Experimental and theoretical study of tracer diffusion in a series of (CoCrFeMn)$_{100-x}$Ni$_x$ alloys
Josua Kottke, Daniel Utt, Mathilde Laurent-Brocq, Adnan Fareed, Daniel Gaertner, Loic Perriere, Lukasz Rogal, Alexander Stukowski, Karsten Albe, Sergiy V. Divinski, Gerhard Wilde
Tracer diffusion of all constituting elements is studied at various temperatures in a series of (CoCrFeMn)$_{100-x}$Ni$_x$ alloys with compositions ranging from pure Ni to the equiatomic CoCrFeMnNi high-entropy alloy. At a given homologous temperature, the measured tracer diffusion coefficients change non-monotonically along the transition from pure Ni to the concentrated alloys and finally to the equiatomic CoCrFeMnNi alloy. This is explained by atomistic Monte-Carlo simulations based on a modified embedded-atom potentials, which reveal that local heterogeneities of the atomic configurations around a vacancy cause correlation effects and induce significant deviations from predictions of the random alloy model.
For (CoCrFeMn)$_{100-x}$Al$_{x}$ high-entropy alloys, we investigate the phase evolution with increasing Al-content (0 $\le$ x $\le$ 20 at.%). From first-principles theory, the Al-doping drives the alloy structurally from FCC to BCC separated by a narrow two-phase region (FCC+BCC), which is well supported by our experiments. We highlight the effect of Al-doping on the formation enthalpy and electronic structure of (CoCrFeMn)$_{100-x}$Al$_{x}$ alloys. As chemical short-range order (SRO) in multicomponent alloys indicates the nascent local order (and entropy changes), as well as expected low-tem…
Tracer diffusion of the substitutional components in (CoCrFeNiMn)$_{1-x}$C$_x$ high-entropy alloys with x = 0.002, 0.005 and 0.008 (in at. fractions) is measured at elevated temperatures from 1173 to 1373 K. Two different characteristic effects of interstitial carbon addition on substitutional diffusion in these FCC alloys are distinguished. At the highest temperature of 1373 K, alloying by C with relatively low concentrations (x = 0.002) retards diffusion of the substitutional elements with respect to those in the C-free alloy. At lower temperatures and/or higher C concentrations (x > 0.005),…
High entropy alloys are a class of materials with many significant improvements in terms of mechanical properties as compared to ``classical'' alloys. The corresponding structure-property relations are not yet entirely clear, but it is commonly believed that the good mechanical performance is strongly related to dislocation interactions with the complex energy landscape formed due to alloying. Although in-situ Transmission Electron Microscopy (TEM) allows high-resolution studies of the structure and dynamics of moving dislocations and makes the local obstacle/energy ``landscape'' directly visi…
The diffusion kinetics in a CoCrFeMnNi high entropy alloy is investigated by a combined radiotracer--interdiffusion experiment applied to a pseudo-binary Co$_{15}$Cr$_{20}$Fe$_{20}$Mn$_{20}$Ni$_{25}$ / Co$_{25}$Cr$_{20}$Fe$_{20}$Mn$_{20}$Ni$_{15}$ couple. As a result, the composition-dependent tracer diffusion coefficients of Co, Cr, Fe and Mn are determined. The elements are characterized by significantly different diffusion rates, with Mn being the fastest element and Co being the slowest one. The elements having originally equiatomic concentration through the diffusion couple are found to r…
Grain boundary self-diffusion of $^{57}$Co, $^{51}$Cr, $^{59}$Fe and $^{54}$Mn in a coarse-grained, single-phase fcc CoCrFeMnNi high entropy alloy is measured in a wide temperature range of 643 to 1273~K in both C- and B-type kinetic regimes after Harrison's classification. The results suggest that the product of the pertinent segregation factors, $s$, and the grain boundary width, $δ$, is about 0.5~nm for all elements at temperatures $T>800$~K. Whereas one short-circuit contribution is observed at higher temperatures above 800~K, the penetration profiles in the C-type kinetic regime (643 -- 7…
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…
Impact of interstitial carbon on local lattice distortions in CoCrFeMnNi high-entropy alloys
Helmholtz-Zentrum Berlin für Materialien und Energie (HZB)（柏林亥姆霍兹材料能源中心）；Institute of Solid State Physics, University of Latvia（拉脱维亚大学固体物理研究所）；Department of Metallurgical and Materials Engineering, Indian Institute of Technology Patna（巴特那印度理工学院冶金与材料工程系）；Deutsches Elektronen-Synchrotron DESY（德国电子同步辐射中心）；Interdisciplinary Centre for Advanced Materials Simulation, Ruhr-Universität Bochum（鲁尔大学波鸿跨学科先进材料模拟中心）；Department of Computational Materials Design, Max-Planck-Institute for Sustainable Materials（马普可持续材料研究所计算材料设计系）；Institute for Materials Science, University of Stuttgart（斯图加特大学材料科学研究所）；Institute of Materials Physics, University of Münster（明斯特大学材料物理研究所）
High entropy alloys (HEAs) have emerged as a new class of multicomponent materials, which have potential for high temperature applications. Phase stability and creep deformation, two key selection criteria for high temperature materials, are predominantly influenced by the diffusion of constituent elements along the grain boundaries (GBs). For the first time, GB diffusion of Ni in chemically homogeneous CoCrFeNi and CoCrFeMnNi HEAs is measured by radiotracer analysis using the $^{63}$Ni isotope. Atom probe tomography confirmed the absence of elemental segregation at GBs that allowed reliable e…
