  The search for local structures within a disordered medium has led to
proposals of several methods for probing transient short-range symmetry in a
homogeneous mono-atomic liquid. We offer a comparison of different
characterizations of such local structure in an in-homogeneous liquid. We
simulate the interfaces between a Lennard-Jones liquid and (i) a flat
Lennard-Jones wall, (ii) a wall of face-centered cubic-packed Lennard-Jones
particles, and (iii) a Lennard-Jones vapor. The interface density distributions
in cases (i) and (ii) have oscillations extending several particle diameters
into the bulk liquid, while that in case (iii) the interface density
distribution monotonically decays from the bulk liquid to the vapor. We search
for transient ordered fluctuations, which we identify with local ordered
structures, using the Aperture Cross Correlation Function of the system. We
find that only particles in the FCC-liquid interface that are in the two layers
closest to the FCC surface exhibit preferred four-fold symmetry. Furthermore,
the absence of three- or five-fold symmetry peaks in the Aperture Cross
Correlation Function of the liquid-vapor interface yields a different picture
of that interface than derived from the high density of bi-pyramidal clusters
found in the Topological Cluster Classification study (Molecular Physics, 109
(7-10), 1393-1402 (2011)). While the Aperture Cross Correlation Function
results need not be viewed as contradictory with the Topological Cluster
Classification results, we argue the advantages of using the former to
characterize transient ordered fluctuations as being both experimentally
accessible in favorable cases and not reliant on a list of structures.
