Incommensurate Superstructure Research Articles

Peculiarities of incommensurate modulation behavior during superstructure creation in case of potential symmetry n = 4

Type or paste your abstract here as prescribed by the journal’s instructions for authors. Type or paste your abstract here as prescribed by the journal’s instructions for authors. Type or paste your abstract here as prescribed by the journal’s instructions for authors. Type or paste your abstract here. This paper deals with dynamics of incommensurate superstructure at the moment of its formation. Lyapunov exponent value spectra, phase portraits, incommensurate modulation wave vector behavior, Fourier spectra and maps of incommensurate phase dynamic modes under changed parameters of long-range interaction (Т) and anisotropic interaction (K) in interval 0.0 ÷ 1.0 were analyzed. The calculations were made in Python environment applying Skipy, JiTCODE libraries. Under low values of Т and K parameters (0.0015 ÷ 0.03) a chaotic state occurs in this system. It is determined by the interaction between different spatial areas of the correlated motion of tetrahedral groups. The interaction of spatial areas of the correlated motion of tetrahedral groups violates the modulation pattern of tetrahedral group motion causing the superstructure chaotic state. The study of Fourier spectra has shown that interaction of spatial areas of tetrahedral group correlated motion of causes the chaotic state that is non-stable and is destroyed by long-range interaction. The impact of surface energy on the interaction of spatial areas of tetrahedral group correlated motion is determined by decreased amplitude of vibrations of tetrahedral groups causing the disappearance of the chaotic state.

Observation of an Incommensurate Charge Density Wave in Monolayer TiSe2/CuSe/Cu(111) Heterostructure

TiSe_{2} is a layered material exhibiting a commensurate (2×2×2) charge density wave (CDW) with a transition temperature of ∼200 K. Recently, incommensurate CDW in bulk TiSe_{2} draws great interest due to its close relationship with the emergence of superconductivity. Here, we report an incommensurate superstructure in monolayer TiSe_{2}/CuSe/Cu(111) heterostructure. Characterizations by low-energy electron diffraction and scanning tunneling microscopy show that the main wave vector of the superstructure is ∼0.41a^{*} or ∼0.59a^{*} (here a^{*} is in-plane reciprocal lattice constant of TiSe_{2}). After ruling out the possibility of moiré superlattices, according to the correlation of the wave vectors of the superstructure and the large indirect band gap below the Fermi level, we propose that the incommensurate superstructure is associated with an incommensurate charge density wave (I-CDW). It is noteworthy that the I-CDW is robust with a transition temperature over 600 K, much higher than that of commensurate CDW in pristine TiSe_{2}. Based on our data and analysis, we present that interface effect may play a key role in the formation of the I-CDW state.

Electronic and vibrational properties of the high T c superconductor Bi2Sr2CaCu2O8: an ab initio study

In this work, ab initio calculations were performed in order to study the vibrational spectra of the Bi2Sr2CaCu2O8 (Bi2212) compound. A structural modulation correction on some atomic positions, producing a distorted structure with lower symmetry, is used for the calculation. We argue that this correction allows to account for an average effect of the incommensurate superstructure, generating a more accurate representation of the real unit cell observed in this compound. A complete and conclusive vibrational assignment is performed, discussing the correspondences with previous experimental and theoretical reports. A brief analysis of the electronic density of states and band structure comparing the tetragonal and distorted unit cell is also included.

Modulated and Incommensurate Superstructures of Atomic–Vacancy Ordering in Refractory Transition Metal Carbides

The formation of partially disordered modifications in refractory nonstoichiometric carbides prone to M6X5-type ordering is considered. In M6X5 superstructures the ray $${\mathbf{k}}_{9}^{{(3)}}$$ of the Lifshitz star {k9} with a current parameter μ9 = 1/2 in the disorder–order phase transition channel is replaced by the rays $${\mathbf{k}}_{5}^{{(6)}}$$ and $${\mathbf{k}}_{5}^{{(5)}}$$ of the non-Lifshitz star {k5} with a variable current parameter 0 < μ5 < 1/2. Depending on the specific value of the index μ5, this replacement leads to various modulated structures that differ by the concentration of vacancies in the defective ( $$1\bar {1}1$$ ) planes of the carbon fcc sublattice and by the modulation period. In the diffraction spectra the positions of the superstructure reflections due to the star {k5} at μ5 ≈ 0.473 correspond to the incommensurate ordered phase experimentally detected in a nonstoichiometric tantalum carbide. The incommensurate phase is close in short-range order in the first coordination sphere to the initial M6X5 superstructures with a reduced long-range order parameter η ≈ 0.6.

