Bcc Lattice Structures Research Articles

Effective strut-based design approach of multi-shaped lattices using equivalent material properties

We propose an effective approach for designing a multi-lattice structure (MLS) that simultaneously considers local densities and the fillet-joint shape of struts to express practical equivalent material properties. The density of each cell is optimized by changing the strut diameter and fillet-joint radius according to loading conditions. The equivalent material properties of MLS, such as elastic modulus and shear modulus, are calculated based on a computational homogenization method. Finite element analyses of the full-shape and homogenized lattice model under external compressive load are conducted to evaluate the equivalent material properties. We also designed an optimized three-point bending structure using the proposed method. Based on the results of the topology optimization, three types of lattices with different relative densities are designed in a local zone considering local deformation modes. The result of this work shows that multi-lattice bending structure has about 86.9 % higher strength than that of a uniform BCC lattice structure with the same weight.

Computational property predictions of Ta\u2013Nb\u2013Hf\u2013Zr high-entropy alloys

Refractory high entropy alloys (R-HEAs) are becoming prominent in recent years because of their properties and uses as high strength and high hardness materials for ambient and high temperature, aerospace and nuclear radiation tolerance applications, orthopedic applications etc. The mechanical properties like yield strength and ductility of TaNbHfZr R-HEA depend on the local nanostructure and chemical ordering, which in term depend on the annealing treatment. In this study we have computationally obtained various properties of the equimolar TaNbHfZr alloy like the role of configurational entropy in the thermodynamic property, rate of evolution of nanostructure morphology in thermally annealed systems, dislocation simulation based quantitative prediction of yield strength, nature of dislocation movement through short range clustering (SRC) and qualitative prediction of ductile to brittle transition behavior. The simulation starts with hybrid Monte Carlo/Molecular Dynamics (MC/MD) based nanostructure evolution of an initial random solid solution alloy structure with BCC lattice structure created with principal axes along [1 1 1], [− 1 1 0] and [− 1 − 1 2] directions suitable for simulation of ½[1 1 1] edge dislocations. Thermodynamic properties are calculated from the change in enthalpy and configurational entropy, which in term is calculated by next-neighbor bond counting statistics. The MC/MD evolved structures mimic the annealing treatment at 1800 °C and the output structures are replicated in periodic directions to make larger 384,000 atom structures used for dislocation simulations. Edge dislocations were utilized to obtain and explain for the critically resolved shear stress (CRSS) for the structures with various degrees of nanostructure evolution by annealing, where extra strengthening was observed because of the formations of SRCs. Lastly the MC/MD evolved structures containing dislocations are subjected to a high shear stress beyond CRSS to investigate the stability of the dislocations and the lattice structures to explain the experimentally observed transition from ductile to brittle behavior for the TaNbHfZr R-HEA.

Evaluation of rods deformation of metal lattice structure in additive manufacturing based on skeleton extraction technology.

The components with lattice structure as filling unit have great application potential in aerospace and other fields. The failure of the lattice structure directly affects the functional characteristics of the parts filled with the lattice structure. Aiming at the problem that it is difficult to evaluate the deformation degree of metal lattice structure after mechanical loading in additive manufacturing, firstly, the point cloud model of lattice structure is obtained by using CT scanning and three-dimensional reconstruction, and then the skeleton of lattice structure is automatically extracted based on L1 median algorithm. Finally, the deformation angle of rods is measured to evaluate the degree of deformation and damage of parts. In this paper, the deformation evaluation of the rods of the BCC lattice is discussed. The experimental results show that the proposed skeleton extraction technology achieves the evaluation of lattice structure deformation. The experimental model is extended to BCC lattice structure with unit cell number of n×n×n. When the ratio of the rods with more than 40% severe deformation to all rods in the lattice structure reaches (2n-1)/2n2 it indicates that the lattice structure has undergone a large degree of deformation and should not continue to serve.

Structure and phase behavior of high-density ice from molecular-dynamics simulations with the ReaxFF potential.

