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Figure 1:Suspended graphene membrane.
Bright-field TEM image of a suspended graphene membrane. Its central part (homogeneous and featureless region indicated by arrows) is monolayer graphene. Electron diffraction images from different areas of the flake show that it is a single crystal without domains. We note scrolled top and bottom edges and a strongly folded region on the right. Scale bar, 500 nm.
图1：悬浮石墨烯膜。
悬浮石墨烯膜的明场TEM图像。它的中心部分（箭头表示的均匀且无特征的区域）是单层石墨烯。来自薄片不同区域的电子衍射图像显示它是一个没有畴的单晶。作者注意到滚动的顶部和底部边缘以及右侧的强烈折叠区域。比例尺，500 nm。
Figure 2:Transmission electron microscopy of graphene.
a, b, TEM images of folded edges for monolayer and bilayer graphene, respectively, using a Philips CM200 TEM. Scale bars, 2 nm. c–e, Electron diffraction patterns from a graphene monolayer under incidence angles of 0°, 14° and 26°, respectively. The tilt axis is horizontal. Here we used a Zeiss 912 TEM operated at 60 kV in the Köhler condition with the smallest (5 μm) condenser aperture. This allowed us to obtain a small, almost parallel beam with an illumination angle of 0.16 mrad and an illumination area of only 250 nm in diameter. The diffraction patterns were recorded on a charge-coupled device (CCD) for further quantitative analysis. The peaks become broader with increasing tilt, and this effect is strongest for peaks further away from the tilt axis. To label equivalent Bragg reflections, we use the Miller–Bravais indices (hkil) for graphite so that the innermost hexagon and the next one correspond to indices (0–110) (2.13 Å spacing) and (1–210) (1.23 Å spacing), respectively. f, Total intensity as a function of tilt angle for the peaks marked in c. To find the intensity values, each of the above Bragg reflections was fitted by a gaussian distribution for every angle, which yielded the peaks’ intensities, positions, heights and widths. The dashed lines are numerical simulations, in which we used a Fourier transform of the projected atomic potentials22,23,24 and the atomic form factors reported in ref. 29. g, The same analysis and simulations for a bilayer graphene membrane.
图2：石墨烯的透射电子显微镜。
a，b，使用Philips CM200 TEM分别获得单层和双层石墨烯折叠边缘的TEM图像。比例尺，2 nm。c-e，分别在0°、14°和26°入射角下石墨烯单层的电子衍射图。倾斜轴是水平的。在这里，他们使用了一台Zeiss 912 TEM，在Köhler条件下工作在60 kV，电容孔径最小（5 μm）。这允许他们获得小的、几乎平行的光束，其照明角度为0.16 mrad，照明面积直径仅为250 nm。衍射图案记录在电荷耦合器件（CCD）上，用于进一步的定量分析。随着倾斜度的增加，峰变宽，这种影响对于远离倾斜度轴的峰最强。为了标注等效Bragg反射，他们对石墨使用Miller–Bravais指数（hkil），使最里面的六边形和下一个六边形分别对应于指数（0-110）（间距2.13 Å）和（1-210）（间距1.23 Å）。f，c中标记的峰的总强度与倾斜角的函数关系。为了找到强度值，将上述每个Bragg反射通过每个角度的高斯分布拟合，从而产生峰值的强度、位置、高度和宽度。虚线是数值模拟，其中他们使用了参考文献29中报道的投影原子势和原子形状因子的傅立叶变换。g，对双层石墨烯膜进行了相同的分析和模拟。
Figure 3:Microscopically corrugated graphene.
a, Flat graphene crystal in real space (perspective view). b, The same for corrugated graphene. The roughness shown imitates quantitatively the roughness found experimentally. c, The reciprocal space for a flat sheet is a set of rods (red) directed perpendicular to the reciprocal lattice of graphene (black hexagon). d, e, For the corrugated sheet, a superposition of the diffracting beams from microscopic flat areas effectively turns the rods into cone-shaped volumes so that diffraction spots become blurred at large angles (indicated by the dotted lines in e) and the effect is more pronounced further away from the tilt axis (compare with Fig. 2). Diffraction patterns obtained at different tilt angles allow us to measure graphene roughness. f, Evolution of diffraction peaks with tilt angle in monolayer graphene. The experimental data are presented in such a way that they closely resemble the schematic view in e. For each tilt angle, the black dotted line represents a cross-section for diffraction peaks (0–110) and (1–210). The peak centres and full widths at half maxima (FWHM) in reciprocal space are marked by crosses and open circles, respectively. In two cases (0° and 34°), the recorded intensities are shown in full by blue curves. All the intensity curves could be well fitted by the gaussian shape. The solid black lines show that the width of the diffraction spots reproduces the conical broadening suggested by our model (d and e). g, FWHM for the (0–110) diffraction peak in monolayer and bilayer membranes and thin graphite (as a reference), as a function of tilt angle. The dashed lines are the linear fits yielding the average roughness. The flat region between 0° to 5°, and also for the reference sample, is due to the intrinsic peak width for the microscope at our settings.
图3：微观波纹石墨烯。
a，真实空间中的扁平石墨烯晶体（透视图）。b，波纹石墨烯也是如此。所示的粗糙度定量地模拟了实验发现的粗糙度。c，平板的倒易空间是一组垂直于石墨烯倒易晶格（黑色六边形）的棒（红色）。d，e，对于波纹片材，来自微观平坦区域的衍射光束的叠加有效地将棒变成锥形体积，使得衍射点在大角度下变得模糊（由e中的虚线表示），并且该效果在远离倾斜轴的地方更明显（与图2相比）。在不同倾斜角下获得的衍射图案允许他们测量石墨烯粗糙度。f，单层石墨烯中衍射峰随倾斜角的演变。实验数据以这样一种方式呈现，它们非常类似于e。对于每个倾斜角，黑色虚线代表衍射峰（0-110）和（1-210）的横截面。倒数空间中半最大值（FWHM）处的峰中心和全宽分别用十字和空心圆标记。在两种情况下（0°和34°），记录的强度由蓝色曲线完整显示。所有的强度曲线都可以很好地用高斯形状拟合。黑色实线显示衍射点的宽度再现了他们模型（d和e）所建议的圆锥形展宽。g，作为倾斜角的函数，单层和双层膜以及薄石墨（作为参考）中（0-110）衍射峰的FWHM。虚线是产生平均粗糙度的线性拟合。0°到5°之间的平坦区域，以及参考样品的平坦区域，是由于显微镜设置下的固有峰宽。
Figure 4:Atomic resolution imaging of graphene membranes.
TEM image of a few-layer graphene membrane near its edge, where the number of dark lines indicates the thickness of two to four layers. Because for few-layer graphene the electron contrast depends strongly on incidence angle, relatively small (a few degrees) variations in the surface normal become visible. The atomic-resolution imaging was achieved by using FEI Titan at an acceleration voltage of 300 kV. Scale bar, 1 nm.
图4：石墨烯膜的原子分辨率成像。
靠近其边缘的几层石墨烯膜的TEM图像，其中暗线的数量表示两到四层的厚度。因为对于几层石墨烯，电子对比度强烈依赖于入射角，所以表面法线相对较小（几度）的变化变得可见。原子分辨率成像是通过使用FEI Titan在300 kV的加速电压下实现的。比例尺，1 nm。
个人简介：
单飞狮
Feishishan2022@foxmail.com
撰稿人|单飞狮
审核|单飞狮
编辑|廖成霜
