Atomic Size Effect Research Articles

Atomic-size and lattice-distortion effects in newly developed high-entropy alloys with multiple principal elements

A critical issue of atomic-size effects in the new class of metallic materials, high entropy alloys (HEAs), containing multi-principal alloying elements is addressed by considering the intrinsic lattice distortion. Although the development effort on these new HEAs has revealed the potential of HEAs for elevated temperature applications, a clear physical description of lattice distortions in these advanced alloys containing different atomic sizes is still lacking at the present time. In this study, we proposed a new model to address the lattice distortion of crystalline lattices in these alloys, and a series of physical parameters to address the atomic-size difference can then be defined. The optimal parameter, α2, is found to be effective in explaining the lattice distortion, intrinsic strain energy and excess entropy in HEAs, as well in other multicomponent alloy systems.

Atomic-size effect and solid solubility of multicomponent alloys

In physical metallurgy, solid solubility of alloys is known to play a vital role in determining their physical/mechanical properties. Hume–Rothery rules show the great effect of size difference between solvent and solute atoms on the solid solubility of binary alloys. However, modern multicomponent systems, such as high-entropy alloys, defy the classic atomic size effect due to the absence of solvent and/or solute atoms. Here, we propose an effective atomic size parameter by considering atomic packing misfitting in multicomponent systems.

Formation of Tsai-type 1/1 approximants in In-Pd-RE (RE: rare earth metal) alloys

The formation of the 1/1 crystal approximant phase (1/1 phase) to the icosahedral phase (i phase) in In-Pd-RE (RE: rare earth metal) systems has been investigated. A new series of 1/1 phases were found in In53Pd33RE14 (RE; Y, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, and Tm) alloys. For Y, Sm, Gd, Tb, Dy, and Ho, the 1/1 phases were found in annealed alloys, indicating that they are thermodynamically stable. The atomic structure of the 1/1 phases was directly observed by high-angle annular dark-field imaging performed via scanning transmission electron microscopy, revealing that the 1/1 phases consisted of a periodic arrangement of Tsai-type icosahedral clusters. Further, the atomic size effect on i phase formation, as well as formation conditions previously reported for other Tsai-type i and 1/1 phases were examined. It was found that the ratio of the atomic radius of base metals such as In and Pd affects i phase formation. Moreover, the appropriate range of the radius ratio for i phase formation was narrower than that for 1/1 phase formation.

Ageing Characteristics of Al-Mg-(Ge,Si)-Cu Alloys

In order to elucidate some of the differences between Al-Mg-Si and Al-Mg-Ge alloys and the role of Cu, a series of Al-Mg-Ge, Al-Mg-Si and Al-Mg-Ge-Si alloys, some of them containing Cu, are investigated by positron annihilation lifetime spectroscopy during natural ageing. Al-Mg-Ge alloys show qualitatively the same evolution of positron lifetime τ1C with time as Al-Mg-Si alloys, namely an initial decrease, followed by a re-increase, after which τ1C drops to an equilibrium value. However, for alloys with equal Mg contents, Ge gives rise to a notably slower ageing kinetics than Si, pointing at effects of atomic size or solute-vacancy binding energies. Adding Cu to both Al-Mg-Ge and Al-Mg-Si alloys slows down the initial formation of clusters but promotes their further growth.

Progress in Visualizing Atomic Size Effects with DFT-Chemical Pressure Analysis: From Isolated Atoms to Trends in AB5 Intermetallics.

