Sc Lattices Research Articles

Structural characterization of epitaxial ScAlN films grown on GaN by low-temperature sputtering

ScAlN has garnered substantial attention for its robust piezoelectric and ferroelectric properties, holding promise for diverse electronic device applications. However, the interplay between its structural attributes and physical properties remains poorly understood. This study systematically elucidates the structural characteristics of epitaxial ScAlN films grown on GaN by low-temperature sputtering. Correlations between Sc composition, lattice constants, and film strains were revealed utilizing high-resolution X-ray diffraction, reciprocal space mapping, and machine learning analyses. Our machine-learning model predicted c-axis lattice constants of ScAlN grown on GaN under various conditions and suggested that sputtering permits coherent growth over a wide compositional range. These findings advance the understanding of ScAlN and provide valuable insights for the research and development of novel ScAlN-based devices.

Numerical simulation and ANN prediction of phase change material embedded within 3D printing lattice structures

This study investigates the phase change material (PCM) embedded within different lattice structures, including SC, BCC and FCC, at various porosities. The examination focuses on understanding the thermal behaviour and heat transfer characteristics during the melting and solidification processes. Key parameters analysed include the maximum temperature of the heater, PCM melting and solidification, and Nusselt number. The results indicate that the maximum temperature of the heater decreases with increasing porosity. The Nusselt numbers for the different lattice structures exhibit similarities, with the SC lattice showing a slightly higher Nusselt number. Melting and solidification times increase with increasing porosity. An artificial neural network trained by the Bayesian Regularization algorithm is used to predict three key parameters. The porosity and time are set as input parameters of the network. The optimal structure of the ANN show high accuracy in estimating the performance of PCM with three lattice structures. The minimum mean square error and the maximum correlation coefficient are 0.00003601 and 0.9998, respectively. The trained ANN is employed to predict the behaviour of PCM with 82 % SC, BCC and FCC. A perfect agreement is observed between ANN predictions and the simulation for PCM with lattice structures featuring 82 % porosity.

Comparative performance evaluation of microarchitected lattices processed via SLS, MJ, and DLP 3D printing methods: Experimental investigation and modelling

Additively manufactured mechanical metamaterials are gaining prominence in lightweight energy-absorption applications due to their exceptional mass-specific properties. Herein, we examine the energy absorption characteristics of micro-architected truss-, shell- and plate-lattice structures, namely, Octet, Kelvin, Gyroid, SC, BCC and FCC over a range of relative densities under quasi-static compression via both experiments and finite element analysis (FEA). Employing different 3D printing methods, namely, Digital Light Processing, Selective Laser Sintering and Material Jetting, the lattices were fabricated using PlasGray™ (photo-resin based plastic), PA12 (Nylon) and VeroWhite (photo-resin based rigid plastic) respectively. Our results indicate that the SC lattice structure outperforms in terms of stiffness and strength, while the Gyroid lattice outperforms in terms of energy absorption efficiency (η). At lower relative densities (<0.3), η reaches up to 61% for the Gyroid lattices made of PlasGray, while only at high relative densities the Octet truss lattices compete with the Gyroid lattices. For Gyroid lattices made of PA12 with a relative density of 0.23, an energy absorption efficiency of 68% was observed. Design maps are presented for all lattice structures processed and tested herein, to demonstrate their relative merits. Moreover, a two-step FEA was executed on a chosen array of lattices to thoroughly investigate the extensive design possibilities, utilising the elastic-plastic, Drucker-Prager, and concrete damage plasticity material models for PlasGray, PA12, and VeroWhite, respectively, with calibration based on experimental results. The results highlight that the tailored design of Gyroid lattices enabled by AM positions them as promising candidates for lightweight energy-absorbing applications.

