Icosahedral Short-range Order Research Articles

Effect of Ti addition on the glass forming ability, crystallization, and plasticity of (Zr64.13Cu15.75Ni10.12Al10)100−xTix bulk metallic glasses

A series of (Zr64.13Cu15.75Ni10.12Al10)100−xTix (x=0–7) bulk metallic glasses were prepared by water-cooled copper mold casting method. The glass forming ability, crystallization behavior, and plasticity of the (Zr64.13Cu15.75Ni10.12Al10)100−xTix alloys with different Ti contents were studied. The reduced glass transition temperature increases with Ti addition and a maximum value of 0.562 is achieved at x=5, indicating that the glass forming ability increases with Ti addition. Compared with that of one crystallization step for the sample without Ti addition, the Ti (x≥2) containing alloys exhibit a two-step crystallization behavior. In addition, the initial crystallization temperature decreases from 744 to 684K as x increases from 0 to 7. Icosahedral quasicrystal phase was found to precipitate in the amorphous matrix in the first crystallization step, implying that strong icosahedral short-range order may exist in the Ti (x≥2) containing alloys. Moreover, the (Zr64.13Cu15.75Ni10.12Al10)100−xTix bulk metallic glasses exhibit excellent plasticity, i.e., a plastic engineering strain in compression larger than 80% for x≤6.

Diffusion in a Cu-Zr metallic glass studied by microsecond-scale molecular dynamics simulations

Icosahedral short-range order (ISRO) has been widely accepted to be dominant in Cu-Zr metallic glasses (MGs). However, the diffusion mechanism and correlation of ISRO and medium-range order (MRO) to diffusion in MGs remain largely unexplored. Here, we perform a long time annealing up to 1.8 \ensuremath{\mu}s in molecular dynamics simulations to study the diffusion mechanism and the relationship between atomic structures and the diffusion path in a $\mathrm{C}{\mathrm{u}}_{64.5}\mathrm{Z}{\mathrm{r}}_{35.5}$ MG. It is found that most of the diffusing events performed by the diffusing atoms are outside ISRO and the Bergman-type MRO. The long-range diffusion in MGs is highly heterogeneous, via collective diffusing events through the liquidlike channels in the glass. Our results clearly demonstrate a strong correlation between the atomic structures and transport in MGs.

Thermodynamic Aspects of Homogeneous Nucleation Enhanced by Icosahedral Short Range Order in Liquid Fcc-Type Alloys

We have recently shown that minute solute element additions to liquid metallic alloys can strongly influence the nucleation of the fcc phase and act as a grain refinement method. Electron back-scattered diffraction observations revealed a concomitant increase in the percentage of nearest neighbor (nn) grains that are in a twin relationship. Furthermore, multiple-twinned (MT) nn grain configurations with a fivefold symmetry around a common h110i direction have been identified, an occurrence that can be explained when the symmetry of the icosahedron is accounted for. It was then conjectured that a new nucleation mechanism occurs in two steps: first, the formation of small icosahedral quasicrystals in the melt, followed by heteroepitaxy of the fcc phase on facets of these quasicrystals. In the present contribution, based on thermodynamics arguments, it is proposed that the first step occurs by spinodal decomposition of the liquid, in a manner similar to Guinier–Preston zones formation in solid state precipitation, while the second step is a transformation of these quasicrystal precursors into MT-fcc nanocrystals once the driving force for this transformation is sufficient to overcome the fcc-liquid interfacial energy and the elastic strains associated with MT-fcc nanoparticles. This explanation sets up guidelines for finding solute elements and composition ranges that favor this grain refinement mechanism.

