Commensurate Modulation Research Articles

Successive Magnetic Transitions of the Kagomé Staircase Compound Co3V2O8 Studied in Various Magnetic Fields

For the spin-3/2 kagome staircase system Co3V2O8, magnetic field (H)-temperature (T) phase diagrams have been constructed for the fields along three principal directions up to 5 T, using results of various macroscopic measurements on single crystal samples and also using neutron diffraction data taken on both powder and single crystal samples under H along c. In zero magnetic field, the system exhibits three transitions at temperatures Tc1~11.2 K, Tc2~8.8 K and Tc3~ (6.0-7.0) K. The single crystal data present clear evidence for the noncollinear nature of the magnetic structures in all magnetically ordered phases below Tc1. The sinusoidal nature of the incommensurate modulation of the ordered moment reported in the former work has been confirmed between Tc1 and Tc2, that is, no higher harmonics of the modulation have been detected even for the present large single crystal. Even in the phase of commensurate modulation between Tc2 and Tc3, we have not detected any higher harmonics of the modulation. The phase diagrams show that the magnetically ordered phases sensitively change to other phases with H, indicating that the geometrical frustration inherent in this system is important for the determination of the phase diagram. No evidence for ferroelectric transitions has been observed in the measurements of the dielectric constant applying the electric fields along three crystallographic axes, a, b and c. Only small dielectric anomalies closely connected with the magnetic phase transitions have been found.

Forms and origin of structure modulation in lazurites

The crystal structure of lazurite, ideally Na6Ca2[Al6Si6O24](SO4,S)2, has a flexible framework formed with four- and six-membered rings of the (Al,Si)O4 tetrahedra shared by vertices. The framework cavities are occupied with Na,Ca cations and S-containing anionic groups. Six modulated lazurite polymorphs have been studied using X-ray diffraction techniques. General and special features of the structure modulation of lazurites are discussed for several different structures. A mechanism of commensurate modulation is revealed using the triclinic structure as an example. The 3D incommensurate modulation of the cubic framework is shown. The commensurate 1D-modulation of the triclinic structure is compared with the incommensurate 1D-modulation of the monoclinic structure. The S-containing groups are believed to play an important role in the formation of the structure modulations.

Structure and phase transitions in Ca2CoSi2O7–Ca2ZnSi2O7 solid-solution crystals

While the incommensurability in melilites is well documented, the underlying atomic configurations and the composition-dependent phase behavior are not yet clear. We have studied the transition from the incommensurate phase to the high-temperature normal phase (IC-N), and to the low-temperature commensurate phase (IC-C) of selected members of the Ca(2)Co(1 - x)Zn(x)Si(2)O(7) system using X-ray and single-crystal electron diffraction, as well as calorimetric measurements. The space group of the unmodulated normal phase and of the basic structure of the incommensurate phase is P42(1)m; the commensurate lock-in superstructure was refined as a pseudomerohedral twin in the orthorhombic space group P2(1)2(1)2. We found that the commensurate modulation is mainly connected with a sawtooth-like periodicity of rotations of the T(1) tetrahedra in the 3 x 3 superstructure. In this structure, the clustering of the low-coordinated Ca(2+) ions is not complete so that only imperfect octagons were detected. Generally, the effect of increasing substitution of Co by Zn was a continuous reduction of the IC-N and IC-C transition temperatures.

Neutron diffraction investigations of zero-field and field-induced magnetic structures of DyNiSn single crystal

Single crystal neutron diffraction studies have been performed on the rare-earth ternary compound, DyNiSn. This crystal exhibits an incommensurate magnetic structure expressed by the propagation vector, Q = (0.662 0.352 0) with its third harmonics at low temperatures. In an external magnetic field applied along the c-axis DyNiSn shows incommensurate modulation with Q = (1 0.315 0) at 1.6 K, while along the easy magnetization direction of the b-axis a commensurate modulation with Q = (2/3 0 0) develops at 2 K. The results along the b-axis are fully consistent with the magnetization curve.

Magnetic-field-induced transition in the lattice modulation of colossal magnetoelectricGdMnO3andTbMnO3compounds

Single-crystal synchrotron x-ray diffraction measurements in strong magnetic fields have been performed for magnetoelectric compounds $\mathrm{Gd}\mathrm{Mn}{\mathrm{O}}_{3}$ and $\mathrm{Tb}\mathrm{Mn}{\mathrm{O}}_{3}$. It has been found that the $\mathbit{P}\ensuremath{\Vert}a$ ferroelectric phase induced by the application of a magnetic field at low temperatures is characterized by commensurate lattice modulation along the orthorhombic $b$ axis with $q=1∕2$ and $q=1∕4$. The lattice modulation is ascribed to antiferromagnetic spin alignment with a modulation vector of $(0\phantom{\rule{0.3em}{0ex}}1∕4\phantom{\rule{0.3em}{0ex}}1)$. The change of the spin structure is directly correlated with the magnetic-field-induced electric phase transition, because any commensurate spin modulation with $(0\phantom{\rule{0.3em}{0ex}}1∕4\phantom{\rule{0.3em}{0ex}}1)$ should break glide planes normal to the $a$ axis of the distorted perovskite with the $Pbnm$ space group.

