Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-25T08:02:22.407Z Has data issue: false hasContentIssue false
  • English
  • Français

A model for evaluating and predicting high-temperature thermal expansion

Published online by Cambridge University Press:  31 January 2011

Kai Wang  and
Robert R. Reeber
Kai Wang
Affiliation:
Department of Geology, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599–3315
Robert R. Reeber
Affiliation:
Department of Geology, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599–3315
Get access

Abstract

In this paper, a new set of experimental data, αVKTV, representing the partial temperature derivative of the work done by the thermal pressure of the solid, is fitted by n terms of a modified Einstein model. Experimental data show that αVKTV, not αVKT, approaches a constant value at high temperature. Based on the observed linear relationship of isothermal bulk modulus with temperature at high temperature, thermal expansion can be evaluated by fitting αVKTV data. Our previous results have shown that at low temperature or for materials with less variable bulk modulus and expansivity, thermal expansion data can be simply approximated by an n term Einstein model. More generally and for many materials, αVKTV data resemble an isochoric specific heat curve. With this method, thermal expansion can be predicted at high temperatures from low and intermediate temperature range data. With accurate thermal expansion data, high temperature bulk moduli can also be predicted.

Type
Articles
Information
Journal of Materials Research , Volume 11 , Issue 7 , July 1996 , pp. 1800 - 1803
Copyright
Copyright © Materials Research Society 1996

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.Merchant, H. D., Srivastava, K. K., and Pandey, H. D., Crit. Rev. in Solid State Phys. 3, 451 (1973).Google Scholar
2.Thermal Expansion of Nonmetallic Solids, edited by Touloukian, Y.S., Taylor, R. K., and Lee, T.Y.R. (IFI/Plenum, New York, 1977), Vol. 13.CrossRefGoogle Scholar
3.Saxena, S. K. and Shen, G., J. Geophys. Res. 97, 19813 (1992).CrossRefGoogle Scholar
4.Wachtman, J. B., Scuderi, T.G., and Cleek, G. W., J. Am. Ceram. Soc. 45, 319 (1962).CrossRefGoogle Scholar
5.Reeber, R. R., Phys. Status Solidi A 32, 321 (1975).CrossRefGoogle Scholar
6.Suzuki, I., J. Phys. Earth 23, 145 (1975).CrossRefGoogle Scholar
7.Blackman, M., Proc. Phys. Soc. London, Sec. B 70, 827 (1957).CrossRefGoogle Scholar
8.Reeber, R. R. and Haas, J. L., in Thermal Expansion, edited by Hahn, T. A. (Plenum, New York, 1984), Vol. 8, p. 31.CrossRefGoogle Scholar
9.Reeber, R. R. and Wang, K., J. Electron. Mater. 26, 63 (1996).CrossRefGoogle Scholar
10.Reeber, R. R. and Wang, K., Mater. Chem. Phys. (1996, in press).Google Scholar
11.Wang, K. and Reeber, R.R., J. Phys. Chem. Solids 56, 895 (1995).CrossRefGoogle Scholar
12.Wang, K. and Reeber, R. R., J. Appl. Crystallogr. 28, 306 (1995).CrossRefGoogle Scholar
13.Grüneisen, E., Hanbuch der Physik 10, 1 (1926).Google Scholar
14.Barron, T. H. K., Philos. Mag. 7, 720 (1955).CrossRefGoogle Scholar
15.Reeber, R. R., Goessel, K., and Wang, K., European J. Min. 7, 1039 (1995).CrossRefGoogle Scholar
16.Wang, K. and Reeber, R.R., Phys. Status Solidi A 146, 621 (1994).CrossRefGoogle Scholar
17.Anderson, O. L., Isaak, D.G., and Oda, H., J. Geophys. Res. 96, 18037 (1991).Google Scholar
18.Anderson, O. L., Isaak, D.G., and Oda, H., Rev. Geophys. 30, 57 (1992).CrossRefGoogle Scholar
19.Anderson, O. L. and Isaak, D.G., in Mineral Physics / Crystallography, A Handbook of Physical Constants, AGU reference shelf, edited by Ahrens, T.J. (AGU, 1995), Vol. 2, p. 64.Google Scholar
20.Encken, A. and Dannöhl, W., Z. Electrochem. 40, 814 (1934), referenced by P.D. Pathak and N.G. Vasavada.27Google Scholar
21.Pathak, P. D. and Pandya, N.V., Curr. Sci. India 28, 320 (1959), referenced by P.D Pathak and N.G. Vasavada.27Google Scholar
22.White, G. K., Proc. R. Soc. London A 286, 204 (1965).Google Scholar
23.Yates, B. and C. H., Panter, Proc. Phys. Soc. 80, 373 (1962).CrossRefGoogle Scholar
24.Buffington, R. M. and Latimer, W.M., J. Am. Chem. Soc. 48, 2305 (1926).CrossRefGoogle Scholar
25.White, G. K. and Collins, J. G., Proc. R. Soc. London A 333, 237 (1973).Google Scholar
26.Enck, F. D. and Dommel, J.G., J. Appl. Phys. 36, 839 (1965).CrossRefGoogle Scholar
27.Pathak, P. D. and Vasavada, N.G., Acta Crystallogr. A26, 655 (1970).CrossRefGoogle Scholar
28.Leadbetter, A. J. and Newshaw, D.M.T., J. Phys. C (Solid State Phys.) 2, 210 (1969).CrossRefGoogle Scholar
29.Wang, K. and Reeber, R.R., Phys. Chem. Minerals (1996, in press).Google Scholar