Skip to main content
SpringerLink
Log in
Book cover

Relaxation of the Chemical Bond pp 457–467Cite as

Theory: Multiple-Field Coupling

  • Chapter
  • First Online:

  • 2152 Accesses

Part of the book series: Springer Series in Chemical Physics ((CHEMICAL,volume 108))

Abstract

Variation in atomic CN, pressure, and temperature relaxes the bond length and bond energy with an association with densification of charge, energy, and mass. Multiple fields coupling takes place in the skin region. Localized densification of energy by size reduction and compression contributes to the mechanical strength; bond order loss and heating and softening modifies the atomic cohesive energy, both of which dominate the detectable quantities of a substance. The performance of the entire specimen can be viewed as the attribute of one bond averaged over all the bonds involved. A detectable quantity can be connected to the averaged bond and its geometric and energetic response to the externally applied stimulus such as coordination environment, temperature, pressure, etc.

This is a preview of subscription content, 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   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   219.99
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

Learn about institutional subscriptions

References

  1. C.Q. Sun, Y. Wang, B.K. Tay, S. Li, H. Huang, Y.B. Zhang, Correlation between the melting point of a nanosolid and the cohesive energy of a surface atom. J. Phys. Chem. B 106(41), 10701–10705 (2002)

    Article  Google Scholar 

  2. G. Ouyang, C.Q. Sun, W.G. Zhu, Pressure-stiffened Raman phonons in group III nitrides: A local bond average approach. J. Phys. Chem. B 112(16), 5027–5031 (2008)

    Article  Google Scholar 

  3. B. Gilbert, H. Zhang, B. Chen, M. Kunz, F. Huang, J.F. Banfield, Compressibility of zinc sulfide nanoparticles. Phys. Rev. B 74(11), 115405 (2006)

    Article  ADS  Google Scholar 

  4. M. Pravica, Z. Quine, E. Romano, X-ray diffraction study of elemental thulium at pressures up to 86 GPa. Phys. Rev. B 74(10), 104107 (2006)

    Article  ADS  Google Scholar 

  5. B. Chen, D. Penwell, L.R. Benedetti, R. Jeanloz, M.B. Kruger, Particle-size effect on the compressibility of nanocrystalline alumina. Phys. Rev. B 66(14), 144101 (2002)

    Article  ADS  Google Scholar 

  6. F. Birch, Finite elastic strain of cubic crystals. Phys. Rev. 71(11), 809–824 (1947)

    Article  ADS  MATH  Google Scholar 

  7. Z.W. Chen, C.Q. Sun, Y.C. Zhou, O.Y. Gang, Size dependence of the pressure-induced phase transition in nanocrystals. J. Chem. Phys. C 112(7), 2423–2427 (2008)

    Article  Google Scholar 

  8. J.L. Hu, W.P. Cai, C.C. Li, Y.J. Gan, L. Chen, In situ x-ray diffraction study of the thermal expansion of silver nanoparticles in ambient air and vacuum. Appl. Phys. Lett. 86(15), 151915 (2005)

    Article  ADS  Google Scholar 

  9. L. Li, Y. Zhang, Y.W. Yang, X.H. Huang, G.H. Li, L.D. Zhang, Diameter-depended thermal expansion properties of Bi nanowire arrays. Appl. Phys. Lett. 87(3), 031912 (2005)

    Article  ADS  Google Scholar 

  10. T. Comaschi, A. Balerna, S. Mobilio, Temperature dependence of the structural parameters of gold nanoparticles investigated with EXAFS. Physical Review B 77(7), 075432 (2008)

    Article  ADS  Google Scholar 

  11. M. Cardona, M.L.W. Thewalt, Isotope effects on the optical spectra of semiconductors. Rev. Mod. Phys. 77(4), 1173–1224 (2005)

    Article  ADS  Google Scholar 

  12. E. Grüneisen, The state of a body. Handb. Phys. 10, 1–52. NASA translation RE2-18-59 W (1926)

    Google Scholar 

  13. M.X. Gu, Y.C. Zhou, C.Q. Sun, Local bond average for the thermally induced lattice expansion. J. Phys. Chem. B 112(27), 7992–7995 (2008)

