Formation Of Modulated Structure Research Articles

Modulated Structure Formation in Dislocation Cells in 316L Stainless Steel Fabricated by Laser Powder Bed Fusion

Metal additive manufacturing enables producing complex geometric structures with high accuracy and breaks the design constraints of traditional manufacturing methods. Laser powder bed fusion, a typical additive manufacturing process, presents a challenge in experimentally understanding the nano-scaled microstructure-process relationship regarding the wide range of process parameters. In this study, we aim to reveal the novel nanoscale structural features by advanced scanning transmission electron microscopy to clarify the formation mechanisms in 316L stainless steel by laser powder bed fusion. Here we show that the slender columnar grains were confined to the centreline of the melt pool along the build direction, and the columnar cell structure at the side branching of the melt pool grew along orthogonal directions to follow drastic changes in thermal gradient across adjacent melt pools. Novel nano-scaled modulated structures have been observed in the dislocation cells parallel to the laser scan direction, which were mainly caused by the elastic strain involving the thermal gradient inside the melt pool and across adjacent melt pools as well as the effective strain field in the dislocation cell interiors. An in-depth understanding of microstructure developments is worthy of fabricating high-performance materials by controlling the additive manufacturing process.

Sequence of Three-, Two-, and One-Dimensional Structures Formed from a Cholesteric Liquid Crystal at Change in the Chirality

In this work the formation of modulated structures in chiral liquid crystals is studied. For different chiral nematics that at low temperature form the usual (with twist in one direction) cholesteric phase, we found that at high temperature in the vicinity of the phase transition into isotropic liquid a universal sequence of structural transformations is observed. Planar cholesteric transforms at short helical pitch into the three-dimensional phases with cubic symmetry (Blue Phases), in two-dimensional structure at intermediate helical pitch and in one-dimensional structure in the plane of the sample at large pitch. The structures possess periodic orientational and translational order on scales much larger than molecular scale. Optical measurements were made on ordered structures obtained near the transition temperature to the isotropic phase. Possible reasons of formation of the structures are discussed on the basis of existing experimental data and theoretical considerations.

Reaction Mechanism of Na-Ion Deintercalation in Na2CoSiO4

Sodium transition metal silicates are potential candidate electrode materials to enable two-electron redox per transition metal ion center. Yet, the electrochemical reaction mechanism remains elusive despite the widely reported electrochemical activity for this class of materials as intercalation cathodes for Na-ion batteries. Adopting monoclinic Na2CoSiO4 as a model compound, we used high-resolution synchrotron X-ray diffraction (XRD) and X-ray pair distribution function (PDF) analysis to elucidate the structure of the partially desodiated Na2-xCoSiO4 phases for the Co3+/Co2+ redox couple. The appearance of satellite reflections in the intermediate Na1.5CoSiO4 and NaCoSiO4 phases manifests the formation of modulated structures, which are induced by Na+/vacancy and Co2+/Co3+ charge orderings. Accounting for these structural orderings is important to understand the function and performance of sodium transition metal silicate electrodes.

Formation of modulated structures induced by oxygen vacancies in α-Fe2O3 nanowires

Two modulated structures caused by long-range ordering of oxygen vacancies have been observed in α-Fe2O3 nanowires (NWs) produced after oxidation of Fe, one being ten times (303¯0) interplanar spacing and the other being six times (112¯0) interplanar spacing. Both types of oxygen vacancy ordering structures have a similar modulation periodicity of 1.45 or 1.50 nm with corresponding atomic ratios of Fe and O (Fe/O) of 0.7407 and 0.7273, respectively. The Fe/O ratios in the NWs with oxygen-vacancy ordering are very close to that of Fe3O4 (0.7500). The similar Fe/O ratio between NWs and Fe3O4 may explain the similar modulation periodicity of different oxygen-vacancy orderings. Electron energy-loss spectroscopy studies show that the Fe/O ratio of NWs is close to that of Fe3O4 when oxygen atoms are not sufficient, which makes the NWs energetically favorable. The elucidation of the mechanism governing the formation of the modulated structures in α-Fe2O3 NWs is critical for controlling the microstructure and correspondingly physicochemical properties of NWs.

