Skip to main content
SpringerLink
Log in

Dynamics and Phase Transitions in Nanosystems

  • Chapter
  • First Online:
Dynamics of Systems on the Nanoscale

Part of the book series: Lecture Notes in Nanoscale Science and Technology ((LNNST,volume 34))

  • 614 Accesses

Abstract

This chapter is devoted to the discussion of phase and structural transitions that occur in nanoscale systems. A particular focus is given to solid–liquid phase transitions, solid–solid martensitic transitions, and spontelectric phenomena. Phase transitions and their conditions are among the most characteristic properties of materials. Computational studies of these phenomena are commonly performed by means of molecular dynamics simulations. Such simulations permit the verification and validation of the force fields used in simulations of thermomechanical properties of various materials which are relevant to various technological applications.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The error data can be found in the original Fig. 2 in Ref. [13].

  2. 2.

    For amorphous NiTi, the dependence does not reveal a prominent maximum but fluctuates around the value of 0.04 \(\upmu \)N/nm, indicating that it is much easier to deform the amorphous sample as compared to the ideal crystalline one.

References

  1. Bréchignac, C., Houdy, P., Lahmani, M. (eds.): Nanometerials and Nanochemistry. Springer, Berlin (2007)

    Google Scholar 

  2. Ferrando, R.: Structure and Properties of Nanoalloys. Elsevier (2016)

    Google Scholar 

  3. Aguado, A., Jarrold, M.: Melting and freezing of metal clusters. Annu. Rev. Phys. Chem. 62, 151–172 (2011)

    Article  ADS  Google Scholar 

  4. Yakubovich, A.V., Sushko, G., Schramm, S., Solov’yov, A.V.: Kinetics of liquid-solid phase transition in large nickel clusters. Phys. Rev. B 88, 035438 (2013)

    Article  ADS  Google Scholar 

  5. Campbell, E.: Fullerene Collision Reactions. Springer Science & Business Media (2003)

    Google Scholar 

  6. Sattler, K.D. (ed.): Handbook of Nanophysics: Clusters and Fullerenes. CRC Press, Boca Raton (2010)

    Google Scholar 

  7. Hussien, A., Yakubovich, A., Solov’yov, A.V., Greiner, W.: Phase transition, formation and fragmentation of fullerenes. Eur. Phys. J. D 57, 207–217 (2010)

    Article  ADS  Google Scholar 

  8. Verkhovtsev, A.V., Korol, A.V., Solov’yov, A.V.: Classical molecular dynamics simulations of fusion and fragmentation in fullerene-fullerene collisions. Eur. Phys. J. D 71, 212 (2017)

    Article  ADS  Google Scholar 

  9. Freddolino, P.L., Harrison, C.B., Liu, Y., Schulten, K.: Challenges in protein folding simulations: timescale, representation, and analysis. Nat. Phys. 6, 751–758 (2010)

    Article  Google Scholar 

  10. Yakubovich, A.V., Solov’yov, A.V.: Quantitative thermodynamic model for globular protein folding. Eur. Phys. J. D 68, 145 (2014)

    Article  ADS  Google Scholar 

  11. Vega, C., Abascal, J.L.F.: Simulating water with rigid non-polarizable models: a general perspective. Phys. Chem. Chem. Phys. 13, 19663–19688 (2011)

    Article  Google Scholar 

  12. Huang, X., Ackland, G.J., Rabe, K.M.: Crystal structures and shape-memory behaviour of NiTi. Nat. Mater. 2, 307–311 (2003)

    Article  ADS  Google Scholar 

  13. Kexel, C., Schramm, S., Solov’yov, A.V.: Atomistic simulation of martensite-austenite phase transition in nanoscale nickel-titanium crystals. Eur. Phys. J. B 88, 221 (2015)

    Article  ADS  Google Scholar 

  14. Schmidt, M., Kusche, R., von Issendorff, B., Haberland, H.: Irregular variations in the melting point of size-selected atomic cluster. Nature 393, 238–240 (1998)

    Article  ADS  Google Scholar 

  15. Haberland, H., Hippler, T., Donges, J., Kostko, O., Schmidt, M., von Issendorff, B.: Melting of sodium clusters: where do the magic numbers come from? Phys. Rev. Lett. 94, 035701 (2005)