Cooling rates dependence of medium-range order development inCu64.5Zr35.5metallic glass

The atomic structure of metallic glasses (MGs) plays an important role in their properties. Numerous molecular dynamics (MD) simulations have revealed icosahedral short-range order (ISRO) as a dominant motif in Cu-Zr metallic glasses. However, the cooling rates utilized in most of the MD simulations (usually on the order of ${10}^{10--13}\phantom{\rule{0.16em}{0ex}}\mathrm{K}/\mathrm{s}$) can be too high to allow the structure to relax into the actual structures. By performing a long sub-${T}_{g}$ annealing of the $\mathrm{C}{\mathrm{u}}_{64.5}\mathrm{Z}{\mathrm{r}}_{35.5}$ alloy model at 700 K up to $2.0\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{s}$ using MD simulations, we systematically address the evolution of medium-range order (MRO) as the cooling rates in MD simulations approach the experimental cooling rates (usually ${10}^{3--6}\phantom{\rule{0.16em}{0ex}}\mathrm{K}/\mathrm{s}$). By reducing the effective cooling rates to as low as $2.8\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}{10}^{7}\phantom{\rule{0.16em}{0ex}}\mathrm{K}/\mathrm{s}$, we found a significant enhancement of the ISRO and Bergman-type MRO. Comparing to the widely used face-, edge-, or vertex-sharing icosahedra, we propose that the Bergman-type MRO is a much more unambiguous metric to characterize the MRO in Cu-Zr MGs. By analyzing the network formed by interpenetrating icosahedra using the graphical theory, we show that the degree of interpenetration of the icosahedra centers increases with decreasing cooling rates. The network becomes aggressively assortative, indicating that higher degree nodes tend to cluster and form backbones in the MG. All these results show that the networks in the models prepared using lower cooling rates strongly deviate from a stringlike morphology.

A DFT study on the heredity-induced coalescence of icosahedral basic clusters in the rapid solidification

A density-function-theory (DFT) calculation conjoining with molecular dynamics (MD) simulation is performed to investigate the structural stability and formation capability of extended icosahedral Agn (n=19, 23, 24, 25) clusters linked by vertex-shared (VS), edge-shared (ES), face-shared (FS) and intercross-shared (IS) atoms in the rapid solidification. The chemical hardness η as a measure of chemical stability has been adopted to characterize and assess the structural stability and configuration hereditary ability of these extended icosahedral clusters, and their heats of formation ΔHR–P in the bi-cluster association mode of Ag13+Agm→Agn (n=19, 23, 24, 25, m=n−13) is also calculated by a transition state (TS) search method on the basis of linear synchronous transit (LST) and quadratic synchronous transit (QST) technique. It is found that the high structural stability of inheritable Ih–Ag13 icosahedral short-range orders (ISROs) and IS-linkages related to icosahedral medium-range orders (IMROs) can be attributed to their large chemical hardness η relative to FS-, ES- and VS-linkages, and to some extent a large released calorie ΔHR–P in the formation of D5h–Ag19 clusters should be responsible for the coalescence preference of IS-linkages in super-cooled liquids and subsequent intensive emergence in rapidly solidified solids. In this case, a strong electronic interaction between core and shared atoms is demonstrated to play a key role in the aggregation of inheritable icosahedral basic clusters.

Structural evolution in the crystallization of rapid cooling silver melt

The structural evolution in a rapid cooling process of silver melt has been investigated at different scales by adopting several analysis methods. The results testify Ostwald’s rule of stages and Frank conjecture upon icosahedron with many specific details. In particular, the cluster-scale analysis by a recent developed method called LSCA (the Largest Standard Cluster Analysis) clarified the complex structural evolution occurred in crystallization: different kinds of local clusters (such as ico-like (ico is the abbreviation of icosahedron), ico-bcc like (bcc, body-centred cubic), bcc, bcc-like structures) in turn have their maximal numbers as temperature decreases. And in a rather wide temperature range the icosahedral short-range order (ISRO) demonstrates a saturated stage (where the amount of ico-like structures keeps stable) that breeds metastable bcc clusters. As the precursor of crystallization, after reaching the maximal number bcc clusters finally decrease, resulting in the final solid being a mixture mainly composed of fcc/hcp (face-centred cubic and hexagonal-closed packed) clusters and to a less degree, bcc clusters. This detailed geometric picture for crystallization of liquid metal is believed to be useful to improve the fundamental understanding of liquid–solid phase transition.

