Interfacial Energy Density Research Articles

Implementing numerical algorithms to optimize the parameters in Kampmann–Wagner Numerical (KWN) precipitation models

The Kampmann–Wagner Numerical (KWN) model of precipitation is a powerful tool to simulate the precipitation of the second phase considering the nucleation, growth, and coarsening. Some quantities such as interfacial energy and nucleation site number density are required to accomplish the simulation. Practically, those quantities are hard to measure in the experiment directly, and the derivation of those quantities through modeling can also be costly. In this work, we hereby adopt the minimization algorithm implemented in the open-source Scipy Python package to derive that important information in terms of very limited experimental data. The convergence and robustness of different algorithms are discussed. Among those algorithms, the Nelder–Mead and Powell algorithms are successfully applied to optimize multiple parameters during KWN modeling. This work will shed light on the design of experiments/processes and facilitate integrated computational materials engineering (ICME).

A novel fatigue life model for MCrAlY coated superalloys considering interfacial microstructure evolution

MCrAlY coatings, extensively utilized for safeguarding turbine blades against oxidation and erosion, encounter impediments due to inter-diffusion between the coating and substrate, thereby exacerbating fatigue life degradation at elevated temperatures. In this study, we introduce a novel approach involving the modification of critical depth in interfacial strain energy density to elucidate the impact of interfacial microstructure evolution on mechanical properties. Building upon this concept, we propose a fatigue life prediction model, which incorporates the dynamic evolution of interfacial structure and mechanical characteristics. Validation against empirical data underscores the commendable precision of the model. Our inquiry not only advances the comprehension of mechanical-chemical coupled behaviors but also yields significant insights for the optimization and maintenance of turbine blades.

Phase field modeling of fracture mechanics for ion-exchanged glass considering large viscoelastic deformation, mechanic–electrochemical coupling

A phase field model is proposed to investigate the fracture mechanics of ion-exchanged glass, which involves significant viscoelastic deformation and stress-diffusion interaction. Based on this theoretical model, the fracture behavior of both double-sided and single-sided ion exchange processes was studied. The results indicate that, compared to single-sided ion exchange, the double-sided process is more likely to induce crack initiation and propagation, ultimately resulting in a notable reduction in glass strength. For both cases, increasing the glass thickness and interfacial energy density will significantly improve the fracture resistance of the glass. Notably, when the glass thickness or interfacial energy density is large enough, the crack can be completely closed, ensuring the integrity of the glass during the ion exchange process. Furthermore, the study conducted a preliminary investigation of two industrially relevant conditions: edging and impurities. The impacts of edging parameters, glass interfacial energy density, and covering radius on glass stress evolution, mechanical deformation, crack initiation, and crack propagation during chemical strengthening were summarized. These findings offer valuable theoretical support and a reference for optimizing chemical strengthening process parameters and enhancing the strength of glass products.

Perpendicular magnetic anisotropy of Cr/CoFeB/MgO modulated by MgO thickness

The dependence of perpendicular magnetic anisotropy (PMA) on the MgO thickness in Cr/CoFeB/MgO/Ta films has been experimentally investigated. A clear PMA is observed in the as-deposited samples with 1.8 nm MgO while no as-deposited PMA is shown in those with 4.0 nm MgO. This may be attributed to the moderate oxidation degree of CoFeB and larger interfacial anisotropy energy density K i to overcome the volume magnetic anisotropy and demagnetization field. On the contrary, samples with 4.0 nm MgO demonstrate PMA only after annealing, which might be due to the oxygen and boron diffusion during the annealing process. These results would provide a method to optimize the design of CoFeB/MgO structures on 3d metals for future applications in perpendicular magnetic devices.

