Metal Lattice Research Articles

Incorporating defects into model predictions of metal lattice-structured materials

Metal lattice structures are optimized for high specific strength properties and are now customizable using additive manufacturing methods. However, many of these methods, like selective laser melting, can introduce defects such as porosity, parasitic material, and disconnected struts into the structure, which can negatively affect mechanical behavior. While there are many computational models used to predict the mechanical response of lattice-structured materials, most use an idealized structure and are often not robust enough to account for defects. In this study, metal lattice structures are characterized for defects and mechanically tested in compression. The defect types and distributions are characterized using x-ray micro-tomography and the tomography analyses is used in two different model predictions. First, in an equivalent continuum model, where the defects are used to predict the variability in mechanical properties, and second, in a finite element analysis, where the predicted stress-strain response for both realistic and idealized structures are compared. Investigating this further, a finite element analysis of an octet lattice quantifies the reduction in strength associated with disconnected struts and captures a dependence on the strut's orientation relative to the loading direction. Overall, incorporating defect information gleaned from tomography data improves predictions of mechanical properties by capturing a more realistic deformation response for lattice-structured material.

Molecular dynamics simulations of hydrogen isotope exchange in tungsten vacancies

Solute hydrogen can cause many damaging processes in the lattices of metals, such as deformation of the material, which can take place in large scales through blistering and embrittlement. Especially in nuclear fusion applications, the trapped hydrogen isotope Tritium in the reactor wall materials can pose a radiological safety hazard. Techniques for hydrogen removal from metals usually require high temperatures. However, an efficient low temperature method to remove hydrogen is the so-called isotope exchange mechanism, where one isotope is being removed from the material by replacing it by another isotope introduced in the material. The atomic scale exchange mechanism of isotope exchange has not yet been determined. In this study we use molecular dynamics simulations to provide an atomic-scale explanation to the processes related to hydrogen isotope exchange in bulk materials. The results show that the lattice mono-vacancies and small vacancy clusters, usually produced in irradiation experiments, exhibit isotope exchange at low temperatures. The isotope exchange process should also be seen in other hydrogen trapping defects with similar trapping properties as vacancies.

Simulating Nonlinear Dynamics of a 3D Crystal Lattice of Metals

Oscillations of crystal lattices determine important material properties such as thermal conductivity, heat capacity, thermal expansion, and many others; therefore, their study is an urgent and important problem. Along with experimental studies of the nonlinear dynamics of a crystal lattice, effective computer simulation techniques such as ab initio simulation and the molecular dynamics method are widely used. Mathematical simulation is less commonly used since the calculation error there can reach 10 %. Herewith, it is the least computationally intensive. This paper describes the process and results of mathematical simulation of the nonlinear dynamics of a 3D crystal lattice of metals using the Lennard-Jones potential in the MatLab software package, which is well-proven for solving technical computing problems. The following main results have been obtained: 3D distribution of atoms over the computational cell has been plotted, proving the possibility of displacement to up to five interatomic distances; the frequency response has been evaluated using the Welch method with a relative RMS error not exceeding 30 %; a graphical dependence between the model and the reference cohesive energy data for a metal HCP cell has been obtained with an error of slightly more than 3 %; an optimal model for piecewise-linear approximation has been calculated, and its 3D interpolation built. All studies performed show good applicability of mathematical simulation to the problems of studying dynamic processes in crystal physics.

Enhanced Electrochemical Oxygen Evolution Reaction on Hydrogen Embrittled CoSe Surface

AbstractIn the design of structurally competent electrodes with prolonged lifecycles, a solid understanding of the gaseous hydrogen interaction in a metal lattice is highly desirable. During hydrogen evolution reaction, ingress of H severely affects the physical and mechanical properties of the material causing catastrophic brittle failures (hydrogen embrittlement). In this work, by chronoamperometry technique, an electrode with CoSe catalyst system is intentionally diffused with H to serve as a hydrogen stressed CoSe electrode. Surprisingly this H‐embrittled CoSe electrode exhibits enhanced oxygen evolution reaction (OER) behavior as confirmed by linear sweep voltammetry (LSV), impedance, and Tafel analysis, a cathodic shift of 80 mV at the current density of 10 mA cm−2, impedance analysis reveals half the time of Rct decreasing in the OER on H‐embrittled CoSe than pristine CoSe. The Tafel slope of the H‐embrittled CoSe exhibits of 30 mV, which is relatively lower than the pristine CoSe at OER condition. These results collectively support the enhanced activity of the H‐embrittled CoSe electrode towards OER. Diffusion of hydrogen into metal lattice is confirmed by the high‐resolution transmission electron microscopy (HR‐TEM) fringes analysis, where a 22% decrease Q2 in the lattice distance is revealed by the H‐embrittled CoSe catalyst.

