Hostname: page-component-7479d7b7d-qs9v7 Total loading time: 0 Render date: 2024-07-13T10:00:20.987Z Has data issue: false hasContentIssue false

Elastic Constants and Coefficients of Thermal Expansion of Laves Phase Cr2X (X=Hf, Nb, Ta, Zr) Alloys

Published online by Cambridge University Press:  10 February 2011

Suklyun Hong
Affiliation:
Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6114
C. L. Fu
Affiliation:
Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6114
Get access

Abstract

To examine the effect of thermal expansion mismatch on cracking in two-phase Cr-Cr2X (X=Hf, Nb, Ta, Zr) alloys, we calculate the elastic constants and associated elastic anharmonicity by the local-density-functional approach from which the coefficients of thermal expansion (CTEs) of Cr and Cr2X are determined. The calculation shows that the CTE of Cr at high temperatures is notably larger than those of Cr2X. If the difference in CTE between Cr and Cr 2X is a primary source of crack initiation, our results fail to explain the experimental observation that, among Cr-Cr2X alloy systems, the ingot cracking occurs mainly in Cr-Cr2Nb. We suggest that for the cracking to occur, thermal mismatch stresses are retained by a hard and supersaturated Cr matrix (e.g., due to the relatively high solubility of Nb in Cr in the case of Cr-Cr2Nb). On the other hand, a soft Cr matrix can accommodate the thermal misfit dislocations plastically even when the CTE difference between Cr and Cr2X is large (e.g., in the case of Cr-Cr2Zr).

Type
Research Article
Copyright
Copyright © Materials Research Society 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Takeyama, M. and Liu, C.T., Mater. Sci. Eng. A 132, 61 (1991).CrossRefGoogle Scholar
2. Thoma, D.J. and Perepezko, J.H., Mater. Sci. Eng. A 156, 97 (1992).CrossRefGoogle Scholar
3. Kumar, K.S. and Miracle, D.B., Intermetallics 2, 257 (1994).Google Scholar
4. Kumar, K.S. and Liu, C.T., Acta mater. 45, 3671 (1997).CrossRefGoogle Scholar
5. Liu, C.T. (unpublished).Google Scholar
6. Ashcroft, N.W. and Mermin, N.D., Solid State Physics, Holt, Rinehart and Winston, 1976, Chap. 25, pp. 487509.Google Scholar
7. Hearmon, R.F.S., An Introduction to Applied Anisotropic Elasticity, Oxford University Press, London, 1961, Chap. VI, pp. 6889.Google Scholar
8. Villars, P. and Calvert, L.D., Pearson's Handbook of Crystallographic Data for Intermetallic Phases, Vol. 2, American Society of Metals, Metals Park, OH, 1985, p. 1908.Google Scholar
9. Hong, S. and Fu, C.L., Intermetallics 7, 5 1998.Google Scholar
10. Bolef, D.I. and de Klerk, J., Phys. Rev. 129, 1063 (1963).Google Scholar
11. White, G.K., Roberts, R.B., and Fawcett, E., J. Phys. F 16, 449 (1986).Google Scholar
12. Thoma, D.J.(unpublished).Google Scholar
13. Binary Alloy Phase Diagram, Vol. 1, Editor-in-chief Massalski, T.B., ASM, Metals Park, OH, 1986. For more recent phase diagram of Cr2Nb, see Ref. [2].Google Scholar