Atomic Size Difference Research Articles

Phase evolution and microware dielectric properties of high-entropy spinel-type (Mg0.2Co0.2Ni0.2Li0.4Zn0.2)Al2O4 ceramics

In this study, high-entropy spinel-type (Mg0.2Co0.2Ni0.2Li0.4Zn0.2)Al2O4 ceramics were synthesized by solid-state reaction method. The raw materials gradually formed spinel aluminates from 700 to 1400 °C and finally formed high-entropy (Mg0.2Co0.2Ni0.2Li0.4Zn0.2)Al2O4 ceramics after calcination at 1400 °C for 4 h. The high-configuration entropy and low average atomic-size difference were beneficial to form single-phase high-entropy ceramics. Partial lattice distortion occurred within the high-entropy (Mg0.2Co0.2Ni0.2Li0.4Zn0.2)Al2O4 ceramics structure, and its grain size gradually increased with increasing sintering temperature. The high-entropy (Mg0.2Co0.2Ni0.2Li0.4Zn0.2)Al2O4 ceramics exhibited good microwave dielectric properties when sintered at 1550 °C for 4 h: dielectric constant (εr) = 7.4, quality factor (Qf) = 58,200 GHz, and temperature coefficient of resonance frequency (τf) = –64 ppm/°C. The εr values were mainly affected by the dielectric polarizability. The Qf values were highly related to the relative density and covalency of A-site bond, whereas the τf values closely depended on the bond strength of A-site.

Study on the influence of Hf, Zr and Mo elements on the mechanical properties of equimolar TiVNbTa refractory high-entropy alloy

The addition of alloying elements would improve the properties of refractory high-entropy alloys at room temperature and high temperatures. Hf, Zr and Mo elements were added in TiVNbTa refractory high-entropy alloys. Mechanical properties and microstructures after deformation were studied through compressive and tensile tests and microstructural characterization. Hf, Zr and Mo elements would increase the ambient strength of TiVNbTa alloy owing to increased atomic size difference and shearing modulus difference. However, Zr and Mo would deteriorate the ambient ductility, and Hf and Zr would decrease the high-temperature strength owing to lower shearing modulus and melting points. Moreover, the Zr-enriched BCC phase would precipitate after compression at 1000°C.

Crystal structure design and chemical stability of radionuclides immobilized on high-entropy garnet ceramics

High-entropy (HE) wasteforms has attracted extensive attention because of its low solubility and the ability to immobilize a variety of nuclides. The atomic size difference (δ) is a necessary condition for designing HE garnet wasteforms (8.29 % ≤ δ ≤ 11.28 %). The leaching experiment shows that the leaching rate of simulated nuclides in the prepared HE garnet wasteforms is about 10-7–10-9 g m-2 · d-1, which is far lower than that of traditional garnet (10-5–10-6 g m-2 · d-1). The dissolution of HE garnet wasteforms cations into the leaching solution is carried out through internal diffusion. The extremely low leaching rate is mainly due to lattice distortion requires greater energy for the movement of cationic in the lattice. This work indicates that HE garnet wasteforms are a noteworthy substrate for immobilizing nuclides.

Effects of atomic size mismatch on glass transition decoupling in high-entropy metallic glasses

The calorimetric and dynamical glass transitions are uncoupled in high entropy metallic glasses (HEMGs). That is, the thermal glass-transition or vitrification temperature (Tg) and α-relaxation temperature (Tα) are uncorrelated as a function of alloy stoichiometry. The underlying mechanism that gives rise to this is not understood, nor is the connection to atomic structure. Here, molecular dynamic (MD) simulations of different HEMG model systems are performed to investigate the glass transition behavior. In addition to the high configurational entropy of mixing (for an ideal solution), we show that the effect of mismatch entropy plays a critical role in decoupling vitrification kinetics/α-relaxation in HEMGs. Microscopically, the atomic size difference contributes significantly to the sluggishness of long-range diffusion and decreased dynamic heterogeneities. This gives rise to a depressed structural α-relaxation. More importantly, we find that HEMGs with the decoupling vitrification kinetics/α-relaxation can show unique mechanical performance, such as better radiation tolerance and higher resistance to shear banding. Our results provide insights into the high entropy effect of glassy metallic materials, and suggest a means for tuning properties of HEMGs.

