Icosahedral Medium-range Order Research Articles

Atomic-scale structures determining the plasticity of metallic glasses viewed from the icosahedral medium-range orders and its spatial distribution

In the study of metallic glasses, the characterization of free volumes and icosahedral clusters has been a longstanding approach to understanding plasticity. However, recent research has illuminated the limitations of exclusively relying on these factors to explain the plastic deformation of metallic glasses. To address this limitation, we have introduced the concept called the h-value in a prior study, which quantifies the spatial distribution of disrupted interpenetrating connections of icosahedra and provides insights into how minor elements influence the deformation behavior of metallic glasses. However, the h-value was only employed on Cu50Zr50, Cu47.5Zr47.5Al5, and (Cu0.5Zr0.5)100-xAgx alloys and provided insight into the correlation between the spatial distribution of icosahedra and plasticity, but it is needed to be validated on a wider range of alloys to confirm the applicability of the h-value. In this study, we utilize a Cu–Zr binary amorphous system, known for its compositional diversity and corresponding wide range of plasticity, to validate and benchmark our approach against experimental results. Our findings underscore the robustness of the h-value as a structural descriptor, representing the degree of spatial distribution within the local structural basis. This metric holds promise as a valuable tool for determining the plasticity of metallic glasses.

Topology of icosahedral network responsible for yielding in CuZr metallic glasses

Metallic glasses exhibit yielding behavior under mechanical deformation. However, the underlying atomic structural basis is still elusive. Here we investigated atomic structural evolution in both average fraction of atomic clusters and their spatial distribution for CuZr metallic glasses during deformation via molecular dynamic simulation. It is found that while the icosahedral clusters in the initial structures of CuZr glassy samples exhibit unique mechanical response to deformation, compared to other types of atomic clusters, its fraction is not key to the yielding of metallic glasses. We further explored the spatial distribution of icosahedral clusters, i.e., icosahedral medium-range order by analyzing the network formed via their interpenetrating connections. It is found that the topology of the icosahedral network plays the essential roles in the yielding of CuZr metallic glasses. Within the icosahedral networks, nodes with degree k > 1 mainly determine the yield strain, which is general in CuZr metallic glasses and independent of the fraction of icosahedral clusters. Moreover, it is also found that the larger the node degree of the interpenetrated icosahedral network is, the higher the yield strain is. Therefore, the disruption of the icosahedral network corresponds to the yielding of metallic glasses. The roles of nodes with degree k = 0 and 1 in the yielding were also elucidated. In addition, the newly formed icosahedral clusters during deformation are found to have almost no impact on the yielding of metallic glasses. Our findings establish a quantitative relation between atomic structures and yielding in CuZr metallic glasses based on the perspective of structural topology, and may shed light on the deformation mechanism of amorphous solids.

Medium Range Ordering in liquid Al-based alloys: towards a machine learning approach of solidification

Ab initio molecular dynamic simulations of liquid Al93Cr7 and Al83Zn10Cr7 alloy have evidenced the presence of an icosahedral short range order (iSRO) which develops into icosahedral medium range order (iMRO) as the melt is undercooled. This atomic arrangement accounts for the presence of Dynamic Heterogeneities characterized by Al fast-dynamics regions and Cr-rich slow-dynamics regions. Characterisation of the medium range order was carried out by a direct connectivity approach. However, given the small size of the simulation (256 atoms), such characterisation remains partial. In order to better describe both iMRO formation and more dilute alloys closer to industrial compositions, a new modelling strategy has been initiated to allow in the long term for large-scale atomic-level simulations. Molecular Dynamics (MD) of million to billion atoms may indeed lead to meaningful results. Exploitation of such large amounts of MD-generated big data can be carried out by means of Machine Learning (ML) tools which provide relevant and powerful analysis methods. An unsupervised ML approach based on topological descriptors using persistent homology concepts is proposed to reveal the structural features of atomic arrangements without a priori knowledge on the studied system. This approach has been applied so far to pure Al melts. Both translational and orientational orderings are thus evidenced together with nucleation pathways, whose revealed features are beyond the hypotheses of the Classical Nucleation Theory.

