Physics of the Solid State
Volumes and Issues
Home » Physics of the Solid State » Year 2024, issue 10 » Article p. 1569
>>>
The effect of a nanocrystal size and shape on the baric and temperature dependences of its properties (R e v i e w)
Russian version
Magomedov M. N. 1
1Institute for geothermal problems and renewable energy – branch of the joint Institute of high temperatures of the Russian Academy of Sciences, Makhachkala, Russia
Email: mahmag4@mail.ru
PDF
The problems of studying the lattice properties of a nanocrystal at various pressures and temperatures are discussed. The changes in the equation of state and baric dependences of various properties of gold during the transition from macro- to nanocrystal of cubic or rod-like shape of 306 atoms were analyzed. The following properties were considered: Debye temperature, first and second Gruneisen parameters, elastic modulus, thermal expansion coefficient, isochoric and isobaric heat capacity, specific free surface energy and its derivative by temperature, melting point. The pressure derivatives of these functions were also considered. The presented dependences are compared with the results of other authors and the problems of calculation of these properties by different methods are discussed. It was shown that at isomorphic-isothermo-isobaric reduction of a nanocrystal size the values of some properties decrease, others - increase, and there are some that can change their size dependence at change of P-T-conditions. It was shown that when the nanocrystal shape deviates from the energy-optimal shape, the size changes of the baric dependences are increase. Keywords: nanocrystal, surface energy, equation of state, thermal expansion, elastic modulus, melting point, gold.
  1. N.R.C. Corsini, W.R. Little, A. Karatutlu, Y. Zhang, O. Ersoy, P.D. Haynes, C. Molteni, N.D.M. Hine, I. Hernandez, J. Gonzalez, F. Rodriguez, V.V. Brazhkin, A. Sapelkin. Nano Lett. 15, 11, 7334 (2015). DOI: 0.1021/acs.nanolett.5b02627
  2. F. Bai, K. Bian, X. Huang, Z. Wang, H. Fan. Chem. Rev. 119, 12, 7673 (2019). DOI: 10.1021/acs.chemrev.9b00023
  3. I.M. Padilla Espinosa, T.D.B. Jacobs, A. Martini. Nanoscale Res. Lett. 17, 1, 96 (2022). DOI: 10.1186/s11671-022-03734-z
  4. W.R. Tyson, W.A. Miller. Surf. Sci. 62, 1, 267 (1977). DOI: 10.1016/0039-6028(77)90442-3
  5. S.N. Zhevnenko, I.S. Petrov, D. Scheiber, V.I. Razumovskiy. Acta Materialia 205, 116565 (2021). DOI: 10.1016/j.actamat.2020.116565
  6. S. Zhu, K. Xie, Q. Lin, R. Cao. Advances. Colloid. Interface Sci. 315, 102905 (2023). DOI: 10.1016/j.cis.2023.102905
  7. X. Zhang, W. Li, H. Kou, J. Shao, Y. Deng, X. Zhang, J. Ma, Y. Li, X. Zhang. J. App. Phys. 125, 18, 185105 (2019). DOI: 10.1063/1.5090301
