Recently, there has been a great interest in predicting novel carbon allotropes. A special attention has been paid to the sp3 allotropes since most studies were conducted in order to elucidate the atomistic structure of the product of the cold graphite compression [1] that is different either from diamond or lonsdaleite phases of carbon. A manifold of computational techniques have been tried to address the problem of crystal structure prediction, e.g. evolutionary algorithms, accelerated molecular dynamics (metadynamics), graph-theoretical approaches etc. However, in many cases the structures predicted by very sophisticated methods were topologically the same as certain crystal structures known to crystal chemists for many years. To give a couple of examples, we mention (a) the bct-4 carbon [2] that is topologically the same as zeolite BCT and (b) suggested dense phase of carbon with the topology of quartz [3]. This motivated us to have a closer look at the databases of hypothetical zeolite networks compiled by Deem [4] and Treacy [5]. First, we focused only on the nets without 3- and/or 4-rings (in total 5074 candidates) that would normally induce too much strain in the carbon structures. Second, we performed ‘geometrical’ relaxation of the nets with the Gavrog Systre package (http://gavrog.org/). From the set of geometrically relaxed structures we extracted 652 nets where the distances to the next-nearest neighbours were by 40% larger than the distances to the nearest neighbours. These structures – that could be considered as stereochemically feasible – were then optimized with the Tersoff force field as implemented in the GULP package (http://projects.ivec.org/gulp/). After this force-field calculation, 257 structures remained 4-coordinated and were subject to further optimizations with the density-functional-based tight-binding method (DFTB) as implemented in the DFTB+ package (http://www.dftb-plus.info/). From the set of the DFTB-optimized structures, we selected 93 representatives that lie within a narrow energetic window (0.40 eV/atom) relative to diamond and performed structural relaxation [at the DFT-GGA(PBE) level] with the SIESTA package (http://departments.icmab.es/leem/siesta/). Finally, we focus on the six structures that are energetically the lowest ones, within 0.10 eV/atom (or even less) relative to diamond. Their energetic, electronic, vibrational and mechanical properties were calculated at the DFT-GGA(PBE) level of theory as implemented in VASP (https://www.vasp.at/) and CRYSTAL (http://www.crystal.unito.it/index.php) program packages. The calculated elastic moduli suggest that these materials are as hard as diamond. The phonon dispersion curves show no imaginary frequencies throughout the Brillouin zones. More strikingly, we found out that the optical gaps of our structures are by ~1 eV larger than the band gap of diamond. This is quite interesting and unexpected result since – to the best of our knowledge – hypothetical sp3 carbon allotropes with the gaps larger than diamond are characteristic for their clathrate-like open frameworks [6] that is not the case for our relatively dense structures. Finite temperature molecular dynamics simulations at the DFTB level of theory (NpT ensemble, p=1 bar, T=300 K) have been performed in order to ensure the dynamical stability of our structures under ambient conditions.
References
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2. K. Umemoto, R. M. Wentzcovitch, S. Saito and T. Miyake, Phys. Rev. Lett. 104, 125504 (2010).
3. Q. Zhu, A. R. Oganov, M. A. Salvado, P. Pertierra and A. O. Lyakhov, Phys. Rev. B 83, 193410 (2011).
4. M. W. Deem, R. Pophale, P. A. Cheeseman and D. J. Earl, J. Phys. Chem. C, 113, 21353 (2009).
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