Molar binding energy of the boron nitride single-walled zigzag and armchair nanotubes is calculated within the qua-si-classical approach. We find that, in the range of ultra small radii, the binding energy of nanotubes exhibit an oscil-latory dependence on tube radius. Nanotubes (1,1), (3,0), and (4,0) are predicted to be more stable species among sin-gle-walled boron nitride nanotubes. The obtained binding energies of BN single-walled nanotubes corrected with zero-point vibration energies lies within the interval (12.01-29.39) eV. In particular, molar binding energy of the ul-tra-large-radius tube is determined as 22.95 eV. The spread of the molar zero-point vibration energy of BN nanotubes itself is (0.25-0.33) eV and its limit for ultra-large-radius tubes is estimated as 0.31 eV. The binding energy peak lo-cated at 2.691 Å corresponds to the equilibrium structural parameter of all realized stable BN nanotubular structures.
KeywordsBinding EnergyZigzag and Armchair NanotubesBN
A. Rubio, J. L. Corkill and M. L. Cohen, “Theory of Graphitic Boron Nitride Nanotubes,” Physical Review B, Vol. 49, No. 7, 1994, pp. 5081-5084.
Z. Weng-Sieh, K. Cherrey, N. G. Chopra, X. Blasé, Y. Miyamoto, A. Rubio, M. L. Cohen, S. G. Louie, A. Zettl and R. Gronsky, “Synthesis of BxCyNz Nanotu-bules,” Physical Review B, Vol. 51, No. 16, 1995, pp. 11229-11232.
N. G. Chopra, R. J. Luyken, K. Cherrey, V. H. Crespi, M. L. Cohen, S. G. Louie and A. Zettl, “Bo-ron-Nitride Nanotubes,” Science, Vol. 269, No. 5226, 1995, pp. 966-967.
K. Suenaga, C. Colliex, N. Demoncy, A. Loie-seau, H. Pascard and F. Willaime, “Synthesis of Nanoparticles and Nanotubes with Well-Separated Layers of Boron Nitride and Carbon,” Science, Vol. 278, No. 5338, 1997, pp. 653- 655.
K. Suenaga, F. Willaime, A. Loieseau and C. Colliex. “Organization of Carbon and Boron Nitride Layers in Mixed Nanoparticles and Nanotubes Synthesized by Arc Discharge,” Applied Physics A, Vol. 68, No. 3, 1999, pp. 301-308.
A. Loiseau, F. Willaime, N. Demoncy, G. Hug and H. Pascard, “Boron Nitride Nanotubes with Reduced Numbers of Layers Synthesized by Arc Discharge,” Physical Review Letters, Vol. 76, No. 25, 1996, pp. 4737-4740.
Y. Saito, M. Maida and T. Matsumoto, “Structures of Boron Nitride Nanotubes with Single-Layer and Multi- Layers Produced by Arc Discharge,” Japanese Journal of Applied Physics, Vol. 38, No. 1A, 1999, pp. 159-163.
Y. Saito and M. Maida, “Square, Pentagon, and Heptagon rings at BN Nanotube Tips,” Journal of Physical Chemistry A, Vol. 103, No. 10, 1999, pp. 1291-1293.
D. Golberg, Y. Bando, M. Eremets, K. Takemura, K. Kurashima and H. Yusa “Nanotubes in Boron Nitride Laser Heated at High Pressure,” Applied Physics Letters, Vol. 69, No. 14, 1996, pp. 2045-2047.
R. Sen, B. C. Satishkumar, A. Govindaraj, K. R. Harikumar, G. Raina, J.-P. Zhang, A. K. Cheetham and C. N. R. Rao, “B-C-N, C-N and B–N Nanotubes Produced by the Pyrolysis of Precursor Molecules over Co Catalysts,” Chemical Physics Letters, Vol. 287, No. 5-6, 1998, pp. 671-676.
D. Golberg, Y. Bando, W. Han, K. Kurashima and T. Sato, “Sin-gle-Walled B Doped Carbon, B/N Doped Carbon, and BN Nanotubes Synthesized from Single-Walled Carbon Nanotubes through a Substitution Reaction,” Chemical Physics Letters, Vol. 308, No. 3-4, 1999, pp. 337-342.
