Abstract
In this paper, a new set of experimental data, αV KT V, 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 αV KT V, not αV KT, 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 αV KT V 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, αV KT V 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.
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References
H. D. Merchant, K. K. Srivastava, and H. D. Pandey, Crit. Rev. in Solid State Phys. 3, 451 (1973).
Thermal Expansion of Nonmetallic Solids, edited by Y.S. Touloukian, R. K. Taylor, and T.Y.R. Lee (IFI/Plenum, New York, 1977), Vol. 13.
S. K. Saxena and G. Shen, J. Geophys. Res. 97, 19 813 (1992).
J. B. Wachtman, T.G. Scuderi, and G. W. Cleek, J. Am. Ceram. Soc. 45, 319 (1962).
R. R. Reeber, Phys. Status Solidi A 32, 321 (1975).
I. Suzuki, J. Phys. Earth 23, 145 (1975).
M. Blackman, Proc. Phys. Soc. London, Sec. B 70, 827 (1957).
R. R. Reeber and J. L. Haas, in Thermal Expansion, edited by T. A. Hahn (Plenum, New York, 1984), Vol. 8, p. 31.
R. R. Reeber and K. Wang, J. Electron. Mater. 26, 63 (1996).
R. R. Reeber and K. Wang, Mater. Chem. Phys. (1996, in press).
K. Wang and R.R. Reeber, J. Phys. Chem. Solids 56, 895 (1995).
K. Wang and R. R. Reeber, J. Appl. Crystallogr. 28, 306 (1995).
E. Grüneisen, Hanbuch der Physik 10, 1 (1926).
T. H. K. Barron, Philos. Mag. 7, 720 (1955).
R. R. Reeber, K. Goessel, and K. Wang, European J. Min. 7, 1039 (1995).
K. Wang and R.R. Reeber, Phys. Status Solidi A 146, 621 (1994).
O. L. Anderson, D.G. Isaak, and H. Oda, J. Geophys. Res. 96, 18 037 (1991).
O. L. Anderson, D.G. Isaak, and H. Oda, Rev. Geophys. 30, 57 (1992).
O. L. Anderson and D.G. Isaak, in Mineral Physics & Crystallography, A Handbook of Physical Constants, AGU reference shelf, edited by T.J. Ahrens (AGU, 1995), Vol. 2, p. 64.
A. Encken and W. Dannöhl, Z. Electrochem. 40, 814 (1934), referenced by P.D. Pathak and N.G. Vasavada.27
P. D. Pathak and N.V. Pandya, Curr. Sci. India 28, 320 (1959), referenced by P.D Pathak and N.G. Vasavada.27
G. K. White, Proc. R. Soc. London A 286, 204 (1965).
B. Yates and Panter, C. H., Proc. Phys. Soc. 80, 373 (1962).
R. M. Buffington and W.M. Latimer, J. Am. Chem. Soc. 48, 2305 (1926).
G. K. White and J. G. Collins, Proc. R. Soc. London A 333, 237 (1973).
F. D. Enck and J.G. Dommel, J. Appl. Phys. 36, 839 (1965).
P. D. Pathak and N.G. Vasavada, Acta Crystallogr. A26, 655 (1970).
A. J. Leadbetter and D. M.T. Newshaw, J. Phys. C (Solid State Phys.) 2, 210 (1969).
K. Wang and R.R. Reeber, Phys. Chem. Minerals (1996, in press).
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Wang, K., Reeber, R.R. A model for evaluating and predicting high-temperature thermal expansion. Journal of Materials Research 11, 1800–1803 (1996). https://doi.org/10.1557/JMR.1996.0226
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DOI: https://doi.org/10.1557/JMR.1996.0226