Anisotropy Of Interfacial Energy Research Articles

Large Perpendicular Magnetic Anisotropy in Ta/CoFeB/MgO on Full-Coverage Monolayer MoS2 and First-Principles Study of Its Electronic Structure.

A perpendicularly magnetized spin injector with a high Curie temperature is a prerequisite for developing spin optoelectronic devices on two-dimensional (2D) materials working at room temperature (RT) with zero applied magnetic field. Here, we report the growth of Ta/CoFeB/MgO structures with large perpendicular magnetic anisotropy (PMA) on full-coverage monolayer (ML) molybdenum disulfide (MoS2). A large perpendicular interface anisotropy energy of 0.975 mJ/m2 has been obtained at the CoFeB/MgO interface, comparable to that observed in magnetic tunnel junction systems. It is found that the insertion of MgO between the ferromagnetic (FM) metal and the 2D material can effectively prevent the diffusion of the FM atoms into the 2D material. Moreover, the MoS2 ML favors a MgO(001) texture and plays a critical role in establishing the large PMA. First-principles calculations on a similar Fe/MgO/MoS2 structure reveal that the MgO thickness can modify the MoS2 band structure, from a direct band gap with 3ML-MgO to an indirect band gap with 7 ML-MgO. The proximity effect induced by Fe results in splitting of 10 meV in the valence band at the Γ point for the 3ML-MgO structure, while it is negligible for the 7 ML-MgO structure. These results pave the way to develop RT spin optoelectronic devices based on 2D transition-metal dichalcogenide materials.

Crystal growth of bcc titanium from the melt and interfacial properties: A molecular dynamics simulation study.

The crystal growth kinetics and interfacial properties of titanium (Ti) are studied using molecular dynamics computer simulation. The interactions between the Ti atoms are modeled via an embedded atom method potential. First, the free solidification method (FSM) is used to determine the melting temperature Tm at zero pressure where the transition from liquid to body-centered cubic crystal occurs. From the simulations with the FSM, the kinetic growth coefficients are also determined for different orientations of the crystal, analyzing how the coupling to the thermostat affects the estimates of the growth coefficients. At Tm, anisotropic interfacial stiffnesses and free energies as well as kinetic growth coefficients are determined from capillary wave fluctuations. The so-obtained growth coefficients from equilibrium fluctuations and without the coupling of the system to a thermostat agree well with those extracted from the FSM calculations.

A numerical study of dendrite growth and microstructure transition in a non-equilibrium solidification

Controlling the thermal condition of a solidification process to obtain a desirable microstructure morphology and then prepare specific materials with excellent mechanical properties or special functions has been attracting many concerns, where the behavior of microstructure morphology transition, especially the columnar-to-equiaxed transition, is one of the most important fundamental issues. This paper introduced a kinetic model for dendrite growth with a large undercooling during a non-equilibrium solidification process using cellular automaton, in which the local thermodynamic equilibrium condition, non-equilibrium partitioned solute, curvature and interface energy anisotropy were considered. The growth rate of dendrite tip was numerically investigated by using the cellular automaton model, and the effects of temperature gradient and cooling rate on the growth rate and morphology features were found. By integrating the simulation results and analytical models, a new microstructure morphology transition criterion for the non-equilibrium solidification depending on the temperature gradient and cooling rate was proposed, in which both the planar-to-columnar and the columnar-to-equiaxed transition were presented.

Phase field simulation of the stress-induced α microstructure in Ti–6Al–4 V alloy and its CPFEM properties evaluation

Variant selection under specific applied stresses during precipitation of α plates from prior-β matrix in Ti–6Al–4 V was investigated by 3D phase field simulations. The model incorporates the Burgers transformation path from β to α phase, with consideration of interfacial energy anisotropy, externally applied stresses and elastic interactions among α variants and β matrix. The Gibbs free energy and atomic mobility data are taken from available thermodynamic and kinetic databases. It was found that external stresses have a profound influence on variant selection, and the selection has a sensitive dependence, as evidenced by both interaction energy calculations and phase field simulations. Compared with normal stresses, shear stresses applied in certain directions were found more effective in accelerating the transformation, with a stronger preference to fewer variants. The volume fractions of various α variants and the final microstructure were determined by both the external stress and the elastic interaction among different variants. The α clusters formed by variants with Type2 misorientation ([1 1 -2 0]/60°) relation were found more favored than those with Type4 ([-10 5 5 -3]/63.26°) under certain applied tensile stress such as along <111>β. The mechanical properties of different microstructures from our phase field simulation under different conditions were calculated for different loading conditions, utilizing crystal plastic finite element simulation. The mechanical behavior of the various microstructures from phase field simulation can be evaluated well before the alloys are fabricated, and therefore it is possible to select microstructure for optimizing the mechanical properties of the alloy through thermomechanical processing based on the two types of simulations.