Connections between structural characteristics and crystal nucleation of Al–Sm glasses near glass transition temperature

A systematic investigation on connections between structural characteristics and crystal nucleation during isothermal devitrification of Al–Sm glasses has been carried out by utilizing molecular dynamics simulations combined with an effective data-driven approach named principal component analysis. The results suggest that icosahedral order dominants the local orders in Al–Sm liquids and glasses, whereas the development of crystal-like clusters has been greatly suppressed. Doping of Sm not only increases the population of icosahedral order in Al–Sm alloys, but also promotes the tendency of formation of icosahedral medium range order. Based on the calculation of local density and bond-orientational order parameters, a distinct decoupling in spatial distributions of fluctuations in local density and bond-orientational order is observed, and an obvious lagging of densification behind structural ordering is unveiled. These facts unambiguously evidence that the bond-orientational order instead of local density is the determinant factor for the origin of crystal nucleation in Al–Sm glass.

Connecting short-range order for the liquid-solid transition of Al-Cu-Fe alloys

Liquid-solid transition processes have always been mysterious, especially those with the participation of quasicrystal (QC) structures, and are generally far less understood than the conventional solidification process. Here, the liquid structure variation of ternary QC-forming Al60Cu37Fe3 with crystal-forming Al50Cu40Fe10 alloy liquids was compared using synchrotron radiation based on high-energy X-ray diffraction (HE-XRD) and reverse Monte Carlo simulation (RMC). It was noted that the types of short-range order structures are almost the same in the Al60Cu37Fe3 and Al50Cu40Fe10 alloy liquids, while the former has more icosahedral short-range order (ISRO) and the latter has less. The medium-range order (MRO) was characterized by the cluster correlation method and visualization analysis. More obvious structural heterogeneity was found in the Al60Cu37Fe3 liquid, which is due to the strong correlation between clusters with high icosahedral order and the weak correlation between crystal clusters. Moreover, strongly correlated ISRO clusters can form icosahedral medium-range order (IMRO) structures by interpenetrating connections forming a stable structure upon cooling, and some other clusters can even enhance the IMRO stability. Such IMRO will be retained in the liquid upon cooling, leading to QC formation. All the findings provide a further understanding of the liquid-solid transition with ISRO participation.

Structural origin of the enhancement in glass-forming ability of binary Ni-Nb metallic glasses

This study aimed to clarify the structural origin of the enhancement in glass-forming ability (GFA) of binary Ni-Nb metallic glasses (MGs). The atomic structures of NixNb100-x(x=50, 59.5, 62.5, 70) alloys were systematically studied using synchrotron total-scattering method and molecular dynamics calculation. The classical molecular dynamics simulations results agree well with the experiments. Ni62.5Nb37.5 alloy has the best glass-forming ability and the densest atomic-packing structure among the four components. The larger fraction of full icosahedron <0, 0, 12, 0> and distorted icosahedron <0, 2, 8, 2> clusters implied that the relatively better GFA was near Ni62.5Nb37.5. Intercross-sharing icosahedral medium-range orders superclusters composed of 2–16 icosahedra interpenetrated at 900 K. The glass structure in Ni62.5Nb37.5 MG was a heterogeneous mixture of interpenetrating icosahedral clusters, forming a chain-like network structure in the matrix. These Ni-centered icosahedra polyhedra, with their high packing density and low mobility, led to high-density atomic packing and slow dynamics, thereby playing an essential role in controlling GFA.

Liquid Structure and Thermophysical Properties of Ternary Ni-Fe-Co Alloys Explored by Molecular Dynamics Simulations and Electrostatic Levitation Experiments

The structure, thermodynamic and dynamic properties of normal and metastable liquid Ni2xFe50−xCo50−x alloys were systematically investigated by combining electrostatic levitation (ESL) experiments and molecular dynamics (MD) simulations. Their composition dependence and mutual interaction were explored in detail. The actual densities of liquid Ni90Fe5Co5, Ni80Fe10Co10, Ni70Fe15Co15 and Ni60Fe20Co20 alloys were measured by ESL experiments in a wide temperature range. The simulated densities of these liquid alloys are in good agreement with the corresponding experimental data. The thermodynamic properties show that all these alloys exhibit a negative excess volume and mixing enthalpy. Meanwhile, their pair distribution functions indicate that Fe and Co atoms easily bond with Ni atoms and have a similar characteristic to each other if compared with Ni atoms. Furthermore, the structure factors validate that there exist icosahedral short-range and medium-range orders of Ni-Ni, Fe-Fe, Fe-Co and Co-Co bonds in these liquid alloys. Additionally, the solute diffusion properties reveal that the correlation between dynamic behavior and alloy composition is determined by the diffusion of Fe and Ni atoms.

