Abstract
The binding energy, equilibrium geometry, and vibrational frequencies of small free Nin clusters (n ≤ 20) are calculated using interatomic interaction potentials found within the embedded atom method. Calculations of the energy parameter of stability ΔE2 and dissociation energy show that the most energetically stable clusters are those with the magic numbers of atoms n = 4, 6, 13, and 19. Calculations of atomic vibrations reveal that the dynamic contribution to the stability of clusters is determined by the minimum vibrational frequency, whose extreme values fall on clusters with the magic numbers of atoms n = 4, 6, 13, and 19. The maximum vibrational frequency varies nonmonotonically, and it has unclear extreme values for clusters with n < 19. This result is consistent with the available experimental data on stable structures of small and medium-sized metal clusters.
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REFERENCES
Alonso, J.A., Structure and Properties of Atomic Nanoclusters, World Sci., 2012, p. 401.
Jagiello, K., Chomicz, B., Avramopoulos, A., Gajewicz, A., Mikolajczyk, A., Bonifassi, P., Papadopoulos, M.G., Leszczynski, J., and Puzyn, T., Size-Dependent Electronic Properties of Nanomaterials: How This Novel Class of Nanodescriptors Supposed to Be Calculated? Struct. Chem., 2017, vol. 28, pp. 635–643. https://doi.org/10.1007/s11224-016-0838-2
Khanna, S.N. and Jena, P., Atomic Clusters: Building Blocks for a Class of Solids, Phys. Rev. B, 1995, vol. 51, pp. 13705–13716. https://doi.org/10.1103/PhysRevB.51.13705
Stroscio, J.A. and Celotta, R.J., Controlling the Dynamics of Single Atom in Lateral Atom Manipulation, Science, 2004, vol. 306, pp. 242–247. https://doi.org/10.1126/science.1102370
Borisova, S.D., Eremeev, S.V., Rusina, G.G., and Chulkov, E.V., Magnetic and Vibrations Properties of Small Chromium Clusters on the Cu(111) Surfaces, Phys. Cem. Chem. Phys., 2021, vol. 23, pp. 7814–7821. https://doi.org/10.1039/D0CP05223J
Rusina, G.G. and Borisova, S.D., Relaxation of the Cu (111) Surface with Small Metallic Clusters, Fiz. Mezomekh., 2009, vol. 12, no. 5, pp. 57–63.
Borisova, S.D., Eremeev, S.V., Rusina, G.G., Stepanyuk, V.S., Bruno, P., and Chulkov, E.V., Vibrations of Small Cobalt Clusters on Low-Index Surfaces of Copper: Tight-Binding Simulations, Phys. Rev. B, 2008, vol. 78, pp. 075428–075432. https://doi.org/10.1103/PhysRevB.78.075428
Henry, C.R., Surface Studies of Supported Model Catalysts, Surf. Sci. Rep., 1998, vol. 31, pp. 235–325. https://doi.org/10.1016/S0167-5729(98)00002-8
Karmakar, S., Kumar, S., Rinaldi, R., and Maruccio, G., Nano-Electronics and Spintronics with Nanoparticles, J. Phys. Conf. Ser., 2011, vol. 292, pp. 012002–012006. https://doi.org/10.1088/1742-6596/292/1/012002
Nour, E.M., Alfaro-Franco, C., Gingerich, K.A., and Laane, J., Spectroscopic Studies of Nickel and Iron Clusters at 12 K, J. Chem. Phys., 1987, vol. 86, pp. 4779–4782. https://doi.org/10.1063/1.452699
Morse, M.D., Hansen, G.P., Langridge-Smith, P.R.R., Zheng, L.-S., Geusic, M.E., Michalopoulos, D.L., and Smalley, R.E., Spectroscopic Studies of the Jet Cooled Nickel Dimmer, J. Chem. Phys., 1984, vol. 80, pp. 5400–5405. https://doi.org/10.1063/1.446646
Billas, M.L., Chatelain, A., and de Heer, W.A., Magnetism of Fe, Co and Ni Clusters in Molecular Beam, J. Magn. Magn. Mater., 1997, vol. 168, pp. 64–84. https://doi.org/10.1016/S0304-8853(96)00694-4
