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Theoretical Prediction of Three-Dimensional $sp^2$-free Graphyne-Based Nanomaterials via Density Functional Theory

Djardiel da S. Gomes, Alexandre F. Fonseca, Marcelo L. Pereira

Abstract

The search for carbon-based materials with tailored dimensionality and properties remains an important topic in materials science, particularly for applications in electronics, photonics, and nanomechanics. Among the emerging platforms in this context, graphyne (GY) represents a class of two-dimensional (2D) carbon allotropes composed of benzene rings connected by acetylenic linkages, yielding networks containing both $sp$- and $sp^2$-hybridized carbon atoms. By analogy with the transformation of $sp^2$ carbon networks such as graphene into $sp^3$-bonded diamond through interlayer covalent bonding, we construct three-dimensional (3D) GY-derived frameworks (3DGY) by covalently connecting stacked $α$-, $β$-, and $γ$-GY sheets via out-of-plane acetylene bridges. This approach converts the original $sp^2$ nodes into $sp^3$ centers while preserving the $sp$ character of the acetylenic segments, producing fully $sp$-$sp^3$ carbon networks. Structural relaxation shows that the $α$-derived framework does not converge to a stable configuration within this scheme, whereas the $β$- and $γ$-3DGY phases form stable architectures. Density functional theory (DFT) calculations, combined with ab initio molecular dynamics (AIMD) simulations, confirm the energetic, thermal, and dynamical stability of these two systems and are further used to investigate their structural, mechanical, electronic, and optical properties. Mechanical analysis reveals anisotropic elastic behavior, whereas electronic structure calculations show indirect band gaps of approximately 0.15 eV for $β$-3DGY and 1.65 eV for γ-3DGY. Optical calculations further reveal anisotropic responses, with absorption extending from the infrared to the visible. These results identify β-3DGY and γ-3DGY as new three-dimensional carbon allotropes with distinct mechanical, electronic, and optical properties.

Theoretical Prediction of Three-Dimensional $sp^2$-free Graphyne-Based Nanomaterials via Density Functional Theory

Abstract

The search for carbon-based materials with tailored dimensionality and properties remains an important topic in materials science, particularly for applications in electronics, photonics, and nanomechanics. Among the emerging platforms in this context, graphyne (GY) represents a class of two-dimensional (2D) carbon allotropes composed of benzene rings connected by acetylenic linkages, yielding networks containing both - and -hybridized carbon atoms. By analogy with the transformation of carbon networks such as graphene into -bonded diamond through interlayer covalent bonding, we construct three-dimensional (3D) GY-derived frameworks (3DGY) by covalently connecting stacked -, -, and -GY sheets via out-of-plane acetylene bridges. This approach converts the original nodes into centers while preserving the character of the acetylenic segments, producing fully - carbon networks. Structural relaxation shows that the -derived framework does not converge to a stable configuration within this scheme, whereas the - and -3DGY phases form stable architectures. Density functional theory (DFT) calculations, combined with ab initio molecular dynamics (AIMD) simulations, confirm the energetic, thermal, and dynamical stability of these two systems and are further used to investigate their structural, mechanical, electronic, and optical properties. Mechanical analysis reveals anisotropic elastic behavior, whereas electronic structure calculations show indirect band gaps of approximately 0.15 eV for -3DGY and 1.65 eV for γ-3DGY. Optical calculations further reveal anisotropic responses, with absorption extending from the infrared to the visible. These results identify β-3DGY and γ-3DGY as new three-dimensional carbon allotropes with distinct mechanical, electronic, and optical properties.
Paper Structure (8 sections, 6 equations, 8 figures)

This paper contains 8 sections, 6 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Methodology
  3. Results and Discussion
  4. Structural properties and stability
  5. Elastic Properties
  6. Electronic Behavior
  7. Optical Response
  8. Conclusions

Figures (8)

  • Figure 1: Optimized structures of the $\beta$-3DGY and $\gamma$-3DGY phases obtained from stacked graphyne layers connected through out-of-plane acetylenic bridges. The red lines highlight the corresponding unit cells.
  • Figure 2: Phonon dispersion curves for $\beta$-3DGY and $\gamma$-3DGY structures.
  • Figure 3: Time evolution of the total energy per atom for $\beta$-3DGY lattices at 300 K and 600 K during 7 ps of AIMD simulation. The inset figures show the top and side views of the final structures.
  • Figure 4: Time evolution of the total energy per atom for $\gamma$-3DGY lattices at 300 K and 1000 K during 7 ps of AIMD simulation. The inset figures show the final atomic configurations.
  • Figure 5: Stress-strain curves of $\beta$-3DGY and $\gamma$-3DGY under uniaxial deformation along the $x$, $y$, and $z$ directions. The left panels show the full stress-strain response up to fracture, while the right panels present enlarged views of the elastic regime ($0$-$1\%$ strain) used to extract the Young's modulus.
  • ...and 3 more figures