Study the atomistic structure of monatomic vanadium under different cooling rates by molecular dynamics simulation

We performed molecular dynamics (MD) simulations with the LAMMPS code in order to understand the rapid solidified processes of refractory body-centered-cubic (BCC) metals V under five different cooling rates (γ1 = 1 × 1011K/s, γ2 = 1 × 1012K/s, γ3 = 1 × 1013K/s, γ4 = 5 × 1013K/s, γ5 = 1 × 1014K/s). It is found that the evolution of energy, volume and density of V are strongly dependents on the cooling rates during the rapid solidification. By analyzing the Abraham-Wendt parameter, discovering the magnitudes of the first minimum and maximum of the radial distribution function (RDF) are more effective parameters for specifying the phase boundary between liquid and super-cooled liquid. Compared to the initial crystallizing occurred in the interface with linked atom chain, the growth model of vitrification is presented through icosahedral medium-range orders (IMROs) with shell structure cored by isolated icosahedra. Further analyzing the variation of the number of icosahedra (ICO), hexagonal-close-packed (HCP), face-centered-cubic (FCC) and BCC clusters as a function of temperature by polyhedral template matching method (PTMM), it is found that the variation of tracking clusters not only occurs in the liquid and super-cooled liquid, but also exist in low temperature region (below the crystallization temperature (Tc) or glass transition temperature (Tg)), which breaks through our previous understanding for the evolution of clusters should only in high temperature region rather than in lower temperature region. In addition, both of the evolution of the density field for crystal and non-crystal exhibited obviously non-homogeneous, which maybe lead to non-uniformity of nucleation and vitrification in some degree, respectively.

P.806 Whole brain long-range study of white matter cellular microstructure using diffusion microscopy MRI in subjects with autism spectrum disorders

Medium-range order structure is the one of the important local structural units in the field of bulk metallic glasses. The rapid solidification of Cu50Zr40Al10 ternary alloy is investigated by molecular dynamics simulation. Simultaneously, the connections between the full icosahedral and defective icosahedral clusters in medium-range order structures of Cu50Zr40Al10 alloy are characterized systematically by the quantitative method and visualization analysis. The results reveal that the icosahedral clusters as the main structures with high structural stability are bonded with each other by interpenetrating connection, and form the triangle, double triangle, triple triangle, tetrahedron and chain connected icosahedral medium-range order clusters. Moreover, the icosahedral and defective icosahedral clusters prefer to link with each other and form the bigger medium-range order clusters with different configurations in this system. These structures keep the high structural stability of icosahedral medium-range order section and the structural variability of chain-like medium-range order structures.

The connection of icosahedral and defective icosahedral clusters in medium-range order structures of CuZrAl alloy

Medium-range order structure is the one of the important local structural units in the field of bulk metallic glasses. The rapid solidification of Cu50Zr40Al10 ternary alloy is investigated by molecular dynamics simulation. Simultaneously, the connections between the full icosahedral and defective icosahedral clusters in medium-range order structures of Cu50Zr40Al10 alloy are characterized systematically by the quantitative method and visualization analysis. The results reveal that the icosahedral clusters as the main structures with high structural stability are bonded with each other by interpenetrating connection, and form the triangle, double triangle, triple triangle, tetrahedron and chain connected icosahedral medium-range order clusters. Moreover, the icosahedral and defective icosahedral clusters prefer to link with each other and form the bigger medium-range order clusters with different configurations in this system. These structures keep the high structural stability of icosahedral medium-range order section and the structural variability of chain-like medium-range order structures.

Evolution of local atomic structures during rapid solidification of liquid metal W

Molecular dynamics (MD) simulations were performed to investigate the evolution of local atomic structure during rapid solidification of liquid metal W. The microstructures were characterized by means of potential energy (PE) per atom, pair distribution function and largest standard cluster analysis (LSCA). Instead of [12/555] perfect icosahedra, the [8/555 2/544 2/433] distorted icosahedra dominated in W monatomic metallic glasses (MGs). With the decrease of temperature, these clusters in metal W systems aggregated steeply into icosahedral medium-range orders (IMROs), especially in the super-cooling liquid region. Moreover, the maximal size [Formula: see text] of IMROs played a control role in the formation of W monatomic MGs rather than the number [Formula: see text]. The mean local fivefold symmetry [Formula: see text] of IMROs was demonstrated to be an effective indicator to characterize the glass transition of monatomic metal W liquids.

