The mean-first-passage-times (MFPTs) for a vacancy that diffuses (via one- and six-jump cycles) in a two dimensional ordered binary alloy are evaluated using the properties of random walks on networks. We investigate the effect of temperature and relative barrier height on the ratio between the MFPTs of the two cycles. We find that the six-jump cycle takes shorter time than the one-jump cycle for the range of parameters considered.
Modeling the Equilibrium Vacancy Concentration in Multi-Principal Element Alloys from First-Principles
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Institute of Materials, École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院材料研究所）；Laboratory of materials design and simulation (MADES), Institute of Materials, École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院材料研究所材料与模拟实验室）；National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院新材料计算设计与发现国家中心）
Atomic-scale calculations indicate that both stress effects and chemical binding contribute to the redistribution of solute in the presence of vacancy clusters in magnesium alloys. As the size of the vacancy cluster increases, chemical binding becomes more important relative to stress. By affecting the diffusivity of vacancies and vacancy clusters, solute atoms facilitate clustering and stabilize the resulting vacancy clusters, increasing their potential to promote solute segregation and to serve as heterogeneous nucleation sites during precipitation. Experimental observation of solute segrega…
Many of the purported virtues of Multi-Principal Element Alloys (MPEAs), such as corrosion, high-temperature oxidation and irradiation resistance, are highly sensitive to vacancy diffusivity. Similarly, solute interdiffusion is governed by vacancy diffusion -- it is often unclear whether MPEAs are truly stable, or effectively stabilized by slow interdiffusion. The considerable composition space afforded to these alloys makes optimizing for desired properties a daunting task; theoretical and computational tools are necessary to guide alloy development. For diffusion, such tools depend on both a…
Alloying elements play an important role in the design of plasma facing materials with good comprehensive properties. Based on first-principles calculations, the stability of alloying element W and its interaction with vacancy defects in Ta-W alloys are studied. The results show that W tends to distribute dispersedly in Ta lattice, and is not likely to form precipitation even with the coexistence of vacancy. The aggregation behaviors of W and vacancy can be affected by their concentration competition. The increase of W atoms has a negative effect on the vacancy clustering, as well as delays th…
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 …
Active room temperature diffusion-less climb of the <a> edge dislocations in model Mg-Al alloys was observed using molecular dynamics simulations. Dislocations on prismatic and pyramidal I planes climb through the basal plane to overcome solute obstacles. This out-of-plane dislocation motion softens the high resistance pyramidal I glide and significantly reduces the anisotropy of dislocation mobility, and could help improve the ductility of Mg. The flow stress scales linearly with solute concentration, cAl. Dislocations climb predominantly in the negative direction, with climb angle on the ord…
Vacancy is known to play a critical role in solid state diffusion and determine many properties of the materials. We report a proof-of-principle result on Mn in the role of tuning vacancy diffusion by an anomalous Friedel Oscillations effect in an equivalent NiCoFeCrMn high entropy alloy. The vacancy induced Friedel Oscillations is destroyed by the presence of the first nearest neighboring Mn, opening a channel for long-range influence on the surrounding atoms from the vacancy, resulting in a lower vacancy diffusion barrier energy, despite of the atom type. The effects lead to a remarkable dif…
The vacancy concentration at finite temperatures is studied for a series of (CoCrFeMn)$_{1-x_\mathrm{Ni}}$Ni$_{x_\mathrm{Ni}}$ alloys by grand-canonical Monte-Carlo (MC) simulations. The vacancy formation energies are calculated from a classical interatomic potential and exhibit a distribution due to the different chemical environments of the vacated sites. In dilute alloys, this distribution features multiple discrete peaks, while concentrated alloys exhibit an unimodal distribution as there are many different chemical environments of similar vacancy formation energy. MC simulations using a n…
The earlier-suggested master equation approach is used to develop the consistent statistical theory of diffusion in alloys using the five-frequency model of FCC alloys as an example. Expressions for the Onsager coefficients in terms of microscopic interatomic interactions and some statistical averages are presented. We discuss methods of calculations of these averages using both the mean-field and the pair-cluster approximation to describe influence of vacancy-solute and solute-solute interactions, and both the nearest-neighbor and the second-shell approximation to describe vacancy correlation…