Electric-field-induced transformation of incommensurate modulations in antiferroelectricPb0.99Nb0.02[(Zr1−xSnx)1−yTiy]0.98O3

Most antiferroelectric ceramics are modified from the prototype ${\mathrm{PbZrO}}_{3}$ by adding Sn and Ti in conjunction with small amount of Nb or La to optimize their properties. These modifiers introduce unique nanoscale structural feature to the ceramics in the form of incommensurate modulations. It was shown previously that the modulation is strongly responsive to a change in chemical composition or temperature. However, its response to an electric field, the driving force in real applications, has not been explored before. In the present work the dynamic evolution of the incommensurate modulation during the electric field-induced antiferroelectric-to-ferroelectric transformation was observed with an in situ transmission electron microscopy (TEM) technique. The results indicate that the incommensurate modulation exists as a transverse Pb-cation displacement wave. The wavelength was found to be quite stable against external electrical stimuli, in sharp contrast to the dramatic change under thermal stimuli reported previously. It is suggested that the appeared incommensurate modulation is an average effect of a mixture of two commensurate modulations. The electric field-induced antiferroelectric-to-ferroelectric transformation proceeds with aligning the Pb-cation displacements, which resembles the process of 90\ifmmode^\circ\else\textdegree\fi{} reorientation and 180\ifmmode^\circ\else\textdegree\fi{} reversal in normal ferroelectrics.

The Real Structure of YbSi1.4 ‐ Commensurately and Incommensurately Modulated Silicon Substructures

AbstractA systematic thermochemical investigation of the binary system Yb/Si revealed the phase YbSi1.4 in pure form that is accessible by reacting the elements at 890 °C in sealed niobium ampoules. According to XRD investigations, the basic structure of YbSi1.4 is orthorhombic (space group: Cmcm; a = 4.159(1), b = 23.510(5), c = 3.775(1) Å). The structure contains blocks with three sheets of trigonal Yb6 prisms that are connected to each other by face‐sharing. Two of these prism sheets are fully occupied by Si whereas the middle one is occupied by ∼ 80 % only, as obtained from the electron density distribution by XRD. Transmission electron microscopy (TEM) investigations show the presence of two distinct ordering variants: YbSi1.4‐I has a unit cell with doubled volume (space group of the structural model: Imm2; aI = 4.16, bI = 7.56, cI = 23.51Å). In the structural model derived from HRTEM images, Si fills 3/4 of the partly occupied Yb6 prisms in a regular way. YbSi1.4‐II exhibits an incommensurate modulation that can be described in the 3 + 1 dimensional superspace group Cmcm(10γ) (No. 63.3). The evaluation of HRTEM images of YbSi1.4‐II revealed parallel domains with the structure of YbSi1.4‐I, with the modulation due to a shift of the domains with respect to each other.

Variety of molecular conducting layers in the family of radical cation salts based on BEDT-TTF with the metal mononitrosyl complex [OsNOCl5]2–

Four new BEDT-TTF radical cation salts with the [OsNOCl5]2− anion have been synthesized: α′-(BEDT-TTF)4[OsNOCl5]·C6H5NO2 (1), δ-(BEDT-TTF)4[OsNOCl5]1.33·(C6H5NO2)0.67 (2), κ-(BEDT-TTF)4[OsNOCl5]·C6H5CN (3) and β-(BEDT-TTF)2[OsNOCl5] (4). The salts were characterized by single-crystal X-ray diffraction, electrical resistance measurements, and electronic band-structure calculations. Evidence for commensurate structural modulations was found for 2 and 3. The crystals of 1, 3 and 4 are semiconductors while those of 2 exhibit a metal-to-insulator transition around 160 K. Analysis of the correlation between the crystal structure, transport properties and electronic structure of these and related salts suggests the possibility of smoothly changing the conductivity of κ-phases with two types of donors and dimers from semiconducting to metallic as well as the need to reconsider the origin of the metal-to-insulator transitions of δ-type salts.

