• B Nageswara Sarma

      Articles written in Bulletin of Materials Science

    • Existence domains for invariant reactions in binary regular solution phase diagrams exhibiting two phases

      B Nageswara Sarma S Srinivas Prasad S Vijayvergiya V Bharath Kumar S Lele

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      The thermodynamic origin of various types of phase diagrams in simple binary systems exhibiting two phases (e.g. a liquid and a solid phase) has been examined using the regular solution model. The necessary conditions for the occurrence of each of these types are identified in terms of the appropriate intersections of the miscibility gap boundaries (in solid/liquid phases) and the liquidus/solidus/iso-𝐺 curves. Thus, the regions of occurrence of the different types of possible phase diagrams in the space of the regular solution interchange energy parameters (𝑊𝛼, 𝑊𝛽) are clearly delineated. This analysis makes it easier to make intelligent initial selections of model (energy) parameters for their optimization in the calculation of phase diagrams using thermodynamic models such as CALPHAD/CVM.

    • Estimation of CE–CVM energy parameters from miscibility gap data

      G Srinivasa Gupta G Vamsi Madhav A Pandey B Nageswara Sarma S Lele

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      The powerful framework of cluster expansion–cluster variation methods (CE–CVM) expresses alloy free energy in terms of energy (model) parameters, macroscopic variables (composition and temperature) and microscopic variables (correlation functions). A simultaneous optimization of thermodynamic and phase equilibria data using CE–CVM is critically dependent on giving good initial values of energy parameters, macroscopic and microscopic variables, respectively. No standard method for obtaining the initial values of the energy parameters is available in literature. As a starting point, a method has been devised to estimate the values of energy parameters from consolute point (miscibility gap maximum) data. Empirical relations among energy parameters, temperature (𝑇c), composition (𝑥c) and 𝑑2}𝑇/𝑑𝑥2 at the consolute point, have been developed using CE–CVM free energy functions for bcc and fcc structures in the tetrahedron and tetrahedron–octahedron approximations, respectively. Thus from the observed data of 𝑇c, 𝑥c and 𝑑2}𝑇/𝑑𝑥2 in the above relations, good initial values of energy parameters can be obtained. Further, a necessary modification to the classical NR method for solving simultaneous nonlinear/transcendental equations with a double root in one variable and a simple root in the other has been presented.

    • Transformations among CE–CVM model parameters for multicomponent systems

      B Nageswara Sarma Shrikant Lele

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      In the development of thermodynamic databases for multicomponent systems using the cluster expansion–cluster variation methods, we need to have a consistent procedure for expressing the model parameters (CECs) of a higher order system in terms of those of the lower order subsystems and to an independent set of parameters which exclusively represent interactions of the higher order systems. Such a procedure is presented in detail in this communication. Furthermore, the details of transformations required to express the model parameters in one basis from those defined in another basis for the same system are also presented.

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