Crystal Direction Research Articles

Directional Crystallization in the Presence of a Mushy Layer with Applications to the Earth’s Inner Core Boundary

We formulate the mathematical model of directional crystallization of a binary melt with a mushy layer (region) between purely solid and liquid phases. This model is complicated by melt convection and pressure-dependent phase transition temperature. Approximate analytical solutions to this nonlinear moving-boundary problem are constructed. Namely, the concentration of impurity, fraction of solid phase, mushy region thickness, average fluid velocity, primary interdendritic spacing, mean radius of a chimney, and a characteristic distance between chimneys in a mushy region are found. Using this analytical solution, we describe the mushy region structure near the inner core boundary of the Earth, which is consistent with computer simulations and estimates existing in recent literature. A scheme illustrating the mushy region arrangement with chimneys at the inner core boundary of the Earth is presented. This arrangement based on the developed theory represents the novelty and importance of our study.

Estimation of directional single crystal elastic properties from nano-indentation by correlation with EBSD and first-principle calculations

In this study, a two-step optimisation process for the estimation of the single crystal stiffness tensor from the indentation modulus is presented. This was accomplished by using a 2-dimensional data correlation method for nano-indentation, EBSD and ab initio data, as well as EDS for phase separation in a multi-phase material. Here, a single-phase Fe-24Ni-0.4C austenitic steel and a two-phase Fe-9.5Ni-0.5Co Seymchan meteorite were used as example materials.In a first step, the combination of high-speed nano-indentation mapping data with elemental and orientation distribution maps allowed the estimation of indentation moduli along specific crystal surface planes normal directions, (001), (011) and (111) using a least squares optimisation based on starting values from DFT or experimentally determined stiffness tensors. A second global optimisation step to estimate the single crystal stiffness tensor using pre-solved solution parameters of the Vlassak-Nix equations yielded reasonable correspondence between the experimentally determined stiffness tensors from correlative nano-indentation data and other methods. The presented method demonstrates generally the possibility to derive directionally sensitive elastic properties from high-speed nano-indentation for cubic materials statistically.

Microstructural evolution and failure mechanism dominated by Bi, Sb cooperative diffusion at p-type thermoelectric pillar Bi-Sb-Te/Sn interface

Bismuth telluride-based thermoelectric devices have attracted much attention in the field of low-quality waste heat recovery below 200 °C. However, the rapid diffusion at the interface between solder and thermoelectric materials was serious after long-term service. The brittle Sn-Te was believed to cause the electrode failure. In this work, it suggested that the regional eutectic melting at the β-Sn/SbSn interface at hot-end electrode was a more important risk to cause the failure, requiring urgent attention. Co-diffusion of Bi and Sb led to partial melting of the Sn-based solder, which did not wet on the SbSn surface and formed solidification cracks. Besides, the distributions and migrations of Bi, Sb, Te, and Sn elements at the interface were investigated, the crystal growth direction of SnTe, SbSn, and nano-Bi phases were analyzed, and the phase composition and phase evolution in complex intermetallic compounds (IMCs) at the Bi-Sb-Te/Sn interface were clarified, combined with SEM, EPMA, and TEM characterization during the aging at 150 °C for 150 h. Based on this failure mechanism, it suggested that the service temperature should be lower than the Sn-Bi eutectic temperature and as low as possible, in the case of without any coating treatment for the consideration of cost.

Bromine versus chlorine substituent in breathing crystals of a copper(I) coordination compound with a triazolamine Schiff base.

It is known that N-[4-(chlorobenzylidene)-4H-1,2,4-triazol-4-amine in reaction with copper(I) perchlorate(VII) forms metastable breathing crystals built up of X-shaped binuclear units containing copper(I) ions in a trigonal coordination sphere. Using trifluoromethanesulfonate instead of perchlorate(VII) affects the self-assembly of the X-shaped units and the breathing function of the resulting crystals. The latter are not breathing crystals. Copper(I) trifluoromethanesulfonate with N-[4-(bromobenzylidene)-4H-1,2,4-triazol-4-amine crystallizes in two forms: open (with the presence of 1D channels) and closed (without 1D channels). Both are characterized by the presence of X-shaped binuclear cationic units and the trigonal coordination sphere of copper(I) ions. The open form has the ability to engage in reversible sorption. The desorption process is associated with the large reorientation of the binuclear units and the reorganization of the intermolecular interactions leading to the closure of the channels. The post-synthetically obtained channel-less form differs from the channel-less form obtained by direct crystallization, the latter being incapable of sorption. The mechanism of the desorption process of the open form is governed by the general principle of dense packing, and the main reason for the sorption process is the formation of directional halogen-halogen interactions. The halogen atom in the para position of the ligands influences the formation of different crystalline forms and also a different mechanism for the desorption process.