Mesoscopic irreversible thermodynamics of aging kinetics of alpha polypeptides [DNA] under various constraints: Special reference to the simple spring mechanics

The mesoscopic irreversible thermodynamic treatment of α-polypeptides and the helical polynucleotides (DNA) furnishes two sets of analytical expressions, which allow us not only to analyze the reversible force–extension experiments performed by atomic force microscopy (AFM) but also to predict the irreversible “aging” kinetics of the single-stranded and double-stranded polynucleotides (ssDNA and dsDNA) helical conformations exposed to aqueous solutions and applied static stress systems under the various constraints. The present physicochemical cage model emphasizes the fact that the global Helmholtz free energy of the helical conformation acts not only under the stored “intrinsic” unusual torsional and bending elastic energies inherited by the unfolded helical structure of the amino-acid (peptides) or the nucleic-acid (nucleotide) backbone but also reveals the importance of the interfacial Helmholtz free energy density associated with the interaction of the side-wall branches within the surrounding aqueous solutions. The analytical expression obtained for the unfolding force vs extension (FE) shows a strong non-linear elasticity behavior under the twist angle constraint when the interfacial Helmholtz energy term is incorporating into the scenario. This behavior is in excellent quantitative agreement with the AFM test results obtained by Idiris et al. (2000) on the poly-L-glutamic acid [Glu(n)-Cys] exposed to aqueous solutions, which show that acidity increases the degrees of helicity.

Perpendicular magnetic anisotropy properties of Co2FeSi/Pt multilayers deposited on amorphous dielectric Ta2O5

Perpendicular magnetic anisotropy (PMA) is the mostsignificant characteristic for the development ofnonvolatile magnetic storage systems with superior performance. Hence, we investigate PMA of Co2FeSi (CFS)/Pt structures deposited on amorphous Ta2O5 of high dielectric constant. This design has the potential to be beneficial for low-power voltage-controlled spintronic devices. Strong PMA around ∼ 106 erg/cm3 is noticed in Ta2O5/[CFS/Pt]3 stacks with CFS thickness ranging from 0.6 ∼ 1.0 nm. The interfacial PMA energy density is found to be ∼ 0.63 erg/cm2. The PMA rises in the beginning with increase in number of repetitions (n), reaches a maximum of1.4x106 erg/cm3 at n = 3, and then falls. Pronounced thickness effects of Ta2O5 buffer on magnetic properties are observed. We clearly demonstrate the process of engineering PMA in the CFS/Pt bilayer structures deposited on Ta2O5 dielectric. Our findings might be useful for designing CFS/Pt multilayers on high-K dielectric for low power consumption spintronic devices.

Electrical breakdown strength and interfacial trap characteristics of Epoxy/POSS nanocomposites

It is well known that the interfacial region between the polymeric matrix and nanofiller plays a very important role in tailoring the electrical insulation properties of nanocomposite. In this study two type of polyhedral-oligomeric-silsesquioxane (POSS) are doped into epoxy (EP) to investigate the tailoring of interfacial traps that can limit the mobility of charge carriers and enhance the breakdown strength. Incorporating acryloxypropyl POSS (AP-POSS) to EP matrix improves the breakdown strength than that of pristine EP and octaphenyl POSS (OP-POSS). The molecular simulation and experiments identifies that the compatibility between EP/POSS and trap depth is dependent on the interfacial interaction energy and crosslinking density. The side groups of AP-POSS has large number of localized energy states and higher electron affinity (EA) that can tailor deeper traps and restrain the mobility of electrons in EP/AP-POSS. The interfacial compatibility of POSS side groups with EP tune the interfacial traps and dielectric characteristics.

Fluctuating hydrodynamics and the Rayleigh–Plateau instability

The Rayleigh-Plateau instability occurs when surface tension makes a fluid column become unstable to small perturbations. At nanometer scales, thermal fluctuations are comparable to interfacial energy densities. Consequently, at these scales, thermal fluctuations play a significant role in the dynamics of the instability. These microscopic effects have previously been investigated numerically using particle-based simulations, such as molecular dynamics (MD), and stochastic partial differential equation-based hydrodynamic models, such as stochastic lubrication theory. In this paper, we present an incompressible fluctuating hydrodynamics model with a diffuse-interface formulation for binary fluid mixtures designed for the study of stochastic interfacial phenomena. An efficient numerical algorithm is outlined and validated in numerical simulations of stable equilibrium interfaces. We present results from simulations of the Rayleigh-Plateau instability for long cylinders pinching into droplets for Ohnesorge numbers of Oh = 0.5 and 5.0. Both stochastic and perturbed deterministic simulations are analyzed and ensemble results show significant differences in the temporal evolution of the minimum radius near pinching. Short cylinders, with lengths less than their circumference, were also investigated. As previously observed in MD simulations, we find that thermal fluctuations cause these to pinch in cases where a perturbed cylinder would be stable deterministically. Finally, we show that the fluctuating hydrodynamics model can be applied to study a broader range of surface tension-driven phenomena.

