Atomic Size Effect Research Articles

Calculation of the Viscosity of Zr-Based Metallic Glass Alloys

With the effects of electronic structure and atomic size being introduced, a revised model to calculate the viscosity of the bulk metallic glass alloys was proposed and the viscosity of ternary Zr-Al-Cu, Zr-Ni-Al and quaternary Zr-Al-Ni-Cu systems are calculated in this paper, and the computed results agree well with the empirical one. The sequence of viscosity of different systems is: VZr-Al-Cu <VZr-Al-Ni<.VZr-Al-Ni-Cu. To Zr-Al-Cu and Zr-Ni-Al, the highest viscosity locates in the composition range of XZr=0.37-0.86, XCu=0-0.40 and XZr = 0.45-0.79, XAl = 0.12-0.50, respectively. And to the Zr-Ni-Al-Cu system with 66.67% Zr, the highest viscosity is obtained in the region of XAl= 0.63-0.80, XNi = 0.14-0.24.

Atomistic simulation study of atomic size effects on B1 (NaCl), B2 (CsCl), and B3 (zinc-blende) crystal stability of binary ionic compounds

Ionic compounds exhibit a variety of crystal structures that can critically affect their applications. Traditionally, relative sizes of cations and anions have been used to explain coordination of ions within the crystals. Such approaches assume atoms to be hard spheres and they cannot explain the observed structures of some crystals. Here we develop an atomistic method and use it to explore the structure-determining factors beyond the limitations of the hard sphere approach. Our approach is based upon a calibrated interatomic potential database that uses independent intrinsic bond lengths to measure atomic sizes. By carrying out extensive atomistic simulations, striking relationships among intrinsic bond lengths are discovered to determine the B1 (NaCl), B2 (CsCl), and B3 (zinc-blende) structure of binary ionic compounds.

Structural phase transition and magnetic properties of Co50Fe50-xSix alloys

The structural and the magnetic properties of Co50Fe50-xSix alloys are investigated by carrying out experimental measurements and electron structure calculation. The alloy series exhibits the highly chemical ordering structure, showing a strong covalent bonding effect. The lattice parameters, molecular moment and Curie temperature linearly decrease with the increase of the Si content. The deviation of the structure is attributed to the atomic size effect. Based on Stearns theories, the decrease of the itinerant 3d (di) electron results in the decrease of Curie temperature due to the substitution of Si for Fe. The change of molecular moment follows the Slater-Pauling rule, but the calculation indicates that the change of the atomic moments is not linear. It implies that the covalent bonding effect is responsible for the magnetic changes. The molecular moment and Curie temperature of Heusler alloy Co2FeSi are measured to be 5.92 B and 777 ℃, respectively. The calculation results also indicate that the half-metallic property of Co2FeSi may not be so perfect as reported, which requires a new design of energy band for the practical application. The investigation also shows that the structural transition and the magnetic structure transition accumulate in a narrow interval of Si content, which may become a good object for studying the interaction between the magnetization and the structure.

Diffusion and viscous flow in bulk glass forming alloys

We review radiotracer diffusion and isotope measurements in bulk glass forming alloys from the glassy state to the equilibrium melt and compare diffusion and viscous flow. In the glassy as well as in the deeply supercooled state below the critical temperature T c, where the mode coupling theory predicts a freezing-in of liquid-like motion, very small isotope effects indicate a highly collective hopping mechanism. Not only in the glassy state but also in the supercooled state below T c the temperature dependence of diffusion is Arrhenius-like with an effective activation enthalpy. A clear decoupling takes place between the diffusivities of the individual components of the alloys and between time scales related to diffusive transport and viscous flow. While the component decoupling is small for the smaller components a vast decoupling of more than 4 orders of magnitude is observed in Pd–Cu–Ni–P alloys between the diffusivity of the large majority component Pd and of the smaller components at the glass transition temperature T g. The diffusivities of all components merge close to the critical temperature T c of mode coupling theory. Above T c, the onset of liquid-like motion is directly evidenced by a gradual drop of the effective activation energy. This strongly supports the mode coupling scenario. The isotope effect measurements show atomic transport up to the equilibrium melt to be far away from the regime of uncorrelated binary collisions. For Pd, in contrast to the behavior of single component molecular glass formers, the Stokes–Einstein equation even holds in the entire temperature range below T c over at least 14 orders of magnitude. Apparently, the majority component Pd forms a slow subsystem in which the other elements move fast. Rearrangement of the Pd atoms thus determines the viscous flow behavior. The decoupling of atomic mobility seems to arise from a complex interplay between chemical short order and atomic size effects that gets more pronounced on approaching the glass transition temperature. The ability of the bulk glass forming alloys to form a slow subsystem in the liquid state appears to be a key to the understanding of their excellent glass forming properties.

