Small Atomic Displacements Research Articles

Collective oscillations of systems of Xe atoms in a groove between two carbon nanotubes

The collective oscillations of systems of Xe atoms adsorbed in a groove between two carbon nanotubes have been studied by the method of molecular dynamics. The one-dimensional and three-chain structures of atoms that appear in such grooves are considered depending on the number of particles, temperature, and external potentials. It is shown that the infinite one-dimensional structures of Xe atoms are stable at finite temperatures only in the presence of such potentials acting in the direction normal to the axis of the structure. The oscillation spectrum is found, which is in accordance with theoretical calculations of the dispersion laws of collective modes. Collective oscillations of three-chain structures have been studied. The theoretical calculation of the laws of dispersion of modes, carried out by the method of equations of motion for small displacements of atoms from the equilibrium position, showed that the collective modes of the system show a great similarity with the corresponding dispersion laws of a one-dimensional chain of atoms. At the same time, it was found that a torsion mode arises, which is characteristic of a three-chain structure. The calculation agrees well with the spectrum of oscillations obtained by the molecular dynamics method. Using the established mode dispersion, the heat capacity of Xe chains is calculated within the framework of the Einstein model. The calculation results are in good agreement with the experimental data in the temperature range of up to 35–40 K, which can be explained if we assume the presence of both one-dimensional and three-chain structures of Xe atoms adsorbed in the grooves between carbon nanotubes. The effect of temperature on the stability of Xe atomic structures on nanotubes has been studied, and it has been shown that one-dimensional structures start to defragment at temperatures higher than 60 K, whereas three-chain structures defragment at temperatures higher than 90 K.

Charge density wave surface reconstruction in a van der Waals layered material

Surface reconstruction plays a vital role in determining the surface electronic structure and chemistry of semiconductors and metal oxides. However, it has been commonly believed that surface reconstruction does not occur in van der Waals layered materials, as they do not undergo significant bond breaking during surface formation. In this study, we present evidence that charge density wave (CDW) order in these materials can, in fact, cause CDW surface reconstruction through interlayer coupling. Using density functional theory calculations on the 1T-TaS2 surface, we reveal that CDW reconstruction, involving concerted small atomic displacements in the subsurface layer, results in a significant modification of the surface electronic structure, transforming it from a Mott insulator to a band insulator. This new form of surface reconstruction explains several previously unexplained observations on the 1T-TaS2 surface and has important implications for interpreting surface phenomena in CDW-ordered layered materials.

Ni3Sn4 and FeAl2 as vacancy variants of the W-type (“bcc”) structure

Abstract Systematization of the vast number of known crystal structures of intermetallic phases is a challenge. One previously proposed group is referred to here as vacancy variants of the W-type structure. Members of this group, may, however, not be easily recognized because of the structural irregularity introduced by the vacancies. Descriptions of the experimentally observed crystal structures of Ni3Sn4 and FeAl2 in terms of vacancy variants of the W-type structure are, respectively, derived by establishing a lattice correspondence with the W-type structure, allowing, in particular, identification of the vacant sites. In both cases only small deviatoric strains are required to obtain the experimentally encountered lattice parameters, and generally small atomic displacements occur from the ideal positions, thus demonstrating significance of the lattice correspondence. The lattice correspondences allow, for both Ni3Sn4 and FeAl2, relating reported microstructure evidence (directions/planes occurring in orientation relationships and crystal habits but also on twinning and slip) with such typical for metals and solid solutions with W-type (“bcc”) structures. This demonstrates that the established lattice correspondences have a significance going beyond a descriptive one, but the underlying W-type structures reveal themselves in the materials’ behavior.

Elastic modelling of lattice distortions in concentrated random alloys

Lattice distortions, i.e. small atomic displacements away from the average lattice, are linked to a number of functional and mechanical properties of concentrated metallic alloys, particularly their yield strength. Here we develop an elastic model of lattice distortions where every atom is modeled as an Eshelby inclusion in a homogeneous elastic matrix. Local environment effects are included by considering fluctuating anisotropic eigenstrain tensors associated to the inclusions. The model is tested on several concentrated alloys, face-centered cubic (FCC) AlMg and FeNiCr alloys, as well as a fictitious body-centered cubic (BCC) binary alloy to study systematically and independently the effects of a size and an elastic modulus mismatch between the constituents. The elastic model predicts lattice distortions well when the size and elastic modulus mismatches are typically less than 5% and 25%, respectively. Interestingly, we find that when the size mismatch is small, as in FeNiCr alloys, the lattice distortion is dominated by the fluctuations of the dilatational eigenstrains rather than their average value as often assumed in elastic models of concentrated alloys. Moreover, models usually assume homogeneous elastic constants, while the limit obtained here of 25% is often exceeded in concentrated alloys, particularly with a BCC structure.

