Atomic Displacement Patterns Research Articles

Subterahertz collective dynamics of polar vortices.

The collective dynamics of topological structures1-6 are of interest from both fundamental and applied perspectives. For example, studies of dynamical properties of magnetic vortices and skyrmions3,4 have not only deepened our understanding of many-body physics but also offered potential applications in data processing and storage7. Topological structures constructed from electrical polarization, rather than electron spin, have recently been realized in ferroelectric superlattices5,6, and these are promising for ultrafast electric-field control of topological orders. However, little is known about the dynamics underlying the functionality of such complex extended nanostructures. Here, using terahertz-field excitation and femtosecond X-ray diffraction measurements, we observe ultrafast collective polarization dynamics that are unique to polar vortices, with orders-of-magnitude higher frequencies and smaller lateral size than those of experimentally realized magnetic vortices3. A previously unseen tunable mode, hereafter referred to as a vortexon, emerges in the form of transient arrays of nanoscale circular patterns of atomic displacements, which reverse their vorticity on picosecond timescales. Its frequency is considerably reduced (softened) at a critical strain, indicating a condensation (freezing) of structural dynamics. We use first-principles-based atomistic calculations and phase-field modelling to reveal the microscopic atomic arrangements and corroborate the frequencies of the vortex modes. The discovery of subterahertz collective dynamics in polar vortices opens opportunities for electric-field-driven data processing in topological structures with ultrahigh speed and density.

Optimal transportation of grain boundaries: A forward model for predicting migration mechanisms

It has been hypothesized that the most likely atomic rearrangement mechanism during grain boundary (GB) migration is the one that minimizes the lengths of atomic displacements in the dichromatic pattern. In this work, we recast the problem of atomic displacement minimization during GB migration as an optimal transport (OT) problem. Under the assumption of a small potential energy barrier for atomic rearrangement, the principle of stationary action applied to GB migration is reduced to the determination of the Wasserstein metric for two point sets. In order to test the minimum distance hypothesis, optimal displacement patterns predicted on the basis of a regularized OT based forward model are compared to molecular dynamics (MD) GB migration data for a variety of GB types and temperatures. Limits of applicability of the minimum distance hypothesis and interesting consequences of the OT formulation are discussed in the context of MD data analysis for twist GBs, general Σ3 twin boundaries and a tilt GB that exhibits shear coupling. The forward model may be used to predict atomic displacement patterns for arbitrary disconnection modes and a variety of metastable states, facilitating the analysis of multimodal GB migration data.

Role of Anharmonic Interactions for Vibration Density of States in α-Cristobalite.

The vibrational density of states (VDOS) of solids in the low-energy regime controls the thermal and transport properties of materials, such as heat capacity, heat conduction, free energy and entropy. In α-Cristobalite, the low-frequency part of vibration density of states (VDOS) has many common features with the Boson peak in silica glass of matched densities. Recent theoretical work reported that anharmonic phonon–phonon interactions were critical for the low-frequency part of VDOS in α-Cristobalite. Therefore, it is urgent to identify the role of different anharmonic interactions from first principles. In this paper, we focus on the main peak of the low-frequency part of VDOS in α-Cristobalite. Calculated by our own developed codes and first principles, we find that the quartic anharmonic interaction can increase the frequency of the peak, while the cubic anharmonic can reduce the frequency and change the shape of the peak. Meanwhile, the anharmonic interactions are critical for the temperature effect. Therefore, we calculated the temperature-dependent property of the peak. We find that the frequency of the peak is directly proportional to the temperature. The atomic displacement patterns of different temperatures also confirm the above conclusion. All our calculations converged well. Moreover, our basic results agree well with other published results. Finally, we highlight that our codes offer a general and reliable way to calculate the VDOS with temperature.

Phonons in Short-Period GaN/AlN Superlattices: Group-Theoretical Analysis, Ab initio Calculations, and Raman Spectra.

We report the results of experimental and theoretical studies of phonon modes in GaN/AlN superlattices (SLs) with a period of several atomic layers, grown by submonolayer digital plasma-assisted molecular-beam epitaxy, which have a great potential for use in quantum and stress engineering. Using detailed group-theoretical analysis, the genesis of the SL vibrational modes from the modes of bulk AlN and GaN crystals is established. Ab initio calculations in the framework of the density functional theory, aimed at studying the phonon states, are performed for SLs with both equal and unequal layer thicknesses. The frequencies of the vibrational modes are calculated, and atomic displacement patterns are obtained. Raman spectra are calculated and compared with the experimental ones. The results of the ab initio calculations are in good agreement with the experimental Raman spectra and the results of the group-theoretical analysis. As a result of comprehensive studies, the correlations between the parameters of acoustic and optical phonons and the structure of SLs are obtained. This opens up new possibilities for the analysis of the structural characteristics of short-period GaN/AlN SLs using Raman spectroscopy. The results obtained can be used to optimize the growth technologies aimed to form structurally perfect short-period GaN/AlN SLs.