Phase-field-crystal dynamics for binary systems: Derivation from dynamical density functional theory, amplitude equation formalism, and applications to alloy heterostructures

The dynamics of phase field crystal (PFC) modeling is derived from dynamical density functional theory (DDFT), for both single-component and binary systems. The derivation is based on a truncation up to the three-point direct correlation functions in DDFT, and the lowest order approximation using scale analysis. The complete amplitude equation formalism for binary PFC is developed to describe the coupled dynamics of slowly varying complex amplitudes of structural profile, zeroth-mode average atomic density, and system concentration field. Effects of noise (corresponding to stochastic amplitude equations) and species-dependent atomic mobilities are also incorporated in this formalism. Results of a sample application to the study of surface segregation and interface intermixing in alloy heterostructures and strained layer growth are presented, showing the effects of different atomic sizes and mobilities of alloy components. A phenomenon of composition overshooting at the interface is found, which can be connected to the surface segregation and enrichment of one of the atomic components observed in recent experiments of alloying heterostructures.

Weakening of the Cu/Cu3Sn(100) Interface by Bi Impurities

We have performed density functional theory calculations to examine the role of Bi impurities in modifying the structure and properties of the Cu/Cu(3)Sn(100) interface. Analysis of the heat of supercell formation reveals that Bi atoms preferentially replace Cu atom in the Cu slab. Substitution of Cu by Bi reduces the adhesion energy of the interface from 1.5 J/m(2) to 1.1 J/m(2), primarily due to the atomic size effect. The size effect leads to expansion of the interface, because surrounding Cu and Sn atoms are pushed away from the misfit Bi atoms. Analysis of electronic density indicates that the local charge density is dispersed around Bi atoms. The presence of a Bi atom makes surrounding atoms less active, which is attributed to the reduction of hybridizations.

Atomic size and chemical effects on the local order ofZr2M(M=Co, Ni, Cu, and Ag) binary liquids

First-principles molecular dynamics simulations are performed to investigate the atomic size and chemical effects on the short-range order (SRO) in superheated and undercooled Zr-based metallic liquids, ${\text{Zr}}_{2}M$ ($M=\text{Co}$, Ni, Cu, and Ag). We demonstrate that the local atomic structures in liquids are quite sensitive to the atomic size ratio and the electronic interactions between component elements. The large negative heats of mixing for $\text{Zr-}M$ do not favor icosahedral SRO in these binary liquids, contrary to the common belief. Full icosahedral structure units are few in the superheated liquids, although the number of icosahedral clusters increases upon undercooling. Comparing ${\text{Zr}}_{2}\text{Co}$, ${\text{Zr}}_{2}\text{Ni}$, and ${\text{Zr}}_{2}\text{Cu}$, all of which have very similar atomic size ratios, we find that the degree of local icosahedral order increases with decreasing interaction strength between the $d$ electrons in Zr-Co, Zr-Ni, and Zr-Cu. A comparison of ${\text{Zr}}_{2}\text{Cu}$ and ${\text{Zr}}_{2}\text{Ag}$ alloys shows that the degree of icosahedral order increases much more in ${\text{Zr}}_{2}\text{Ag}$ than in ${\text{Zr}}_{2}\text{Cu}$ with decreasing temperature. The difference in atomic sizes of Cu and Ag may account for the subtle discrepancy in the evolution of short-range ordering in undercooled ${\text{Zr}}_{2}\text{Cu}$ and ${\text{Zr}}_{2}\text{Ag}$ liquids.

The effect of atomic force microscope probe size on indentation tests simulated using realistic surface forces

The effects of the size and shape of an indenter tip used in a nanoscale indentation test (such as with an atomic force microscope) are studied using realistic, finite-range surface forces to describe the contact and extended-range interaction of the indenter and sample. Sphero-conical indenters with tips ranging from sharp-pointed to very rounded tips (similar to spherical tips) are studied. A continuum Lennard-Jones adhesion potential and a Poisson-Boltzmann exponential repulsion law are used to study adhesive and repulsive-only interactions, respectively. The size of the tip affects the qualitative response for an adhesive surface force potential, with increasingly rounded tips exhibiting a more pronounced jump into contact and a greater overall adhesion. The effects of tip size are less pronounced for pure repulsion.

