  The structure of the electrical double layer (EDL) formed near graphene in
aqueous environments strongly impacts its performance for a plethora of
applications, including capacitive deionization. In particular, adsorption and
organization of multivalent counterions near the graphene interface can promote
nonclassical behaviors of EDL including overcharging followed by co-ion
adsorption. In this paper, we characterize the EDL formed near an electrified
graphene interface in dilute aqueous $YCl_3$ solution using in situ high
resolution x-ray reflectivity (also known as crystal truncation rod (CTR)) and
resonant anomalous x-ray reflectivity (RAXR). These interfacial-specific
techniques reveal the electron density profiles with molecular-scale
resolution. We find that yttrium ions ($Y^{3+}$) readily adsorb to the
negatively charged graphene surface to form an extended ion profile. This ion
distribution resembles a classical diffuse layer but with a significantly high
ion coverage, i.e., 1 $Y^{3+}$ per 11.4 $\pm$ 1.6 A$^2$, compared to the value
calculated from the capacitance measured by cyclic voltammetry (1 $Y^{3+}$ per
~240 A$^2$). Such overcharging can be explained by co-adsorption of chloride
that effectively screens the excess positive charge. The adsorbed $Y^{3+}$
profile also shows a molecular-scale gap ($\geq$5 A) from the top graphene
surfaces, which is attributed to the presence of intervening water molecules
between the adsorbents and adsorbates as well as the lack of inner-sphere
surface complexation on chemically inert graphene. We also demonstrate
controlled adsorption by varying the applied potential and reveal consistent
$Y^{3+}$ ion position with respect to the surface and increasing cation
coverage with decreasing applied potential.