Design and Development of High-Entropy Alloys with a Tailored Composition and Phase Structure Based on Thermodynamic Parameters and Film Thickness Using a Novel Combinatorial Target.

This study presents a novel synthesis route for high-entropy alloys (HEAs) and high-entropy metallic glass (HEMG) using radio frequency (RF) magnetron sputtering and controlling the HEA phase selection according to atomic size difference (δ) and film thickness. The preparation of HEAs using sputtering requires either multitargets or the preparation of a target containing at least five distinct elements. In developing HEA-preparation techniques, the emergence of a novel sputtering target system is promising to prepare a wide range of HEAs. A new HEA-preparation technique is developed to avoid multitargets and configure the target elements with the required components in a single target system. Because of a customizable target facility, initially, a TiZrNbMoTaCr target emerged with an amorphous phase owing to a high δ value of 7.6, which was followed by a solid solution (SS) by lowering the δ value to 5 (≤6.6). Thus, this system was tested for the first time to prepare TiZrNbMoTa HEA and TiZrNbMoTa HEMG via RF magnetron sputtering. Both films were analyzed using X-ray diffraction (XRD), X-ray photoelectron spectroscopy, field emission scanning electron microscopy cross-sectional thickness, and atomic force microscopy (AFM). Furthermore, HEMG showed higher hardness 10.3 (±0.17) GPa, modulus 186 (±7) GPa, elastic deformation (0.055) and plastic deformation (0.032 GPa), smooth surface, lower corrosion current density (Icorr), and robust cell viability compared to CP-Ti and HEA. XRD analysis of the film showed SS with a body-centered cubic (BCC) structure with (110) as the preferred orientation. The valence electron concentration [VEC = 4.8 (<6.87)] also confirmed the BCC structure. Furthermore, the morphology of the thin film was analyzed through AFM, revealing a smooth surface for HEMG. Inclusively, the concept of configurational entropy (ΔSmix) is applied and the crystalline phase is achieved at room temperature, optimizing the processing by avoiding further furnace usage.

Prediction of phases in high entropy alloys using machine learning

Predicting the phases of high entropy alloys (HEAs) is a complex task as it depends on a large number of thermal, physical and geometrical parameters. The phases consist of intermetallic (IM) and amorphous (AM) forms. As, the trial-and-error approach is exhaustive and time-consuming process for both experiments and numerical simulations. Standard statistical models such as XGboost, random forest, adaboost, decision tree, logistic regression, support vector machine (SVM) and k-nearest neighbors (KNN) were adopted. The XGboost algorithm yields the better accuracy (90 %). Machine learning methods well predicted the phases and also identified the main significant variables such as mean atomic radius, atomic size difference, mixing enthalpy, ideal mixing entropy and valence electron concentration, which are in consistence with experimental results. As a whole, it is recommended that the widespread use of machine learning approaches could accelerate HEA process with tailored configurations. The use of multiple models in ensemble learning reduces the risk of overfitting, increases the accuracy of predictions, and enhances the generalizability of models.

On the influence of enthalpy of formation on lattice distortion and intrinsic ductility of concentrated refractory alloys

Valence electron concentration (VEC), atomic size difference (δ), and Pugh’s ratio (B/G) are a few of the empirical parameters widely used to design ductile refractory alloys. Here, we used the intrinsic ductility parameter (D), which is the ratio of surface energy (γs) and unstable stacking fault energy (γusfe), to design ductile refractory alloy. We found that the D correctly captures the experimentally observed ductility in concentrated refractory alloys. Here, we studied the enthalpy of formation (ΔEf), lattice distortion, and D of 9 refractory metals and 36 equiatomic refractory alloys using density functional theory simulations. We found that the ΔEf strongly influences the D of concentrated refractory alloys. The positive ΔEf and δ lead to large lattice distortion in concentrated refractory alloys. However, we did not find a strong correlation between lattice distortion and D in the presently studied alloys. We found that the success of VEC and Pugh’s ratio in designing ductile refractory alloys has a strong dependence on the underlying ΔEf of the alloy. We have developed a bottom-up method, which drastically reduces the number of alloys to be studied, to design ductile concentrated refractory alloys that can be thermodynamically stable.

