo shape of the model investigated is due to periodical coronene-like spacers. The resultant structure is compartmented, having geometrical aberrations in the vicinity of spacers. There is no degredation in the average coordination number. The geometrical aberrations in the vicinity of spacers are due to curvature induced by the pentagons of the resultant geometry.

The structural stability of carbon nanotori have been investigated by performing molecular-dynamics simulations. The systems considered are C₁₇₀, C₂₅₀, C₃₆₀, C₅₂₀ and C₇₅₀ tori, which have been constructed using a recently developed algorithm based on the idea of Fonseca et al. Calculations, have been realized bu using an empirical many-body potential energy function for carbon. It has been found that all the nanotori considered are stable under heat treatment.

Junction formation in crossed C(10,0) single wall carbon nanotubes under pressure has been investigated, using classical molecular-dynamics simulations at 1 K. It has been found that a stable mechanical juntion was formed by means of placing two crossed single wall carbon nanotubes between two rigid graphene layers which move toward each other.

Various molecular electronic properties of boron-nitride nanotube ring doped four different single-wall carbon nanotubes are investigated theoretically by performing self-consistent-field molecular-orbital semi-empirical and density functional theory calculations. Results are compared with corresponding carbon nanotubes. It is seen that polar nature of the boron-nitride nanotube ring lead to a spontaneous polarization, an electrostatic potential barrier occurs in metallic carbon nanotube models, and these models may be obtained exothermically from carbon nanotubes.

The structural and electronic properties of armchair and zigzag models of single-wall GaN nanotubes have been investigated by performing semi-empirical molecular orbital self-consistent field calculations at the level of PM3 method within the RHF formulation. It has been found that these structures are stable and endothermic. The armchair model has zero net dipole moment, whereas the zigzag model has nonzero net dipole moment. It has been found that GaN armchair tube with even number of hexagonal rings on the circumference has more excess charge on it and thus this tube may have better conducting properties, they may be candidates to be used as good conducting nanowires.

Electronic properties of five carbon nanotori (C₁₇₀, C₂₅₀, C₃₆₀, C₅₂₀ and C₇₅₀) have been investigated by performing Extended-Hückel type calculations. Carbon nanotori considered is of Fonseca type having five-fold symmetry. It has been found that highest occupied molecular orbital - lowest unoccupied molecular orbital gaps of nanotori are very small, thus they may contain mobile electrons; pentagons and heptagons in the knee-regions act as an electron trap; and all the nanotori have a DOS distribution with common features.

An algorithm to generate toroidal or helical cage structures has been developed. Any toroidal or helical structure can be generated following four stages. In the first stage a Fonseca type unit cell and its symmetrical counterpart is formed which represents one-fifth of a toroid. In the second stage one-fifth fragment of the torus is fully obtained by applying geometry optimization to the structure obtained in the first stage. In the third stage the torus fragment obtained in the second stage is reproduced five times and connected to each other to generate either toroidal or helical structure. In the last stage a final optimization process is reapplied to get the complete structure desired.

We have investigated the Casimir-Polder effect for various geometries such as concentric spherical shells, a spherical shell within a cubic shell and spherical shell within a pyramidal shell. Simulations have been performed by static calculations. Simulation results agreed with theoretical predictions.