TEM Study of Two-Dimensional Incommensurate Modulationin Layered La2-2xCa1+2xMn2O7 (0.6 < x < 0.8)

Ruddlesden−Popper n = 2 compounds La2-2xCa1+2xMn2O7 with 0.6 ≤ x ≤ 0.8 were synthesized by a citrate gel technique and studied by transmission electron microscopy. Electron diffraction identified the presence of eight satellite reflections around fundamental spots of the basic tetragonal I4/mmm structure. The satellite reflections belong to two sets of two-dimensional incommensurate modulation, and the sets are rotated with respect to each other around [001] by ∼29°. The modulation is sensitive to electron-beam irradiation and rapidly degrades under a focused beam. In situ heating experiments indicated the existence of possible tetragonal-to-incommensurate phase transition around 350 °C, although the presence of the modulation persists up to 500 °C. High-resolution imaging proves that the modulation in the real space is truly two-dimensional and incommensurate and not a combination of one-dimensional commensurate modulations. Such modulation has never been observed before for La−Ca−Mn−O or any other perov...

Manifestation of Spatial Modulation in the Vibration Spectra of (N(CH3)4)2CuCl4Crystals

The specific manifestations of the spatial modulation in the vibration spectra of (N(CH3)4)2CuCl4 crystals have been investigated. It has been shown that because of the narrow temperature range of existence of the incommensurate phase and the complexity of the spectra being analyzed, reliable resolution of additional modes arising under the influence of both incommensurate and commensurate modulation is only possible using a computer approximation of the spectra obtained. In accordance with the theoretical models considered, additional modes have been observed mainly in the region of low-frequency skeletal vibrations exhibiting a marked dispersion.

La-induced conversion between the ferroelectric and antiferroelectric incommensurate phases inPb1−xLax(Zr1−yTiy)O3

In La-substituted Pb 1 - x La x (Zr 0 . 9 5 Ti 0 . 0 5 )O 3 , an increase in the La content x served to convert the ferroelectric incommensurate (FI) phase into the antiferroelectric incommensurate (AI) phase around x=0.01. Inorder to elucidate the physical origin of the conversion between the FI and AI phases, the crystallographic features of the successive phase transitions related to these incommensurate phases have been investigated by transmission electron microscopy. It was found that the FI-to-AI transition actually occurred on cooling in the x =0.01 sample, and that in the x=0.03 sample, for instance, the AI phase basically consisted of four phases with commensurate modulations. The successive transitions among these four phases and the antiferroelectric commensurate (AC) phase were also suggested to proceed by the continuous change in a wave front of the modulation wave. In addition, the ferroelectric cluster (FS) state was found to exist in the paraelectric cubic (PC) phase above the AI phase. Because the M 3 and R 2 5 rotational displacements of the oxygen octahedra are, respectively, involved in the Fl phase and the FS state, the conversion between the FI and AI phases should be associated with that between these rotational displacements.

The Structure of Diaqua (15-Crown-5) Copper (II) Dinitrate Described in (3+1)-Dimensional Superspace

Diaqua (15-crown-5) copper (II) dinitrate is an organic salt presenting an one-dimensional commensurate modulation. The diffraction pattern is characterized by strong Bragg reflections and weaker superstructure reflections (satellites). The structure is described in the superspace formalism as a modulated structure in (3+ 1) dimensions with occupational and displacive modulation functions.

A multi-carrier technique for ultrasonic Doppler vibrometry

A novel and simple technique for a signal-to-noise-ratio augmenting in ultrasonic Doppler vibrometry is presented. The approach involves sending two probe frequencies separated by twice the modulation frequency. By adjusting the mutual phase of the carriers, the overlapped sideband can be twice as large as the nonoverlapped ones. Moreover, the phase-demodulated signal is also larger than is obtained in the case of one-carrier operation. Parallel results of electronic phase modulation and ultrasonic Doppler vibrometry (with commensurate modulation strengths) are presented. A practical implementation of the method to probe vibrations of a rough surface is then described. [Work supported by ONR.]

The Commensurately Modulated Structure of K2TeOF4.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Epitaxial Ce and the magnetism of single-crystal Ce/Nd superlattices

The chemical structure of epitaxial $\ensuremath{\gamma}$ cerium and the chemical and magnetic structures of cerium/neodymium superlattices have been studied using x-ray and neutron diffraction techniques. The samples were grown using molecular-beam epitaxy, optimized to yield the desired Ce allotropes. The x-ray measurements show that, in the superlattices, both constituents adopt the dhcp structure and that the stacking sequence remains intact down to $T\ensuremath{\sim}2\mathrm{K};$ these are the first measurements of magnetic ordering in single-crystal dhcp Ce. The magnetic structure of the superlattices with thicker Nd layers exhibit incommensurate order and ferromagnetism on separate sublattices in a similar manner to Nd under applied pressure. The sample with thickest Ce layers has a magnetic structure similar to bulk $\ensuremath{\beta}$ Ce, which has commensurate transverse modulation with a propagation wave vector [1/2 0 0] and moments along the hexagonal a direction. These two types of magnetic order appear to be mutually exclusive. $\ensuremath{\gamma}$ Ce is the high-temperature fcc phase of Ce, our single-phase epitaxial sample is observed to go through a new, but partial, structural transition not previously seen in the bulk material.

