Skip to content
1887
  1. Home
  2. A-Z Publications
  3. Johnson Matthey Technology Review
  4. Volume 68, Issue 1
  5. Article
Volume 68, Issue 1
  • ISSN: 2056-5135
file format pdf download PDF

Abstract

The propagation of ultrasonic waves in the hexagonal closed packed (hcp) structured lanthanide metal titanium has been investigated in the temperature range 300–1000 K. For this, initially the higher-order elastic constants (second-order elastic constants (SOECs) and third-order elastic constants (TOECs)) were computed using the Lennard-Jones interaction potential model. With the help of SOECs, other elastic moduli such as Young’s modulus (), bulk modulus (), shear modulus (), Poisson’s ratio (σ) and Pugh’s ratio () were computed using the Voigt-Reuss-Hill approximation. Three types of orientation-dependent ultrasonic velocities, including Debye average velocities, were evaluated using the calculated SOECs and density of titanium in the same temperature range. Thermophysical properties such as lattice thermal conductivity, thermal relaxation time, thermal energy density, specific heat at constant volume and acoustic coupling constant were evaluated under the same physical conditions. The ultrasonic attenuation due to phonon-phonon interaction is most significant under the chosen physical conditions. The ultrasonic properties of titanium are correlated with thermophysical properties to understand the microstructural features and nature of the material.

© Johnson Matthey
Loading

Article metrics loading...

/content/journals/10.1595/205651323X16653975448311
2022-10-10
2024-07-10
Loading full text...

Full text loading...

/deliver/fulltext/jmtr/68/1/Singh1_16a_Imp.html?itemId=/content/journals/10.1595/205651323X16653975448311&mimeType=html&fmt=ahah