We report a molecular dynamics simulation study of dense ice modeled by the reactive force field (ReaxFF) potential, focusing on the possibility of phase changes between crystalline and plastic phases as observed in earlier simulation studies with rigid water models. It is demonstrated that the present model system exhibits phase transitions, or crossovers, among ice VII and two plastic ices with face-centered cubic (fcc) and body-centered cubic (bcc) lattice structures. The phase diagram derived from the ReaxFF potential is different from those of the rigid water models in that the bcc plastic phase lies on the high-pressure side of ice VII and does the fcc plastic phase on the low-pressure side of ice VII. The phase boundary between the fcc and bcc plastic phases on the pressure, temperature plane extends to the high-temperature region from the triple point of ice VII, fcc plastic, and bcc plastic phases. Proton hopping, i.e., delocalization of a proton, along between two neighboring oxygen atoms in dense ice is observed for the ReaxFF potential but only at pressures and temperatures both much higher than those at which ice VII-plastic ice transitions are observed.

α ↔ γ phase transformation in iron: comparative study of the influence of the interatomic interaction potential

Only few available interatomic interaction potentials implement the α ↔ γ phase transformation in iron by featuring a stable low-temperature bcc and high-temperature fcc lattice structure. Among these are the potentials by Meyer and Entel (1998 Phys. Rev. B 57 5140), by Müller et al (2007 J. Phys.: Condens. Matter 19 326220) and by Lee et al (2012 J. Phys.: Condens. Matter 24 225404). We study how these potentials model the phase transformation during heating and cooling; in order to help initiating the transformation, the simulation volume contains a grain boundary. For the martensitic transformation occurring on cooling an fcc structure, we additionally study two potentials that only implement a stable bcc structure of iron, by Zhou et al (2004 Phys. Rev. B 69 144113) and by Mendelev et al (2003 Philos. Mag. 83 3977). We find that not only the transition temperature depends on the potential, but that also the height of the energy barrier between fcc and bcc phase governs whether the transformation takes place at all. In addition, details of the emerging microstructure depend on the potential, such as the fcc/hcp fraction formed in the α → γ transformation, or the twinning induced in and the lattice orientation of the bcc phase in the γ → α transformation.

Systematic development of ab initio tight-binding models for hexagonal metals

A systematic method for building an extensible tight-binding model from ab initio calculations has been developed and tested on two hexagonal metals: Zr and Mg. The errors introduced at each level of approximation are discussed and quantified. For bulk materials, using a limited basis set of $spd$ orbitals is shown to be sufficient to reproduce with high accuracy bulk energy versus volume curves for fcc, bcc, and hcp lattice structures, as well as the electronic density of states. However, the two-center approximation introduces errors of several tenths of eV in the pair potential, crystal-field terms, and hopping integrals. Environmentally dependent corrections to the former two have been implemented, significantly improving the accuracy. Two-center hopping integrals were corrected by taking many-center hopping integrals for a set of structures of interest, rotating them into the bond reference frame, and then fitting a smooth function through these values. Finally, a pair potential was fitted to correct remaining errors. However, this procedure is not sufficient to ensure transferability of the model, especially when point defects are introduced. In particular, it is shown to be problematic when interstitial elements are added to the model, as demonstrated in the case of octahedral self-interstitial atoms.

Investigation on the static and dynamic behavior of BCC lattice structure with quatrefoil node manufactured using fused deposition modelling additive manufacturing

This paper presents a vibration characteristics of BCC lattice structure with quatrefoil node which has been made using the fused deposition modelling (FDM) additive manufacturing (AM) technique. By conducting vibration testing, the effect of strut diameter design parameter on the natural frequency values of the BCC lattice structure with quatrefoil node is investigated. The results showed that the natural frequency values of the lattice structure material can be greatly affected by the strut diameter sizes due to increase in stiffness as the strut diameter increases. The mathematical equation is also derived to calculate the total area moments of inertia of the lattice structure model and the validity of this developed model is shown through comparison of the results with experimental work of the three-point bending test which shown similar increase trend. Thus, this study provides information on the influence of strut diameter design parameter on its vibration characteristic.

Preliminary Study on the Natural Frequency of Additively Manufactured Bcc Lattice Structure with Hollow Struts

Preliminary Study on the Natural Frequency of Additively Manufactured Bcc Lattice Structure with Hollow Struts

Improving mechanical performance of fused deposition modeling lattice structures by a snap-fitting method

A snap-fitting method is introduced into fused deposition modeling (FDM) technique to fabricate BCC lattice structures of polylactic acid (PLA plus) with relative densities ranging from 2.1% to 8.3%. This method makes it possible to deposit all the filaments along the length direction of the strut. The measured peak strengths, compressive moduli and energy absorptions per unit volume of the snap-fitted FDM structures are improved by 37.6%–65.3%, 11.4%–39.6% and 67%–270%, respectively, compared with the conventional integrated FDM structures of the same relative density. Apart from improved mechanical properties, good surface quality and higher printing efficiency are also achieved in this method. Analytical models considering node volume are developed and able to predict the peak strengths and the compressive moduli of the integrated FDM structures and the snap-fitted FDM structures, for all relative densities tested. The paper also demonstrated that this method can be extended to other additive manufacturing technologies such as PolyJet.