    Article  Google Scholar 

  14. G.A. Slack, S.F. Bartram, Thermal expansion of some diamond-like crystals. J. Appl. Phys. 46(1), 89–98 (1975)

    Article  ADS  Google Scholar 

  15. R.R. Reeber, K. Wang, Lattice parameters and thermal expansion of GaN. J. Mater. Res. 15(1), 40–44 (2000)

    Article  ADS  Google Scholar 

  16. Q.H. Tang, T.C. Wang, B.S. Shang, and F. Liu, Thermodynamic properties and constitutive relations of crystals at finite temperature. Sci. China-Phys. Mech. Astron. G 55, 933, (2012)

    Google Scholar 

  17. Y.J. Su, H. Wei, R.G. Gao, Z. Yang, J. Zhang, Z.H. Zhong, Y.F. Zhang, Exceptional negative thermal expansion and viscoelastic properties of graphene oxide paper. Carbon 50(8), 2804–2809 (2012)

    Article  Google Scholar 

  18. C. Martinek, F.A. Hummel, Linear thermal expansion of 3 tungstates. J. Am. Ceram. Soc. 51(4), 227 (1968)

    Article  Google Scholar 

  19. T.A. Mary, J.S.O. Evans, T. Vogt, A.W. Sleight, Negative thermal expansion from 0.3 to 1050 Kelvin in ZrW2O8. Science 272(5258), 90–92 (1996)

    Article  ADS  Google Scholar 

  20. C.Q. Sun, Dominance of broken bonds and nonbonding electrons at the nanoscale. Nanoscale 2(10), 1930–1961 (2010)

    Article  ADS  Google Scholar 

  21. R.J. Bruls, H.T. Hintzen, G. de With, R. Metselaar, J.C. van Miltenburg, The temperature dependence of the Gruneisen parameters of MgSiN2, AlN and beta-Si3N4. J. Phys. Chem. Solids 62(4), 783–792 (2001)

    Article  ADS  Google Scholar 

  22. A.U. Sheleg, W.A. Savastenko, Fiz. Mat. Nauk 3, 126 (1976)

    Google Scholar 

  23. J. Kim, J.A. Freitas, P.B. Klein, S. Jang, F. Ren, S.J. Pearton, The effect of thermally induced stress on device temperature measurements by Raman spectroscopy. Electrochem. Solid State Lett. 8(12), G345–G347 (2005)

    Article  Google Scholar 

  24. K.G. Lyon, G.L. Salinger, C.A. Swenson, G.K. White, Linear thermal-expansion measurements on silicon from 6 to 340 K. J. Appl. Phys. 48(3), 865–868 (1977)

    Article  ADS  Google Scholar 

  25. R.B. Roberts, Thermal-expansion reference data—silicon 300–850 K. J. Phys. D-Appl. Phys. 14(10), L163–L166 (1981)

    Article  ADS  Google Scholar 

  26. H.P. Singh, Determination of thermal expansion of germanium rhodium and iridium by x-rays. Acta. Crystallogr. Sect. A. A 24, 469 (1968)

    Google Scholar 

  27. T. Sato, K. Ohashi, T. Sudoh, K. Haruna, H. Maeta, Thermal expansion of a high purity synthetic diamond single crystal at low temperatures. Phys. Rev. B 65(9), 092102 (2002)

    Article  ADS  Google Scholar 

  28. C. Giles, C. Adriano, A.F. Lubambo, C. Cusatis, I. Mazzaro, M.G. Honnicke, Diamond thermal expansion measurement using transmitted X-ray back-diffraction. J. Synchrotron Radiat. 12, 349–353 (2005)

    Article  Google Scholar 

  29. K. Haruna, H. Maeta, K. Ohashi, T. Koike, Thermal-expansion coefficient of synthetic diamond single-crystal at low-temperatures. Jpn. J. Appl. Phys. Part 1-Regul. Pap. Short Notes Rev Pap. 31(8), 2527–2529 (1992)

    Google Scholar 

  30. F.C. Nix, D. MacNair, The thermal expansion of pure metals copper, gold, aluminum, nickel, and iron. Phys. Rev. 60(8), 597–605 (1941)