D. Golberg, W. Han, Y. Bando, L. Bourgeois, K. Kurashima and T. Sato, “Fine Structure of Boron Nitride Nanotubes Produced from Carbon Nanotubes by a Substitution Reaction,” Journal of Applied Physics, Vol. 86, No. 4, 1999, pp. 2364-2366.
Y. Chen, L. T. Chadderton, J. F. Gerald and J. S. Williams, “A Solid-State Process for Formation of Boron Nitride Nanotubes,” Applied Physics Letters, Vol. 74, No. 20, 1999, pp. 2960-2962.
T. S. Bartnitskaya, G. S. Oleinik, V. V. Pokropivnyi, N. V. Danilenko, V. M. Vershchaka and A. V. Kotko, “Na- notubes from Graphite-Like BN,” Superhard Materials, No. 6, 1998, pp. 71-74.
T. S. Bartnitskaya, G. S. Oleinik, A. V. Pokropivnyi and V. V. Pokropivnyi, “Synthesis, Structure, and Formation Mechanism of Boron Nitride Nanotubes,” JEPT Letters, Vol. 69, No. 2, 1999, pp. 163-168.
C. Colazo-Davila, E. Bengu, L. D. Marks and M. Kirk, “Nucleation of Cubic Boron Nitride Thin Films,” Diamond Related Materials, Vol. 8, No. 6, 1999, pp. 1091- 1100.
T. Oku, T. Hirano, M. Kuno, T. Kusunose, K. Niihara and K. Suganuma, “Synthesis, Atomic Structures, and Properties of Carbon and Boron Nitride Fullerene Materials,” Materials Science and Engineering B, Vol. 74, No. 1-3, 2000, pp. 206-217.
J. Wang, V. K. Kayastha, Y. K. Yap, Z. Fan, J. G. Lu, Z. Pan, I. N. Ivanov, A. A. Puretzky and D. B. Geohegan, “Low Temperature Growth of Boron Nitride Nano-tubes on Substrates,” Nano Letters, Vol. 5, No. 12, 2005, pp. 2528-2532.
L. L. Sartinska, S. Barchikovski, N. Wagenda, B. M. Rud’ and I. I. Timofeeva, “Laser Induced Modification of Surface Structures,” Applied Surface Science, Vol. 253, No. 9, 2007, pp. 4295-4299.
L. L. Sartinska, A. A. Frolov, A. Yu. Koval’, N. A. Danilenko, I. I. Timofeeva and B. M. Rud’, “Transformation of Fine-Grained Graphite-Like Boron Nitride Induced by Concentrated Light Energy,” Materials Chemistry and Physics, Vol. 109, No. 1, 2008, pp. 20-25.
M. V. P. Altoe, J. P. Sprunck, J.-C. P. Gabriel and K. Bradley, “Nanococoon Seeds for BN Nanotube Growth,” Journal of Materials Science, Vol. 38, No. 24, 2003, pp. 4805-4810.
M. W. Smith, K. C. Jordan, C. Park, J.-W. Kim, P. T. Lillehei, R. Crooks and J. S. Harrison, “Very Long Single- and Few-Walled Boron Nitride Nanotubes via the Pressurized Vapor/Condenser Method,” Nanotechnology, Vol. 20, No. 50, 2009, pp. 505604-505610.
X. Blasé, J.-C. Charlier, A. de Vita and R. Car, “Theory of Composite BxCyNz Nanotube Heterojunctions,” Applied Physics Letters, Vol. 70, No. 2, 1997, pp. 197-199.
X. Blasé, J.-C. Charlier, A. de Vita and R. Car, “Structural and Electrical Properties of Com-posite BxCyNz Nanotubes and Heterojunctions,” Applied Physics A, Vol. 68, No. 3, 1999, pp. 293-300.