Interface characteristics in ZrB2-based ceramics containing SiC and/or ZrC particles via hot-pressing sintering

ZrB2-based ceramics containing SiC and/or ZrC were prepared by hot-pressing sintering. The characteristics of different interfaces in the sintered ceramics and their relationships with chemical compositions were investigated via SEM, HRTEM, EBSD and dihedral angle analysis. Atoms at ZrB2-ZrB2 grain boundaries (GBs) preferentially arrange orderly when ZrC is introduced into ZrB2 matrix. The percentages of rounded ZrB2-ZrB2 GBs at micro-scale decrease from 68.8% in ZrB2-20SiC (number in vol%) to 31.1% in ZrB2-20ZrC. Atomic arrangement at ZrB2-ZrC interfaces satisfies unique orientation relationship that (101)ZrB2 is parallel to (110)ZrC and [010]ZrB2 is parallel to [11¯0]ZrC simultaneously. Interfacial energies of different interfaces were studied by dihedral angle analysis, which indicates that ZrB2-ZrC interfaces have lower interfacial energies and ZrB2-ZrB2 GBs exhibit anisotropic interfacial energies in the ceramics containing ZrC.

Phase Field Modelling of Morphologies Driven by Tetragonal Interfacial Energy Anisotropy

A wide range of morphologies, such as dipyramids, rods, plates, and their truncated variants with more than one type of facet, are experimentally observed in tetragonal systems. In many cases, the ...

The formation mechanism of special globular surface grain during the solidification of laser surface remelted near β titanium alloys

During laser materials processing, the cooling rate (R) and thermal gradient (G) near the molten pool surface region are much higher than those in the traditional casting conditions, which may result in special solidification microstructures. In this study, the surface microstructure of near β titanium alloys was investigated by conducting both laser surface remelting experiments and phase-field simulations. It was found that the grains nucleated near the surface region of the molten pool exhibit near globular shape with 〈110〉-oriented side branches, which are very different from the ordinary dendrite morphology in casting conditions. Phase-field simulations were used to detect the formation mechanism of such special surface grain morphology. It was illustrated that the surface grain morphology is determined by the combined effect of high cooling rate (R) and high vertical thermal gradient (G). The high R results in the morphology transition from needle-like dendrite to near globular shape by increasing the undercooling and reducing the impact of anisotropy of interface energy. The high G promotes the grain contour to be more close to globular and facilitates the fins-like side branches to develop along 〈110〉 direction. Furthermore, a selection map of surface grain morphology at various thermal conditions (R and G) was established, which can be applied to predict the surface grain morphology.

On $$\varGamma $$-Convergence of a Variational Model for Lithium-Ion Batteries

A singularly perturbed phase field model used to model lithium-ion batteries including chemical and elastic effects is considered. The underlying energy is given by $$I_\epsilon [u,c ] := \int_\Omega \left( \frac{1}{\epsilon} f(c) + \epsilon\|\nabla c\|^2 + \frac{1}{\epsilon}\mathbb{C} (e(u)-ce_0) : (e(u)-ce_0)\right) dx, $$ where $f$ is a double well potential, $\mathbb{C}$ is a symmetric positive definite fourth order tensor, $c$ is the normalized lithium-ion density, and $u$ is the material displacement. The integrand contains elements close to those in energy functionals arising in both the theory of fluid-fluid and solid-solid phase transitions. For a strictly star-shaped, Lipschitz domain $\Omega \subset \mathbb{R}^2,$ it is proven that $\Gamma - \lim_{\epsilon\to 0} I_\epsilon = I_0,$ where $I_0$ is finite only for pairs $(u,c)$ such that $f(c) = 0$ and the symmetrized gradient $e(u) = ce_0$ almost everywhere. Furthermore, $I_0$ is characterized as the integral of an anisotropic interfacial energy density over sharp interfaces given by the jumpset of $c.$

Enhanced Interface-Driven Perpendicular Magnetic Anisotropy by Symmetry Control in Oxide Superlattices

Perpendicular magnetic anisotropy (PMA) has recently been shown to emerge at interfaces of 3d and 5d transition-metal oxides (TMOs). However, strategies to systematically stabilize such interface-driven PMA still remains elusive, hindering further applications of this design approach. Here, tuning crystal symmetry is shown to be an effective means to engineer this interfacial phenomenon. The evolution of PMA strength as a function of ferromagnetic oxide thickness quantitatively reveals the competition between volume- and interface-specific contributions that determine the magnetic anisotropy. By applying different degrees of epitaxial strain, the relative contributions to PMA are modulated, clearly revealing their correlations with crystal symmetries. To be more specific, the volume anisotropy energy is found to be correlated with the tetragonal distortion of the ferromagnetic layer, while the interface anisotropy energy is mainly modulated by the octahedral tilting at the interface. With these insights, superlattices with enhanced interface-driven PMA and higher Curie temperature are realized. These findings reveal a route to engineering interface-driven PMA and associated magnetic phenomena in TMO heterostructures for future spintronic applications.