Al-rich [formula omitted][formula omitted](1 0 0), (1 1 0) and (1 1 1) surface structures

Based on previous photoemission findings, the influence of newly observed aluminum surface segregation at the low (110), (100) and (111) index surfaces of the A2 body-centered Fe0.85Al0.15 random alloy is explored. Scanning Tunneling Microscopy, Low-Energy Electron Diffraction and Grazing-Incidence X-ray Diffraction are combined to explore surface structures and topographies. The formation of a surface composition close to the B2Fe0.5Al0.5 occurs with the appearance of (i) a long-range pseudo-hexagonal incommensurate superstructure with a periodicity of ~18 Å on the (110) surface, (ii) a (1×1) termination on the (100) surface and (iii) a intense vicinal faceting of the (111) surface in the form of triangular pits.

The dependence of the Fourier spectrum of oscillations of the amplitude function of the incommensurate superstructure on the magnitude of the anisotropic interaction interacting with Dzialoszynski invariant

The dependence of the Fourier spectrum of oscillations of the amplitude function of the incommensurate superstructure on the magnitude of the anisotropic interaction interacting with Dzialoszynski invariant

Evolution of incommensurate superstructure and electronic structure with Pb substitution in (Bi2−xPbx)Sr2CaCu2O8+δ superconductors**Project supported by the National Key Research and Development Program of China (Grant Nos. 2016YFA0300300 and 2017YFA0302900), the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grant Nos. XDB07020300 and XDB25000000), the National Natural Science Foundation of China (Grant Nos. 11334010 and 11534007), and the

High-quality Bi2−xPbxSr2CaCu2O8+δ (Bi2212) single crystals have been successfully grown by the traveling solvent floating zone technique with a wide range of Pb substitution (x = 0–0.8). The samples are characterized by transmission electron microscope (TEM) and measured by high resolution laser-based angle-resolved photoemission spectroscopy (ARPES) with different photon energies. A systematic evolution of the electronic structure and superstructure with Pb substitution has been revealed for the first time. The superstructure shows a significant change with Pb substitution and the incommensurate modulation vector () decreases with increasing Pb substitution. In the meantime, the superstructure intensity from ARPES measurements also decreases dramatically with increasing Pb concentration. The superstructure in Bi2212 can be effectively suppressed by Pb substitution and it nearly disappears with a Pb substitution of x=0.8. We also find that the superstructure bands in ARPES measurements depend sensitively on the photon energy of lasers used; they can become even stronger than the main band when using a laser photon energy of 10.897 eV. These results provide important information on the origin of the incommensurate superstructure and its control and suppression in bismuth-based high temperature superconductors.

TEM study of incommensurate superstructure in Pb1−0.5xNbx((Zr0.52Sn0.48)0.955Ti0.045)1−xO3 ceramics with 0–1 switching characteristic strain and high energy storage density