Evidence for cooling-rate-dependent icosahedral short-range order in a Cu–Zr–Al metallic glass

Samples of Cu47.5Zr47.5Al5metallic glass were prepared at different cooling rate,R. The dependence of the X-ray diffraction patterns onRwas analysed by comparing them with corresponding patterns of computer-simulated models generated at different cooling rates as well. The observed changes in the experimental diffraction patterns are reproduced by the simulations, showing an increasing fraction of icosahedral clusters with decreasing cooling rate. The difference of the fractions of icosahedrally coordinated atoms in mould-cast and rapidly quenched Cu47.5Zr47.5Al5averages to 3 (1)%. Different frozen-in thermal displacements and different density are ruled out as a possible origin for the experimental observations.

Impact of deformation on the atomic structures and dynamics of a Cu-Zr metallic glass: A molecular dynamics study

Despite numerous studies on the atomic structures of Cu-Zr metallic glasses (MGs), their inherent structural ordering, e.g., medium-range order (MRO), remains difficult to describe. Specifically lacking is an understanding of how the MRO responds to deformation and the associated changes in atomic mobility. In this paper, we focus on the impact of deformation on MRO and associated effect on diffusion in a well-relaxed $\mathrm{C}{\mathrm{u}}_{64.5}\mathrm{Z}{\mathrm{r}}_{35.5}$ MG by molecular dynamics simulations. The Cu-Zr MG exhibits a larger elastic limit of 0.035 and a yield stress of 3.5 GPa. The cluster alignment method was employed to characterize the icosahedral short-range order (ISRO) and Bergman-type medium-range order (BMRO) in the models upon loading and unloading. From this analysis, we find the disruption of both ISRO and BMRO occurs as the strain reaches about 0.02, well below the elastic limit. Within the elastic limit, the total fractions of ISRO or BMRO can be fully recovered upon unloading. The diffusivity increases six to eight times in regions undergoing plastic deformation, which is due to the dramatic disruption of the ISRO and BMRO. By mapping the spatial distributions of the mobile atoms, we demonstrate the increase in atomic mobility is due to the extended regions of disrupted ISRO and more importantly BMRO.

Strong correlations of dynamical and structural heterogeneities with localized soft modes in a Cu-Zr metallic glass

Structural and dynamical heterogeneities in metallic glasses, while intensely studied, remain an enigma. For instance, whether and how the dynamical and structural heterogeneities are correlated is still an outstanding question. Meanwhile, the nature of the impact of medium-range order (MRO) on the dynamical heterogeneity remains elusive. In this paper, we analyzed the structural and dynamical heterogeneities in both as-quenched and relaxed Cu64.5Zr35.5 metallic glasses based on the atomistic trajectories collected from molecular dynamics simulations. We found that the majority of the mobile atoms are not involved in icosahedral clusters or Bergman superclusters, indicating that dynamical heterogeneities are strongly correlated with structural heterogeneities. The Bergman-type MRO has an even stronger correlation with the dynamical heterogeneity than the icosahedral short range order. Moreover, we found that the localized soft vibration modes below 1.0 THz are mostly concentrated on the mobile atoms. These results suggest that the vibrational properties can be conveniently utilized to predict the atomic mobility in metallic glasses, which can bridge the studies of dynamical heterogeneity by experiments and simulations.

Dynamic properties and local order in liquid Al-Ni alloys

Ab initio molecular dynamics simulations are used to describe the connection between dynamic and structural properties in liquid Al90Ni10 and Al80Ni20 alloys at various temperatures. We find that self-diffusion coefficients and viscosity are strongly composition-dependent while their temperature dependence follows an Arrhenius-type behavior, in close agreement with experiment. Through comparisons between both alloys and the corresponding pure elements, we demonstrate that the composition and temperature dependence of these transport properties can be related to the detailed description of the short-range order and more particularly to the interplay between icosahedral short-range order and chemical short-range order. Finally, all our results are used to discuss the known correlation between transport properties and the two-body excess entropy.

