Article pubs.acs.org/JPCC
Supertetrahedral Aluminum − A New Allotropic Ultralight Crystalline Form of Aluminum Iliya V. Getmanskii,† Vitaliy V. Koval,† Ruslan M. Minyaev,*,† Alexander I. Boldyrev,*,†,‡ and Vladimir I. Minkin† †
Institute of Physical and Organic Chemistry, Southern Federal University, 194/2 Stachka Ave., 344090, Rostov-on-Don, Russian Federation ‡ Department of Chemistry and Biochemistry, Utah State University, Logan, Utah 84322, United States S Supporting Information *
ABSTRACT: A new metastable ultralight crystalline form of aluminum has been computationally designed using density functional calculations with imposing periodic boundary conditions. The geometric and electronic structures of the predicted new allotrope were calculated on the basis of a diamond lattice in which all carbon atoms are replaced by aluminum Al4 tetrahedra. The new form of crystalline aluminum has an extremely low density of 0.61 g/cm3 and would float in water. The new aluminum form is a semimetal and shows high plasticity.
1. INTRODUCTION The computational design of novel two- and three-dimensional materials with the nonstandard structures and potentially useful properties is rapidly growing into an important area of the materials science. We have previously theoretically predicted and investigated electronic and spatial structures of the new allotropic forms of supertetrahedral boron,1,2 built on the basis of a diamond lattice in which carbon atoms were replaced by boron tetrahedrons. The logic of this replacement is based on the kinetic stability of the tetrahedral boron structure B4H4, which, due to electron deficiency of a boron atom, does not conform to the global minimum at the corresponding potential energy surface (PES), but belongs to its local minimum and preserves stability under substitution of the hydrogen atoms.3,4 Unlike tetraborane B 4 H4 , alumotetrahedrane Al 4H4 , as calculations show,3 corresponds to the global minimum on the PES and one can be expected that the crystal structure of supertetrahedral aluminum will also have dynamic stability. The present study motivated by the interest in the insight into new types of two- and three-dimensional aluminumcontaining structures is aimed at the theoretical study based on the quantum chemical calculations using a density functional theory (DFT) with periodic boundary conditions.5−8 The geometric structure of a solid is constructed on the basis of a diamond lattice in which carbon atoms are replaced by aluminum Al4 tetrahedra. Such a structure is called supertetrahedral aluminum (STAl). A schematic depiction of the STAl crystal structure is given in Figure 1.
Figure 1. Schematic depiction of the supertetrahedral aluminum crystal structure.
wave cutoff energy of 750 eV of the associated pseudopotentials was used. The Brillouin zone has been sampled by the Monkhorst−Pack method12 with an automatic generated grid of 15 × 15 × 15. The calculated geometric characteristics of the studied systems have been visualized by using the VESTA program.13
2. METHODS The calculations have been performed using the program VASP (Vienna Ab initio Simulation Package) 5−8 with PAW pseudopotentials9,10 and the PBEsol functional.11 The plane© XXXX American Chemical Society
Received: July 31, 2017 Revised: September 15, 2017 Published: September 18, 2017 A
DOI: 10.1021/acs.jpcc.7b07565 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C
Table 1. Calculated Lattice Constant (a, in Å), Cohesive Energy (Ec, in eV/Atom), Wyckoff Position Coordinates for X Atom (x, x, x), Inter-tetrahedral Bond Length (d1, in Å), Intra-tetrahedral X−X Bond Length (d2, in Å), Density (ρ, in g/cm3), and Vickers Hardness (H, in GPa) for cF-X8 (X = B, C, Al) Structures structure
a
Ec
x
d1
d2
ρ
HGao
HSimunek
HTian
cF-B8 cF-C8 cF-Al8
8.548 7.486 13.322
−5.77 −7.01 −2.65
0.07036 0.07056 0.06924
1.61 1.41 2.57
1.70 1.49 2.60
0.92 1.52 0.61
27.4 60.2 3.8
15.2 36.3 1.7
1.3 3.4 0.4
Table 2. Calculated Elastic Constants (cij, in GPa), Bulk Modulus (K, in GPa), Shear Modulus (G, in GPa), Young’s Modulus (E, in GPa), and Poisson’s Ratio (ν) for cF-X8 (X = B, C, Al) Structures (Ecut is the plane-wave cutoff energy, in eV) structure
Ecut
c11
c12
c44
K
G
E
ν
cF-B8 cF-C8 cF-Al8
750 750 550
78.13 198.87 13.82
63.00 146.81 10.53
26.04 69.48 4.24
68.04 164.16 11.63
15.91 46.88 2.90
44.20 128.30 8.04
0.392 0.370 0.385
STAl would float in water. Vickers hardness calculated according to various formulas (HGao, HSimunek, HTian)19−21 for the aluminum system has the lowest value from the triad under consideration (see Table 1). The Poisson’s ratio (ν = 0.385), which characterizes the elastic and plastic properties of the material (see Table 2), is quite high for all materials under consideration. For example, for conventional structural forms of aluminum and lead, this coefficient has values of 0.34 and 0.44, and the calculated value of 0.385 indicates sufficiently high plastic properties of STAl.22 Small values of the shear modulus (G) and elastic constants (cij) also indicate this. However, the Young’s modulus (E), which characterizes the strength characteristics of this material, is not very high. Thus, the calculated Young’s modulus for STAl has a value of 8.04 GPa, located between the values for lead (18 GPa) and ice (3 GPa).23 The calculated band structure of STAl is shown in Figure 2, and the phonon spectrum is presented in Figure 3.