Perpendicular magnetic anisotropy, tunneling magnetoresistance and spin-transfer torque effect in magnetic tunnel junctions with Nb layers

Nb and its compounds are widely used in quantum computing due to their high superconducting transition temperatures and high critical fields. Devices that combine superconducting performance and spintronic non-volatility could deliver unique functionality. Here we report the study of magnetic tunnel junctions with Nb as the heavy metal layers. An interfacial perpendicular magnetic anisotropy energy density of 1.85 mJ/m2 was obtained in Nb/CoFeB/MgO heterostructures. The tunneling magnetoresistance was evaluated in junctions with different thickness combinations and different annealing conditions. An optimized magnetoresistance of 120% was obtained at room temperature, with a damping parameter of 0.011 determined by ferromagnetic resonance. In addition, spin-transfer torque switching has also been successfully observed in these junctions with a quasistatic switching current density of 7.3 times ;10^{5} A/cm2.

Engineering perpendicular magnetic properties of Pt/Co2MnSi multilayered structures capped with dielectric Ta2O5

Pt/Co2MnSi (CMS) multilayered structures capped with high-K dielectric Ta2O5 are sputter-grown and perpendicular magnetic properties are systematically investigated. Strong PMA with the order of 106 erg/cm3 is observed with ultrathin CMS thickness in the range of 0.6∼0.8 nm. An interfacial perpendicular anisotropy energy density of Ks=∼0.52 erg/cm2 is obtained. When the repetition number of Pt/CMS bilayer is greater than two strong PMA can be demonstrated, which may be ascribed to enhanced exchange coupling between CMS layers. In the case of a large repetition number n ≥ 6 switching starting at negative field occurs, indicating nucleation process dominates. Reduced coercivity and saturation magnetization are witnessed in the stacks with increasing thickness of Ta2O5 capping, which can be mainly ascribed to the oxidation effect at the top interface. Our results show perpendicular magnetic properties of Pt/CMS multilayered structures with high-K dielectric Ta2O5 may be engineered for perpendicular spintronic devices.

Strong perpendicular magnetic anisotropy of Pt/Co/AlN structure

In this study, the perpendicular magnetic anisotropy (PMA) and microstructure of Pt/Co/AlN stacks were investigated. At a Co thickness of 0.5 nm, the magnetic moment was not observed in the as-deposited state, but after annealing, it increased significantly. Furthermore, a strong PMA was obtained in the annealed samples; after annealing at 300 °C and 400 °C, the effective PMA energy densities were 2.28 and 1.96 × 107 erg/cm3, respectively. Similar behavior was observed for samples with thicker Co layers. The magnetic dead layer and interfacial PMA energy density were also investigated to determine the interfacial effects on PMA. The occurrence of strong PMA was supported by high-resolution cross-sectional transmission electron microscopy results, demonstrating a well-defined layered structure for the annealed Pt/Co/AlN samples.

Enhanced magnetoresistance in perpendicular magnetic tunneling junctions with MgAl2O4 barrier

Perpendicular magnetic tunnel junction with MgAl2O4 barrier is investigated. It is found that reactive RF sputtering with O2 is essential to obtain strong perpendicular magnetic anisotropy and large tunneling magnetoresistance in MgAl2O4-based junctions. An interfacial perpendicular magnetic anisotropy energy density of 2.25 mJ/m2 is obtained for the samples annealed at 400 °C. An enhanced magnetoresistance of 60% has also been achieved. The Vhalf, bias voltage at which tunneling magnetoresistance drops to half of the zero-bias value, is found to be about 1 V, which is substantially higher than that of MgO-based junctions.

