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A Three-Dimensional Dodecaphenylyne-Derived Carbon Allotrope with Anisotropic and Auxetic-Like Mechanical Behavior

Kleuton A. L. Lima, José A. dos S. Laranjeira, Bill D. A. Huacarpuma, Nicolas F. Martins, Julio R. Sambrano, Douglas S. Galvão, Luiz A. Ribeiro

TL;DR

3D-DPhyne addresses the design of a robust 3D carbon framework derived from a 2D multiring lattice (dodecaphenylyne) and assesses its structural, electronic, optical, and mechanical properties with first-principles calculations. The work demonstrates a tetragonal $P4_{2}/mmc$ network in which four-, six-, and twelve-membered rings with mixed sp/sp^2 bonding yield a fully covalent, $π$-conjugated 3D framework and metallic character, evidenced by bands crossing the Fermi level and $p$-orbital dominance near $E_F$. It reveals broadband optical absorption in the visible and UV with low reflectivity, and a highly anisotropic elastic response, including Poisson's ratio values that can be auxetic-like in certain directions. The findings highlight the potential of dimensional crossover in carbon networks to realize materials with direction-dependent stiffness and unusual mechanical responses, offering a platform for novel carbon-based metamaterials and opto-electro-mechanical applications.

Abstract

We introduce 3D-DPhyne, a novel three-dimensional (3D) carbon allotrope derived from the dodecaphenylyne framework, and investigate its structural, electronic, optical, and mechanical properties using first-principles calculations. The proposed structure forms a tetragonal, topologically complex network of four-, six-, and twelve-membered carbon rings with mixed sp/sp^2 hybridization and a formation energy of -7.87 eV/atom, comparable to other stable carbon allotropes. Phonon dispersion calculations show no imaginary modes, and ab initio molecular dynamics simulations at 1000~K confirm robust thermal stability without bond breaking. Electronic structure analysis reveals metallic character, with multiple bands crossing the Fermi level and dominant contributions from carbon p orbitals, consistent with a fully delocalized 3D $π$-conjugated network. The optical response is anisotropic, exhibiting strong absorption in the visible and ultraviolet regions and low reflectivity across a broad range of photon energies. Mechanical analysis reveals pronounced elastic anisotropy, with Young's modulus varying from approximately 40 to 490 GPa depending on direction. Poisson's ratio displays unconventional directional behavior, including auxetic-like responses.

A Three-Dimensional Dodecaphenylyne-Derived Carbon Allotrope with Anisotropic and Auxetic-Like Mechanical Behavior

TL;DR

3D-DPhyne addresses the design of a robust 3D carbon framework derived from a 2D multiring lattice (dodecaphenylyne) and assesses its structural, electronic, optical, and mechanical properties with first-principles calculations. The work demonstrates a tetragonal network in which four-, six-, and twelve-membered rings with mixed sp/sp^2 bonding yield a fully covalent, -conjugated 3D framework and metallic character, evidenced by bands crossing the Fermi level and -orbital dominance near . It reveals broadband optical absorption in the visible and UV with low reflectivity, and a highly anisotropic elastic response, including Poisson's ratio values that can be auxetic-like in certain directions. The findings highlight the potential of dimensional crossover in carbon networks to realize materials with direction-dependent stiffness and unusual mechanical responses, offering a platform for novel carbon-based metamaterials and opto-electro-mechanical applications.

Abstract

We introduce 3D-DPhyne, a novel three-dimensional (3D) carbon allotrope derived from the dodecaphenylyne framework, and investigate its structural, electronic, optical, and mechanical properties using first-principles calculations. The proposed structure forms a tetragonal, topologically complex network of four-, six-, and twelve-membered carbon rings with mixed sp/sp^2 hybridization and a formation energy of -7.87 eV/atom, comparable to other stable carbon allotropes. Phonon dispersion calculations show no imaginary modes, and ab initio molecular dynamics simulations at 1000~K confirm robust thermal stability without bond breaking. Electronic structure analysis reveals metallic character, with multiple bands crossing the Fermi level and dominant contributions from carbon p orbitals, consistent with a fully delocalized 3D -conjugated network. The optical response is anisotropic, exhibiting strong absorption in the visible and ultraviolet regions and low reflectivity across a broad range of photon energies. Mechanical analysis reveals pronounced elastic anisotropy, with Young's modulus varying from approximately 40 to 490 GPa depending on direction. Poisson's ratio displays unconventional directional behavior, including auxetic-like responses.

Paper Structure

This paper contains 4 sections, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Results
  4. Conclusion

Figures (5)

  • Figure 1: Optimized crystal structure of 3D-DPhyne. (a) Conventional unit cell highlighting the tetragonal lattice vectors $\vec{a}$, $\vec{b}$, and $\vec{c}$. (b) Top view along the $c$ axis, showing the nearly square in-plane projection and multiring arrangement. (c) Side view revealing the 3D covalent connectivity and the alternation of planar and nonplanar ring motifs. The structure consists of an interconnected network of four-, six-, and twelve-membered carbon rings with mixed sp/sp$^{2}$ hybridization, crystallizing in the $P4_{2}/mmc$ (No. 131) space group.
  • Figure 2: Dynamical and thermal stability of 3D-DPhyne. (a) Phonon dispersion relations calculated along high-symmetry directions of the Brillouin zone. (b) Time evolution of the total energy per atom obtained from AIMD simulations at 1000 K in the NVT ensemble over 5 ps. The inset shows the final atomic configuration.
  • Figure 3: Electronic properties of 3D-DPhyne. (a) Electronic band structure calculated along high-symmetry directions of the Brillouin zone. The Fermi level is set to zero energy. (b) Projected density of states (PDOS), highlighting the dominant contribution of carbon $p$ orbitals near the Fermi level. (c) Real-space isosurfaces of the highest occupied crystal orbital (HOCO) and the lowest unoccupied crystal orbital (LUCO).
  • Figure 4: Optical properties of 3D-DPhyne obtained from the frequency-dependent complex dielectric function. (a) Absorption coefficient $\alpha(\omega)$, (b) Reflectivity $R(\omega)$, and (c) Refractive index $\eta(\omega)$ as a function of photon energy. The shaded area indicates the visible energy region.
  • Figure 5: Three-dimensional directional dependence of the elastic properties of 3D-DPhyne. (a) Young's modulus $E(\mathbf{n})$, (b) shear modulus $G(\mathbf{n})$, and (c) Poisson's ratio $\nu(\mathbf{n})$ represented as polar surfaces.