A study of hydride precipitation in zirconium

Zirconium-based alloys used in nuclear reactors are susceptible to hydrogen pickup. When the hydrogen concentration in the solid solution exceeds the threshold limit (terminal solubility), a solid-state phase transformation occurs in these alloys. The zirconium hydride phase so precipitated is brittle and may influence the integrity of in-core structural components by various mechanisms, such as hydride blistering, delayed hydride cracking (DHC) etc. Precipitation which usually occurs by nucleation, growth and coarsening is typically influenced by the coherent stresses as well as the external stress field. In this work, Eshelby-type analyses are carried out to understand the mechanics and energetics associated with precipitation of zirconium hydrides. In particular, the role of elastic mismatch between the matrix and inclusion and the external stress in controlling the morphology and orientation of a hydride precipitate is analyzed. Elastic calculations lead to several interesting findings and reveal that under the influence of an external stress, a hydride precipitate has a tendency to reorientate along a certain crystallographic plane of the zirconium matrix. Incorporation of hydride plasticity, in our proposed scheme, leads to hydride reorientation at realistic magnitudes of applied stress. The strong anisotropy in interfacial energy, however, causes a hydride precipitate to remain parallel to the basal plane. Potential applications of our proposed numerical scheme to other relevant fields are also discussed.

Comprehensive Phase Field Study on Directionally-Solidified MoSi&lt;sub&gt;2&lt;/sub&gt;/Mo&lt;sub&gt;5&lt;/sub&gt;Si&lt;sub&gt;3&lt;/sub&gt; Eutectic Alloy

MoSi2/Mo5Si3 eutectic composites have been considered as one of the promising candidates for ultra-high temperature structural applications owing to their high melting point, good oxidation resistance, and low mass density. Their mechanical properties can be improved by controlling the eutectic structure (i.e. script lamellar structure) in directional solidification. It is important to elucidate the dominant factors underlining the unique pattern formation. We conducted a comprehensive phase field study to examine the influence of various factors on the MoSi2/Mo5Si3 eutectic microstructure with complicated morphology. First, the inclined lamellae have been attributed to the minimization of elastic strain energy due to the lattice mismatch between MoSi2 and Mo5Si3, which are partially relaxed by forming semi-coherent phase boundaries. Second, the maze-like pattern on the horizontal cross-section appeared when a two-fold anisotropy of interfacial energy is superimposed on the MoSi2/Mo5Si3 boundary. Third, the random and intersected lamellae have been obtained by assuming the instability of the solid-liquid interface and introducing successive nucleation of Mo5Si3 phase. These findings provide guidance for manipulating the eutectic structure and act as footsteps for further theoretical investigation.

Effect of Ta insertion between Pt and CoFeB on interfacial magnetic anisotropy in Pt/CoFeB/MgO multilayer thin-film stack

The effect of a thin Ta layer inserted between Pt and CoFeB layers on perpendicular magnetic anisotropy (PMA) with MgO barrier layer has been studied. The crystallinity was studied by performing high-resolution x-ray diffraction (HR-XRD) technique. While the crystal peak of Pt is observed in all sample stack that is oriented as (111) face-centered cubic crystal structure, a very weak and broad α-Ta (110) peak is observed when Ta layer thickness is above 0.8 nm. Magneto-optical Kerr effect (MOKE) measurements show that the PMA could be enhanced by inserting Ta layer between Pt and CoFeB layer. The magnetically dead layer thickness (tdead) and the interfacial anisotropy energy density (Ki) of the various Ta-inserted layer thickness were found as 0.135 nm; 0.75 erg/cm2, 0.141 nm; 1.02 erg/cm2, 0.187 nm; 1.15 erg/cm2, for tTa = 0.0, 0.5, and 1.0 nm, respectively. Both tdead and Ki increase with Ta-inserted layer thickness in Pt/Ta(t)/CoFeB/MgO multilayer film stack. The sources of interfacial magnetic anisotropy can be hybridization, crystallinity properties, and/or B/Ta diffusion effect at the interfaces in Pt/Ta(t)/CoFeB/MgO multilayer film stack.