    Article  ADS  Google Scholar 

  31. C. Kittel, Intrduction to Solid State Physics. 8 edn. (New York, Willey, 2005)

    Google Scholar 

  32. http://www.infoplease.com/periodictable.php

  33. K.K. Nanda, S.N. Sahu, S.N. Behera, Liquid-drop model for the size-dependent melting of low-dimensional systems. Phys. Rev. A 66(1), 013208 (2002)

    Article  ADS  Google Scholar 

  34. Z.W. Chen, M.X. Gu, C.Q. Sun, X.Y. Zhang, R.P. Liu, Ultrastiff carbides uncovered in first principles. Appl. Phys. Lett. 91(6), 061905 (2007)

    Article  ADS  Google Scholar 

  35. Y.J. Tian, B. Xu, D.L. Yu, Y.M. Ma, Y.B. Wang, Y.B. Jiang, W.T. Hu, C.C. Tang, Y.F. Gao, K. Luo, Z.S. Zhao, L.M. Wang, B. Wen, J.L. He, Z.Y. Liu, Ultrahard nanotwinned cubic boron nitride. Nature 493(7432), 385–388 (2013)

    Article  ADS  Google Scholar 

  36. F.M. Gao, J.L. He, E.D. Wu, S.M. Liu, D.L. Yu, D.C. Li, S.Y. Zhang, Y.J. Tian, Hardness of covalent crystals. Phys. Rev. Lett. 91(1), 015502 (2003)

    Article  ADS  Google Scholar 

  37. X.J. Guo, L. Li, Z.Y. Liu, D.L. Yu, J.L. He, R.P. Liu, B. Xu, Y.J. Tian, H.T. Wang, Hardness of covalent compounds: Roles of metallic component and d valence electrons. J. Appl. Phys. 104(2), 2956594 (2008)

    Article  Google Scholar 

  38. M. Born, Thermodynamics of crystals and melting. J. Chem. Phys. 7(8), 591–603 (1939)

    Article  ADS  Google Scholar 

  39. C.Q. Sun, C.M. Li, S. Li, B.K. Tay, Breaking limit of atomic distance in an impurity-free monatomic chain. Phys. Rev. B 69(24), 245402 (2004)

    Article  ADS  Google Scholar 

  40. D.G. Eskin, Suyitno, L. Katgerman, Mechanical properties in the semi-solid state and hot tearing of aluminium alloys. Prog. Mater Sci. 49(5), 629–711 (2004)

    Article  Google Scholar 

  41. J. Campbell, Castings. (Butterworth-Heinemann, Oxford, 1991)

    Google Scholar 

  42. M.X. Gu, Y.C. Zhou, L.K. Pan, Z. Sun, S.Z. Wang, C.Q. Sun, Temperature dependence of the elastic and vibronic behavior of Si, Ge, and diamond crystals. J. Appl. Phys. 102(8), 083524 (2007)

    Article  ADS  Google Scholar 

  43. M.X. Gu, L.K. Pan, B.K. Tay, C.Q. Sun, Atomistic origin and temperature dependence of Raman optical redshift in nanostructures: a broken bond rule. J. Raman Spec. 38(6), 780–788 (2007)

    Article  ADS  Google Scholar 

  44. M.X. Gu, L.K. Pan, T.C.A. Yeung, B.K. Tay, C.Q. Sun, Atomistic origin of the thermally driven softening of Raman optical phonons in group III nitrides. J. Chem. Phys. C 111(36), 13606–13610 (2007)

    Article  Google Scholar 

  45. M. Zhao, W.T. Zheng, J.C. Li, Z. Wen, M.X. Gu, C.Q. Sun, Atomistic origin, temperature dependence, and responsibilities of surface energetics: An extended broken-bond rule. Phys. Rev. B 75(8), 085427 (2007)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore

    Chang Q. Sun

Authors
  1. Chang Q. Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chang Q. Sun .

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media Singapore

About this chapter

Cite this chapter

Sun, C.Q. (2014). Theory: Multiple-Field Coupling. In: Relaxation of the Chemical Bond. Springer Series in Chemical Physics, vol 108. Springer, Singapore. https://doi.org/10.1007/978-981-4585-21-7_23

Download citation

Publish with us

Policies and ethics

Search

Navigation