Bcc Unit Cell Research Articles

Design and Evaluation of Two Proposed Hybrid FCC-BCC Lattice Structures for Enhanced Mechanical Performance

Lattice structures are an innovative solution to increase the strength-to-weight ratio of a structure. In this study, two polymeric hybrid lattice structures—"FRB" (a heterogenous structure which is indeed a BCC structure reinforced by FCC unit cells dispersed in a way to form a chessboard pattern in each layer) and the "Multifunctional" (a homogenous structure whose unit cells are a combination of FCC and BCC unit cells where their central nodes are connected)—are proposed, fabricated via liquid crystal display 3D printing technique, and their mechanical characteristics are evaluated under quasi-static loading, experimentally and numerically. The results indicate a 15.71% increase in compressive strength and a 103.75% improvement in volumetric energy absorption for the FRB structure compared to BCC. The Multifunctional structure revealed a 74.30% increase in compressive strength along with a 111.30% improvement in volumetric energy absorption compared to BCC, though it exhibited a 13.33% decrease in specific energy absorption compared to the FCC structure. Both the proposed designs have merits; the FRB structure suitable for lightweight energy absorption and the Multifunctional structure appropriate for high load-bearing applications where the overall weight is not the primary concern.

Thermal Management of Microelectronic Devices Using Nanofluid with Metal foam Heat Sink.

Microelectronic components are used in a variety of applications that range from processing units to smart devices. These components are prone to malfunctions at high temperatures exceeding 373 K in the form of heat dissipation. To resolve this issue, in microelectronic components, a cooling system is required. This issue can be better dealt with by using a combination of metal foam, heat sinks, and nanofluids. This study investigates the effect of using a rectangular-finned heat sink integrated with metal foam between the fins, and different water-based nanofluids as the working fluid for cooling purposes. A 3D numerical model of the metal foam with a BCC-unit cell structure is used. Various parameters are analyzed: temperature, pressure drop, overall heat transfer coefficient, Nusselt number, and flow rate. Fluid flows through the metal foam in a turbulent flow with a Reynold's number ranging from 2100 to 6500. The optimum fin height, thickness, spacing, and base thickness for the heat sink are analyzed, and for the metal foam, the material, porosity, and pore density are investigated. In addition, the volume fraction, nanoparticle material, and flow rate for the nanofluid is obtained. The results showed that the use of metal foam enhanced the thermal performance of the heat sink, and nanofluids provided better thermal management than pure water. For both cases, a higher Nusselt number, overall heat transfer coefficient, and better temperature reduction is achieved. CuO nanofluid and high-porosity low-pore-density metal foam provided the optimum results, namely a base temperature of 314 K, compared to 341 K, with a pressure drop of 130 Pa. A trade-off was achieved between the temperature reduction and pumping power, as higher concentrations of nanofluid provided better thermal management and resulted in a large pressure drop.

Elastic axial stiffness properties of lattice structures: Analytical approach and experimental validation for bcc and f2cc,z unit cells

Additive manufacturing (AM) is a key technology for the individualized and resource-efficient production of structural components. Recent developments in manufacturing technologies enable improved quality of additively manufactured components and therefore they become more and more important in lightweight constructions. An example is the substitution of solid material by porous lattice structures. Those embedded lattice structures lead to highly weight-efficient structures. Most recent investigations focus on numerical and experimental studies to describe the mechanical behavior of lattice structures. In this paper, a method to determine analytical expressions for the axial stiffness properties of lattice structures is presented. The displacement method and direct stiffness method are used to derive symbolic parameter-dependent formulas for the axial stiffnesses and effective Young’s moduli for f2cc,z, and bcc unit cells. Furthermore, an empirical approach based on Finite Element simulations is presented to describe the stiffness reduction for non-embedded or rather free lattice structures. The results are further validated by physical experiments. Stereolithography is used for specimen production. f2cc,z, and bcc lattice structures are embedded in thin-walled rectangular aluminum tubes and tested under compression load. Furthermore, lattices without a surrounding tube are tested. The analytical and empirical solutions are in good agreement with the experimental and numerical results.