    Article  ADS  Google Scholar 

  16. Wang, Z.W., Toikkanen, O., Quinn, B.M., Palmer, R.E.: Real-space observation of prolate monolayer-protected Au\(_{38}\) clusters using aberration-corrected scanning transmission electron microscopy. Small 7, 1542–1545 (2011)

    Article  Google Scholar 

  17. Wang, Z.W., Palmer, R.E.: Determination of the ground-state atomic structures of size-selected Au nanoclusters by electron-beam-induced transformation. Phys. Rev. Lett. 108, 245502 (2012)

    Article  ADS  Google Scholar 

  18. Zhao, G., Perilla, J.R., Yufenyuy, E.L., Meng, X., Chen, B., Ning, J., Ahn, J., Gronenborn, A.M., Schulten, K., Aiken, C., et al.: Mature HIV-1 capsid structure by cryo-electron microscopy and all-atom molecular dynamics. Nature 497, 643–646 (2013)

    Article  ADS  Google Scholar 

  19. Solov’yov, I.A., Yakubovich, A.V., Nikolaev, P., Volkovets, I., Solov’yov, A.V.: MesoBioNano Explorer - a universal program for multiscale computer simulations of complex molecular structure and dynamics. J. Comput. Chem. 33, 2412–2439 (2012)

    Google Scholar 

  20. Bang, J.H., Suslick, K.S.: Applications of ultrasound to the synthesis of nanostructured materials. Adv. Mater. 22, 1039–1059 (2010)

    Article  Google Scholar 

  21. Yoo, C.S., Holmes, N.C., Ross, M., Webb, D.J., Pike, C.: Shock temperatures and melting of iron at earth core conditions. Phys. Rev. Lett. 70, 3931–3934 (1993)

    Article  ADS  Google Scholar 

  22. Belonoshko, A.B., Burakovsky, L., Chen, S.P., Johansson, B., Mikhaylushkin, A.S., Preston, D.L., Simak, S.I., Swift, D.C.: Molybdenum at high pressure and temperature: melting from another solid phase. Phys. Rev. Lett. 100, 135701 (2008)

    Article  ADS  Google Scholar 

  23. Vashishta, P., Kalia, R.K., Nakano, A.: Multimillion atom simulations of dynamics of oxidation of an aluminum nanoparticle and nanoindentation on ceramics. J. Phys. Chem. B 110, 3727–3733 (2006)

    Article  Google Scholar 

  24. Verkhovtsev, A.V., Yakubovich, A.V., Sushko, G.B., Hanauske, M., Solov’yov, A.V.: Molecular dynamics simulations of the nanoindentation process of titanium crystal. Comput. Mater. Sci. 76, 20–26 (2013)

    Article  Google Scholar 

  25. Turnbull, D.: Kinetics of solidification of supercooled liquid mercury droplets. J. Chem. Phys. 20, 411–424 (1952)

    Article  ADS  Google Scholar 

  26. Pawlow, P.: Über die Abhängigkeit des Schmelzpunktes von der Oberflächenenergie eines festen Körpers. Z. Phys. Chem. 65, 1–35 (1909)

    Article  Google Scholar 

  27. Lai, S.L., Guo, J.Y., Petrova, V., Ramanath, G., Allen, L.H.: Size-dependent melting properties of small tin particles: nanocalorimetric measurements. Phys. Rev. Lett. 77, 99–102 (1996)

    Article  ADS  Google Scholar 

  28. Buffat, P., Borel, J.P.: Size effect on the melting temperature of gold particles. Phys. Rev. A 13, 2287–2298 (1976)

    Article  ADS  Google Scholar 

  29. Lyalin, A., Hussien, A., Solov’yov, A.V., Greiner, W.: Impurity effect on the melting of nickel clusters as seen via molecular dynamics simulations. Phys. Rev. B 79, 165403 (2009)

    Article  ADS  Google Scholar 

  30. Jiang, A., Awasthi, N., Kolmogorov, A.N., Setyawan, W., Börjesson, A., Bolton, K., Harutyunyan, A.R., Curtarolo, S.: Theoretical study of the thermal behavior of free and alumina-supported Fe-C nanoparticles. Phys. Rev. B 75, 205426 (2007)

