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Thermodynamic properties of TiC nanowire from first principles

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Abstract

We have investigated the thermodynamic properties of titanium carbide (TiC) nanowire within the framework of density functional theory and quasi-harmonic approximation via calculating the temperature dependence of a number of thermodynamic quantities including entropy, number of microstates, total and free energies, and specific heat. The level of disorder of the nanowire has been found to be larger than that of the bulk mainly due to expansion in only one direction, which accordingly results in acquiring more spatial degrees of freedom. A linear function of temperature has been also found for the low-temperature specific heat of the nanowire being in a remarkable agreement with the general \(T^{\text{n}}\)-law for Debye systems. Results firmly establish a direct correlation between the spatial expansion of a TiC compound and its low-temperature specific heat and entropy.

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References

  1. Price DL, Cooper BR, Wills JM. Full-potential linear-muffin-tin-orbital study of brittle fracture in titanium carbide. Phys. Rev. B. 1992;46:11368.

    Article  CAS  Google Scholar 

  2. Chen Y, Wang H. Growth morphologies and mechanism of TiC in the laser surface alloyed coating on the substrate of TiAl intermetallics. J. Alloys Compd. 2003;351:304–8.

    Article  CAS  Google Scholar 

  3. Ruberto C, Lundqvist BI. Nature of adsorption on TiC (111) investigated with density-functional calculation. Phys. Rev. B. 2007;75:235438.

    Article  Google Scholar 

  4. Fang L, Wang L, Gong J, Dai H, Miao D. First-principles study of bulk and (001) surface of TiC. Trans. Nonferrous Met. Soc. China. 2010;20:857–62.

    Article  CAS  Google Scholar 

  5. Wang ZQ, Liu XF, Liu YH, Zhang JY, Yu LN, Bian XF. Structural heredity of TiC and its influences on refinement behaviors of AlTiC master alloy. Trans. Nonferrous Met. Soc. China. 2003;13:790–3.

    CAS  Google Scholar 

  6. Song MS, Huang B, Zhang MX, Li GJ. Study of formation behavior of TiC ceramic obtained by self-propagating high-temperature synthesis from Al–Ti–C elemental powders. Int. J. Refract. Met. Hard Mater. 2009;27:584–9.

    Article  CAS  Google Scholar 

  7. Hojou K, Otsu H, Furuno S, Sasajima N, Izui K. In situ observation of damage evolution in TiC during hydrogen and deuterium ion irradiation at low temperatures. J. Nucl. Mater. 1996;239:279–83.

    Article  CAS  Google Scholar 

  8. Jones MI, Mccoll IR, Grant DM, Parker KG, Parker TL. Protein adsorption and platelet attachment and activation on TiN, TiC, and DLC coatings on titanium for cardiovascular applications. J. Biomed. Mater. Res. B. 2000;54:413–21.

    Article  Google Scholar 

  9. Jafari M, Khajehmiri Z. Mechanical properties of TiC nanowire from DFT calculations. Iran. J. Sci. Technol. Trans. Sci. 2018;42:1623.

    Article  Google Scholar 

  10. Mahmoodian R, Hamdi M, Hassan MA, Akbari A. Mechanical and chemical characterization of a TiC/C system synthesized using a focus plasma arc. PLoS ONE. 2015;10:0130836.

    Google Scholar 

  11. Houska C. Thermal expansion and atomic vibration amplitudes for TiC, TiN, ZrC, ZrN, and pure tungsten. J. Phys. Chem. Solids. 1964;25:359–66.

    Article  CAS  Google Scholar 

  12. Dodd S, Cankurtaran M, James B. Ultrasonic determination of the elastic and nonlinear acoustic properties of transition-metal carbide ceramics: TiC and TaC. J. Mater. Sci. 2003;38:1107–15.

