Effects of crystallographic structure and Cr on the rate of void nucleation in BCC Fe: An atomistic simulation study

Atomistic Monte Carlo simulations based on modified embedded-atom method (MEAM) interatomic potentials have been carried out to clarify the differences in swelling rates between bcc and fcc Fe and between pure bcc Fe and bcc Fe−Cr alloys. Assuming that the transient regimes prior to the onset of steady-state swelling correspond to the void nucleation stage, the effect of crystallographic structure (bcc vs. fcc) or Cr alloying on the void nucleation rate under a given amount of supersaturated vacancies was examined. It was found that the void nucleation rate is much higher in fcc Fe than in bcc Fe. Randomly distributed Cr atoms slightly increase the void nucleation rate in bcc Fe, but microstructural evolutions such as the precipitation of Cr-rich phase have more decisive effects, serving as a vacancy sink. The reasons for the individual results are rationalized in terms of the binding energy of vacancy clusters and the size difference between Fe and Cr atoms.     

Lattice Instabilities and Phase Transformations in Fe from Atomistic Simulations

The stability of the body- and face-centered cubic lattices corresponding to the α and γ phases of Fe, respectively, as well as the transformation of one phase to the other were investigated by atomistic simulations. Two interatomic potentials were used: the embedded atom method (EAM) potential of Meyer and Entel and the bond order potential (BOP) developed by Müller et al. The suitability of the potentials for investigating structural transformations in Fe was verified using nonequilibrium free energy calculations and molecular dynamics simulations. The results showed that the EAM potential is capable of describing the bcc → fcc and fcc → bcc transformations whereas no transformation was observed for the computationally more expensive BOP potential with the simulation set up used.     

Composition and non-equilibrium crystallization in partially devitrified co-rich soft magnetic nanocomposite alloys

The body-centered cubic (bcc) phase tends to preferentially nucleate during solidification of highly undercooled liquid droplets of binary alloy systems, including Fe–Co, Fe–Ni and Fe–Cr–Ni. We investigate a similar tendency during the partial devitrification of Co-rich amorphous precursors of composition (Co_1?xFe_x)₈₈Zr₇B₄Cu₁ by identifying the structure and composition of the nanocrystalline grains. The Co:Fe ratio of the bcc nanocrystals varies linearly with the Co:Fe ratio of the amorphous precursor, and can lie well within the single-phase face-centered cubic (fcc) region of the Fe–Co phase diagram at the crystallization temperature. Classical nucleation theory therefore suggests several potential explanations for the preferential nucleation of bcc phase from an amorphous precursor, including: (i) a reduced amorphous/bcc interface energy as compared to the close-packed phases; (ii) a lower strain of precipitation for bcc nuclei as compared to close-packed fcc and hexagonal close-packed nuclei; and (iii) stabilization of the bcc phase by dissolved glass-formers such as Zr and B.     

Nucleation of Ni–Fe alloy near the spinodal

In molecular dynamics simulations, “non-classical” nucleation around the spinodal in Fe–Ni alloys is observed by controlling the composition. With increasing Fe concentration, metastable body-centered cubic (bcc) clusters are formed during pre-crystallization under the influence of the spinodal, and then grow into face-centered cubic (fcc)-ordered critical nuclei. When the composition reaches 75 at.% Fe, this transformation is suppressed and the bcc, rather than fcc, symmetry dominates the structure of critical nuclei, a typical nucleation behavior near the spinodal. Further increase in the Fe concentration depresses nucleation below the spinodal temperature. As a consequence, two transient bcc phases characterized by high and low densities appear upon reaching the critical size.     

