On Thermodynamic Analysis of Substances with Negative Coefficient of Thermal Expansion

Kal Renganathan Sharma

Lone Star College-North Harris, Houston, USA.

DOI: 10.4236/eng.2013.511102                

Abstract

There are reports in the literature on the discovery of novel materials that were observed to shrink upon heating. Treatment of these materials in the same manner as the materials with positive coefficient of thermal expansion can lead to the misinterpretation of the laws of thermodynamics. This is because volume expansivity is usually defined at constant pressure. Negative values for volume expansivity can be shown using Maxwell’s reciprocity relations to lead to negative values for absolute temperature for ideal gas. For real systems, using Helmholz free energy analysis at equilibrium an expression for the volume expansivity was derived. It can be seen that this expression would be always positive for real physical changes, either heating or cooling. Isentropic volume expansivity is proposed as better suited for analysis of materials with negative thermal expansion, NTE and composites used in space such as Hubble telescope and Chandra telescope with zero coefficient of thermal expansion. This kind of a switch from isobaric to isentropic has precedence in the history of development of speed of sound.

Keywords

Negative Thermal Expansion; NTE Materials; Helmholz Free Energy; Second Law of Thermodynamics; Speed of Sound; Volume Expansivity

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	J. M. Smith, H. C. Van Ness and M. M. Abbott, “Introduction to Chemical Engineering Thermodynamics,” 7th Edition, McGraw Hill Professional, New York, 2005,
[2]	M. B. Jakubinek, C. A. Whitman and M. A. White, “Negative Thermal Expansion Materials: Thermal Properties and Implications for Composite Materials,” Journal of Thermal Analysis and Calorimetry, Vol. 99, No. 1, pp. 165-172.
[3]	D. R. Askleland and P. P. Phule, “The Science and Engineering of Materials,” PWS-Kent, Boston.
[4]	L. A. Stepanov, “Thermodynamics of Substances with Negative Thermal Expansion Coefficient,” Computer Modelling & New Technologies, Vol. 4, No. 2, 2000, pp. 72-74.
[5]	J. D. Anderson, “Modern Compressible Flow with Historical Perspective,” Third Edition, McGraw Hill Professional, New York, 2003.
[6]	Sir Isaac Newton, “Philosophiae Naturalis Principia Mathematica,” 1687.
[7]	P. S. M. de Laplace, “Sur la Vitesse du son dans L’aire et Dan L’eau,” Annales de Chimie et de Physique,1816.
[8]	K. R. Sharma, “Polymer Thermodynamics: Blends, Copolymers and Reversible Copolymerization,” CRC Press, Taylor Francis Group, Bacon Raton, 2010.
[9]	C. Kittel and H. Kroemer, “Thermal Physics,” 2nd Edition, Freeman & Co., New York, 1980.
[10]	W. Miller, C. W. Smith, D. S. Mackenzie and K. E. Evans, “Negative Thermal Expansion: A Review,” Journal of Material Science, Vol. 44, 2009, pp. 5441-5451. http://dx.doi.org/10.1007/s10853-009-3692-4
[11]	J. S. O. Evans, W. I. F. Davis and A. W. Sleight, “Structural Investigation of the Negative-Thermal-Expansion Material ZrW2O8,” Acta Crystallographica B, Vol. 55, No. 3, 1999, pp. 333-340.
[12]	A. W. Sleight, “Negative Thermal Expansion Material,” US Patent 5,322,559, 1994.
[13]	J. D. Jorgensen, Z. Hu and S. Short, “Pressure-Induced Cubic to Orthorhombic Phase Transformation in the Negative Thermal Expansion Material HfW2O8,” Journal of Applied Physics, Vol. 89, No. 6, 2001, pp. 3184-3188.
[14]	C. Lind, A. P. Wilkinson, Z. Hu, S. Short and J. D. Jorgensen, “Synthesis and Properties of the Negative Thernal Expansion Material Cubic ZrMo2O8,” Chemistry of Materials, Vol. 10, No. 9, 1998, pp. 2335-2337. http://dx.doi.org/10.1021/cm980438m
[15]	D. S. Bhange and Veda, “Negative Thermal Expansion in Silicalite-1 and Zirconium Silicalite-1 having MFI Structure,” Materials Research Bulletin, Vol. 41, No. 7, pp. 1392-1402. http://dx.doi.org/10.1016/j.materresbull.2005.12.002
[16]	J. Li, A. Yokochi, T. G. Amos and A. W. Sleight, “Strong Negative Thermal Expansion along the O-Cu-O Linkage in CuScO2”, Chemistry of Materials, Vol. 14, No. 6, 2002, pp. 2602-2606. http://dx.doi.org/10.1021/cm011633v
[17]	R. H. Baughman and E. A. Turi, “Negative Thermal Expansion of a Polydiacetyelene Single Crystal”, Journal of Polymer Science Part B: Polymer Physics, Vol. 11, 1973, pp. 2453-2466.
[18]	P. Rupnowski, M. Gentz, J. K. Sutter and A. M. Kumosa, “An Evaluation of Elastic Properties and Coefficients of Thermal Expansion of Graphite Fibers from Macroscopicc Composite Input Data,” Proceedings of Royal Society A, Vol. 461, 2005, pp. 347-369.