DOI: 10.1063/1.1733128. Conversion of Cv[T, V(T)] to Cv[T, V(0°K)] with Application to Na and Cu

Conversion of Cv[T, V(T)] to Cv[T, V(0°K)] with Application to Na and Cu

10.1063/1.1733128

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

The thermodynamic quantity E(T)= ∫ V0V(∂Cv/∂V)TdV=Cv[T,V(T)]−Cv[T,V(0∘K)]may be evaluated in terms of the thermal expansion and the coefficients, ai's, in the solid equation of state and their derivatives. Slater's procedure for E(T) is extended herein to the case in which the ai's are arbitrary functions of temperature and pressure. This E(T) is then transformed to a second equivalent form in terms of the bulk modulus and its temperature and pressure derivatives. It is seen that Cv[T, V(0)] may be determined entirely from experimental data. The lattice specific heat CL[T,V(0)]=Cv[T,V(0)]−Tγe[V(0)], this form being the physically correct way of calculating CL from electronic specific heat measured at low temperatures, is determined for Na and Cu. The CL[T, V(0)] of Na is compared with the Born—von Kármán theoretical Ctheoret calculated by C. B. Clark; this comparison indicating an anharmonic CL of the form Ctheoret (1+AT+BTn), (5&lt;n&lt;6), where A is only one-sixth that calculated by Leibfried and Ludwig for Cp[T, V(T)]. Comparison of CL[T, V(0)] of copper with theoretical specific heat calculated by the author shows quantitative agreement (within 0.2% from 50° to 300°K) thus indicating the adequacy of the central force model with nearest- and next-nearest-neighbor forces used.

Bibliography

Overton, W. C. (1962). Conversion of Cv[T, V(T)] to Cv[T, V(0Â°K)] with Application to Na and Cu. The Journal of Chemical Physics, 37(12), 2975â2985.

Authors 1

William C. Overton (first)

References 37 Referenced 22

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Dates

Type	When
Created	20 years, 7 months ago (Jan. 5, 2005, 10:29 p.m.)
Deposited	1 year, 6 months ago (Feb. 8, 2024, 4:18 p.m.)
Indexed	1 year ago (Aug. 13, 2024, 6:11 p.m.)
Issued	62 years, 8 months ago (Dec. 15, 1962)
Published	62 years, 8 months ago (Dec. 15, 1962)
Published Print	62 years, 8 months ago (Dec. 15, 1962)

Funders 0

None

BibTeX

@article{Overton_1962, title={Conversion of Cv[T, V(T)] to Cv[T, V(0°K)] with Application to Na and Cu}, volume={37}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1733128}, DOI={10.1063/1.1733128}, number={12}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Overton, William C.}, year={1962}, month=dec, pages={2975–2985} }

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  "abstract": "<jats:p>The thermodynamic quantity E(T)= \u222b V0V(\u2202Cv/\u2202V)TdV=Cv[T,V(T)]\u2212Cv[T,V(0\u2218K)]may be evaluated in terms of the thermal expansion and the coefficients, ai's, in the solid equation of state and their derivatives. Slater's procedure for E(T) is extended herein to the case in which the ai's are arbitrary functions of temperature and pressure. This E(T) is then transformed to a second equivalent form in terms of the bulk modulus and its temperature and pressure derivatives. It is seen that Cv[T, V(0)] may be determined entirely from experimental data. The lattice specific heat CL[T,V(0)]=Cv[T,V(0)]\u2212T\u03b3e[V(0)], this form being the physically correct way of calculating CL from electronic specific heat measured at low temperatures, is determined for Na and Cu. The CL[T, V(0)] of Na is compared with the Born\u2014von K\u00e1rm\u00e1n theoretical Ctheoret calculated by C. B. Clark; this comparison indicating an anharmonic CL of the form Ctheoret (1+AT+BTn), (5&amp;lt;n&amp;lt;6), where A is only one-sixth that calculated by Leibfried and Ludwig for Cp[T, V(T)]. Comparison of CL[T, V(0)] of copper with theoretical specific heat calculated by the author shows quantitative agreement (within 0.2% from 50\u00b0 to 300\u00b0K) thus indicating the adequacy of the central force model with nearest- and next-nearest-neighbor forces used.</jats:p>",
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