Metallicity and thermopower of the misfit cobaltite[Bi2Ba1.8Co0.2O4]RS[CoO2]2

The misfit cobaltite, [Bi 2 Ba 1 . 8 Co 0 . 2 O 4 ] R S [CoO 2 ] 2 , built up from the stacking of rocksalt-type layers (RS) and single hexagonal [CoO 2 ] layers (H), has been synthesized. This complex structure, described in a commensurate monoclinic supercell, exhibits a double commensurate modulation: a misfit modulation with b R S /b H =2 and an intrinsic modulation of the RS layers [q i =0.2(a R S +b R S )]. This oxide is characterized by an enhanced metallic behavior with respect to the misfit Bi(Pb)/Sr/Co/O cobaltites and in contrast to these compounds by a positive magnetoresistance and significantly smaller values of the thermoelectric power (<100 μV K - 1 ). A comparison of its behavior with those of Sr 2 RuO 4 and of the heavy-fermion-like oxide LiV 2 O 4 is presented.

The First Mixed Valence Radical Cation Salts of BEDT-TTF with the Photochromic Metal Mononitrosyl Complexes [RuNO X5] 2− ( X=Br, Cl) as Counterions

New bis(ethylenedithio)tetrathiafulvalene BEDT-TTF radical cation salts with the [RuNOX 5] 2− (X=Br, Cl) anions have been synthesized. The crystal structures of κ-(BEDT-TTF) 4[RuNOBr 5]·C 6H 5CN (1): a=8.747(2), b=12.088(1), c=17.300(2) Å, α=95.63(1), β=91.93(2), γ=94.79(2)°, V=1812.3(5) Å 3, P 1 , Z=1 and δ-(BEDT-TTF) 4[RuNOCl 5] 1.33 (2): a=6.721(1), b=15.016(2), c=35.386(3) Å, α=92.804(8), V=3567.0(8) Å 3, I2/ c, Z=2 have been determined. Their electronic band structures and transport properties have been studied. The radical cation salts κ-(BEDT-TTF) 4[RuNOCl 5]·C 6H 5CN (3) and δ-(BEDT-TTF) 4[RuNOBr 5] (4) have also been found to exist and are isostructural to 1 and 2, respectively. Evidence for commensurate and incommensurate structural modulations was found for 2 and 4, respectively. The crystals of 1 and 3 are semiconductors while those of 2 and 4 exhibit an M–I transition at 50 and 80 K, respectively.

Synthesis of and incommensurate charge and orbital ordering in La1/2Sr3/2MnO4 layered perovskite

Polycrystalline bulky samples of La1/2Sr3/2MnO4 were systhesized by conventional solid-state reaction in air. Composition analysis by energy dispersive X-ray spectrometer indicated that the average composition of the sample is La0.45 Sr1.49 MnO4 with a minor fluctuation. The [001] zone-axis electron diffraction patterns taken at about 100 K revealed the presence of superlattice peaks, due to the incommensurate charge and orbital ordering. The incommensurate modulation wave vector is k = δ[110]T*, with δ = 0. 19. Such an incommensurate modulation may be described as a random distribution of two commensurate modulations with δ= 1/4 and 1/6.

Electron crystallographic image-processing investigation and superstructure determination for (Pb0.5Sr0.3Cu0.2)Sr2(Ca0.6Sr0.4)Cu2Oy.

An electron crystallographic image-processing technique based on the combination of high-resolution electron microscopy and electron diffraction has been developed to investigate the commensurate structural modulation in the high-Tc superconductor (Pb0.5Sr0.3Cu0.2)Sr2(Ca0.6Sr0.4)Cu2Oy. After symmetry averaging, a structure image was obtained by image deconvolution at the resolution limited by that of the electron microscope. Then phase extension was employed to enhance the image resolution up to about 1.25 A by means of the electron diffraction data corrected with an empirical method. In the final projected potential map, the occupational and/or positional modulation is clearly observed for all atoms, including oxygen. The key points of determining superstructures by the technique are studied and discussed.

Synthesis and structure of bis(triethanolamine)europium(II) diperchlorate

The crystal structure of the title compound was determined at 293 and 100 K. The structure contains bis(triethanolamine)europium(II) cations, and perchlorate anions. The metal ion coordination environment is composed of two N and six O atoms. At room temperature, all triethanolamine molecules are partially disordered. On going to 100 K, the disorder partially disappears, giving rise to a commensurate modulation of the structure.