Vacancy is one of the most frequent defects in metals. We study the impacts of magnetism on vacancy formation properties in fcc Ni, and in bcc and fcc Fe, via density functional theory (DFT) and effective interaction models combined with Monte Carlo simulations. Overall, the predicted vacancy formation energies and equilibrium vacancy concentrations are in good agreement with experimental data, available only at the high-temperature paramagnetic regime. Effects of magnetic transitions on vacancy formation energies are found to be more important in bcc Fe than in fcc Fe and Ni. The distinct behaviour is correlated to the relative roles of longitudinal and transversal spin excitations. At variance with the bcc-Fe case, we note a clear effect of longitudinal spin excitations on the magnetic free energy of vacancy formation in fcc Fe and Ni, leading to its steady variation above the respective magnetic transition temperature. Below the Néel point, such effect in fcc Fe is comparable but opposite to the one of the transversal excitations. Regarding fcc Ni, although neglecting the longitudinal spin excitations induces an overestimation of the Curie temperature by 220 K, no additional effect is visible below the Curie point. The distinct effects on the three systems are closely linked to DFT predictions of the dependence of vacancy formation energy on the variation of local magnetic-moment magnitudes and orientations.
Extensive atomistic simulations based on the quasiparticle (QA) approach are performed to determine the momentous aspects of the displacive fcc/bcc phase transformation in a binary system. We demonstrate that the QA is able to predict the major structural characteristics of fcc/bcc phase transformations, including the growth of a bcc nuclei in a fcc matrix, and eventually the formation of an internally twinned structure consisting in two variants with Kurdjumov-Sachs orientation relationship. At atomic level, we determine the defect structure of twinning boundaries and fcc/bcc interfaces, and …
Density functional calculations for metallic lithium along a cuboidal bcc-to-fcc transformation path demonstrate that the bcc phase is quasi-degenerate with the fcc phase with a very small activation barrier of 0.1~kJ/mol, but becomes the dominant phase at higher temperatures in accordance with Landau theory. This resolves the long-standing controversy about the two phases for lithium.
The possibility of solid solution formation in high entropy alloys (HEAs) has been calculated for alloys with four to seven elements, using a rule previously reported. Thirty elements were included: transition elements of the fourth, fifth and sixth periods of the periodic table, and aluminum. A total of 2,799,486 systems were analyzed. The percentage of solid solutions that would be formed in HEAs decreases from 35.9% to 26.4%, as the number of elements increases from four to seven. The structure of the solid solutions, fcc, bcc or a mixture of fcc and bcc, that would be formed, has been pred…
From our previous models of martensitic transformation, the continuous matrices of atomic displacements and lattice deformations from face-centred-cubic (fcc) to body centred-cubic (bcc) phases are calculated in agreement with different possible final orientation relationships, such as Bain, Pitsch and Kurdjumov-Sachs (KS). The angular distortion introduced in the calculations appears a natural order parameter of transition. The distortion corresponding to KS is the only one that respects the parallelism of a dense direction and of a dense plane of both the fcc and bcc phases. This paper gives…
The occurrence of bcc-fcc ($α$-$γ$) and fcc-bcc ($γ$-$δ$) phase transitions in magnetic iron stems from the interplay between magnetic excitations and lattice vibrations. However, this fact has never been proven by a direct dynamic simulation, treating non-collinear magnetic fluctuations and dynamics of atoms, and their coupling at a finite temperature. Starting from a large set of data generated by ab initio simulations, we derive non-collinear magnetic many-body potentials for bcc and fcc iron describing fluctuations in the vicinity of near perfect lattice positions. We then use spin-lattice…
This work generalizes our previous works on fcc-bcc martensitic transformations to the larger family of transformations in the fcc-bcc-hcp system and to fcc-fcc mechanical twinning. The analytical expressions of the atomic displacements and lattice distortions are calculated directly from the orientation relationships without any adjustment of free parameter; the unique assumption is that the atoms are hard-spheres that cannot interpenetrate themselves. The habit planes are predicted on the simple criterion that they are unrotated by the distortion, and the results are compared to experimental…