Regulation of Near-Field Radiative Heat Transfer between Multilayer BP/hBN Heterostructures.

As an allotrope of phosphorus and a promising 2D semiconductor, black phosphorus (BP) exhibits in-plane anisotropy along its armchair and zigzag crystal directions, allowing for efficient regulation of near-field radiative heat transfer (NFRHT). In this work, we investigate the NFRHT between two multilayer BP/hBN heterostructures and theoretically demonstrate that thermal regulation can be realized by tuning the electron density and rotation angle of BP. Results show that a larger electron density leads to the coupling of anisotropic surface plasmon polaritons (SPPs) of BP with hyperbolic modes of hBN, and rotation of BP changes the anisotropic characteristic of coupled SPPs on both sides, whereby a regulation ratio of 5.8 can be obtained. We also analyze the effects of period number, hBN layer thickness, and topmost-layer material on the NFRHT. This work may be beneficial for efficient nanoscale thermal management and physical understanding of radiative heat transfer based on anisotropic SPPs.

Atomistic analysis of the phase transformation and wear regimes of textured Wurtzite-SiC hexagonality using molecular dynamics simulation

The surface nano-polishing features and wear regime of textured Silicon carbide (SiC) substrates are studied using molecular dynamics modelling. Surface groove-shaped textures improve nano-polishing performance. This method also reduces subsurface wear damage. Switching from cutting to adhering regime can enhance surface roughness, frictional coefficient, and wear regime by decreasing depth. Specifically, reducing polishing depths improved surface roughness from 1.77% to 9.33%. Increasing polishing speed or crystal direction indicates an adherent wear regime and improves surface roughness from 2.6% to 9.61%. Nano-polishing the (0001) plane produced more heat than other planes. Thus, the (0001) plane has more graphene-like structure atoms and is closer to completion than other planes. This discovery helps texture SiC-based materials increase their anti-friction and wear properties.

A compressive-shear biaxial stress field model for analyzing the anisotropic mechanical behavior of nanotwinned diamond

Synthetic nanotwinned diamond (Nt-D) with unprecedented hardness and toughness is an ideal material for manufacturing ultra-precision cutting tools. It is urgent to investigate the surface formation mechanism of Nt-D under complex stress fields. Here, we developed a compressive-shear biaxial stress field model to study the extreme anisotropic mechanical behavior of Nt-D. It was found that graphitization occurred in all shear directions of the Nt-D (0001) plane through the microstructure evolution of 2H-diamond, 4H-diamond, 6H-diamond, and 9R-diamond, in which the stress release mechanism was accompanied by partial slips in certain specific crystal directions such as 〈1010〉. In addition, the generalized stacking fault energy calculation indicates that the partial slip in 6H- and 9R-diamonds is mainly attributed to the low slip energy barrier between adjacent interlayer. These results expand our understanding of the surface formation mechanism of Nt-D and will contribute to the manufacturing of new-generation ultra-precision tools.

The Role of Te, As, Bi, and Sb in the Noble Metals (Pt, Pd, Au, Ag) and Microphases during Crystallization of a Cu-Fe-S Melt