    Article  CAS  Google Scholar 

  13. Dubrovinskaia NA, Dubrovinskya LS, Saxenaa SK, Ahujab R, Johanssonb B. High-pressure study of titanium carbide. J. Alloys Compd. 1999;289:24–7.

    Article  CAS  Google Scholar 

  14. Winkler B, Juarez-Arellano EA, Friedrich A, Bayarjargal L, Yan J, Clark SM. Reaction of titanium with carbon in a laser heated diamond anvil cell and reevaluation of a proposed pressure-induced structural phase transition of TiC. J. Alloys Compd. 2009;478:392–7.

    Article  CAS  Google Scholar 

  15. Postnikov A, Entel P. Ab initio simulations of Fe and TiC clusters. Phase Transit. 2004;77:149–59.

    Article  CAS  Google Scholar 

  16. Mecabih S, Amrane N, Nabi Z, Abbar B, Aourag H. Description of structural and electronic properties of TiC and ZrC by generalized gradient approximation. Physica. 2000;285:392–6.

    Article  CAS  Google Scholar 

  17. Dridi Z, Bouhafs B, Ruterana P, Aourag H. First-principles calculations of vacancy effects on structural and electronic properties of \(\text{ TiC }_x\) and \(\text{ TiN }_x\). J. Phys.: Condens. Matter. 2002;14:10237.

    CAS  Google Scholar 

  18. Jochym PT, Parlinski K, Sternik M. TiC lattice dynamics from ab initio calculations. Eur. Phys. J. B. 1999;10:9–13.

    Article  CAS  Google Scholar 

  19. Yang Y, Lu H, Yu C, Chen JM. First-principles calculations of mechanical properties of TiC and TiN. J. Alloys Compd. 2009;485:542–7.

    Article  CAS  Google Scholar 

  20. Xia X, Zhan J, Zhong Y, Wang X, Tu J, Fan HJ. Single-crystalline, metallic TiC nanowires for highly robust and wide-temperature electrochemical energy storage. Small. 2017;13:1602742.

    Article  Google Scholar 

  21. Dang DY, Fan JL, Gong HR. Thermodynamic and mechanical properties of TiC from ab initio calculation. J. Appl. Phys. 2014;116:033509.

    Article  Google Scholar 

  22. Liu K, Zhou X-L, Chen H-H, Lu L-Y. Phase transition and thermodynamic properties of TiN under pressure via first-principles calculations. J. Therm. Anal. Calorim. 2012;110:973–8.

    Article  CAS  Google Scholar 

  23. Jafari M, Hajiyani HR. Optical properties of \(\alpha\), \(\beta\) and \(\omega\) structure of Titanium: ab initio approach. Comput. Mater. Sci. 2011;50:2549–53.

    Article  CAS  Google Scholar 

  24. Jafari M, Hajiyani HR, Sohrabikia Z, Galavani H. First-principles calculations of optical properties of titanium nanochains. Comput. Mater. Sci. 2013;77:224–9.

    Article  CAS  Google Scholar 

  25. Sohrabikia Z, Jafari M. Electronic and magnetic properties of linear and dimerized titanium nanochains under compressive and tensile strain. J. Clust. Sci. 2016;27:183–91.

    Article  CAS  Google Scholar 

  26. Jafari M, Ghanad S. Optoelectrical properties of TiC nanowires from density functional theory. J. Optoelectron. Adv. Mater. 2015;17:318–22.

    CAS  Google Scholar 

  27. Perdew JP, Burke K, Ernzerhof M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996;77:3865–8.

    Article  CAS  Google Scholar 

  28. Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, Ceresoli D, Chiarotti GL, Cococcioni M, Dabo I, Corso AD, de Gironcoli S, Fabris S, Fratesi G, Gebauer R, Gerstmann U, Gougoussis C, Kokalj A, Lazzeri M, Martin-Samos L, Marzari N, Mauri F, Mazzarello R, Paolini S, Pasquarello A, Paulatto L, Sbraccia C, Scandolo S, Sclauzero G, Seitsonen AP, Smogunov A, Umari P, Wentzcovitch RM. Quantum ESPRESSO a modular and open-source software project for quantum simulations of materials. J. Phys.: Condens. Matter. 2009;21:395502–21.