Magnetic FeM (M = Ag, Co, Cu, and Ni) nanocrystals as electrocatalysts for hydrogen evolution reaction

Iron-based magnetic nanocrystals (FeM@OAm, M = Ag, Co, Cu, and Ni; OAm = oleylamine) electrocatalysts have been successfully synthesized via oleylamine reduction of metal salts method. FeCo is arranged in a body-centered cubic (bcc) unit cell, while FeNi, FeAg, and FeCu are in a face-centered cubic (fcc) structure. All the samples have different morphologies with a diameter average size varying of 6.4 ± 1.0 to 21.7 ± 5.1 nm, depending on the bimetallic composition. The samples have ferrimagnetic behavior with low coercive field and high saturation magnetization values at room temperature. Furthermore, it has been shown that FeAg fits better in the solid solution category. Among heterogeneous electrocatalysts synthesized, FeCo nanocrystals show lower overpotential (−564 mV) in comparison to FeAg (−584 mV), FeNi (−666 mV), and FeCu (−591 mV). The Tafel plots showed that the hydrogen evolution reaction (HER) activity for electrocatalyst following a mixed of Volmer−Heyrovsky reaction mechanism, suggests that reaction Volmer is the determining step. In addition, all electrocatalysts showed stability in tests of continuous operations showing only low potential variation. The EIS study shows system characterized by two time-constant, both of them may related to the kinetics of the HER related to the charge transfer kinetics and the hydrogen adsorption. Thus, these materials are sustainable for electrochemical water splitting since showed acceptable electrocatalytic performance toward HER in alkaline media with excellent physical stability and abundance of active sites for HER.

Use of first principles and Thermo-Calc to identify potential low elastic modulus titanium-based alloys for biomedical applications

High alloyed β-phase stabilised titanium alloys are known to have low elastic moduli comparable to that of the human bone (≈30 GPa). The β-phase in titanium alloys exhibits an elastic modulus of about 60-80 GPa, which is nearly half that of α-phase (100-120 GPa). In this work, an attempt to develop a β-phase titanium-based alloy through first-principles calculations and Thermo-Calc calculations for biomedical applications was conducted. First-principles calculations were performed using the CASTEP code on a simple 2-atom bcc unit cell to predict the theoretical elastic modulus and mechanical stability of the Ti-Nb-Ta-Zr (TNTZ) system at 0 K. Thermo-Calc was used to determine the phase proportion diagrams of the proposed alloys at 500℃. The alloy comprised Ti-Nbx-Ta25-Zr5 (x = 5, 10, 20, 30, 40) (at.%). The theoretical results suggested that increasing niobium content introduced both mechanical (cʹ > 0) stability of the alloys. Alloy Ti-Nb5-Ta25-Zr5 gave the lowest elastic modulus of 55.23 ± 24.45 GPa which is half the elastic modulus of pure titanium (α phase). The phase proportion diagrams showed that up to 58.6 mol.% of β phase was retained at 20 at.% Nb, although the Voigt-Reuss-Hill Young’s modulus calculated from first principles increased with increasing niobium content while the α/β phase transformation temperature decreased down to 551.3℃ at 40 at.% Nb.

Temperature dependence of electron-phonon interactions in vanadium

First-principles calculations were used to study the Fermi surface of body-centered cubic vanadium at elevated temperatures. Supercell calculations accounted for effects of thermal atom displacements on band energies, and band unfolding was used to project the spectral weight of the electron states into the Brillouin zone of a standard bcc unit cell. An electronic topological transition (ETT, or Lifshitz transition) occurred near the $\mathrm{\ensuremath{\Gamma}}$ point with increasing temperature, but the large thermal smearings from the atomic disorder and the Fermi-Dirac distribution reduced the effect of this ETT on the electron-phonon interactions. The phonon dispersions showed thermal stiffening of their Kohn anomalies near the $\mathrm{\ensuremath{\Gamma}}$ point and of the longitudinal N phonon mode. In general the effects of the ETT were overcome by the thermal smearing of the Fermi surface that reduces the spanning vector densities for anomalous phonon modes.

