Figure 1

(a,b) Atomic force microscopy images measured in atmospheric conditions on an Ir(111) single crystal covered with graphene grown under ultrahigh vacuum. Note the interconnected network of wrinkles, which reveals the presence of graphene over the whole surface.Reuse & Permissions

Figure 2

Sketch of the first to fifth graphene BZs and their centers for Ir (${\Gamma }^0\to 4_{\mathrm{Ir}}$) (red) and graphene (${\Gamma }^0\to 4_{\mathrm{C}}$) (blue) where the scattered intensity was measured. Blue ellipses represent in-plane cuts of graphene diffraction rods, characterized by their position, yielding the average projected lattice parameter, as well as by their $Q_{\mathrm{r}}$ radial and $\omega$ azimuthal widths. For the sake of clarity, the moiré diffraction peaks are omitted from this sketch but are shown in the close-up view, which marks the measurable moiré peaks and gives a geometric construction explaining the observed width of these peaks.Reuse & Permissions

Figure 3

(a) In-plane radial scans at RT close to the third BZ center for Ir (${\Gamma }_{\mathrm{Ir}}^2$) and graphene (${\Gamma }_{\mathrm{C}}^2$) revealing the Ir CTR (red), the graphene rod (blue), and a moiré peak (${\Gamma }_{\mathrm{m}}^2$, gray), as a function of radial momentum transfer ($Q_{\mathrm{r}}$) and reciprocal space lattice units ($h$). The position of the commensurate structures with 9 Ir cells matching 10 C ones and 19 Ir cells matching 21 C ones are marked. (b) In-plane radial scans measured for another sample (thus having different structure; see Sec. 5), with and without Pt clusters on top (squares and circles, respectively), close to the second-order BZ center for Ir (${\Gamma }_{\mathrm{Ir}}^1$) and graphene (${\Gamma }_{\mathrm{C}}^1$), revealing that moiré peaks (${\Gamma }^{,}{1}_{\mathrm{m}}$) appear and that the graphene peak is reinforced due to the presence of Pt clusters. Peaks in (b) include two components originating from two Ir crystallites. ${\Gamma }_{\mathrm{C}}^1$ is thus fit with two Gaussians, whose centers do not change upon Pt cluster deposition. Insets: sketch of the moiré reciprocal lattice.Reuse & Permissions

Figure 4

(a) Radial scans for graphene grown at $T_{\mathrm{g}}=1070$ K and measured at RT, at different peak orders (${\Gamma }^1\to 4_{\mathrm{C}}$), vertically shifted for clarity. (b) Graphene radial scans FWHM ($\Delta Q_{\mathrm{r}}$) as a function of peak order (${\Gamma }^0\to 4_{\mathrm{C}}$), at RT and 1070 K, and linear fits (lines). (c) Azimuthal angle scans, for graphene grown at $T_{\mathrm{g}}=1070$ K and measured at RT, at different peak orders (${\Gamma }^1\to 4_{\mathrm{C}}$), vertically shifted for clarity. For ${\Gamma }_{\mathrm{C}}^4$, the azimuthal angle scan (blue circles) has been smoothened (solid lighter blue line) for easing the assessment of the scan FWHM. (d) Graphene radial ($\Delta Q_{\mathrm{r}}$) and azimuthal ($\Delta \omega$) FWHM as a function of the sample temperature for the second-order peaks.Reuse & Permissions

Figure 5

STM topograph of graphene/Ir(111) measured with a 10.9 nA tunneling current and a 0.2 V bias. Solid lines follow the moiré lattice, and white dots mark centers of carbon rings. The two triangles share only one edge, evidencing an in-plane shear.Reuse & Permissions

Figure 6

(a) Radial scans close to the third BZ center at 1070 K (light red and light blue), and the same sample at RT (red and blue). Note that the RT measurement corresponds to a sample decorated with Pt clusters reducing counting times [see Fig. 3b]. (b) Spread of in-plane projections, $a_{\parallel }$, of $a_{\mathrm{C}}$, measured at RT, as a function of the growth temperature $T_{\mathrm{g}}$, for two series of measurements (yellow and red data points). The orange point corresponds to a sample grown at 1170 K and studied at 1070 K.Reuse & Permissions

Figure 7

Construction of the distribution of projections of lattice parameters in graphene, $\left\{a_{\parallel }\right\}$, from the distribution of lattice parameters, $\left\{a_{\mathrm{C}}\right\}$, taking the nanorippling of graphene along the moiré into account. The purple histogram shows a distribution of graphene lattice parameters randomly chosen in a standard normal (Gaussian) distribution (as a guide for the eye, the corresponding Gaussian function is plotted with a purple line), with FWHM corresponding to the increase of the width of the graphene peak as a function of BZ order in the radial direction [Fig. 4b]. The gray histogram is the distribution of in-plane projections yielded by nanorippling for one specific value of the lattice parameter. The cyan histogram includes all such distributions, each corresponding to all lattice parameter values included in the distribution shown in the purple histogram. The distributions were derived by taking into account 10 moiré unit cells in a one-dimensional model. The inset shows a side view of this model along a $\langle 11\overline{2}\rangle$ direction in Ir illustrating the nanorippling-induced $\{a_{\parallel },1\}$ distribution for a specific $a_{\mathrm{C}}$, and the periodic strain in the last Ir plane (red shades, $\varepsilon$ amplitude). The characteristic lengths of the model, the moiré lattice parameter $a_{\mathrm{m}}$, the graphene lattice parameter $a$, its in-plane projection $a_{\parallel }$, and the nanorippling amplitude $s$ are shown. The $\sqrt{3}$ factor corresponds to the $\langle 11\overline{2}\rangle$ direction.Reuse & Permissions

Figure 8

Graphene deformations mapped onto a regular mesh with hexagons at its nodes, whose shapes represent amplified deformations (strain, rotation, shear), for two cases: $\sim$60-nm domains, each having distinct lattice parameter (a), and a domain wall ($\sim$100 nm) between two domains having the same lattice parameter (b).Reuse & Permissions