Pb1−0.5xNbx((Zr0.52Sn0.48)0.955Ti0.045)1−xO3(PNZST-100x (x = 0.01, 0.02, 0.03, 0.04)) antiferroelectric (AFE) ceramics were prepared using a solid-state method. X-ray diffraction analysis indicates a structural evolution from the tetragonal phase to the pseudocubic phase. When x = 0.02, the ceramic exhibits an enhanced energy storage density of 1.37 J/cm3, and a strain, with 0–1 switching characteristics, of 0.22%. Selected-area electron diffraction (SAED), high-resolution transmission electron microscopy imaging, and in-situ TEM analyses indicate that there are two kinds of superlattice reflections, including the 1/2(hkl) superlattice reflection (h, k, and l: all odd) and 1/6.67(a* + b*) one-dimensional incommensurate superlattice reflections. The origin of the 1/2(hkl) superlattice reflection was the tilting of a-a-a- oxygen octahedra. Therefore, the 1/2(hkl) reflections were no longer superlattice reflections, but fundamental reflections in the trigonal system; hence, the reciprocal vector was re-expressed as $$H\, = \,ha^{*} \, + \,kb^{*} \, + \,lc^{*} \, \pm \,1/6.67\left( {a^{*} \, + \,b^{*} } \right),$$ where h, k, and l are integers and (− h + k + l) = 3n. The incommensurate structure of the PNZST-2 ceramic originated from the displacement of Pb2+.

The features of behavior of the Lyapunov's exponents from the symmetry of thermodynamic potential described by lifshitz invariant

The influence of the thermodynamic potential ( n ) symmetry on the behavior of the Lyapunov exponents is investigated. The calculation of the system of second-order differential equations was performed by a multi-step variable-order BDF method. The Lyapunov coefficients were calculated using Python software using Skipy, JiTCODE libraries. It is established that for values of n ≥ 5, the dynamics of the incommensurate superstructure is determined by the spatial change in the amplitude of the order parameter (the first integral of the motion of the incommensurate superstructure). For n < 5, the dynamics of a incommensurate superstructure is determined by the spatial change of the phase of the order parameter and its perturbation. It is shown that the dynamics of the superstructure is not affected by the ferroelectric or ferroelastic nature of the incommensurate superstructure. In order to obtain a detailed picture of the dynamics of the incommensurate superstructure, phase portraits were investigated in the coordinates R , R `, and φ at different values of the anisotropic interaction of the superstructure and the initial phase values of the order parameter φ 0 . It is established that the dynamics of this system is determined by the cascades of transition to chaos and areas of self-organization of the superstructure. It is shown that at the final stage of the transition to chaos, the system is characterized by the emergence of a chaotic attractor, which has a more complex phase portrait structure. The projection of such an attractor consists of two symmetrical parts with respect to the axis of the abscissa. The movement of a typical trajectory of a chaotic attractor can be divided into two phases. In the first phase of the trajectory, chaotic movements are made along the turns of the upper (lower) part of the attractor from time to time, passing to the boundary of the localization region where the stability of the upper (lower) symmetric boundary cycles is lost. At an unpredictable time, the trajectory moves from the upper (lower) part of the attractor to its upper (lower) part. This process is repeated infinitely many times. Thus, the transition to chaos has features characteristic of the Feigenbaum scenario (infinite cascade of bifurcations of doubling cycles), and for mixing (unpredictable mixing between the upper and lower parts of the emerging chaotic attractor). The self-organization process can be associated with the localization of a wave vector of incommensurate superstructure at a commensurate higher order value. It is shown that the distortion of the order parameter phase at the edge of the crystal can be related to boundary conditions in the first approximation. According to the authors, such cascading transitions to chaos are related to the modes of existence of a incommensurate superstructure. The emergence of chaos in the third stage is caused by the transition of a incommensurate superstructure to its stochastic mode of existence. In a stochastic mode of existence of a incommensurate superstructure, a chaotic, possibly incommensurate phase arises, which is a prototype of this chaotic state. It should be noted that the initial conditions (boundary conditions) stabilize the system, thereby leading to the removal of the degeneracy of the system, and the transition of a incommensurate superstructure to a state characterized by the existence of long-period proportional phases. Key words: incommensurate superstructures, phase portraits, Lyapunov’s exponents.