Quasi-equilibrium directional crystallization was performed on a melt composition (at. %): 18.50 Cu, 32.50 Fe, 48.73 S, 0.03 Pt, Pd, Ag, Au, Te, As, Bi, Sb, and Sn, which closely resembles the Cu-rich massive ores found in the platinum-copper-nickel deposits of Norilsk. Base metal sulfides (BMS) such as pyrrhotite solid solution (Fe,Cu)S1±δ (Poss), non-stoichiometric cubanite Cu1.1Fe1.9S3 (Cbn*), and intermediate solid solution Cu1.0Fe1.2S2.0 (Iss) are progressively precipitated from the melt during the crystallization process. The content of noble metals and semimetals in the structure of BMS is below the detection limit of SEM-EDS analysis. Only tin exhibits significant solubility in Cbn* and Iss, meanwhile Pt, Pd, Au, Ag, As, Bi, Sb, and Te are present as discrete composite inclusions, comprising up to 11 individual phases, within their matrices. These microphases correspond to native Au, native Bi, hessite Ag2Te, sperrylite Pt(As,S)2, hedleyite Bi2Te, michenerite PdTeBi, froodite PdBi2, a solid solution of sudburite-sobolevskite-kotulskite Pd(Sb, Bi)xTe1−x, geversite PtSb2, and a multicomponent solid solution based on geversite Me(TABS)2, where Me = Σ(Pt, Pd, Fe, Cu) and TABS = Σ(Te, As, Bi, Sb, Sn). Most of the inclusions occur as thin layers between BMS grain boundaries or appear drop-shaped and subhedral to isometric grains within the sulfide matrix. Only a small fraction of the trace elements form mineral inclusions of sizes ≤ 0.5 μm in Poss, most likely including PtAs2 and (Pt,Pd)S. It is likely that the simultaneous presence of noble metals (Pt, Pd, Au, Ag) and semimetals (As, Te, Bi, Sb) in the sulfide melt leads to the appearance of liquid droplets in the parent sulfide melt after pyrrhotite crystallization. The solidification of droplets during the early stages of Cbn* crystallization may occur simultaneously with the cooling of later fractions of the sulfide melt, resulting in the formation of Iss. In addition, abundant gas voids containing micro-inclusions were observed in Cbn* and Iss. These inclusions showed similar chemical and mineral compositions to those in BMS matrices, i.e., the presence of gas bubbles did not affect the main features of noble metal fractionation and evolution. Therefore, it is reasonable to assume that ore particles suspended in the melt are either trapped by defects at the crystallization front or transported towards gas bubbles via the Marangoni effect.

In-Situ Microscale Compression Testing of Li-Si Micropillars

Silicon is considered as an ideal anode material for high-capacity Li-ion batteries (LIB) thanks to its high theoretical capacity, but the commercial viability is severely hampered by considerable volume expansion of Si upon lithiation that can lead to mechanical failure (e.g., cracks and delamination). Hence, understanding the mechanical behaviors of the Li-Si system is of high interest, but the experimental studies have been limited to thin film electrodes by means of wafer curvature measurements or nanoindentation. In this work, we for the first time present in-situ microscale compression testing of Li-Si micropillars and extract the key mechanical properties (e.g., Young’s modulus, yield strength, and fracture energy) from the resulting stress-strain curves. Prior to testing, Si micropillars of various sizes/shapes and oriented at different crystal directions were lithiated/delithiated at room temperature. We then performed the microscale compression testing on these lithiated Si micropillars using a flat-head indenter in environmental scanning electron microscope (ESEM) while obtaining live video images for data-image correlation. The results suggest that the measured elastic moduli of the Li-Si system agree with the values obtained from the standard nanoindentation experiments but with much smaller variance. The precise nature of these experiments allows us to observe the mechanical properties dependent on the crystal orientation of Si and lithiation rate. In addition, various failure behaviors of Li-Si under compressive stresses will be presented, which is difficult to be obtained through the existing experimental techniques.

A first-principles study of interstitial oxygen on the strength/ductility of α-Ti: Crystal structures, elastic properties and electronic structures

Interstitial oxygen (O) is one of the most critical impurity elements for titanium (Ti) and its alloys. This study adopts the first-principles method based on the density function theory (DFT) to calculate the lattice constants, elastic properties and electronic structures of the pure Ti and Ti-O(O) structures with different O contents. Results show that the c/a lattice parameter increases with the increase of O content and reaches the maximum value of 1.642 when O content is 20 at%. In addition, the bulk modulus (B), shear modulus (G) and G/B of the Ti-O(O) structures gradually increase with the increase of O content, and the corresponding ductility becomes worse. Furthermore, interstitial O atom makes a uniform transformation of the metal bond shift toward a more covalent direction, which strongly influences the ductility of Ti-O(O) structures. Furthermore, the interstitial O leads to the great difference in the chemical bond behavior of the crystals in different directions, which shows anisotropy on the micro level. The aim of this study is to reveal the effect of interstitial O on the mechanical properties of Ti alloys, and also to provide reference for reasonable control of O content of Ti alloys in industrial production.