The notion of atomic size poses an important challenge to chemical theory: empirical evidence has long established that atoms have spatial requirements, which are summarized in tables of covalent, ionic, metallic, and van der Waals radii. Considerations based on these radii play a central role in the design and interpretation of experiments, but few methods are available to directly support arguments based on atomic size using electronic structure methods. Recently, we described an approach to elucidating atomic size effects using theoretical calculations: the DFT-Chemical Pressure analysis, which visualizes the local pressures arising in crystal structures from the interactions of atomic size and electronic effects. Using this approach, a variety of structural phenomena in intermetallic phases have already been understood in terms that provide guidance to new synthetic experiments. However, the applicability of the DFT-CP method to the broad range of the structures encountered in the solid state is limited by two issues: (1) the difficulty of interpreting the intense pressure features that appear in atomic core regions and (2) the need to divide space among pairs of interacting atoms in a meaningful way. In this article, we describe general solutions to these issues. In addressing the first issue, we explore the CP analysis of a test case in which no core pressures would be expected to arise: isolated atoms in large boxes. Our calculations reveal that intense core pressures do indeed arise in these virtually pressure-less model systems and allow us to trace the issue to the shifts in the voxel positions relative to atomic centers upon expanding and contracting the unit cell. A compensatory grid unwarping procedure is introduced to remedy this artifact. The second issue revolves around the difficulty of interpreting the pressure map in terms of interatomic interactions in a way that respects the size differences of the atoms and avoids artificial geometrical constraints. In approaching this challenge, we have developed a scheme for allocating the grid pressures to contacts inspired by the Hirshfeld charge analysis. Here, each voxel is allocated to the contact between the two atoms whose free atom electron densities show the largest values at that position. In this way, the differing sizes of atoms are naturally included in the division of space without resorting to empirical radii. The use of the improved DFT-CP method is illustrated through analyses of the applicability of radius ratio arguments to Laves phase structures and the structural preferences of AB5 intermetallics between the CaCu5 and AuBe5 structure types.

Universal local strain in solid-state amorphization: The atomic size effect in binary alloys

The atomic size effect in binary alloy systems during solid-state amorphization by particle irradiation is studied using molecular dynamics simulations. The critical dosage of irradiation for amorphization is decreased by increasing the atomic size mismatch or the solute concentration. The analysis of the atomic level strain shows that that the atomic-level strain distribution depends on the atomic species in the crystalline lattice, while it is almost the same in all glass systems. Amorphization occurs when the atomic-level strain reaches the universal critical value, which is independent of packing fraction, density, concentration and atomic size ratio. The nature of the universal strain is discussed in relation to the glass transition phenomenon.

Structure and Growth Mechanism of V/Ag Multilayers with Different Periodic Thickness Fabricated by Magnetron Sputtering Deposition

V/Ag multilayers with different periodic thicknesses were fabricated by magnetron sputtering deposition. The columnar structure and the orientation relationship of the multilayers were investigated by transmission electron microscopy, high resolution transmission electron microscopy, selected-area electron diffraction and X-ray diffraction. It was found that the multilayered structure became flatter as increasing individual layer thickness from 2 to 6 nm, and then became waved as the individual layer thickness increases to 8 nm. At the beginning of the growth, the morphology of the multilayers with small periodic thickness was influenced mainly by thermodynamic instabilities, and the morphology of the multilayers with larger periodic thickness was mainly influenced mainly by the columnar growth of V. When the waved interfaces were formed, the continuum growth of the multilayers was also influenced by the shadowing effect and the finite atomic size effect. All of these factors resulted in the columnar structure of the multilayers. Multilayers with small periodic thickness presented strong orientation relationship. Nano-hardness tests indicated that multilayers with flat sublayer morphology and clear interfaces exhibited larger hardness.

First-principles study of the stability and migration of Kr, I and Xe in ZrO2

The stability and migration of Kr, I and Xe in bulk ZrO2 and on the ZrO2 (111) surface have been studied by standard density functional theory (DFT) and the DFT-D2 method that corrects for the van der Waals interaction. Both methods show that Kr and Xe prefer to incorporate in the bulk phase rather than adsorb on the surface, and Xe is very mobile in the bulk state. For Kr and Xe adsorption on the surface, van der Waals interaction dominates, causing the weak interaction between the adsorbate and substrate. Iodine is found to have comparable stability in both phases and forms 〈I–O〉 bonds with strong covalency. It exhibits higher mobility on the surface than in the bulk ZrO2, and diffusion from bulk-like state to surface state is an exothermic process. The fission product behavior in ZrO2 is shown to be a complicated synergetic effect of fission product atomic size, electron negativity, occupation site and phase structure of the host.