First-principles simulation of the elastic properties of multicomponent amorphous steels

The local atomic structure and elastic properties of two series of multicomponent amorphous steels---with and without phosphorus addition---have been investigated by ab initio molecular dynamics. A comparison of neutron pair-distribution functions allowed the difference in local atomic organization for these two series to be explained in terms of the atomic size effect. The conclusions drawn on the basis of ``empirical'' consideration were confirmed by the results of first-principles simulations. The structural models obtained in the course of ab initio molecular-dynamics calculations were used for the simulation of the elastic properties and the results of the modeling revealed a close agreement with the experiment. This allowed us to elucidate a role of particular chemical elements in improving the ductility of particular compositions.

Assessment of a time-of-flight detection technique for measuring small velocities of cold atoms

A low noise time-of-flight detection system for laser cooled atoms has been constructed and incrementally optimized. Here, a thorough description of the construction is presented along with an analysis of the capabilities of the system. The quality of the detection (the resolution, the reproducibility, the sensitivity, etc.) is crucial for, e.g., the ability to see details in the velocity distribution profile, which is of interest for fundamental studies of statistical physics and of the laser cooling processes, and for detection of small initial velocities of an atomic cloud, important, e.g., when studying small drifts induced by Brownian motors and ratchets. We estimate the signal-to-noise ratio of our signal to be better than 1000:1 for a typical single shot, and we discuss the effect of the initial atomic cloud size, the probe size, and the effects of the wave packet spread during the fall time on the measured quantities. We show that the shape of the velocity distribution is well conserved during the mapping done in the detection, i.e., in the convolution with the probe beam, and that velocities as small as a few percent of the single photon recoil velocity can be resolved.

Interaction potential for indium phosphide: a molecular dynamics and first-principles studyof the elastic constants, generalized stacking fault and surface energies

Indium phosphide is investigated using molecular dynamics (MD) simulations anddensity-functional theory calculations. MD simulations use a proposed effective interactionpotential for InP fitted to a selected experimental dataset of properties. The potentialconsists of two- and three-body terms that represent atomic-size effects, charge–charge,charge–dipole and dipole–dipole interactions as well as covalent bond bending andstretching. Predictions are made for the elastic constants as a function of density andtemperature, the generalized stacking fault energy and the low-index surface energies.

Computational analysis of the atomic size effect in bulk metallic glasses and their liquid precursors

The atomic size effect and its consequences for the ability of multicomponent liquid alloys to form bulk metallic glasses are analyzed in terms of the generalized Bernal’s model for liquids, following the hypothesis that maximum density in the liquid state improves the glass-forming ability. The maximum density that can be achieved in the liquid state is studied in the 2( N-1) dimensional parameter space of N-component systems. Computer simulations reveal that the size ratio of largest to smallest atoms are most relevant for achieving the maximum packing for N = 3–5, whereas the number of components plays a minor role. At small size ratio, the maximum packing density can be achieved by different atomic size distributions, whereas for medium size ratios the maximum density is always correlated to a concave size distribution. The relationship of the results to Miracle´s efficient cluster packing model is also discussed.

Influence of the static atomic displacement on atomic resolution Z-contrast imaging

The influence of static atomic displacements, due to atomic size effects in alloys with atoms having different covalent or ionic radii, on high angle annular dark field image contrast is studied quantitatively by simulations and experiments. We show that the static displacements can have a large influence on the Z contrast, depending on the alloy composition and on the scanning transmission electron microscopy specimen thickness. This influence has to be taken into account for quantitative chemistry measurement based on Z-contrast imaging.

Atomic size effect on the structures and stability of X 7M (X=Al and In;M=Si −,Ge −,N and P) clusters

Based on the density functional theory, geometric and electronic properties of X 7M (X=Al and In; M=Si −, Ge −, N and P) clusters are studied. The lowest-energy structures for Al 7Si −, Al 7Ge − and Al 7P are largely different from that of Al 7C −. The size effect of impurity atom on the structures and stability has been analyzed. In 7C − and In 7N are found to have the same geometry as Al 7C −, in which the host atoms form a cage with C 3 v symmetry with impurity atoms locating at the central site. A significantly large HOMO–LUMO gap, low-electron affinity, and high ionization potential are the characters of a magic cluster found for In 7N, which may have potential application in cluster-assembled materials.

Diffusion of tungsten in α-iron

Tracer diffusion coefficient of 181W in α-iron has been determined in the temperature range between 833 and 1173 K using a serial sputter-microsectioning method. The temperature dependence of the diffusion coefficient, D, over the whole temperature range of α-iron across the Curie temperature (T C = 1043 K), can be expressed by where s is the ratio of the spontaneous magnetization at T K to that at 0 K. The factor 0.086 in the above equation is smaller than 0.156 for the self-diffusion, showing that the influence of the magnetic transformation on the diffusion of tungsten in α-iron is smaller than that on the self-diffusion. The activation energy 287 kJ/mol for tungsten diffusion in the paramagnetic iron is much higher than 250.6 kJ/mol for the self-diffusion. Atomic size effect is predominant in the activation energies for diffusion of transition elements in the paramagnetic α-iron.