V. V. Pokropivnyj, V. V. Skorokhod, G. S. Oleinik, A. V. Kurdyumov, T. S. Bartnitskaya, A. V. Pokropivnyj, A. G. Sisonyuk and D. M. Sheichenko, “Boron Nitride Analogs of Fullerenes (the Fulbo-renes), Nanotubes, and Fullerites (the Fulborenites),” Journal of Solid State Chemistry, Vol. 154, No. 1, 2000, pp. 214-215.
J. H. Lee, “A Study on a Boron-Nitride Nano-tube as a Gigahertz Oscillator,” The Journal of the Korean Physical Society, Vol. 49, No. 1, 2006, pp. 172-176.
V. Verma and K. Dharamvir, “BNNT in Contact with h BN Sheet and Other BNNT and DW BNNT as GHz Oscillator,” Interna-tional Journal of Nanosystems, Vol. 1, No. 1, 2008, pp. 27-34.
B. Baumeier, P. Krüger and J. Pollmann, “Struc-tural, Elastic, and Electronic Properties of SiC, BN, and BeO Nanotubes,” Physical Review B, Vol. 76, 2007, p. 085407.
Y.-H. Kim, K. J. Chang and S. G. Louie, “Elec-tronic Structure of Radially Deformed BN and BC3 Nanotubes,” Physical Review B, Vol. 63, 2001, p. 205408.
G. Y. Guo and J. C. Lin, “Second-Harmonic Generation and Linear Electro-Optical Coefficients of BN Nanotubes,” Physical Review B, Vol. 72, 2005, p. 075416.
G. Y. Guo and J. C. Lin, “Erratum: Second-Harmonic Generation and Linear Elec-tro-Optical Coefficients of BN Nanotubes,” Physical Review B, Vol. 77, 2008, p. 049901 (E).
C. Zhi, Y. Bando, C. Tang and D. Golberg, “Engineering of Electronic Structure of Bo-ron-Nitride Nanotubes by Covalent Functionalization,” Physical Review B, Vol. 74, 2006, p. 153413.
C. Zhi, Y. Bando, C. Tang and D. Golberg, “Publisher’s Note: Engineering of Electronic Structure of Boron-Ni- tride Nanotubes by Covalent Functionalization,” Physical Review B, Vol. 74, 2006, p. 199902 (E).
W.-Q. Han, C. W. Chang and A. Zettl, “Encapsulation of One-Dimensional Potassium Halide Crystals within BN Nanotubes,” Nano Letters, Vol. 4, No. 7, 2004, pp. 1355- 1357.
K. Yum and M.-F. Yu, “Measurement of Wetting Properties of Individual Boron Nitride Nanotubes with the Wil-helmy Method Using a Nanotube-Based Force Sensor,” Nano Letters, Vol. 6, No. 2, 2006, pp. 329-333.
S. A. Shevlin and Z. X. Guo, “Hydrogen Sorption in Defective Hexagonal BN Sheets and BN Nanotubes,” Physical Review B, Vol. 76, 2007, p. 024104.
E. Durgun, Y. R. Jang and S. Ciraci, “Hydrogen Storage Capacity of Ti Doped Boron-Nitride and B/Be Substitut- ed Carbon Nanotubes,” Physical Review B, Vol. 76, 2007, p. 073413.
Ch. Tang, Y. Bando, X. Ding, Sh. Qi and D. Golberg, “Catalyzed Collapse and Enhanced Hydrogen Storage of BN Nanotubes,” Journal of the American Chemical Society, Vol. 124, No. 49, 2002, pp. 14550-14551.
C. Zhi, Y. Bando, C. Tang and D. Golberg. “Immobilization of Proteins on Boron Nitride Nanotubes,” Journal of the American Chemical Society, Vol. 127, No. 49, 2005, pp. 17144-17145.
C. Zhi, Y. Bando, C. Tang, R. Xie, T. Se-kiguchi and D. Golberg, “Perfectly Dissolved Boron Nitride Nanotubes Due to Polymer Wrapping,” Journal of the American Chemical Society, Vol. 127, No. 46, 2005, pp. 15996- 15997.
M. C?té, P. D. Haynes and C. Molteni, “Boron Nitride Polymers: Building Blocks for Organic Electronic De-vices,” Physical Review B, Vol. 63, 2001, p. 125207.