A formalism for the vacancy formation energies in random alloys within the single-site mean-filed approximation, where vacancy-vacancy interaction is neglected, is outlined. It is shown that the alloy configurational entropy can substantially reduce the concentration of vacancies at high temperatures. The energetics of vacancies in random Cu-0.5Ni-0.5 alloy is considered as a numerical example illustrating the developed formalism. It is shown that the effective formation energy is increases with temperature, however, in this particular system it is still below the mean value of the vacancy for…
First-principles calculations of the thermodynamic factor of multicomponent alloys
Laboratory of materials design and simulation (MADES), Institute of Materials, École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院材料研究所材料设计与模拟实验室）；Materials department, University of California, Santa Barbara（加州大学圣巴巴拉分校材料系）
The mobility of vacancies in alloys may limit dislocation climb. Using a combined density functional theory and kinetic Monte Carlo approach we investigate vacancy diffusion in Ni-Re, Ni-W, and Ni-Ta binary alloys up to 10 at.% solute concentration. We introduce an interaction model that takes into account the chemical environment close to the diffusing atom to capture the effect of solute-host and solute-solute interactions on the diffusion barriers. In contrast to an ideal solid solution it is not only the diffusion barrier of the solute atom that influences the vacancy mobility, but primari…
Tailoring the degree of structural disorder in Ge-Sb-Te alloys is important for the development of non-volatile phase-change memory and neuro-inspired computing. Upon crystallization from the amorphous phase, these alloys form a cubic rocksalt-like structure with a high content of intrinsic vacancies. Further thermal annealing results in a gradual structural transition towards a layered structure and an insulator-to-metal transition. In this work, we elucidate the atomic-level details of the structural transition in crystalline GeSb2Te4 by in situ high-resolution transmission electron microsco…
The development of long range order in nickel-chromium alloys is of great technological interest but the kinetics and mechanisms of the transformation are poorly understood. The present research utilizes a combined computational and experimental approach to elucidate the mechanism by which phosphorus accelerates the ordering rate of stoichiometric Ni_2Cr in Ni-Cr alloys. A series of Ni-33%Cr-x%P samples (in atomic percent) were fabricated with phosphorus concentrations, x = <0.005-0.1 at.% and aged between 373 and 470°C for times up to 3000 h. The first-principles modeling considers fcc Ni wit…
Phase selection in Ti-Zr-Hf-Al high-entropy alloys was investigated by in-situ high-energy X$-$ray diffraction, single-crystal X$-$ray diffraction, and density-functional theory based electronic-structure methods that address disorder and vacancies, predicting formation enthalpy and chemical short-range order (SRO). Samples with varying Al content were synthesized, characterized, and computationally assessed to ascertain the composition-dependent phase selection, as increased Al content often acts as a stabilizer of a body-centered-cubic structure. Equiatomic TiZrHfAl was especially interestin…
We present a proof-of-principle demonstration of a universal law for the element Mn, which greatly enhances vacancy diffusion through an anomalous Friedel Oscillation effect in a series of Ni-based concentrated solid-solution alloys, regardless of the type of atom involved. The antiferromagnetic element Mn possesses a unique half-filled 3d electron structure, creating split virtual bound states near the Fermi energy level and producing a large local magnetic moment after vacancy formation. The resultant electron spin oscillations reduce the number of electrons involved in charge density oscill…
Multi-principal element alloys (MPEAs) continue to garner interest as structural and plasma-facing materials due to their structure stability and increased resistance to radiation damage. Despite sensitivity of mechanical behavior to irradiation and point-defect formation, there has been scant attention on understanding vacancy stability and diffusion in refractory-based MPEAs. Using density-functional theory, we examine vacancy stability and diffusion barriers in body-centered cubic (Mo0.95W0.05)0.85Ta0.10(TiZr)0.05. The results in this MPEA show strong dependence on environment, originating …
The influence of hydrogen on the structural evolutions of an Al-Mg-Si alloy during natural and artificial ageing was investigated experimentally. The aim of the study was a better understanding of interactions between hydrogen and crystalline defects and especially vacancies. Experimental data demonstrate that during natural ageing in hydrogen environment, the hardening response is delayed. This is attributed to a slower recovery of excess vacancies linked to a lower mobility. To confirm and quantify the influence of hydrogen on the vacancy migration energy, artificial ageing was carried out i…