Glass formability and thermal stability of Al–Ni–Y–Be amorphous alloys

In this study, the role of Be in glass forming ability (GFA) and thermal stability of (Al 85Ni 7Y 8) 100− x Be x ( x = 0–6 at.%) amorphous alloys has been investigated in an attempt to understand small atomic size effect in Al–TM–RE (TM: transition metal, RE: rare earth metal) alloy system. The supercooled liquid region (Δ T x = T x − T g, where T x and T g are the onset crystallization and the glass transition temperatures, respectively), reduced glass transition temperature ( T rg = T g/ T L, where T L is the liquidus temperature), K (=( T x − T g)/( T L − T x)), γ (= T x/( T g + T L)) and the activation energy for primary crystallization ( E a), became slightly increased by the addition of 2% Be. The higher GFA representing parameters and thermal stability for the (Al 85Ni 7Y 8) 98Be 2 alloy, however, did not result in a practically enhanced glass formability.

Calculation of Gibbs energy of Zr [sbnd]Al [sbnd]Ni, Zr [sbnd]Al [sbnd]Cu, Al [sbnd]Ni [sbnd]Cu and Zr [sbnd]Al [sbnd]Ni [sbnd]Cu liquid alloys based on quasiregular solution model

With the effects of electronic structure and atomic size being introduced, the mixing enthalpy as well as the Gibbs energy of the ternary Zr Al Cu, Ni Al Cu, Zr Ni Al and quaternary Zr Al Ni Cu systems are calculated based on quasiregular solution model. The computed results agree well with the experimental data. The sequence of Gibbs energies of different systems is: G Zr Al Ni Cu < G Zr Al Ni < G Zr Al Cu < G Cu Al Ni . To Zr Al Cu, Ni Al Cu and Zr Ni Al, the lowest Gibbs energy locates in the composition range of X Zr = 0.39–0.61, X Al = 0.38–0.61; X Ni = 0.39–0.61, X Al = 0.38–0.60 and X Zr = 0.32–0.67, X Al = 0.32–0.66, respectively. And to the Zr Ni Al Cu system with 66.67% Zr, the lowest Gibbs energy is obtained in the region of X Al = 0.63–0.80, X Ni = 0.14–0.24.

Atomic Size Effect in Impurity Induced Grain Boundary Embrittlement

Bismuth segregated to the grain boundary in Cu is known to promote brittle fracture of this material. Schweinfest et al. [Nature 432 (2004) 1008-1011] reported first-principles quantum mechanical calculations on the electronic and structural properties of a Cu grain boundary with and without segregated Bi and argue that the grain boundary weakening induced by Bi is a simple atomic size effect. But their conclusion is incomplete for both Bi and Pb because it fails to distinguish the chemical and mechanical (atomic size) contributions, as obtained with our recently developed first-principles based phenomenological theory.

Effects of Atomic Size for Voronoi Tessellation Technique on Binary and Ternary Systems of Metallic Glasses

A number of researchers are still employing the ordinary Voronoi tessellation technique to explore the atomic structures of metallic glasses. However, the ordinary Voronoi tessellation technique does not take into consideration the size of each atom, and this essentially leads to differences in the atomic volume and structure, such as the number of atoms with FCC or icosahedral structure. An alternative way, the radical plane technique, is applied to binary and ternary systems: such as Zr, ZrCu, ZrCuAl, ZrB, and ZrFeB. In the radical plane technique, the face is placed on the position in proportion to the atomic size. In this study, we found that the differences cannot be negligible. In some cases, the difference in the results between the two techniques is more than 50%.

Dynamics and nano-clustering of alkali metals (Na, K) on the Si(1 1 1)-(7×7) surface

We report scanning tunneling microscopy and work function measurement studies on Na (K) adsorption on the Si(1 1 1)-(7×7) surface at room temperature and sub-monolayer coverage. A systematic comparison is reported on their dynamics and clustering behaviors to reveal the atomic size effect. We find that both Na and K form two-dimensional gases at room temperature and coverage<0.08 ML. K shows faster diffusion speed and stronger charge transfer to the Si substrate as compared to Na. At coverage >0.08 ML, both Na and K form magic clusters consisting of six Na(K) atoms. However, the clustering behaviors of Na and K are very different. In the K case, there is no intermixing between K and Si atoms, and the K clusters are very mobile inside the half (7×7) unit cell, whereas Na clusters are unmovable due to the site-exchange between Na atoms and the Si adatoms.