This book is the first monograph in the scientific literature, dedicated to the FCC-BCC transformation in iron-based alloys, in which the dynamical approach is used for the explanation of the martensite growth stage. The rapid growth of a cooling martensite crystal is considered as a self-organized process controlled by the quasi-longitudinal lattice displacement waves (DW). The regime of the DW initial excitation is rigid. DW have the frequencies ~$10^{10} sec^{-1}$ from the hypersound band and the amplitudes providing the level of deformation ~$10^{-3}$. The conditions that are necessary for…
We investigate the topology of the spin-polarized charge density in bcc and fcc iron. While the total spin-density is found to possess the topology of the non-magnetic prototypical structures, in some cases the spin-polarized densities are characterized by unique topologies; for example, the spin-polarized charge densities of bcc and high-spin fcc iron are atypical of any known for non-magnetic materials. In these cases, the two spin-densities are correlated: the spin-minority electrons have directional bond paths with deep minima in the minority density, while the spin-majority electrons fill…
The effect of the film thickness and temperature on structural phase transformations in infinite films of bcc zirconium with (001) crystallographic orientation is studied by the molecular dynamics method with a many-body potential of interatomic interaction obtained within the embedded atom model. It is shown that the mechanism, sequence and final structures of phase transitions in bcc Zr films essentially depend on the film thickness. The films with (001) surface up to 6.1 nm thick experience an orientational transition into the bcc (110) phase through an intermediate metastable fcc phase, an…
Modeling changes in atomic structure around a vacancy with increasing temperature and calculation of temperature dependences of vacancy characteristics in bcc iron
Machine-learning potentials for materials, namely the moment tensor potentials (MTPs), were validated using experimental EXAFS spectra for the first time. The MTPs for four metals (bcc W and Mo, fcc Cu and Ni) were obtained by the active learning algorithm of fitting to the results of the calculations using density functional theory (DFT). The MTP accuracy was assessed by comparing metal K-edge EXAFS spectra obtained experimentally and computed from the results of molecular dynamics (MD) simulations. The sensitivity of the method to various aspects of the MD and DFT models was demonstrated usi…
The phase stability of fcc and bcc magnetic binary Fe-Cr, Fe-Ni, Cr-Ni alloys and ternary Fe-Cr-Ni alloys is investigated using a combination of density functional theory (DFT), Cluster Expansion (CE) and Magnetic Cluster Expansion (MCE). Energies, magnetic moments, and volumes of more than 500 alloy structures are evaluated using DFT, and the most stable magnetic configurations are compared with experimental data. Deviations from the Vegard law in fcc Fe-Cr-Ni alloys, associated with non-linear variation of atomic magnetic moments as functions of alloy composition, are observed. Accuracy of t…
Molecular dynamics (MD) simulation of dislocation migration requires semi-empirical potentials of the interatomic interaction. While there are many reliable semi-empirical potentials for the bcc Fe, the number of the available potentials for the fcc is very limited. In the present study we tested three EAM potentials for the fcc Fe (ABCH97 [Phil. Mag. A, 75, 713-732 (1997)], BCT13 [MSMSE 21, 085004 (2013)] and ZFS18 [J. Comp. Chem. 39, 2420-2431 (2018)]) from literature. It was found that the ABCH97 potential does not provide that the fcc phase is the most stable at any temperature. On the oth…
Magnetic and transport properties of near-stoichiometric metastable FexMnyGaz alloys (46<x<52, 17<y25, 26<z<30) with face-centered cubic (FCC), body-centered cubic (BCC), and two-phase (FCC+BCC) structures are investigated. The experimental results are analyzed in terms of first-principles calculations of stoichiometric Fe2MnGa alloy with the L21, L12, and the tetragonally distorted L21 structural orderings. It is shown that the pure BCC and FCC phases have distinct magnetic and transport properties. Two-phase Fe2MnGa alloys have magnetic and transport properties typical of the mixed BCC and F…
The summary of the models offered by the author revealing features of the physical mechanisms controlling processes of martensite crystal formation is resulted. The rapid growth of a cooling martensite crystal is considered as a self-organized process controlled by the quasi-longitudinal lattice displacement waves (DW). It is shown, that processes of the heterogeneous nucleation and wave growth have the genetic connection in case of spontaneous fcc-bcc martensitic transformation. The exposition of strain martensite formation is considered in the context of a cryston model.
