Ordering and dimensional crossovers in metallic glasses and liquids

David Z. Chen, Qi An, William A. Goddard, III, and Julia R. Greer

Phys. Rev. B 95, 024103 – Published 4 January 2017

Abstract

The atomic-level structures of liquids and glasses are amorphous, lacking long-range order. We characterize the atomic structures by integrating radial distribution functions (RDF) from molecular dynamics (MD) simulations for several metallic liquids and glasses: $C u_{46} Z r_{54}, N i_{80} A l_{20}, N i_{33.3} Z r_{66.7}$ , and $P d_{82} S i_{18}$ . Resulting cumulative coordination numbers (CN) show that metallic liquids have a dimension of $d = 2.55 \pm 0.06$ from the center atom to the first coordination shell and metallic glasses have $d = 2.71 \pm 0.04$ , both less than 3. Between the first and second coordination shells, both phases crossover to a dimension of $d = 3$ , as for a crystal. Observations from discrete atom center-of-mass position counting are corroborated by continuously counting Cu glass- and liquid-phase atoms on an artificial grid, which accounts for the occupied atomic volume. Results from Cu grid analysis show short-range $d = 2.65$ for Cu liquid and $d = 2.76$ for Cu glass. Cu grid structures crossover to $d = 3$ at $ξ \sim 8 Å$ ( $\sim 3$ atomic diameters). We study the evolution of local structural dimensions during quenching and discuss its correlation with the glass transition phenomenon.

Received 1 February 2016
Revised 8 November 2016

DOI:https://doi.org/10.1103/PhysRevB.95.024103

Physics Subject Headings (PhySH)

Structural properties

Amorphous materials

Molecular dynamics Percolation theory

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

David Z. Chen^1,*, Qi An², William A. Goddard, III², and Julia R. Greer^1,3

¹Division of Engineering and Applied Sciences, California Institute of Technology, Pasadena, California, 91125, USA
²Materials and Process Simulation Center, California Institute of Technology, Pasadena, California, 91125, USA
³The Kavli Nanoscience Institute, California Institute of Technology, Pasadena, California, 91125, USA

^*Corresponding author: dzchen@caltech.edu

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Issue

Vol. 95, Iss. 2 — 1 January 2017

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Images

Figure 1
(a) Diagram of expected crossover in log-log plot of mass versus radius. Short-range fractal dimension $d_{f}$ crosses over to long-range dimension d at the correlation length $ξ$ . b) Radial distribution functions for $C u_{46} Z r_{54} (F F_{2})$ in the glass and liquid phase. Dashed lines indicate positions for the first peak, $r_{1}$ , and coordination shells, $r_{is}$ , where $i = 1 - 4$ .
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Figure 2
Log-log plots of total atom number $(CN + 1)$ versus radius, r, showing local dimension in metallic glasses of $C u_{46} Z r_{54}$ (a) $F F_{1}$ , (b) $F F_{2}$ , (c) $N i_{80} A l_{20}$ , (d) $N i_{33.3} Z r_{66.7}$ , and (e) $P d_{82} S i_{18}$ . Short-range dimension, $d = 2.71 \pm 0.04$ , is measured through a linear fit between the radius of the center atom and the outer radius of the first coordination shell. Long-range dimension, $d = 3$ , is measured from a linear fit of points beyond the outer radius of the second coordination shell.
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Figure 3
Log-log plots of total atom number $(CN + 1)$ versus radius, r, showing local dimension for metallic liquids of $C u_{46} Z r_{54}$ (a) $F F_{1}$ at 2500 K, (b) $F F_{2}$ at 2000 K, (c) $N i_{80} A l_{20}$ at 3000 K, (d) $N i_{33.3} Z r_{66.7}$ at 2500 K, and (e) $P d_{82} S i_{18}$ at 2000 K. Short-range dimension, $d = 2.55 \pm 0.06$ , is measured through linear fit between the radius of the center atom and the outer radius of the first coordination shell. Long-range dimension, $d = 3$ , is measured from a linear fit of points beyond the outer radius of the second coordination shell.
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Figure 4
Comparison of crossovers in pure Cu systems using discrete and grid counting methods. (a) $d \sim 2.90$ in Cu crystal (300 K), $d \sim 2.69$ in Cu glass (300 K), and $d \sim 2.51$ in Cu liquid (2500 K) below $ξ$ with CN counted by atom center positions. (b) Schematic of the grid procedure. Cu atoms in the simulation box (left) are replaced by effective grid points representing their physical volume. Grid points capture the overall atomic structure (see 1 Å slice, right). (c) Crossovers in dimension from $d \sim 2.65$ and $d \sim 2.76$ to $d \sim 3$ for Cu liquid and glass, respectively, using a grid method for continuous counting. Here $C N_{grid}$ is the normalized coordination number based on counting grids within each atom. Secondary axis (right side): $d (\ln (C N_{grid})) / d (\ln (r))$ versus r showing a distinct crossover near $ξ \sim 8 Å$ .
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Figure 5
Temperature effects on local dimensions in Cu glass and liquids using grid counting. (a) $\ln (C N_{grid})$ versus r and $d (\ln (C N_{grid})) / d (\ln (r))$ versus r plots at temperatures from 600–2100 K at 300 K intervals. We define heuristically intervals for short-range dimension, $d_{s}, \sim 1.2 - 3.2 r_{Cu}$ , and valley dimension, $d_{v}, \sim 2 - 3.2 r_{Cu}$ , where the local dimension is largely temperature insensitive but appears to be sensitive to the liquid/glass phase. $r_{Cu} = 1.28 Å$ . (b) $d_{s}$ and $d_{v}$ versus temperature; $d_{s}$ increases roughly linearly as temperature is decreased, and $d_{v}$ appears sensitive to the glass transition $(T_{g} \sim 1150 K)$ .
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Figure 6
$d_{v}$ versus ϕ showing a connection between the maximally random jammed $(MRJ, ϕ \sim 0.64)$ state and onset of $T_{g}$ .
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