Fractal atomic-level percolation in metallic glasses

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Science  18 Sep 2015:
Vol. 349, Issue 6254, pp. 1306-1310
DOI: 10.1126/science.aab1233
  • Fig. 1 In situ diffraction and volume results.

    (A) Three-dimensional reconstructed sample volumes from in situ transmission x-ray microscopy data at ~0 GPa. (B) In situ x-ray diffraction data with increasing pressure (arb., arbitrary units). (C) Volume scaling with scattering vectors q1 and q2 for Cu46Zr46Al5Be3 and La62Al14Cu11.7Ag2.3Ni5Co5 metallic glasses.

  • Fig. 2 Dimensionality crossover in simulations.

    (A) The Cu46Zr54 from FF1 and FF2 both exhibit a transition in dimensionality from ~2.5 to 3 between r2 and r3. (B) Ni80Al20 exhibits a transition in dimensionality from ~2.5 to 3 between r1 and r2. The insets show corresponding RDF curves with the correlation lengths ξ indicated.

  • Fig. 3 Concepts in fractals and percolation.

    (A and B) Site lattice percolation for p < pc (A) and p > pc (B). White squares are “occupied,” black squares are “unoccupied,” and blue squares are percolating. (C) Illustrative example of a lattice made up of Sierpinski gaskets with correlation length ξ, adopted from (23). This lattice is fractal over the short range and homogeneous over the long range. (D) MD simulation of the Cu46Zr54 system at room temperature with full periodic boundaries (Cu, blue; Zr, yellow). (E) Cu46Zr54 with all atoms removed, except for those belonging to icosahedrons.

  • Fig. 4 Simulated properties during supercooling.

    (A) Dimensionality from r1 during supercooling. (B) Volume versus temperature behavior (solid black line), shown with guidelines (red dotted line) and Tg (~763 K, solid black arrow). Inset snapshots show atom vectors (red) generated from reference temperatures ~540 K above the indicated temperatures (dotted black arrows) for a slice 3 Å thick (roughly the nearest-neighbor distance). Dots are atom centers (Cu, blue; Zr, yellow).

Supplementary Materials

  • Fractal atomic-level percolation in metallic glasses

    David Z. Chen, Crystal Y. Shi, Qi An, Qiaoshi Zeng, Wendy L. Mao, William A. Goddard III, Julia R. Greer

    Materials/Methods, Supplementary Text, Tables, Figures, and/or References

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    • Materials and Methods
    • Supplementary Text
    • Figs. S1 to S3
    • Captions for Databases S1 to S4

    Additional Data

    Database S1
    Diffraction data for the Cu46Zr46Al5Be3 sample
    Database S2
    RDF data for the Cu46Zr54 MD sample using FF1
    Database S3
    RDF data for the Cu46Zr54 MD sample using FF2
    Database S4
    RDF data for the Ni80Al20 MD sample