1 C5 as simplest ultrahard allotrope w ith mixed sp2sp3 carbon hybridizatio ns from first principles.

2025-04-27 1 0 701.63KB 15 页 10玖币

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C5 as simplest ultrahard allotrope with mixed sp2/sp3 carbon

hybridizations from first principles.

Samir F. Matar*

Lebanese German University (LGU), Sahel-Alma, Jounieh (P.O.Box 206), Lebanon.

https://orcid.org/0000-0001-5419-358X

* Email: s.matar@lgu.edu.lb

Abstract

From crystal chemistry rationale and density functional DFT calculations, novel tetragonal

carbon C5 is proposed as simplest ultrahard allotrope with mixed hybrid carbon hybridizations

(sp2/sp3). Novel pentacarbon is identified as cohesive and stable both dynamically and

mechanically. Whereas charge density is localized about tetrahedral C-sp3, it is found

delocalized around trigonal C-sp2 resulting in metallic behavior. The anisotropic structure

characteristics caused by the aligned trigonal carbon along the tetragonal c-axis provide high

Vickers hardness with a magnitude close to diamond.

Keywords: Carbon; ultra-hard; hybridization; DFT; phonons; elastic constants.

1- Introduction and context

Diamond, as natural gem and man-made for applications, is recognized as the hardest material

[1]. In last decades large research efforts were devoted to identifying novel allotropes of carbon

close to diamond using modern materials research software as USPEX (Universal Structure

Predictor: Evolutionary Xtallography) [2]. Regarding carbon, in view of the large number of

claimed stoichiometries and structures, a database: SACADA was built regrouping all known

carbon allotropes thus helping researchers in their endeavor and letting avoid claiming existing

systems as novel allotropes [3].

Another initial pathway that could be used complementarily to modern materials research

software lies in crystal chemistry rationale calling for structural ‘engineering’. Recently, body-

centered tetragonal C4 (Figure 1a) was proposed by us in space group I4m2 as one of the

simplest three-dimensional (3D) carbon networks with the purpose of serving as seed-template

for other original chemical compounds [6]. Using TopCryst crystallography package [7] C4 was

found with “dia” topology -for diamond- as categorized for several chemical compounds in

Reticular Chemistry Structure Resource (RCSR) Database [8].

In this work, starting from C4, we build novel tetragonal pentacarbon C5 through crystal

chemistry followed by full geometry relaxations using calculations based on the quantum

mechanics density functional theory DFT [9]. Analyzed through TopCryst, the fully geometry

relaxed structure of C5 was found to be in an original topology within RCSR Database. The

novel allotrope characterized with both sp2 and sp3 carbon hybridizations was found cohesive,

and stable both mechanically and dynamically accompanied with large hardness magnitude

slightly below diamond. It needs to be mentioned at this point that a mixed carbon hybridization

(sp2 and sp3), cubic ‘pentadiamond’ was reported in 2020 as a novel allotrope with high

mechanical properties close to diamond, but the paper was later retracted due to calculational

errors on the mechanical properties admitted by the authors [10]. The relevance of mixed carbon

hybridization is in the change of the electronic structure of insulating diamond, bringing

metallic-like behaviors leading to applications.

After this contextual introduction (Section 1) and next Section 2 reporting the computational

framework, the crystal chemistry rationale leading to novel tetragonal C5 is discussed in Section

3. Section 4 is devoted to illustrating qualitatively the charge density projections on the atoms

and between them. The mechanical and dynamic stabilities and properties are detailed in

sections 5 and 6 respectively. The electronic band structures and density of states are discussed

in Section 7 with a concluding statement.

2- Computational framework

For the search for the ground state structures of the devised structures, geometry optimizations

calculations onto the ground state with minimal energies were performed using DFT-based

plane-wave Vienna Ab initio Simulation Package (VASP) [11,12]. For the carbon atomic

potential including valence states, the projector augmented wave (PAW) method was applied

[12,13]. Treating at the same level the exchange X and the correlation C, the exchange-

correlation (XC) effects were considered using a generalized gradient approximation (GGA)

[14]. The relaxation of the atoms onto ground state geometry was done applying a conjugate-

gradient algorithm [14]. A tetrahedron method [15] with corrections made with Methfessel-

Paxton scheme [16] was applied for geometry optimization and energy calculations. A special

k-point sampling [17] was applied for approximating the reciprocal space Brillouin-zone (BZ)

integrals. For good reliability, the optimization of the structural parameters was carried out

along with successive self-consistent cycles while increasing k-mesh until the forces on atoms

were less than 0.02 eV/Å and the stress components below 0.003 eV/Å3.

Besides the elastic constants calculated to infer the mechanical stabilities and hardness,

calculations of phonon dispersion curves were also carried out to verify the dynamic stability

of the new carbon allotropes (template C3 and novel C5). For the purpose, the phonon modes

were computed considering the harmonic approximation via finite displacements of the atoms

around their equilibrium positions to obtain the forces from the summation over the different

configurations. The phonon dispersion curves along the direction of the Brillouin zone are

subsequently obtained using "Phonopy" interface code based on Python language [18]. Finally,

the electronic band structures and density of states were obtained with the full-potential

augmented spherical wave ASW method based on DFT using the same GGA scheme [19].

3- Crystal chemistry and characteristics of C5

Body center tetragonal C4 structure (Fig. 1a) consists of two distinct carbon sites with 2-

atoms occupancy: C1 at the corner and body center positions developing C4 tetrahedra with C2

positioned at the faces (Table 1a). We highlight that all lattice parameters of the structures in

Table 1 result from unconstrained geometry optimizations to the energy ground states. The

removal of the body center carbon breaks the body-center symmetry and leads to C3 where

tetrahedra are at the 8 corners of the structure forming a two-dimensional like stacking along c-

tetragonal direction (Fig. 1b). Such modification leads to symmetry lowering and the space

group changes from I4m2, N°119 down to P4m2, N°115. The second column of Table 1 shows

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摘要：

1C5assimplestultrahardallotropewithmixedsp2/sp3carbonhybridizationsfromfirstprinciples.SamirF.Matar*LebaneseGermanUniversity(LGU),Sahel-Alma,Jounieh(P.O.Box206),Lebanon.https://orcid.org/0000-0001-5419-358X*Email:s.matar@lgu.edu.lbAbstractFromcrystalchemistryrationaleanddensityfunctionalDFTcalculati...

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1 C5 as simplest ultrahard allotrope w ith mixed sp2sp3 carbon hybridizatio ns from first principles.

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