Volume-based thermoelasticity: Thermal expansion coefficients and the Gr ¨ uneisen ratio Leslie Glasser n Nanochemistry Research Institute, Department of Chemistry, Curtin University, G.P.O Box U1987, Perth, WA 6845, Australia article info Article history: Received 5 September 2011 Accepted 7 October 2011 Available online 17 October 2011 Keywords: A. Inorganic compounds D. Thermal expansion D. Thermodynamic properties abstract In an extension of our current studies of volume-based thermodynamics and thermoelasticity (VBT), we here consider the parameters at ambient temperature of the dimensionless Gr + uneisen ratio (or Gr + uneisen parameter), g th , which is a standard descriptor of the thermophysical properties of solids: g th ¼aK T V m /C v ¼aV m /bC v It has earlier been established that the isothermal volume compressibility, b (which is the reciprocal of the bulk modulus, K T ), and the ambient-temperature heat capacity, Cp, are strongly linearly correlated with the molar volume, V m , among groups of materials with similar structures. Here, we examine possible correlations between the volumetric thermal expansion coefficient, a (the remaining Gr + uneisen parameter), and molar volume. Using the high-temperature limiting value, a1, as a surrogate for a, we find that a is essentially uncorrelated with volume among a range of materials. As a consequence of the lack of correlation through volume of a with the other Gr + uneisen parameters, we conclude that the dimensionless Gr + uneisen ratio at ambient temperatures itself is thereby poorly constant across materials and cannot be reliably used for predictive purposes. It is noted that, for thermodynamic reasons, the values of g th generally range from about 0.5 to 3, clustering around 2. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction Thermodynamics is fundamental in understanding the beha- viour of materials, both chemical and physical. Experimental thermodynamics is, however, not much practised because it is demanding and difficult; as a consequence, thermodynamic data is unavailable for many materials. This data absence can, at least partially, be filled by the theoretical methods but these, too, are demanding and require specialist expertise. This provides the opportunity for the use of empirical predictive methods based upon extrapolations from the behaviour of related materials. While the resulting values may be approximate, they fill impor- tant data gaps. Over the recent years, we have developed empirical volume- based thermodynamic (VBT) correlations by which thermody- namic quantities, such as entropies, heat capacities, lattice enthalpies and formation enthalpies, may be reliably estimated by linear correlation with molar (or formula unit) volume, V m , across ranges of generally ionic materials, independent of struc- tural details. [1–4]. Extending beyond standard chemical thermo- dynamics, we have lately also examined thermoelastic relations, observing that compressibility, b, is proportional to formula volume within groups of materials of similar structure and with a common anion (for example, silicate clinopyroxenes (ABSi 2 O 6 ), chalcopyrites (ABX 2 ) and perovskites (ABO 3 )) [5,6]. The thermodynamic and thermoelastic parameters of a solid are conveniently related through the dimensionless Gr + uneisen ratio (or Gr + uneisen parameter) [7–10] g th ¼ aK T V m =C v ¼ aV m =bC v where C v is heat capacity under conditions of constant volume and C v ¼ C p a 2 V m K T T ¼ C p a 2 V m T =b where C p is the heat capacity under conditions of constant pressure and a the coefficient of cubic thermal expansion ¼ð1=V m Þð@V m =@T Þ p while the compressibility, b or k, is defined by b, k ¼ 1 V @V m @p   T ¼ 1 B , 1 K T Here, the bulk modulus, B or K T , which is the reciprocal of the coefficient of isothermal compressibility, represents the resis- tance to bulk compression of the material (also known as incompressibility) and this form is generally favoured by geophysicists. Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/jpcs Journal of Physics and Chemistry of Solids 0022-3697/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2011.10.008 n Tel.: þ61 8 9266 3126; fax : þ61 8 9266 4699. E-mail address: l.glasser@curtin.edu.au Journal of Physics and Chemistry of Solids 73 (2012) 139–141