    Article  ADS  Google Scholar 

  31. Ruban, A.V., Abrikosov, I.A.: Configurational thermodynamics of alloys from first principles: effective cluster interactions. Rep. Prog. Phys. 71, 046501 (2008)

    Article  ADS  Google Scholar 

  32. Aguado, A., López, J.M., Alonso, J.A., Stott, M.J.: Melting in large sodium clusters: an orbital-free molecular dynamics study. J. Phys. Chem. B 105, 2386–2392 (2001)

    Article  Google Scholar 

  33. Goringe, C.M., Bowler, D.R., Hernández, E.: Tight-binding modelling of materials. Rep. Prog. Phys. 60, 1447–1512 (1999)

    Article  ADS  Google Scholar 

  34. Verkhovtsev, A.V., Schramm, S., Solov’yov, A.V.: Molecular dynamics study of the stability of a carbon nanotube atop a catalytic nanoparticle. Eur. Phys. J. D 68, 246 (2014)

    Article  ADS  Google Scholar 

  35. Goddard, W., Brenner, D., Lyshevski, S., Iafrate, G.: Handbook of Nanoscience, Engineering, and Technology. CRC Press, Boca Raton (2007)

    Book  Google Scholar 

  36. Harutyunyan, A., Tokune, T., Mora, E.: Liquid as a required catalyst phase for carbon single-walled nanotube growth. Appl. Phys. Lett. 87, 051919 (2005)

    Article  ADS  Google Scholar 

  37. Mishin, Y., Asta, M., Li, J.: Atomistic modeling of interfaces and their impact on microstructure and properties. Acta Mater. 58, 1117–1151 (2010)

    Article  ADS  Google Scholar 

  38. Daw, M.S., Foiles, S.M., Baskes, M.I.: The embedded-atom method: a review of theory and application. Mater. Sci. Rep. 9, 251–310 (1993)

    Article  Google Scholar 

  39. Sutton, A.P., Chen, J.: Long-range Finnis-Sinclair potentials. Philos. Mag. Lett. 61, 139–146 (1990)

    Article  ADS  Google Scholar 

  40. Nayak, S., Khanna, S., Rao, B., Jena, P.: Physics of nickel clusters: energetics and equilibrium geometries. J. Phys. Chem. A 101, 1072–1080 (1997)

    Article  Google Scholar 

  41. Landau, L.D., Lifshitz, E.M.: Course of Theoretical Physics, vol. 5. Statistical Physics, Part I. Butterworth-Heinemann, Oxford (1980)

    Google Scholar 

  42. Qi, Y., Çağin, T., Johnson, W.L., Goddard, W.A., III.: Melting and crystallization in Ni nanoclusters: the mesoscale regime. J. Chem. Phys. 115, 385–394 (2001)

    Article  ADS  Google Scholar 

  43. Landau, L.D., Lifshitz, E.M.: Course of Theoretical Physics, vol. 6. Fluid Mechanics. Reed-Elsevier, Oxford (1979)

    Google Scholar 

  44. Çağin, T., Qi, Y., Li, H., Kimura, Y., Ikeda, H., Johnson, W.L., Goddard, W.A., III.: Calculation of mechanical, thermodynamic and transport properties of metallic glass formers. MRS Symp. Ser. 554, 43–48 (1999)

    Article  Google Scholar 

  45. Bedoya-Martínez, O.N., Kaczmarski, M., Hernández, E.R.: Melting temperature of FCC metals using empirical potentials. J. Phys.: Condens. Matter 18, 8049–8062 (2006)

    Google Scholar 

  46. Cleri, F., Rosato, V.: Tight-binding potentials for transition metals and alloys. Phys. Rev. B 48, 22–33 (1993)

    Article  ADS  Google Scholar 

  47. Alemany, M.M.G., Diéguez, O., Rey, C., Gallego, L.J.: Molecular-dynamics study of the dynamic properties of FCC transition and simple metals in the liquid phase using the second-moment approximation to the tight-binding method. Phys. Rev. B 60, 9208–9211 (1999)