Galaxies “Boiling off” Electrons Due to the Photo-Electric Effect Leading to a New Model of the IGM and a Possible Mechanism for “Dark Matter”

The Intergalactic Medium (IGM) is commonly thought to be occupied by approximately one atom of Hydrogen per cubic metre of space either as neutral Hydrogen or partially/fully ionised. This cannot be true as galaxies will “boil off” electrons from their outer surfaces by the photo-electric effect and so the IGM must be filled with electrons. UV and X-ray photons, as they leave the galaxy, can remove an electron from a Hydrogen atom at the surface of the galaxy, give it sufficient energy to escape the gravitational pull of the galaxy and go on to fill the IGM. A typical galaxy emits approximately 5×1047 X-ray photons each second. All of which pass through the outer surface of the galaxy and have sufficient energy to eject an electron and send it off to the IGM. Adding to these photons in the UV and gamma, we can see that galaxies are ejecting large amounts of electrons each second that go on to fill the IGM. Data from FRB 121102 give the value for the electron number density in the IGM as ne ≈ 0.5 m-3. Under certain conditions, an electron gas will crystallise into a Wigner-Seitz crystal. Here the electrical potential energy of repulsion between the electrons dominates their kinetic energy and the electrons form on a BCC lattice structure. The electrons oscillate, performing SHM about their lattice positions. With ne ≈ 0.5 m-3 the electrons in the IGM satisfy the energy criteria for crystallisation to occur when interacting with other electrons within a sphere far less in radius than the corresponding Debye sphere. Thus, the conditions are met for the electrons to form an “electron glass.” Since the electrons in their BCC formation are spatially coherent, light will travel through the crystals in a straight line and thus objections to “Tired Light” theories are now removed since images will neither be destroyed nor “blurred.” Charges are not created but separated, if the electrons are removed from the galaxy and sent to fill the IGM; the remaining protons are left behind. These are “thermal” and will not have sufficient energy to escape but will be held gravitationally to that galaxy. Could these too form a spherical Wigner-Seitz sphere around that galaxy? Since the structure would be transparent, light would pass through in straight lines and thus we would not see it. They would however, interact gravitationally with the galaxy and have an effect on the rotation curves of single galaxies and on the motion of galactic clusters. Just as we cannot see the clear water in a fish tank when we look at the fish, the transparent, crystalline sphere of protons around galaxies would be “dark”.

Grain-Dependent Passivation of Iron in Sulfuric Acid Solution

Passive films formed on single grains of a polycrystalline pure iron substrate were investigated in 0.05 mol dm−3 sulfuric acid with a micro-capillary cell (MCC). Passivation behavior under the condition of potentiostatic polarization was strongly dependent on the crystallographic orientation of the substrate surface. Electrochemical impedance spectroscopy revealed that the charge transfer resistance of the passivated surface was determined by the substrate orientation. Galvanostatic reduction and XPS analysis of the surface passivated using the MCC showed that the substrate orientation affected the chemical state of iron in the oxide. The results suggested that the aging of the passive film formed on the iron substrate depended on its crystallographic orientation due to the differences in surface energy of the substrate surface that has a bcc lattice structure. It was concluded that the grain dependency on the electric property of the passive film arose from the compositional differences of the oxide film.

Mechanical properties of non-accreting neutron star crusts

The mechanical properties of a neutron star crust, such as breaking strain and shear modulus, have implications for the detection of gravitational waves from a neutron star as well as bursts from Soft Gamma-ray Repeaters (SGRs). These properties are calculated here for three different crustal compositions for a non-accreting neutron star that results from three different cooling histories, as well as for a pure iron crust. A simple shear is simulated using molecular dynamics to the crustal compositions by deforming the simulation box. The breaking strain and shear modulus are found to be similar in the four cases, with a breaking strain of ~0.1 and a shear modulus of ~10^{30} dyne cm^{-2} at a density of \rho = 10^{14} g cm^{-3} for simulations with an initially perfect BCC lattice. With these crustal properties and the observed properties of {PSR J2124-3358} the predicted strain amplitude of gravitational waves for a maximally deformed crust is found to be greater than the observational upper limits from LIGO. This suggests that the neutron star crust in this case may not be maximally deformed or it may not have a perfect BCC lattice structure. The implications of the calculated crustal properties of bursts from SGRs are also explored. The mechanical properties found for a perfect BCC lattice structure find that crustal events alone can not be ruled out for triggering the energy in SGR bursts.