3. RESULTS AND DISCUSSION Geometry optimization of the crystal reveals that the supertetrahedral structure of the system is stable. The optimized crystal lattice (Figure 1) is a cubic face-centered with eight aluminum atoms in a primitive unit cell with a group of spatial symmetry − Fd3̅m (number 227). The parameter of the unit cell, calculated during optimization, was equal to a = 13.322 Å. In this case, the aluminum atoms occupy Wyckoff position 32e with the coordinates (0.06924, 0.06924, 0.06924). It is worth to note that the calculated length of the covalent bond between aluminum atoms belonging to different tetrahedra is 2.573 Å, while the length of the covalent bond between aluminum atoms belonging to the same tetrahedron turned out to be slightly larger, namely, 2.609 Å. This is explained by the fact that the inter-tetrahedron Al−Al bonds are ordinary two-center two-electron (2c-2e) covalent bonds, while the intra-tetrahedron bonds, as in the boron tetrahedron B4H4,4,14 are weaker three-center two-electron (3c-2e) covalent bonds. This was confirmed by the AdNDP15 calculations of the molecular model Al4(Al4H3)4 of the STAl crystal structure. This analysis reveals four 3c-2e covalent bonds with 1.908 electron occupation for the central aluminum tetrahedron and four 2c2e covalent bonds with 1.993 electron occupation for Al−Al bonds between the central Al4 tetrahedron and the peripheral tetrahedra. The calculated lengths of the Al−Al intra- and intertetrahedron bonds are close to the sum of the covalent radii of two aluminum atoms 2.50 Å (1.25 Å).16 Similar values of lengths of the Al−Al bonds were obtained in calculations of the supermolecular model of crystalline aluminum,2 and also in the cluster Al2Cr3.17 This bond length is also similar to the Al−Al bond (2.55 Å) in the Al2H62− dianion in the recently synthesized [{( D e p Nacnac)Mg} 2 (μ-H)] 2 [H 3 Al-AlH 3 ] (DepNacnac = [(DepNCMe)2CH]−, Dep = 2,6-diethylphenyl) compound.18 The characteristics obtained for the three boron, carbon, and aluminum supertetrahedral systems with the same symmetry are compared in Table 1. As can be seen from Table 1, the cohesive energy (Ec) has the greatest value for the carbon system and the lowest value for the aluminum system. The cohesive energy of STAl is appreciably lower that the cohesive energy of the crystalline metallic aluminum, which is 3.82 eV/atom. According to the calculations STAl has a density (ρ) equal to 0.61 g/cm3, which is close to the density of the least dense solid of lithium, 0.534 g/cm3, and significantly lower than the density of water and density of pure crystalline aluminum, 2.7 g/cm3. It means that
Figure 2. Calculated electronic band structure along high-symmetry lines in the first Brillouin zone (left panel) and electronic density of states (right panel) for cF-Al8.
From the calculations of the band electronic structure of the system shown in Figure 2, it follows that the width of the forbidden band is negligible; i.e., the calculated material has good electrical conductivity and is a semimetal. The calculated phonon spectrum, shown in Figure 3, indicates the dynamic stability of the STAl, since it does not have low-frequency branches entering the imaginary region. The calculated dielectric constant for a static field is 403.5. The calculated plots of the real and imaginary parts of the dielectric constant B
DOI: 10.1021/acs.jpcc.7b07565 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C *E-mail:
[email protected] (A.I.B.). ORCID
Alexander I. Boldyrev: 0000-0002-8277-3669 Author Contributions
The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS The work was supported by the Russian Ministry of Science and Education (agreement No. 14.Y26.31.0016) and by the USA National Science Foundation (grant CHEM-1361413) to A.I.B.
Figure 3. Calculated phonon dispersion curves along high-symmetry lines in the first Brillouin zone (left panel) and phonon density of states (right panel) for cF-Al8.
■
versus the photon energy are shown in Figure 4 and indicate that the absorption of light occurs in the region of the blue region of the visible spectrum (the visible spectrum in the figure is marked in yellow).
Figure 4. Frequency dependence of the real (red curve) and imaginary (blue curve) parts of complex dielectric permittivity for cF-Al8.
4. CONCLUSIONS In summary, we designed a new form of aluminum allotrope on the basis of a diamond lattice in which carbon atoms are replaced by aluminum Al4 tetrahedra. Follow-up quantum chemical calculations confirmed that the three-dimensional supertetrahedral aluminum crystal structure is indeed a metastable phase of aluminum with an extraordinary low density of 0.61 g/cm3. The new material is a semimetal with high plasticity. If made, this new material may have many applications due to the fact that it is a metal and at the same time it has extremely low density.
