B2 Phases and their Defect Structures: Part II. Ab initio Vibrational and Electronic Free Energy in the Al-Ni-Pt-Ru Syst
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B2 Phases and their Defect Structures: Part II. Ab initio Vibrational and Electronic Free Energy in the Al-Ni-Pt-Ru System Raymundo Arroyave1, Sara Prins1,2 and Zi-Kui Liu1 1 Dept. Mat. Sci. & Eng., Pennsylvania State University, University Park, PA 16802, USA 2 CSIR-NML, P.O. Box 395, Pretoria, 0001, South Africa ABSTRACT In this work, we calculate the finite temperature thermodynamic properties of the binary B2 phases in the Al-Ni-Pt-Ru system, particularly the B2 RuAl phase in the Pt-Al-Ru ternary, through the incorporation of the vibrational and electronic contributions to the total free energy. The harmonic approximation is used to consider the atomic vibrations, with the quasi-harmonic correction to account for volume expansion effects on the vibrational entropy as the temperature increases. The vibrational entropy calculations are incorporated through the supercell approach. The calculated phonon dispersion curves show that the B2 PtRu structure is mechanically unstable at low temperatures, while B2 PtAl is marginally stable. The thermal electronic contribution is added to the total free energy. Finally, the formation enthalpies and entropies of B2 RuAl are calculated as a function of temperature. INTRODUCTION The B2 phases in the Al-Ni-Pt-Ru system are important in Thermal Barrier Coating (TBC) applications for jet engine turbine blades. TBCs consist of three layers: a ceramic top coat, a thermally grown oxide (TGO), and a bond coat (BC) [1]. The BC layer is used to match the thermal expansion coefficients of the ceramic thermal barrier and the super alloy substrate and also serves as an Al source so the TGO formed during operation is Al2O3 instead of other oxides. The most commonly used bond coat material is the B2 NiAl phase. Despite the success of the TBC technology, it is necessary to improve the durability of the TBC, which is affected by the formation and growth of the TGO layer, as well as by the stability of the BC [1]. Besides the binary NiAl B2 phase, additions of Pt[2] and Ru [3] have been considered as there seems to be evidence that they improve the thermodynamic stability and mechanical properties of the BC. Improvement of current TBC technologies depends on the understanding of the mechanisms behind the decomposition and transformation of the B2 BC layers as well as their interaction with the TGO and the alloy substrate. Using thermodynamic models based on the CALPHAD approach [4], for example, it may be possible to predict likely reaction sequences and phase equilibria resulting from the interactions of the B2 phases with their surroundings. In part I, ab initio techniques were used to calculate the formation energies of the stoichiometric B2 phases in the Pt-Al-Ru system as well as the energetics of the possible point defects that could exist in these structures. In this work, we complement the results at 0 K with calculations of the thermochemical properties of the perfect stoichiometric B2 phases in the PtRu-Al system at finite temperatures. Entropic contributions to the total fre
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