Ordering and dimensional crossovers in metallic glasses and liquids
  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: Cu46Zr54, Ni80Al20, Ni33.3Zr66.7, and Pd82Si18. Resulting cumulative coordination numbers (CN) show that metallic liquids have a dimension of d = 2.55 +/- 0.06 from the center atom to the first coordination shell and metallic glasses have d = 2.71 +/- 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 {\xi}~8 {\AA} (~3 atomic diameters). We study the evolution of local structural dimensions during quenching and discuss its correlation with the glass transition phenomenon. 
David Z. Chen, Qi An, William. A. Goddard III, Julia R. Greer
cond-mat.mtrl-sci cond-mat.soft