Ab-initio calculations of substitutional co-segregation interactions at coherent bcc Fe-Cu interfaces

Cu rich precipitates (CRPs) are commonly observed to form core-shell structures in neutron irradiated pressure vessel steels. The core region is typically composed of pure Cu whilst the shell is formed of other solute elements including Ni and Si. In this work we calculate the segregation energies for Ni and Si substitutional defects segregating to coherent Fe-Cu interfaces decorated with different types of point defect (vacancies and other solute substitutional defects). By comparing these values to those found for Ni and Si segregation to clean Fe-Cu interfaces we can establish how the presence of point defects on the interface influences solute segregation behaviours. Interestingly we find that the segregation of Ni to Si decorated interfaces and the segregation of Si to Ni decorated interfaces demonstrate a relatively strong co-segregation interaction. We additionally observe that both solute species experience more attractive segregation to vacancy decorated Fe-Cu interfaces. These findings suggest that mixed solute interactions and the presence of vacancies may both play an important role in assisting the formation of large solute shell regions in CRPs. We further observe that the presence of Ni and vacancies on coherent Fe-Cu interfaces both result in substantial reductions in interfacial energy density. These findings support experimental predictions and indicate both features may significantly contribute to CRP formation.

Periodic homogenization in the context of structured deformations

An energy for first-order structured deformations in the context of periodic homogenization is obtained. This energy, defined in principle by relaxation of an initial energy of integral-type featuring contributions of bulk and interfacial terms, is proved to possess an integral representation in terms of relaxed bulk and interfacial energy densities. These energy densities, in turn, are obtained via asymptotic cell formulae defined by suitably averaging, over larger and larger cubes, the bulk and surface contributions of the initial energy. The integral representation theorem, the main result of this paper, is obtained by mixing blow-up techniques, typical in the context of structured deformations, with the averaging process underlying the theory of homogenization.

Magnetic properties of amorphous ferrromagnetic Co2MnSi/Pt multilayers

Ferrromagnetic Co2MnSi (CMS)/Pt multilayer with perpendicular magnetic anisotropy (PMA) is investigated. A series of amorphous CMS/Pt multilayers with various interface numbers are fabricated by sputtering method. PMA is found to be strongly related to the individual thickness of the CMS/Pt bilayer and the repetition number. For the intermediate Pt spacer thicker than 1.2 nm PMA is demonstrated in the multilayers with CMS thickness in the range of 0.3∼0.7 nm. The effective perpendicular anisotropy energy is measured to be in the order of 102 kJ/m3 in magnitude. The interfacial anisotropy energy density is determined to be 0.58 mJ/m2 per interface. With increasing repetition number wasp-waist shaped magnetization hysteresis appears, showing the switching mechanism with multi-domain feature. Our findings provide some useful information to explore CMS/Pt multilayer-based structures with large PMA for next-generation spintronic devices.

An extended peridynamic model for dynamic fracture of laminated glass considering interfacial debonding

In this work, an extended peridynamic (PD) model considering interfacial debonding is proposed to investigate the dynamic fracture behavior of laminated glass under low-velocity and high-velocity impacting loads. The interaction between different materials is described by adding an interfacial force term into the governing equations, which is derived from the energy density function of the interfacial bonds. A potential function term sourced from the cohesive zone model (CZM) is reconstructed and then introduced into the peridynamic model to describe the cohesive interfaces. The failure criterion of interfacial debonding is determined by the calculation of interface fracture energy and interfacial energy density. Two benchmark examples, a through-cracked tensile test and a drop-weight test, have been conducted to establish the validity of the proposed model. The proposed model and approach are then employed to investigate the dynamic fracture mechanism of laminated glass under high-velocity impacting loads.