References

  1. Hao Y., Zhu J., Zhang L., Qu J., and Ren H. Solid State Sci., 2010, 12, (8), 1473 LINK https://doi.org/10.1016/j.solidstatesciences.2010.06.010 [Google Scholar]
  2. Skriver H. L. Phys. Rev. B, 1985, 31, (4), 1909 LINK https://doi.org/10.1103/physrevb.31.1909 [Google Scholar]
  3. Yamaguchi T., Morishita H., Iwase S., Yamada S., Furuta T., and Saito T. SAE Technical Paper 2000-01-0905, SAE International, Warrendale, USA, 6th March, 2000 LINK https://saemobilus.sae.org/content/2000-01-0905/
  4. Kuroda D., Niinomi M., Morinaga M., Kato Y., and Yashiro T. Mater. Sci. Eng.: A, 1998, 243, (1–2), 244 LINK https://doi.org/10.1016/s0921-5093(97)00808-3 [Google Scholar]
  5. Mridha S., and Baker T. N. Mater. Sci. Eng.: A, 1994, 188, (1–2), 229 LINK https://doi.org/10.1016/0921-5093(94)90376-x [Google Scholar]
  6. Ettaqi S., Hays V., Hantzpergue J. J., Saindrenan G., and Remy J. C. Surf. Coat. Technol., 1998, 100–101, 428 LINK https://doi.org/10.1016/s0257-8972(97)00664-6 [Google Scholar]
  7. Jamieson J. C. Science, 1963, 140, (3562), 72 LINK https://doi.org/10.1126/science.140.3562.72 [Google Scholar]
  8. Mendelev M. I., Underwood T. L., and Ackland G. J. J. Chem. Phys., 2016, 145, (15), 154102 LINK https://doi.org/10.1063/1.4964654 [Google Scholar]
  9. Hong T., Watson-Yang T. J., Guo X.-Q., Freeman A. J., Oguchi T., and Xu J. Phys. Rev. B, 1991, 43, (3), 1940 LINK https://doi.org/10.1103/physrevb.43.1940 [Google Scholar]
  10. Zhu Y. D., Yan M. F., Zhang Y. X., and Zhang C. S. Comput. Mater. Sci., 2016, 123, 70 LINK https://doi.org/10.1016/j.commatsci.2016.06.015 [Google Scholar]
  11. Tan J. H., Zhu K. J., and Peng J. H. Chin . J. Comput. Phys., 2017, 34, 365 [Google Scholar]
  12. Jian Y., Huang Z., Xing J., Sun L., Liu Y., and Gao P. Mater. Chem. Phys., 2019, 221, 311 LINK https://doi.org/10.1016/j.matchemphys.2018.09.055 [Google Scholar]
  13. Liu L., Wang Z.-Q., Hu C.-E., Cheng Y., and Ji G.-F. Solid State Commun., 2017, 263, 10 LINK https://doi.org/10.1016/j.ssc.2017.06.011 [Google Scholar]
  14. Shang S. L., Kim D. E., Zacherl C. L., Wang Y., Du Y., and Liu Z. K. J. Appl. Phys., 2012, 112, (5), 053515 LINK https://doi.org/10.1063/1.4749406 [Google Scholar]
  15. Wu X., Liu L., Li W., Wang R., and Liu Q. Comput. Condens. Matter, 2014, 1, 38 LINK https://doi.org/10.1016/j.cocom.2014.10.005 [Google Scholar]
  16. Luo F., Guo Z.-C., Zhang X.-L., Yuan C.-Y., and Cai L.-C. Philos. Mag. Lett., 2015, 95, (4), 211 LINK https://doi.org/10.1080/09500839.2015.1031846 [Google Scholar]
  17. Destefanis M., Ravoux C., Cossard A., and Erba A. Minerals, 2019, 9, (1), 16 LINK https://doi.org/10.3390/min9010016 [Google Scholar]
  18. Liu Z.-L., Yang J.-H., Cai L.-C., Jing F.-Q., and Alfè D. Phys. Rev. B, 2011, 83, (14), 144113 LINK https://doi.org/10.1103/physrevb.83.144113 [Google Scholar]
  19. Shang S.-L., Zhang H., Wang Y., and Liu Z.-K. J. Phys.: Condens. Matter, 2010, 22, (37), 375403 LINK https://doi.org/10.1088/0953-8984/22/37/375403 [Google Scholar]
  20. Wang Y., Wang J. J., Zhang H., Manga V. R., Shang S. L., Chen L.-Q., and Liu Z.-K. J. Phys.: Condens. Matter, 2010, 22, (22), 225404 LINK https://doi.org/10.1088/0953-8984/22/22/225404 [Google Scholar]
  21. Olsson P.A.T. Comput. Mater. Sci., 2015, 99, 361 LINK https://doi.org/10.1016/j.commatsci.2015.01.005 [Google Scholar]