Relation between Crystal Structure and Transition Temperature of Superconducting Metals and Alloys

Using the Roeser–Huber equation, which was originally developed for high temperature superconductors (HTSc) (H. Roeser et al., Acta Astronautica 62 (2008) 733), we present a calculation of the superconducting transition temperatures, T c , of some elements with fcc unit cells (Pb, Al), some elements with bcc unit cells (Nb, V), Sn with a tetragonal unit cell and several simple metallic alloys (NbN, NbTi, the A15 compounds and MgB 2 ). All calculations used only the crystallographic information and available data of the electronic configuration of the constituents. The model itself is based on viewing superconductivity as a resonance effect, and the superconducting charge carriers moving through the crystal interact with a typical crystal distance, x. It is found that all calculated T c -data fall within a narrow error margin on a straight line when plotting ( 2 x ) 2 vs. 1 / T c like in the case for HTSc. Furthermore, we discuss the problems when obtaining data for T c from the literature or from experiments, which are needed for comparison with the calculated data. The T c -data presented here agree reasonably well with the literature data.

Hydrogen storage in high-entropy alloys with varying degree of local lattice strain

We have investigated the structure and hydrogen storage properties of a series of Ti, V, Zr, Nb and Ta based high-entropy alloys (HEAs) with varying degree of local lattice strain by means of synchrotron radiation powder X-ray diffraction, scanning electron microscopy, thermogravimetric analysis, differential scanning calorimetry and manometric measurements in a Sieverts apparatus. The obtained alloys have body-centred cubic (bcc) crystal structures and form face-centred cubic (fcc) metal hydrides with hydrogen-to-metal ratios close to 2. No correlation between the hydrogen storage capacity and the local lattice strain δr is observed in this work. Both bcc and fcc unit cells expand linearly with the zirconium-to-metal ratio [Zr]/[M], and increased concentration of Zr stabilizes the hydrides. When heated, the hydrides decompose into the original bcc alloys if [Zr]/[M]<12.5 at.%. The hydrides phase-separate in a hydrogen-induced decomposition type process for [Zr]/[M]≥12.5 at.%. The result is then a combination of two bcc phases, one with a larger and the other with a smaller unit cell than the original bcc alloy.

Design of Functionally Graded Lattice Structures using B-splines for Additive Manufacturing

Abstract Additive manufacturing methods have recently been used to make light-weight parts using lattice structures for various applications. Functionally graded lattice structures (FGLs) are structures that are designed using lattices with a varying distribution of porosity by virtue of varying the volume fractions of each unit cell in the 3D design domain. This graded design helps to achieve advanced properties related to structural strength, allow functionalities such as bone ingrowth and optimum heat transfer etc. Compliance minimization is one such classic problem where topology optimization techniques are used to determine the optimum distribution of material in the design domain while obtaining the desired reduction in weight. This material distribution is typically populated with lattices of variable volume fraction unit cells to generate FGLs. Truss type unit cells such as BCC are commonly used to develop FGLs. To develop such structures with truss type unit cells there is a need for a methodology that can maintain smooth connectivity among unit cells of varying densities. This paper discusses a new method to achieve smoothly connected FGLs, based on a BCC unit cell geometry, using a B-spline surface-based unit cell design methodology. The lead author’s previous work in [1] on generating bifurcating geometries using B-spline surfaces is extended to lattices as a case of multi-furcation geometries. First, a control polyhedron net is developed on the basis of desired unit cell geometry which is then further processed to construct water-tight boundary representation of the unit cell using a 3 rd order B-spline surface. This design methodology is used in conjunction with an algorithm to populate the density distribution from SIMP based topology optimization using unit cells with different volume fractions. The resulting lattice structure is compared with a uniform density lattice structure of similar light-weighting. It is shown that the methodology discussed in this paper could be successfully used to construct FGLs with high stiffness.

