3D Bcc Research Articles

Unit cell volumes of the silicon- and germanium-containing solid solutions based on the 3d bcc transition metals

Abstract The unit cell parameters and the unit cell volumes were investigated for Si- and Ge-containing solid solutions based on the 3d body-centred cubic transition metals. Excepting the high-temperature solid solution δ-Mn(Si), the solubility of Si increases with increasing number of 3d electrons. In contradiction to the large atomic volume of Si, which is substantially larger than that of the 3d transition metals, the unit cell volume of the terminal solid solutions decreases with increasing Si content. For solid solutions showing a large homogeneity range – α-Fe(Si) and α-Fe(Ge) –, the partial atomic volumes of Si and Ge were evaluated. Comparing the quasihomological Al- and Si-containing solid solutions α-Fe(Al) and α-Fe(Si), the higher bond energy occurs between atoms of Si and Fe than between Al and Fe atoms. Taking into consideration the homology of metalloids in the solid solutions α-Fe(Si) and α-Fe(Ge), the higher bond energy can also be expected between Si and Fe than between Ge and Fe atoms.

Bayesian force fields from active learning for simulation of inter-dimensional transformation of stanene

We present a way to dramatically accelerate Gaussian process models for interatomic force fields based on many-body kernels by mapping both forces and uncertainties onto functions of low-dimensional features. This allows for automated active learning of models combining near-quantum accuracy, built-in uncertainty, and constant cost of evaluation that is comparable to classical analytical models, capable of simulating millions of atoms. Using this approach, we perform large-scale molecular dynamics simulations of the stability of the stanene monolayer. We discover an unusual phase transformation mechanism of 2D stanene, where ripples lead to nucleation of bilayer defects, densification into a disordered multilayer structure, followed by formation of bulk liquid at high temperature or nucleation and growth of the 3D bcc crystal at low temperature. The presented method opens possibilities for rapid development of fast accurate uncertainty-aware models for simulating long-time large-scale dynamics of complex materials.

Thermal Activation and Ductile vs. Brittle Behavior of Microcracks in 3D BCC Iron Crystals under Biaxial Loading by Atomistic Simulations

We present the results of free 3D molecular dynamics (MD) simulations, focused on the influence of temperature on the ductile-brittle behavior of a pre-existing central Griffith through microcrack (1¯10)[110] (crack plane/crack front) under biaxial loading σA and σB in tension mode I. At temperatures of 300 K and 600 K, the MD results provide new information on the threshold values of the stress intensity factor K and the energy release rate G, needed for the emission of <111>{112} blunting dislocations that support crack stability. A simple procedure for the evaluation of thermal activation from MD results is proposed in the paper. 3D atomistic results are compared with continuum predictions on thermal activation of the crack induced dislocation generation. At elevated temperature T and biaxiality ratios σB/σA ≤ 0.8 dislocation emission in MD is observed, supported by thermal activation energy of about ~30 kBT. With increasing temperature, the ductile-brittle transition moves to a higher biaxiality ratios in comparison with the situation at temperature of ~0 K. Near the transition, dislocation emission occurs at lower loadings than expected by continuum predictions. For the ratios σB/σA ≥ 1, the elevated temperature facilitates (surprisingly) the microcrack growth below Griffith level.

Dislocation emission and crack growth in 3D bcc iron crystals under biaxial loading by atomistic simulations

This paper is devoted to the study of the ductile-brittle behavior of a central nanocrack (1¯10)[110] (crack plane/crack front) under biaxial loading via free 3D molecular dynamics (MD) simulations, as well as the comparison of MD results with continuum predictions concerning T-stress. The so called T-stress is a constant stress component acting along the crack plane, which should be considered (together with the stress intensity factor K) in the assessment of brittle-ductile behavior, namely, in the case of the short cracks. Previous 2D atomistic simulations under plane strain conditions indicated that the level of T-stress (controlled by the biaxiality ratio σB/σA from the external loading) affects dislocation emission from the crack and can cause the ductile-brittle transition. The plane strain simulations using the periodic or translational boundary conditions in the bcc lattice have certain limitations: they enable the in-plane dislocation emission (Burgers vector lies in the observation plane), but they do not allow the complete dislocation emission on the all slip systems favored by the shear stress. As presented, our new free 3D atomistic simulations (without periodic or symmetry conditions) enable the activity of the all favored slip systems. Thus, they offer a more realistic insight into the microscopic processes generated by the crack itself in dependence on the T-stress level.