Al–Fe–Ge: New ternary compounds and phase equilibria at 800 °C

The isothermal sections of Al-Fe-Ge at 800 °C and 780 °C were studied by a combination of SEM/EDX with X-ray powder diffraction. Two new ternary compounds were structurally characterised by means of single-crystal XRD measurements: Al3-xFeGe2+x, I4/mcm, a = 6.2303(11) Å, c = 9.710(2) Å, V = 376.9 ų, Z = 4, Rint = 0.031, wR2 = 0.038 and Al1+xFeGe1-x, Fddd, a = 8.627(2) Å, b = 4.9139(8) Å, c = 16.369(3) Å, V = 693.9 ų, Z = 16, Rint = 0.039, wR2 = 0.053, which crystallise in the Ga5Pd and CuMg2 structure types, respectively. Considerable solid solution ranges mainly based on Al/Ge substitution were found for all binary and ternary phases present in this section. An apparently incommensurate superstructure of Al5Fe2 is triggered by Ge-additions.

Specific Structural Disorder in an Anion Layer and Its Influence on Conducting Properties of New Crystals of the (BEDT-TTF)4A+[M3+(ox)3]G Family, Where G Is 2-Halopyridine; M Is Cr, Ga; A+ Is [K0.8(H3O)0.2

New crystals (1–4) of organic conductors based on the radical cation salts of the bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF) with paramagnetic and diamagnetic tris(oxalato)metallate anions {A+[M3+(ox)3]3−G}2−, where M is Cr, Ga; G is 2-chloropyridine, 2-bromopyridine; and A+ is [K0.8(H3O)0.2]+ have been prepared and their crystal structure and transport properties were studied. All crystals belong to the monoclinic group of the (BEDT-TTF)4A+[M3+(ox)3]G family with β″-packing type of conducting BEDT-TTF layers. In contrast to the known superconducting crystals with M3+ = Fe3+ and G = 2-chloro- or 2-bromopyridine (Tc = 4.0–4.3 K), crystals with Cr3+ and Ga3+ ions exhibit metallic properties down to 0.5 K without superconducting transition. Upon cooling these crystals, the incommensurate superstructure appears, which has never been observed before in the numerous β″-salts of the family. In addition, orthorhombic (sp. group Pbca) semiconducting crystals α″-(BEDT-TTF)5[Ga(ox)3]·3.4·H2O·0.6 EtOH (5) were obtained. It is a new compound in the family of BEDT-TTF crystals with tris(oxalato)metallate anions.

The incommensurately modulated crystal structure of roshchinite, Cu0.09Ag1.04Pb0.65Sb2.82As0.37S6.08

Abstract The Pb–Ag–Sb sulfide roshchinite, Cu0.09Ag1.04Pb0.65Sb2.82As0.37S6.08, is a lillianite homologue N=4 with a complex incommensurate superstructure in the 8.46 Å direction of the orthorhombic crystal lattice with a 19.0804(1) Å, b 8.4591(2) Å and c 12.9451(3) Å, superspace group Pbcn(0σ 20)00s, q=0.41458(3)b*. A structure solution and refinement in (3+1) superspace, based on 10,019 observed reflections and 437 refined parameters was terminated at Robs (wR) equal to 7.27 (8.07)% using satellites up to second order; Robs is 4.82 for main reflections only. The Pb atoms in trigonal coordination prisms on planes of unit-cell twinning are semiperiodically replaced by antimony. The marginal columns of (311)PbS slabs of the Sb–Ag based structure which is based on PbS-like topology contain Sb, Ag(Cu) and mixed Ag/Sb sites in a complicated sequence. Central portions of the slabs are occupied by Sb–S crankshaft chains, best exposed on the (100)PbS planes, which run diagonally across the slabs. In these planes, in their majority the chains display Sb3S4 form and two opposing orientations, zig-zagging along the [010] direction. Every six chains, a parallel configuration of two chains occurs, but occasionally this interval is reduced to five chains. This, together with related compositional changes in the Pb– and Ag–Sb column, explains the one-dimensionally incommensurate character of roshchinite. Modestly elevated contents of As replacing Sb are the probable reason of modulation and non-commensurability in roshchinite.