Low temperature synthesis of iron containing carbon nanoparticles in critical carbon dioxide

We develop a low temperature, organic solvent-free method of producing iron containing carbon (Fe@C) nanoparticles. We show that Fe@C nanoparticles are self-assembled by mixing ferrocene with sub-critical (25.0 °C), near-critical (31.0 °C) and super-critical (41.0 °C) carbon dioxide and irradiating the solutions with UV laser of 266-nm wavelength. The diameter of the iron particles varies from 1 to 100 nm, whereas that of Fe@C particles ranges from 200 nm to 1 μm. Bamboo-shaped structures are also formed by iron particles and carbon layers. There is no appreciable effect of the temperature on the quantity and diameter distributions of the particles produced. The Fe@C nanoparticles show soft ferromagnetic characteristics. Iron particles are crystallised, composed of bcc and fcc lattice structures, and the carbon shells are graphitised after irradiation of electron beams.

Measurements of Diffusible Hydrogen Contents at Elevated Temperatures using Different Hot Extraction Techniques — An International Round Robin Test

This international round robin test served to scrutinize the procedures specified in ISO/DIS 3690:2009 for determining the diffusible hydrogen content in weld metals with bcc-lattice structure. It was specifically intended to check in what respect the specifications defined in the indicated standards for specimen preparation, storage and hydrogen analysis provide comparable measurement results. The round robin test is presented comprising comparative measurements at various degassing temperatures using hot extraction techniques and a thermal conductivity detector (TCD). A major focus of this investigation was the examination of the maximum degassing temperature for analysing the diffusible hydrogen in materials with bcc-lattice structure. The analyses were performed using two different stick electrodes and three different filler wires. As a significant result it was found that no deviations or increases, were detected in the measured contents of diffusible hydrogen for the investigated degassing temperatures ranging between 45 °C and 400 °C. Hydrogen analyses for contents below HD = 1.5 ml/100 g with the hot extraction techniques in conjunction with TCD applied in this study led to considerable relative standard deviations.

Comparative Study between Hot Extraction Methods and Mercury Method — A National Round Robin Test

A round robin test is presented comprising comparative measurements using hot extraction at different degassing temperatures as well as the mercury method. A major focus of the investigation was verification of the maximum degassing temperature for analysing the diffusible hydrogen in weld metals with bcc-lattice structure. The analyses were executed using a basic stick electrode with high weld metal cracking, a high-alloyed supermartensitic filler wire with different hydrogen contents in the shielding gas and a high-strength solid wire. The results show that degassing temperatures of 150 °C and 400 °C do not lead to an increase in the measured contents of diffusible hydrogen as compared to measurements at room temperature. The measuring techniques and procedures specified in ISO/DIS 3690:2009 for determining the diffusible hydrogen content in weld metals with bcc-lattice structure yield approximately the same results. This is to say that the mercury method and the hot extraction methods with thermal conductivity detector (TCD) can be regarded as equivalent reference methods.

Influence of low temperatures on the fracture micromechanism of materials with bcc and fcc lattice structures under single loading conditions

General regularities of the influence of the local stress state of a material on the plastic zone formation at the crack tip and the fracture micromechanism of materials with bcc and fcc lattice structures under single loading (static, impact, high-speed pulsed) conditions have been established. Schemes of plastic zone formation under plane strain, plane stress, and in the transient region from plane strain to plane stress are proposed.

A Study of Texture Evolution during Deformation and Annealing in Fe 3 wt.-% Si by Orientation Contrast Microscopy