Giant enhancement of magnetostriction in Pt doped FeGa ribbons

FeGa alloys are among the most promising magnetostrictive materials. How to improve the magnetostriction of FeGa has been a long-term concern. In this work, trace amount of Pt doped FeGa-(Fe0.83Ga0.17)100–xPtx (x = 0, 0.2, 0.4, and 0.6) was fabricated using melt-spinning technique. The magnetostriction, crystal structure, and magnetocrystalline anisotropy of the ribbon samples were studied, revealing that the conforming between the crystal growth direction and the easy magnetization axis, and the enlarged lattice parameter both contribute to the enhancement of magnetostriction, which reached the maximum λ⊥ of −1369 ppm at the optimum composition x = 0.4. Finally, transmission electron microscopy was performed to show that nanoinclusions exist not only in Pt-doped but also in Pt-free samples, demonstrating that the nanoinclusions do not play the dominant role in magnetostriction improvement. This work may accelerate the design of highly magnetostrictive FeGa alloys and other magnetic functional materials, which are required of large magnetostriction.

Near-field radiative modulator based on α-MoO3 films

Near-field radiative heat transfer (NFRHT) has great potential in thermal management and energy harvesting due to the giant radiative heat flux. Modulation of NFRHT is another important research direction, where relative rotation between the emitter and receiver is a typical method. However, the enhancement of modulation contrast (MC) is mainly concerned in previous works, while large heat flux is not taken into account. In this work, we investigate the heat transfer coefficient (HTC) between α-MoO3 films along different crystal directions of α-MoO3. We take account of the modulator with high heat flux and high MC. The results show that the HTC and MC can reach 223.2 W/(m2·K) (36 times of blackbody limit) and 6.33 at a gap distance of 100 nm when NFRHT is along [010] crystal direction of α-MoO3, respectively. These are attributed to the excitation and mismatch of hyperbolic phonon polaritons (HPhPs). Furthermore, when NFRHT is along [100] and [001] crystal directions of α-MoO3, MCs reach 5.84 and 2.38, respectively. The results are strongly related to the crystal direction. In addition, the impact of film thickness on the MC for different crystal directions is investigated. This work is conducive to the applications of hyperbolic materials in non-contact thermal modulators.

In-situ fusion process and Cu–Sn compounds evolution mechanism of nano-intermetallic compound mixed solder joints

This study investigated the fusion and phase-transformation processes of nano-intermetallic compound (nano-IMC) mixed solder pastes. In particular, the interfacial reaction with the Cu substrate, the kinetics and mechanism of Cu6Sn5 growth inside the solder joint, and the shear strength of the solder joint were investigated. In-situ SEM and XRD results showed that the SAC305 and Sn–10Cu powders fused and the liquid solder ball completely melted at 227 °C. A higher initial Cu concentration in the mixed solder joints resulted in a lower Cu concentration gradient that inhibited the diffusion of Cu atoms. The growth activation energy of the IMC layer of a SAC305 + 20 wt% Sn–10Cu solder joint was 104.81 kJ/mol, which was higher than that of the SAC305 IMC layer (75.75 kJ/mol). During aging, Cu6Sn5 rods within the mixed solder joint formed gullies on the outer facets, and the Cu6Sn5 rods continued to grow along the [0001] crystal direction. The number of Sn grains and the proportion of high-angle grain boundaries in the mixed solder joints were higher after reflow. After aging at 150 °C for 1000 h, the shear strength of the SAC305 + 20 wt% Sn–10Cu solder joints was 34.25 MPa, slightly higher than that of SAC305 (33.12 MPa).