    Article  ADS  Google Scholar 

  48. Shibuta, Y., Suzuki, T.: Melting and solidification point of FCC-metal nanoparticles with respect to particle size: a molecular dynamics study. Chem. Phys. Lett. 498, 323–327 (2010)

    Article  ADS  Google Scholar 

  49. Darby, S., Mortimer-Jones, T.V., Johnston, R.L., Roberts, C.J.: Theoretical study of Cu-Au nanoalloy clusters using a genetic algorithm. J. Chem. Phys. 116, 1536–1550 (2002)

    Article  ADS  Google Scholar 

  50. Aguado, A., González, L.E., López, J.M.: Thermal properties of impurity-doped clusters: orbital-free molecular dynamics simulations of the melting like transition in Li\(_1\)Na\(_{54}\) and Cs\(_1\)Na\(_{54}\). J. Phys. Chem. B 108, 11722–11731 (2004)

    Article  Google Scholar 

  51. Chandrachud, P., Joshi, K., Kanhere, D.G.: Thermodynamics of carbon-doped Al and Ga clusters: ab initio molecular dynamics simulations. Phys. Rev. B 76, 235423 (2007)

    Article  ADS  Google Scholar 

  52. Hock, C., Straßburg, S., Haberland, H., von Issendorff, B., Aguado, A., Schmidt, M.: Melting-point depression by insoluble impurities: a finite size effect. Phys. Rev. Lett. 101, 023401 (2008)

    Article  ADS  Google Scholar 

  53. Mottet, C., Rossi, G., Baletto, F., Ferrando, R.: Single impurity effect on the melting of nanoclusters. Phys. Rev. Lett. 95, 035501 (2005)

    Article  ADS  Google Scholar 

  54. Yamaguchi, Y., Maruyama, S.: A molecular dynamics study on the formation of metallofullerene. Eur. Phys. J. D 9, 385–388 (1999)

    Article  ADS  Google Scholar 

  55. Shibuta, Y., Maruyama, S.: Bond-order potential for transition metal carbide cluster for the growth simulation of a single-walled carbon nanotube. Comput. Mater. Sci. 39, 842–848 (2007)

    Article  Google Scholar 

  56. Martinez-Limia, A., Zhao, J., Balbuena, P.: Molecular dynamics study of the initial stages of catalyzed single-wall carbon nanotubes growth: force field development. J. Mol. Model. 13, 595–600 (2007)

    Article  Google Scholar 

  57. Solov’yov, I.A., Solov’yov, A.V., Greiner, W., Koshelev, A., Shutovich, A.: Cluster growing process and a sequence of magic numbers. Phys. Rev. Lett. 90, 053401 (2003)

    Article  ADS  Google Scholar 

  58. Solov’yov, I.A., Solov’yov, A.V., Greiner, W.: Fusion process of Lennard-Jones clusters: global minima and magic numbers formation. Int. J. Mod. Phys. E 13, 697–736 (2004)

    Article  ADS  Google Scholar 

  59. Obolensky, O.I., Solov’yov, I.A., Solov’yov, A.V., Greiner, W.: Fusion and fission of atomic clusters: recent advances. Comput. Lett. 1, 313–318 (2005)

    Article  MATH  Google Scholar 

  60. Lyalin, A., Solov’yov, I.A., Solov’yov, A.V., Greiner, W.: Evolution of the electronic and ionic structure of Mg clusters with increase in cluster size. Phys. Rev. A 67, 063203 (2003)

    Article  ADS  Google Scholar 

  61. Lyalin, A., Solov’yov, A.V., Greiner, W.: Structure and magnetism of lanthanum clusters. Phys. Rev. A 74, 043201 (2006)

    Article  ADS  Google Scholar 

  62. Lyalin, A., Solov’yov, I.A., Solov’yov, A.V., Greiner, W.: Interplay of electronic and geometry shell effects in properties of neutral and charged Sr clusters. Phys. Rev. A 75, 053201 (2007)

    Article  ADS  Google Scholar 

  63. Alonso, J.A. (ed.): Structure and Properties of Atomic Nanoclusters. Imperial College Press, London (2005)

    Google Scholar 

  64. Zhang, Z., Hua, W., Xiao, S.: Shell and subshell periodic structures of icosahedral nickel nanoclusters. J. Chem. Phys. 122, 214501 (2005)