The effect of melt-spinning processing parameters on crystal structure and magnetic properties in Fe–Mn–Ga alloys

We have succeeded to fabricate body-centered cubic (bcc) single phase of Fe–Mn–Ga alloys using melt-spinning technique. Heusler type L2₁ structure of Fe₂MnGa alloy are predicted to have half-metallic properties, however bulk Fe₂MnGa alloys crystallize into face-centered cubic (fcc) lattice with small admixture of bcc phase. By changing either ejection temperature or rotation speed of melt-spinning processing parameters, fcc or bcc lattice can be obtained from same precursor ingot. For stoichiometric Fe₂MnGa as-spun alloy, super-lattice diffraction peaks indicative of L2₁ structure are observed from XRD measurements. The as-spun bcc alloys transform into ferromagnetic hexagonal lattice by thermal annealing.     

Modified embedded-atom method interatomic potentials for pure Mn and the Fe–Mn system

Modified embedded-atom method (MEAM) interatomic potentials for pure Mn and the Fe–Mn binary system have been developed using a previously developed MEAM potential for Fe. The potentials can describe various fundamental physical properties of pure Mn (cohesive energy, structural energy differences, lattice parameters, elastic constants, vacancy formation energy, surface energy, etc.) and alloy behaviors (enthalpy of mixing in face-centered cubic and liquid phases, composition dependency of lattice parameters in various solid solutions) in reasonable agreement with experimental information or other empirical approaches. The applicability of the potential to atomistic investigations on a wide range of mechanical or deformation properties of the Fe–Mn alloys is demonstrated.     

An atomistic analysis of the interface mobility in a massive transformation

A new multi-lattice kinetic Monte Carlo method has been used for an atomistic study on the interpretation of the interface mobility parameter for a massive face-centred cubic (fcc) to body-centred cubic (bcc) transformation in a single element system. For lateral growth of bcc in a system with an fcc(1 1 1)//bcc(1 1 0) and fcc[1 1 ]//bcc[0 0 ] interface orientation the overall activation energy for the interface mobility parameter is governed by energetically unfavourable atomic jumps. The atoms on the fcc lattice often cannot jump directly to bcc lattice sites because neighbouring atoms block the empty bcc sites. By single unfavourable jumps and by groups of unfavourable jumps a path from fcc to bcc is created. The necessity of these unfavourable jumps leads to an overall activation energy considerably larger than the activation energy barrier for a single atomic jump.     

Application of classical nucleation theory to phase selection and composition of nucleated nanocrystals during crystallization of Co-rich (Co,Fe)-based amorphous precursors

Classical steady-state nucleation theory is applied to Co-rich Fe,Co-based alloys to provide a rationale for experimental observations during the nanocrystallization of Co-rich (Co,Fe)₈₉Zr₇B₄ and (Co,Fe)₈₈Zr₇B₄Cu₁ amorphous precursors. The amorphous precursor free energy is estimated using density functional theory. This simple theory suggests: (i) strain or interface energy effects could explain a tendency for a body-centered cubic (bcc) phase to form during crystallization. Dissolved glass formers (Zr,B) in crystalline phases may also contribute; (ii) similar face-centered cubic (fcc) and hexagonal close-packed (hcp) free energies could explain the presence of some hcp phase after crystallization even though fcc is stable at the crystallization temperature; (iii) nanocrystal compositions vary monotonically with the Co:Fe ratio of the amorphous precursor even when multiple phases are nucleating because nucleation is not dictated by the common tangency condition governing bulk phase equilibria; and (iv) Fe-enrichment of the bcc phase can be attributed to a relatively small free energy difference between the amorphous and bcc phases for high Co-containing alloys.     

Modified embedded-atom method interatomic potentials for the Fe–Ti–C and Fe–Ti–N ternary systems

Modified embedded-atom method (MEAM) interatomic potentials for the Fe–Ti–C and Fe–Ti–N ternary systems have been developed based on the previously developed MEAM potentials for sub-unary and binary systems. An attempt was made to find a way to determine ternary potential parameters using the corresponding binary parameters. The calculated coherent interface properties, interfacial energy, work of separation and misfit strain energy between body-centered cubic Fe and NaCl-type TiC or TiN were reasonable when compared with relevant first-principles calculations under the same condition. The applicability of the present potentials for atomistic simulations to investigate nucleation kinetics of TiC or TiN precipitates and their effects on mechanical properties in steels is also demonstrated.     