Spin excitations in metallic kagome lattice FeSn and CoSn

In two-dimensional (2D) metallic kagome lattice materials, destructive interference of electronic hopping pathways around the kagome bracket can produce nearly localized electrons, and thus electronic bands that are flat in momentum space. When ferromagnetic order breaks the degeneracy of the electronic bands and splits them into the spin-up majority and spin-down minority electronic bands, quasiparticle excitations between the spin-up and spin-down flat bands should form a narrow localized spin-excitation Stoner continuum coexisting with well-defined spin waves in the long wavelengths. Here we report inelastic neutron scattering studies of spin excitations in 2D metallic kagome lattice antiferromagnetic FeSn and paramagnetic CoSn, where angle resolved photoemission spectroscopy experiments found spin-polarized and nonpolarized flat bands, respectively, below the Fermi level. Our measurements on FeSn and CoSn reveal well-defined spin waves extending above 140 meV and correlated paramagnetic scattering around Γ point below 90 meV, respectively. In addition, we observed non-dispersive excitations at ~170 meV and ~360 meV arising mostly from hydrocarbon scattering of the CYTOP-M used to glue the samples to aluminum holder. Therefore, our results established the evolution of spin excitations in FeSn and CoSn, and identified anomalous flat modes overlooked by the neutron scattering community for many years.

Compressive and Energy Absorption Properties of Pyramidal Lattice Structures by Various Preparation Methods.

Metallic three-dimensional lattice structures exhibit many favorable mechanical properties including high specific strength, high mechanical efficiency and superior energy absorption capability, being prospective in a variety of engineering fields such as light aerospace and transportation structures as well as impact protection apparatus. In order to further compare the mechanical properties and better understand the energy absorption characteristics of metal lattice structures, enhanced pyramidal lattice structures of three strut materials was prepared by 3D printing combined with investment casting and direct metal additive manufacturing. The compressive behavior and energy absorption property are theoretically analyzed by finite element simulation and verified by experiments. It is shown that the manufacturing method of 3D printing combined with investment casting eliminates stress fluctuations in plateau stages. The relatively ideal structure is given by examination of stress–strain behavior of lattice structures with varied parameters. Moreover, the theoretical equation of compressive strength is established that can predicts equivalent modulus and absorbed energy of lattice structures.

Multiaxial static strength of a 3D printed metallic lattice structure exhibiting brittle behavior

AbstractThis paper focuses on numerical the prediction of multiaxial static strength of lattice structures. We analyze a body‐centered cubic cell printed with Selective Laser Melting in AlSi10Mg aluminum alloy. Parent material is experimentally characterized, and the Gurson‐Tveergard‐Needleman (GTN) damage model is calibrated to predict failure in numerical simulations. The GTN model is used to predict failure of the lattice structures exhibiting brittle localized fracture, and it is validated through static tests. The results of experimental tension/compression monotonic tests on lattice samples are compared with the results of numerical simulations performed on as‐built geometry reconstructed by X‐ray computed tomography, showing a good correlation. Combining the damage model with computational micromechanics, multiaxial loading conditions are simulated to investigate the effective multiaxial strength of the lattice material. Yielding and failure loci are found by fitting a batch of points obtained by some multiaxial loading simulations. A formulation based on the criterion proposed by Tsai and Wu (1971) for anisotropic materials provides a good description of yielding and failure behavior under multiaxial load. Results are discussed, with a specific focus on the effect of as‐built defects on multiaxial strength, by comparing the resistance domains of as‐manufactured and as‐designed lattices.