Insights into hydrogen-induced vacancy stability and creep in chemically complex alloys
Ames National Laboratory, US Department of Energy, Iowa State University（艾姆斯国家实验室，美国能源部，爱荷华州立大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Department of Materials Science & Engineering, Iowa State University（爱荷华州立大学材料科学与工程系）
Impurity diffusion coefficients are entirely obtained from a low cost classical molecular statics technique (CMST). In particular, we show how the CMST is appropriate in order to describe the impurity diffusion behavior mediated by a vacancy mechanism. In the context of the five-frequency model, CMST allows to calculate all the microscopic parameters, namely: the free energy of vacancy formation, the vacancy-solute binding energy and the involved jump frequencies, from them, we obtain the macroscopic transport magnitudes such as: correlation factor, solvent-enhancement factor, Onsager and diff…
We present the results of a systematic study using the density functional theory (within the local density approximation) of the effects of biaxial strain and composition on the self-diffusion of Si and Ge in SiGe alloys diffusing by a vacancy mechanism. The biaxial strain dependence of the vacancy formation energy was reconfirmed with previous calculations. The effect of biaxial strain on the interaction potential energy between a substitutional Ge atom and a vacancy was calculated. These calculations were used to estimate the change in the activation energy (due to biaxial strain) for the se…
We observe that pressure-induced amorphization of Ga2SeTe2 (a III-VI semiconductor) is directly influenced by the periodicity of its intrinsic defect structures. Specimens with periodic and semi-periodic two-dimensional vacancy structures become amorphous around 10-11 GPa in contrast to those with aperiodic structures, which amorphize around 7-8 GPa. The result is a notable instance of altering material phase-change properties via rearrangement of stoichiometric vacancies as opposed to adjusting their concentrations. Based on our experimental findings, we posit that periodic two-dimensional va…
Accurate prediction of vacancy migration energy barriers, $ΔE_a$, in multi-component alloys is extremely challenging yet critical for the development of diffusional transformation kinetics needed to model alloy behavior in many technological applications. Here, results from $ΔE_a$ and the energy driving force $ΔE$ of many (>1000) vacancy migration events calculated using density functional theory and nudged elastic band method show large changes (~1eV) of $ΔE_a$ in different local chemical environments of the model face-centered cubic Al-Mg-Zn alloys. Due to local lattice distortion effects in…
It is shown that a temperature window between the Curie temperatures of martensite and austenite phases around the room temperature can be obtained by a vacancy-tuning strategy in Mn-poor Mn1-xCoGe alloys (0 <= x <= 0.050). Based on this, a martensitic transformation from paramagnetic austenite to ferromagnetic martensite with a large magnetization difference can be realized in this window. This gives rise to a magnetic-field-induced martensitic transformation and a large magnetocaloric effect in the Mn1-xCoGe system. The decrease of the transformation temperature and of the thermal hysteresis…
A vacancy-mediated collective diffusion model is used to compute a thermally-induced (spinodal) phase separation in a typical fcc bi-metallic surface alloy at low median concentration of vacancies, focusing on the effect of the ratio, $Γ=Γ_A/Γ_B$, of the jump rates to the vacant sites of the two types of atoms. The model is formulated for the diffusion of one atomic species and vacancies, employing the kinetic transport coefficients derived by Moleko \emph{et al.} (Phil. Mag. A 59, 141 (1989)). It is demonstrated that for A$_{0.7}$B$_{0.3}$ alloy, $Γ\sim 50$ results in suppression of phase sep…
Impurity diffusion in Zr is potentially important for many applications of Zr alloys, and in particular for their use of nuclear reactor cladding. However, significant uncertainty presently exists about which elements are vacancy vs. interstitial diffusers, which can inhibit understanding and prediction of their behavior under different temperature, irradiation, and alloying conditions. Therefore, first-principles calculations based on density functional theory (DFT) have been employed to predict the temperature-dependent dilute impurity diffusion coefficients for 14 substitutional alloying el…