Design and fabrication of Co2FeSi/Pt multilayers with perpendicular magnetic anisotropy

A series of multilayers consisting of Co2FeSi (CFS) and Pt are sputtered. Perpendicular magnetic anisotropy (PMA) is demonstrated in the CFS/Pt multilayers with CFS thickness in the range of 0.4 ∼ 1.0 nm. The individual thicknesses of Pt spacer and Co2FeSi layer as well as interface numbers are shown to strongly affect PMA. Two-step switching is observed in the multilayers with 8 nm Pt spacer, showing typically decoupled feature. The effective perpendicular anisotropy energy is determined to be in the order of 106 erg/cm3. The interfacial perpendicular anisotropy energy density is estimated to be 0.32 erg/cm2. The magnetic reversal with multi-domain feature is observed with increasing interface number. Sufficiently large saturation magnetization is derived from the multilayers with various repetitions. The thickness of magnetic dead layer is found to increase with the number of interface, which may be ascribed to more interdiffusion occurring at the multi-interfaces. Our results provide some useful information for the design and development of spintronic devices based on CFS/Pt multilayers.

Thermodynamically Stable Colloidal Solids: Interfacial Thermodynamics from the Particle Size Distribution.

True thermodynamic stability of a solid colloidal dispersion is generally unexpected, so much that thorough experimental validation of proposed stable systems remains incomplete. Such dispersions are under investigated and would be of interest due to their long-term stability and insensitivity to preparation pathway. We apply classical nucleation theory (CNT) to such colloidal systems, providing a relationship which links the size-dependent interfacial free energy density of the particles to their size distribution, and use this expression in the fitting of previously reported size distributions for putatively thermodynamically stable nanoparticles. Experimental data from a gold-thiol system exhibiting inverse coarsening or "digestive ripening" can be well-described in terms of a power-law dependence of the interfacial free energy on radius based on capacitive charging of the nanoparticles, going as , as suggested by prior authors. Data from magnetite nanoparticles in highly basic solutions also can be well-fit using the CNT relation, but with going as . Slightly better fits are possible if the power of the radius is non-integral, but we stress that more complex models of will require richer data sets to avoid the problem of overfitting. Some parameters of the fits are still robustly at odds with earlier models that implicitly assumed absolute thermodynamic stability: first, the extrapolated free energy density of the flat surface in these systems is small and positive, rather than strongly negative; second, the shape of the distributions indicates the solution phase to be supersaturated in monomer relative to the bulk, and thus that these two systems may only be metastable. For future work, we derive expressions for the important statistical thermodynamic and chemical parameters of the interface energy in terms of 1) the surfactant concentration, 2) the temperature dependence, and 3) the concentrations of particles in the tail of the distribution.

Uniform energy distribution in a pattern-forming system of surface charges

We consider a variational model for a charge density u\in\{-1,1\} on a (hyper)plane, with a short-range attraction coming from the interfacial energy and a long-range repulsion coming from the electrostatic energy. This competition leads to pattern formation. We prove that the interfacial energy density is (asymptotically) equidistributed at scales large compared to the scale of the pattern. We follow the strategy laid out by Alberti, Choksi and Otto (2009). The challenge comes from the reduced screening capabilities of surface charges compared to the volume charges considered in the aforementioned work.

Ultra-thin interfacial domain wall less than 1 nm based on TbxCo100−x/Cu/[Co/Pt]2 heterostructures for multi-level magnetic pillar memory

We propose a new pillar type of multi-level memory with TbxCo100−x/Cu/[Co/Pt]2 heterostructures to achieve high storage density and controllable domain wall position in-memory applications. The structure consists of amorphous ferrimagnetic Tb–Co alloy films and ferromagnetic Co/Pt multilayers separated by less than one monolayer of Cu. Here, we observe that the interfacial domain wall energy density can be controlled by changing the interlayer thickness of Cu and Tb–Co composition. We also observe two competing mechanisms, one leading to an increase and the other to a decrease, corresponding to the effect of Tb content on saturation magnetization and coercivity of heterostructures. Theoretical and experimental results show that by tuning the Tb–Co composition, we were able to decrease domain wall (DW) width and precisely control the DW position of the multilayer structure. The interfacial domain wall width is significantly decreased to less than 1 nm compared to other reports. Moreover, controlling the DW position and width offers a novel multi-level magnetic memory with high performance compared to conventional memory applications.