Abstract
The heat capacity at constant pressure C p of alpha (HCP) titanium from 200 to 1000 K has been analyzed for contributions from lattice vibrations and electron excitations. Experimental data in the literature have been used to obtain the heat capacity at constant volume C V by the dilation correction. From C V has been subtracted an harmonic lattice contribution C VH given by the Debye heat capacity using a single Debye temperature and an electronic contribution C VE . The difference C V −(C VH +C VE ) is positive, and from about 600 to 1000 K it is real in the sense that it is larger than the experimental uncertainty in C V . This difference is attributed to an anharmonic lattice vibration contribution C VA . Two models for C VE have been used. One, which includes electron-phonon enhancement, leads to a C VA of about 15% of C V at 1000 K. The other takes into account the shift in the density of states with temperature and leads to a C VA of about 5% of C V
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References
M. Zemansky, Heat and Thermodynamics, 3rd ed. (McGraw-Hill, New York, 1951).
W. M. Cash and C. R. Brooks, J. Chem. Thermo. (in press).
V. O. Shestopal, Sov. Phys.—Solid State 7:2798 (1966).
K. Clusius and P. Franzosini, Z. Phys. Chem. (Frankfurt) 16:194 (1958).
B. Stalinski and Z. Bieganski, Roczniki Chem. 35:273 (1961).
C. W. Kothen and H. L. Johnston, J. Am. Chem. Soc. 75:3101 (1953).
R. H. Willens, Air Force Office of Sci. Res. Rep. No. 1839 (1961).
R. L. P. Berry and G. V. Raynor, Research 6:21S (1953).
J. Spreadborough and J. W. Christian, Proc. Phys. Soc. (London) 74:609 (1959).
F. L. Yaggee, E. R. Gilbert, and J. W. Styles, J. Less-Common Metals 19:39 (1969).
P. Hidnert, J. Res. Natl. Bur. Stds. 30:101 (1943).
E. S. Greiner and W. C. Ellis, Trans. AIME 180:657 (1949).
H. E. McCoy, Trans. ASM 57:743 (1964).
E. S. Fisher and C. J. Renken. Phys. Rev. 135:A482 (1964).
V. A. Korshunov, Phys. Met. Metallog. 42(2):54 (1976).
K. A. Gschneidner, In Solid State Physics, Vol. 16, F. Seitz and D. Turnbull, ed., (Academic Press, New York, 1964).
E. W. Collins and J. C. Ho, Phys. Rev. B 2:235 (1970).
M. Shimizu, T. Takahashi, and A. Katsuki, J. Phys. Soc. Japan 18:1192 (1963).
G. Grimvall, J. Phys. Chem. Solids 29:1221 (1968).
F. Y. Fradin, Solid State Commun. 16:1193 (1975).
S. L. Altmann and C. J. Bradley, Proc. Phys. Soc. 92:764 (1967).
G. Cordoba and C. R. Brooks, Phys. Stat. Sol. (a) 6:581 (1971).
C. R. Brooks and R. E. Bingham, J. Phys. Chem. Solids 29:1553 (1968).
C. R. Brooks, J. Phys. Chem. Solids 29:1377 (1968).
G. Cordoba and C. R. Brooks, Phys. Stat. Sol. (a) 13:K111 (1972).
C.-C. Yeh and C. R. Brooks, High Temp. Sci. 19:545 (1973).
C. R. Brooks, Phys. Stat. Sol. (b) 89:K123 (1978).
A. A. Maradudin and P. A. Flinn, Ann. Phys. 15:337 (1961).
R. C. Shukla, Int. J. Thermophys. 1:73 (1980).
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Brooks, C.R. Contributions to the heat capacity of alpha (HCP) titanium from 200–1000 K. Int J Thermophys 2, 371–380 (1981). https://doi.org/10.1007/BF00498767
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DOI: https://doi.org/10.1007/BF00498767