Raman spectrum of layered tilkerodeite (Pd2HgSe3) topological insulator: the palladium analogue of jacutingaite (Pt2HgSe3)

The layered mineral tilkerodeite (Pd2HgSe3), the palladium analogue of jacutingaite (Pt2HgSe3), is a promising quantum spin hall insulator for low-power nanospintronics. In this context, a fast and reliable assessment of its structure is key for exploring fundamental properties and architecture of new Pd2HgSe3-based devices. Here, we investigate the first-order Raman spectrum in high-quality, single-crystal bulk tilkerodeite, and analyze the wavenumber relation to its isostructural jacutingaite analogue. By using polarized Raman spectroscopy, symmetry analysis, and first-principles calculations, we assigned all the Raman-active phonons in tilkerodeite, unveiling their wavenumbers, atomic displacement patterns, and symmetries. Our calculations used several exchange–correlation functionals within the density functional perturbation theory framework, reproducing both structure and Raman-active phonon wavenumbers in excellent agreement with experiments. Also, it was found that the influence of the spin–orbit coupling can be neglected in the study of these properties. Finally, we compared the wavenumber and atomic displacement patterns of corresponding Raman-active modes in tilkerodeite and jacutingaite, and found that the effect of the Pd and Pt masses can be neglected on reasoning their wavenumber differences. From this analysis, tilkerodeite is found to be mechanically weaker than jacutingaite against the atomic displacement patterns of these modes. Our findings advance the understanding of the structural properties of a recently discovered layered topological insulator, fundamental to further exploring its electronic, optical, thermal, and mechanical properties, and for device fabrication.

Origin of the vortex displacement field in twisted bilayer graphene

A model description of patterns of atomic displacements in twisted bilayer systems has been proposed. The model is based on the consideration of several dislocation ensembles, employing a language that is widely used for grain boundaries and film/substrate systems. We demonstrate explicitly how the dislocation language relates to vortex lattice motives found in experiment and simulations. We show that three ensembles of parallel screw dislocations are sufficient both to describe the rotation of the layers as a whole, and for the vortexlike displacements resulting from elastic relaxation. The results give a clear explanation of the observed features of the structural state such as vortices, accompanied by alternating stacking.

Building ferroelectric from the bottom up: The machine learning analysis of the atomic-scale ferroelectric distortions

Recent advances in scanning transmission electron microscopy (STEM) have enabled direct visualization of the atomic structure of ferroic materials, enabling the determination of atomic column positions with approximately picometer precision. This, in turn, enabled direct mapping of ferroelectric and ferroelastic order parameter fields via the top-down approach, where the atomic coordinates are directly mapped on the mesoscopic order parameters. Here, we explore the alternative bottom-up approach, where the atomic coordinates derived from the STEM image are used to explore the extant atomic displacement patterns in the material and build the collection of the building blocks for the distorted lattice. This approach is illustrated for the La-doped BiFeO3 system.

Nature of localized phonon modes of tilt grain boundaries in graphene

In this work, it is reported an investigation of the phonon spectrum of polycrystalline models of graphene, using ab-initio calculations of the phonon dispersion and phonon modes of these systems. Four different models of polycrystalline graphene are considered: one where the lattices of adjacent grains have a relative translation between them, with a translational grain boundary connecting the grains, and three models where the lattices of adjacent grains are tilted relative to each other, with tilt grain boundaries connecting adjacent grains. It is found that tilt grain boundaries introduce high-frequency non-dispersive phonon modes in the phonon spectrum of polycrystalline graphene, and that these modes are strongly localized in the core of the grain boundaries, while no such high-frequency localized modes are found in the case of the translational boundary system. By computing phonon group velocities and specific heats of each system in our study, and by analyzing in detail the patterns of atomic displacements of these localized modes, a consistent interpretation is provided for the experimentally observed trends of the lattice thermal conductivity of polycrystalline graphene samples, as a function of the grain-boundary tilt angle.

