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NTRODUCTION

IT is well known that elastic properties, in particular the information on their temperature, pressure, and composition variation, are windows to understanding the cohesive characteristics of substances.[1,2] Being an equation of state parameter, the elastic modulus, especially the isothermal bulk modulus (BT) or inverse compressibility (jT), is an extensively investigated physical quantity on both experimental and theoretical grounds.[3–5] Thanks to numerous advances in the area of theoretical and computational materials sciences,[6,7] the elastic properties of many materials, spanning diverse bonding and structural characteristics, can now be calculated reliably, incorporating the influence of temperature, pressure, and chemical composition variations.[8] On the experimental front, the

SUBRAMANIAN RAJU is with the Calorimetry & Materials Modeling Section, Metallurgy & Materials Group of Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam, 603102, India. Contact e-mail: [email protected] SAROJA SAIBABA is with the Physical Metallurgy Division, Homi Bhabha National Institute (HBNI), Mumbai, and also with the Metallurgy and Materials Group of Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam, 603102, India. Manuscript submitted October 31, 2016. Article published online May 30, 2017 METALLURGICAL AND MATERIALS TRANSACTIONS A

maturing of experimental tools like resonant ultrasound spectroscopy (RUS),[9] Brillouin spectroscopy,[10] impulse excitation resonance frequency measurement technique (IET),[11] the classical ultrasonic pulse-echo transit time measurement, etc.[12] have enabled the accurate experimental determination of elastic properties of a spectrum of single and polycrystalline materials over a range of temperature and pressure.[3,13–15] Thus, a fair amount of materials elastic property data has been accrued in open literature, and the situation can now be exploited profitably for carrying out a rigorous thermodynamic analysis, which would hopefully shed some fundamental insights into the thermodynamic link that elastic properties possess with other related physical quantities. In addition, an investigation of the interlinked nature of the composition and temperature (pressure) dependency of different thermodynamic properties through appropriate physically based models is of immense significance in establishing the internal thermodynamic consistency among related thermophysical quantities. It is in such perspective that we develop in this study a phenomenological framework, which is aimed at an integrated analysis of the composition and temperature dependence of bulk modulus through corresponding variations in formation or mixing enthalpy. To begin with, the fundamental thermodynamic aspects of bulk modulus are briefly outlined in the following section.

VOLUME 48A, AUGUST 2017—3927

II.

THEORETICAL DEVELOPMENT

A. Thermodynamics of Bulk Modulus The thermodynamic definition of isothermal bulk modulus BT is given by the following relation[16]: BT ¼ Vð@p=@VÞT

½1

Here, V repres