Effects of Al addition on atomic structure of Cu-Zr metallic glass

The atomic structures of Cu52Zr48 and Cu45Zr48Al7 metallic glasses (MGs) have been studied by molecular dynamic simulations. The results reveal that the molar volume of the Cu45Zr48Al7 MG is smaller than that of the Cu52Zr48 MG, although the size of the Al atom is larger than that of the Cu atom, implying an enhanced atomic packing density achieved by introducing Al into the ternary MG. Bond shortening in unlike atomic pairs Zr-Al and Cu-Al is observed in the Cu45Zr48Al7 MG, which is attributed to strong interactions between Al and (Zr, Cu) atoms. Meanwhile, the atomic packing efficiency is enhanced by the minor addition of Al. Compared with the Cu52Zr48 binary MG, the potential energy of the ternary MG decreases and the glass transition temperature increases. Structural analyses indicate that more Cu- and Al-centered full icosahedral clusters emerge in the Cu45Zr48Al7 MG as some Cu atoms are substituted by Al. Furthermore, the addition of Al leads to more icosahedral medium-range orders in the ternary MG. The increase of full icosahedral clusters and the enhancement of the packing density are responsible for the improved glass-forming ability of Cu45Zr48Al7.

Enhancement of plasticity in Zr-Cu-Ni-Al-Ti bulk metallic glass by heterogeneous microstructure

Icosahedral phase was found as a primary precipitated phase in the Zr70−xCu12.5Ni10Al7.5Tix (x=0–8) BMGs with two or three steps of crystallization process. Remarkable plasticity was realized in a wide range of alloy composition. The enhanced plasticity is attributed to the presence of icosahedral medium-range order clusters and the local heterogeneous distribution of free volume.

Influence of Cr on local order and dynamic properties of liquid and undercooled Al–Zn alloys

Using ab initio molecular dynamics, we present a systematic study of structural and transport properties of liquid Al90Zn10 and Al83Zn10Cr7 alloys. In the liquid phase, we find that Cr additions promote the formation of a heterogeneous local ordering characterized by a strong five-fold symmetry (icosahedral short-range order (ISRO)) around Cr atoms. In the undercooled phase, we observe the extension of ISRO to icosahedral medium-range order (IMRO) length scale referring to Cr atoms. In examining dynamic properties, we show that this Cr induced structural heterogeneity leads to a substantial decoupling of Cr diffusion from the diffusion of Al and Zn components by a factor of 3 at 1000 K, the liquidus temperature. Below this temperature, the formation of IMRO gives rise to a non-Arrhenian temperature dependence of diffusivity and viscosity, a breakdown of the Stokes-Einstein relation, as well as the onset of dynamic heterogeneities. Using the isoconfigurational ensemble method, we evidence that the structural origin of dynamics heterogeneities is clearly related to IMRO. Finally we discuss the role of IMRO in a quasicrystal-enhanced nucleation mechanism discovered recently in Al–Zn–Cr alloys.

Interfacial free energy and medium range order: Proof of an inverse of Frank's hypothesis

We study the relation of crystal-liquid interfacial free energy and medium range order in the quasicrystal-forming $\mathrm{T}{\mathrm{i}}_{37}\mathrm{Z}{\mathrm{r}}_{42}\mathrm{N}{\mathrm{i}}_{21}$ liquid from undercooling experiment and ab initio molecular dynamics (MD) simulation. Adding a small amount of Ag to the liquid significantly reduces the degree of undercooling, which is suggestive of small interfacial free energy, and thus very similar atomic configuration between the liquid and the icosahedral quasicrystal phases. Using ab initio MD study, we find that Ag atoms predominantly form a bond with Zr atoms in the short range and, further, Ag-Zr pairs are extended in the liquid, as a medium range order which is identical to the global structural feature reported recently [Liu et al., Phys. Rev. Lett. 105, 155501 (2010)]. This result may expect extremely small undercooling if the icosahedral medium range order exists in a liquid forming an icosahedral quasicrystal, which implies the ambiguity of clear distinction of heterogeneous and homogeneous nucleation.

Deformation behavior of Al-rich metallic glasses under nanoindentation

To clarify the deformation behavior of Al-rich metallic glasses (MGs), two kinds of Al-rich MGs (i.e. bulk and ribbon samples) with different frozen-in excess volume have been analyzed under nanoindentation. It was found that, with the decrease of frozen-in excess volume, the serration behavior becomes inconspicuous together with the increase of hardness. Further, shear transformation zones (STZs), related to the occurrence of shear banding, have been evaluated by different methods: the cooperative shearing model (CSM), the rate-jump method (RJM) and the dynamic-mechanical response (DMR). In contrast, the STZ volumes, calculated by the RJM, increase from 2.77nm3 in the bulk to 3.59nm3 in the ribbon, which are in good agreement with 2.60nm3 obtained from the icosahedral supercluster medium-range order structure model in Al-rich MGs. This result reflects that an intrinsic correlation exists between the formation of STZs and the medium-range orders (MROs). Moreover, the variation trend of the STZ volume was analyzed in terms of the frozen-in excess volume content.