Isotopic dependence of the frequency of optical vibrations in molybdenum monohydride

It is currently known that three hydrides – PdHx, MoHx, and TiHx – exhibit an inverse isotope effect in superconductivity. Namely, the phase with a heavier hydrogen isotope, deuterium, has a higher critical temperature. Hydrides and deuterides of palladium have intensively been studied both experimentally and theoretically, but the origin of the isotope effect has not been established with certainty. The commonly accepted explanation is that the effect is likely to be due to the strong anharmonicity of the optical hydrogen vibrations, which was considered to be responsible for the large deviation of the ratio of the fundamental optical frequencies ωH/ωD = 1.51 from the harmonic value 2 ≈ 1.41. In the present paper, powder samples of MoH1.1(1) and MoD1.07(3) were synthesized under a hydrogen / deuterium pressure of several gigapascals and studied by inelastic neutron scattering (INS) at ambient pressure and T = 10 K. The INS study demonstrated that optical vibrations of H atoms in MoH1.1 and D atoms in MoD1.07 are harmonic and the ratio of fundamental optical frequencies ωH/ωD = 1.44 is close to the harmonic value 2 ≈ 1.41. This shows that anharmonicity is not a necessary condition for the presence of the inverse isotope effect. The MoD1.07 sample was additionally studied by neutron diffraction (ND) at ambient pressure and T = 100 K. In agreement with previous ND results for MoH1.2, the ND study of MoD1.07 showed that deuterium atoms occupied almost all octahedral interstitial sites in its hexagonal close-packed metal lattice and formed a NiAs-type crystal structure with the composition close to MoD. The overstoichiometric composition MoD1.07 of the deuteride is likely to result from a small fraction D/Mo ~ 0.07 of deuterium atoms partially occupying the tetrahedral interstices.

Geometric frustration on the trillium lattice in a magnetic metal–organic framework

In the dense metal-organic framework Na[Mn(HCOO)$_3$], Mn$^{2+}$ ions ($S=\frac{5}{2}$) occupy the nodes of a `trillium' hyperkagome net. We show that this material exhibits a variety of behaviour characteristic of geometric frustration: the N\'eel transition is suppressed well below the characteristic magnetic interaction strength; short-range magnetic order persists far above the N\'eel temperature; and the magnetic susceptibility exhibits a pseudo-plateau at $\frac{1}{3}$-saturation magnetisation. We demonstrate that a simple nearest-neighbour Heisenberg antiferromagnet model accounts quantitatively for each observation, and hence Na[Mn(HCOO)$_3$] is the first experimental realisation of this model on the trillium net. We develop a mapping between this trillium model and that on the two-dimensional Shastry-Sutherland lattice, and demonstrate how both link geometric frustration within the classical spin liquid regime to a strong magnetocaloric response at low fields.

Thermal characterization of 3D-Printed lattices based on triply periodic minimal surfaces embedded with organic phase change material

Owing to their high latent heat of fusion and thermal stability, organic phase change materials (PCMs) are lucrative candidates for utilization in latent heat thermal energy storage systems (LHTES). However, since their low thermal conductivity inhibits their direct usage in such systems, they are often impregnated into a thermally conductive metallic matrix, which exhibits an effective thermal conductivity superior to that of PCM alone. In this study, metallic lattices based on Triply periodic minimal surfaces (TPMSs) are utilized as thermal conductivity enhancers for organic PCMs. TPMS are a class of periodic cellular materials that have been recently studied in several structural, thermo-mechanical, and other applications showing promising performance. However, their utilization with PCM in LHTES systems is a relatively uncharted area of research. Using selective laser sintering technique; four metallic TPMS structures were fabricated, i.e., diamond, gyroid, I-graph and wrapped package-graph (IWP), and primitive, and were later impregnated with two organic PCMs (i.e., RT62HC and RT64HC). The thermal conductivity of both PCMs and TPMS-PCM composite were measured using Transient Plane Source (TPS) method. It was found that the TPMS structures enhanced the thermal conductivity of the PCMs. Moreover, for a fixed porosity and unit cell size, the effective thermal conductivity was found to be a function of the TPMS architecture. A preliminary numerical analysis to compare the heat performance of PCM-alone and PCM embedded with TPMS (primitive) showed clear superiority of the TPMS-PCM composite over the PCM-alone case. Therefore, the utilization of TPMS structures in LHTES could be promising in a bid to increase the performance of organic PCMs.