Electronic, Optical, and Lattice Dynamical Properties of Tetracalcium Trialuminate (Ca₄Al₆O13).

The electronic, optical, and lattice dynamical properties of tetracalcium trialuminate (Ca4Al6O13) with a special sodalite cage structure were calculated based on the density functional theory. Theoretical results show that Ca4Al6O13 is ductile and weakly anisotropic. The calculated Young’s modulus and Poisson ratio are 34.18 GPa and 0.32, respectively. Ca4Al6O13 is an indirect-gap semiconductor with a band gap of 5.41 eV. The top of the valence band derives from O 2p states, and the bottom of conduction band consists of Ca 3d states. Transitions from O 2p, 2s states to empty Ca 4s, 3d and Al 3s, 3p states constitute the major peaks of the imaginary part of the dielectric function. Ca4Al6O13 is a good UV absorber for photoelectric devices due to the high absorption coefficient and low reflectivity. The lattice vibration analysis reveals that O atoms contribute to the high-frequency portions of the phonon spectra, while Ca and Al atoms make important contributions to the middle- and low-frequency portions. At the center of the first Brillouin zone, lattice vibrations include the Raman active modes (E, A1), infrared active mode (T2), and silentmodes (T1, A2). Typical atomic displacement patterns were also investigated to understand the vibration modes more intuitively.

Effects of Biaxial Strains and High Pressure on the Structural, Electronic, and Vibrational Properties of DC‐HgM2Te4 (M = Al, In)

First‐principles calculations are performed to study the effects of biaxial strains and high pressure on the structural, electronic, and lattice dynamical properties of defect chalcopyrite HgM2Te4 (M = Al, In) semiconductors. The evolutions of optimized structural parameters, band‐gap energy, crystal‐field splitting energy, and ‐point phonon frequencies with the biaxial strain and pressure have been analyzed. The optimized lattice parameters are reasonable compared with the existing experimental results. Both compounds undergo an indirect to direct band gap transition under tensile , however, the semiconductors retain their indirect band gap character under pressure. The increasing pressure pushes the crystal‐field‐splitting hole (CH) band downwards; in contrast, the increasing biaxial strain makes the CH band shift upwards, which results in that the crystal‐field splitting energies decrease from positive to negative. The pressure‐induced softness of low‐frequency modes around the X point suggests that both compounds become dynamically instable. Atomic displacement patterns show that the high frequency modes are mainly determined by the vibrations of group‐III cations.

Crystal Structure, Defects, Magnetic and Dielectric Properties of the Layered Bi3n+1Ti7Fe3n-3O9n+11 Perovskite-Anatase Intergrowths.

The Bi3n+1Ti7Fe3n-3O9n+11 materials are built of (001)p plane-parallel perovskite blocks with a thickness of n (Ti,Fe)O6 octahedra, separated by periodic translational interfaces. The interfaces are based on anatase-like chains of edge-sharing (Ti,Fe)O6 octahedra. Together with the octahedra of the perovskite blocks, they create S-shaped tunnels stabilized by lone pair Bi3+ cations. In this work, the structure of the n = 4-6 Bi3n+1Ti7Fe3n-3O9n+11 homologues is analyzed in detail using advanced transmission electron microscopy, powder X-ray diffraction, and Mössbauer spectroscopy. The connectivity of the anatase-like chains to the perovskite blocks results in a 3ap periodicity along the interfaces, so that they can be located either on top of each other or with shifts of ±ap along [100]p. The ordered arrangement of the interfaces gives rise to orthorhombic Immm and monoclinic A2/m polymorphs with the unit cell parameters a = 3ap, b = bp, c = 2(n + 1)cp and a = 3ap, b = bp, c = 2(n + 1)cp - ap, respectively. While the n = 3 compound is orthorhombic, the monoclinic modification is more favorable in higher homologues. The Bi3n+1Ti7Fe3n-3O9n+11 structures demonstrate intricate patterns of atomic displacements in the perovskite blocks, which are supported by the stereochemical activity of the Bi3+ cations. These patterns are coupled to the cationic coordination of the oxygen atoms in the (Ti,Fe)O2 layers at the border of the perovskite blocks. The coupling is strong in the n = 3, 4 homologues, but gradually reduces with the increasing thickness of the perovskite blocks, so that, in the n = 6 compound, the dominant mode of atomic displacements is aligned along the interface planes. The displacements in the adjacent perovskite blocks tend to order antiparallel, resulting in an overall antipolar structure. The Bi3n+1Ti7Fe3n-3O9n+11 materials demonstrate an unusual diversity of structure defects. The n = 4-6 homologues are robust antiferromagnets below TN = 135, 220, and 295 K, respectively. They show a high dielectric constant that weakly increases with temperature and is relatively insensitive to the Ti/Fe ratio.