Formation of modulated structures in single-crystalline hexagonal α-Fe2O3 nanowires

The microstructures and growth mechanism of Fe2O3 nanowires (NWs) synthesized by thermal oxidation of iron are studied in detail by transmission electron microscopy. Three different structures, single-crystalline, bicrystalline, and tricrystalline, are observed in the NWs. It is found that single-crystalline Fe2O3 NWs have a hexagonal structure while bicrystalline and tricrystalline NWs possess a cubic one. The differences in the electronic structures of the three Fe2O3 NWs are examined by electron energy-loss spectroscopy. A modulated structure with a periodicity of 1.53 nm is observed in single-crystalline Fe2O3 NWs, but not in bicrystalline or tricrystalline Fe2O3 NWs. The formation of the modulated structure in single-crystalline NWs is attributed to the periodical appearance of stacking faults, because of the shear stress occurred during the growth process. NWs possessing a cubic γ-Fe2O3 structure tend to coalesce into the bicrystalline or tricrystalline NWs whereas NWs with the hexagonal α-Fe2O3 structure prefer to grow as single-crystalline NWs. The formation mechanism of Fe2O3 NWs with the different morphologies is discussed.

Spatially modulated structures in nematic colloids: Statistical thermodynamics and kinetics

We examine the spatial distribution of rigid-sphere-like particles in a nematic host. Using a continuum model we analyse the conditions necessary for the appearance of a modulated lamellar structure. There is a long-range effective interaction between the particles, which can lead to the formation of superstructures. In general, this interaction includes several contributions: van der Waals-type direct interaction and indirect interaction via the director field distortions. The latter depends on the temperature of the sample, the coupling energy between a colloidal particle and a nematic host, and the particle concentration. This effective interaction controls the spatial structure and the kinetic properties of the system. We obtained the analytical expression for the temperature when the system loses the stability with respect to the modulated structure formation. Typical contours of the diffuse light scattering are presented.

Langevin dynamics of fluctuation-induced first-order phase transitions: Self-consistent Hartree approximation

The Langevin dynamics of a system exhibiting a Fluctuation Induced First Order Phase Transition is solved within the self consistent Hartree Approximation. Competition between interactions at short and long length scales gives rise to spatial modulations in the order parameter, like stripes in 2d and lamellae in 3d. We show that when the time scale of observation is small compared with the time needed to the formation of modulated structures, the dynamics is dominated by a standard ferromagnetic contribution plus a correction term. However, once these structures are formed, the long time dynamics is no longer pure ferromagnetic. After a quench from a disordered state to low temperatures the system develops growing domains of stripes (lamellae). Due to the character of the transition, the paramagnetic phase is metastable at all finite temperatures, and the correlation length diverges only at T=0. Consequently, the temperature is a relevant variable, for $T>0$ the system exhibits interrupted aging while for T=0 the system ages for all time scales. Furthermore, for all $T$, the exponent associated with the aging phenomena is independent of the dimension of the system.

The Sodalite Family - A Simple but Versatile Framework Structure

A particular family of crystalline microporous solids, the so-called sodalite family, is presented in various chemical, topological, geometrical, and crystallographic aspects. It is shown that the sodalite structure can be decomposed into three partial structures, namely i) the sodalite framework of all-corner connected TO4 tetrahedra, ii) a virtual lattice of cage cations, and iii) isolated cage anions. Important properties and features can be explained by interactions of the partial structures. In some cases the interactions are frustrated, resulting in the formation of modulated structures. Substitution effects occur on all three partial structures and occasionally have dramatic effects on phase transitions and phase diagrams.

Modulated structure formation in demixing paraffin blends

Small angle scattering (SANS and SAXS) and differential scanning calorimetry have been measured from C28:C36 normal paraffin mixtures of varying composition quenched from the melt. Satellite peaks are observed in the SAXS whose offset in Q, relative to Bragg diffraction peaks associated with the average structure, are composition dependent. The offset is close to the position of the most intense peak observed in SANS. Scattering from the quenched structures is consistent with a correlated displacement and substitutional disorder model yielding modulations that are incommensurate with the average lattice. DSC shows an additional endotherm in the mixtures that is not present in the pure components and is associated with this superstructure formation.

Crystal-structure modulation in the anomalous low-temperature phase of PrFe4P12

Nature of mysterious phase transition of the filled-skutterudite PrFe4P12 has been studied by X-ray diffraction experiments. Superlattice reflections characterized by a wave vector q=(1,0,0) were observed below the transition temperature of 6.5 K at zero magnetic field. The observed pattern in the reciprocal space is explained by the formation of modulated structure with dominant Fe-ion displacements by about 0.02% of the lattice constant. This result is consistent with the theoretically predicted nesting of Fermi surface producing a gap formation in electronic structure.