    Article  ADS  Google Scholar 

  65. Ferrando, R., Jellinek, J., Johnston, R.L.: Nanoalloys: from theory to applications of alloy clusters and nanoparticles. Chem. Rev. 108, 845–910 (2008)

    Article  Google Scholar 

  66. Ding, F., Bolton, K., Rosén, A.: Iron-carbide cluster thermal dynamics for catalyzed carbon nanotube growth. J. Vac. Sci. Technol. A 22, 1471–1476 (2004)

    Article  ADS  Google Scholar 

  67. Cleveland, C.L., Landman, U.: The energetics and structure of nickel clusters: size dependence. J. Chem. Phys. 94, 7376–7396 (1991)

    Article  ADS  Google Scholar 

  68. Doye, J.P.K., Wales, D.J., Berry, R.S.: The effect of the range of the potential on the structures of clusters. J. Chem. Phys. 103, 4234–4249 (1995)

    Article  ADS  Google Scholar 

  69. Rice, S.A. (ed.): Advances in Chemical Physics, vol. 137. Wiley (2008)

    Google Scholar 

  70. Finnis, M.W., Sinclair, J.E.: A simple empirical N-body potential for transition metals. Philos. Mag. A. 50, 45–55 (1984)

    Article  ADS  Google Scholar 

  71. Gupta, R.P.: Lattice relaxation at metal surface. Phys. Rev. B 23, 6265–6270 (1981)

    Article  ADS  Google Scholar 

  72. Daw, M.S., Baskes, M.I.: Semiempirical, quantum mechanical calculation of hydrogen embrittlement in metals. Phys. Rev. Lett. 50, 1285–1288 (1983)

    Article  ADS  Google Scholar 

  73. Daw, M.S., Baskes, M.I.: Embedded-atom method: derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B 29, 6443–6453 (1984)

    Article  ADS  Google Scholar 

  74. Lewis, L.J., Jensen, P., Barrat, J.L.: Melting, freezing, and coalescence of gold nanoclusters. Phys. Rev. B 56, 2248–2257 (1997)

    Article  ADS  Google Scholar 

  75. Ryu, S., Weinberger, C.R., Baskes, M.I., Cai, W.: Improved modified embedded-atom method potentials for gold and silicon. Model. Simul. Mater. Sci. Eng. 17, 075008 (2009)

    Article  ADS  Google Scholar 

  76. Kim, Y.M., Lee, B.J., Baskes, M.I.: Modified embedded-atom method interatomic potentials for Ti and Zr. Phys. Rev. B 74, 014101 (2006)

    Article  ADS  Google Scholar 

  77. Sushko, G.B., Verkhovtsev, A.V., Yakubovich, A.V., Schramm, S., Solov’yov, A.V.: Molecular dynamics simulation of self-diffusion processes in titanium in bulk material, on grain junctions and on surface. J. Phys. Chem. A 118, 6685–6691 (2014)

    Article  Google Scholar 

  78. Sushko, G.B., Verkhovtsev, A.V., Kexel, C., Korol, A.V., Schramm, S., Solov’yov, A.V.: Reconciling simulated melting and ground-state properties of metals with a modified embedded-atom method potential. J. Phys.: Condens. Matter 28, 145201 (2016)

    Google Scholar 

  79. Verkhovtsev, A.V.: Computational modeling of nanomaterials for biomedical applications. Ph.D. thesis, Goethe-Universität, Frankfurt am Main (2016)

    Google Scholar 

  80. Lindemann, F.A.: Über die Berechnung molekularer Eigenfrequenzen. Z. Phys. 19, 609–612 (1910)

    MATH  Google Scholar 

  81. Nelson, D.R.: Defects and Geometry in Condensed Matter Physics. Cambridge University Press, Cambridge (2002)

    Google Scholar 

  82. Tomanek, D., Aligia, A.A., Balseiro, C.A.: Calculation of elastic strain and electronic effects on surface segregation. Phys. Rev. B 32, 5051–5056 (1985)

    Article  ADS  Google Scholar 

  83. Dzugutov, M.: Glass formation in a simple monatomic liquid with icosahedral inherent local order. Phys. Rev. A 46, R2984–R2987 (1992)