Bergman-type medium-range order in rapidly quenched Ag0.74Ge0.26 eutectic alloy studied by ab initio molecular dynamics simulation

The structure of liquid and rapidly quenched amorphous Ag0.74Ge0.26 alloy at the eutectic composition was studied by ab initio molecular dynamics (MD) simulations. The local structural properties were systematically investigated from the liquid at 1123K to amorphous solid at 300K. The pair-correlation function at 976K from the MD simulations agrees well with the experimental data. The local structures were also analyzed using Honeycutt–Andersen (HA) indices, Voronoi tessellation and the atomic cluster alignment (ACA) method. The HA indices analysis reveals that there is a high population of pentagonal bipyramid structure which become more predominant upon solidification. Voronoi tessellation analysis indicates strong icosahedral short-range order (SRO) in the liquid and amorphous samples generated by the MD simulations. Using the ACA method, the development of icosahedral SRO upon cooling is further confirmed and a Bergman medium-range order is also observed. The analysis of structural properties and chemical short-range order suggests that Ag atoms tend to have a Bergman-like packing, while the dispersed Ge atoms prevent the alloy from forming a long-range order upon cooling. The Bergman medium-range order is also confirmed by the constrained reversed Monte Carlo results.

Temperature dependence of the electrical resistivity of Mg–Zn–Y quasicrystal alloy

Resistivity of Mg63.5Zn34Y2.5 alloy including icosahedral quasicrystalline phase (I-phase) was measured. It shows that the quasicrystal alloy has a negative temperature coefficient of resistivity (TCR) before melting of I-phase. The TCR shows a reversible transition at ~1073K during heating and cooling processes, involving evolution of icosahedral short-range orders (ISROs) inheriting from I-phase. The pre-existing ISROs act as templates in liquid and promote the nucleation of I-phase.

Local fivefold symmetry in liquid and undercooled Ni probed by x-ray absorption spectroscopy and computer simulations

Presence and significance of fivefold configurations in liquid metals are investigated by combining x-ray absorption spectroscopy and computer simulations (molecular dynamics and reverse Monte Carlo) in liquid and undercooled liquid nickel. We show that icosahedral short-range ordering (ISRO), probed by common-neighbor (CNA) and spherical invariant (${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{W}}_{6}$) analysis, involves a limited fraction (14--18% in undercooled nickel for different structural models) of local atomic configurations. The emerging picture for the liquid structure is that of a mixture of nearly icosahedral structures embedded in a disordered network mainly composed of fragments of highly distorted icosahedra (40--45% of the total), structures reminiscent of the crystalline phase, and other configurations.

Effects of sub-Tg annealing on Cu64.5Zr35.5 glasses: A molecular dynamics study

Creating metallic glasses by cooling liquid melts in molecular dynamics simulations faces a well-known challenge that the cooling rate is too fast compared with experiments. Taking the prototypical Cu64.5Zr35.5 glasses as an example, we propose an efficient cooling strategy in which most of the computer time is spent on a prolonged isothermal process slightly below the glass-transition temperature, Tg. The glassy sample prepared in this way demonstrates significant energetic stability, slow dynamics, and well-developed short-range icosahedral order. By conventional uniform cooling, similar properties can only be obtained using a cooling rate more than 15 times slower.

Sluggish mobility and strong icosahedral ordering in Mg–Zn–Ca liquid and glassy alloys

The dynamic properties and atomic configuration of Mg, Mg–Zn, Mg–Zn–Ca and Mg–Zn–Ca–Cu liquid and solid systems were comprehensively studied using ab initio molecular dynamics calculation. The viscosities of an Mg–Zn–Ca alloy were measured from 700K to 960K. It was found that Zn and Ca in Mg liquid induce remarkable slowing down of atoms, but Cu acted as a stimulus to the diffusion. Icosahedral short-range orders are most dominant in Mg–Zn–Ca alloys in view of the existence of a majority of 1551 type of bond pairs, 〈0,0,12,0〉 type of Voronoi polyhedra. Icosahedral medium-range orders can be formed in Mg–Zn–Ca alloys by the perfect icosahedra via the linkage of vertex-, edge-, face- and intercross-shared atoms. It is suggested that the high glass forming ability of Mg–Zn–Ca alloys is essentially related to the sluggish mobility and strong icosahedral short- and medium-range ordering in the undercooled liquid.