University of California, Irvine（加州大学尔湾分校）；University of New Mexico（新墨西哥大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Massachusetts Institute of Technology（麻省理工学院）；University of California, San Diego（加州大学圣地亚哥分校）；Johns Hopkins University（约翰斯·霍普金斯大学）；Stony Brook University（石溪大学）；University of Arizona（亚利桑那大学）；Los Alamos National Lab（洛斯阿拉莫斯国家实验室）；University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）
Impurity diffusion coefficients are entirely obtained from a low cost classical molecular statics technique (CMST). In particular, we show how CMST is appropriate in order to describe the impurity diffusion behavior mediated by a vacancy mechanism. In the context of the five-frequency model, CMST allows to calculate all the microscopic parameters, namely: the free energy of vacancy formation, the vacancy-solute binding energy and the involved jump frequencies, from them, we obtain the macroscopic transport magnitudes such as: correlation factor, solvent-enhancement factor, Onsager and diffusio…
One intriguing finding in graphene is the vacancy-induced magnetism that highlights the interesting interaction between local magnetic moments and conduction electrons. Within density functional theory, the current understanding of the ground state is that a Stoner instability gives rise to ferromagnetism of $π$ electrons aligned with the localized moment of a $σ$ dangling bond and the induced $π$ magnetic moments vanish at low vacancy concentrations. However, the observed Kondo effect suggests that $π$ electrons around the vacancy should antiferromagnetically couple to the local moment and ca…
Hexagonal superlattice formed by sodium multi-vacancy cluster ordering in Na$_{0.77}$CoO$_2$ has been proposed based on synchrotron X-ray Laue diffraction study on electrochemically fine-tuned single crystals. The title compound sits closely to the proposed lower end of the miscibility gap of x ~ 0.77-0.82 phase separated range. The average sodium vacancy cluster size is estimated to be 4.5 Na vacancies per layer within a large superlattice size of sqrt{19}a*sqrt{19}a*3c. The exceptionally large Na vacancy cluster size favors large twinned simple hexagonal superlattice of sqrt{19}a, in competi…
High-entropy alloys (HEAs), which have been intensely studied due to their excellent mechanical properties, generally refer to alloys with multiple equimolar or nearly equimolar elements. According to this definition, Si-Ge-Sn alloys with equal or comparable concentrations of the three Group IV elements belong to the category of HEAs. As a result, the equimolar elements of Si-Ge-Sn alloys likely cause their atomic structures to exhibit the same core effects of metallic HEAs such as lattice distortion. Here we apply density functional theory (DFT) calculations to show that the SiGeSn HEA indeed…
We examine the interdiffusion in multicomponent systems using the approach analogically to one developed earlier for description of interdiffusion in binary alloys. This approach in opposite to traditional theory, takes into consideration an active role of vacancies, equilibrium distribution of which is not supposed. In this case, in equations for flux components there are contributions conditioned by vacancy concentration gradient. As the vacancy diffusion coefficient is much larger than those for the components, a counteraction to this process will equalize the fluxes of components and, cons…
Electron-positron momentum distributions measured by the coincidence Doppler broadening method can be used in the chemical analysis of the annihilation environment, typically a vacancy-impurity complex in a solid. In the present work, we study possibilities for a quantitative analysis, i.e., for distinguishing the average numbers of different atomic species around the defect. First-principles electronic structure calculations self-consistently determining electron and positron densities and ion positions are performed for vacancy-solute complexes in Al-Cu, Al-Mg-Cu, and Al-Mg-Cu-Ag alloys. The…
Multi-principal element alloys (MPEAs) are exciting systems showing remarkable properties compared to conventional materials due to their exceedingly large compositional space and spatially varying chemical environment. However, predicting fundamental properties from the local chemical environment is challenging due to the large scale of the problem. To investigate this fundamental problem, we employ a combination of atomistic simulations (using ab-initio and molecular dynamics) and convolutional neural networks (CNNs) to evaluate point defect and migration energies in an equimolar CoFeCrNi MP…
Using a first-principles cluster expansion, we shed light on the solid-state phase diagram and structure of the recently discovered high-performance thermoelectrics, Pb-Ag-Sb-Te alloys. The observed nanoscale inhomogeneities are shown to be coherent precipitates of ordered (Ag)m(Sb)n(Te)m+n phases, such as AgSbTe2, all immiscible with rocksalt PbTe. The solubility is high for PbTe in AgSbTe2 and low for (Ag,Sb)Te in PbTe (8% vs. 0.6% at 850 K). The differences in the phonon spectra of PbTe and AgSbTe2 confirm that the inhomogeneities enhance the thermoelectric performance.