    Article  ADS  Google Scholar 

  84. Lai, W.S., Liu, B.X.: Lattice stability of some Ni-Ti alloy phases versus their chemical composition and disordering. J. Phys.: Condens. Matter 12, L53–L57 (2000)

    Google Scholar 

  85. Kittel, C.: Introduction to Solid State Physics. Wiley, USA (2005)

    MATH  Google Scholar 

  86. Verkhovtsev, A.V., Korol, A.V., Sushko, G.B., Schramm, S., Solov’yov, A.V.: Generalized correction to embedded-atom potentials for simulation of equilibrium and nonequilbrium properties of metals. St. Petersburg Polytech. State Univ. J.: Phys. Math. 13, 23–41 (2020)

    Google Scholar 

  87. Calvo, F.: Thermodynamics of nanoalloys. Phys. Chem. Chem. Phys. 17, 27922–27939 (2015)

    Article  Google Scholar 

  88. Magnin, Y., Zappelli, A., Amara, H., Ducastelle, F., Bichara, C.: Size dependent phase diagrams of nickel-carbon nanoparticles. Phys. Rev. Lett. 115, 205502 (2015)

    Article  ADS  Google Scholar 

  89. Engelmann, Y., Bogaerts, A., Neyts, E.C.: Thermodynamics at the nanoscale: phase diagrams of nickel-carbon nanoclusters and equilibrium constants for phase transitions. Nanoscale 6, 11981–11987 (2014)

    Article  ADS  Google Scholar 

  90. Mishnaevsky, L., Levashov, E., Valiev, R.Z., Segurado, J., Sabirov, I., Enikeev, N., Prokoshkin, S., Solov’yov, A.V., Korotitskiy, A., Gutmanas, E., Gotman, I., Rabkin, E., Psakh’e, S., Dluhos, L., Seefeldt, M., Smolin, A.: Nanostructured titanium-based materials for medical implants: modeling and development. Mater. Sci. Eng. R: Rep. 81, 1–19 (2014)

    Article  Google Scholar 

  91. Bram, M., Ahmad-Khanlou, A., Heckmann, A., Fuchs, B., Buchkremer, H.P., Stöver, D.: Powder metallurgical fabrication processes for NiTi shape memory alloy parts. Mater. Sci. Eng. A 337, 254–263 (2002)

    Article  Google Scholar 

  92. Pasturel, A., Colinet, C., Manh, D.N., Paxton, A.T., Van Schilfgaarde, M.: Electronic structure and phase stability study in the Ni-Ti system. Phys. Rev. B 52, 15176–15190 (1995)

    Article  ADS  Google Scholar 

  93. Jellinek, J., Krissinel, E.B.: Ni\(_n\)Al\(_m\) alloy clusters: analysis of structural forms and their energy ordering. Chem. Phys. Lett. 258, 283–292 (1996)

    Article  ADS  Google Scholar 

  94. Huang, S.P., Balbuena, P.B.: Melting of bimetallic Cu-Ni nanoclusters. J. Phys. Chem. B 106, 7225–7236 (2002)

    Article  Google Scholar 

  95. Kexel, C., Verkhovtsev, A.V., Sushko, G.B., Korol, A.V., Schramm, S., Solov’yov, A.V.: Toward the exploration of the NiTi phase diagram with a classical force field. J. Phys. Chem. C 120, 25043–25052 (2016)

    Article  Google Scholar 

  96. Qi, Y., Çağın, T., Kimura, Y., Goddard, W.A., III.: Molecular-dynamics simulations of glass formation and crystallization in binary liquid metals: Cu-Ag and Cu-Ni. Phys. Rev. B 59, 3527–3533 (1999)

    Article  ADS  Google Scholar 

  97. Massalski, T.B., Okamoto, H., Subramanian, P.R., Kacprzak, L.: Binary Alloy Phase Diagrams, 2 edn. ASM International (1990)

    Google Scholar 

  98. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equation of state calculations by fast computing machines. J. Chem. Phys. 21, 1087–1092 (1953)