Atomic distribution, local structure and cation size effect in o-R1−xCaxMnO3 (R = Dy, Y, and Ho)

We propose new interatomic potentials for the small rare-earth-based orthorhombic RMnO3 (R = Dy, Y, Ho), which accurately model the structural properties of these extreme cases of lanthanide manganate series. They are further employed to investigate the intrinsic defects in o-RMnO3 and the cation distribution and local structure in o-R1−xCaxMnO3 (R = Dy, Y, Ho). Schottky disorders are found to be the dominant structural defects, and the possibility of a small degree of anti-site disorder of R and Mn ions over A and B sites is found. The introduced Ca dopants tend to form chemically and structurally like CaMnO3 clusters in the lightly doped system, which can be regarded as representations of microscopic phase separation. The local structural disorder is reduced with increasing doping density. For o-R0.5Ca0.5MnO3 (R = Dy, Y, Ho), the charge ordering state is intrinsically favored, and the layer stripe model is shown to be energetically more favorable and structurally more reasonable. Moreover, the tendency to form charge ordered stripes increases with the decrease of R size. The local structure in the layer stripe pattern deviates largely from the average structure: RMnO3-like and CaMnO3-like layers are formed. The size of R ion has a significant influence on the doping effect on Jahn–Teller (JT) distortion and a manganate with a larger R will experience a larger reduction on the anisotropy of Mn–O bonds in Mn3+O6 octahedra. However, the change of octahedral tilting upon doping does not vary much with R radii.

First-Principles Elucidation of Atomic Size Effects Using DFT-Chemical Pressure Analysis: Origins of Ca36Sn23's Long-Period Superstructure.

The space requirements of atoms are empirically known to play key roles in determining structure and reactivity across compounds ranging from simple molecules to extended solid state phases. Despite the importance of this concept, the effects of atomic size on stability remain difficult to extract from quantum mechanical calculations. Recently, we outlined a quantitative yet visual and intuitive approach to the theoretical analysis of atomic size in periodic structures: the DFT-Chemical Pressure (DFT-CP) analysis. In this Article, we describe the methodological details of this DFT-CP procedure, with a particular emphasis on refinements of the method to make it useful for a wider variety of systems. A central improvement is a new integration scheme with broader applicability than our earlier Voronoi cell method: contact volume space-partitioning. In this approach, we make explicit our assumption that the pressure at each voxel is most strongly influenced by its two closest atoms. The unit cell is divided into regions corresponding to individual interatomic contacts, with each region containing all points that share the same two closest atoms. The voxel pressures within each contact region are then averaged, resulting in effective interatomic pressures. The method is illustrated through the verification of the role of Ca-Ca repulsion (deduced earlier from empirical considerations by Corbett and co-workers) in the long-period superstructure of the W5Si3 type exhibited by Ca36Sn23.

Structure of liquid Cu–Sb alloys by ab initio molecular dynamics simulations, high temperature X-ray diffraction, and resistivity

Structure of Cu–Sb melts has been studied by ab initio molecular dynamics simulations, high-temperature X-ray diffraction and resistivity measurements. Over the whole concentration range, heterogeneous coordination numbers are larger than that of homogeneous atoms. This indicates preferential Cu–Sb coordination in Cu–Sb melts. A drop is observed in maximum position of simulated Sb–Sb partial distribution functions around Cu75Sb25, which reveals the rapid increase of Sb–Sb coordination. Around eutectic melts, main peak splitting is observed in both structure factor and simulated total pair distribution functions, which reveals the co-existence of Cu–Sb heterogeneous and Sb–Sb clusters. Abnormal changes in temperature coefficient of resistivity are observed around pure Sb and in compound-forming range, which are well interpreted as reinforcement of Peierls distortion and Cu3Sb compound clusters, respectively. Structural inhomogeneity that results from atomic size effect also has been discussed by analyzing concentration dependence of Warren–Cowley parameters and concentration correlation functions.

Alloy microstructures with atomic size effects: A Monte Carlo study under the lattice statics formalism

