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Vibrational Properties of Germanane and Fluorinated Germanene in the Chair, Boat, and Zigzag-Line Configurations

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Vibrational Properties of Germanane and Fluorinated Germanene in the Chair, Boat, and Zigzag-Line Configurations Journal of Physics: Condensed Matter PAPER Vibrational properties of germanane and fluorinated germanene in the chair, boat, and zigzag-line configurations To cite this article: J Rivera-Julio et al 2019 J. Phys.: Condens. Matter 31 075301 View the article online for updates and enhancements. This content was downloaded from IP address 168.96.255.109 on 15/02/2019 at 18:26 IOP Journal of Physics: Condensed Matter Journal of Physics: Condensed Matter J. Phys.: Condens. Matter J. Phys.: Condens. Matter 31 (2019) 075301 (10pp) https://doi.org/10.1088/1361-648X/aaf45f 31 Vibrational properties of germanane and 2019 fluorinated germanene in the chair, boat, © 2019 IOP Publishing Ltd and zigzag-line configurations JCOMEL J Rivera-Julio1,2 , A González-García2,3 , R González-Hernández3, W López-Pérez3, F M Peeters2 and A D Hernández-Nieves1 075301 1 Condensed matter theory group, Centro Atomico Bariloche and CONICET, S. C. de Bariloche, 8400 S. C. de Bariloche, Argentina J Rivera-Julio et al 2 Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium 3 Grupo de Investigación en Física Aplicada, Departamento de Física, Universidad del Norte, Barranquilla, Colombia Vibrational properties of germanane and fluorinated germanene in the chair, boat, and zigzag-line configurations E-mail: [email protected], [email protected], [email protected], Printed in the UK [email protected], [email protected] and [email protected] Received 12 October 2018, revised 14 November 2018 CM Accepted for publication 27 November 2018 Published 2 January 2019 10.1088/1361-648X/aaf45f Abstract The electronic and vibrational properties of germanane and fluorinated germanene are studied within density functional theory (DFT) and density functional perturbation theory frameworks. Paper Different structural configurations of germanane and fluorinated germanene are investigated. The energy difference between the different configurations are consistently smaller than the energy of thermal fluctuations for all the analyzed DFT functionals LDA, GGA, and hybrid 1361-648X functionals, which implies that, in principle, it is possible to find these different configurations in different regions of the sample as minority phases or local defects. We calculate the Raman and infrared spectra for these configurations by using ab initio calculations and 7 compare it with available experimental spectra for germanane. Our results show the presence of minority phases compatible with the configurations analyzed in this work. As these low energy configurations are metastable the present work shows that the synthesis of these energy competing phases is feasible by selectively changing the synthesis conditions, which is an opportunity to expand in this way the availability of new two-dimensional compounds. Keywords: density functional perturbation theory, germanane, fluorinated germanene (Some figures may appear in colour only in the online journal) 1. Introduction Hydrogenated graphene (graphane) [8], graphene fluoride [9], and hydrogenated germanene [10] were recently realized New two-dimensional (2D) materials such as silicene and ger- experimentally by following this procedure. manene have been synthesized recently [1, 2]. These materials For the case of a complete (100%) coverage with adatoms, have a hexagonal honeycomb structure similar to that of gra- many possible metastable arrangements have been considered phene [3], and are made of respectively Si and Ge atoms [4]. theoretically for these new compounds [11–13]. For example, Contrary to graphene they are not flat, but have a periodically in [12] a cluster expansion method for absorption was applied buckled topology [5–7]. on hydrogen chemisorbed on graphene in order to explore The chemical modification of graphene, silicene, and ger- all the possible configurations. First principle calcul ations of manene with hydrogen and fluorine atoms generate other the formation energy for graphane gave, at zero temperature, new two-dimensional crystals where the adatoms form that the chair configuration is the lowest energy configuration ordered arrangements on the pristine compounds [8–10]. among all the possibilities but there is a very small difference 1361-648X/19/075301+10$33.00 1 © 2019 IOP Publishing Ltd Printed in the UK J. Phys.: Condens. Matter 31 (2019) 075301 J Rivera-Julio et al in formation energy with other configurations specially the vacuum spacing between the adjacent cells to avoid interac- zigzag, boat, and chair configurations [12]. The same result tions. All the structures were relaxed using respectively the has been consistently found in the chemical modification of criteria of forces and stresses on atoms of 0.001 eV ˚A and graphene, silicene, and germanene based compounds [11–13]. 