Second-Nearest-Neighbor Correlations from Connection of Atomic Packing Motifs in Metallic Glasses and Liquids

Introduction

• Second-neighbor correlations beyond the first-neighbor shell are proposed as a useful starting point for characterizing medium-range order.These correlations are reflected in the second RDF peak.Source: Introduction · pp. 2–3
• Earlier work proposed that the ways packing motifs connect may provide a common origin for pair correlations and splitting of the second RDF peak.Coordination polyhedra can share one, two, three, or four atoms.Source: Introduction · p. 3
• The study asks whether connection schemes vary across alloys and cooling conditions, account for split second RDF peaks, and differ in stiffness.It also asks whether these relationships hold across packing motifs and between metallic glasses and their parent liquids.Source: Introduction · pp. 3–4
• The authors conduct molecular-dynamics simulations of representative model metallic-glass systems with different constituents and cooling rates.The systems use embedded-atom-method potentials optimized for five alloy systems.Source: Introduction · p. 4

• Ta's liquid inherent structure and quenched glass both show a split second peak, but the Zr46Cu46Al8 glass does not.Source: General properties of polyhedra… · pp. 5–6
• The first three connection types share a vertex, edge, or face, respectively; the 4-atom type shares a distorted quadrilateral or squashed tetrahedron.Source: General properties of polyhedra… · p. 5
• Each of four connection schemes has a characteristic second-neighbor distance, so their superimposed contributions form the broad second RDF peak and can produce sub-peaks.Source: General properties of polyhedra… · pp. 5–6
• MD peak positions closely match geometric predictions, supporting cluster connections as the primary source of second-peak locations.Source: General properties of polyhedra… · p. 7
• At liquidus temperatures, 1- and 2-atom connection counts depend weakly on coordination number, whereas 3- and 4-atom counts rise nearly linearly, likely reflecting cluster proximity.Source: General properties of polyhedra… · p. 8
• Characteristic connection schemes and associated values are reported as universally the same; supercooling, especially near the glass transition, alters preferences for 2- and 3-atom clusters, so liquid Fig. 3(b) correlations need not be the same in glass.Source: General properties of polyhedra… · p. 8

Influence of structural ordering during cooling on cluster connections

• The relative fractions of the four connection schemes determine the second RDF peak’s composition and shape, and can sometimes cause its splitting.An increased fraction of three-atom connections is associated with higher intensity at the first sub-peak.Source: Influence of structural ordering… · pp. 8–10
• One-atom connections remain almost unchanged between liquid and glass, while two-, three-, and four-atom connection numbers change during cooling.The relative fractions of one-atom and four-atom connections are respectively the highest and lowest among the studied samples.Source: Influence of structural ordering… · pp. 8–9
• Slower cooling produces more structural ordering, with a larger increase in three-atom connections and decreases in two- and four-atom connections.This cooling-rate dependence is illustrated for Cu64Zr36 samples subjected to different quenching procedures.Source: Influence of structural ordering… · p. 9
• Three-atom connections increase at the expense of two- and four-atom connections, while the total number of cluster connections remains essentially unchanged.The three-atom scheme corresponds to face sharing, preferred over edge or squashed-tetrahedra sharing.Source: Influence of structural ordering… · p. 9

Splitting of second peak in the radial distribution functions

• The second RDF peak is split in the inherent structure of an equilibrium Ta liquid, supporting an origin in cluster connections rather than newly developed local order.The reported liquid lacks extended icosahedral or crystalline topological order.Source: Splitting of second peak in the radial… · p. 10
• The split peak can be inherited from the liquid’s inherent structure without new local order appearing toward the glass transition.In the high-temperature instantaneous liquid, thermal vibrations smear the splitting, which is not observed there.Source: Splitting of second peak in the radial… · p. 11
• Uneven contributions from connection schemes can split the second peak, with one- and three-atom contributions stronger than those from two- and four-atom connections.The text relates this unevenness to the splitting of the second peak in the RDF.Source: Splitting of second peak in the radial… · p. 11
• Cooling-driven enhancement of three-atom connections at the expense of two- and four-atom connections may shift the sub-peaks and change their intensity.The Ta glass has a more pronounced first sub-peak than the inherent structure of the Ta liquid.Source: Splitting of second peak in the radial… · p. 11