Knickelbein, M.B., Nickel Clusters: The Influence of Adsorbates on Magnetic Moments, J. Chem. Phys., 2002, vol. 116, pp. 9703–9711. https://doi.org/10.1063/1.1477175
Bucher, J.P., Douglass, D.C., and Bloomfield, L.A., Magnetic Properties of Free Cobalt Clusters, Phys. Rev. Lett., 1991, vol. 66, pp. 3052–3055. https://doi.org/10.1103/PhysRevLett.66.3052
Castro, M., Jamorski, C., and Salahub, D.R., Structure, Bonding and Magnetism of Small Fen, Con and Nin Clusters, n ≤ 5, Chem. Phys. Lett., 1997, vol. 271, pp. 133–142. https://doi.org/10.1016/S0009-2614(97)00420-X
Andriotis, A.N. and Menon, M., Tight-Binding Molecular-Dynamics Study of Ferromagnetic Clusters, Phys. Rev. B, 1998, vol. 57, pp. 10069–10081. https://doi.org/10.1103/PhysRevB.57.10069
Rodríguez-López, J.L., Aguilera-Granja, F., Michaelian, K., and Vega, A., Structure and Magnetism of Cobalt Clusters, Phys. Rev. B, 2003, vol. 67, pp. 174413–174419. https://doi.org/10.1103/PhysRevB.67.174413
Borisova, S.D., Rusina, G.G., and Chulkov, E.V., Structure and Vibrational Properties of Cobalt Clusters (n ≤ 20), Phys. Solid State, 2010, vol. 52, no. 4, pp. 838–843.
Futschek, T., Hafner, J., and Marsman, M., Stable Structural and Magnetic Isomers of Small Transition-Metal Clusters from the Ni Group: An Ab Initio Density-Functional Study, J. Condens. Matter, 2006, vol. 18, pp. 9703–9748. https://doi.org/10.1088/0953-8984/18/42/016
Grigoryan, V.G. and Springborg, M., Structural and Energetic Properties of Nickel Clusters: 2 ≤ n ≤ 150, Phys. Rev. B, 2004, vol. 70, pp. 205415–205430. https://doi.org/10.1103/PhysRevB.70.205415
Haslett, T.L., Moskovits, M., and Weitzman, A.L., Dissociation Energies of Transition Metal Diatomics, J. Molec. Spectroscopy, 1989, vol. 135, pp. 259–269. https://doi.org/10.1016/0022-2852(89)90155-0
Kreibig, U. and Vollmer, M., Optical Properties of Metal Clusters, Berlin: Springer-Verlag, 1995.
Vajda, S., Wolf, S., Leisner, T., Busolt, U., Wöste, L., and Wales, D.J., Reactions of Size-Selected Positively Charged Nickel Clusters with Carbon Monoxide in Molecular Beams, J. Chem. Phys., 1997, vol. 107, pp. 3492–3497. https://doi.org/10.1063/1.474688
Daw, M.S. and Baskes, M.I., Semiempirical Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals, Phys. Rev. Lett., 1983, vol. 50, pp. 1285–1288. https://doi.org/10.1103/PhysRevLett.50.1285
Levesque, D. and Verlet, L., Molecular Dynamic and Time Reversibility, J. Statistic. Phys., 1993, vol. 72, no. 3/4, pp. 519–537. https://doi.org/10.1007/BF01048022
Bersuker, I.B., The Jahn–Teller Effect and Vibronic Interactions in Modern Chemistry, New York: Springer New York, 1984.
Rusina, G.G., Borisova, S.D., and Chulkov, E.V., Structure and Analysis of Atomic Vibrations in Clusters of Cun (n ≤ 20), Russ. J. Phys. Chem. A, 2013, vol. 87, no. 2, pp. 233–239. https://doi.org/10.1134/s0036024413020271
Mackay, A.L., A Dense Non-Crystallographic Packing of Equal Spheres, Acta Crystallogr., 1962, vol. 15, pp. 916–918. https://doi.org/10.1107/S0365110X6200239X
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Borisova, S.D., Rusina, G.G. Structure and Vibrations of Free Nin Clusters (n ≤ 20). Phys Mesomech 27, 197–204 (2024). https://doi.org/10.1134/S1029959924020085
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DOI: https://doi.org/10.1134/S1029959924020085