CoFeNiTix and CrFeNiTix high entropy alloy thin films microstructure formation

High entropy alloys (HEA) composition-structure relationships are crucial for guiding their design and applications. Here, we use a combined experimental and molecular dynamics (MD) approach to investigate phase formation during physical vapor deposition (PVD) of CoFeNiTix and CrFeNiTix HEA thin films. We vary titanium molar ratio from 0 to 1 to understand the role of a larger element in the alloy mixture. The experiments show that a high titanium content favors amorphous phase formation in the samples produced by magnetron co-sputtering. In contrast, a low titanium content results in the formation of a face-centered cubic (FCC) structure in both HEA families. This effect of titanium content on the stability of the amorphous and FCC phases is reproduced in PVD MD simulations. The threshold titanium molar ratio is identified to be ∼0.53 and ∼0.16 for the CoFeNiTix and CrFeNiTix films in the experiments, and ∼0.53 and ∼0.53 in the MD simulations. In addition, the atomistic modeling allows for energy versus volume calculations with increasing titanium content, which demonstrate the stabilization of the amorphous phase with respect to crystalline structures. To isolate the effect of atomic sizes, additional simulations are performed using an average-atom model, which disregards differences in atomic radii while preserving the average properties of the alloy. In these simulations, the energetic stability of the amorphous phase disappears. The combined experimental and simulation results demonstrate that the formation of the amorphous phase in HEA thin films generated by PVD is directly caused by the atomic size difference.

Unravel hardening mechanism of AlCrNbSiTi high-entropy alloy coatings

Novel high-entropy alloys (HEAs) coatings deposited using physical vapour deposition technique are potential candidates of protective coatings due to their excellent performance. However, the correlation between properties and microstructure of HEAs coatings has not been completely established and the hardening mechanism remains unclear. In this paper, the AlCrNbSiTi HEA coatings were deposited under different bias voltages by radio-frequency magnetron sputtering. The morphology, chemical composition, structure, mechanical properties and thermal stability are discussed in detail. All coatings exhibit smooth surface without obvious elemental segregation and the columnar structure tends to densify with increasing bias. The coatings possess a nanocomposite structure of amorphous-nanocrystalline silicides, in agreement with the results calculated based on three phase prediction parameters (ΔHmix: enthalpy of mixing, δ: atomic size difference and Ω: ratio of entropy of mixing ΔSmix to ΔHmix). The coating deposited at bias of − 50 V presents optimal mechanical properties with nanohardness of ∼15.2 GPa, scratch crack propagation resistance of 1042 N2 and wear rate of 5.4 × 10−8 mm3N−1m−1. Annealing treatment further unravels that the presence of hard silicides is the hardening mechanism of coatings with super-hardness of ∼24 GPa. The results indicate that the AlCrNbSiTi coating is a promising protective coating with broad industrial application prospects.

An end-to-end machine learning framework exploring phase formation for high entropy alloys

Exploring the rules of high entropy alloys (HEAs) phase formation has clear guiding significance for the design of new alloys. An end-to-end framework was proposed to select the feature subset and machine learning (ML) model from the feature pool and model pool, respectively. In this framework, each model in the pool is to determine its materials feature subset based on the feature importance. The final model was confirmed through the evaluation of the fitting result of every model and its feature subset. This method extracts important factors affecting the phase formation of HEAs. The results show that the chosen model could classify 430 HEAs into five phases, with test accuracy of 87.8%. And the model analysis suggests that the formation of single-phase solid solution is often inhibited when the atomic size difference is greater than 8.295%.

Prediction of glass-forming ability in ternary alloys based on machine learning method

In this paper, six machine learning (ML) models including k-nearest neighbour, adaptive boosting, gradient boosting regression tree, extreme gradient boosting tree, support vector regression (SVR) and random forest were built in the frame of ternary alloys to predict the critical size of glass formation (Dmax) based on 840 alloy data. Composition, atomic size difference, enthalpy of mixing, electronegativity difference, and valence electron concentration were selected as input features. The features were selected by Pearson correlation analysis and target value of Dmax was transformed into the logarithmic form. The determination coefficient and root mean square error were used to evaluate the prediction performance of models. The result showed that the SVR model has a good generalization ability. Additionally, the prediction ability of SVR was verified in Zr−Al−Co and La−Al−Co alloy systems. It is thus suggested that ML has great potential in predicting and pinpointing the amorphous composition with good glass-forming ability.