M. Ishigami, J. D. Sau, Sh. Aloni, M. L. Cohen and A. Zettl, “Ob-servation of the Giant Stark Effect in Boron-Nitride Nanotubes,” Physical Review Letters, Vol. 94, 2005, p. 056804.
J. Cumings and A. Zettl, “Mass-Production of Boron Nitride Double-Wall Nanotubes and Nanococones,” Chemical Physics Letters, Vol. 316, No. 3-4, 2000, pp. 211-216.
Y. Chen, J. Zou, S. J. Campbell and G. le Caer, “Boron Nitride Nanotubes: Pronounced Resistance to Oxidation,” Applied Physics Letters, Vol. 84, No. 13, 2004, pp. 2430- 2432.
E. Bengu and L. D. Marks, “Single-Walled BN Nanostructures,” Physical Review Letters, Vol. 86, No. 11, 2001, pp. 2385-2387.
C. Tang, Y. Bando, Y. Huang, S. Yue, C. Gu, F. F. Xu and D. Golberg, “Fluorination and Electrical Conductivity of BN Nanotubes,” Journal of the American Chemical Society, Vol. 127, No. 18, 2005, pp. 6552-6553.
E. J. Mele and P. Král, “Electric Polarization of Heteropolar Nanotubes as a Geometric Phase,” Physical Review Letters, Vol. 88, 2002, p. 056803.
N. Sai and E. J. Mele, “Microscopic Theory for Nanotube Piezoelectricity,” Physical Review B, Vol. 68, 2003, p. 241405.
S. M. Nakhmanson, A. Calzolari, V. Meunier, J. Bernholc and M. Buongiorno Nardelli, “Spontaneous Polarization and Piezoelectricity in Boron Nitride Nanotubes,” Physical Review B, Vol. 67, 2003, p. 235406.
N. G. Lebedev and L. A. Chernozatonski?, “Quantum- Chemical Calculations of the Piezoelectric Characteristics of Boron Nitride and Carbon Nanotubes,” Physics of the Solid State, Vol. 48, No. 10, 2006, pp. 2028-2034.
Y. Zhang, K. Suenaga, C. Colliex and S. Iijima, “Coaxial Nanocable: Silicon Carbide and Silicon Oxide Sheathed with Boron Nitride and Carbon,” Science, Vol. 281, No. 5379, 1998, pp. 973-975.
A. Zobelli, A. Gloter, C. P. Ewels, G. Seifert and C. Colliex, “Electron Knock-on Cross Section of Carbon and Boron Nitride Nanotubes,” Physical Review B, Vol. 75, 2007, p. 245402.
I. V. Weiz, “Supplement II,” In: K.-P. Huber and G. Herzberg, Constants of Diatomic Molecules, Part 2: Mo-lecules N2–ZrO, Mir, Moscow, 1984, pp. 295-366.
O. I. Bukhtyarov, S. P. Kurlov and B. M. Lipenskikh, “Calculation of the Structure and Physicochemical Properties of B-Based Systems by the Computer Modeling Method,” In: Abstracts of the 8th International Symposium on Boron, Borides, Carbides, Nitrides, and Related Compounds, Tbilisi, October 1984, pp. 135-136.
J. L. Masse and M. B?rlocher, “Etude par la Méthode du Autocohérent (Self-Consistent) de la Molécule BN,” Helvetica Chimia Acta, Vol. 47, No. 1, 1964, pp. 314- 318.
Yu. G. Khajt and V. I. Baranovskij, “Ab Initio Calculations of the BN Molecule,” Journal of Structural Chemi-stry, Vol. 21, No. 1, 1980, pp. 153-154.
H. Bredohl, J. Dubois, Y. Houbrechts and P. Nzohabonayo, “The Singlet Bands of BN,” Journal of Physics B, Vol. 17, No. 1, 1984, pp. 95-98.
C. M. Marian, M. Gastreich and J. D. Gale, “Empirical Two-Body Potential for Solid Silicon Nitride, Boron Nitride, and Borosilazane Modifications,” Physical Review B, Vol. 62, No. 5, 2000, pp. 3117-3124.
