Skip to main content
SpringerLink
Log in

Constitutive Modeling for CdTe Single Crystals

  • Published:
Metallurgical and Materials Transactions A Aims and scope Submit manuscript

Abstract

To understand the role of thermal stresses in the generation, multiplication, and propagation of dislocations in CdTe single crystals produced by directional solidification, constitutive models which accurately reflect the elastic-viscoplastic behavior of CdTe over a wide range of temperatures are needed. In this article, the relevant reported mechanical behavior of CdTe is reviewed and discussed. Constitutive equations developed for single slip, isothermal behavior of elemental semiconductor crystals by Haasen and co-workers, which include dislocation density as the important internal variable, are then extended to include an additional dislocation arrangement internal variable as well as a high-temperature, time-dependent recovery behavior. The constitutive framework is incorporated in a continuum slip framework to include the possibility of multiple slip and to relate slip system shear strain rates to the macroscopic plastic strain rate. Comparison of the model with available experimental data for the small strain case over a wide range of temperatures is presented. Slip system interaction is included. These constitutive equations can then be used in computational analyses of thermal stress generation for comparison with characterized crystals grown in microgravity and ground-based experiments.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Parfeniuk, F. Weinberg, I.V. Samarasekera, C. Schvezov, and L. Li:J. Cryst. Growth, 1992, vol. 119, pp. 261–70.

    Article  Google Scholar 

  2. E.L. Hall and J.B. Vander Sande:J. Am. Cer. Soc, 1978, vol. 61, pp. 417–25.

    Article  Google Scholar 

  3. S. Rai, S. Mahajan, D.J. Michel, H.H. Smith, S. McDevitt, and C.J. Johnson:Mater. Sci. Eng., 1991, vol. B10, pp. 219–25.

    Article  Google Scholar 

  4. R. Balasubramanian and W.R. Wilcox:Mater. Sci. Eng., 1993, vol. B16, pp. 1–7.

    Article  Google Scholar 

  5. E.Y. Gutmanas, N. Travitzky, U. Plitt, and P. Haasen:Scripta Metall., 1979, vol. 13, pp. 293–97.

    Article  Google Scholar 

  6. S.V. Lubenets and L.S. Fomenko:Sov. Phys.—Sol. St., 1989, vol. 31, pp. 256–59.

    Google Scholar 

  7. S. Cole, A.F.W. Willoughby, and M. Brown:J. Mater. Sci., 1985, vol. 20, 274–88.

    Article  Google Scholar 

  8. L. Carlsson and C.N. Ahlquist:J. Appl. Phys., 1972, vol. 43, pp. 2529–36.

    Article  Google Scholar 

  9. F. Buch and C.N. Ahlquist:J. Appl. Phys., 1974, vol. 45, pp. 1756–61.

    Article  Google Scholar 

  10. K. Maeda, K. Nakagawa, and S. Takeuchi:Phys. Status Solidi (a), 1978, vol. 48, pp. 587–91.

    Article  Google Scholar 

  11. E.Y. Gutmanas and P. Haasen:Phys. Status Solidi (a), 1981, vol. 63, pp. 193–202.

    Article  Google Scholar 

  12. E.Y. Gutmanas, N. Travitzky, and P. Haasen:Phys. Status Solidi (a), 1979, vol. 51, pp. 435–44.

    Article  Google Scholar 

  13. K. Guergouri, R. Triboulet, A. Tromson-Carli, and Y. Marfaing:J. Cryst. Growth, 1988, vol. 86, pp. 61–65.

    Article  Google Scholar 

  14. S. Cole:J. Mater. Sci., 1980, vol. 15, pp. 2591–96.

    Article  Google Scholar 

  15. D. Imhoff, A. Zozime, and R. Triboulet,J. Phys. III France, 1991, vol. 1, pp. 1841–53.

    Article  Google Scholar 

  16. H. Alexander and P. Haasen:Advances in Solid State Physics, vol. 22, F. Scitz, D. Turnbull, and H. Ehrenreich, eds., 1968, vol. 22, pp. 27–158.

  17. H.J. McSkimin and D.G. Thomas:J. Appl. Phys., 1962, vol. 33, pp. 56–59.

    Article  Google Scholar 

  18. Yu.Kh. Vekilov and A.P. Rusakov:Sov. Phys.—Sol. St., 1971, vol. 13, pp. 956–60.

    Google Scholar 

  19. D. Berlincourt, H. Jaffe, and L.R. Shiozawa:Phys. Rev., 1963, vol. 129, pp. 1009–17.

    Article  Google Scholar 

  20. R.D. Greenough and S.B. Palmer:J. Phys. D: Appl. Phys., 1973, vol. 6, pp. 587–92.

    Article  Google Scholar 

  21. R.F.S. Hearmon:An Introduction to Applied Anisotropie Elasticity, Oxford University Press, London, 1961.

    Google Scholar 

  22. R.W. Hertzberg:Deformation and Fracture Mechanics of Engineering Materials, 2nd ed., John Wiley and Sons, New York, NY, 1983.