A Monte Carlo approach to simulate dendritic microstructures during binary alloy solidification

A Monte Carlo (MC) approach to model the evolution of microstructures during the binary alloy solidification process has been presented. The evolution of these microstructures is comprehensively modelled by ensuring a local minimization of free energy taking into account the contributions of the free energy change during phase transformation, solid-liquid interfacial energy, interfacial energy anisotropy and grain boundary energy, which are some of the ignored aspects of the existing MC models. Further, the effect of imposed orientation is also represented in this model. The proposed method is able to simulate the preferential growth of cubic structures in ⟨100⟩ direction, growth of large number of grains and competition among them, and also incorporates the grain boundary energetics. The model is applied to simulate the growth of free and constrained dendrites, the transition from stable to cellular and dendritic growth under different growth conditions. Growth of multiple grains, the competition during columnar growth, columnar to equiaxed transition by seeding the undercooled melt with solid phase and the impingement of equiaxed grains has also been simulated using this model.

Phase-field simulations of dendritic morphologies in hot-dip galvanized Zn-Al coatings

The growth morphologies of dendrites in thin Zn-0.2 wt% Al coating layers are investigated as a function of the inclination axis and angle of the Zn basal plane with respect to the coating plane using three-dimensional (3D) phase-field simulations under realistic process conditions. In addition to the well-known growth direction families of 〈101¯0〉 and 〈0001〉, we incorporate a third preferred growth direction family into interface kinetic anisotropy based on the recent suggestion by Kim et al. [Metall. Mater. Trans. A 50 (2019), 3186–3200]. When this interface kinetic anisotropy is combined with the isotropic interface energy in the phase-field model, the 3D simulations realistically reproduce most of the morphological characteristics of the dendrites observed in experiments. These include the asymmetric morphologies about the inclination axis, morphological changes with the inclination angle, and angular variations between the primary aims. However, simulations using the experimental estimates of the interface energy anisotropy fail to reproduce characteristic morphologies, such as the four- and eight-fold dendrites, even when combined with strong interface kinetic effects. The present study establishes the existence of a third preferred growth direction family, which is close to the directions normal to the 12¯11planes, and the importance of the interface kinetic anisotropy over the interface energy anisotropy in the dendritic solidification of Zn-rich alloys.

Crystallographic and Morphological Evidence of Solid–Solid Interfacial Energy Anisotropy in the Sn-Zn Eutectic System

In this paper, we explore the morphological evolution during two-phase growth in the Sn-Zn eutectic system, which has a particularly low volume fraction of the minority Zn phase. The reason for this choice is its exotic nature, as even with such a low volume fraction, the reported morphology is “broken-lamellar,” in contrast to the usually expected hexagonal arrangement of Zn rods in the Sn matrix. Thus, the main objective of the study is to investigate the reasons behind this phenomenon. We begin by presenting experimental results detailing the morphology and crystallography of the eutectic microstructures under various combinations of thermal gradients and velocities in directional solidification conditions. Based on the crystallography and further specially designed experiments we find that the solid–solid interface between the Sn and Zn crystal is anisotropic. On the basis of the results, we propose a hypothesis that the presence of solid–solid interfacial energy anisotropy leads to the formation of predominantly broken-lamellar structures, even when the minority fraction is significantly low.

Role of Solid–Solid Interfacial Energy Anisotropy in the Formation of Broken Lamellar Structures in Eutectic Systems

Eutectic solidification gives rise to a wide range of microstructures. A commonly observed morphology is the periodic arrangement of lamellar plates with well-defined orientations of the solid–solid interface in a given eutectic grain. It is typically believed that this form of morphology develops due to the presence of solid–solid interfacial energy anisotropy. In this paper, we provide evidence using phase-field simulations where our focus is on alloys where the minority phase fraction is low. Our aim is to establish the role of solid–solid interfacial energy anisotropy in the stabilization of broken lamellar structures in such systems in contrast to the formation of a rod microstructure. In this regard, we conduct phase-field simulations for different strengths of anisotropy in both constrained and extended settings, using which we clarify the mechanisms by which a lamellar arrangement gets stabilized in the presence of anisotropy in the solid–solid interfacial energy.