L. Chkhartishvili, “Quasi-Classical Analysis of Boron- Nitrogen Binding,” In: Proceedings of the 2nd International Boron Symposium, Eski?ehir, Turkey, September 2004, pp. 165-171.
L. Chkhartishvili, D. Lezhava, O. Tsagareishvili and D. Gulua, “Ground State Parameters of B2, BC, BN, and BO Diatomic Molecules,” Transactions of the AMIAG, Vol. 1, 1999, pp. 295-300.
L. Chkhartishvili, D. Lezhava and O. Tsagareishvili, “Quasi-Classical Determination of Electronic Energies and Vibration Frequencies in Boron Compounds,” Journal of Solid State Chemistry, Vol. 154, No. 1, 2000, pp. 148-152.
A. Gaydon, “Dissociation Energies and Spectra of Diatomic Molecules,” Chapman & Hall, London, 1947.
K. P. Huber and G. Herzberg, “Molecular Spectra and Molecular Structure: IV. Constants of Diatomic Molecules,” van Nostrand Reinhold Co, New York, 1979.
M. Lorenz, J. Agreiter, A. M. Smith and V. E. Bondybey, “Electronic Structure of Diatomic Boron Nitride,” Journal of Chemical Physics, Vol. 104, No. 8, 1996, pp. 3143- 3146.
L. Chkhartishvili, “Zero-Point Vibration Energy within Qua-si-Classical Approximation: Boron Nitrides,” Proceedings of the TSU (Physics), Vol. 40, 2006, pp. 130-138.
V. I. Vedeneev, L. V. Gurvich, V. N. Kondrat’ev, V. A. Medvedev and E. A. Frankevich, “Chemical Bonds Breaking Energies, Ionization Potentials and Electron Affinities,” Academy of Sciences of USSR, Moscow, 1962.
G. Meloni, M. Sai Baba and K. A. Gingerich, “Knudsen Cell Mass Spectrometric Investigation of the B2N Molecule,” Journal of Chemical Physics, Vol. 113, No. 20, 2000, pp. 8995-8999.
R. Vanderbosch, “Gas-Phase Anions Containing B and N,” Physical Review A, Vol. 67, 2003, p. 013203.
S. V. Lisenkov, G. A. Vinogradov, T. Y. Astakhova and N. G. Lebedev, “Non-Spiral ‘Haeckelite-Type’ BN-Nanotubes,” JETP Letters, Vol. 81, No. 7, 2005, pp. 431-436.
A. Zunger, “A Molecular Calculation of Electronic Properties of Layered Crystals: I. Truncated Crystal Approach for Hexagonal Boron Nitride,” Journal of Physics C, Vol. 7, No. 1, 1974, pp. 76-95.
A. Zunger, “A Molecular Calculation of Electronic Properties of Layered Crystals: II. Periodic Small Cluster Calculation for Graphite and Boron Nitride,” Journal of Physics C, Vol. 7, No. 1, 1974, pp. 96-106.
D. L. Strout, “Structure and Stability of Boron Nitrides: Isomers of B12N12,” Journal of Physical Chemistry A, Vol. 104, No. 15, 2000, pp. 3364-3366.
L. S. Chkhartishvili, “Quasi-Classical Estimates of the Lattice Constant and Band Gap of a Crystal: Two-Dimensional Boron Nitride,” Physics of the Solid State, Vol. 46, No. 11, 2004, pp. 2126-2133.
L. S. Chkhartishvili, “Analytical Optimization of the Lattice Parameter Using the Binding Energy Calculated in the Quasi-Classical Approximation,” Physics of the Solid State, Vol. 48, No. 5, 2006, pp. 846-853.
L. Chkhartishvili and D. Lezhava, “Zero-Point Vibration Effect on Crystal Binding Energy: Quasi-Classical Calculation for Layered Boron Nitride,” Transactions of the GTU, Vol. 439, 2001, pp. 87-90.