We present in this paper atomic scale Monte Carlo simulations of microstructure evolutions in the presence of atomic size mismatch, performed on a rigid lattice. The lattice statics formalism is used to obtain effective pair interactions (EPIs) from a continuous empirical description of alloy energetics that includes elastic relaxations in the harmonic approximation. These EPIs are long-ranged and are introduced in a Monte Carlo scheme to compute alloy properties. The influence of atomic size mismatch on EPIs as well as on microstructure evolutions is investigated in the case of a model binary fcc alloy. The microstructure evolution with atomic size mismatch operates mainly by shape changes and by the development of spatial correlations between precipitates. Our aim is also to provide a method to include elastic effects at the atomic scale starting from material macroscopic data, without any requirement of realistic continuous interatomic potential calibration. A commonly found approach in microscopic mean-field simulations is to use, at the atomic scale, effective elastic interactions inherited from continuum linear elasticity. We derive here a different and original method: the discrete lattice approach (DLA) that both converges to the continuum theory of elasticity (long-range aspect) and takes into account the discreteness of the lattice. It allows us to correctly reproduce the whole range of elastic interactions, down to the atomic scale, successfully improving the simple use of continuum elasticity, without the prior knowledge of any interatomic potential. Finally, the accuracy of the DLA is quantitatively verified through a detailed comparison between the microstructural evolutions obtained with this approach and the original lattice statics approach.

Roles of Zr and Y in cast microstructure of M951 nickel-based superalloy

The influence of Zr and Y on the cast microstructure of a nickel-based superalloy was investigated by optical microscopy (OM), scanning electron microscopy(SEM), electron probe micro-analysis (EPMA) and X-ray diffraction (XRD). The γ+γ′ eutectic volume in the superalloy rises notably with the increase of Zr or Y content. Meanwhile, the morphologies of primary MC carbides change from needle and platelet-like to blocky shape with increasing Zr and Y doped. The XRD results show that the primary MC carbide lattice constant increases with Zr and Y additions, and EPMA investigation shows that the platelet-like MC carbides contain primarily Nb and C, while those carbides in blocky shape have 39.2% Zr and 39.6% Nb in average,. These influences on the cast microstructure can be attributed to the atomic size effects of Zr and Y.

Site occupation behavior of sulfur and phosphorus in NiAl, TiAl and FeAl

The site occupation behavior of sulfur and phosphorus in the binary NiAl, TiAl and FeAl alloys is investigated by first-principles calculations. Using a supercell approach, the enthalpies of formation of vacancies, antisites, and substitutional defects are calculated for the three binary alloys. The distributions of S and P in the three alloys and their dependence on Al composition are investigated based on a thermodynamical model. The predicted existence of the dominant defects agrees well with available experimental results and theoretical results. At 1273 K, P atoms occupy exclusively the Al sites in the three alloys, and S atoms occupy exclusively the Al sites in FeAl alloys. However, the concentration of S atoms occupying Ni (Ti) sites increases and that located at Al sites decreases as the Al content increases in NiAl (TiAl). These results cannot be determined from considering only the effects of atomic size and electronegativity on the site occupations. Instead, these results can be understood in terms of differences between the enthalpies of formation for impurity I occupying different sublattices coupled with the configurational entropy differences.

Plasmon energy and lattice energy of binary tetrahedral semiconductors and I–VII ionic compounds

Two simple empirical relations have been proposed to estimate lattice energy from plasmon energy and bond length of binary tetrahedral semiconductors A N B8−N (N = 2) and I–VII ionic solids. The estimated values are in excellent agreement with the experimental and reported values. Attempt has been made to give a physical basis of the proposed correlation it has been shown that the constants appearing in the proposed relation are characteristics of crystal structures. Effects of atomic size, coordination and ionicity on the lattice energy have also been discussed.

DFT-Chemical Pressure Analysis: Visualizing the Role of Atomic Size in Shaping the Structures of Inorganic Materials

Atomic size effects have long played a role in our empirical understanding of inorganic crystal structures. At the level of electronic structure calculations, however, the contribution of atomic size remains difficult to analyze, both alone and relative to other influences. In this paper, we extend the concepts outlined in a recent communication to develop a theoretical method for revealing the impact of the space requirements of atoms: the density functional theory-chemical pressure (DFT-CP) analysis. The influence of atomic size is most pronounced when the optimization of bonding contacts is impeded by steric repulsion at other contacts, resulting in nonideal interatomic distances. Such contacts are associated with chemical pressures (CPs) acting upon the atoms involved. The DFT-CP analysis allows for the calculation and interpretation of the CP distributions within crystal structures using DFT results. The method is demonstrated using the stability of the Ca(2)Ag(7) structure over the simpler CaCu(5)-type alternative adopted by its Sr-analogue, SrAg(5). A hypothetical CaCu(5)-type CaAg(5) phase is found to exhibit large negative pressures on each Ca atom, which are concentrated in two symmetry-related interstitial spaces on opposite sides of the Ca nucleus. In moving to the Ca(2)Ag(7) structure, relief comes to each Ca atom as a defect plane is introduced into one of these two negative-pressure regions, breaking the symmetry equivalence of the two sides and yielding a more compact Ca coordination environment. These results illustrate how the DFT-CP analysis can visually and intuitively portray how atomic size interacts with electronics in determining structure, and bridge theoretical and experimental approaches toward understanding the structural chemistry of inorganic materials.