Design and optimization of composite phase change material for cylindrical thermal energy storage

Phase change materials store thermal energy in the form of latent heat, and are often integrated with high thermal conductivity metals to make composites that have both high power density and large energy storage capacity. In this study, we provide a theoretical framework to design and optimize cylindrical composites with three figures of merit – minimization of temperature rise, maximization of the effective volumetric heat capacity and maximization of the effective heat capacity based on mass. We validate the figures of merit experimentally by 3D printing AlSi12 alloy and using octadecane as phase change material for a heat flux of 13.3 Wcm−2 and heating time of 10 s. The metal component volume fractions in the printed structures vary from 15% to 70% for straight fin structures, 10% to 70% for the SC lattice structures, and 20% to 70% for branching fin structures. When minimizing temperature rise, the optimum volume fraction of thermally conductive material is 0.5–0.7. When maximizing the effective volumetric heat capacity, the optimum volume fraction for the high conductivity material is 0.3–0.5. Finally, when maximizing the effective heat capacity by mass in cylindrical composites, the optimum volume fraction for the high conductivity material is 0.2–0.3. Importantly, the optimum values depend on the applied thermal load, which is not captured in existing figures of merit for thermal storage systems. The volumetric and mass based heat capacity values of the optimized composites identified in this study are at least 10x higher when compared to single component PCMs that are widely used for volumetric and mass based thermal storage systems. The figures of merit developed here can assess the performance of most composite PCM systems and help to design future cylindrical composites while accounting for the thermal loads specific to the thermal storage application.

Comparison of Benchmark HP Model Proteins on Face-Centered Cubic and Simple Cubic Lattices using Replica-Exchange Wang-Landau Sampling

The HP model represents protein sequences by coarse-graining amino acid types as either hydrophobic (H) or polar (P). This model has been studied extensively, where the simple cubic (sc) lattice is a commonly used for simplicity and efficiency, despite a limited ability to geometrically represent protein structures. One straightforward improvement is to instead use the face-centered cubic (fcc) lattice, which offers a more realistic geometry while retaining simplicity. Using the replica-exchange Wang-Landau algorithm, the ground state energies and full density of states are predicted for a set of biologically-motivated HP sequences on the fcc lattice. A direct thermodynamic comparison is made between the folding on fcc and sc lattices, and structural properties are calculated to further examine the folding on the fcc lattice.

Site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in two and three dimensions.

Extended-range percolation on various regular lattices, including all 11 Archimedean lattices in two dimensions and the simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) lattices in three dimensions, is investigated. In two dimensions, correlations between coordination number z and site thresholds p_{c} for Archimedean lattices up to 10th nearest neighbors (NN) are seen by plotting z versus 1/p_{c} and z versus -1/ln(1-p_{c}) using the data of d'Iribarne etal. [J. Phys. A 32, 2611 (1999)JPHAC50305-447010.1088/0305-4470/32/14/002] and others. The results show that all the plots overlap on a line with a slope consistent with the theoretically predicted asymptotic value of zp_{c}∼4η_{c}=4.51235, where η_{c} is the continuum threshold for disks. In three dimensions, precise site and bond thresholds for bcc and fcc lattices with 2nd and 3rd NN, and bond thresholds for the sc lattice with up to the 13th NN, are obtained by Monte Carlo simulations, using an efficient single-cluster growth method. For site percolation, the values of thresholds for different types of lattices with compact neighborhoods also collapse together, and linear fitting is consistent with the predicted value of zp_{c}∼8η_{c}=2.7351, where η_{c} is the continuum threshold for spheres. For bond percolation, Bethe-lattice behavior p_{c}=1/(z-1) is expected to hold for large z, and the finite-z correction is confirmed to satisfy zp_{c}-1∼a_{1}z^{-x}, with x=2/3 for three dimensions as predicted by Frei and Perkins [Electron. J. Probab. 21, 56 (2016)1083-648910.1214/16-EJP6] and by Xu etal. [Phys. Rev. E 103, 022127 (2021)2470-004510.1103/PhysRevE.103.022127]. Our analysis indicates that for compact neighborhoods, the asymptotic behavior of zp_{c} has universal properties, depending only on the dimension of the system and whether site or bond percolation but not on the type of lattice.