Symmetry relation database and its application to ferroelectric materials discovery

The ability to understand the atomistic mechanisms that occur in the solid phase transition is of crucial importance in materials research. To investigate the displacive phase transition at the atomic scale, we have implemented a numerical algorithm to automate the detection of the symmetry relations between any two candidate crystal structures. Using this algorithm, we systematically screen all possible polar-nonpolar structure pairs from the entire Materials Project database and establish a database of $\sim$4500 pairs that possess a close symmetry relation. These pairs can be connected through a continuous phase transition with small atomic displacements. From this database, we identify several new ferroelectric materials that have never been reported in the past. In addition to the screening of ferroelectric materials, the symmetry relation database may also be used for other areas, such as material structure prediction and new materials discovery.

The seeds and homogeneous nucleation of photoinduced nonthermal melting in semiconductors due to self-amplified local dynamic instability.

Laser-induced nonthermal melting in semiconductors has been studied over the past four decades, but the underlying mechanism is still under debate. Here, by using an advanced real-time time-dependent density functional theory simulation, we reveal that the photoexcitation-induced ultrafast nonthermal melting in silicon occurs via homogeneous nucleation with random seeds originating from a self-amplified local dynamic instability. Because of this local dynamic instability, any initial small random thermal displacements of atoms can be amplified by a charge transfer of photoexcited carriers, which, in turn, creates a local self-trapping center for the excited carriers and yields the random nucleation seeds. Because a sufficient amount of photoexcited hot carriers must be cooled down to band edges before participating in the self-amplification of local lattice distortions, the time needed for hot carrier cooling is the response for the longer melting time scales at shorter laser wavelengths. This finding provides fresh insights into photoinduced ultrafast nonthermal melting.

The structure and collective oscillations of linear systems of particles with van der Waals interaction

The simulation of a system of particles, located in the plane, with van der Waals interaction described by the Lennard-Jones potential is carried out. The possibility of the existence of a solitary chain of particles, as well as the formation of linear systems of two and three chains, has been established. The spectrum of vibrations of the systems was determined for various configurations and the characteristic frequencies of the vibrations were found. The dispersion law of collective modes is calculated theoretically by the method of equations of motion for small displacements of atoms from their equilibrium position when analyzing the compatibility condition for the arising system of equations. The obtained values of the characteristic frequencies are in rather good agreement with the results obtained in the Fourier analysis of the time dependence of the displacements of particles from their equilibrium positions along and across the system.

Tracing microscopic atomic displacements using polarized Raman spectroscopy: a case study on BaTiO3

Here, we demonstrate the power of polarized Raman spectroscopy (PRS) in tracing microscopic atomic displacements in a single crystalline material. Crystalline materials often show extremely small microscopic atomic displacements as a function of temperature, pressure, electric and magnetic field or across phase transition which can be traced by our defined method using routinely available Raman spectrometers and with the knowledge of Raman tensors and phonon deformation potentials. Importantly, the information is directional and provides a vital information about the root cause of polarization in ferroelectrics, multiferroics. In this article, the method is demonstrated by carrying out the temperature and directional dependent PRS study on BaTiO3 single crystal, where the Ti ion displacement across the various phase transitions is well documented. The value of the ferroelectric polarization and its component along different crystallographic axes as well as their temperature variations calculated from the Ti displacement obtained by our defined method matches well with the reported results obtained from other techniques. This method thus can be applied to obtain quantitative information of atomic displacements in a crystalline solid.

Simple model of nitrogen protrusions forming nanostripes within hexagonal FeN on Cu(001)

Hexagonal FeN monolayers on Cu(001) show a stripe pattern composed of dark and bright stripes as observed recently by scanning tunneling microscopy (STM). The nanostripes are formed by more or less protruded nitrogen atoms in the center of iron triangles. Here a simple model is proposed to interpret those results. It uses a planar Fourier analysis with two different wave vectors to calculate small displacements of Fe atoms caused by lattice mismatch stress. The area of displaced Fe atom triangles is used as a measure for the protrusion of N atoms in their center. Proper selection of the wave vectors allows to visualize the dominant protrusions of (3×3) ordered nitrogen atoms. The wave vectors selected are related to Fe configurations which minimize lattice mismatch stress. Hard spheres are used to model Cu-Fe and Fe-Fe interactions in search of a minimal configuration energy. The model explains key elements of the stripe configuration. The model is kept simple, so just the most basic features of the STM experiments are covered. The limits of the model are discussed and ways for extending it are proposed.