Strain modulation around inclusions in an annealed natural cordierite

A natural ferromagnesian cordierite which had been annealed at 1355°C has been found, by TEM, to contain submicroscopic cross hatched modulated microstructures (tweed) localised near Al 2 O 3 inclusions, while most of the sample, apart from some melting features, remained homogeneous and orthorhombic in symmetry. SAED patterns from regions with the tweed textures exhibited splitting parallel to [310] * and [110] * of the orthorhombic cell. Such features in cordierite have been interpreted in previous investigations as intermediate metastable states formed during the high-to-low transition associated with Al,Si ordering. Such metastable states appear to be favoured in K-bearing cordierites because the substitution Si 4+ + □ channel → K + + Al 3+ , which increases the number of the Al-O-Al bonds, hinders the development of long range Al,Si ordering and the high-to-low transition. In the present cordierite studied here, the mechanism of modulated structure formation is most probably similar but the chemical exchange involved is different and of the type R 2+ + Si 4+ → 2Al 3+ (where R 2+ is an octahedral cation). This entails the presence of some Al in octahedral coordination. It is suggested that octahedral Al would stabilise the hexagonal form of cordierite.

Structure and optical properties of Ge/Si superlattice grown at Si substrate by MBE at different temperatures

Multilayer structures in silicon containing submonolayers of Ge in the matrix were grown by MBE on Si substrates at different temperatures. An additional peak at 1.068 eV was observed in photoluminescence spectra (PL) from the samples grown at T=600, 650 and 700 °C, whereas it was absent in specimens grown at 750 °C. Electron microscopy structure investigations showed a high density of spherical, coherent Ge inclusions in samples grown at 650 °C, whereas they were not generated at higher growth temperature, such as at 750 °C. This fact indicates that the observed PL peak is unambiguously related to the Ge inclusions. High temperature growth at 750 °C results in formation of modulated structure where the composition sinusoidally changes with periodicities between 1.2 and 0.44 nm along 113 and 112 directions, respectively. This results in a distortion of the cubic symmetry and in a relaxation of the misfit stress causing changes in the electronic properties.

Computational investigations on the microstructure formation in multi-component alloy systems based on the phase field method

On the basis of the phase field method, the microstructure formation due to the phase decomposition is computationally evaluated for the multi-component alloy systems of Fe-Al-Co and In-GaAsP by using the thermodynamic data related of the systems. The composition dependence of atomic interchange energy is taken into account. The elasticity and mobility of atoms are assumed to depend on the local order parameters such as composition, degree of order and so on. The time-dependent morphological changes of the microstructure are demonstrated for the formation of modulated structure by spinodal decomposition, strain induced morphological changes of precipitates, the order-disorder phase transition and so on.

Computer simulations of the phase transformation in real alloy systems based on the phase field method

The kinetic simulation based on the non-linear diffusion equation becomes a very powerful method in fundamental understanding of the dynamics of phase transformation with recent remarkable development of the computer. In the present study, we calculate the dynamics of microstructure changes in real alloy systems, i.e. Fe–Mo, Al–Zn and Fe–Al–Co based on the phase field method. The composition dependencies of atomic interchange energy are taken into account so as to be applicable for the phase diagram of the real alloy systems. The elasticity and mobility of atoms are assumed to depend on the local order parameters such as the composition, the degree of order, etc. Time dependent morphological changes of the microstructure such as formation of modulated structure by spinodal decomposition, strain induced morphological changes of precipitates, the order–disorder phase transition with phase decomposition will be demonstrated. The results simulated are quantitatively in good agreement with the experimental results in the real alloy systems.

