Supplementary information files for Stacking-mediated diffusion of ruthenium nanoclusters in bilayer graphene and graphite

Supplementary files for article Stacking-mediated diffusion of ruthenium nanoclusters in bilayer graphene and graphite The diffusion, penetration and intercalation of metallic atomic dopants is an important question for various graphite applications in engineering and nanotechnology. We have performed systematic first-principles calculations of the behaviour of ruthenium nanoclusters on a graphene monolayer and intercalated into a bilayer. Our computational results show that at a sufficiently high density of single Ru atom interstitials, intercalated atoms can shear the surrounding lattice to an AA stacking configuration, an effect which weakens with increasing cluster size. Moreover, the interlayer stacking configuration, in turn, has a significant effect on cluster diffusion. We therefore find different trends in diffusivity as a function of cluster size and interlayer stacking. For monolayer graphene and an AA graphene bilayer, the formation of small clusters generally lowers diffusion barriers, while the opposite behaviour is found for the preferred AB stacking configuration. These results demonstrate that conditions of local impurity concentration and interlayer disregistry are able to regulate the diffusivity of metallic impurities in graphite.《双层石墨烯与石墨中钌纳米团簇的堆垛介导扩散》论文补充材料 金属原子掺杂剂的扩散、渗透与插层，是工程与纳米技术领域各类石墨基应用中的核心科学问题。本研究针对单层石墨烯表面以及插层进入双层石墨烯的钌纳米团簇（ruthenium nanoclusters）行为开展了系统性第一性原理计算（first-principles calculations）。计算结果表明，当单个钌原子间隙缺陷的密度足够高时，插层原子可使周围晶格发生剪切并形成AA堆垛构型（AA stacking configuration），该效应随团簇尺寸增大而逐渐减弱。此外，层间堆垛构型反过来对团簇扩散具有显著影响。因此，本研究发现扩散率随团簇尺寸与层间堆垛构型的变化呈现出不同的演化趋势。对于单层石墨烯与AA堆垛双层石墨烯而言，小团簇的形成通常会降低扩散势垒（diffusion barriers）；而对于更稳定的AB堆垛构型（AB stacking configuration），则呈现出完全相反的规律。上述研究结果表明，局部杂质浓度与层间错配（interlayer disregistry）的条件，能够调控石墨中金属杂质的扩散率。