Anisotropic Electron Conductance Driven by Reaction Byproducts on a Porous Network of Dibromobenzothiadiazole on Cu(110).

Efficiency in charge-transport is a fundamental but demanding prerequisite to allow better exploitation of molecular functionalities in organic electronics and energy-conversion systems. Here, we report on a mechanism that enables a one-dimensional conductance structure by connecting discrete molecular states at 2.1 eV through the pores of a metal-organic network on Cu(110). Two adjacent, periodic and isoenergetic contributions, namely a molecular resonance and the confined surface-state, add-up leading to anisotropic structures, as channels, observable in real-space conductance images. The adsorption configurations of Br atoms, inorganic byproduct of the redox-reacted 4,7-dibromobenzo[c]-1,2,5-thiadiazole (2Br-BTD) molecules on the copper surface, drive the confinement of the Cu surface state within the pores and critically control the channel continuity. Small displacements of the Br atoms change the local surface potential misaligning the energy levels. This work visualizes the effect of order-disorder transitions caused by the movement of single atoms in the electronic properties of two-dimensional organic networks.

Pressure effect on structural stability and optical absorption of triclinic NbS3 from DFT and many-body perturbation calculations

In this paper, we investigated the structural stability, mechanical, vibrational, electronic, and optical properties; and the exciton binding energy of the quasi 1D transition metal trichalcogenide NbS3 under pressure. The structural properties are in good agreement with previous computational and experimental studies. Calculated elastic constants satisfy the Born stability criteria and suggest that NbS3 is mechanically stable against distortion under pressure up to 4.84 GPa. Vibrational properties via phonon calculations showed that NbS3 is dynamically stable when submitted to small atomic displacements. The results predict the maximum optical absorption coefficient of the bulk NbS3 at 5.13 × 105 cm−1 and it occurs in the visible range spectrum at 3.09 eV. From G0W0 and BSE calculations, we found that the size of the optical bandgap reduces from 1.01 to 0.48 eV as the pressure increases from 0 to 4 GPa. Our calculations also predicted the existence of bound excitons with binding energy ranges from 130 to 160 meV.

Structure of amorphous Cu2GeTe3 and the implications for its phase-change properties

The structure of amorphous ${\mathrm{Cu}}_{2}{\mathrm{GeTe}}_{3}$ is investigated by a combination of anomalous x-ray scattering and extended x-ray absorption fine-structure experiments. The experimental data are analyzed with reverse Monte Carlo modeling, and they are interpreted in terms of short-range-order parameters as well as by using ring statistics and persistent homology to study the intermediate-range order. Based on this information, the structural relationship of the amorphous phase to the corresponding crystal is discussed. It is found that the amorphous network can be rationalized by small atomic displacements of the crystal structure, directed toward the intrinsic void regions. This structural similarity establishes the possibility of a fast phase-change process. On the other hand, the atomic rearrangements also lead to the formation of new chemical bonds and to distortions on the intermediate-range-order level. These are realized by a collapse and contraction of the strict hexagonal ring arrangements of the crystal and by the formation of small, triangular rings as well as Cu cluster configurations. These structural features allow for a new understanding of the phase-change property contrast of this material, especially concerning the density change and the optical contrast.

X-ray dose-dependent structural changes of the [2Fe-2S] ferredoxin from Chlamydomonas reinhardtii.

Plant-type ferredoxin (Fd) is an electron transfer protein in chloroplast. Redox-dependent structural change of Fd controls its association with and dissociation from Fd-dependent enzymes. Among many X-ray structures of oxidized Fd have been reported so far, very likely a given number of them was partially reduced by strong X-ray. To understand the precise structural change between reduced and oxidized Fd, it is important to know whether the crystals of oxidized Fd may or may not be reduced during the X-ray experiment. We prepared the thin plate-shaped Fd crystals from Chlamydomonas reinhardtii and monitored its absorption spectra during experiment. Absorption spectra of oxidized Fd crystals were clearly changed to that of reduced form in an X-ray dose-dependent manner. In another independent experiment, the X-ray diffraction images obtained from different parts of one single crystal were sorted and merged to form two datasets with low and high X-ray doses. An Fo-Fo map calculated from the two datasets showed that X-ray reduction causes a small displacement of the iron atoms in the [2Fe-2S] cluster. Both our spectroscopic and crystallographic studies confirm X-ray dose-dependent reduction of Fd, and suggest a structural basis for its initial reduction step especially in the core of the cluster.