First principles study of the ground state magnetic properties of hypothetical B2-Fe50Al50 multilayers

The ground state structural, electronic and magnetic properties of multilayers of B2 Fe-Al stoichiometric (Fe50Al50) phase were studied by first principles calculations in the framework of the density functional theory as a function of the number of layers. From the cohesive energy point of view all, the studied multilayers are more stable in the ferromagnetic state. The calculated equilibrium lattice parameter of the B2-Fe50Al50 phase in the multilayers is smaller than that in bulk. The calculations of the magnetic properties show an enhancement of the total magnetic moment of the B2-Fe50Al50 phase on going from bulk to multilayers structures. The total and partial density of states curves indicate changes in the electronic configuration of surface Fe atoms (relative to that observed in bulk Fe50Al50) in all the studied multilayers. For Fe atoms located at sites in the inner layers, there were observed significant modifications in their electronic distribution only for multilayers with low number of bcc unit cell layers (2 and 4). The increase of the magnetic moment of the multilayers is discussed in terms of the observed enhancement of the local magnetic moment of Fe atoms.

A FEM study on mechanical behavior of cellular lattice materials based on combined elements

The mechanical behavior of AlSi10Mg alloy lattice materials with rhombic dodecahedron and BCC unit cells fabricated by selective laser melting was investigated in this paper. Tensile tests were carried out to obtain material properties, mechanical response and failure characteristic. The results show that rhombic dodecahedron and BCC cellular lattice have variant tensile strength and stiffness. Various fracture features are also observed to be related to its configuration. Scanning electron microscope images of fracture surface demonstrate the lattice material resulted in ductile fracture. Finite element models based on combined elements were established. Afterwards, numerical analysis was conducted by ABAQUS. The FE results which could be employed to make some useful predictions are consistent with the experimental results.

Lattice Monte Carlo Simulations in Search of Zeolite Analogues: Effects of Structure Directing Agents

We use parallel tempering Monte Carlo simulations to search for crystalline states of a lattice model of silica polymerization in the presence of structure directing agents (SDAs). Following previous work where we have discretized continuous space into a body-centered cubic (bcc) lattice, we have modeled tetrahedral molecules (T(OH)4) as corner-sharing tetrahedra on a bcc unit cell. The SDAs were represented as quasi-spherical species with diameters of 6.4 and 10.4 Å to study the effect of SDA size on the resulting crystal structures. Our parallel tempering Monte Carlo simulations produce fully connected crystalline structures finding the emergence of 3D microporous materials with SDAs occupying the pore spaces and 2D layered materials with SDAs occupying the gallery space in between layers. We have found that the strength of SDA–oxygen attraction plays a significant role in directing final micropore structures. For relatively strong attractions (>1.2 kcal/mol SDA–oxygen contacts) we have found only 2D layered materials; for attractions below this cutoff we observed 3D microporous crystals; and for no attraction—modeling the SDA as a quasi-hard sphere—we again found only 2D layered materials. In the space of 3D microporous crystals, we have also found that using larger SDAs or a lower concentration of a given SDA generate crystals with larger rings.

Electronic correlations in Fe at Earth's inner core conditions: Effects of alloying with Ni

We have studied the body-centered cubic (bcc), face-centered cubic (fcc), and hexagonal close-packed (hcp) phases of Fe alloyed with 25 at.% of Ni at Earth's core conditions using an ab initio local density approximation + dynamical mean-field theory approach. The alloys have been modeled by ordered crystal structures based on the bcc, fcc, and hcp unit cells with the minimum possible cell size allowing for the proper composition. Our calculations demonstrate that the strength of electronic correlations on the Fe $3d$ shell is highly sensitive to the phase and local environment. In the bcc phase, the $3d$ electrons at the Fe site with Fe only nearest neighbors remain rather strongly correlated, even at extreme pressure-temperature conditions, with the local and uniform magnetic susceptibility exhibiting a Curie-Weiss-like temperature evolution and the quasiparticle lifetime \ensuremath{\Gamma} featuring a non-Fermi-liquid temperature dependence. In contrast, for the corresponding Fe site in the hcp phase, we predict a weakly correlated Fermi-liquid state with a temperature-independent local susceptibility and a quadratic temperature dependence of \ensuremath{\Gamma}. The iron sites with nickel atoms in the local environment exhibit behavior in the range between those two extreme cases, with the strength of correlations gradually increasing along the hcp-fcc-bcc sequence. Further, the intersite magnetic interactions in the bcc and hcp phases are also strongly affected by the presence of Ni nearest neighbors. The sensitivity to the local environment is related to modifications of the Fe partial density of states due to mixing with Ni $3d$ states.

