Estimation of Enthalpy of Formation of Liquid Transition Metal Alloys: A Modified Prescription Based on Macroscopic Atom
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THE standard enthalpy of formation (DoHf) of alloys at 298.15 K (25 C) and 1 bar pressure is an important thermodynamic quantity that has tremendous basic and applied significance in the domain of thermodynamic stability of materials.[1] In the first, it is one of the few directly measureable thermodynamic quantities, albeit with considerable experimental difficulty, by means of appropriate calorimetry techniques.[2] The knowledge of DoHf thus measured[2–10] together with suitable model the formation entropy based estimation of DoS,[11–17] f constitutes one of the fundamental cornerstones of any comprehensive thermochemical database of a substance. On a more fundamental basis, the availability of reliable experimental data on DoHf, especially its dependence on composition is a great boon for condensed matter theoreticians, who are interested in understanding and modeling alloy phase stability on transparent and transferable physical basis.[17–27] This is because of the fact that both the sign and numerical values of DoHf, and its variation as a function of composition and other
SUBRAMANIAN RAJU, Head, is with Calorimetry & Materials Modelling Section, Metallurgy and Materials Group, Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam, 603012, India. SAROJA SAIBABA, Head, is with Microscopy & Thermophysical Properties Division, Metallurgy and Materials Group, Indira Gandhi Centre for Atomic Research, and also Senior Professor with Homi Bhabha National Institute (HBNI), Mumbai, India. Contact e-mail: [email protected] Manuscript submitted February 23, 2016. Article published online July 5, 2016 METALLURGICAL AND MATERIALS TRANSACTIONS A
structural order parameters[26] represent the most compact statement about the nature of cohesive forces of alloy phases.[27] Stated in an alternate fashion, the successful reproduction of experimentally measured or critically assessed formation enthalpy data constitutes a critical test for the validity of the basic theoretical description of alloy phase Hamiltonian.[17,27] As mentioned before, DoHf is difficult to measure very accurately and also to be estimated in terms of suitable models of alloying.[3–10,17] Thus, for an arbitrary A1xBx alloy (A: solvent; B: solute) it follows that DoHf is given by the obvious relation:[1] Do Hf ¼ Ho ðA1x Bx Þ ð1 xÞHoA xHoB :
½1
The above expression indicates that DoHf is basically a difference quantity between two intrinsically large (standard) enthalpy (Ho) values. The sign and magnitude of DoHf is a quantitative reflection of subtle compensating physicochemical effects operating during the process of alloy formation.[18–24] Thus, unless, the calorimetry experiments are performed in a careful and properly calibrated manner,[2,6] significant error margins are incurred in the experimental estimates of formation enthalpy. This is a serious issue in the case of alloys possessing relatively small DoHf values. In addition, factors like reactivity of molten alloys with crucible material, the uncertainties involved in the measurement
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