In situ straining experiments were performed in a TEM on an equimolar CoCrFeMnNi (Cantor) high entropy alloy at room and cryogenic temperature. Perfect and partial dislocation activity were recorded in both cases. Twinning directly follows the development of partial dislocation shearing that has various origins (perfect dislocation splitting, anchoring). It is shown that, although twinning is more frequently observed at liquid nitrogen temperature, its prevalence depends mainly on crystal orientation. As a result, twinning and perfect dislocation plasticity are likely to occur jointly in rando…
The bulk quaternary equiatomic CoCrFeNi alloy is studied extensively in literature. Under experimental conditions, it shows a single-phase fcc structure and its physical and mechanical properties are similar to those of the quinary equiatomic CoCrFeMnNi alloy. Many studies in literature have focused on the mechanical properties of bulk nanocrystalline high entropy alloys or compositionally complex alloys, and their microstructure evolution upon annealing. The thin film processing route offers an excellent alternative to form nanocrystalline alloys. Due to the high nucleation rate and high dens…
The problem of estimation of the tracer diffusion coefficients is solved by utilizing a novel tracer-interdiffusion couple technique even in the absence suitable radioisotope of one of the components and absence of reliable thermodynamic parameters. This is demonstrated by generating reliable and reproducible mobility data in the alloys of the Fe-Ga system with a strong composition dependence of the diffusion coefficients. Tracer- (59Fe) and inter-diffusion are simultaneously measured in three couples Fe/Fe-16Ga, Fe/Fe-24Ga and Fe-16Ga/Fe-24Ga at 1143 K. The results obtained for the couples wi…
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…
The estimation of (n-1)2 interdiffusion coefficients in an n component system requires (n-1) diffusion paths to intersect or pass closely in the (n-1) dimensional space according to the body diagonal diffusion couple method. These interdiffusion coefficients are related to n(n-1) intrinsic (or n tracer diffusion coefficients), which cannot be estimated easily following the Kirkendall marker experiment in a multicomponent system despite their importance for understanding the atomic mechanism of diffusion and the physico-mechanical properties of materials. In this study, the estimation of tracer…
Comprehensive Mapping of Tracer Diffusivities Across Composition Space in Ternary NiAlTi and Quinary NiCoFeAlTi High-Entropy Alloy Using Diffusion Couple Experiments and Physics Informed Neural Network Inversion
In-Situ TEM Observation of Solid-State Phase Evolution in High-Entropy Alloy Nanoparticles
University of Petroleum and Energy Studies (UPES)（石油与能源大学）；Indian Institute of Technology, Kharagpur（印度理工学院哈格普尔分校）；Brazilian Centre for Research in Energy and Materials（巴西能源与材料研究中心）；State University of Campinas（坎皮纳斯州立大学）；Rice University（莱斯大学）；Federal University of ABC (UFABC)（ABC联邦大学）；Michigan Technological University（密歇根理工大学）
Extracting Composition-Dependent Diffusion Coefficients Over a Very Large Composition Range in NiCoFeCrMn High Entropy Alloy Following Strategic Design of Diffusion Couples and Physics Informed Neural Network Numerical Method
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…
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…
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…
Estimating the diffusion coefficients experimentally in a four-component inhomogeneous alloy following the conventional diffusion couple method by intersecting three couples at the same composition is difficult unless a small composition range of constant diffusivity is identified. Additionally, the intrinsic diffusion coefficients of the components cannot be estimated in a system with more than two components. To solve these issues, we have followed the pseudo-binary and pseudo-ternary diffusion couple methods for estimating the diffusion coefficients at the equiatomic composition of NiCoFeCr…
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）
High entropy alloys (HEAs) are considered as a novel class of materials with a large number of components available in nearly equatomic proportions. One of the characteristic properties of HEAs was believed to be so-called "sluggish" diffusion. The faith on this myth instead of rigorous experimental analysis played such a dominant role that the first set of data on interdiffusion, in fact based on an improper analysis, were cited in hundreds of articles to state the presence of sluggishness of diffusion rates in high entropy alloys. In this review, the recent data on atomic diffusion in HEAs a…
Grain boundary tracer diffusion of Ni, Fe and Cr was studied in a Ni-base 602CA coarse-grained alloy. A co-existence of several short-circuit contributions was distinguished at higher temperatures in Harrison's B-type regime (773-873 K), which were related to different families of high-angle grain boundaries with distinct coverages by precipitates and segregation levels as revealed by HAADF-STEM combined with EDX measurements. Annealing at 873 K for 18 hours resulted in Cr23C6-type carbides coexisting with an α-Cr-Mn-enriched phase in addition to sequential segregation layers of Al, Fe and Ni …
Using an atom-vacancy exchange algorithm, we investigate the kinetics of the order-disorder transition in an fcc A_3B binary alloy model following a temperature quench from the disordered phase. We observe two clearly distinct ordering scenarios depending on whether the final temperature T_f falls above or below the ordering spinodal T_{sp}, which is deduced from simulations at equilibrium. For shallow quenches (T_f>T_{sp}) we identify an incubation time tau_{inc} which characterizes the onset of ordering through the formation of overcritical ordered nuclei. The algorithm we use together with …