Enhancing the Entrepreneurial and Intrapreneurial Attributes of Engineering Graduates: A Review Proposal for Metallurgy and Materials Engineering Undergraduate Curricula at Two African Universities

This paper explores the potential opportunities to enhance the entrepreneurial and intrapreneurial attributes of graduates in the Metallurgy and Materials Engineering curricula at two universities in Zimbabwe and South Africa. Due to the diminishing geographical constraints between Zimbabwe and South Africa, and the strong juxtaposition between the two economies, this paper adopts a simplified comparative education methodology to benchmark education best practices between these two countries. While the reviewed curricula in their present form may be providing learners with opportunities for disciplinary problem solving and inquiry-based learning, this paper proposes a body-centred cubic (bcc) model to integrate a new dimension of entrepreneurial and intrapreneurial education into the teaching and learning space. Based on the 3D bcc lattice with six planes, where the first five planes represent the current curricula, pedagogy practices and desired attributes, the sixth plane is taken to represent the additional dimensions of the desired entrepreneurial and intrapreneurial attributes.

Stability and Free Energy of Nanocrystal Chains and Superlattices

We discuss the stability and free energy of 1D (chains), 2D (planar superlattices), and 3D (bcc or fcc superlattices) nanocrystals (having hydrocarbons as capping ligands) structures. We start by introducing the method to compute the pressure and free energy. We then analyze the magnitude of many body (or nonadditive) effects, those not described by two body interactions. For 3D superlattices, we examine the relative stability of fcc vs bcc as well as the prevalence of rotator vs crystal phases. We identify a bundling phenomena that occurs during bcc assembly, when next to nearest neighbors begin to make contact. We precisely calculate the density and lattice constant as well as the presence of ligand vortices and find that overall, the simulations fully support the recently introduced Orbifold Topological Model (OTM). By comparing our results with the considerable experimental data available in the literature, we identify a number of subtle effects.

Growth of 3D edge cracks in mode I and T-stress on the atomistic level

We present results of 3D molecular dynamic (MD) simulations accompanied by stress calculations on the atomistic level in 3D bcc iron crystals with edge cracks (1¯10)[110]. Two different crack lengths in samples of SEN type loaded uniaxially in mode I were treated with negative and positive values of T-stress according to the continuum prediction by Fett for constant stress boundary condition. Atomistic results are compared with continuum predictions, including influence of T-stress on the ductile-brittle behavior of cracks.

Sample Geometry and the Brittle-Ductile Behavior of Edge Cracks in 3D Atomistic Simulations by Molecular Dynamics

We present new results of molecular dynamic (MD) simulations in 3D bcc iron crystals with edge cracks (001)[010] and (-110)[110] loaded in mode I. Different sample geometries of SEN type were tested with negative and positive values of T-stress according to continuum prediction by Fett.

Growth of a brittle crack (0 0 1) in 3D bcc iron crystal with a Cu nano-particle

We present new results of molecular dynamics (MD) in 3D bcc Fe–Cu crystal with embedded central through crack (001)[110] of Griffith type loaded in mode I. Such sample geometry and border conditions in MD were chosen to invoke a cleavage crack extension through a bcc Cu nano-particle placed in front of the crack. The stress field and bond breakage caused by the crack and Cu inhomogeneity are analysed on the atomistic level. The character of crack extension and corresponding wave patterns are studied in the Fe–Cu system. The study is motivated by a question how a small Cu bcc precipitate changes the brittle behavior of the crack in comparison with pure bcc iron loaded in mode I.