Electrical steels, in particular Fe-Si alloys, are used as magnetic flux carrier in transformers and motors because of their excellent magnetic properties. They owe these magnetic properties in part to the presence of specific texture components such as the Goss ({110} <001>) or the cube components ({001} <010>), but also to the chemical composition which is optimum with 6.5 wt. % Si. This high silicon content provides a stable BCC lattice structure to the alloy over the entire solid state domain, but also renders the material more brittle. This embrittlement, which is induced by ordering phenomena, makes it impossible to produce the alloy in a conventional rolling process unless a specific thermomechanical route at high temperature is applied. In order to examine the working behaviour of high Si electrical steels, a series of room temperature plane strain compression tests was carried out on a Fe-3%Si alloy in hot band condition. The samples were compressed with a constant strain rate of 20 s-1 to a reduction of 10, 35 and 70% and subsequently annealed for different times at 800 and 900°C in an electrical furnace without protecting atmosphere. The hot rolled microstructure displayed an average grain size of 195 7m and the texture showed on the cube component ({001} <010>) of maximum 5x random levels. After plane strain compression the samples developed the conventional α (<110> // RD) / γ (<111> // ND) fibre texture by plastic shear which was also accommodated, in part, by mechanical twinning. With regard to the annealed material, it was observed that the recrystallisation started in grains with the higher stored energy and within the shear bands. After a reduction of 70% the samples that were annealed at 800°C for 4 hours displayed an average grain size of 27 7m and a relative maximum of 4x random on the cube component. Also other less intense components such as the rotated cube ({001} <110>) and the Goss ({110} <001>) were present in the annealing texture. The samples that were annealed at 900°C, after a reduction of 70%, were characterized by an average grain size of 36 7m and by the appearance of the {111} <121> γ fibre component with an intensity of 4.7.

Structures and magnetic properties in nano-crystalline Fe-rich Fe-Ni and Fe-Co alloys

Nano-crystalline magnetic alloys of Fe-Ni and Fe-Co are fabricated by high-energy milling. The coexistence of bcc and fcc lattice structures is observed in some of Fe-Ni alloys, as opposed to Fe-Co ones which exhibit the bcc phase only. The grain sizes increase linearly with the lattice strains for Fe-Co, and exponentially so for Fe-Ni. The cut-off frequency decreases with increasing nickel content in Fe-Ni alloys, but increases with increasing cobalt content in Fe-Co alloys. The larger the cut-off frequency is, the smaller the initial permeability. Resonant behaviour is observed in the pure Fe and Fe-Ni samples, which is replaced by relaxant behaviour in Fe-Co, implying that the Co plays an important role in hindering the resonance. The initial permeability at 10 kHz varies inverse proportionally with the coercivity H c . It reaches a maximum while H c goes to a minimum at 7.69 at.% Ni or Co. It is interesting that average atomic moments of nanocrystalline alloys are inconsistent with the Slater-Pauling relation.

SANS study of hydrophobic effects on pressure-induced micro- and macrophase separations of block copolymers

Hydrophobic effects on pressure-induced microphase separation of block copolymers were investigated by using small-angle neutron scattering (SANS). A block copolymer, pEOEOVE- b-pMOVE aqueous solution, which shows LCSTs (at 40 and 60 ∘ C , for pEOEOVE and pMOVE homopolymers, respectively) was used. A phase diagram was obtained by tracing light-transmittance at 632.8 nm by increasing temperature ( T) at various pressures ( P), which was a convex-upward function. The change in the slope of the phase boundary curve could be explained by volume change associated with mixing as well as “iceberg” formation. SANS revealed that a microphase separation took place by pressurizing or increasing temperature. At 28 ∘ C , the correlation length was observed to show continuous increase with divergence at 350 MPa. This result showed that the block copolymers at 28 ∘ C underwent macrophase separation and the transition was a second-order transition. At 45 ∘ C , under atmospheric pressure, the SANS curve suggested formation of a BCC lattice structure with micelles composed of a central core of pEOEOVE. By pressurizing, the SANS peak related to the microphase separation disappeared, meaning dissolution of block copolymers. However, by further pressurizing, another peak re-appeared at 250 MPa. This peak indicates the microphase separation of block copolymers is different from those observed under low pressures.

Long time stress relaxation of a triblock copolymer with asymmetric composition

The long-time stress relaxation was examined for poly(styrene)-poly(ethylene- co-butylene)-polystyrene triblock copolymer with asymmetric composition in the microphase separated state. Stress relaxation data from a parallel plate rheometer were extended to very long times by using a newly built compression instrument. Three properties were measured, the relaxation time spectrum, the equilibrium modulus, and the instantaneous modulus. Relaxation experiments over several months (without zero drift) allowed determination of extremely long relaxation times as found in soft solids and in liquids near the gel point. In this way, we can distinguish solid from liquid behavior within the experimental time frame. The BCC lattice structure of the test polymer behaves as liquid except at low temperature where an equilibrium modulus was observed in an experiment that lasted over a period of 4 months. The corresponding instantaneous modulus was observed to be constant for the same material and for the same time period.