Atomic structure evolution during solidification of liquid niobium from ab initio molecular dynamics simulations

Atomic structure transitions of liquid niobium during solidification, at different temperatures from 3200 to 1500 K, were studied by using ab initio molecular dynamics simulations. The local atomic structure variations with temperature are investigated by using the pair-correlation function, the structure factor, the bond-angle distribution function, the Honeycutt–Anderson index, Voronoi tessellation and the cluster alignment methods. Our results clearly show that, upon quenching, the icosahedral short-range order dominates in the stable liquid and supercooled liquid states before the system transforms to crystalline body-center cubic phase at a temperature of about 1830 K.

New Roles for Icosahedral Clusters in Intermetallic Phases: Micelle-like Segregation of Ca–Cd and Cu–Cd Interactions in Ca10Cd27Cu2

Despite significant progress in the structural characterization of the quasicrystalline state, the chemical origins of long- and short-range icosahedral order remain mysterious and a subject of debate. In this Article, we present the crystal structure of a new complex intermetallic phase, Ca10Cd27Cu2 (mC234.24), whose geometrical features offer clues to the driving forces underlying the icosahedral clusters that occur in Bergman-type quasicrystals. Ca10Cd27Cu2 adopts a C-centered monoclinic superstructure of the 1/1 Bergman approximant structure, in which [110] layers of Bergman clusters in the 1/1 structure are separated through the insertion of additional atoms (accompanied by substantial positional disorder). An examination of the coordination environments of Ca and Cu (in the ordered regions) reveals that the structure can be viewed as a combination of coordination polyhedra present in the nearest binary phases in the Ca-Cd-Cu compositional space. A notable feature is the separation of Ca-Cd and Cu-Cd interactions, with Bergman clusters emerging as Ca-Cd Friauf polyhedra (derived from the MgZn2-type CaCd2 phase) encapsulate a Cu-Cd icosahedron similar to those appearing in Cu2Cd5. DFT chemical pressure calculations on nearby binary phases point to the importance of this segregation of Ca-Cd and Cu-Cd interactions. The mismatch in atomic size between Cu and Cd leads to an inability to satisfy Ca-Cu and Ca-Cd interactions simultaneously in the Friauf polyhedra of the nearby Laves phase CaCd2. The relegation of the Cu atoms to icosahedra prevents this frustration while nucleating the formation of Bergman clusters.

Liquid Aluminum: atomic diffusion and viscosity from ab initio molecular dynamics.

We present a study of dynamic properties of liquid aluminum using density-functional theory within the local-density (LDA) and generalized gradient (GGA) approximations. We determine the temperature dependence of the self-diffusion coefficient as well the viscosity using direct methods. Comparisons with experimental data favor the LDA approximation to compute dynamic properties of liquid aluminum. We show that the GGA approximation induce more important backscattering effects due to an enhancement of the icosahedral short range order (ISRO) that impact directly dynamic properties like the self-diffusion coefficient. All these results are then used to test the Stokes-Einstein relation and the universal scaling law relating the diffusion coefficient and the excess entropy of a liquid.

High-pressure melting of tantalum from the modified Z method

We examined the validity of the modified Z method to predict the high-pressure melting curve of the body-centered-cubic transition metals, e.g., tantalum, in the molecular dynamics simulations using an extended Finnis-Sinclair potential. A unique feature was observed that a solid system evolves into the steady interphase of the solid and the liquid. In spite of simple running processes, the melting curve extracted from the solid-liquid coexistence states composed of only 960 atoms reaches an excellent agreement with that of the two-phase method in the literature. The liquid microstructure at the melting curve is dominated by the icosahedral short-range order, almost independent of the pressure up to 400 GPa.

Local order and dynamic properties of liquid and undercooled Cu55Hf45 and Cu62Hf38 alloys by ab initio molecular dynamics

Atomic structures of liquid and undercooled Cu55Hf45 and Cu62Hf38 alloys have been studied using first-principles molecular dynamics simulations. It is found that both chemical short-range order and icosahedral short-range order are more pronounced at xCu = 0.55. We also evidence differences with the atomic structures of parent CuxZr1-x alloys. In examining the dynamic properties, we show that diffusivity and viscosity are closely related to the local structures of these two alloys. More particularly, we show that the icosahedral ordering is responsible for the more pronounced slowing down of the dynamics in the Cu55Hf45 alloy leading to a non-Arrhenius behavior in the undercooled region.