Resistance of amorphous TiAlCrZrSi/polyimide high entropy alloy films to atomic oxygen erosion

To alleviate the atomic oxygen (AO) degradation of the polyimide deployed in the low Earth orbit (LEO) environment, we fabricate a set of amorphous TiAlCrZrSi/polyimide films under various negative bias values via the 3rd generation co-filter cathode vacuum arc (C-FCVA). Our rational technical design realizes the noninterference regulation and filtration of mixed multielement plasma compositions. In addition, the atomic size difference (δ, 0.075–0.081), mixing enthalpy (ΔHmix, −48.98 to −46.84 kJ mol−1), and mixing entropy (ΔSmix, 12.83–12.91 J K−1 mol−1) are all within the range of parameters required for the formation of amorphous TiAlCrZrSi high-entropy alloys (HEAs). Moreover, the TiAlCrZrSi/polyimide (no bias) film can realize an equilibrium of AO resistance and durability (Ey = 2.02 × 10−26 cm3 atom−1), which is only 0.67 % of that calculated for pristine polyimide. This can be attributed to the excellent AO penetration barrier ability of the generated HEA oxide scales. Furthermore, the thickening of HEA films can reduce the sensitivity of residual defects to AO undercutting erosion, as discussed by the existing empirical theoretical models.

Ab initio study of effects of Al on the defect behaviors of AlxCoCrFeNi high entropy alloys

The influence of Al on the defect behaviors of AlxCoCrFeNi high-entropy alloys (HEAs) is studied by ab initio calculations. The lattice distortion, defect formation energies, and defect migration energies were calculated for different Al concentrations ranging from 0 to 6.25 at. %. First, the increase in the lattice distortion of AlxCoCrFeNi by the addition of Al is demonstrated, but the increment is smaller than that predicted by the atomic size difference of constituent elements. Second, although formation energies of Al vacancies and dumbbells containing Al are higher, the addition of Al decreases the average formation energies of vacancies and interstitials, which is probably due to the Al-induced local strain field and lattice distortion. The migration energies of interstitials and vacancies exhibit opposite variations, the migration energies of interstitials are increased while that of vacancies are decreased with the Al content. Moreover, the distributions of formation and migration energies of both defects are significantly broadening with increasing Al content, which could further enhance the characteristic effects of HEAs and play a more important role in the irradiation resistances of HEAs. Based on the calculation results, the effects of Al on the irradiation responses of AlxCoCrFeNi are discussed.

Formation of Zr-rich BCC phase and its relation on the hydrogen storage properties of TiVNbZr high entropy alloy

Due to the large difference in atomic size between Zr and Nb, TiVNbZr high entropy alloy possesses greater lattice distortion. The change of Zr content can affect the stability of hydrides, which can have an important impact on the hydrogen storage performance. In order to explore the effect of Zr/Nb on hydrogen storage properties, Ti32.5V27.5Nb40-xZrx (x = 7.5, 10, 12.5, 15) high entropy alloys composed of BCC phase are designed. It is found that with the increase of Zr/Nb, the dendritic microstructures first disappear and then gradually become coarse. The Zr-rich BCC phase and the Nb-rich BCC phase appear in the interdendritic and dendritic regions, respectively. Ti32.5V27.5Nb25Zr15 shows excellent activation performance, which is related to the Zr-rich BCC phase with the most catalytic phase on the surface. The hydrogen storage performance of low Zr/Nb composition is better at low temperature, and that of high Zr/Nb composition becomes better after rising to high temperature. This is because with the change of Zr/Nb, low temperature can promote the hydrogen absorption reaction and high temperature can increase the diffusion rate of hydrogen atoms in the interstitial positions of the alloy. Ti32.5V27.5Nb32.5Zr7.5 achieves the best hydrogen absorption capacity of 1.71 wt % at 150 °C. All components undergo a transition from the BCC phase to the FCC phase during the hydrogen absorption process, and then change to a single-phase BCC structure after dehydrogenation. With the increase of Zr content, the first step desorption temperature raises in turn, owing to the stronger thermal stability of hydride.