Morphological/Dynamic Instability of Directional Crystallization in a Finite Domain with Intense Convection

This study is devoted to the morphological/dynamic instability analysis of directional crystallization processes in finite domains with allowance for melt convection. At first, a linear instability theory for steady-state crystallization with a planar solid/liquid interface in the presence of convection was developed. We derived and analyzed a dispersion relation showing the existence of morphological instability over a wide range of wavenumbers. This instability results from perturbations arriving at the solid/liquid interface from the cooled wall through the solid phase. Also, we showed that a planar solid/liquid interface can be unstable when it comes to dynamic perturbations with a zero wavenumber (perturbations in its steady-state velocity). A branch of stable solutions for dynamic perturbations is available too. The crystallizing system can choose one of these branches (unstable or stable) depending of the action of convection. The result of morphological and dynamic instabilities is the appearance of a two-phase (mushy) layer ahead of the planar solid/liquid interface. Therefore, our next step was to analyze the dynamic instability of steady-state crystallization with a mushy layer, which was replaced by a discontinuity interface between the purely solid and liquid phases. This analysis showed the existence of dynamic instability over a wide range of crystallization velocities. This instability appears in the solid material at the cooled wall and propagates to the discontinuity interface, mimicking the properties of a mushy layer. As this takes place, at a certain crystallization velocity, a bifurcation of solutions occurs, leading to the existence of unstable and stable crystallization branches simultaneously. In this case, the system chooses one of them depending of the effect of the convection as before. In general, the crystallizing system may be morphologically/dynamically unstable when it comes to small perturbations arriving at the phase interface due to fluctuations in the heat and mass exchange equipment (e.g., fluctuations in the freezer temperature).

The effect of crystal anisotropy on fracture toughness and strength of ZrB2 microcantilevers

AbstractThe influence of crystal anisotropy on the micromechanical properties of ceramic grains plays an important role in the design of the macromechanical performance of bulk polycrystalline samples. To this end, the effect of crystal orientation on fracture toughness and strength was investigated by microcantilever bending experiments combined with finite element method (FEM) simulations in grains of a polycrystalline ZrB2 sample. The sample was prepared by hot pressing and the crystal orientations were determined by electron backscatter diffraction after careful surface preparation. The bending tests were carried out on notched and unnotched microcantilevers cut from specific grains along the prismatic (⊥ to c‐axis), basal (∥ to c‐axis), and intermediate (45° to c‐axis) directions of ZrB2 crystals using focused ion beam milling. The fracture toughness and strength were determined by FEM‐derived analytical solutions. The fracture strength was similar with values of about 11–12 GPa in every direction. Enhanced plasticity was found in the intermediate direction of unnotched beams as compared to the other two brittle orientations. The fracture toughness was found to be 30% higher in the intermediate direction (4.1 MPa m0.5) than those measured for the basal (3.1 MPa m0.5) and prismatic directions (3.3 MPa m0.5). These findings were explained by the orientation dependence of slip system activations which provide a new way in the design of textured polycrystalline ZrB2 ceramics toward enhanced damage tolerance.

PbF2–CdF2–SrF2 Ternary Solid Solution: Crystal Growth and Investigation

Crystals based on alkaline earth metal difluorides are widely used optical materials. In this study, in order to expand the range of optical matrices, multicomponent Pb1−x−yCdxSryF2 (0.27 < x < 0.55, 0.06 < y < 0.18) solid solution crystals with a fluorite structure (sp. gr. Fm-3m) were grown from melt using the vertical directional crystallization technique for the first time. The densities and refractive indices of the grown crystals vary depending on the quantitative content components (x and y) in the ranges of 6.6039(5)–7.5232(5) g/cm3 and 1.6403–1.7084, respectively. The optical transmission and electrochemical impedance spectra were studied. The homogenous composition regions of non-cellular crystallization of this ternary solid solution at a crystallization rate of 6 mm/h and an interface temperature gradient of 80 deg/cm were experimentally determined as 0.30 < x < 0.35, 0 < y < 0.6. These grown crystalline materials may be of interest as high-density highly refractive cubic isomorphic hosts and low-temperature ionic conductors (~2 × 10−5 S/cm at room temperature) for various applications.