Properties of Icosahedral Clusters and Medium-Range Order in AlCuZr Alloy

The evolution characteristics of icosahedral clusters during the rapid solidification of Al10Cu50Zr40 alloy under cooling rates of 1.0 × 1011 K/s are investigated based on molecular dynamics simulations. The structural properties of short-range order and medium-range order of Al10Cu50Zr40 alloy are analyzed by several structural characterization methods. It is found that the icosahedral cluster is the dominant short range order structure. Simultaneously, the medium -range order structural evolutions are described in detail by quantitative method and visualization technology during the rapid solidification. The results reveal that the medium-range order icosahedral clusters are bonding with each other by chain, triangle, tetrahedral and their combination structures, and have excellent structural stability and configural continuity with the temperature decreasing. The medium-range order clusters that consist of , and interlocked with each other and built the densely packed network structures.

Effect of Al on the atomic structure in Zr50Cu40Al10 metallic glass

The icosahedral short-range order and medium-range order of Zr50Cu50 and Zr50Cu40Al10 metallic glasses have been investigated by molecular dynamics simulations. Our analysis shows that, although the replacement of a few percent of Cu by Al enlarges the population of full icosahedra (FIs), the degree of interpenetrating aggregation for FIs is reduced which might be caused by the strong avoidance of Al-centered FIs in the ternary system. However, this fact does not mean the weakness of icosahedral medium range order in Zr50Cu40Al10 metallic glass. If the interpenetrating and non-interpenetrating connections are both considered, the largest super-cluster formed by the connected FIs in Zr50Cu40Al10 is rather larger than that in Zr50Cu50, which might play an important role in slowing down the kinetics and thus enlarge the glass-forming ability.

Characterization of nano-quasicrystal-formation in correlation to the local structure in Zr-based metallic glasses containing Pd

Abstract The effect of a noble metal (Pd) on the local atomic structure of the glassy state and the transformation behavior of quasicrystal (QC) precipitation in Zr 70 (Cu and Ni) 30-x Pd x (x = 0, 5, 10, 20) alloys were investigated. A QC phase precipitates in Zr-Cu glassy alloys at Pd concentrations of 5–20 at.% and in Zr-Ni glassy alloys at Pd concentrations of 10–20 at.%. The radial distribution function (RDF) indicates a change in the local atomic structure upon the addition of Pd. The QC phase is abruptly formed from the glassy structure above a certain temperature. The activation energy for nucleation is much larger than that for the precipitation of conventional intermetallic compounds. The QC growth is suddenly suppressed when their diameter reaches approximately 20 nm. The cooperative motion of icosahedral clusters as the precipitation mechanism was discussed. It was assumed that QC nucleus has a Zr-centered icosahedral medium-range order (MRO) as its core, and it grows by the aggregation of surrounding small icosahedral clusters. Noble metals might play a role of stabilizing the individual Zr-centered icosahedral MROs.

Critical scaling of icosahedral medium-range order in CuZr metallic glass-forming liquids.

The temperature evolution of icosahedral medium-range order formed by interpenetrating icosahedra in CuZr metallic glassforming liquids was investigated via molecular dynamics simulations. Scaling analysis based on percolation theory was employed, and it is found that the size distribution of clusters formed by the central atoms of icosahedra at various temperatures follows a very good scaling law with the cluster number density scaled by S−τ and the cluster size S scaled by |1 − Tc/T|−1/σ, respectively. Here Tc is scaling crossover-temperature. τ and σ are scaling exponents. The critical scaling behaviour suggests that there would be a structural phase transition manifested by percolation of locally favoured structures underlying the glass transition, if the liquid could be cooled slowly enough but without crystallization intervening. Furthermore, it is revealed that when icosahedral short-range order (ISRO) extends to medium-range length scale by connection, the atomic configurations of ISROs will be optimized from distorted ones towards more regular ones gradually, which significantly lowers the energies of ISROs and introduces geometric frustration simultaneously. Both factors make key impacts on the drastic dynamic slow-down of supercooled liquids. Our findings provide direct structure-property relationship for understanding the nature of glass transition.