MECHANICAL PROPERTIES AND TOPOLOGICAL CHANGES IN A Fe-CRYSTAL WITH FIXED AND MIGRATING H-ATOM: A NUMERICAL STUDY

A numerical study, within the framework of molecular statics, is conducted to assess the effect of a fixed and migrating hydrogen atom on the stress–strain data and the topological changes taking place in a 3D BCC α-iron crystal subjected to a tensile elongation. A pair-wise Morse potential is used to describe the interatomic forces. The results for a crystal with 2324 iron atoms show that the presence of a hydrogen atom, either migrating or fixed, produces relatively small effect on the stress–strain data within the elastic and some plastic range of loading. However, the topological changes, represented by the changes in the nearest neighbors for each atom within the cut-off distance after each displacement increment, are substantially different. Similarly, a comparison of the changes in the atomic potential energies when the sudden drop in stresses takes place shows differences between the two cases.

Searching for Next Single-Phase High-Entropy Alloy Compositions

There has been considerable technological interest in high-entropy alloys (HEAs) since the initial publications on the topic appeared in 2004. However, only several of the alloys investigated are truly single-phase solid solution compositions. These include the FCC alloys CoCrFeNi and CoCrFeMnNi based on 3d transition metals elements and BCC alloys NbMoTaW, NbMoTaVW, and HfNbTaTiZr based on refractory metals. The search for new single-phase HEAs compositions has been hindered by a lack of an effective scientific strategy for alloy design. This report shows that the chemical interactions and atomic diffusivities predicted from ab initio molecular dynamics simulations which are closely related to primary crystallization during solidification can be used to assist in identifying single phase high-entropy solid solution compositions. Further, combining these simulations with phase diagram calculations via the CALPHAD method and inspection of existing phase diagrams is an effective strategy to accelerate the discovery of new single-phase HEAs. This methodology was used to predict new single-phase HEA compositions. These are FCC alloys comprised of CoFeMnNi, CuNiPdPt and CuNiPdPtRh, and HCP alloys of CoOsReRu.

A Line Generation Algorithm over 3D Body-centered Cubic Lattice

New line generation algorithm is proposed for generating lines over 3D body-centered cubic lattice, a kind of optimal lattice in 3D space. The main contribution in this paper is employing the 3D Bresenham algorithm, a popular algorithm for generating 3D lines on a cubic lattice, to produce the BCC lattice occupied by 3D lines, with the help of the adjunct parallelepiped space, having the same center and basis vectors with the BCC lattice. The adjunct parallelepiped line is easy to generate by employing the existed 3D cubic Bresenhan algorithm. Due to the one-to-one correspondence between the parallelogram cells of parallelepiped space and the voxels of the BCC space, the 3D BCC line generation algorithm is gained. The whole procedure is characterized by a simple discriminator and a derivation for this discriminator given in the paper confirms that all calculations can be realized using only integer arithmetic which is to implement on computer.

3D atomistic simulation of fatigue behavior of a ductile crack in bcc iron

We present results of 3D molecular dynamic (MD) simulations of the ductile–brittle behavior at an edge ( 1 ¯ 1 0 ) [1 1 0] crack in bcc iron loaded cyclically in mode I at temperature of 300 K. This crack in 3D bcc iron crystal under monotonic uniaxial tension loading in mode I emits dislocations in the inclined 〈1 1 1〉{1 1 2} slip systems and it is stable up to very high loads, in qualitative agreement with experiments and continuum predictions. Our question is how the cyclic loading changes the crack behavior and its stability.

Ductile-Brittle Behavior along Crack Front and T-Stress

We present new results of molecular dynamic (MD) simulations in 3D bcc iron crystals with embedded central through crack (001)[110] of Griffith type loaded in mode I. Two different sample geometries of the same crystallographic orientation were tested with negative and positive values of the T-stress, which change the ductile-brittle behavior along the crack front in 3D. This phenomenon is explained in the framework of stress analysis, both on the continuum and atomistic level.

On reliability of molecular statics simulations of plasticity in crystals

A perfect 3D BCC crystal is subjected to tensile deformation, using a molecular statics approach, in order to investigate the reliability of the plastic part of the stress–strain data. The uniqueness of the stress–strain data serves as a criterion for the assessment of simulation reliability. Three magnitudes of displacement increments are considered for this purpose. For each magnitude the convergence criterion of relaxation to a minimum energy state is set the same. It is shown that the magnitude of the displacement increment does affect the stress–strain data and, for a given convergence criterion, there is a minimum magnitude below which the plastic part of the stress–strain data does not change. The related issue of dislocation formation at different displacement increments is also addressed.