Understanding Solid-Solid (fcc→ω+bcc) Transition at Atomic Scale

An atomic transition model of a face-centered cubic (fcc) crystal to a primitive hexagonal ω and body-centered cubic (bcc) structures has been crystallographically built. The fcc structure can transform into the ω structure through a local shuffling or displacement of atoms about 0.4014 Å in iron for a _{fcc iron} = 3.59 Å. The bcc structure can form either after the ω formation or concurrently by the similar mechanism, or the ω structure can be treated as an intermediate stage during the transition of fcc → bcc. Such a transition (fcc → ω + bcc transition) can be confirmed by Widmanstätten pattern formed in an iron meteorite, pearlitic structure and martensite composed of bcc-ferrite and ultra-fine ω particles in iron-carbon steels. The present fcc-bcc orientation relationship matches with Pitsch’s one.     

Phase transformation of Cu precipitates from bcc to fcc in Fe–3Si–2Cu alloy

Phase transition of Cu precipitates during aging of an Fe–3Si–2Cu alloy was studied by transmission electron microscopy. The precipitation of 3–5-nm-sized body-centered cubic (bcc) Cu in ferrite matrix was confirmed by high-angle annular dark-field scanning transmission electron microscopy imaging. The bcc Cu precipitates transformed to 9R Cu as they grew. Many 9R Cu precipitates were twinned, but untwinned 9R Cu particles were also observed. The 9R Cu transformed to twinned face-centered cubic (fcc) Cu by the glide of ±a/3 [1 0 0]_9R Shockley-type partial dislocations. Formation of the 3R structure previously reported could not be confirmed in this study. Finally, twins in fcc Cu precipitates disappeared to form stable fcc Cu particles. The importance of electron beam-orientation-dependent moiré fringes in the correct identification of Cu structure is discussed in detail.     

Changes in vibrational entropy during the early stages of chemical unmixing in fcc Cu–6% Fe

A nanocrystalline face-centered cubic (fcc) solid solution of 6% Fe in Cu was prepared by high-energy ball milling, and annealed at temperatures from 200 to 360 °C to induce chemical unmixing. The chemical state of the material was characterized by three-dimensional atom probe microscopy, Mössbauer spectrometry and X-ray powder diffractometry. The unmixing was heterogeneous, with iron atoms forming iron-rich zones that thicken with further annealing. The phonon partial density of states (pDOS) of ⁵⁷Fe was measured by nuclear resonant inelastic X-ray scattering, showing the pDOS of the as-prepared material to be that of an fcc crystal. The features of this pDOS became broader in the early stages of unmixing, but only small changes in average phonon frequencies occurred until the body-centered cubic (bcc) phase began to form. The vibrational entropy calculated from the pDOS underwent little change during the early stage of annealing, but decreased rapidly when the bcc phase formed in the material.     

Empirical design of single phase high-entropy alloys with high hardness

We collect the available basic properties of nearly 100 high-entropy alloys (HEAs) with a single face centered cubic (fcc) or body centered cubic (bcc) phase. HEAs crystallizing in the fcc structure are mainly composed of the late 3d elements (LTM-HEAs), whereas HEAs consisting of the early (refractory) transition elements and the LTM-HEAs containing an increased level of bcc stabilizer form the bcc structure. Guided by the solid solution theory, we investigate the structure and hardness of HEAs as a function of the valence electron concentration (VEC) and the atomic size difference (δ). The fcc structure is found for VEC between 7.80 and 9.50, whereas the structure is bcc for VEC between 4.33 and 7.55. High strength is obtained for an average valence electron number VEC ∼ 6.80 and for an average atomic size difference δ ≈ 6%. Based on these empirical correlations, one can design the high-entropy alloys with desired hardness.     