Formation mechanism of α lamellae during β→α transformation in polycrystalline dual-phase Ti alloys

Phase field simulations incorporating contributions from chemical free energy and anisotropic interfacial energy are presented for the β→α transformation in Ti-6Al-4 V alloy to investigate the growth mechanism of α lamellae of various morphologies from undercooled β matrix. The α colony close to realistic microstructure was generated by coupling the Thermo-Calc thermodynamic parameters of α and β phases with the phase field governing equations. The simulations show that α lamellar side branches with feathery morphology can form under a certain combination of interfacial energy anisotropy and temperature. α lamellae tend to grow slowly at high heat treatment temperature and become wider and thicker as temperature increase from 800 to 900 °C provided that the interfacial energy anisotropy ratio kx: ky was set as 0.1: 0.6. Besides, higher interfacial energy anisotropy can accelerate the formation of α lamellae, and the equilibrium shape of α lamellae changes from rod to plate as the interface energy anisotropy ratio kx: ky vary from 0.1: 0.4 to 0.1: 0.8 under 820 °C. Experiments were conducted to study the α lamellar side branches in Ti-6Al-4 V (Ti-6.01Al-3.98 V, wt.%) and Ti-4211 (Ti-4.02Al-2.52V-1.54Mo-1.03Fe, wt.%) alloys with lamellar microstructure. Electron backscatter diffraction (EBSD) results show that α lamellar side branches and their related lamellae share the same orientation. The predicted temperature range for α lamellar side branches formation under various interfacial energy anisotropy is consistent with experimental results.

Equilibrium shape of misfitting precipitates with anisotropic elasticity and anisotropic interfacial energy

Extended finite element method and anisotropic level set method are coupled to determine locally stable equilibrium shapes of homogeneous and inhomogeneous precipitates in a large matrix. The bulk elasticity and the interfacial energy density are both allowed to be anisotropic while the misfit strain is kept dilatational. The anisotropy in the crystalline interfacial energies, incorporated through a dependence on the orientation, renders the evolution equation unstable for certain orientation regimes. The equation is regularized by adding a curvature term in the interface energy density which in turn requires the level set method to be modified suitably. The developed methodology is verified for several existing solutions before obtaining new results in the presence of anisotropic interfacial energy. Equilibrium shapes are obtained both for single and multiple precipitates with an emphasis on the interplay between the anisotropies in bulk elasticity and interface energy density.

Three-Dimensional CA-LBM Model of Silicon Facet Formation during Directional Solidification

A new 3D cellular automata-lattice Boltzmann method (CA-LBM) coupling model is proposed to simulate the formation of facet and facet dendrites in directional solidification. In this model, the CA method is used to simulate the crystal growth process and the LBM method is used to simulate the physical field in the calculation area. A new three-dimensional anisotropic function is introduced, and the model is modified by interpolation and neighborhood restriction. We add the remelting calculation model. The interaction between interface energy anisotropy and dynamic anisotropy is solved reasonably. The growth process and morphology of small plane and small plane dendrites were simulated.

Exotic colony formation in Sn-Te eutectic system

Eutectics are self-organized composite materials that exhibit a wide variety of microstructural features. Besides intrinsic materials properties like interfacial energies or diffusivities as well as the nature of the phase diagrams, the process parameters such as magnitude and orientation of the temperature gradient as well as the velocity of the growth interface influence the evolution of the microstructure. Recently, we have observed the evolution of complex patterns due to addition of ternary impurities in the binary Sn-Te system that contains, in addition to (Te), an intermetallic SnTe phase with a cubic crystal structure. This paper examines in detail the origin of such a microstructure that arises due to a two-phase growth instability induced by impurity addition. The binary eutectics (Sn-Te) and ternary eutectics (Sn-Te with an impurity addition) are directionally solidified at different interfacial velocities in order to study the morphological evolution. The binary alloy exhibits a rod-like or an interconnected string of rods morphology while the addition of a third component leads to a diffusive instability (similar to a Mullins-Sekerka instability) that results in the formation of two-phase colonies. The onset of instability depends on both the growth velocity and impurity concentration while the growth direction of the cells is normal to the {0001} planes of (Te) and {111} planes of SnTe. Through the extensive use of multiple characterization techniques, we have explored the morphological characteristics and crystallography of these colonies. The colonies have a complex internal structure that bears a three-fold symmetry reminiscent of the trigonal symmetry of the (Te) crystal, arising possibly because of strong anisotropy in the solid-liquid interfacial energy or in the kinetics of growth. For the different impurity additions (Ag or Sb), the internal eutectic morphology of the colony, due to the addition of Ag is different from that observed for the addition of Sb. The latter leads to the formation of lamellae while a rod-like feature could be observed for impurities like Ag. The complex patterns exhibit a structural hierarchy that provides opportunities for designing novel materials.