    Article  ADS  MATH  Google Scholar 

  99. Singh, R.N., Sommer, F.: Segregation and immiscibility in liquid binary alloys. Rep. Prog. Phys. 60, 57–150 (1997)

    Article  ADS  Google Scholar 

  100. Otsuka, K., Kakeshita, T.: Science and technology of shape-memory alloys: new developments. MRS Bull. 27, 91–100 (2002)

    Article  Google Scholar 

  101. Prokoshkin, S.D., Korotitskiy, A.V., Brailovski, V., Turenne, S., Khmelevskaya, I.Y., Trubitsyna, I.B.: On the lattice parameters of phases in binary Ti-Ni shape memory alloys. Acta Mater. 52, 4479–4492 (2004)

    Article  ADS  Google Scholar 

  102. Ye, J., Mishra, R.K., Pelton, A.R., Minor, A.M.: Direct observation of the NiTi martensitic phase transformation in nanoscale volumes. Acta Mater. 58, 490–498 (2010)

    Article  ADS  Google Scholar 

  103. Mutter, D., Nielaba, P.: Simulation of the thermally induced austenitic phase transition in NiTi nanoparticles. Eur. Phys. J. B 84, 109–113 (2011)

    Article  ADS  Google Scholar 

  104. Ashcroft, N.W., Mermin, N.D.: Solid State Physics. Holt, Rinehart and Winston, New York (1976)

    MATH  Google Scholar 

  105. Allen, M.P., Tildesley, D.J.: Computer Simulation of Liquids. Oxford University Press (1987)

    Google Scholar 

  106. Wang, F.E., Buehler, W.J., Pickart, S.J.: Crystal structure and a unique “martensitic’’ transition of TiNi. J. Appl. Phys. 36, 3232–3239 (1965)

    Article  ADS  Google Scholar 

  107. Wasilewski, R.J., Butler, S.R., Hanlon, J.E.: On the martensitic transformation in TiNi. Met. Sci. 1, 104–110 (1967)

    Article  Google Scholar 

  108. Calvo, F., Spiegelmann, F.: Mechanisms of phase transitions in sodium clusters: from molecular to bulk behavior. J. Chem. Phys. 112, 2888–2908 (2000)

    Article  ADS  Google Scholar 

  109. Plekan, O., Rosu-Finsen, A., Cassidy, A.M., Lasne, J., McCoustra, M.R.S., Field, D.: A review of recent progress in understanding the spontelectric state of matter. Eur. Phys. J. D 71, 162 (2017)

    Article  ADS  Google Scholar 

  110. Balog, R., Cicman, P., Jones, N.C., Field, D.: Spontaneous dipole alignment in films of N\(_2\)O. Phys. Rev. Lett. 102, 073003 (2009)

    Article  ADS  Google Scholar 

  111. Kexel, C., Solov’yov, A.V.: Predicting dipole orientations in spontelectric methyl formate. Eur. Phys. J. D 75, 89 (2021)

    Article  ADS  Google Scholar 

  112. Plekan, O., Cassidy, A., Balog, R., Jones, N.C., Field, D.: Spontaneous electric fields in films of cis-methyl formate. Phys. Chem. Chem. Phys. 14, 9972–9976 (2012)

    Article  Google Scholar 

  113. Hussain, C.M. (ed.): Handbook of Functionalized Nanomaterials for Industrial Applications. Elsevier (2020)

    Google Scholar 

  114. You, Z. (ed.): Materials Science and Industrial Applications. Trans Tech Publications Ltd., Switzerland (2019)

    Google Scholar 

  115. Verlinden, B., Driver, J., Samajdar, I., Doherty, R.D.: Thermo-Mechanical Processing of Metallic Materials. Elsevier (2007)

    Google Scholar 

  116. Fischer-Cripps, A.C.: Nanoindentation, 3rd edn. Springer Science+Business Media, LLC, New York (2011)

    Book  Google Scholar 

  117. Schuh, C.A.: Nanoindentation studies of materials. Mater. Today 9, 32–40 (2006)

    Article  Google Scholar 

  118. Sushko, G.B., Verkhovtsev, A.V., Yakubovich, A.V., Solov’yov, A.V.: Molecular dynamics simulations of nanoindentation of nickel-titanium crystal. J. Phys.: Conf. Ser. 438, 012021 (2013)