  8. H. Amara, J. Nelayah, J. Creuze, A. Chmielewski, D. Alloyeau, C. Ricolleau, B. Legrand. Phys. Rev. B 105, 16, 165403 (2022). DOI: 10.1103/PhysRevB.105.165403
  9. E.H. Abdul-Hafidh. J. Nanoparticle Res. 24, 12, 266 (2022). DOI: 10.1007/s11051-022-05638-6
  10. M.N. Magomedov. Phys. Rev. B 109, 3, 035405 (2024). DOI: 10.1103/PhysRevB.109.035405
  11. M.N. Magomedov. Phys. Solid State 62, 12, 2280 (2020). DOI: 10.1134/S1063783420120197
  12. M.N. Magomedov. Tech. Phys. 58, 9, 1297 (2013). DOI: 10.1134/S106378421309020X
  13. M.N. Magomedov. Phys. Solid State 46, 5, 954 (2004). DOI: 10.1134/1.1744976
  14. M.N. Magomedov. Crystallogr. Reps 62, 3, 480 (2017). DOI: 10.1134/S1063774517030142
  15. L.A. Girifalco, Statistical Physics of Materials, J. Wiley and Sons Ltd., New York (1973). 346 p
  16. M.N. Magomedov. Phys. Solid State 63, 10, 1465 (2021). DOI: 10.1134/S1063783421090250
  17. P. Richard, A. Castellano, R. Bejaud, L. Baguet, J. Bouchet, G. Geneste, F. Bottin. Phys. Rev. Lett. 131, 20, 206101 (2023). DOI: 10.1103/PhysRevLett.131.206101
  18. D.E. Fratanduono, M. Millot, D.G. Braun, S.J. Ali, A. Fernandez-Panella, C.T. Seagle, J.-P. Davis, J.L. Brown, Y. Akahama, R.G. Kraus, M.C. Marshall, R.F. Smith, E.F. O'Bannon III, J.M. Mcnaney, J.H. Eggert. Science 372, 6546, 1063 (2021). DOI: 10.1126/science.abh0364
  19. M.N. Magomedov. Phys. Solid State 64, 7, 765 (2022). DOI: 10.21883/PSS.2022.07.54579.319
  20. G. Weck, V. Recoules, J.A. Queyroux, F. Datchi, J. Bouchet, S. Ninet, G. Garbarino, M. Mezouar, P. Loubeyre. Phys. Rev. B 101, 1, 014106 (2020). DOI: 10.1103/PhysRevB.101.014106
  21. P. Cheyssac, R. Kofman, R. Garrigos. Phys. Scripta 38, 2, 164 (1988). DOI: 10.1088/0031-8949/38/2/009
  22. R. Garrigos, P. Cheyssac, R. Kofman. Z. Phys. D 12, 1- 4, 497 (1989). DOI: 10.1007/BF01427006
  23. S.L. Lai, J.Y. Guo, V. Petrova, G. Ramanath, L.H. Allen. Phys. Rev. Lett. 77, 1, 99 (1996). DOI: 10.1103/PhysRevLett.77.99
  24. G. Kellermann, A.F. Craievich. Phys. Rev. B 78, 5, 054106 (2008). DOI: 10.1103/physrevb.78.054106
  25. F. Ercolessi, W. Andreoni, E. Tosatti. Phys. Rev. Lett. 66, 7, 911 (1991). DOI: 10.1103/physrevlett.66.911
  26. Y. Qi, T. Cav gin, W.L. Johnson, W.A. Goddard III. J. Chem. Phys. 115, 1, 385 (2001). DOI: 10.1063/1.1373664
  27. T.S. Zhu, M. Li. Mater. Res. Bull. 63, 253 (2015). DOI: 10.1016/j.materresbull.2014.12.010
  28. M.N. Magomedov. Tech. Phys. 56, 9, 1277 (2011). DOI: 10.1134/S106378421109012X
  29. M.N. Magomedov. Tech. Phys. 59, 5, 675 (2014). DOI: 10.1134/S1063784214050211
  30. M.N. Magomedov. Tech. Phys. 61, 5, 730 (2016). DOI: 10.1134/S1063784216050157
  31. M.N. Magomedov. J. Mol. Liq. 285, 106 (2019). DOI: 10.1016/j.molliq.2019.04.032
  32. M.N. Magomedov. Phys. Solid State 66, 3, 428 (2024). DOI: 10.61011/PSS.2024.03.57947.272
  33. P.I. Dorogokupets, T.S. Sokolova, B.S. Danilov, K.D. Litasov. Geodynamicsn \& Tectonophysics 3, 2, 129 (2012). DOI: 10.5800/GT-2012-3-2-0067
