  Many material properties can be traced back to properties of their grain
boundaries. Grain boundary energy (GBE), as a result, is a key quantity of
interest in the analysis and modeling of microstructure. A standard method for
calculating grain boundary energy is molecular dynamics (MD); however,
on-the-fly MD calculations are not tenable due to the extensive computational
time required. Lattice matching (LM) is a reduced-order method for estimating
GBE quickly; however, it has only been tested against a relatively limited set
of data, and does not have a suitable means for assessing error. In this work,
we use the recently published dataset of Homer et al. [1] to assess the
performance of LM over the full range of GB space, and to equip LM with a
metric for error estimation. LM is used to generate energy estimates, along
with predictions of facet morphology, for each of the 7,304 boundaries in the
Homer dataset. In keeping with prior work, it is observed that LM predictions
of low energy boundaries matches well with MD results. Moreover, there is a
good general agreement between LM and MD, and it is apparent that the error
scales approximately linearly with the predicted energy value; this makes it
possible to establish an empirical estimate on error for future LM
calculations. An essential part of the LM method is the faceting relaxation,
which corrects the expected energy by convexification across the compact space
(S2) of boundary plane orientations. The original Homer dataset did not allow
for faceting, but upon extended annealing, it was shown that facet patterns
similar to those predicted by LM were emerging.