Irradiation-induced vacancy evolution in face-centered cubic (FCC) Ni under mechanical strains was studied using molecular dynamics simulations. Applied hydrostatic strain led to different stable forms of vacancy clusters, i.e., voids under strain >= +2% and stacking fault tetrahedras (SFTs) under strain <= 0. Direct transitions between SFT and void revealed that increasing strain magnitude facilitated the thermodynamic stability and dynamical evolution. The estimated free energy difference could well validate the dynamical simulations results by accounting for entropic contribution, which was…
Nickel islands are grown on W(110) at elevated temperatures. Islands with a thickness of two layers are investigated with scanning tunneling microscopy. Spectroscopic measurements reveal that nanometer sized areas of the islands exhibit distinctly different apparent heights and dI/dV spectra. Spin polarized and paramagnetic band structure calculations indicate that the spectral features are due to fcc(111) and bcc(110) orientations of the Ni film, respectively.
We develop and analyze a two-mode phase-field-crystal model to describe fcc ordering. The model is formulated by coupling two different sets of crystal density waves corresponding to <111> and <200> reciprocal lattice vectors, which are chosen to form triads so as to produce a simple free- energy landscape with coexistence of crystal and liquid phases. The feasibility of the approach is demonstrated with numerical examples of polycrystalline and (111) twin growth. We use a two-mode amplitude expansion to characterize analytically the free-energy landscape of the model, identifying parameter ra…
The phonon dispersions of the bcc and fcc phases of pure iron (α-Fe, γ-Fe and δ-Fe) at ambient pressure were investigated close to the respective phase transition temperatures. In the open bcc structure the transverse phonons along T1 [ξξ0] and T1 [ξξ2ξ] are of particularly low energy. The eigenvectors of these phonons correspond to displacements needed for the transformation to the fcc γ-phase. Especially these phonons, but also all other phonons soften considerably with increasing temperature. Comparing thermodynamic properties of the fcc and the two bcc phases it is shown that the high temp…
Molecular dynamics simulations are performed to investigate the structural phase transition in body-centered cubic (bcc) single crystal iron under high strain rate loading. We study the nucleation and growth of the hexagonal-close-packed (hcp) and face-centered-cubic (fcc) phases, and their crystal orientation dependence. Results reveal that the transition pressures are less dependent on the crystal orientations ($\mathtt{\sim}$14 GPa for loading along [001], [011], and [111] directions). However, the pressure interval of mixed phase for [011] loading is much shorter than loading along other o…
In this paper, we developed a thermodynamically consistent approach to account for the Gibbs energy of pure metallic element with thermal vacancy over wide temperature range. Taking body centered cubic (bcc) W for a demonstration, the strong nonlinear increase for temperature dependence of heat capacities at high temperatures and a nonlinear Arrhenius plots of vacancy concentration in bcc W can be nicely reproduced by the obtained Gibbs energy. The successful description of thermal vacancy on abnormal thermodynamic behaviors in bcc W indicates that the presently proposed thermodynamically cons…
Within the harmonic approximation, the effects of lattice vibration on the thermodynamics of nano-sized coherent clusters in bcc-Fe consisting of vacancies and/or copper are investigated. A combination of on-lattice simulated annealing based on Metropolis Monte Carlo simulations and off-lattice relaxation by Molecular Dynamics is applied to obtain the most stable cluster configurations at T = 0 K. The most recent interatomic potential built within the framework of the embedded atom method for the Fe-Cu system is used. The vibrational part of the total free energy of defect clusters in bcc-Fe i…
Bulk Au-Fe alloys separate into Au-based fcc and Fe-based bcc phases, but L1$_0$ and L1$_2$ orderings were reported in single-phase Au-Fe nanoparticles. Motivated by these observations, we study the structural and ordering energetics in this alloy by combining density functional theory (DFT) calculations with effective Hamiltonian techniques: a cluster expansion with structural filters, and the configuration-dependent lattice deformation model. The phase separation tendency in Au-Fe persists even if the fcc-bcc decomposition is suppressed. The relative stability of disordered bcc and fcc phase…