  34. E.N. Ahmedov. J. Phys.: Conf. Ser. 1348, 012002, 1 (2019). DOI: 10.1088/1742-6596/1348/1/012002
  35. S.P. Kramynin. Phys. Met. Metallography 123, 2, 107 (2022). DOI: 10.1134/S0031918X22020065
  36. S.P. Kramynin. J. Phys. Chem. Solids 152, 109964 (2021). DOI: 10.1016/j.jpcs.2021.109964
  37. S.P. Kramynin. Solid State Sci. 124, 106814 (2022). DOI: 10.1016/j.solidstatesciences.2022.106814
  38. I.F. Golovnev, E.I. Golovneva. Phys. Mesomech. 23, 3, 189 (2020). DOI: 10.1134/S1029959920030017
  39. M. Zhao, Y. Xia. Nature Rev. Mater. 5, 6, 440 (2020). DOI: 10.1038/s41578-020-0183-3
  40. S. Xiong, W. Qi, Y. Cheng, B. Huang, M. Wang, Y. Li. Phys. Chem. Chem.Phys. 13, 22, 10652 (2011). DOI: 10.1039/c0cp90161j
  41. M. Zhu, J. Liu, Q. Huang, J. Dong, X. Yang. J. Phys. D 55, 48, 485303 (2022). DOI: 10.1088/1361-6463/ac9485
  42. E. Purushotham, V. Radhika. Mater. Today: Proc. 47, 15, 4993 (2021). DOI: 10.1016/j.matpr.2021.04.451
  43. C.Q. Sun. Progress. Mater. Sci. 54, 2, 179 (2009). DOI: 10.1016/j.pmatsci.2008.08.001
  44. M. Goyal, B.R.K. Gupta. Mod. Phys. Lett. B 33, 26, 1950310 (2019). DOI: 10.1142/s021798491950310x
  45. M.N. Magomedov. J. Surf. Investigation. X-ray, Synchrotron. Neutron Techniques 6, 1, 86 (2012). DOI: 10.1134/S1027451012010132
  46. Y.F. Zhu, J.S. Lian, Q. Jiang. J. Phys. Chem. C 113, 39, 16896 (2009). DOI: 10.1021/jp902097f
  47. V. Pandey, M. Kumar. Pramana 97, 3, 88 (2023). DOI: 10.1007/s12043-023-02552-x
  48. G. Kellermann, F.L.C. Pereira, A.F. Craievich. J. Non-Cryst. Solids 635, 122995 (2024). DOI: 10.1016/j.jnoncrysol.2024.122995
  49. D. Shekhawat, M. Vauth, J. Pezoldt. Inorganics 10, 4, 56 (2022). DOI: 10.3390/inorganics10040056
  50. S. Schonecker, X. Li, B. Johansson, S.K. Kwon, L. Vitos. Sci. Rep. 5, 1, 14860 (2015). DOI: 10.1038/srep14860
  51. T. Cheng, D. Fang, Y. Yang. App. Surf. Sci. 393, 364 (2017). DOI: 10.1016/j.apsusc.2016.09.147
  52. D. Scheiber, O. Renk, M. Popov, L. Romaner. Phys. Rev. B 101, 17, 174103 (2020). DOI: 10.1103/PhysRevB.101.174103
  53. A.O. Tipeev, J.P. Rino, E.D. Zanotto. J. Chem. Phys. 155, 9, 094101 (2021). DOI: 10.1063/5.0059882
  54. A. Forslund, A. Ruban. Phys. Rev. B 105, 4, 045403 (2022). DOI: 10.1103/PhysRevB.105.045403
  55. C. Li, S. Lu, S. Divinski, L. Vitos. Acta Mater. 255, 119074 (2023). DOI: 10.1016/j.actamat.2023.119074
  56. V.M. Samsonov, S.A. Vasilev, I.V. Talyzin, K.K. Nebyvalova, V.V. Puitov. Russ. J. Phys. Chem. A 97, 8, 1751 (2023). DOI: 10.1134/S003602442308023X
  57. G. Kellermann, F.L.C. Pereira, A.F. Craievich. J. Appl. Cryst. 53, 2, 455 (2020). DOI: 10.1107/S1600576720002101
  58. L. Keerthana, G. Dharmalingam. J. Phys. Chem. Solids 185, 111800 (2024). DOI: 10.1016/j.jpcs.2023.111800