An analysis of the phonon dispersion curves of lead hafnate in the cubic phase using lattice-dynamical models

We have analyzed the phonon dispersion curves in the paraelectric phase of a lead hafnate crystal (PbHfO3) by means of two different lattice-dynamical models. Both the rigid-ion model and the shell one provided an acceptable description of the available experimental data. The atomic displacement patterns were qualitatively different for the two models. In the rigid-ion model the motion in the characteristic low-energy flattened transverse acoustic branch contained both lead and hafnium displacements, while for the shell model it corresponded mainly to lead displacements with the small contribution of oxygen displacements. The shell model allows simultaneous description of the phonon dispersion curves and the correct value of the dielectric constant.

Effects of biaxial strains on the structural, electronic, elastic and lattice vibrational properties in t-BC2N and z-BC2N

The effects of in-plane biaxial strains on the structural, electronic, elastic and lattice dynamical properties of tetragonal t-BC2N and z-BC2N are investigated using first-principles calculations within generalized-gradient approximation (GGA) and HSE06 range-separated hybrid functionals. We find that all the elastic constants, bulk, shear and Young’s moduli decrease (increase) almost linearly with increasing tensile (compressive) strains. However, strain-induced changes in band gaps are highly asymmetric and nonlinear. t-BC2N undergoes an indirect → direct band-gap transition at εxx = −1.36%, whereas z-BC2N is always a direct band-gap material for −2.5% < εxx < 2.5%. The crystal-field splitting energy Δcf decreases from positive to negative at a certain tensile strain. The infrared(IR)-active phonon frequencies exhibit substantial red (blue) shifts under tensile (compressive) strains. The atomic displacement patterns corresponding to typical strong IR-active vibrational modes are analysized. Our calculated results show that strain can serve as an exploitable tool for engineering physical properties of t-BC2N and z-BC2N.

Ab initio investigation of surface phonons on the (001) surface of KCl

Abstract We present an ab initio investigation of localised and resonant phonons on the relaxed KCl(001) surface. Our calculated results are in good accordance with recent high-resolution helium atom scattering measurements. The energy locations and atomic displacement patterns corresponding to a few characteristic surface phonons, such as the Rayleigh, Love, Wallis and Lucas modes, have been identified, and compared and contrasted with their counterparts obtained from a previous shell model calculation.

Factor Group Analysis on the Deformed Pyrochlore-Structure Hydroxyl Transition Metal Halides

Factor group analysis on the deformed pyrochlore-structure hydroxyl transition metal halidesM2(OH)3X(M= Co, Fe and Mn;X= Cl, Br and I) with the crystal symmetry ≡D3d5of space group No. 166 for their infrared (IR) and Raman spectroscopic studies are, for the fist time to the best of our knowledge, reported. Through a standard factor group analysis, we predict that there are 17 IR active normal modes (7A2u+ 10Eu) and 12 Raman active modes (5A1g+ 7Eg), caused by five atomic site groups [HOM3], [OM3], [MO4X2], [ClM3] and [MO6], where the black body letters represent the site atoms. In addition we figure out all the atomic displacement patterns of 12 Raman active normal modes, and point out these results are completely same as those of the famous geometric frustration material Herbertsmithite ZnCu3(OH)6Cl2.

Stability and spectroscopy of Mg sulfate minerals: Role of hydration on sulfur isotope partitioning

We study hydrated magnesium sulfate minerals from first-principles calculations based on density-functional theory. We determine the heat of hydration for MgSO4· n H2O, compute the Raman and infrared spectra for several phases and calculate the S isotope partitioning as a function of hydration. We find that epsomite and meridianiite with, respectively, n = 7 and n = 11 water molecules per MgSO4 unit are particularly stable with respect to other individual or combinations of hydration states. The Raman spectra of all phases present clear SO4 features that are easily identifiable. We use this to show one can use the vibrational spectroscopic information as an identification tool in a remote environment, like the martian surface. We discuss the character and atomic displacement pattern of all vibration modes and compute the 34S/32S partitioning; this work shows that hydration favors enrichment in the lighter S isotope 32S with respect to the heavier 34S, which is accumulated in the less hydrous structures. We show for the first time that the signature of 34S/32S partitioning could be observed by in situ spectroscopy on the surface of Mars. Moreover this can be related to the diurnal cycle of hydration and dehydration and hence it can improve the modeling of the water circulation on Mars.