Effects of lattice distortion and chemical short-range ordering on the incipient behavior of Ti-based multi-principal element alloys: MD simulations and DFT calculations

One of key factors in designing high-performance alloys is to understand their incipient behavior. To get detailed real-time atomic scale evolutions of multi-principal element alloys (MPEAs) during nanoindentation incipient yielding, molecular dynamics (MD) simulations were carried out. Emphases are given to the effects of lattice distortion (LD) and chemical short-range ordering (CSRO) on the initiation of plasticity in body-centered cubic (BCC) MPEAs. The initial plastic mechanism is embryo nucleation assisted and the incipient behavior is strongly affected by LD and CSRO. Specifically, the embryo nucleation load Pe is reduced by LD and CSRO and the incipient drop P0 is lowered by LDI that only comes from atomic size difference and further declined by CSRO. This is because LD and CSRO could boost embryo nucleation, which can act as precursors for dislocation nucleation. This is consistent with the free-end nudged elastic band observations. Although Pe is weakened by LDII generated by introducing extra elements, P0 is intensified because severe LD could dominate the following process. The dislocation starvation mechanism is found in an average-atom (AA) model. However, it is replaced by dislocation interactions due to LD and CSRO. Density functional theory (DFT) calculations suggest that charge density distribution and the amount of directional Al-Al bonding would play a critical role in the onset of plastic deformation. When a larger indenter radius was used in MD simulations, the dislocation starvation mechanism is absent in AA model due to the reduced maximum shear stress. Instead, the dislocation propagation prevails. With respect to the orientation effect, three investigated orientations demonstrate a distinct yielding behavior.

Revisiting the phase stability rules in the design of high-entropy alloys: A case study of quaternary alloys produced by mechanical alloying

High-entropy alloys (HEAs) are potential candidates for many structural applications because of their outstanding mechanical properties. Achieving solid solution (SS) in HEAs is desirable since intermetallic compounds (IMs) can, in most cases, be deleterious. While empirical phase stability rules have been widely used to predict SS or IM phases in HEAs, there are substantial reported cases of their breakdown. To assess the effectiveness of the empirical rules—atomic size difference (δ), mixing enthalpy (ΔHmix), mixing entropy (ΔSmix), entropy to enthalpy ratio (Ω), electronegativity difference (△χ), and valence electron concentration (VEC), a systematic study that isolates the effect of processing pathway was conducted. As a starting point and as a benchmark, an existing equiatomic AlCoCrFe BCC HEA was correctly predicted (following the classical empirical rules) and developed. This was followed by the SS FCC prediction and development of five novel semi-equiatomic AlTiCuZn-based quaternary HEAs (Al0.57TiCuZn, AlTi0.45CuZn, Al0.45TiCuZn, AlTiCu1.76Zn, and AlTiCu2Zn) by mechanical alloying. Among the AlTiCuZn-based HEAs, only AlTi0.45CuZn showed SS, but with FCC + HCP phase contradicting the traditional VEC rule that predicts FCC. Using AlTi0.45CuZn as a guide, conservative SS formation criteria for AlTiCuZn-based HEAs were determined—Ω≥ 1.6, δ≤ 5%, and ΔHmix≥ -8 kJ/mol, while retaining conventional ΔSmix and △χ range. Also, FCC + HCP phase formation is stable at 7.5 ≤VEC≤ 8.4. The revised rules were verified by correctly predicting the phases in newly-fabricated non-equiatomic HEAs—AlTi0.37CuZn0.97 and AlTi0.56Cu1.24Zn1.2. This study shows that the range of empirical phase stability model values is not fixed, but alloy-dependent due to the differences in bonding nature of HEA-constituting elements.

Prediction of phase selection of amorphous alloys and high entropy alloys by artificial neural network