This thesis is a theoretical study of thermodynamic, point-defect formation and diffusion properties in Fe-Ni alloys with a focus on the magnetochemical effects. The results are derived from density functional theory (DFT) calculations and Monte Carlo (MC) simulations using a DFT-parametrized effective interaction model (EIM) with explicit atomic and spin variables. The first part of this work is focused on thermodynamics. We compute via DFT energetic, magnetic and vibrational properties and the bcc-fcc phase diagram, revealing the relative importance between magnetic and vibrational entropies…
The consequences of hydrogen on the formation and growth of GP zones during natural ageing in an Al-5Cu alloy is investigated experimentally down to the atomic scale and numerically using ab initio calculations. As observed through scanning/transmission electron microscopy, the hardening kinetic is delayed due to a slower growth of GP zones during natural ageing when hydrogen is incorporated. According to ab initio calculations, the delayed hardening results from hydrogen trapped in vacancies that reduce significantly the diffusion coefficient of copper and the self diffusion of aluminium. Thi…
Lattice vacancy migration barriers in Fe-Ni alloys, and why Ni atoms diffuse slowly: An ab initio study
United Kingdom Atomic Energy Authority（英国原子能管理局）；University of Warwick（华威大学）；H.H. Wills Physics Laboratory, University of Bristol（布里斯托大学H.H.威尔斯物理实验室）；Northeastern University（东北大学）
Al-Mg-Si alloys with total solute contents ranging from 0.8 to 1.4 wt.% were solutionised, quenched and then artificially aged (AA) at 180 °C, after which positron annihilation lifetime spectroscopy was applied to obtain information about precipitation and vacancy evolution during preceding ageing. Hardness and electrical resistivity measurements were carried out to complement these measurements. AA was carried out in four different heating media, which allowed for varying the heating rate from 2.4 K/s to 170 K/s. The main result of the study is that there is a competition between vacancy loss…
Vacancy mechanism plays a dominant role in the atomic migration when a close-packed disordered alloy undergoes ordering transition. However, the calculation of thermal vacancy formation energies (VFEs) of random solid solutions is usually cumbersome due to the difficulty in considering various local atomic environments. Here, we propose a transparent way that combines coherent potential approximation and supercell-local cluster expansion to investigate VFEs of random solid solutions. This method is used to study the effects of temperature, strain and magnetism on the VFEs of random A1-FePt all…
Although the equilibrium composition of many alloy surfaces is well understood, the rate of transient surface segregation during annealing is not known, despite its crucial effect on alloy corrosion and catalytic reactions occurring on overlapping timescales. In this work, CuNi bimetallic alloys representing (100) surface facets are annealed in vacuum using atomistic simulations to observe the effect of vacancy diffusion on surface separation. We employ multi-timescale methods to sample the early transient, intermediate, and equilibrium states of slab surfaces during the separation process, in…
The origin of the spin-glass state in (Fe,Sn)4N alloys is studied on the basis of a Heisenberg Hamiltonian with parameters derived from first principles within the magnetic force theorem applied in the framework of the disordered local moments method and local spin-density approximation. We show that in the alloy concentration range where the spin-glass state is stable only one Fe sublattice is intrinsically magnetic and the interatomic exchange magnetic interactions are essentially short ranged due to effects of chemical and magnetic disorder. The magnetic Fe atoms with well-localized spin mo…
We have used the indium/copper surface alloy to study the dynamics of surface vacancies on the Cu(001) surface. Individual indium atoms that are embedded within the first layer of the crystal, are used as probes to detect the rapid diffusion of surface vacancies. STM measurements show that these indium atoms make multi-lattice-spacing jumps separated by long time intervals. Temperature dependent waiting time distributions show that the creation and diffusion of thermal vacancies form an Arrhenius type process with individual long jumps being caused by one vacancy only. The length of the long j…
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…
There has been considerable interest in chalcogenide alloys with high concentrations of native vacancies that lead to properties desirable for thermoelectric and phase-change materials. Recently, vacancy ordering has been identified as the mechanism for metal-insulator transitions observed in GeSb2Te4 and an unexpectedly low thermal conductivity in Ga2Te3. Here, we report the direct observation of vacancy ordering in Ga2SeTe2 utilizing aberration-corrected electron microscopy. Images reveal a cation-anion dumbbell inversion associated with the accommodation of vacancy ordering across the entir…
