Chapter 5 Alignment of graphene islands on low symmetric Cu substrates
5.2 Structures of low symmetric Cu substrates
In this section, the structures of various low symmetric Cu surface will be introduced. Except the three high symmetric surfaces, i.e., C6V Cu(111), C4V Cu(100) and C2V Cu(110), all other Cu surfaces are low symmetric with CS or C1 symmetries, which are composed of a large number of high symmetric terraces connected step edges along an unidirectional direction (Figure 5.1). According to the terrace configuration, low symmetric surfaces can be classified into three categories, named Cu{111}-based, Cu{100}-based and Cu{110}-based low symmetric surfaces. The differences of low symmetric surfaces of the same category are mainly from the structures and densities of their step edges.
There are two types of step edges: straight steps and tilted steps (see Figure 5.1), according to their atomic configurations. The edge atoms of straight steps have the exact same coordination number while that of tilted steps show a different coordination environment. To characterize different step edges of low symmetric surfaces, the straight steps are considered as basic vectors and any tilted steps can be constructed by two vectors with different ratios. As shown in Figure 5.1, for Cu{111}-based low symmetric surfaces, there are two step vectors along Cu<110> and Cu<211> directions, respectively.
Tilted steps are composed by either <110> segments with <211> kinks or <211> segments with <110>
kinks. Here, a segment means that the length of the component is larger than its corresponding unit length and a kink corresponds its unit length. For Cu{100}-based low symmetric surfaces, the two step vectors are Cu<110> and Cu<100>, respectively, and tilted steps can be constructed by either <110>
segments with <100> kinks or <100> segments with <110> kinks. In contrast with the above two categories, step edges on Cu{110}-based low symmetric surfaces have three types of straight steps and results in three step vectors: Cu<110>, Cu<211> and Cu<100>. Tilted steps can be classified into four types: <110> segments with <211> kinks, <211> segments with <110> kinks, <211> segments with
<100> kinks, and <100> segments with <211> kinks. To make it simply, we use SE<kink>
𝑖×<segment>
to describe an arbitrary step edge, in which the directions of segment and kink composed to the step edge are shown in the superscript and subscript, respectively, and i denotes the times of unit length for the segment. It is worth noting that high-index low symmetric surfaces with straight steps, SE0<segment>
, are generally CS symmetry that shows mirror symmetry with respect to the direction perpendicular to the straight step except the C1 Cu{110}-based low symmetric surface with SE0<211> steps, while surfaces with tilted steps are all C1 symmetric.
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Figure 5.1 The configurations of various low symmetric Cu surfaces, where SE<kink>
𝑖×<segment>
represents a step edge with a segment direction denoting in superscript and a kink direction denoting in subscript, and i is the number of unit cells in the segment.
Although step edges (either straight or tilted steps) on high-index low symmetric surfaces are ideally unidirectional with a constant direction, they are usually highly fluctuated and are composed of various segments along different directions in practice, especially under the high temperatures for 2D materials CVD synthesis.276,345 Therefore, the effect of the step edge variation on the alignment of 2D materials grown on the substrates is also critical and will be addressed in this chapter.
Figure 5.2 sketched the structures of Cu{111}-based, Cu{100}-based, and Cu{110}-based low symmetric surfaces, respectively, with step edge directions ranging from -180~180°, which can show the structures of all types of step edges composed of different step edge segments and kinks. In Figure 5.2(a), the atomic configurations of three Cu{111}-based low symmetric surfaces are displayed at the outer side, where the same terrace but different step edges can be clearly seen. Due to all low symmetric surfaces has the exact Cu[110] direction, therefore here the Cu[110] step edge is chosen as reference of
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0° for all three categories of low symmetic surfaces, and other step edge dierction are describe by the their relative angles with the Cu[110] direction.
Figure 5.2 Sketches of three categories of low symmetic surfaces, i.e., Cu{111}-based (a), Cu{100}- based (b) and Cu{110}-based (c) high-index low symmetric surfaces. Various surfaces with different step edge direction are distinguished by different colors, and the straight step direction is marked by dashed lines. (d-f) The evolution of step kink density versus step edge direction as a function of step edge orientation for Cu{100}-based, Cu{100}-based and Cu{110}-based high-index low symmetric surfaces, respectively. The Cu[110] direction is chosen as reference of 0° for all three categories of low symmetic surfaces .
Due to the 6-fold symmetric the Cu(111) surface, the periodicity of the step edge orientation is 0°~60°. Considering the mirror symmetry with respect to the Cu<110> and Cu<211> directions, the step edge orientation can be further restricted into 0°~30°, which varies from Cu<110> to Cu<211>
direction. Figure 5.2 (d) shows the evolution of the kink density as a function of the Cu step edge orientation. At 0° and 30°, the two SE0<110> and SE0<211> have no kinks and therefore with a kink density of 0. With the step orientation deviating from the straight steps, the kink density keeps increasing. Depending on the main components of the tilted step edges, they can be further classified into <110> dominated steps (SE<211>𝑖×<110>) and <211> dominated steps (SE<110>𝑖×<211>). At 19.11°, the tilted step (SE<211><110> or to say SE<110><211>) is composed of <110> kink and <211> kink that are alternatively
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connected and thus shows the highest density of kinks. Figures 5.2 (b) and (e) show the structure of Cu{100}-based high-index low symmetric substrates and the kink density profile as a function of the Cu step edge orientation, respectively. Due to C4V symmetry of the Cu(100) surface, the non-repeating range of the step edge orientation for the kink density profile is 0°~45°, which varies from one Cu<110>
direction to its neighboring Cu<100> direction. The highest kink density appears at SE<100><110> or SE<110><100> at a step edge direction of 26.57°. Due to the C2V symmetry of the Cu(110) surface, the non- repeating range of step edge orientation on Cu{110}-based high-index low symmetric substrates is 0°~90°, which varies from one Cu<110> direction to the neighboring Cu<112> direction and then to the neighboring Cu<001> direction. In the 0°~35.26°, 35.26°~70.53°, and 70.53°~90° ranges, step edges are dominated by <110> segments (SE<211>𝑖×<110>), <211> segments (SE<110>𝑖×<211> and SE<100>𝑖×<211>), and <100> segments (SE<211>𝑖×<100>), respectively.