Cluster connection dependence of elastic deformation

• Three-atom connections have the stiffest elastic response, while two- and four-atom connections deform more than the macroscopic strain.One-atom connections have elastic strain nearly equivalent to the macroscopic deformation.Source: Cluster connection dependence of… · p. 12
• Sharing triangulated faces between tetrahedra is likely to raise the energy barrier of potential-energy basins, which is known to increase shear modulus.This is offered as a possible explanation for the stiffness of three-atom connections.Source: Cluster connection dependence of… · p. 12
• During cooling, the fraction of stiff three-atom connections grows as more flexible two- and four-atom connections decline; one-atom connections remain insensitive to structural ordering.The one-atom connections’ elastic response remains equivalent to macroscopic deformation.Source: Cluster connection dependence of… · p. 12

Methods

• The simulations cover eight metallic-glass models across Cu64Zr36, Ni80P20, Al90La10, Mg65Cu25Y10, and Zr46Cu46Al8, with 128,000 atoms per model.The simulation boxes exceed 10 nm, and liquids are equilibrated before quenching to 300 K at controlled cooling rates.Source: Methods · p. 13
• Short-range order is analyzed using Voronoi tessellation on inherent structures obtained by conjugate-gradient energy minimization.The minimization uses energy and force thresholds of 10^-6 eV and 10^-6 eV/Հଷ; liquid structure analysis averages 100 configurations over 1 ns.Source: Methods · p. 13
• Athermal quasi-static shear is applied in the nominal elastic regime to avoid strain-rate effects and thermal fluctuations, with simple shear in the y-z direction.The stated strain range is zero to 0.05.Source: Methods · p. 13
• Connection-specific strain is calculated by fitting a locally affine transformation to map cluster-neighbor separations between configurations, then deriving the Lagrangian strain.The y-z component is used as the atomic cluster strain for that connection scheme.Source: Methods · pp. 13–14

Fig. 4

• Fig. 4 plots connected clusters per atom at 300 K and the change from liquidus temperature for four schemes across samples #1–8.The first four samples are Cu64Zr36 glasses prepared at increasing cooling rates.Source: Figure 4 · p. 24

Table I

• Table I lists metallic-glass samples prepared by molecular-dynamics simulation; sample #1’s effective cooling rate is approximately 10^9 K/s.Its quench rate within the supercooled region determines the stated effective rate.Source: Table I · p. 20, Figure legends · p. 20

Fig. 1

• Fig. 1 compares Ta-liquid and glass radial distribution functions and schematically defines four coordination-polyhedron connection schemes by one to four shared atoms.Its inset relates second-neighbor correlations to the second RDF peak.Source: Figure 1 · p. 21

Fig. 2

• Fig. 2 decomposes 300 K RDFs for Ni80P20 and Zr46Cu46Al8 glasses into nearest-neighbor and second-neighbor contributions from four cluster-connection schemes.Both samples were simulated at a cooling rate of 10^10 K/s; insets magnify large-distance RDFs.Source: Figure 2 · p. 22

Fig. 3

• Fig. 3 relates average bond length R1 to second-neighbor distance R2* and plots connected-cluster count against nearest-neighbor coordination number at each species’ liquidus temperature.Data points represent species in the listed samples; solid lines show geometric calculations.Source: Figure 3 · p. 23

Fig. 5

• Fig. 5 relates cluster shear strains for different connection schemes to imposed macroscopic shear strain across samples #1–8.The dashed line marks equality between cluster and macroscopic strain.Source: Figure legends · p. 19, Figure 5 · p. 25