Effective stiffness, strength, buckling and anisotropy of foams based on nine unique triple periodic minimal surfaces

Recent advancements in the field of additive manufacturing has led to an increased interest in the study of cellular architectures especially triply periodic minimal surfaces (TPMS) and their properties. In this study, 9 sheet-based TPMS architectures are studied by comparing their effective stiffness, strength, buckling and anisotropic properties. The TPMS lattices are generated using level set equations where the relative density of each lattice is varied to study the effective properties as a function of relative density. Finite element models of these lattices are built to study the elastic and plastic deformation behaviour under uniaxial, shear, hydrostatic and buckling loading conditions. Effective properties such as Young’s modulus, shear modulus, bulk modulus, Poisson’s ratio and strengths under uniaxial, shear, hydrostatic and buckling loading are computed against each other and other common lattice structures. In addition, anisotropic behaviour as well as the orientation dependence of the properties of each lattice are also studied. The geometric efficiency criterion is predominantly used to evaluate the different structures and the results obtained are consolidated in both quantitative and qualitative manner. SC lattice outperforms all the other lattices in terms of strength and stiffness efficiencies at lower and higher relative densities. On the other hand, I2 − Y** lattice shows the weakest stiffness and strength efficiency especially at higher relative densities. The current study focuses on the properties of some unique lattice architectures that have not been studied previously and shows promising efficiencies compared to the common architectures studied such as the Gyroid lattice. This study opens the door for employing these lattices in various applications and the results are very useful to multi-scale topology-optimization studies.

Investigation on solid particles erosion resistance of laser cladded CoCrFeNiTi high entropy alloy coating

High entropy alloy (HEA) as coating material has more economical application value. In this study, CoCrFeNiTi HEA coating without cracks and pores was successfully prepared on 304 stainless steel substrate by laser cladding. The phase structure of the CoCrFeNiTi HEA coating was composed of main phase with an FCC lattice, Fe and Cr rich phase with an SC lattice and CoTi2 type Laves phase. The microstructure of the prepared coating consisted of bonding zone and cladding zone. It was an obviously metallurgical bonding between the coating and substrate and typical columnar dendrites were generated with growth direction perpendicular to the interface in the bonding zone. The cladding zone showed a typical long strip proeutectic structure and a lamellar eutectic structure. The average microhardness of CoCrFeNiTi HEA coating reached to 568 HV0.2, which was approximately 2.5 times higher than that of the substrate (236 HV0.2). Erosion tests were conducted on both CoCrFeNiTi HEA coatings and the substrates with an erosion angle of 30 and 90°. The results showed that CoCrFeNiTi HEA coating exhibited much lower erosion rates with an erosion angle of 30° (0.68 mg/cm2) and 90° (0.42 mg/cm2). Ploughing and micro-cutting were the two primary erosion mechanisms of material loss for CoCrFeNiTi HEA coating at oblique erosion angles, while the erosion mechanism was replaced by the formation of craters at vertical erosion angles.

Precise bond percolation thresholds on several four-dimensional lattices

We study bond percolation on several four-dimensional (4D) lattices, including the simple (hyper) cubic (SC), the SC with combinations of nearest neighbors and second nearest neighbors (SC-NN+2NN), the body-centered cubic (BCC), and the face-centered cubic (FCC) lattices, using an efficient single-cluster growth algorithm. For the SC lattice, we find $p_c = 0.1601312(2)$, which confirms previous results (based on other methods), and find a new value $p_c=0.035827(1)$ for the SC-NN+2NN lattice, which was not studied previously for bond percolation. For the 4D BCC and FCC lattices, we obtain $p_c=0.074212(1)$ and 0.049517(1), which are substantially more precise than previous values. We also find critical exponents $\tau = 2.3135(5)$ and $\Omega = 0.40(3)$, consistent with previous numerical results and the recent four-loop series result of Gracey [Phys. Rev. D 92, 025012, (2015)].