Analysis of Pyridine, Picoline and Lutidine’s Adsorption Behavior on The Al (111)-lattice

The reactivity and adsorption behavior of five organic inhibitors of pyridine and its derivatives of 2-picoline, 3-picoline, 4-picoline, and 2,4-lutidine at the Al(111) lattice in hydrochloric acid was studied by the principle of the HF and B3LYP level using the 6-31G and LANL2DZ basis sets from the program package gaussian 03. The compound was adsorbed on the metal lattice based on the calculated results, mainly in their protonated forms. In the Al (111)-lattice, the charge is transferred to the inhibitor, and the organic inhibitor is adsorbed at the Al (111)-lattice in an inclined state. The quantum chemical calculations of molecular reactivity show that the frontier orbitals of the four additives are distributed around the nitrogen atom of the pyridine ring, the aluminum atom of Al (111)-lattice, and active electrophilic centers are located on the nitrogen atoms of the pyridine ring. All five molecules were adsorbed with the chemical adsorption on the Al (111)-lattice, and the order of adsorption was 2-picoline>2, 4-lutidine> 4-picoline> 3-picoline> pyridine. The N atoms of four derivatives form N-Al bonds with the Al atoms of the Al (111)-lattice, which makes derivatives stably adsorb on the Al lattice.

Uncertainty quantification of microstructure variability and mechanical behavior of additively manufactured lattice structures

Process-induced defects are the leading cause of discrepancies between as-designed and as-manufactured additive manufacturing (AM) product behavior. Especially for metal lattices, the variations in the printed geometry cannot be neglected. Therefore, the evaluation of the influence of microstructural variability on their mechanical behavior is crucial for the quality assessment of the produced structures. Commonly, the as-manufactured geometry can be obtained by computed tomography (CT). However, to incorporate all process-induced defects into the numerical analysis is often computationally demanding. Thus, commonly this task is limited to a predefined set of considered variations, such as strut size or strut diameter. In this work, a CT-based binary random field is proposed to generate statistically equivalent geometries of periodic metal lattices. The proposed random field model in combination with the Finite Cell Method (FCM), an immersed boundary method, allows to efficiently evaluate the influence of the underlying microstructure on the variability of the mechanical behavior of AM products. Numerical analysis of two lattices manufactured at different scales shows an excellent agreement with experimental data. Furthermore, it provides a unique insight into the effects of the process on the occurring geometrical variations and final mechanical behavior.

Tuning of Static and Dynamic Mechanical Response of Laser Powder Bed Fused AlSi10Mg Lattice Structures through Heat Treatments

The use of additive manufacturing allows the production of complex designs, including metallic lattice structures, which combine lightness and good mechanical properties. Herein, the production of AlSi10Mg lattice structures by laser powder bed fusion is explored and consistent processing parameters are selected. Thereafter, it is demonstrated that heat treatments, specifically designed on the basis of the alloy's metallurgy, can be used to selectively induce different microstructural modifications and, consequently, finely tune the static and dynamic mechanical behavior of the aluminum lattice structures. In particular, removal of residual stresses results to be the dominant factor in allowing a smooth quasistatic compressive behavior and improving the structure's ability to absorb energy during collapse. On the contrary, the increase in ductility connected to the spheroidization of the Si network is shown to be of paramount importance in improving the structure's dynamic damping ability by allowing local plasticization.

Transition metal carbides and nitrides as catalysts for thermochemical reactions

Transition metal carbides and nitrides (TMCs and TMNs) have attracted much attention due to their unique physical and chemical properties brought by the incorporation of interstitial carbon and nitrogen into the crystal lattice of the parent metals. Recent advances in utilizing TMCs and TMNs have revealed their intriguing catalytic properties in many industrially important reactions, including heteroatom removal, CO2 activation, alcohol reforming, and water–gas shift reactions. The promising activity, selectivity, and stability of TMCs and TMNs, either as catalysts or as supports for other metals, are often attributed to their strong interactions with the adsorbates, tunable surface properties, as well as the synergy with supported metals. This review summarizes the synthesis and characterization of TMC and TMN model surfaces and powder catalysts, and uses several case studies to demonstrate their unique catalytic properties in these important reactions. A discussion is also provided regarding the challenges and opportunities associated with the utilization of TMCs and TMNs in thermocatalysis.

On the effect of the node and building orientation on the fatigue behavior of L‐PBF Ti6Al4V lattice structure sub‐unital elements

Despite the great potential of additively manufactured (AM) metallic lattice materials, a comprehensive understanding of their mechanical behavior, particularly fatigue, has yet to be achieved. The role of the sub-unital lattice elements, that is, the struts and the nodes (or strut junctions), is rarely explored, even though it is well known that fatigue is a local phenomenon, determined by the small features of a structure (defects and local geometrical discontinuities). In this work, the mechanical behavior of nodes and struts has been investigated by designing laser powder bed fusion (L-PBF) Ti6Al4V single strut specimens, with a node placed in the central part of the gauge length. The specimens were manufactured according to four different building orientations, namely, 90°, 45°, 15°, and 0° to the build plane. The influence of the fillet radius at the node and of the printing direction on the fatigue strength has been examined.