Hierarchical twin microstructure in modulated 10M Ni–Mn-Ga single crystals. An analysis including shuffling of atomic layers

The trained and self-accommodated martensite microstructures of 10M Ni–Mn-Ga single crystals were studied by back scattered electron imaging and electron backscatter diffraction in a scanning electron microscope. These data were then compared with theoretical calculations using a long periodic commensurate modulated monoclinic lattice and Gautam and Howe (G-H) model in order to establish twin boundary (TB) hierarchy according to their surface energy. The whole spectrum of TBs including type I, type II, and compound twins were detected and theoretically predicted. Using the G-H model and long periodic structure along with a small displacement of atoms connected with lattice modulation allowed to calculate all twin elements including their surface energy. These data are then confronted with theoretical predictions of classical continuum mechanics and minimum shear approaches, which disregard the lattice modulation. As it is shown including the modulation modifies the twin systems (twinning plane and twinning direction) for some TBs. Moreover, it strongly affects the interfacial energy which allows to rank TBs in the 10M Ni–Mn-Ga system. Large differences in surface energy between different TBs are associated with atomic interface configurations and de-shuffling of atoms to form a coherent twin plane. Therefore, unlike the classical geometrical concepts, the G-H model allows to perform not only a quantitative but also qualitative analysis of all possible twin boundaries. As a result of new approach, a model that involves interfacial energy, shuffling of atoms and homogenous shear type deformation for TB determination is presented. In addition, irrational or step-like planes not only for type II but also for type I twin boundaries is predicted. Furthermore, a description of twin formation with respect to two different reference systems is completed, i.e. parent-based and monoclinic ones. In this way, a hierarchical twin microstructure of 10M martensite is established.

Group-theoretical analysis of structural instability, vacancy ordering and magnetic transitions in the system troilite (FeS)-pyrrhotite (Fe1-xS).

A group-theoretical framework to describe vacancy ordering and magnetism in the Fe1-xS system is developed. This framework is used to determine the sequence of crystal structures consistent with the observed magnetic structures of troilite (FeS), and to determine the crystallographic nature of the low-temperature Besnus transition in Fe0.875S. It is concluded that the Besnus transition is a magnetically driven transition characterized by the rotation of the moments out of the crystallographic plane to which they are confined above the transition, accompanied by small atomic displacements that lower the symmetry from monoclinic to triclinic at low temperatures. Based on the phase diagram, magnetically driven phase transitions at low temperatures are predicted in all the commensurate superstructures of pyrrhotite. Based on the phase diagram, magnetically driven spin reorientations at low temperatures are predicted in all the commensurate superstructures of pyrrhotite. The exact nature of the spin rotation is determined by the symmetry of the vacancy-ordered state and based on this spin-flop transitions in 3C and 5C pyrrhotite and a continuous rotation akin to that seen in 4C pyrrhotite are predicted. A Besnus-type transition is also possible in 6C pyrrhotite. Furthermore, it is clarified that 3C and 4C pyrrhotite carry a ferrimagnetic moment whereas 5C and 6C are antiferromagnetic.

Vibrational modes and quantum zero-point energy of hydrogen in ZrH0.0155 and ZrH2

We report on an inelastic neutron scattering study of the proton dynamics in ZrH0.0155 and ε-ZrH2. In particular, we present measurements of the incoherent dynamic structure factor, generalized vibrational density of states, and proton momentum distribution of these two materials. Our results are generally consistent with theoretical predictions of Elsässer et al. [Mat. Res. Soc. Symp. Proc. 453 221–226 (1997)]. They argued that the effective Born-Oppenheimer potential experienced by the hydrogen atoms in ε-ZrH2 is nearly isotropic and harmonic at energies below 0.3 eV, but becomes anisotropic and anharmonic for higher energies. At low temperatures, the proton momentum distribution is dominated by the quantum-mechanical ground state of the protons. We find that it assumes a Gaussian shape, consistent with the concept that the potential surface is approximately harmonic for small displacements of the hydrogen atoms. However, the anharmonicity of the potential becomes readily apparent in the excited states of the hydrogen atoms, as the harmonic approximation breaks down in the description of the multiphonon bands.