Criticality and Burnup Study on Different TRISO Modelling of HTR Pebble

Modeling of high temperature reactor core (HTR) of pebble bed type has been widely developed before, but the calculation of reactor core in equilibrium condition has not been developed much, especially in Indonesia. The initial approach to see the effect of modeling and simplification that will be used in full-scale HTR modeling can start to be done on the smallest level i.e. TRISO and single pebble. The purpose of this study was to analyze the effect of TRISO particle modeling in the HTR fuel pebble using MCNPX. The modeling variations that will be carried out include modeling of complete TRISO particles, modeling using homogenized TRISO coating layers and full homogenized TRISO. Then another variation is on the TRISO dispersion pattern inside pebble that will be modeled uniformly distributed using several types of TRISO unit, HCP, SC, FCC and BCC lattice. For all variations mentioned above, K-INF calculations will be performed and burnup calculation only performed on single pebble modelling. The modeling using fuel kernels and cover (homogenized buffer, PyC and SiC) gives K-INF values that are not much different than the complete TRISO modeling (fuel kernel, buffer, PyC and SiC on each different zone). The different from fully homogenized modeling is the value of K-INF becomes lower than the complete modeling. Then for all types of TRISO unit, modeling using homogenized TRISO requires longer pebble burnup computation time than other modeling, whereas modeling of homogenized cover types gives a shorter pebble burnup computation time.

A finite element based fast eigensolver for three dimensional anisotropic photonic crystals

The standard Yee's scheme for the Maxwell eigenvalue problem places the discrete electric field variable at the midpoints of the edges of the grid cells. It performs well when the permittivity is a scalar field. However, when the permittivity is a Hermitian full tensor field it would generate un-physical complex eigenvalues or frequencies. In this paper, we propose a finite element method which can be interpreted as a modified Yee's scheme to overcome this difficulty. This interpretation enables us to create a fast FFT eigensolver that can compute very effectively the band structure of the anisotropic photonic crystal with SC and FCC lattices. Furthermore, we overcome the usual large null space associated with the Maxwell eigenvalue problem by deriving a null-space free discrete eigenvalue problem which involves a crucial Hermitian positive definite linear system to be solved in each of the iteration steps. It is demonstrated that the CG method without preconditioning converges in 37 iterations even when the dimension of a matrix is as large as 5,184,000.

Effective diffusivity in lattices of impermeable superballs

We perform simulations of obstructed diffusion in periodic lattice configurations of solid, nonoverlapping, impermeable superballs to study effective diffusivity as a function of shape and solid volume fraction for simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) lattices. In the simulations, point particles diffuse in the intermediate space between the solid superballs. For sc lattices, we find that for a constant solid volume fraction, the optimal effective diffusivity is obtained for a particular superball between a sphere and a cube, whereas for bcc and fcc lattices, no such optimum exists. Further, we investigate the prediction of the effective diffusivity in these systems using an approximate analytical expression based on two- and three-point correlation functions and the microstructural parameter ${\ensuremath{\zeta}}_{2}$.

Random walks on lattices. Influence of competing reaction centers on diffusion-controlled processes

