Construction of a disorder variable from Steinhardt order parameters in binary mixtures at high densities in three dimensions

Using molecular dynamics simulation, we investigate the structural disorder in crystal, polycrystal, and glass in a Lennard-Jones binary mixture composed of N(1) + N(2) = 4096 particles at a low temperature in three dimensions. The size ratio σ(2)/σ(1) between the large and small particles is either 1.2 or 1.4. The crossovers among these states occur, as the composition of the large particles c = N(2)/(N(1) + N(2)) is varied. We define a disorder variable D(j) for each particle j in terms of local bond order parameters based on spherical harmonics (Steinhardt order parameters). Stacking faults and grain boundaries in fcc polycrystal and mesoscopic structural heterogeneity in glass are then visualized. At small c, disturbances of large particles is stronger for larger σ(2)/σ(1). At large c, the transition between glass and polycrystal occurs nearly discontinuously at c = c(c) ~ 0.8. At σ(2)/σ(1) = 1.4, microphase separation occurs in polycrystal states with c > c(c), where fcc crystal grains comprising the large particles are enclosed by amorphous layers composed of the two particle species.