0.2 GPa. The convergence tolerance of energy in the calcul- All these previous theoretical studies shows that although ations was set to 0.5 meV per atom. the chair conformation is the most stable one, the energy bar- The sampling of the Brillouin zone needed for the conv- rier with other possible configurations is rather large, and ergence of the wave functions in a phonon calculation requires, therefore the other configurations are metastable [11–13]. Due in most cases, an equal number of discrete k-points as a a self- to the extremely small energy difference between the configu- consistent total energy calculation [20]. But the convergence rations, some disorder in the repartition of the alternation of of the phonon dispersion relations require a discrete q-mesh adatoms below and above the two-dimensional plane could with a lower number of q-points. For the phonon dispersions, be present in the final product, as well, is also very plausible, we used a 5 5 1 q-grid in the Brillouin zone. The phonon the presence of islands of the other configurations in a mostly dispersion curves× × were obtained by diagonalization of the chair conformation material. dynamical matrices calculated using density functional per- Nowadays, Raman spectroscopy is regarded as one of the turbation theory (DFPT) [20]. The convergence thresholds for main techniques for structural testing of 2D materials [14]. In the self-consistent calcul ation and the phonon calculations 7 14 fact, Raman spectroscopy results reported by first principles are 10− and 10− Ry, respectively. The Raman and infrared studies have predicted the vibrational modes of many mat- spectra were study with LDA calculations done with norm erials which have been verified later by experiments [15, 16]. conserving pseudopotentials as implemented in the Quantum- Encouraged by the recent synthesis and exfoliation of GeH Expresso package [18]. The eigendisplacements and phonon (germanane) single layers [10, 17], we have studied the vibra- modes were classified according to group theory by using the tional properties of different configurations of germanane and tools available online in the Bilbao Crystallographic Server fluorogermanene to compare them with the experimentally [21]. available Raman and infrared spectra [10]. Our simulated Raman and infrared spectra, and its subsequent comparison with the experiments, confirm the presence of other meta- 3. Results and discussion stable configurations as minority phases in a mostly chair conformation material. 3.1. Structural parameters and phonon dispersions of ger- We will first describe in section 2, the computational manene, germanane, and fluorogermanene methods used in our work. Then, the main results obtained To investigate the vibrational properties of germanane and flu- will be discussed in section 3. In section 3.1, the structural orogermanene it is very useful to start by discussing the vibra- parameters and the phonon dispersion curve of germanene, tional properties of germanene that is their parent compound GeH, and GeF will be analyzed and its phonon dispersion without coverage with hydrogen or fluorine atoms. As shown relation will be presented and discussed. In section 3.2, we in table 1, our result for the lattice parameter (bond length) study directly from ab initio calculations the Raman and of germanene are very close to the experimental values even infrared spectra of different configurations of germanane and when the experiments refers to germanene on a Pt/Ge sub- fluorogermanene. This allows a direct comparison with avail- strate [22, 23]. Our results for the buckling height of Ge is able experiments in germanane. Finally, the main conclusions also in good agreement with other theoretical studies [5, 22, of this work will be summarized in section 4. 24–26]. The calculated phonon dispersion of germanene is shown 2. Computational details in figure 1. The low buckled honeycomb germanene is stable, because there are no imaginary frequencies in the phonon dis- The calculations were performed by using spin-polarized den- persion. It means that there are no soft modes and, therefore, sity functional theory (DFT), as implemented in the simulation there is no sign of any dynamical instability, in agreement package Quantum-Expresso [18]. Exchange and correlation with previous results [25]. effects were treated, in most of the calculations, within the An understanding of this phonon dispersion is essential generalized gradient approximation (GGA) of the Perdew– to interpret its Raman spectra. The point-group symmetry 3 Burke–Ernzerhoff (PBE) functional [19]. The energy differ- of germanene, due to the buckling, is D3d [27], space group ence
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