Synthesis, Microstructure, and Electrical Conductivity of Eutectic Composites in MF2–RF3 (M = Ca, Sr, Ba; R = La–Nd) Systems

Multiphase fluoride polycrystalline eutectics pRF3 × qMF2 forming in the MF2–RF3 (M = Ca, Sr, Ba; R = La–Nd) binary systems were synthesized by the directional crystallization technique from a melt. The phase composition, morphology, and temperature dependences of fluorine ionic conductivity in fabricated composites were studied in detail. The pRF3 × qMF2 (p and q are the mole percentages of components) eutectic composites consist of both extremely saturated fluorite-type structure M1−xRxF2+x solid solutions and the tysonite-type R1−yMyF3−y ones. Microsized growth blocks with a fine lamellar structure are typical for synthesized composites. The thinnest (from 3 μm) and longest lamellae are observed in the 68LaF3 × 32BaF2 composition. The ionic conductivity values of pRF3 × qMF2 composites are determined by the phase composition, practically do not depend on their morphological features, and reach 10−3–10−2 S/cm at 500 K (with an ion transport activation enthalpy of about 0.5–0.6 eV). Crystallized eutectics are superior to any single-phase M1−xRxF2+x solid solutions and ball-milling R1−yMyF3−y nanoceramics in terms of ion-conducting properties. These fluoride materials represent an alternative to widely applied tysonite-type ceramic composites in various electrochemical devices and require further in-depth studies.

Interdimensional radial discrete diffraction in Mathieu photonic lattices.

We demonstrate transitional dimensionality of discrete diffraction in radial-elliptical photonic lattices. Varying the order, characteristic structure size, and ellipticity of the Mathieu beams used for the photonic lattices generation, we control the shape of discrete diffraction distribution over the combination of the radial direction with the circular, elliptic, or hyperbolic. We also investigate the transition from one-dimensional to two-dimensional discrete diffraction by varying the input probe beam position. The most pronounced discrete diffraction is observed along the crystal anisotropy direction.

Influence of neutron irradiation on X-ray diffraction, Raman spectrum and photoluminescence from pyrolytic and hot-pressed hexagonal boron nitride

Hexagonal boron nitride (hBN) is considered as an ideal semiconductor material for solid-state neutron detector, owing to its large neutron scattering section because of the low atomic number of B and excellent physical properties. Here we study the influence of neutron irradiation on crystal structure and on intermediate energy state (IMES) levels induced by the presence of impurities and defects in hBN. Large-size and thick pyrolytic and hot-pressed hBN (PBN and HBN) samples, which can be directly applied for neutron detector devices, are prepared and bombarded by neutrons with different irradiation fluences. The SEM and TEM are used to observe the sample difference of PBN and HBN. X-ray diffraction and Raman spectroscopy are applied to examine the influence of neutron irradiation on lattice structures along different crystal directions of PBN and HBN samples. Photoluminescence (PL) is employed to study the effect of neutron irradiation on IMESs in these samples. We find that the neutron irradiation does not alter the in-plane lattice structures of both PBN and HBN samples, but it can release the inter-layer tensions induced by sample growth of the PBN samples. Interestingly and surprisingly, the neutron irradiation does not affect the IMES levels responsible for PL generation, where PL is attributed mainly from phonon-assisted radiative electron-hole coupling for both PBN and HBN samples. Furthermore, the results indicate that the neutron irradiation can weaken the effective carrier-phonon coupling and exciton transitions in PBN and HBN samples. Overall, both PBN and HBN samples show some degree of the resistance to neutron irradiation in terms of these basic physical properties. The interesting and important findings from this work can help us to gain an in-depth understanding of the influence of neutron irradiation on basic physical properties of hBN materials. These effects can be taken into account when designing and applying the hBN materials for neutron detectors.

Global Crystallographic Texture of Pyrite in Fossil Wood (Jurassic, Oryol Region, Russia)

Many works are devoted to the study of the crystallographic texture of primary skeletal minerals of animals. But how the directions of mineral crystals that replace the organic matter in the fossil state are oriented is unknown. Here we investigated the crystallographic texture of pyrite grown on an organic matrix and without it. Jurassic pyritized wood (Middle Jurassic, Callovian) was studied by the neutron diffraction method. The global crystallographic texture of pyrite in nodules and fossil wood is compared. It was found that in both cases, the isoline patterns of pole figures and texture sharpness are similar to the same characteristics of abiogenic calcite. But the orientations of pyrite crystals in wood are more ordered, the isolines are closer, and the regions of maximum pole density are wider. That is, the pyrite crystals that replaced the petrified wood are more ordered. This was influenced by the organic matrix on which the crystals grew. Repetition of a fossil mollusk shell shape without using its shell as a matrix for crystal growth does not lead to an increase in the crystallographic texture sharpness. This is illustrated by an example of the inner core calcite shell of the gastropod mollusk Bellerophon sp.