We study diffusion–reaction processes on periodic simple cubic (sc) lattices and square planar lattices. We consider a single diffusing reactant undergoing an irreversible reaction upon first encounter with a static co-reactant placed at a given site (“one-walker problem”). We also allow for a competing reaction, namely, instantaneous trapping of the diffusing reactant at any other site (with probability s) before interacting with the static co-reactant. We use a generating function approach and Markov theory, as well as MC simulations, to determine the mean walklength 〈n〉 of the diffusing reactant before either of the two competing reactions takes place. To investigate the dependence of 〈n〉 on lattice size we compute the first, finite size corrections to the Green function of the sc lattice, correcting results reported in the literature. Using these results, space exploration properties and first-passage properties (e.g. walklength statistics, mean number of distinct sites visited, statistics of return to the origin, etc.) of both conventional (immortal) walks and mortal walks can be determined. In this context, we develop a novel approach based on a two-point Padé approximant for the Green function. Finally, we study by means of MC simulations the more complex case where both reactant and co-reactant undergo synchronous nearest-neighbor displacements (“two-walker problem”). Here, we assume that reactant and co-reactant can individually be trapped with probability s at any lattice site, or can undergo an irreversible reaction on first encounter at any site. When s=0 we find that, both for the one-walker and the two-walker problem, for lattices with (approximately) the same number of sites, the mean walklength is smaller (and hence the reaction efficiency greater) in d=3 than in d=2. Increasing s tends to reduce differences in system dimensionality, and distinctions between the one-walker problem and the two-walker problem. Our model provides a good starting point to develop studies on the efficiency of apparently diverse diffusion–reaction processes, such as diffusion on a partially poisoned catalytic substrate or photosynthetic trapping of excitations.

The Ising universality class in dimension three: Corrections to scaling

Simulation data are analyzed for four 3D spin-1∕2 Ising models: on the FCC lattice, the BCC lattice, the SC lattice and the Diamond lattice. The observables studied are the susceptibility, the reduced second moment correlation length, and the normalized Binder cumulant. From measurements covering the entire paramagnetic temperature regime the corrections to scaling are estimated. We conclude that a correction term having an exponent which is consistent within the statistics with the bootstrap value of the universal subleading thermal confluent correction exponent, θ2∼2.454(3), is almost always present with a significant amplitude. In all four models, for the normalized Binder cumulant the leading confluent correction term has zero amplitude. This implies that the universal ratio of leading confluent correction amplitudes aχ4∕aχ=2 in the 3D Ising universality class.

Interaction in equilibrium plasmas of charged macroparticles located in nodes of cubic lattices

Interaction of two charged pointlike macroparticles located at nodes of simple cubic (sc), body-centered cubic (bcc) and face-centered cubic (fcc) lattices in an equilibrium plasma is studied within the linearized Poisson-Boltzmann model. It is shown that the boundary shape has a strong influence on the electrostatic interaction between two macroparticles, which switches from repulsion at small interparticle distances to attraction as it approaches the halflength of a computational cell. It is found that in a case of dust particles arranged in the nodes of the sc, bcc and fcc lattices, the electrostatic force acting on them is equal to zero and the nature of the interaction changes from repulsion to attraction; hence, the infinite sc, bcc and fcc lattices of charged dust particles are thermodynamically stable at rather low temperatures.

Asymptotic behavior of local dipolar fields in thin films

A simple method, based on layer by layer direct summation, is used to determine the local dipolar fields in uniformly magnetized thin films. The results show that the dipolar constants converge ~1/m where the number of spins in a square film is given by (2m+1)2. Dipolar field results for sc, bcc, fcc, and hexagonal lattices are presented and discussed. The results can be used to calculate local dipolar fields in films with either ferromagnetic, antiferromagnetic, spiral, exponential decay behavior, provided the magnetic order only changes normal to the film. Differences between the atomistic (local fields) and macroscopic fields (Maxwellian) are also examined. For the latter, the macro B-field inside the film is uniform and falls to zero sharply outside, in accord with Maxwell boundary conditions. In contrast, the local field for the atomistic point dipole model is highly non-linear inside and falls to zero at about three lattice spacing outside the film. Finally, it is argued that the continuum field B (used by the micromagnetic community) and the local field Bloc(r) (used by the FMR community) will lead to differing values for the overall demagnetization energy.