First-principles study of structural, elastic and lattice dynamical properties of chalcopyrite BeSiV2 and MgSiV2 (V = P, As, Sb)

First-principles calculations of the structural, elastic and lattice dynamical properties of chalcopyrite BeSiV2 and MgSiV2 (V=P, As, Sb) have been performed within density functional theory using norm-conserving pseudopotentials and generalized-gradient approximation. The obtained equilibrium structural parameters are in good agreement with available experimental and theoretical results. Single-crystal elastic constants, linear and volume compressibilities, shear anisotropic factors, as well as polycrystalline bulk, shear and Young’s modulus and Poisson’s ratio have been predicted. Our results show that, compared with BeSiV2, more pronounced tetragonal distortion and larger elastic anisotropy in both compression and shear have been found in MgSiV2 compounds. Chalcopyrite BeSiV2 and MgSiV2 have been classified as brittle and ductile materials, respectively. Phonon dispersion relations, phonon density of states, infrared absorption spectra and Raman scattering spectra have been calculated using the linear response method. Besides, the phonon frequencies and atomic displacement patterns for Raman-active (E, B2, B1 and A1), infrared-active (E and B2), and silent (A2) modes at zone-center Γ point have been analyzed in detail. The character of vibrational spectra have been found to be governed by both chemical bonding strengths and masses of structural units. Moreover, the Si–V bonding is remarkably stronger than the Mg–V bonding in MgSiV2 chalcopyrite semiconductors.

Ab initio investigation of surface phonons on the (0 0 1) surface of ZrC

We presented an ab initio pseudopotential study within the generalized gradient density functional approximation of the structural and electronic properties of the ZrC(001) surface. The calculated structural parameters for the ZrC(001) surface accord very well with previous experimental findings. The ZrC(001) surface is metallic, because at least one surface state crosses the Fermi level in the gap region of the projected electronic spectrum. Using our atomic and electronic structures, surface phonon dispersion curves are calculated by employing a linear response approach on the density functional perturbation theory. The calculated phonon spectrum compares very well with the experimental data. The atomic displacement patterns of the zone-center and zone-edge phonon modes are presented and analyzed for the ZrC(001) surface, carefully. Using this analyzation, energy locations and polarization characteristics of Love, Wallis, Lucas, and Fuchs–Kliewer modes have been determined.

Canonical magnetic insulators with isotropic magnetoelectric coupling

We have performed an exhaustive representation-theory-based search for the simplest structures allowing isotropic magnetoelectric coupling. We find 30 such structures, all sharing a common pattern of atomic displacements in the direction of atomic magnetic moments. We focus on one of these 30 canonical structures and find that it is generically realized in a class of fractionally substituted pyrochlore compounds with an all-in-all-out magnetic order. Furthermore, we find that these substituted pyrochlore compounds have a substantial Chern-Simons orbital magnetoelectric component (\theta=0.1--0.2). While this component is also formally present in strong Z_2 topological insulators (\theta=\pi), its effects are observable there only if time-reversal symmetry is broken at the surface.

Normal mode determination of perovskite crystal structures with octahedral rotations: theory and applications

Nuclear site analysis methods are used to enumerate the normal modes of ABX3 perovskite polymorphs with octahedral rotations. We provide the modes of the 14 subgroups of the cubic aristotype describing the Glazer octahedral tilt patterns, which are obtained from rotations of the BX6 octahedra with different sense and amplitude about high-symmetry axes. We tabulate all normal modes of each tilt system and specify the contribution of each atomic species to the mode displacement pattern, elucidating the physical meaning of the symmetry unique modes. We have systematically generated 705 schematic atomic displacement patterns for the normal modes of all 15 (14 rotated + 1 unrotated) Glazer tilt systems. We show through some illustrative examples how to use these tables to identify the octahedral rotations, symmetric breathing, and first-order Jahn–Teller anti-symmetric breathing distortions of the BX6 octahedra, and the associated Raman selection rules. We anticipate that these tables and schematics will be useful in understanding the lattice dynamics of bulk perovskites and could serve as a reference point in elucidating the atomic origins of a wide range of physical properties of synthetic perovskite thin films and superlattices.