To avoid the lack of unified physical significance of the random combination of characteristic parameters, and to solve the problem that there are many factors influencing the phase selection by multiple parameters, four characteristic parameters with potential energy distribution were selected to predict the phase selection of three type of amorphous alloys (AM), solid solution alloys (SS) and high entropy alloys containing intermetallic compounds (IM) by artificial neural network (ANN) in machine learning. To improve the prediction accuracy, the combination of three different parameters can be used to predict the phase of AM and IM alloys, and the combination of four different parameters can be used to predict the phase of SS alloys. For the AM and IM alloys, the partial three parameter combinations with the lowest mean square error (MSE) values have highest prediction accuracy, for SS alloys, the four parameter combination with the lowest MSE value has highest prediction accuracy. Based on the correspondence between the correlation coefficient (R) values and the prediction accuracy, it can be concluded that the current ANN model is accurate in predicting the phase selection of three type of alloys, and is the good learning model. The sensitivity matrix (S) values indicate that the atomic size difference (δ) have a greater impact on the phases of AM, SS and IM alloys; however, the corresponding S values of mixing enthalpy (ΔHm) in the AM and SS alloys have the weak influence. The current learning model and the combination of three or four characteristic parameters can predict the AM and SS phase varified by X-ray diffraction of new Ti-Cu-Ni-Zr (AM) and Fe-Co-Ni-Cu-Ti (SS) alloys, thus accelerating the composition design and phase composition selection of new alloys.

Compositionally tailored order-disorder of cation-anion sublattices in Cu2Te1-xSx solid solution thermoelectric materials

High performance thermoelectric Cu2Te1-xSx solid solutions can surprisingly be formed over a wide compositional range even with big atomic size difference between S and Te. The Cu sublattice has been found to be partially ordered and even shows amorphous substructures in some compositions, while S/Te is considered to form a chemically disordered yet crystalline sublattice. However, precise order-disorder configurations of cation-anion sublattices and their evolution upon compositional change still remain unclear. Meanwhile, the appearance of diffuse reflections on the electron diffraction patterns suggests occurrence of short-range order whose structures are not yet solved. Here, atomic structures of Cu2Te1-xSx (x = 0.1, 0.2, 0.4, 0.5, 0.6 and 0.8) have been investigated by transmission electron microscopy in both real and reciprocal spaces. The high-angle annular dark field atomic imaging indicates an approximate hexagonal stacking for S/Te atoms in all solution compositions. However, location of Cu atoms in numerous interstices of the chalcogen sublattice varies by S/Te atomic ratio, leading to change in order-disorder configurations of Cu or even nanoscale phase separation. Diffuse scattering with different geometries are identified to arise from chemical short-range order in forms of sulphur-rich atomic layers on (0001) and lath-like tellurium aggregation on {10-10}. The as-observed compositionally tailored solid solution structures and short-range order structures are found to be strongly correlated to the electron and phonon transportation in Cu2Te1-xSx. The present work indicates a promising strategy for designing solid solutions having large atomic-size mismatch which may generate abundant order/disorder atomic configurations hence greatly improve the thermoelectric properties.

Phase stability and possible superconductivity of new 4d and 5d transition metal high-entropy alloys

We report the synthesis of new equimolar high-entropy alloys formed from five or six 4d/5d transition metals that are each from a different Group of the Periodic Table. These include MoReRuRhPt and MoReRuIrPt, which appear to crystallise as single hexagonal close-packed phases and so are isostructural and isoelectronic to the high-pressure phase of the well-known high-entropy alloy CrMnFeCoNi. Other compositions crystallise as mixed phases, which we rationalise using the atomic size difference, δ, and the electronegativity difference, Δχ, of the constituent elements. Finally, we find signs of superconductivity in eight of these new systems.

Short-range order and compositional phase stability in refractory high-entropy alloys via first-principles theory and atomistic modeling: NbMoTa, NbMoTaW, and VNbMoTaW

Using an all-electron, first-principles, Landau-type theory, we study the nature of short-range order and compositional phase stability in equiatomic refractory high-entropy alloys, NbMoTa, NbMoTaW, and VNbMoTaW. We also investigate selected binary subsystems to provide insight into the physical mechanisms driving order. Our approach examines the short-range order of the solid solutions directly, infers disorder/order transitions, and also extracts parameters suitable for atomistic modeling of diffusional phase transformations. We find a hierarchy of relationships between the chemical species in these materials which promote ordering tendencies. The most dominant is a relative atomic size difference between the $3d$ element, V, and the other $4d$ and $5d$ elements which drives a $B32$-like order. For systems where V is not present, ordering is dominated by the difference in filling of valence states; pairs of elements that are isoelectronic remain weakly correlated to low temperatures, while pairs with a valence difference present $B2$-like order. Our estimated order-disorder transition temperature in VNbMoTaW is sufficiently high for us to suggest that SRO in this material may be experimentally observable.