Using an ab initio approach, we explore the stability of small vacancy and vacancy-chromium clusters in dilute body-centred cubic Fe-Cr alloys. To explain experimental observations described in C.D. Hardie et al., J. Nucl. Mater. 439, 33 (2013) and showing the occurrence of Cr segregation in low-Cr alloys, we investigate if chromium can form stable bound configurations with vacancies in alloys with chromium concentration below the low-temperature chromium solubility limit of 10-11 at. %. We find that a single vacancy can attract up to four Cr atoms in the most energetically favourable cluster …
Martensitic transformation in steels is responsible for their very high strength and has thus been studied for more than one century since the first works of Martens. However, there is not yet simple physical theory. A rigorous classification of the crystallographic subgroupoids (packets) of the KS variants and the continuity between the KS, NW and Pitsch variants are introduced to represent the crystallographic intricacy associated to the martensite transformation. From this analysis, a new simple theory based on Pitsch distortion is proposed. The distortion respects the hard sphere packing o…
A classical molecular static technique (CMST) and DFT calculations using SIESTA, are employed here to characterize the self diffusion and the tracer solute diffusion in the bulk of BCC diluted $FeCr$ alloy driven by both vacancy and interstitial migration. For the first time in the literature, a six-frequency model (developed by Okamura and Allnatt) involved in a second nearest neighbor binding approach is adapted for calculations in a real system. We obtain microscopic parameters, namely: i) the free energy of vacancy formation and the vacancy-solute binding energy, ii) the involved jump freq…
We have developed a new and user-friendly interface energy calculation method that avoids problems deriving from numerical differences between bulk and slab calculations, such as the number of k points along the direction perpendicular to the interface. We have applied this to 36 bcc-fcc metal interfaces in the (100) orientation and found a clear dependence of the interface energy on the difference between the work functions of the two metals, on the one hand, and the total number of d electrons on the other. Greater mechanical deformations were observed in fcc crystals than in their bcc count…
Twenty-one distinct AlxCoCrFeNi alloys were rapidly prepared by laser alloying an equiatomic CoCrFeNi substrate with Al powder to create an alloy library ranging x=0.15-1.32. Variations in crystal structure, microstructure and mechanical properties were investigated using X-ray diffraction, scanning electron microscopy, scanning transmission electron microscopy and nanoindentation. With increasing Al content, the crystal structure transitioned from a disordered FCC to a mixture of disordered BCC and ordered B2 structures. While the onset of BCC/B2 formation was consistent with previously repor…
We measured the temperature dependent equilibrium vacancy concentration using in-situ positron annihilation spectroscopy in order to determine the enthalpy $H_\text{f}$ and entropy $S_\text{f}$ of vacancy formation in elementary fcc-La. The Arrhenius law applied for the data analysis, however, is shown to fail in explaining the unexpected high values for both $S_\text{f}$ and $H_\text{f}$: in particular $S_\text{f}=17(2)~k_\text{B}$ is one order of magnitude larger compared to other elemental metals, and the experimental value of $H_\text{f}$ is found to be more than three standard deviations …
We determine from first-principles the Curie temperature Tc for bulk Co in the hcp, fcc, bcc, and tetragonalized bct phases, for FeCo alloys, and for bcc and bct Fe. For bcc-Co, Tc=1420 K is predicted. This would be the highest Curie temperature among the Co phases, suggesting that bcc-Co/MgO/bcc-Co tunnel junctions offer high magnetoresistance ratios even at room temperature. The Curie temperatures are calculated by mapping ab initio results to a Heisenberg model, which is solved by a Monte Carlo method.
