  Durable interest in developing a framework for the detailed structure of
glassy materials has produced numerous structural descriptors that trade off
between general applicability and interpretability. However, none approach the
combination of simplicity and wide-ranging predictive power of the
lattice-grain-defect framework for crystalline materials. Working from the
hypothesis that the local atomic environments of a glassy material are
constrained by enthalpy minimization to a low-dimensional manifold in atomic
coordinate space, we develop a novel generalized distance function, the
Gaussian Integral Inner Product (GIIP) distance, in connection with
agglomerative clustering and diffusion maps, to parameterize that manifold.
Applying this approach to a two-dimensional model crystal and a
three-dimensional binary model metallic glass results in parameters
interpretable as coordination number, composition, volumetric strain, and local
symmetry. In particular, we show that a more slowly quenched glass has a higher
degree of local tetrahedral symmetry at the expense of cyclic symmetry. While
these descriptors require post-hoc interpretation, they minimize bias rooted in
crystalline materials science and illuminate a range of structural trends that
might otherwise be missed.