  59. G. de With. Chem. Rev. 123, 23, 13713 (2023). DOI: 10.1021/acs.chemrev.3c00489
  60. M.N. Magomedov. Phys. Solid State 65, 5, 708-717 (2023). DOI: 10.21883/PSS.2023.05.56040.46
  61. M.N. Magomedov. Phys. Met. Metallography 105, 2, 116 (2008). DOI: 10.1134/S0031918X08020038
  62. M.N. Magomedov. Phys. Solid State 66, 2, 221 (2024). DOI: 10.61011/PSS.2024.02.57919.241
  63. D. Errandonea. J. Appl. Phys. 108, 3, 033517 (2010). DOI: 10.1063/1.3468149
  64. D.M. Foster, T. Pavloudis, J. Kioseoglou, R.E. Palmer. Nature Commun. 10, 1, 2583 (2019). DOI: 10.1038/s41467-019-10713-z
  65. J. Chen, X. Fan, J. Liu, C. Gu, Y. Shi, D.J. Singh, W. Zheng. J. Phys. Chem. C 124, 13, 7414 (2020). DOI: 10.1021/acs.jpcc.9b10769
  66. C. Zeni, K. Rossi, T. Pavloudis, J. Kioseoglou, S. de Gironcoli, R.E. Palmer, F. Baletto. Nature Commun. 12, 1, 6056 (2021). DOI: 10.1038/s41467-021-26199-7
  67. B.K. Pandey, R.L. Jaiswal. Physica B: Condensed Matter 651, 414602 (2023). DOI: 10.1016/j.physb.2022.414602
  68. H. Sheng, B. Xiao, X. Jiang. Physica B: Condens. Matter 667, 415193 (2023). DOI: 10.1016/j.physb.2023.415193
  69. G. Poletaev, A. Sannikov, Y. Bebikhov, A. Semenov. Mol. Simul. 50, 10, 1 (2024). DOI: 10.1080/08927022.2024.2342972
  70. E.N. Ahmedov. Physica B: Condens. Matter 571, 252 (2019). DOI: 10.1016/j.physb.2019.07.027
  71. B.S. Murty, M.K. Datta, S.K. Pabi. S\=adhan\=a 28, 1- 2, 23 (2003). DOI: 10.1007/BF02717124
  72. M.S. Omar. Int. J. Thermophys. 37, 1, 11 (2016). DOI: 10.1007/s10765-015-2026-9
  73. Y.H. Zhao, Y.T. Zhu. Rev. Adv. Mater. Sci. 48, 1, 52 (2017). https://www.ipme.ru/e-journals/RAMS/ no_14817/04_14817_zhao.pdf
  74. M.S. Omar. J. Therm. Anal. Calorim. 148, 24, 14023 (2023). DOI: 10.1007/s10973-023-12689-x
  75. M. Mohr, A. Caron, P. Herbeck-Engel, R. Bennewitz, P. Gluche, K. Bruhne, H.-J. Fecht. J. Appl. Phys. 116, 12, 124308 (2014). DOI: 10.1063/1.4896729
  76. W. Li, X. Wang, L. Gao, Y. Lu, W. Wang. Materials 12, 23, 3913 (2019). DOI: 10.3390/ma12233913
  77. J.J. Li, B.B. Lu, H.J. Zhou, C.Y. Tian, Y.H. Xian, G.M. Hu, R. Xia. Phys. Lett. A 383, 16, 1922 (2019). DOI: 10.1016/j.physleta.2018.10.053
  78. X. Ou, Y. Shen, Y. Yang, Z. You, P. Wang, Y. Yang, X. Tian. Materials 16, 13, 4618 (2023). DOI: 10.3390/ma16134618
  79. Y.Q. Hu, J.F. Xu, L. Su, Y.H. Zhang, S.H. Ding, Y.H. Shen, R. Xia. Mater. Chem. Phys. 296, 127270 (2023). DOI: 10.1016/j.matchemphys.2022.127270
  80. M. Popov, V. Churkin, D. Ovsyannikov, A. Khabibrakhmanov, A. Kirichenko, E. Skryleva, Y. Parkhomenko, M. Kuznetsov, S. Nosukhin, P. Sorokin, S. Terentiev, V. Blank. Diam. Relat. Mater. 96, 52 (2019). DOI: 10.1016/j.diamond.2019.04.033
  81. M.N. Magomedov. J. Surface Investigation. X-ray, Synchrotron Neutron Techn. 9, 6, 1236 (2015). DOI: 10.1134/S1027451015060154