  22. Dragoni D., Ceresoli D., and Marzari N. Phys. Rev. B, 2015, 91, (10), 104105 LINK https://doi.org/10.1103/physrevb.91.104105 [Google Scholar]
  23. Xie Y., Peng K., and Yang X. J. Cent. South Univ. Tech., 2001,8, (2), 83 LINK https://doi.org/10.1007/s11771-001-0031-6 [Google Scholar]
  24. Xia H., Parthasarathy G., Luo H., Vohra Y. K., and Ruoff A. L. Phys. Rev. B, 1990, 42, (10), 6736 LINK https://doi.org/10.1103/physrevb.42.6736 [Google Scholar]
  25. Fisher E. S., and Renken C. J. Phys. Rev., 1964, 135, (2A), A482 LINK https://doi.org/10.1103/physrev.135.a482 [Google Scholar]
  26. Ikehata H., Nagasako N., Furuta T., Fukumoto A., Miwa K., and Saito T. Phys. Rev. B, 2004, 70, (17), 174113 LINK https://doi.org/10.1103/physrevb.70.174113 [Google Scholar]
  27. Song Y., Yang R., Li D., Hu Z., and Guo Z. J. Comput.-Aided Mater. Des., 1999, 6, (2–3), 355 LINK https://doi.org/10.1023/a:1008762206967 [Google Scholar]
  28. Song Y., Yang R., and Guo Z.-X. Mater. Trans., 2002, 43, (12), 3028 LINK https://doi.org/10.2320/matertrans.43.3028 [Google Scholar]
  29. Song Y., Guo Z. X., and Yang R. Phil. Mag. A, 2002, 82, (7), 1345 LINK https://doi.org/10.1080/01418610208235676 [Google Scholar]
  30. Argaman U., and Makov G. Comput. Mater. Sci., 2020, 184, 109917 LINK https://doi.org/10.1016/j.commatsci.2020.109917 [Google Scholar]
  31. Lobkis O. I., and Rokhlin S. I. Appl. Phys. Lett., 2010, 96, (16), 161905 LINK https://doi.org/10.1063/1.3416910 [Google Scholar]
  32. Britton T. B., Liang H., Dunne F.P.E., and Wilkinson A. J. Proc. R. Soc. A, 2010, 466, (2115), 695 LINK https://doi.org/10.1098/rspa.2009.0455 [Google Scholar]
  33. Kwon J., Brandes M. C., Sudharshan Phani P., Pilchak A. P., Gao Y. F., George E. P., Pharr G. M., and Mills M. J. Acta Mater., 2013, 61, (13), 4743 LINK https://doi.org/10.1016/j.actamat.2013.05.005 [Google Scholar]
  34. Siu K. W., Ngan A.H.W., and Jones I. P. Int. J. Plast., 2011, 27, (5), 788 LINK https://doi.org/10.1016/j.ijplas.2010.09.007 [Google Scholar]
  35. Kim Y.-M., Lee B.-J., and Baskes M. I. Phys. Rev. B, 2006, 74, (1), 014101 LINK https://doi.org/10.1103/physrevb.74.014101 [Google Scholar]
  36. Zhang Y., Zhao Y., Hou H., Wen Z., and Duan M. Mater. Res. Express, 2018, 5, (2), 026527 LINK https://doi.org/10.1088/2053-1591/aaaf7d [Google Scholar]
  37. Spreadborough J., and Christian J. W. Proc. Phys. Soc., 1959, 74, (5), 609 LINK https://doi.org/10.1088/0370-1328/74/5/314 [Google Scholar]
  38. Tane M., Okuda Y., Todaka Y., Ogi H., and Nagakubo A. Acta Mater., 2013, 61, (20), 7543 LINK https://doi.org/10.1016/j.actamat.2013.08.036 [Google Scholar]
  39. Singh S. P., Singh G., Verma A. K., Jaiswal A. K., and Yadav R. R. Met. Mater. Int., 2021, 27, (8), 2541 LINK https://doi.org/10.1007/s12540-020-00633-9 [Google Scholar]
  40. Pandey D. K., Singh D., and Yadav R. R. Appl. Acoust., 2007, 68, (7), 766 LINK https://doi.org/10.1016/j.apacoust.2006.04.004 [Google Scholar]
  41. Yadav C. P., Pandey D. K., and Singh D. Indian J. Phys., 2019, 93, (9), 1147 LINK https://doi.org/10.1007/s12648-019-01389-8 [Google Scholar]
  42. Yadav N., Singh S. P., Maddheshiya A. K., Yadawa P. K., and Yadav R. R. Phase Trans., 2020, 93, (9), 883 LINK https://doi.org/10.1080/01411594.2020.1813290 [Google Scholar]