The interaction between vacancies and edge dislocations in face centered cubic metals (Al, Au, Cu, Ni) is studied at different length scales. Using empirical potentials and static relaxation, atomic simulations give us a precise description of this interaction, mostly in the case when the separation distance between both defects is small. At larger distances, elasticity theory can be used to predict this interaction. From the comparison between both approaches we obtain the minimal separation distance where elasticity applies and we estimate the degree of refinement required in the calculation…
Recently, a dislocation free deformation mechanism was proposed by Kiritani et al., based on a series of experiments where thin foils of fcc metals were deformed at very high strain rates. In the experimental study, they observed a large density of stacking fault tetrahedra, but very low dislocation densities in the foils after deformation. This was interpreted as evidence for a new dislocation-free deformation mechanism, resulting in a very high vacancy production rate. In this paper we investigate this proposition using large-scale computer simulations of bulk and thin films of copper. To fa…
Dimension reduction procedure is the recipe to represent defects in two dimensional dislocation dynamics according to the changes in the geometrical properties of the defects triggered by different conditions such as radiation, high temperature, or pressure. In the present study, this procedure is extended to incorporate further features related to the presence of defects with a special focus on face-centered cubic/body-centered cubic alloys used for diverse engineering purposes. In order to reflect the microstructural state of the alloy on the computational cell of two dimensional dislocation…
The behavior of metals at high pressure is of great importance to the fields of shock physics, geophysics, astrophysics, and nuclear materials. In order to further understand the properties of metals at high pressures we studied the equation of state of aluminum using first-principles techniques up to 2500 GPa, pressures within reach of the planned L.L.N.L. National Ignition Facility. Our simulations use density-functional theory and density-functional perturbation theory in the generalized gradient approximation at 0K. We found core overlaps to become relevant beyond pressures of 1200 GPa. Th…
In this work, Fe100-xNix nanoparticle systems in the invar region (x = 29, 32, and 37) were prepared by the method of chemical co-precipitation. X-Ray Diffraction (XRD) patterns confirmed the coexistence of both bcc and fcc phases for x = 29 and 32. However, only fcc phase was observed for x = 37. Scanning Electron Microscope (SEM) images indicated that the particle size is ~ 120-500 nm, and is almost independent of x. Mössbauer spectroscopy (MS) on the prepared nanoparticles indicated the development of a paramagnetic phase characteristic of the low-spin (antitaenite) fcc phase, in addition t…
Structural stability of paramagnetic (PM) body-centered cubic (bcc) Fe under pressure is investigated based on first-principles phonon calculations. Spin configurations of the PM phase are approximated using a binary special quasi-random structure (SQS) with a supercell approach. The behavior of phonon modes can be associated with pressure-induced phase transitions to the face-centered cubic (fcc) and hexagonal close-packed (hcp) structures as follows: For the PM phase, it is found that the low-frequency transverse mode at the N point (N$_4^-$ mode), which corresponds to a bcc-hcp phase transi…
We present an analysis of the time evolution of self-interstitial atom and vacancy (point defect) populations in pure bcc metals under constant irradiation flux conditions. Mean-field rate equations are developed in parallel to a kinetic Monte Carlo (kMC) model. When only considering the elementary processes of defect production, defect migration, recombination and absorption at sinks, the kMC model and rate equations are shown to be equivalent and the time evolution of the point defect populations is analyzed using simple scaling arguments. We show that the typically large mismatch of the rat…
Utilizing an atomistic computational model which handles both translational and spin degrees of freedom, combined molecular and spin dynamics simulations have been performed to investigate the effect of vacancy defects on spin wave excitations in ferromagnetic iron. Fourier transforms of space and time-displaced correlation functions yield the dynamic structure factor, providing characteristic frequencies and lifetimes of the spin wave modes. Comparison of the system with a 5% vacancy concentration with pure lattice data shows a decrease in frequency as well as a decrease in lifetime for all t…