K.-H. Hellwege and O. von Madelung, Eds., “Boron Nitride (BN),” In: Landolt-B?rnstein, Numerical Data and Functional Relationships in Science and Technology, New Series, Group III: Crystal and Solid State Physics, Volume 17: Semiconductors, Subvolume g: Physics of Non-Tetrahedrally Bonded Binary Compounds III, Springer-Verlag, Berlin, 1982.
Y.-N. Xu and W. Y. Ching, “Calculation of Ground-State and Optical Properties of Boron Nitrides in the Hexagonal, Cubic, and Wurtzite Structures,” Physical Review B, Vol. 44-I, No. 15, 1991, pp. 7784-7798.
K. Albe, “Theoretical Study of Boron Nitride Modifications at Hydrostatic Pressures,” Physical Review B, Vol. 55-II, No. 10, 1997, pp. 6203-6210.
D. D. Wagmann, W. H. Evans, V. B. Parker, J. Halow, S. M. Bairly and R. H. Shumn, Eds., Selected Values of Chemical Thermodynamic Properties, National Bureau of Standards, Washington, 1968.
S. N. Grinyaev, F. V. Konusov and V. V. Lopatin, “Deep Levels of Nitrogen Vacancy Complexes in Graphite-Like Boron Nitride,” Physics of the Solid State, Vol. 44, No. 2, 2002, pp. 286-293.
M. S. C. Mazzoni, R. W. Nunes, S. Azevedo and H. Chacham, “Electronic Structure and Energetics of BxCyNz Layered Structures,” Physical Review B, Vol. 73, 2006, p. 073108.
S. V. Lisenkov, G. A. Vonogradov, T. Y. Astakhova and N. G. Lebedev, “Geometric Structure and Electronic Properties of Planar and Nanotubular BN Structures of the Haeckelite Type,” Physics of the Solid State, Vol. 48, No. 1, 2006, pp. 192-198.
O. E. Alon, “Symmetry Properties of Single-Walled Boron Nitride Nanotubes,” Physical Review B, Vol. 64, 2001, p. 153408.
V. V. Pokropivnyi, “Non-Carbon Nanotubes (Review). 2. Types and Structure,” Powder Metallurgy and Metal Ceramics, Vol. 40, No. 11-12, 2002, pp. 582-594.
M. Menon and D. Srivastava, “Structure of Boron Nitride Nanotubes: Tube Closing Versus Chirality,” Chemical Physics Letters, Vol. 307, No. 5-6, 1999, pp. 407-412.
J.-C. Charlier, X. Blase, A. de Vita and R. Car, “Microscopic Growth Mechanisms for Carbon and Boron-Ni- tride Nanotubes,” Applied Physics A, Vol. 68, No. 3, 1999, pp. 267-273.
L. S. Chkhartishvili, “On Sizes of Boron Nitride Nanotubes,” In: Proceedings of the 18th International Symposium “Thin Films in Optics in Nanoelectronics,” Kharkiv, October 2006, pp. 367-373.
Z. Peralta–Inga, P. Lane, J. S. Murray, S. Boyd, M. E. Grice, C. J. O’Connor and P. Politzer, “Characterization of Surface Electrostatic Potentials of Some (5,5) and (n,1) Carbon and Boron/Nitrogen Model Nanotubes,” Nano Letters, Vol. 3, No. 1, 2003, pp. 21-28.
D. Golberg, Y. Bando, L. Bourgeois, K. Kurashima and T. Sato, “Insights into the Structure of BN Nanotubes,” Applied Physics Letters, Vol. 77, No. 13, 2000, pp. 1979- 1981.
S. Okada, S. Saito and A. Oshiyama, “Inter-Wall Interaction and Electronic Structure of Double-Walled BN Nanotubes,” Physical Review B, Vol. 65, No. 16, 2002, p. 165410.
Y. B. Kuz’ma and N. F. Chaban, “Boron Containing Binary and Ternary Systems: Handbook,” Metallurgiya, Moscow, 1990.
E. Hernández, C. Goze, P. Bernier and A. Rubio, “Elastic properties of C and BxCyNz Composite Nanotubes,” Physical Review Letters, Vol. 80, No. 20, 1998, pp. 4502- 4505.