  82. V.N. Likhachev, G.A. Vinogradov, M.I. Alymov. Phys. Lett. A 357, 3, 236 (2006). DOI: 10.1016/j.physleta.2006.04.050
  83. I. Avramov, M. Michailov. J. Phys.: Condens. Matter 20, 29, 295224 (2008). DOI: 10.1088/0953-8984/20/29/295224
  84. H. Lei, J. Li, J. Luo. Nanoscale 7, 15, 6762 (2015). DOI: 10.1039/C5NR00056D
  85. R. Carles, P. Benzo, B. Pecassou, C. Bonafos. Sci. Rep. 6, 1, 39164 (2016). DOI: 10.1038/srep39164
  86. T. Vasina, J. Bernard, Magali Benoit, F. Calvo. Phys. Rev. B 105, 24, 245406 (2022). DOI: 10.1103/PhysRevB.105.245406
  87. K. Gu, H. Wu, J. Su, P. Sun, P.H. Tan, H. Zhong. Nano Lett. 24, 13, 4038 (2024). DOI: 10.1021/acs.nanolett.4c01021
  88. K. Michaelian, I. Santamaria-Holek. Entropy 19, 7, 314 (2017). DOI: 10.3390/e19070314
  89. A.I. Oliva, G.G. Comparan-Rodriguez, V. Sosa, A.I. Oliva-Aviles. J. Mater. Sci. 58, 20, 8563 (2023). DOI: 10.1007/s10853-023-08536-x
  90. P. Villain, P. Beauchamp, K.F. Badawi, P. Goudeau, P.-O. Renault. Scr. Mater. 50, 9, 1247 (2004). DOI: 10.1016/j.scriptamat.2004.01.033
  91. M. Krief, Y. Ashkenazy. Phys. Rev. Res. 6, 2, 023253 (2024). DOI: 10.1103/PhysRevResearch.6.023253
  92. B. Grabowski, L. Ismer, T. Hickel, J. Neugebauer. Phys. Rev. B 79, 13, 134106 (2009). DOI: 10.1103/PhysRevB.79.134106
  93. C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer, G. Kresse, A. Janotti, C.G. Van de Walle. Rev. Mod. Phys. 86, 1, 253 (2014). DOI: 10.1103/RevModPhys.86.253
  94. D.D. Satikunvar, N.K. Bhatt, B.Y. Thakore. J. App. Phys. 129, 3, 035107 (2021). DOI: 10.1063/5.0022981
  95. M. Borinaga, I. Errea, M. Calandra, F. Mauri, A. Bergara. Phys. Rev. B 93, 17, 174308 (2016). DOI: 10.1103/PhysRevB.93.174308
  96. I. Loa, F. Landgren. J. Phys.: Condens. Matter 36, 18, 185401 (2024). DOI: 10.1088/1361-648X/ad1e08
  97. M.N. Magomedov. Tech. Phys. 55, 9, 1373 (2010). DOI: 10.1134/S1063784210090227
  98. M. Matsui. J. Phys.: Conf. Ser. --- IOP Publ. 215, 1, 012197 (2010). DOI: 10.1088/1742-6596/215/1/012197
  99. X. Huang, F. Li, Q. Zhou, Y. Meng, K.D. Litasov, X. Wang, B. Liu, T. Cui. Sci. Rep. 6, 19923 (2016). DOI: 10.1038/srep19923
  100. A.M. Molodets, A.A. Golyshev, D.V. Shakhrai. J. Exp. Theor. Phys. 124, 3, 469 (2017). DOI: 10.1134/S1063776117030049
  101. D.K. Belashchenko. Physics. Uspekhi 63, 12, 1161 (2020). DOI: 10.3367/UFNe.2020.01.038761.

Подсчитывается количество просмотров абстрактов ("html" на диаграммах) и полных версий статей ("pdf"). Просмотры с одинаковых IP-адресов засчитываются, если происходят с интервалом не менее 2-х часов.

Дата начала обработки статистических данных - 27 января 2016 г.

Publisher:

Ioffe Institute

Institute Officers:

Director: Sergei V. Ivanov

Contact us:

26 Polytekhnicheskaya, Saint Petersburg 194021, Russian Federation
Fax: +7 (812) 297 1017
Phone: +7 (812) 297 2245
E-mail: post@mail.ioffe.ru