    Google Scholar 

  119. Kramer, K.H.: Implants for surgery – a survey on metallic materials. In: Materials for Medical Engineering, vol. 2, pp. 9–29. Wiley-VCH, Weinheim (2005)

    Google Scholar 

  120. Geetha, M., Singh, A.K., Asokamani, R., Gogia, A.K.: Ti based biomaterials, the ultimate choice for orthopaedic implants - a review. Prog. Mater. Sci. 54, 397–425 (2009)

    Article  Google Scholar 

  121. Prymak, O., Bogdanski, D., Koller, M., Esenwein, S., Muhr, G., Beckmann, F., Donath, T., Assad, M., Epple, M.: Morphological characterization and in vitro biocompatibility of a porous nickel-titanium alloy. Biomaterials 26, 5801–5807 (2005)

    Article  Google Scholar 

  122. Brailovski, V., Prokoshkin, S., Gauthier, M., Inaekyan, K., Dubinskiy, S., Petrzhik, M., Filonov, M.: Bulk and porous metastable beta Ti-Nb-Zr(Ta) alloys for biomedical applications. Mater. Sci. Eng. C 31, 643–657 (2001)

    Article  Google Scholar 

  123. Sushko, G.B., Verkhovtsev, A.V., Solov’yov, A.V.: Validation of classical force fields for the description of thermo-mechanical properties of transition metal materials. J. Phys. Chem. A 118, 8426–8436 (2014)

    Article  Google Scholar 

  124. Verkhovtsev, A.V., Sushko, G.B., Yakubovich, A.V., Solov’yov, A.V.: Benchmarking of classical force fields by ab initio calculations of atomic clusters: Ti and Ni-Ti case. Comput. Theor. Chem. 1021, 101–108 (2013)

    Article  Google Scholar 

  125. Oliver, W.C., Pharr, G.M.: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564–1583 (1992)

    Article  ADS  Google Scholar 

  126. Levashov, E.A., Petrzhik, M.I., Shtansky, D.V., Kiryukhantsev-Korneev, P.V., Sheveyko, A.N., Valiev, R.Z., Gunderov, D.V., Prokoshkin, S.D., Korotitskiy, A.V., Smolin, A.Y.: Nanostructured titanium alloys and multicomponent bioactive films: mechanical behavior at indentation. Mater. Sci. Eng. A 570, 51–62 (2013)

    Article  Google Scholar 

  127. Landau, L.D., Lifshitz, E.M.: Course of Theoretical Physics, vol. 7. Theory of Elasticity. Elsevier, Amsterdam (2006)

    Google Scholar 

  128. Rajagopalan, S., Little, A.L., Bourke, M.A.M., Vaidyanathan, R.: Elastic modulus of shape-memory NiTi from in situ neutron diffraction during macroscopic loading, instrumented indentation, and extensometry. Appl. Phys. Lett. 86, 081901 (2005)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the possibility to perform computer simulations at Goethe-HLR cluster of the Frankfurt Center for Scientific Computing.

Author information

Authors and Affiliations

  1. MBN Research Center gGmbH, Altenhöferallee 3, 60438, Frankfurt am Main, Germany

    Alexey V. Verkhovtsev & Andrey V. Solov’yov

Authors
  1. Alexey V. Verkhovtsev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrey V. Solov’yov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexey V. Verkhovtsev .

Editor information

Editors and Affiliations

  1. Carl von Ossietzky University Oldenburg, Oldenburg, Germany

    Ilia A. Solov'yov

  2. MBN Research Center, Frankfurt am Main, Germany

    Alexey V. Verkhovtsev

  3. MBN Research Center, Frankfurt am Main, Germany

    Andrei V. Korol

  4. MBN Research Center, Frankfurt am Main, Germany

    Andrey V. Solov'yov

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Verkhovtsev, A.V., Solov’yov, A.V. (2022). Dynamics and Phase Transitions in Nanosystems. In: Solov'yov, I.A., Verkhovtsev, A.V., Korol, A.V., Solov'yov, A.V. (eds) Dynamics of Systems on the Nanoscale. Lecture Notes in Nanoscale Science and Technology, vol 34. Springer, Cham. https://doi.org/10.1007/978-3-030-99291-0_6

Download citation

Publish with us

Policies and ethics

Search

Navigation