    Google Scholar 

  29. Vanderbilt D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B. 1990;41:7892.

    Article  CAS  Google Scholar 

  30. Methfessel M, Paxton AT. High-precision sampling for Brillouin-zone integration in metals. Phys. Rev. B. 1989;40:3616–21.

    Article  CAS  Google Scholar 

  31. Murnaghan FD. The compressibility of media under extreme pressures. Proc. Natl. Acad. Sci. USA. 1944;30:244–7.

    Article  CAS  Google Scholar 

  32. Birch F. Finite elastic strain of cubic crystals. Phys. Rev. 1947;71:809–24.

    Article  CAS  Google Scholar 

  33. Fletcher R. Practical methods of optimization. 2nd ed. New York: Wiley; 1987.

    Google Scholar 

  34. Billeter SR, Turnera AJ, Thiel W. Linear scaling geometry optimisation and transition state search in hybrid delocalised internal coordinates. Phys. Chem. Chem. Phys. 2000;2:2177–86.

    Article  CAS  Google Scholar 

  35. Kokalj A. XCrySDen—a new program for displaying crystalline structures and electron densities. J. Mol. Graph. Modell. 1999;17:176–9.

    Article  CAS  Google Scholar 

  36. Wang Y, Liu ZK, Chen LQ. Thermodynamic properties of Al, Ni, NiAl, and Ni\(_3\)Al from first-principles calculations. Acta Mater. 2004;52:2665–71.

    Article  CAS  Google Scholar 

  37. Mohri T, Chen Y. First-principles investigation of L10-disorder phase equilibria of Fe–Ni, –Pd and –Pt binary alloy systems. J. Alloys Compd. 2004;383:23–31.

    Article  CAS  Google Scholar 

  38. Moruzzi VL, Janak JF, Schwarz K. Calculated thermal properties of metals. Phys. Rev. B. 1988;37:790–9.

    Article  CAS  Google Scholar 

  39. Shang S, Böttger AJ. A combined cluster variation method and ab initio approach to the gamma-Fe[N]/gamma’-Fe4N1-x phase equilibrium. Acta Mater. 2005;53:255–64.

    Article  CAS  Google Scholar 

  40. Arroyave R, Shin D, Liu ZK. Ab initio thermodynamic properties of stoichiometric phases in the Ni–Al system. Acta Mater. 2005;53:1809–19.

    Article  CAS  Google Scholar 

  41. Kohanoff J. Electronic structure calculations for solids and molecules: theory and computational methods. 1st ed. Cambridge: Cambridge University Press; 2006.

    Book  Google Scholar 

  42. Kittel C. Introduction to solid state physics. New York: Wiley; 1996.

    Google Scholar 

  43. Wallace D. Thermodynamics of crystals. New York: Dover; 1998.

    Google Scholar 

  44. Pathria RK, Beale PD. Statistical mechanics. 3rd ed. Oxford: Butterworth-Heinemann; 2011.

    Google Scholar 

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Authors and Affiliations

  1. Department of Physics, K. N. Toosi University of Technology, Tehran, Iran

    Mahmoud Jafari, Ashkan Shekaari & Najmeh Delavari

  2. School of Civil Engineering, Iran University of Science and Technology, Tehran, Iran

    Reza Jafari

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  1. Mahmoud Jafari
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  2. Ashkan Shekaari
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  4. Reza Jafari
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Jafari, M., Shekaari, A., Delavari, N. et al. Thermodynamic properties of TiC nanowire from first principles. J Therm Anal Calorim 138, 1167–1173 (2019). https://doi.org/10.1007/s10973-019-08280-y

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