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Structure and Vibrations of Free Nin Clusters (n ≤ 20)

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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

  1. Alonso, J.A., Structure and Properties of Atomic Nanoclusters, World Sci., 2012, p. 401.

  2. 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

    Article  Google Scholar 

  3. 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

    Article  ADS  Google Scholar 

  4. 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

    Article  ADS  Google Scholar 

  5. 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

    Article  Google Scholar 

  6. 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.

    Google Scholar 

  7. 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

    Article  ADS  Google Scholar 

  8. 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

    Article  ADS  Google Scholar 

  9. 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

  10. 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

    Article  ADS  Google Scholar 

  11. 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

    Article  ADS  Google Scholar 

  12. 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

    Article  ADS  Google Scholar 

  13. 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

    Article  ADS  Google Scholar 

  14. 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

    Article  ADS  Google Scholar 

  15. 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

  16. 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

    Article  ADS  Google Scholar 

  17. 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

    Article  ADS  Google Scholar 

  18. 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.

  19. 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

    Article  ADS  Google Scholar 

  20. 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

  21. 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

    Article  ADS  Google Scholar 

  22. Kreibig, U. and Vollmer, M., Optical Properties of Metal Clusters, Berlin: Springer-Verlag, 1995.

  23. 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

  24. 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

    Article  ADS  Google Scholar 

  25. 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

    Article  ADS  Google Scholar 

  26. Bersuker, I.B., The Jahn–Teller Effect and Vibronic Interactions in Modern Chemistry, New York: Springer New York, 1984.

  27. 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

  28. 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

    Article  Google Scholar 

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Funding

The investigation was performed within the government statement of work for ISPMS SB RAS (research line FWRW-2022-0001).

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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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