Relationships of Macroscopic Characteristics of a Solid with the Binding Energy of an Ion in a Metal Lattice

Relationships of Macroscopic Characteristics of a Solid with the Binding Energy of an Ion in a Metal Lattice

Electronic States and the Anomalous Hall Effect in Strongly Correlated Topological Systems

We treat elementary excitations, the spin-liquid state, and the anomalous Hall effect (including the quantum one in purely 2D situation) in layered highly correlated systems. The mechanisms of the formation of a topological state associated with bare flat energy bands, correlations, and spin-orbit interactions, including the appearance of correlated Chern bands, are analyzed. A two-band picture of the spectrum in metallic kagome lattices is proposed, which involves a transition from the ferromagnetic state, a flat strongly correlated band, and a band of light Dirac electrons. In this case, the effect of separation of the spin and charge degrees of freedom turns out to be significant. The application of the representations of the Kotliar-Rukenstein auxiliary bosons and the Ribeiro-Wen dopons to this problem is discussed.

Multiscale Analysis of High Damping Composites Using the Finite Cell and the Mortar Method

Metal lattice structures filled with a damping material such as polymer can exhibit high stiffness and good damping properties. Mechanical simulations of parts made from these composites can however require a large modeling and computational effort because relevant features such as complex geometries need to be represented on multiple scales. The finite cell method (FCM) and numerical homogenization are potential remedies for this problem. Moreover, if the microstructures are placed in between the components of assemblies for vibration reduction, a modified mortar technique can further increase the efficiency of the complete simulation process. With this method, it is possible to discretize the components separately and to integrate the viscoelastic behavior of the composite damping layer into their weak coupling. This paper provides a multiscale computational material design framework for such layers, based on FCM and the modified mortar technique. Its efficiency even in the case of complex microstructures is demonstrated in numerical studies. Therein, computational homogenization is first performed on various microstructures before the resulting effective material parameters are used in larger-scale simulation models to investigate their effect and to verify the employed methods.

Precipitation-induced transition in the mechanical behavior of 3D printed Inconel 718 bcc lattices

This work aims to investigate the effect of microstructure on the mechanical behavior of metallic lattice structures. With that purpose, Inconel 718 bcc lattices were manufactured by selective laser melting and their room temperature compressive behavior was compared in the as-built and aged conditions. A distinct transition from bending-dominated to stretch-dominated behavior takes place following the aging treatment as the as-built supersaturated solid solution (containing a minor fraction of nanoparticles) transforms into a microstructure with a comparatively large fraction of precipitates with dimensions spanning several hundred nanometers. Precipitation leads to a stiffer and stronger structure, with a higher capacity to absorb energy. The obtained mechanical property results are compared to the predictions of the Maxwell criterion and the Gibson-Ashby model for bcc lattices. It is shown that microstructure variations explain, at least partially, the low correlation between the bcc experimental data in the literature with the model predictions.

Crushing of additively manufactured thin-walled metallic lattices: Two-scale strain localization analysis

The response of architectured structures is characterized by multi-scale kinematics, which complex relation and effect on the engineering load response is still not completely understood and therefore needs further investigations. More precisely, the lack of experimental methods enabling to provide multi-scale data remains a key issue. The paper presents an experimental and numerical analysis of crushing tests performed on thin-walled auxetic metallic lattices manufactured by Directed Energy Deposition. The work is focused on the two-scale strain localization occurring (a) at the microscopic scale of the unit cell and (b) at the macroscopic scale corresponding to the homogenized continuum. The structures of interest are defined as the extrusion of a 2D auxetic wireframe and allow the application of an adapted digital image correlation scheme dedicated to the identification of the kinematics at the two considered scales. In particular, the microscopic kinematics are studied by following the deformation of lattice crossings, while the macroscopic strains are deduced from the motion of virtual unit cell corners. The results show that the global elastic-plastic response of the lattices is completely driven by the formation of plastic hinges at specific locations, leading to characteristic deformation patterns and eventually a collective behavior of neighboring unit cells. Companion finite element computations show an excellent match with experiments and thus enable to assess the effect of modeling assumptions, unit cell geometry, strain rate and geometrical imperfections in the global response of the architecture material.