H. J. Xiang, J. Yang, J. G. Hou and Q. Zhu, “First-Prin- ciples Study of Small-Radius Single-Walled BN Nanotubes,” Physical Review B, Vol. 68, 2003, p. 035427.
L. Wirtz, A. Rubio, R. A. de la Concha and A. Loiseau, “Ab initio Calculations of the Lattice Dynamics of Boron Nitride Nanotubes,” Physical Review B, Vol. 68, 2003, p. 045425.
L. Wirtz, M. Lazzeri, F. Mauri and A. Rubio, “Raman Spectra of BN Nanotubes: Ab Initio and Bond-Polari- zability Model Calculations,” Physical Review B, Vol. 71, 2005, p. 241402 (R).
H. F. Bettinger, T. Dumitric?, G. E. Scuseria and B. I. Yakobson, “Mechanically Induced Defects and Strength of BN Nanotubes,” Physical Review B, Vol. 65, 2002, p. 041406.
Y. Miyamoto, A. Rubio, S. Berber, M. Yoon and D. To- mánek, “Spectroscopic Characterization of Stone–Wales Defects in Nanotubes,” Physical Review B, Vol. 69, 2004, p. 121413 (R).
G. Y. Gou, B. C. Pan and L. Shi, “Theoretical Study of Size-Dependent Properties of BN Nanotubes with Intrinsic Defects,” Physical Review B, Vol. 76, 2007, p. 155414.
E. Hernandez, C. Goze, P. Bernier and A. Rubio, “Elastic Properties of Single-Wall Nanotubes,” Applied Physics A, Vol. 68, No. 3, 1999, pp. 287-292.
D. Srivastava, M. Menon and K.-J. Cho, “Anisotropic Nanomechanics of Boron Nitride Nanotubes: Nanostructured “Skin” Effect,” Physical Review B, Vol. 63, 2001, p. 195413.
T. Dumitric? and B. I. Yakobson, “Rate Theory of Yield in Boron Nitride Nanotubes,” Physical Review B, Vol. 72, 2005, p. 035418.
L. Chkhartishvili, “Quasi-Classical Theory of Substance Ground State,” Technical University Press, Tbilisi, 2004.
L. Chkhartishvili, “Quasi-Classical Method of Calculation of Substance Structural and Electronic Energy Spectrum Parameters,” Tbilisi University Press, Tbilisi, 2006.
L. Chkhartishvili, “Selection of Equilibrium Configurations for Crystalline and Molecular Structures Based on Quasi-Classical Inter-Atomic Potential,” Transactions of the GTU, No. 427, 1999, pp. 13-19.
L. Chkhartishvili, “On Quasi-Classical Estimations of Boron Nanotubes Ground-State Parameters,” Journal of Physics: Conference Series, Vol. 176, 2009, p. 012013.
L. Chkhartishvili, “Molar Binding Energy of the Boron Nanosystems,” In: Proceedings of the 4th International Boron Symposium, Osmangazi University Press, Eski?ehir, Turkey, 2009, pp. 153-160.
L. Chkhartishvili, “Ground State Parameters of Wurtzite Boron Nitride: Quasi-Classical Estimations,” In: Proceedings of the 1st International Boron Symposium, Dumlupinar University Press, Kütahya, 2002, pp. 139- 143.
L. Chkhartishvili, “Boron Nitride Nanosystems of Regular Geometry,” Journal of Physics: Conference Series, Vol. 176, 2009, p. 012014.
L. S. Chkhartishvili, “Equilibrium Geometry of Ultra- Small-Radius Boron Nitride Nanotubes,” Material Science of Nanostructures, No. 1, 2009, pp. 33-44.
Ch. Froese–Fischer, “The Hartree–Fock Method for Atoms: A Numerical Approach,” Wiley, New York, 1977.
R. J. Boscovich, “Philosophiae Naturalis Theoria Redacta ad Inicam Legem Vitium in Natura Existentiam,” Collegio Romano, Milano, 1758.
T. L Hill and R. V. Chamberlin, “Fluctuations in Energy in Completely Open Small Systems,” Nano Letters, Vol. 2, No. 6, 2002, pp. 609-613.