Stress wave radiation from the cleavage crack extension in 3D bcc iron crystals

We hereby present new results for molecular dynamic (MD) and finite element (FEM) simulations in 3D bcc iron crystals, with embedded central through crack (0 0 1)[1 1 0] of Griffith type, loaded in mode I. The sample geometry and border conditions in MD were chosen in such a way as to invoke a cleavage crack extension. The stress field and acoustic emission sources caused by the crack were analysed on both the atomistic and continuum level.

Transonic twins in 3D bcc iron crystal

In this paper we verify previous 2D (plane strain) predictions on transonic twinning by means of new free 3D atomistic simulations by molecular dynamic (MD) technique and via analyses of acoustic emission sources in bcc iron crystal with an embedded central through crack (0 0 1)[1 1 0] loaded in mode I. MD simulations in 3D are completed by stress calculations on the atomistic and continuum level to analyze shielding or anti-shielding effect caused by the twins.

Modeling of hydrogen-assisted cracking in iron crystal using a quasi-Newton method

A Quasi-Newton method was applied in the context of a molecular statics approach to simulate the phenomenon of hydrogen embrittlement of an iron lattice. The atomic system is treated as a truss-type structure. The interatomic forces between the hydrogen-iron and the iron-iron atoms are defined by Morse and modified Morse potential functions, respectively. Two-dimensional hexagonal and 3D bcc crystal structures were subjected to tensile numerical tests. It was shown that the Inverse Broyden's Algorithm-a quasi-Newton method-provides a computationally efficient technique for modeling of the hydrogen-assisted cracking in iron crystal. Simulation results demonstrate that atoms of hydrogen placed near the crack tip produce a strong deformation and crack propagation effect in iron lattice, leading to a decrease in the residual strength of numerically tested samples.

Crack Orientation versus Ductile-Brittle Behavior in 3D Atomistic Simulations

The paper presents results of molecular dynamic (MD) simulations in 3D bcc iron crystals with edge pre-existing cracks (001)[110] and (110) [110] (crack plane/crack front) loaded uni-axially in tension mode I at temperature of 300 K. The iron crystals in MD have the same orientation and similar geometry as in our recent fracture tests performed at room temperature on iron (3wt.%Si) single crystals [1].

A model for calculating the errors of 2D bulk analysis relative to the true 3D bulk composition of an object, with application to chondrules

Certain problems in Geosciences require knowledge of the chemical bulk composition of objects, such as, for example, minerals or lithic clasts. This 3D bulk chemical composition (bcc) is often difficult to obtain, but if the object is prepared as a thin or thick polished section a 2D bcc can be easily determined using, for example, an electron microprobe. The 2D bcc contains an error relative to the true 3D bcc that is unknown. Here I present a computer program that calculates this error, which is represented as the standard deviation of the 2D bcc relative to the real 3D bcc. A requirement for such calculations is an approximate structure of the 3D object. In petrological applications, the known fabrics of rocks facilitate modeling. The size of the standard deviation depends on (1) the modal abundance of the phases, (2) the element concentration differences between phases and (3) the distribution of the phases, i.e. the homogeneity/heterogeneity of the object considered. A newly introduced parameter “ τ” is used as a measure of this homogeneity/heterogeneity. Accessory phases, which do not necessarily appear in 2D thin sections, are a second source of error, in particular if they contain high concentrations of specific elements. An abundance of only 1 vol% of an accessory phase may raise the 3D bcc of an element by up to a factor of ∼8. The code can be queried as to whether broad beam, point, line or area analysis technique is best for obtaining 2D bcc. No general conclusion can be deduced, as the error rates of these techniques depend on the specific structure of the object considered. As an example chondrules—rapidly solidified melt droplets of chondritic meteorites—are used. It is demonstrated that 2D bcc may be used to reveal trends in the chemistry of 3D objects.