Insights into the fivefold symmetry of the amorphous Sb-based change materials in the rapid phase change from first principles

In materials science, it is widely believed that the fivefold symmetry in the amorphous phase will suppress crystallization because of its structural incompatibility with the crystal phase. The Sb-based phase change materials dominated by the fivefold rings, however, display the ultrafast growth-dominated phase change from amorphous to crystalline phase and exhibit significant property contrast consequently when they are heated by a laser or electrical pulse. To resolve the paradox, the long-time ab initio molecular dynamics calculation is carried out to simulate the crystallization cycle of the amorphous Ge15Sb85 under non-isothermal condition. The calculation results are in a reasonable agreement with experimental data. In particular, it is found that a transient phase state exists just before the crystallization onset temperature of the amorphous Ge15Sb85, in which the predominant fivefold rings in half-chair conformation undergo rapid conversion into the puckered sixfold rings. It is further demonstrated that such rings conversion via a route of the bond exchange model involves small atomic displacements and results in the structural motif similarity between the transient and the crystalline states. This thus reduces the crystal–amorphous interfacial energy promoting crystal nucleation consequently. The subsequent electronic calculations indicated that such conversion of the dominant rings in the amorphous Ge15Sb85 may be triggered by the increased pp orbital hybridizations and modulated by the diminished sp electron mixing. It is anticipated that the findings presented will provide a stepping-stone for the rational design of the Sb-based phase change materials.

On the sensitivity of convergent beam low energy electron diffraction patterns to small atomic displacements

Abstract Multiple scattering simulations are developed and applied to assess the potential of convergent beam low-energy electron diffraction (CBLEED) to distinguish between various reconstructions of the Si(001) surface. This is found to be readily achievable through changes in pattern symmetry. A displacement R-factor approach is used to incorporate the angular content of CBLEED discs and identify optimal energy ranges for structure refinement. Defining a disc R-factor, optimal diffraction orders are identified which demonstrate an enhanced sensitivity to small atomic displacements. Using this approach, it was found that respective dimer height and length displacements as small as ±0.06 A and ±0.20 A could be detected.

Structural evolution of La2Ti2O7 at elevated temperatures.

Structural evolution of a La2Ti2O7 ferroelectric compound possessing perovskite-type slabs at elevated temperatures was investigated using the single-crystal X-ray diffraction technique. The monoclinic low-temperature phase (L) transformed into the orthorhombic high-temperature phase (H) via an incommensurately modulated phase (IC) between ∼989 and ∼1080 K. The L-IC transition was considered to be of the first order, with the L+IC two-phase co-existing region between ∼989 and ∼1027 K. The structure of IC was determined from the (3+1)-dimensional superspace representation with a modulation vector q = αao (α ≃ 0.49), where ao is the a-axis vector of the basic cell. The structural modulation originated from the variation of the tilt angle of the TiO6 octahedra in the perovskite-type slab in association with small positional displacements of La atoms. The IC-H transition took place at ∼1080 K and was close to the second order. During the IC-H transition, nanoscale flat plate domains having either a cell twin of the L-type structural modules or a cell twin of the alternating H- and L-type structural modules began to appear in the approximant structure of IC. The thickness of the flat plate domains then grew rapidly along the modulation vector in proportion to (½ - α)-1 as α approached ½ with decreasing temperature. In the two-phase L+IC co-existing region, the IC phase consisting of the two types of cell twins was gradually replaced with the low-temperature monoclinic phase L, which is not cell twinned but rather twinned macroscopically by the L-type structural modules.

Two Different Mechanisms of Metal Cluster Formation in the Rhombohedral Spinel Structures: AlV2O4 and CuZr1.86(1)S4

An unusual case of the structural mechanisms of inorganic crystals formation is considered theoretically on the example of the AlV2O4 and CuZr1.86(1)S4 isosymmetric rhombohedral spinels with the same character of the atom distribution on the Wyckoff positions. It is shown that the difference in structures is due to the critical influence of the order parameter value that describes the real (in the case of AlV2O4) and virtual (in the case of CuZr1.86(1)S4) structural phase transitions. Owing to the low value of the order parameter, the phase transition to the rhombohedral AlV2O4 structure is associated with relatively small atomic displacements and the formation of heptamer structural blocks in the V sublattices. In contrast, the virtual phase transition to the rhombohedral CuZr1.86(1)S4 structure is associated with high value of the order parameter and giant atomic displacements. As a result, the Cu and Zr atoms form metal nanoclusters—a “bunch” of dimers. The CuZr1.86(1)S4 is a second substance (the first example is CuTi2S4) with a new type of self-organization of atoms, in which the metal clusters are formed by the atoms from two (but not one, as in the known materials) geometrically frustrating spinel sublattices.