Graphene at Liquid Copper Catalysts: Atomic‐Scale Agreement of Experimental and First‐Principles Adsorption Height

Abstract

Liquid metal catalysts have recently attracted attention for synthesizing high-quality 2D materials facilitated via the catalysts' perfectly smooth surface. However, the microscopic catalytic processes occurring at the surface are still largely unclear because liquid metals escape the accessibility of traditional experimental and computational surface science approaches. Hence, numerous controversies are found regarding different applications, with graphene (Gr) growth on liquid copper (Cu) as a prominent prototype. In this work, novel in situ and in silico techniques are employed to achieve an atomic-level characterization of the graphene adsorption height above liquid Cu, reaching quantitative agreement within 0.1 Å between experiment and theory. The results are obtained via in situ synchrotron X-ray reflectivity (XRR) measurements over wide-range q-vectors and large-scale molecular dynamics simulations based on efficient machine-learning (ML) potentials trained to first-principles density functional theory (DFT) data. The computational insight is demonstrated to be robust against inherent DFT errors and reveals the nature of graphene binding to be highly comparable at liquid Cu and solid Cu(111). Transporting the predictive first-principles quality via ML potentials to the scales required for liquid metal catalysis thus provides a powerful approach to reach microscopic understanding, analogous to the established computational approaches for catalysis at solid surfaces.

Employing Surface Curvature for Spatially Resolved X-Ray Reflectivity: Graphene Domains on Liquid Copper

“…The reason is that this position on the XRR curve is close to the minimum of the first Kiessig fringe (itself related to the height of the graphene layer above the liquid copper). [12,20,21,37] The red and green curves in Figure 3a are obtained consequently at different times of the growth (7.4 and 9.0 min after opening the CH4 valve, respectively), resulting in partial coverage of the copper surface with graphene flakes. The growth coverage was monitored in real time with radiation-mode optical microscopy.…”

“…[38] The slabs include Cu (bulk), C (single atomic layer), and a void in between. [12,20,21] The fitting parameters are combined in Table 1. We define the interlayer Cu-C gap as the distance between the inflection point of the Cu slab and the center of the C layer, i.e., dvoid + dGr/2, where dvoid is the thickness of the void and dGr is the thickness of the graphene layer (C atomic radius) as illustrated in Figure S2.…”

“…The simultaneous and disentangled presence of the specular reflection from the bare and graphene-covered surface can be used to measure the two corresponding XRR curves with one single conventional αi-2αi angular scan. In our previous work, [20,21] we characterized the height of the graphene on Cu, also called the 'gap' between the surface of the liquid catalyst and the graphene layer fully covering the surface, as this parameter is related to the interlayer van der Waals binding force between the metal and the carbon layer. However, it is unknown whether the gap value is identical for isolated flakes of graphene.…”

“…The drop in the intensity around the qz = 0.8 Å -1 is due to the Kiessig minimum, related to the height separation between the liquid surface and the graphene sheet. [12,21] Typically, the analysis of such patches with XRR is quite problematic unless supported by additional information such as diffuse off-specular scattering measurements or obtained by grazing incidence small angle X-ray scattering (GISAXS). However, these methods are applicable mainly for islands of nanometric size (up to a few microns in the best cases) [22,23] and are not sensitive to larger objects at the μm to mm scale.…”

Employing Surface Curvature for Spatially Resolved X‐Ray Reflectivity: Graphene Domains on Liquid Copper

“…The simultaneous and disentangled presence of the specular reflection from the bare and graphene-covered surface can be used to measure the two corresponding XRR curves with one single conventional α i -2α i angular scan. In our previous work, [20,21] we characterized the height of the graphene on Cu, also called the "gap" between the surface of the liquid catalyst and the graphene layer fully covering the surface, as this parameter is related to the interlayer van der Waals binding force between the metal and the carbon layer. However, it is unknown whether the gap value is identical for isolated flakes of graphene.…”