Evidence of a phase with two-dimensional positional order in a side group liquid crystalline polymer

X-ray scattering studies were performed to elucidate the structure and the character of the correlations in a mesophase with two-dimensional positional order formed in a side group polymer. X-ray diffraction patterns of oriented fibres display weak diffuse lines in the direction parallel to the orientation of the side groups and a regular pattern of strong diffuse spots in the perpendicular direction, indicating positional order on the local scale. The side groups are close packed within a two-dimensional (2D) centred orthorhombic lattice and are tilted with respect to their nearest neighbours. The positional order is anisotropic and is limited by a correlation length of about 30-40A, that is approximately six involved in the short range order. In the direction along the normal to the 2D system shows no translational order. This phase displays the same unit cell symmetry and direction of tilt as the layers of the K phase and is designated as TDK, where the first two letters stand for 'two-dimensional'. Unexpectedly, we found a regular pattern of weak diffuse spots in the small angle scattering region. These indicate a short range modulated structure with the vector of modulation lying in the plane of the 2D packing of the side chains is proposed to explain the formation of modulated structure and the anisotropic character of the positional correlations. to eight side groups are plane, the order. A simple model of the

Shear-Induced Modulated Structure in Blend of Polycarbonate/Nylon6-co-12 Random Copolymer

The morphology of the polycarbonate (PC)/Nylonl2 blend was compared with that of PC/Nylon6-12 random copolymer (Nylon6-co-12, 6 content: 64 mol%) blend. Specific interaction between PC and Nylon was not detected by FT-IR. DSC and DMA data indicated the presence of double Tg’s, corresponding to each component. For the Nylon6-co-12 blend, particles of a minor phase were smaller than those of the other blend. In PC/Nylon6-co-12(50/50) blend, a modulated structure was obtained when melt mixed at 500 s−1. On the other hand, in PC/Nylon12 (50/50) blend, isolated dispersion particles were observed. The formation of modulated structure was interpreted in terms of shear-induced miscibility. PC and Nylon6-co-12 may be miscible under a high shear field in twin-screw kneader, whereas PC and Nylon12 are immiscible under the same processing conditions.

Hierarchical pattern formation in elastic materials

We study hierarchical structures such as branched twins in elastic materials based on a model of martensitic materials in which hierarchical twinning near the habit plane (austenite-martensite interface) is a new and crucial ingredient. The model includes (1) a triple-well potential ( θ 6 model) in local strain, (2) strain gradient terms up to second order in strain and fourth-order in gradient, and (3) all symmetry-allowed compositional fluctuation-induced strain gradient terms which favor hierarchical structures and enable communication between macroscopic (cm) and microscopic (A˚) regions essential for shape memory. Below the transition temperature ( T 0 ) we obtain the conditions under which branching of twins is energetically favorable. This hierarchy of length scales provides a related hierarchy of time scales and thus the possibility of non-exponential decay. Results based on 2D simulations of the time-dependent Ginzburg-Landau (TDGL) equation are shown for twins, tweed and hierarchy formation. We also apply stability analysis to study the formation of modulated structures at early time and obtain an approximate phase diagram for the model.

Modulated quasicrystal structures

Abstract A model for the formation of modulated structures frequently observed in icosahedral alloys of the Al[sbnd]Cu[sbnd]Fe type and representing an intermediate phase at the icosahedral phase-crystalline approximant transition is proposed. An assumption that this structural modulation may be due to a weak decagonality of the icosahedral phase is advanced. In our model, two different types of modulated structure can be distinguished. Such a decagonality originating both from phason strains and from a probable anisotropy of icosahedral shells has been considered.

Decomposition and modulated structure formation during amorphous Si 1 − xGe x crystallization

The crystallization process in undoped amorphous Si 1 − x Ge x films with x = 0.09–0.54 and those deposited on silicon oxide by molecular beam processing, was studied by X-ray diffraction and transmission electron microscopy. Amorphous SiGe decomposed via a Ge-rich phase precipitation during the crystallization at 600–850 °C for periods from 10 s to 12 h. The degree of decomposition increased with temperature. In addition, a new modulated SiGe structure, stapled perpendicular to 〈110〉 was observed. This modulated structure of SiGe was found to be stable during high-temperature annealings.

Phase Separation in the SiC–AlN Pseudobinary System: The Role of Coherency Strain Energy

SiC–AlN polycrystalline samples of equimolar composition were fabricated by hot‐pressing. Single‐phase samples were annealed over a range of temperatures between 1600° and 2000°C for up to 1145 h to effect the formation of modulated structures. Electron diffraction from the [2110] zone axis showed four distinct satellite spots around every main diffraction spot with modulations occurring orthogonal to {0112} planes. The direction of modulation experimentally observed is consistent with that determined by the minimization of the coherency strain energy. Computer simulation was conducted to generate the morphology of modulated structures. The simulated microstructure was found to be very similar to that observed experimentally.