  We study the formation rate of binary black hole mergers formed through
gravitational-wave emission between unbound, single black holes in globular
clusters. While the formation of these binaries in very dense systems such as
galactic nuclei has been well studied, we show here that this process can
operate in lower-density stellar systems as well, forming binaries at a rate
similar to other proposed pathways for creating eccentric mergers. Recent
advances in post-Newtonian cluster dynamics indicate that a large fraction of
dynamically-assembled binary black holes merge inside their host clusters
during weak and strong binary-single and binary-binary interactions, and that
these systems may retain measurable eccentricities as they travel through the
LIGO and LISA sensitivity bands. Using an analytic approach to modeling binary
black holes from globular clusters, we show that the formation of merging
binaries from previously unbound black holes can operate at a similar rate to
mergers forming during strong binary encounters, and that these binaries
inhabit a unique region of the gravitational-wave frequency space which can be
identified by proposed deci-Hertz space-based detectors.
