A Thermodynamic Perspective of the Composition Dependence of Bulk Modulus in Terms of Electron Density and Molar Volume
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INTRODUCTION
A comprehensive knowledge of the elastic properties of various engineering materials,[1–17] encompassing their temperature,[18–22] pressure,[23–25] and composition dependencies,[15,26,27] is of great importance to the performance of advanced engineering machinery.[28,29] In addition, such data are also of central interest to the basic understanding of bonding forces in materials.[23,30,31] Thus, if a robust description of the total binding energy (Eb) could be defined using established models of solid state cohesion,[32,33] and suitable descriptions of pressure, temperature, composition, and structural ordering effects are superposed as additive
SUBRAMANIAN RAJU is with the Physical Metallurgy Division, Materials Characterization Group, Metallurgy & Materials Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, 603102, India. Contact e-mail: [email protected] Manuscript submitted October 10, 2018. Article published online April 24, 2019 3320—VOLUME 50A, JULY 2019
contributions,[25,34–36] it then becomes possible to establish generalized correlations among various thermodynamic quantities.[37–44] This classical approach based on equation of state (EoS) methodology has been extensively employed in the area of high temperature-high pressure thermophysics, where the experimental measurements of thermophysical quantities like molar volume (V), bulk modulus (BT), volume thermal expansivity (ap), average sound velocity (cav), etc, are systematically analyzed to obtain a wholesome perspective of thermodynamic stability under extreme temperature and pressure conditions.[8,12,23] These diverse theoretical developments notwithstanding, there are only few studies devoted exclusively to establishing robust thermodynamic models for the composition dependence of different thermophysical quantities.[26,27,36,45–48] At present, this remains an issue of great relevance in a comprehensive interrelated description of thermodynamics and thermophysical properties of multicomponent systems.[36,45–48] Within the framework of modern CALPHAD methodology, the effects of composition on thermophysical quantities can be described through a combination of first principles and semiempirical METALLURGICAL AND MATERIALS TRANSACTIONS A
formalisms.[15,36,45,48] In the past two decades, implementation of the effects of composition and structural order through first principles methodology has gained currency for many alloy systems.[16,26–28,34–36,45–47,49–51] Nonetheless, it is still advantageous and useful to understand the composition-induced changes of elastic properties, in particular the bulk modulus, in terms of a thermodynamic framework that is related to corresponding changes in another measurable thermodynamic quantity, namely atomic volume, and which is amenable for accurate experimental quantification. It is in such a spirit, we have proposed recently a bridging thermodynamic framework connecting DHf, the standard molar enthalpy of formation with DBT, the change in bulk modulus due to alloying.[52] This connection has be
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