First-principles theoretical analysis of pure and hydrogenated crystalline carbon phases and nanostructures

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Abstract

We report a detailed theoretical analysis of the structures of various crystalline phases of pure and hydrogenated carbon. Using first-principles density functional theory calculations, we propose possible structures for the experimentally observed phases of carbon nanocrystals through incorporation of interstitial hydrogen atoms, at proper concentrations, into cubic carbon lattices. The results of our analysis provide possible interpretations for the structures of i-carbon, a cubic phase with lattice parameter a = 4.25 Å, a body-centered cubic carbon phase with a = 3.1 Å, and n-diamond, a face-centered cubic phase with a = 3.57 Å.

Graphical abstract

We report results from a detailed analysis of the structures of various crystalline phases of pure and hydrogenated carbon.

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Introduction

Carbon exists in a variety of different allotropes, such as cubic diamond, hexagonal diamond [1], [2], graphite, carbynes [3], fullerenes [4], and carbon nanotubes [5]. In addition to these well known forms, various other forms such as i-carbon [6], [7], a cubic phase with lattice parameter a = 4.25 Å, a body-centered cubic (bcc) carbon phase with a = 3.1 Å[8], and n-diamond [9], [10], [11], a face-centered cubic (fcc) phase with a = 3.57 Å have been reported in experiments. All of these allotropes contribute to a rich and complex phase diagram of carbon.

The structural differences among these allotropes result in diverse properties that are desirable for numerous technological applications. For example, carbon phases synthesized at the nanometer scale have been suggested for applications in four broad areas, namely dispersions and coatings, high-surface-area materials (e.g., for drug delivery or energy storage), consolidated materials, and functional nanostructures (e.g., for transistors) [12]. In spite of their potential significance, however, the structure and stability of some of these new phases of carbon (i-carbon, n-diamond, and the new bcc phase) remain elusive. The structure and stability of these carbon allotropes are required in order to investigate their mechanical, electronic, and optical properties, thereby enabling numerous applications.

It has been well established that hydrogen plays a critical role in determining the crystallinity of group-IV nanostructured materials grown by plasma deposition [13]. For example, the ability to deposit diamond thin films from a gas phase consisting of hydrocarbons heavily diluted in hydrogen has been studied extensively [14]. Another example is the transformation of amorphous silicon films to nanocrystalline ones upon exposure to atomic hydrogen [13], even at room temperature [15]. In addition to the formation of diamond, the formation of several other carbon allotropes has been reported based on electron diffraction from small crystals found in carbon films deposited by plasmas [7], [8], [16] or by ion beams [17], [18], as well as in carbonaceous material made by shock compression of graphite [6], [10].

Here, we present a detailed analysis of various crystalline phases of carbon, which are candidate structures to explain the aforementioned experimentally observed carbon phases, as well as the potential role of hydrogen in determining the structures of the resulting carbon nanocrystals. Specifically, we focus on the structures of i-carbon (a = 4.25 Å), the new bcc carbon phase (a = 3.1 Å), and n-diamond (a = 3.57 Å) and analyze them based on comparison of experimental and calculated optimal lattice parameters, calculated formation energies, as well as simulated and experimentally observed electron diffraction peaks. Toward this end, we have employed first-principles density functional theory (DFT) calculations to compute the optimal lattice parameters and formation energies for pure, as well as hydrogenated crystalline phases of carbon. In this study, H atoms are introduced at various proper concentrations in high-symmetry interstitial sites of cubic carbon lattices that yield CxHy (x, y  3) phases.

Section snippets

Computational methods

Our analysis of pure and hydrogenated bulk carbon phases was based on first-principles density functional theory (DFT) calculations implemented within the generalized gradient approximation (GGA) [19]. We employed bulk supercells [20], plane-wave basis sets [20], and ultrasoft pseudopotentials [21], as implemented in the Vasp code [22]. We used a Monkhorst-Pack scheme for integration in reciprocal space [20]. To guarantee the precision of our calculations, for each lattice structure and

Results and discussion

Our theoretical results can be used to interpret the structures of experimentally observed phases of carbon nanocrystals under the assumption that the nanocrystals observed in the experiments (up to 20 nm in diameter) are present in their bulk phases. Considering a cubic allotrope of carbon with a basis of 2–4 atoms per conventional cubic unit cell with a lattice parameter of ∼5 Å and an average nanocrystal size of 5 nm yields approximately 2000–4000 atoms in the nanocrystal. This justifies the

Conclusions

This study presented an analysis based on first-principles DFT calculations of H incorporation into the lattices of crystalline carbon phases at interstitial lattice sites and elucidated the effects of H on the lattice expansion and lattice stability with increasing H concentration. Prior to the analysis of H incorporation, we examined various crystalline phases of pure carbon as possible candidates for experimentally observed phases of carbon nanocrystals. However, none of the pure carbon

Acknowledgement

This work was supported by the NSF through Award Nos. CBET-0613501, CBET-0613629, CTS-0417770, and CMMI-0531171.

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