Increased magnetic moment induced by lattice expansion from α-Fe to α′-Fe8N

Buffer-free and epitaxial α-Fe and α′-Fe8Nx thin films have been grown by RF magnetron sputtering onto MgO (100) substrates. The film thicknesses were determined with high accuracy by evaluating the Kiessig fringes of X-ray reflectometry measurements allowing a precise volume estimation. A gradual increase of the nitrogen content in the plasma led to an expansion of the iron bcc unit cell along the [001] direction resulting finally in a tetragonal distortion of about 10% corresponding to the formation of α′-Fe8N. The α-Fe lattice expansion was accompanied by an increase in magnetic moment to 2.61 ± 0.06μB per Fe atom and a considerable increase in anisotropy. These experiments show that—without requiring any additional ordering of the nitrogen atoms—the lattice expansion of α-Fe itself is the origin of the increased magnetic moment in α′-Fe8N.

Effect of Ti/Cr content on the microstructures and hydrogen storage properties of Laves phase-related body-centered-cubic solid solution alloys

A series of BCC/C14 mixed phase alloys with the chemical composition of Ti13.6+xZr2.1V44Cr13.2−xMn6.9Fe2.7Co1.4Ni15.7Al0.3, x=0, 2, 4, 6, 8, 10, and 12, was fabricated, and their structural, gaseous phase and electrochemical hydrogen storage properties were studied. Raising the maximum pressure for measuring the gaseous hydrogen storage capacity allowed these alloys to reach full activation, and the maximum discharge capacities ranged from 375 to 463mAhg−1. As the Ti/Cr ratio in the alloy composition increased, the maximum gaseous hydrogen storage capacity improved due to the expansion in both BCC and C14 unit cells. However, reversibility decreased due to the higher stability of the hydride phase, as indicated by the lower equilibrium pressures measured for these alloys. As with most other metal hydride alloys, the electrochemical capacities measured at 50 and 4mAg−1 fell between the boundaries set by the maximum and reversible gaseous hydrogen storage capacities. The poorer high-rate dischargeability observed with higher Ti/Cr ratios was attributed to the lower surface exchange current (less catalytic). Two other negative impacts observed with higher Ti/Cr ratios in the alloy composition are poorer cycle stability and lower open-circuit voltage.

Elastic softening of β-type Ti–Nb alloys by indium (In) additions

Recent developments showed that β-type Ti–Nb alloys are good candidates for hard tissue replacement and repair. However, their elastic moduli are still to be further reduced to match Young׳s modulus values of human bone, in order to avoid stress shielding. In the present study, the effect of indium (In) additions on the structural characteristics and elastic modulus of Ti–40Nb was investigated by experimental and theoretical (ab initio) methods. Several β−type (Ti–40Nb)–xIn alloys (with x≤5.2wt%) were produced by cold-crucible casting and subsequent heat treatments (solid solutioning in the β-field followed by water quenching). All studied alloys completely retain the β-phase in the quenched condition. Room temperature mechanical tests revealed ultimate compressive strengths exceeding 770MPa, large plastic strains (>20%) and a remarkable strain hardening. The addition of up to 5.2wt% indium leads to a noticeable decrease of the elastic modulus from 69GPa to 49GPa, which is closer to that of cortical bone (<30GPa). Young׳s modulus is closely related to the bcc lattice stability and bonding characteristics. The presence of In atoms softens the parent bcc crystal lattice, as reflected by a lower elastic modulus and reduced yield strength. Ab initio and XRD data agree that upon In substitution the bcc unit cell volume increases almost linearly. The bonding characteristics of In were studied in detail, focusing on the energies that appeared from the EDOSs significant for possible hybridizations. It came out that minor In additions introduce low energy states with s character that present antibonding features with the Ti first neighboring atoms as well as with the Ti-Nb second neighboring atoms thus weakening the chemical bonds and leading to elastic softening. These results could be of use in the design of low rigidity β-type Ti-alloys with non-toxic additions, suitable for orthopedic applications.