■
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b07565. Cartesian coordinates of atoms, translation vectors in Cartesian coordinates, and free energies for cF-Al8, cF-B8, cF-C8 structures (PDF)
■
REFERENCES
(1) Getmanskii, I. V.; Minyaev, R. M.; Steglenko, D. V.; Koval, V. V.; Zaitsev, S. A.; Minkin, V. I. From Two- to Three-Dimensional Structures of a Supertetrahedral Boran Using Density Functional Calculations. Angew. Chem., Int. Ed. 2017, 56, 10118−10122. (2) Minyaev, R. M.; Getmanskii, I. V.; Minkin, V. I. Supertetrahedral Aluminum and Silicon Structures and Their Hybrid Analogues. Russ. J. Inorg. Chem. 2014, 59, 332−336 (Zh. Neorg. Khim. 2014, 59, 487−491 (in Russian)). (3) Haunschild, R.; Frenking, G. Tetrahedranes. A Theoretical Study of Singlet E4H4 Molecules (E = C−Pb and B−Tl). Mol. Phys. 2009, 107, 911−922. (4) Olson, J. K.; Boldyrev, A. I. Ab Initio Search for Global Minimum Structures of Neutral and Anionic B4H4 Clusters. Chem. Phys. 2011, 379, 1−5. (5) Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Liquid Metals. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 47, 558−561. (6) Kresse, G.; Hafner, J. Ab Initio Molecular-Dynamics Simulation of the Liquid-Metal−Amorphous-Semiconductor Transition in Germanium. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 49, 14251−14269. (7) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169−11186. (8) Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (9) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953−17979. (10) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 1758−1775. (11) Perdew, J. P.; Ruzsinszky, A.; Csonka, G. I.; Vydrov, O. A.; Scuseria, G. E.; Constantin, L. A.; Zhou, X.; Burke, K. Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces. Phys. Rev. Lett. 2008, 100, 136406. (12) Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B 1976, 13, 5188−5192. (13) Momma, K.; Izumi, F. VESTA 3 for Three-Dimensional Visualization of Crystal, Volumetric and Morphology Data. J. Appl. Crystallogr. 2011, 44, 1272−1276. (14) Minyaev, R. M.; Popov, I. A.; Koval, V. V.; Boldyrev, A. I.; Minkin, V. I. Supertetrahedral B80H20, C80H20, and Al80H20 Analogs of Dodecahedrane and Their Substituted Molecules. Struct. Chem. 2015, 26, 223−229. (15) Zubarev, D. Yu.; Boldyrev, A. I. Developing Paradigms of Chemical Bonding: Adaptive Natural Density Partitioning. Phys. Chem. Chem. Phys. 2008, 10, 5207−5217. (16) The Elements, 2nd ed.; Emsley, J., Ed.; Clarendon Press: Oxford, U.K., 1991.
AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected] (R.M.M.). C
DOI: 10.1021/acs.jpcc.7b07565 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C (17) Chachkov, D. V.; Mikhailov, O. V. Molecular Structures of Polynuclear Metal Clusters by Data of DFT Calculations. I. AlFe3 (Hetero-bi)tetranuclear Cluster. Vestn. Kazan. Tekhnol. Univ. 2016, 19, 18−21 (in Russian). (18) Bonyhady, S.; Holzmann, J. N.; Frenking, G.; Stasch, A.; Jones, C. Synthesis, Characterization, and Computational Analysis of the Dialanate Dianion, [H3Al-AlH3]2−: A Valence Isoelectronic Analogue of Ethane. Angew. Chem., Int. Ed. 2017, 56, 8527−8531. (19) Gao, F.; He, J.; Wu, E.; Liu, S.; Yu, D.; Li, D.; Zhang, S.; Tian, Y. Hardness of Covalent Crystals. Phys. Rev. Lett. 2003, 91, 015502. (20) Šimůnek, A.; Vackár,̌ J. Hardness of Covalent and Ionic Crystals: First-Principle Calculations. Phys. Rev. Lett. 2006, 96, 085501. (21) Xu, B.; Tian, Y. Superhard Materials: Recent Research Progress and Prospects. Sci. China Mater. 2015, 58, 132−142. (22) Goldstein, R. V.; Gorodtsov, V. A.; Lisovenko, D. S. Auxetic Mechanics of Crystalline Materials. Mech. Solids 2010, 45, 529−545 (Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela 2010, 4, 43−62 (in Russian)). (23) Anur’ev, V. I. Spravochnik Konstruktora Mashinostroitelya, 8th ed.; Zhestkova, I. N., Ed.; Mashinostroenie: Moscow, 2001; Vol. 1, p 34 (in Russian).
D
DOI: 10.1021/acs.jpcc.7b07565 J. Phys. Chem. C XXXX, XXX, XXX−XXX
