K. Sivasubramanian

The high temperature bulk modulus of aluminium: an assessment using experimental enthalpy and thermal expansion data

Abstract There exists a certain ambiguity with regard to the actual high-temperature bulk modulus of aluminium. In particular, there is a considerable disparity between various single crystal elastic constant measurements. This point has not been addressed on the theoretical front as well. In view of this situation, we seek to assess the existing bulk modulus data for their internal thermodynamic consistency and also obtain a reliable estimate using experimental data on thermal expansion, enthalpy and specific heat. The procedure adopted for this purpose makes use of a thermodynamic framework that relates thermal and elastic properties through Gruneisens hypothesis. The present analysis suggests that the oft-cited data of Gerlich and Fisher and the older one due to Sutton are not fully consistent with the existing thermal property data. The more recent data of Tallon and Wolfenden, although in better consonance with the requirements of thermodynamic consistency, are also found to be less reliable. A fresh calculation of the bulk modulus is made such that the estimated values exhibit a high degree of thermodynamic legitimacy with the selected thermal property data.

Estimating enthalpy and bulk modulus from thermal expansion data — a case study with α-Al2O3 and SiC

Abstract A simple thermodynamic framework has been formulated for calculating elastic properties from a knowledge of thermal expansivity and specific heat or vice versa. This approach rests on the validity of two plausible assumptions. In the first, by assuming the ratio (λ) of thermal expansivity (αV) to isobaric specific heat (CP) to be temperature independent, certain approximate expressions connecting rather explicitly the temperature dependence of volume and enthalpy with that of bulk modulus have been derived. In the second step, where this ratio happens to be mildly temperature dependent, a different functional relationship between thermal and elastic quantities has been established by invoking the temperature independence of Anderson-Gruneisen (δS) parameter. The application potential of these relations in estimating the thermophysical data for the missing quantities from known ones has been investigated against α-Al2O3 and SiC by estimating their bulk moduli from respective thermal expansion and enthalpy data.

Thermodynamic approximations for the mixed temperature and pressure derivative of bulk modulus: a case study on MgO

Abstract A thermodynamic framework for evaluating the mixed pressure (P), temperature (T) and derivative of bulk modulus ( ∂ 2 B T / ∂ P ∂ T ) is developed under the assumption that the pure thermal derivative of isothermal bulk modulus (∂BT/∂T)V is zero. An analysis of the thermodynamic consequences of this assumption led to the following approximations for ∂ 2 B T /∂P ∂T : (i) ( ∂ 2 B T / ∂ P ∂ T)=δ T α V ; (ii) ( ∂ 2 B T / ∂ P ∂T)=(γ G /b)( ∂ C V / ∂ P) T and (iii) ( ∂ 2 B T / ∂ P ∂T)=kC P , where δT, αV, γG, CP, CV stand, respectively, for the isothermal Anderson–Gruneisen parameter, isobaric volume thermal expansivity, thermal Gruneisen parameter, isobaric and isochoric specific heats. The temperature-independent thermoelastic constants b and k represent ( ∂ ln B T / ∂ V) P −1 and ( ∂ ln B T / ∂ H) P , respectively. The approximations developed in this study are applied to MgO and the estimated ( ∂ 2 B T / ∂ P ∂ T) values compare favourably with the experimental results.

On the isobaric volume dependence of the ratio between volume thermal expansivity and specific heat (αV/CP)

A thermodynamic analysis of the temperature sensitivity of the ratio (λ) between volume thermal expansivity (αV) and isobaric specific heat (CP) is presented. By invoking the temperature independence of the thermal Gruneisen parameter (γG), some simple approximations are derived for the isobaric volume dependence of the ratio αV/CP. In addition, the temperature dependence of γG has also been investigated under the condition that there exists a linear scaling relation between bulk modulus (BS) and enthalpy increment (ΔH). The relations suggested in this study form a consistent thermodynamic framework that serves to relate thermal and elastic properties on a general system-independent basis. As an illustrative application, the isobaric volume dependence of αV/CP has been estimated for MgO and the results are found to be in good agreement with experiment.

A study on the thermal expansion characteristics of Inconel-82® filler wire by high temperature X-ray diffraction

Abstract The lattice parameter ( a ) change with respect to temperature ( T ) has been measured by high temperature X-ray diffraction (HT-XRD) technique for Inconel-82® 1 filler wire used in the TIG welding of a dissimilar joint involving Inconel-600® and commercially pure iron. By taking proper precautions to minimise the temperature gradient across the sample thickness, and by suitably calibrating the shift in 2 θ produced as a result of sample buckling at high temperatures, we could obtain fairly reliable estimates of lattice parameter in the temperature range 300–1200 K. The lattice parameter and the coefficient of mean linear thermal expansion at 300 K, have been found to be 3.546(2)×10 −10 m and 11.03×10 −6 K −1 , respectively.

An integrated thermodynamic approach towards correlating thermal and elastic properties: development of some simple scaling relations

Abstract This study presents a detailed thermodynamic analysis of the intricate interrelationship existing between thermal and elastic properties. By invoking only the principles of classical thermodynamics, the multifarious consequences of a possible linear relationship between logarithmic bulk modulus and relative enthalpy at constant pressure are probed. In particular, we identify two linear scaling relations between molar volume and relative enthalpy and between molar volume and logarithmic bulk modulus. These relations are valid at temperatures exceeding the Debye temperature. In addition, certain interesting deductions with respect to the temperature dependences of the Anderson–Gruneisen parameter and the volume thermal expansivity to isobaric specific heat ratio are obtained. In brief, a simple thermodynamic protocol that will be of use in an integrated treatment of the elastic and thermal quantities has been developed. As an illustrative case study, the high temperature bulk modulus of copper is estimated from its thermal properties data using the proposed framework.

The relation between bulk modulus and relative enthalpy: a broad-based thermodynamic analysis and a case study on aluminium

By postulating a linear relationship between logarithmic bulk modulus and relative enthalpy, we have developed in this paper a thermodynamic framework that provides a link between thermal properties and bulk modulus under constant pressure. The proposed model could be used in analysing the consistency of various bulk modulus estimates of aluminium through an integrated treatment of its thermal and elastic properties.