The influence of surface energy on incommensurate superstructures

The influence of surface energy on incommensurate superstructures

Неоднорідні стани в тонкошарових кристалах з неспівмірною надструктурою

Неоднорідні стани в тонкошарових кристалах з неспівмірною надструктурою

Multi-steps Methods for Calculating the Phase Portrait of the Incommensurate Superstructure with the Lifshitz's Invariant

Multi-steps Methods for Calculating the Phase Portrait of the Incommensurate Superstructure with the Lifshitz's Invariant

Properties of Anisotropic Interaction of the Incommensurate Superstructure as Described by Dziloshinsky’s Invariant

Properties of Anisotropic Interaction of the Incommensurate Superstructure as Described by Dziloshinsky’s Invariant

The influence of mechanical stresses on incommensurate superstructures of thin-layer crystals

The influence of mechanical stresses on incommensurate superstructures of thin-layer crystals

Direct observation of electronic-liquid-crystal phase transitions and their microscopic origin in La1/3Ca2/3MnO3.

The ground-state electronic order in doped manganites is frequently associated with a lattice modulation, contributing to their many interesting properties. However, measuring the thermal evolution of the lattice superstructure with reciprocal-space probes alone can lead to ambiguous results with competing interpretations. Here we provide direct observations of the evolution of the superstructure in La1/3Ca2/3MnO3 in real space, as well as reciprocal space, using transmission electron microscopic (TEM) techniques. We show that the transitions are the consequence of a proliferation of dislocations plus electronic phase separation. The resulting states are well described by the symmetries associated with electronic-liquid-crystal (ELC) phases. Moreover, our results resolve the long-standing controversy over the origin of the incommensurate superstructure and suggest a new structural model that is consistent with recent theoretical calculations.

Electromagnetic radiation of electrons in corrugated graphene

Bremsstrahlung in corrugated single-layer graphene in the presence of a ballistic transport current is analyzed. Radiation of a similar nature is observed in undulators and wigglers. Regular and chaotic corrugations (ripples) are considered. It is shown that the quadratic relation between the Monge membrane function and the synthetic calibration field leads to the appearance of a central peak in the radiation spectral density. Possible formation mechanisms of single-layer graphene corrugation are proposed. In one case, the corrugation is considered as an incommensurate superstructure in a two-dimensional crystal, resulting from instability developing in the optical phonon subsystem with the formation of a periodic soliton train. Corrugation results from the interaction of subsystems. Another possible mechanism consists in instability of the membrane flat state due to strong fluctuations characteristic of two-dimensional systems.

B-cation effect on relaxor behavior and electric properties in Sr2NaNb5−xSbxO15 tungsten bronze ceramics

Sr2NaNb5−xSbxO15 ceramics (SNNS, x=0.0, 0.3, 0.5, 1.0) with ‘filled’ tungsten bronze structure were prepared by the conventional solid-state reaction method. Effects of introducing Sb concentration in B-sites on the microstructure, dielectric and ferroelectric properties were investigated in detail. With increasing of Sb concentration, the crystal structure of SNNS ceramics distorted slightly from the TB orthorhombic Ccm2 phase to tetragonal P4bm phase, and then to paraelectric P4/mbm phase at room temperature. The smaller ionic radius of Sb5+ (0.60Å) compared with that of Nb5+ (0.64Å) contributed to the shrinkage of crystal structure. It was found that accompanying with the introduction of Sb, some unique dielectric and ferroelectric behavior emerged for SNNS ceramics. Only the samples with x<0.5 showed additional dielectric anomaly in low-temperature range, which was attributed to the incommensurate superstructure ICS-associated dielectric dispersion process caused by local structural fluctuation. With increasing of Sb concentration, Tc shifted to lower temperatures, and the diffuse phase transition and relaxor behavior appeared to be exceptionally induced around Tc at higher Sb concentration. The underlying mechanisms of relaxor behavior induced by different Sb concentration in B-sites for SNNS ceramics were clarified in detail. Moreover, the ferroelectric properties deteriorated and even disappeared at higher Sb concentration, because the ceramics showed P4/mbm phase structure as a result of decreasing of Tc to lower than room temperature.