Atomic-scale compositional characterization of a nanocrystalline AlCrCuFeNiZn high-entropy alloy using atom probe tomography

We have studied a nanocrystalline AlCrCuFeNiZn high-entropy alloy synthesized by ball milling followed by hot compaction at 600 °C for 15 min at 650 MPa. X-ray diffraction reveals that the mechanically alloyed powder consists of a solid-solution body-centered cubic (bcc) matrix containing 12 vol.% face-centered cubic (fcc) phase. After hot compaction, it consists of 60 vol.% bcc and 40 vol.% fcc. Composition analysis by atom probe tomography shows that the material is not a homogeneous fcc–bcc solid solution but instead a composite of bcc structured Ni–Al-, Cr–Fe- and Fe–Cr-based regions and of fcc Cu–Zn-based regions. The Cu–Zn-rich phase has 30 at.% Zn α-brass composition. It segregates predominantly along grain boundaries thereby stabilizing the nanocrystalline microstructure and preventing grain growth. The Cr- and Fe-rich bcc regions were presumably formed by spinodal decomposition of a Cr–Fe phase that was inherited from the hot compacted state. The Ni–Al phase remains stable even after hot compaction and forms the dominant bcc matrix phase. The crystallite sizes are in the range of 20–30 nm as determined by transmission electron microscopy. The hot compacted alloy exhibited very high hardness of 870 ± 10 HV. The results reveal that phase decomposition rather than homogeneous mixing is prevalent in this alloy. Hence, our current observations fail to justify the present high-entropy alloy design concept. Therefore, a strategy guided more by structure and thermodynamics for designing high-entropy alloys is encouraged as a pathway towards exploiting the solid-solution and stability idea inherent in this concept.     

Mechanisms of martensitic phase transformations in body-centered cubic structural metals and alloys: Molecular dynamics simulations

Two different mechanisms of the stress-induced martensitic phase transformation at the crack tip in body-centered cubic (bcc) structural metals and alloys have been studied by molecular dynamics simulations. For cracks with 〈1 0 0〉 crack fronts, the bcc (B2) to face-centered cubic (fcc) (L1₀) phase transformation along the Bain stretch occurs. Whereas for cracks with 〈1 1 0〉 crack fronts, either the bcc (B2) to fcc (L1₀) or the bcc (B2) to hexagonal close-packed (hcp) transformation is the candidate. We have found that the combination of local stress and crystal orientation plays an important role in the mechanism of the martensitic transformation. Thus a simple way to determine the mechanism of the martensitic transformation is developed. The complicated deformation behaviors at the crack tip in bcc iron and B2 NiAl are discussed in terms of this method.     

The mechanisms of the fcc–bcc martensitic transformation revealed by pole figures

Face-centered cubic (fcc) to body-centered cubic (bcc) martensitic transformations occur in many materials, such as steels, FeNi meteorites or brass. The phenomenological theory has been the accepted theory for these transformations for more than half a century. However, it cannot explain the continuous singular features in the experimental electron backscatter diffraction or X-ray diffraction pole figures. Here we show that such patterns can be simulated by one discrete orientation relationship and two continuous rotations that correspond to a trace of the transformation mechanisms. A new theory of martensite transformation that is in full agreement with the experimental pole figures is proposed. In this theory, the fcc–bcc transformation results from a fcc–hexagonal close-packed (hcp) step followed by an hcp–bcc step. The advantages of this two-step theory over the phenomenological theory are discussed.     

连续升温、降温过程中纯Fe的微观结构分析

通过分子动力学模拟,采用较先进的键型指数法HA及原子团类型指数法CTIM-2,对Fe连续升温、降温过程中微观结构进行模拟研究.结果表明:连续升温过程,Fe的微观结构变化是bcc→fcc\hcp→bcc→液体；连续降温过程,Fe的微观结构变化是液体→fcc\hcp.Fe凝固结束没有形成大量的高温bcc晶体,原因是在高温液态中bcc结构原子稳定性较差,fcc和hcp结构原子更易稳定存在.此外,温度变化速率过快,可诱导晶体生长过程中发生层错,促使Fe在升温、降温过程出现fcc和hcp晶体的交替分层分布,这与fcc和hcp晶体的原子能量相近、晶体的致密度相同、原子空间堆垛方式局部相同有关.     