  43. Mason W. P., and Bateman T. B. J. Acoust. Soc. Am., 1966, 40, (4), 852 LINK https://doi.org/10.1121/1.1910158 [Google Scholar]
  44. Verma S. K., Yadav R. R., Yadav A. K., and Joshi B. Mater. Lett., 2010, 64, (15), 1677 LINK https://doi.org/10.1016/j.matlet.2010.04.063 [Google Scholar]
  45. Singh S. P., Singh G., Verma A. K., Yadawa P. K., and Yadav R. R. Pramana, 2019, 93, (5), 83 LINK https://doi.org/10.1007/s12043-019-1846-8 [Google Scholar]
  46. Brugger K. Phys. Rev., 1964, 133, (6A), A1611 LINK https://doi.org/10.1103/physrev.133.a1611 [Google Scholar]
  47. Dhawan P. K., Wan M., Verma S. K., Pandey D. K., and Yadav R. R. J. Appl. Phys., 2015, 117, (7), 074307 LINK https://doi.org/10.1063/1.4913289 [Google Scholar]
  48. Morelli D. T., Slack G. A., ‘High Lattice Thermal Conductivity Solids’, in “High Thermal Conductivity Materials”, eds. Shindé S.L., and Goela J. S. Springer Science and Business Media Inc, New York, USA, 2006, pp. 37–68 LINK https://doi.org/10.1007/0-387-25100-6_2 [Google Scholar]
  49. Pandey D. K., Yadawa P. K., and Yadav R. R. Mater. Lett., 2007, 61, (30), 5194 LINK https://doi.org/10.1016/j.matlet.2007.04.028 [Google Scholar]
  50. Singh D., Pandey D. K., Singh D. K., and Yadav R. R. Appl. Acoust., 2011, 72, (10), 737 LINK https://doi.org/10.1016/j.apacoust.2011.04.002 [Google Scholar]
  51. Ogi H., Kai S., Ledbetter H., Tarumi R., Hirao M., and Takashima K. Acta Mater., 2004, 52, (7), 2075 LINK https://doi.org/10.1016/j.actamat.2004.01.002 [Google Scholar]
  52. Turkdal N., Deligoz E., Ozisik H., and Ozisik H. B. Phase Trans., 2017, 90, (6), 598 LINK https://doi.org/10.1080/01411594.2016.1252979 [Google Scholar]
  53. Rao R. R., and Rajput A. Phys. Rev. B, 1979, 19, (6), 3323 LINK https://doi.org/10.1103/physrevb.19.3323 [Google Scholar]
  54. Rao R. R., and Rajput A. Phil. Mag. A, 1979, 40, (6), 769 LINK https://doi.org/10.1080/01418617908234873 [Google Scholar]
  55. Singh S. P., Yadawa P. K., Dhawan P. K., Verma A. K., and Yadav R. R. Cryogenics, 2019, 100, 105 LINK https://doi.org/10.1016/j.cryogenics.2019.03.006 [Google Scholar]
  56. Gray D. E. “American Institute of Physics Handbook”, 3rd Edn., McGraw-Hill, New York, USA, 1956, p. 44 [Google Scholar]
  57. Takahashi Y., Yamawaki M., and Yamamoto K. J. Nucl. Mater., 1988, 154, (1), 141 LINK https://doi.org/10.1016/0022-3115(88)90127-4 [Google Scholar]
  58. Pandey D. K., Singh D., and Yadav R. R. Appl. Acoust., 2007, 68, (7), 766 LINK https://doi.org/10.1016/j.apacoust.2006.04.004 [Google Scholar]
  59. Yadav A. K., Yadawa P. K., Yadav R. R., and Pandey D. K. J. Acoust. Soc. India, 2005, 33, 193 [Google Scholar]
  60. Yadawa P. K., Pandey D. K., and Yadav R. R. J. Acoust. Soc. India, 2005, 33, 186 [Google Scholar]
  61. Singh D., Pandey D. K., and Yadawa P. K. Cent. Eur. J. Phys., 2009, 7, (1), 198 LINK https://doi.org/10.2478/s11534-008-0130-1 [Google Scholar]
/content/journals/10.1595/205651323X16653975448311
Loading
Non-Linear Thermophysical Behaviour of Transition Metal Titanium
Johnson Matthey Technology Review 68, 37 (2024); https://doi.org/10.1595/205651323X16653975448311
/content/journals/10.1595/205651323X16653975448311
/content/journals/10.1595/205651323X16653975448311
Loading

Data & Media loading...

  • Article Type: Research Article

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error