Examination of Bond Properties through Infrared Spectroscopy and Molecular Modeling in the General Chemistry Laboratory

A concerted effort has been made to increase the opportunities for undergraduate students to address scientific problems employing the processes used by practicing chemists. As part of this effort, an infrared (IR) spectroscopy and molecular modeling experiment was developed for the first-year general chemistry laboratory course. In the experiment, students explore the dynamic nature of the covalent bond in a hands-on, inquiry-based approach by experimenting with mass and spring systems, using molecular modeling software, and performing IR spectroscopy on a series of structurally related compounds. Students see the effect of bond order, atomic size, and molecular weight on bond strength, bond length, and vibrational frequency. As an added benefit, students are introduced to scientific instrumentation and tools that can then be expanded upon in later laboratory classes.

A New Model for the Configurational Entropy of Mixing in Liquid Alloys Based on Short-Range Order

A new model has been developed to calculate the configurational entropy of mixing in liquid alloys involving consideration of chemical and topological short-range order. The entropy of mixing for an equiatomic random mixture was naturally reached by this model. The application of this model to both hypothetic and real binary liquid alloys demonstrated that the chemical short-range order always decreased the configurational entropy of mixing, whereas complicated behavior was found with the atomic size effect. The configurational entropy of mixing increased when the larger atoms entered into the matrix of the smaller atoms, whereas it decreased when the smaller atoms were mixed into the matrix of the larger atoms. The maximum of the configurational entropy of mixing was not located at the eutectic composition in these alloys.

Microstructural characterization and amorphous phase formation in Co40Fe22Ta8B30 powders produced by mechanical alloying

In this work, microstructural evolution and amorphous phase formation in Co40Fe22Ta8B30 alloy produced by mechanical alloying (MA) of the elemental powder mixture under argon gas atmosphere was investigated. Milling time had a profound effect on the phase transformation, microstructure, morphological evolution and thermal behavior of the powders. These effects were studied by the X-ray powder diffraction (XRD) in reflection mode using Cu Kα and in transmission configuration using synchrotron radiation, transmission electron microscopy (TEM), scanning electron microscopy (SEM) and differential scanning calorimetry (DSC). The results showed that at the early stage of the milling, microstructure consisted of nanocrystalline bcc-(Fe, Co) phases and unreacted tantalum.Further milling, produced an amorphous phase, which became a dominant phase with a fraction of 96wt% after 200h milling. The DSC profile of 200h milled powders demonstrated a huge and broad exothermic hump due to the structural relaxation, followed by a single exothermic peak, indicating the crystallization of the amorphous phase. Further XRD studies in transmission mode by synchrotron radiation revealed that the crystalline products were (Co, Fe)20.82Ta2.18B6, (Co, Fe)21 Ta2 B6, and (Co, Fe)3B2. The amorphization mechanisms were discussed in terms of severe grain refinement, atomic size effect, the concept of local topological instability and the heat of mixing of the reactants.

Study of the Microstructure of High-Entropy Alloys AlFeCuCoNiCrTi<sub>X</sub> (x=0, 05, 1.0)

The microstructure of high-entropy Alloys AlFeCuCoNiCrTix (x=0, 05, 1.0) with different titanium contents had been studied. The results showed that: (1) The microstructure of AlFeCuCoNiCrTix exhibited the trend from dendritic structure to eutectic-cell structure as the titanium contents increasing and spinodal decomposition, nanoprecipitation and amorphous phase can be also observed; (2) Composition segregation appeared (especially Cu) and Ti promoted the segregation of Cu; (3) Alloys was consisted of FCC and BCC, and phases gradually converted from FCC+BCC1 to FCC+BCC1+BCC2 with addition of titanium and BCC2 became the leading phase; (4) Both ordering and spinodal decomposition coincided due to the difference of atomic size and high entropy effect.