A fundamental study of the extent of meaningful application of Maxwell׳s and Wiener׳s equations to the permeability of binary composite materials. Part II: A useful explicit analytical approach

The Maxwell equation relates the permeability P of a dispersion of particles A (modeled as hard congruent non-interacting spheres) in a continuous matrix B, to the ratio of the permeabilities of the components α=PA/PB and the corresponding volume fractions vA, vB (=1−vA). Originally devised for use at vA→0, the validity of the said equation for practical purposes was shown, by analytical methods, to extend to congruent weakly interacting spheres packed in regular cubic lattices, in the low to medium vA range; while the equation itself extends further up to the correct upper limit P=PA at vA=1. Replacing a simple cubic (s.c.) lattice of spheres with an identical lattice of cubes, overcomes this limitation (because cubes can pack up to vA=1) but only at the expense of losing analytical mathematical tractability. However, an analytical limiting form of the s.c. lattice of cubes could be derived near the limit vA→1 and shown to agree with the Maxwell equation. Even so, a large gap of unexplored territory was obviously still left in the remaining medium to high vA range. The gap in missing data was successfully filled in Part I by the use of a numerical computation approach, which showed that the result obtained at vA→1 is valid for practical purposes throughout the medium to high vA range; thus confirming the applicability of the Maxwell equation to sc lattices of cubes (and correspondingly of the Wiener equation in the case of anisometric particles) in this vA region. The gap in analytical treatment is filled to a large extent, in the present companion paper, by the development of an approach combining two different analytical limiting forms of the s.c. lattice-of-cubes model (as well as comparable limiting forms applicable to anisometric particles treated by the Wiener equation). We show here that this approach (referred to in the main text as the BP II model) provides (to a high degree of approximation in the practically important region of 0≤α≤10) a satisfactory analytical theoretical basis for meaningful application of the Maxwell equation in the higher vA range, comparable with that afforded by the existing lattice-of-spheres analytical treatments in the lower vA region.

Applications of a versatile modelling approach to 3D atom probe simulations

The article addresses application examples of a flexible simulation approach, which is based on an irregular mesh of Voronoi cells. The detailed atomic structure of APT field emitters is represented by Wigner–Seitz cells. In this way, arbitrary crystal structures can be modelled. The electric field results from the solution of the Poisson equation. The evaporation sequence of atoms from the emitter surface is enabled by calculation of the field-induced force, which acts on the surface cells. Presented examples show simulated field desorption maps of a cubic fcc <111> structure in comparison to the close-packed hcp <0001> structure. Additionally, the desorption maps of the cubic sc, bcc, and fcc lattices in <011> orientation are presented. The effect of inhomogeneous evaporation conditions on the emitter apex curvature is demonstrated. Reconstructions derived from the simulation of Σ5 GBs differently inclined with respect to the emitter axis are analyzed. Finally, the stress exerted on an embedded nano-particle during the simulated evaporation with inhomogeneous evaporation thresholds is estimated.

Effective Mass of Bound and Resonant Two-Electron Pairs in a Simple Cubic Lattice

A good candidate for mechanism of high temperature superconductivity (HTS) is the Bose condensation of tightly bound pairs. Thus the properties of single pair are a good starting point for investigations of HTS in the strong coupling limit. An important property is the pair's ability to move, described by its e ective mass m∗. Although HTS materials are often considered two-dimensional (2D) they have in fact quasi-2D, strongly anisotropic 3D structure. There are also other strongly correlated 3D materials exhibiting superconductivity, like heavy fermion superconductors, Chevrel phases or doped BaBiO3 [1]. That warrants investigation of 3D systems. Current paper reports calculations of pair's e ective mass within tUWJ model on generic simple cubic (sc) lattice.

Equivalence Transformations among Ising Models

Using topology, fractal analysis and investigation of lattice formation process we find two types of equivalence transformations among Ising models: topological equivalence transformation and formation equivalence transformation. With the help of the transformations and the known data of the critical points of simple cubic (sc) lattice and planar square (sq) lattice we get directly the critical points for face-centered cubic (fcc) lattice, body-centered cubic (bcc) lattice and diamond (d) lattice. The transformation itself results no error in the calculation. Other than Monte Carlo method and series expansion approach the equivalence transformations help us simplify much more greatly the calculation of the critical points for the three-dimensional models and understand much more deeply the structural connection among Ising models.