We have performed molecular dynamic simulations of a Martensitic bcc->hcp transformation in a homogeneous system. The system evolves into three Martensitic variants, sharing a common nearest neighbor vector along a bcc <111> direction, plus an fcc region. Nucleation occurs locally, followed by subsequent growth. We monitor the time-dependent scattering S(q,t) during the transformation, and find anomalous, Brillouin zone-dependent scattering similar to that observed experimentally in a number of systems above the transformation temperature. This scattering is shown to be related to the elastic …
In this work we propose a method for the structural relaxation of magnetic materials in the paramagnetic regime, in an adiabatic fast-magnetism approximation within the disordered local moment (DLM) picture in the framework of density functional theory (DFT). The method is straight forward to implement using any $ab$ $initio$ code that allows for structural relaxations. We illustrate the importance of considering the disordered magnetic state during lattice relaxations by calculating formation energies and geometries for an Fe vacancy and C insterstitial atom in bcc Fe as well as bcc Fe$_{1-x}…
The effect of spin fluctuations on the $α$ (bcc) - $γ$ (fcc) - $δ$ (bcc) structural phase transitions in iron is investigated with a tight-binding (TB) model. The orthogonal $d$-valent TB model is combined with thermodynamic integration, spin-space averaging and Hamiltonian Monte Carlo to compute the temperature-dependent free-energy difference between bcc and fcc iron. We demonstrate that the TB model captures experimentally observed phonon spectra of bcc iron at elevated temperatures. Our calculations show that spin fluctuations are crucial for both, the $α$ - $γ$ and the $γ$ - $δ$ phase tra…
The impurity Green's function exact to the first order in the vacancy concentration has been calculated in the framework of the five frequency model (5FM). The solution in terms of determinant ratios has been obtained with the use of the Cramer's rule. The determinant sizes varied from 54 for the most general case to three for the four frequency model. Both analytical and numerical techniques has been used to analyze the solution. Special attention has been devoted to the case of strong impurity-vacancy (I-v) binding in order to substantiate the picture of diffusion via bound I-v pairs develop…
We use first-principles techniques to re-examine the suggestion that transitions seen in high-P experiments on Mo are solid-solid transitions from the bcc structure to either the fcc or hcp structures. We confirm that in the harmonic approximation the free energies of fcc and hcp structures become lower than that of bcc at P > 325 GPa and T below the melting curve, as reported recently. However, we show that if anharmonic effects are fully included this is no longer true. We calculate fully anharmonic free energies of high-T crystal phases by integration of the thermal average stress with resp…
From Phase Prediction to Phase Design: A ReAct Agent Framework for High-Entropy Alloy Discovery
Luxembourg Institute of Science and Technology (LIST)（卢森堡科学与技术研究院）；Department of Physics and Materials Science, University of Luxembourg（卢森堡大学物理与材料科学系）
Nanolamellar Hybrid High-Entropy Alloys with Superior Micromechanical Properties
WPI, International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University（九州大学 碳中性能源研究国际研究所）；Department of Automotive Science, Graduate School of Integrated Frontier Sciences, Kyushu University（九州大学 前沿融合科学研究生院 汽车科学系）；Department of Materials Science and Engineering, Kumamoto University（熊本大学 材料科学与工程系）；Department of Mechanical Engineering, Kyushu University（九州大学 机械工程系）；Univ Rouen Normandie, INSA Rouen Normandie, CNRS, Groupe de Physique des Matériaux, UMR6634（鲁昂诺曼底大学 鲁昂诺曼底国立应用科学学院 法国国家科学研究中心 材料物理小组）；Interdisciplinary Research Center, Liaoning Academy of Materials（辽宁材料研究院 交叉研究中心）
We use a transfer-matrix method to study the disorder-induced metal-insulator transition. We take isotropic nearest- neighbor hopping and an onsite potential with uniformly distributed disorder. Following previous work done on the simple cubic lattice, we perform numerical calculations for the body centered cubic and face centered cubic lattices, which are more common in nature. We obtain the localization length from calculated Lyapunov exponents for different system sizes. This data is analyzed using finite-size scaling to find the critical parameters. We create an energy-disorder phase diagr…