    Google Scholar 

  23. E.L. Hall and J.B. Vander Sande:Phil. Mag. A, 1978, vol. 37, pp. 137–45.

    Article  Google Scholar 

  24. R. Balasubramanian:Ph.D. Thesis, Clarkson University, Potsdam, NY, 1992.

    Google Scholar 

  25. R.B. Schwarz:Scripta Metall, 1982, vol. 16, pp. 385–90.

    Article  Google Scholar 

  26. A. Fissel, M. Schenk, and A. Engel:Cryst. Res. Technol, 1989, vol. 24, pp. 557–65.

    Article  Google Scholar 

  27. A. Fissel and M. Schenk:Cryst. Res. Technol, 1990, vol. 25, pp. 89- 95.

    Article  Google Scholar 

  28. A. Fissel and M. Schenk:J. Mater. Sci.: Mater. Electr., 1992, vol. 3, pp. 147–56.

    Google Scholar 

  29. F.R.N. Nabarro, Z.S. Basinski, and D.B. Holt:Adv. Phys., 1964, vol. 13 (50), 1964, pp. 193–323.

    Article  Google Scholar 

  30. P.B. Hirsch: inThe Physics of Metals 2. Defects, P.B. Hirsch, ed., Cambridge University Press, London, 1975, pp. 189–246.

    Google Scholar 

  31. S.J. Basinski and Z.S. Basinski: inDislocations in Solids, F.R.N. Nabarro, ed., North Holland, New York, NY, 1979, pp. 263–362.

    Google Scholar 

  32. W.G. Johnston and J.J. Gilman:J. Appl. Phys., 1959, vol. 30, pp. 129–44.

    Article  Google Scholar 

  33. E. Peissker, P. Haasen, and H. Alexander,Phil. Mag., 1961, vol. 7, pp. 1279–1363.

    Article  Google Scholar 

  34. C.T. Tsai, M.W. Yao, and A. Chait,J. Cryst. Growth, 1992, vol. 125, pp. 69–80.

    Article  Google Scholar 

  35. P. Franciosi, M. Berveiller, and A. Zaoui:Acta Metall, 1980, vol. 28, pp. 273–83.

    Article  Google Scholar 

  36. G.I. Taylor:Proc. R. Soc, 1934, vol. 145, pp. 362–87.

    Article  Google Scholar 

  37. S. McDevitt, B.E. Dean, D.G. Ryding, F.J. Scheltens, and S. Mahajan:Mater. Lett, 1986, vol. 4, pp. 451–54.

    Article  Google Scholar 

  38. M. Wada, J. Suzuki, and H. Hosomatsu:Jpn. J. Appl. Phys., 1986, vol. 25, pp. L780-L782.

    Article  Google Scholar 

  39. J.L. Bassani and T.-Y. Wu:Proc. R. Soc, 1991, vol. 435, pp. 21–41.

    Article  Google Scholar 

  40. J.R. Rice:J. Mech. Phys. Sol, 1971, vol. 19, pp. 433–55.

    Article  Google Scholar 

  41. R.J. Asaro:ASME J. Appl. Mech., 1983, vol. 50, pp. 921–34.

    Article  Google Scholar 

  42. S.S. Chern and F.A. Kroger:J. Sol. St. Chem., 1975, vol. 14, pp. 44- 51.

    Article  Google Scholar 

  43. A. Orlova and B. Sieber:Acta Metall, 1984, vol. 32, pp. 1045–52.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical and Aeronautical Engineering, Clarkson University, 13699-5729, Potsdam, NY

    J. C. Moosbrugger (Associate Professor)

  2. Advanced Technology and Development Center, Northrup-Grumman Corporation MSA0126, 11714, Bethpage, NY

    A. Levy (Principal Engineer)

Authors
  1. J. C. Moosbrugger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Levy
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This article is based on a presentation made in the symposium entitled “Microgravity Solidification, Theory and Experimental Results” as a part of the 1993 TMS Fall meeting, October 17-21, 1993, Pittsburgh, PA, under the auspices of the TMS Solidification Committee.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moosbrugger, J.C., Levy, A. Constitutive Modeling for CdTe Single Crystals. Metall Mater Trans A 26, 2687–2697 (1995). https://doi.org/10.1007/BF02669425

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02669425

Keywords

Search

Navigation