Electrons charge concentration and melting point of bcc metals

The study presents a new method to determine the melting point of bcc metals. The method uses unit cell parameters and the atomic number Z of the chemical element. Based on these data, one can calculate the total charge of electrons belonging to a single atom and volume V of the space occupied by the atom. The value of Ζ/V (average charge electron density in a volume occupied by the atom) is proportional to the melting point of metals with the bcc lattice (Tbcc). Taking into account the number of atoms per bcc unit cell, a suitable model has been proposed. Calculations made with the use of this model show good agreement with literature data.

Defect kinetics on experimental timescales using atomistic simulations

In his last few years, Patrick Veyssière became involved in atomic-scale molecular dynamics simulations that give access to the full atomistic details of dislocation/dislocation and dislocation/defect interactions. Such simulations are, however, very limited in time and do not allow the study of diffusional processes, such as vacancy migration. For such processes, one needs to explore the configuration space in search of activated states, whose energy barriers control the slow thermal-activated kinetics of defects. Here, we present work, performed in the context of a France–China project and initiated by Patrick Veyssière, where we study the long-term evolution of vacancy supersaturations in fcc metals. We employed a combination of saddle-point search methods (activation–relaxation technique, automated basin climbing method and nudged elastic band method) and kinetic Monte Carlo simulations to reach experimental timescales while retaining atomistic fidelity. The simulations identified a specific and, so far, unidentified cluster, the pentavacancy, made of five vacancies forming a bcc unit cell in the fcc lattice, which plays a central role in vacancy clustering in aluminium.

In Situ Characterization of Lattice Structure Evolution during Phase Transformation of Zr‐2.5Nb

AbstractThe α–β phase transformation behavior of Zr‐2.5Nb (in mass%) has been characterized in real time during an in situ neutron diffraction experiment. The Zr‐2.5Nb material in the current study consists, at room temperature, of α‐Zr phase (hcp) and two β phases (bcc), a Nb rich β‐Nb phase and retained, Zr rich, β‐Zr(Nb) phase. It is suggested that this is related to a quench off the equilibrium solubility of Nb atoms in the Zr bcc unit cells. Vegard's law combined with thermal expansion is applied to calculate the composition of the β‐phase, which is compared with the phase diagram, revealing the system's kinetic behavior for approaching equilibrium.

The structure of nitrogen-supersaturated ferrite produced by ball milling

Highly supersaturated solid solutions of nitrogen in ferrite (bcc) were produced by ball milling of various powder mixtures of α-iron and ε-Fe3N1.08. The microstructure and the crystal structure of the product phases were examined as a function of nitrogen content using X-ray powder diffraction, high-resolution electron microscopy and Mössbauer spectroscopy. It was found that the grain size decreases with increasing nitrogen content. Unexpected shifts of the reflections in the X-ray powder diffraction patterns of the supersaturated N-ferrites, depending on the hkl values of the reflections and nitrogen content, were observed. These shifts cannot be explained by tetragonal distortion of the bcc unit cell, but they are in accordance with the occurrence of a certain type of stacking faults on bcc {211} planes. This result, together with the observation of some isolated fcc crystals (by high-resolution electron microscopy) and a drop in microstrain for high nitrogen contents, demonstrates that unconventional deformation mechanisms are operative in these materials below a certain grain size, leading to a breakdown of the classical Hall–Petch relation for mechanical strengthening.