放电等离子烧结双相AlCrCoFeNi2.1 高熵合金的微观组织、耐腐蚀性能和力学性能

采用放电等离子烧结法在不同温度下制备AlCrCoFeNi_2.1高熵合金（HEA）,并对其微观组织、耐腐蚀性能和力学性能进行了研究。结果表明,烧结后的AlCrCoFeNi_2.1 HEA最大相对密度可达99.18%;该HEA主要由体心立方（bcc）相和面心立方（fcc）相组成,其比例分别为20.6%和79.4%。与fcc相相比,AlCrCoFeNi_2.1 HEA中bcc相的再结晶组织和变形组织更多,且bcc相在3.5%（质量分数）NaCl溶液中更容易被腐蚀。随着应变速率的增加,bcc相和fcc相的压力恢复速率降低,硬化效果增强。在1050 ℃下烧结的AlCrCoFeNi_2.1 HEA具有较高的极限抗拉伸强度,这主要归因于晶界强化、固溶强化和合金粒子之间良好的界面结合。该HEA的断裂形式包括bcc相的脆性断裂和fcc相的韧性断裂。     

Computational thermodynamics and the kinetics of martensitic transformation

To assist the science-based design of alloys with martensitic microstructure, a multicomponent database kMART (kinetics of MARtensitic Transformation) encompassing the components Al, C, Co, Cr, Cu, Fe, Mn, Mo, N, Nb, Ni, Pd, Re, Si, Ti, V, and W has been developed to calculate the driving force for martensitic transformation. Built upon the SSOL database of the Thermo-Calc software system, a large number of interaction parameters of the SSOL database have been modified, and many new interaction parameters, both binary and ternary, have been introduced to account for the heat of transformation, T ₀ temperatures, and the composition dependence of magnetic properties. The critical driving force for face-centered cubic (fcc) → body-centered cubic (bcc) heterogeneous martensitic nucleation in multicomponent alloys is modeled as the sum of a strain energy term, a defect-size-dependent interfacial energy term, and a composition-dependent interfacial work term. Using our multicomponent thermodynamic database, a model for barrierless heterogeneous martensitic nucleation, a model for the composition and temperature dependence of the shear modulus, and a set of unique interfacial kinetic parameters, we have demonstrated the efficacy of predicting the fcc → bcc martensitic start temperature (M _s ) in multicomponent alloys with an accuracy of ± 40 K over a very wide composition range.     

Microstructures,tensile properties and serrated flow of AlxCrMnFeCoNi high entropy alloys

Microstructures and mechanical properties of dual-phase Al_xCrMnFeCoNi (x=0.4, 0.5, 0.6, at.%) alloys were investigated. Thermomechanical processing leads to a microstructural evolution from cast dendritic structures to equiaxed ones, consisting of face-centered cubic (fcc) and body-centered cubic (bcc) phases in the two states. The volume fraction of bcc phase increases and the size of fcc grain decreases with increasing Al content, resulting in remarkably improved tensile strength. Specifically, the serrated flow occurring at the medium temperatures varies from type A+B to B+C or C as the testing temperature increases. The average serration amplitude of these Al-containing alloys is larger than that of CoCrFeNiMn alloy due to the enhanced pinning effect. The early small strain produces low-density of dislocation arrays and bowed dislocations in fcc grains while the dislocation climb and shearing mechanism dominate inside bcc grains. The cross-slip and kinks of dislocations are frequently observed and high-density-tangled dislocations lead to dislocation cells after plastic deformation with a high strain.