## 1 Introduction
### Introduction to Graphyne  
GR is a hypothesized carbon allotrope that resembles G but has a distinct arrangement of carbon atoms grouped in a two-dimensional lattice structure. The lattice structure of GR is identical to the honeycomb structure of G, except the C-C bonds are occasionally replaced with -C\(\equiv\)C- bonds. GR can have many lattice configurations because such substitutions can occur at different C-C bonds. The structures of GR are categorized into four types based on the distinct combinations of -C\(\equiv\)C-, namely, \(\alpha\)-graphyne, \(\beta\)-graphyne, \(\gamma\)-graphyne, and 6,6,12-graphyne [70]. Except for 6,6,12-graphyne, which has rectangular symmetry, and the initial cell has a rectangular shape with in-plane anisotropy, most GRs have hexagonal symmetry like G. Among them is \(\alpha\)-graphyne, which can be created by replacing all carbon-carbon bonds in graphyne with acetylenic (-C\(\equiv\)C-) links. \(\beta\)-graphyne is formed when two-thirds of the carbon-carbon bonds in G are replaced by acetylenic linkages, and \(\gamma\)-graphyne is formed when one-third of the carbon-carbon bonds in GR are replaced by acetylenic links. An \(\alpha\)-graphyne has the greatest percentage of acetylenic links (100%). The percentage of acetylenic links in \(\beta\)-graphyne, \(\gamma\)-graphyne, and 6,6,12-graphyne is 66.67%, 33.33%, and 41.67%, respectively [71]. Graphyne is an allotrope of carbon consisting of a one-atom-thick sheet of sp and sp\({}^{2}\) hybridized bonding in the crystal lattice. GR features a two-dimensional crystal lattice and is expected to be synthesized in the future, as only its molecular fragments have been produced so far [72; 73]. Due to various arrangements of double and triple bonding, there are discrete types of GR [9; 65; 74; 75]. Because of its structure and applications, a study of graphyne with its application is presented in Figure 3 from 2017 to 2024. Prior to 1960, the existence of GR was only hypothesized. However, following the discovery of fullerene, GR began to attract significant attention from materials scientists [76]. Since 1980, scientists have been working on finding the synthesis method and theoretical properties of the GR. Due to an acetylenic linkage that connects the hexagons, G converts into GR. Compared with graphite and diamond, the GR has a slightly different electronic structure and shows some manifesting properties compared with other materials [65]. There are various types of GR (Figure 4), but \(\gamma\)-GR is known as the common form of GR. The \(\gamma\)-GR has 12 carbon atoms in a unit cell. Figure 3: Visualization of the methodological evolution and application areas of graphyne research from 2015 to 2024. (Created by VOSVIEWWR). In the form of infinite sheets or nano-flakes, GR shows extraordinary mechanical properties that attracted research to investigate them [77,78]. Cranford and Buehler synthesized GR flakes and investigated the mechanical properties by utilizing ReaxFF interatomic potential [77,78]. For accurate values, a time step of 2 fs was considered to calculate mechanical properties against higher frequency [79]. Due to the electronic (Dirac cone-like) and mechanical properties of GR, the application of G is limited in field-effect transistors with a high on-off ratio because of its zero-band-gap properties. Additionally, it is used in logic and high-speed switching devices [78, 79, 80, 81]. By utilizing the hydrogenation process, the band gap of the G can be increased [82, 83, 84, 85, 86]. By 100% hydrogenation, the G can be converted into GR and is known as a theoretical nonmagnetic semiconductor (SC) with a stoichiometry of CH [87]. Due to the hydrogenation process, the sp\({}^{2}\) hybridization was converted into sp\({}^{3}\), and the hydrogen atom changed its direction along the G sheet. In the annealing process, the G can be retrieved from GR [87].