# THERMODYNAMIC MODELING AND PREDICTION OF ELASTIC AND THERMAL EXPANSION PROPERTIES OF NI-BASE SUPERALLOYS: APPLICATION TO NI-AL-PT-CR-HF SYSTEM WITH γ AND γ' PHASES

Open Access

- Graduate Program:
- Materials Science and Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- August 09, 2011
- Committee Members:
- Zi Kui Liu, Dissertation Advisor
- Zi Kui Liu, Committee Chair
- Long Qing Chen, Committee Member
- Digby D Macdonald, Committee Member
- Jorge Osvaldo Sofo, Committee Member

- Keywords:
- thermodynamic modeling
- Ni-base superalloys
- elastic property
- thermal expansion property

- Abstract:
- A computational prediction of materials performance is becoming increasingly important for the development of new materials. In the case of multicomponent materials such as Ni base superalloys, it is very important to understand the effect of each alloying element on the phase stability and mechanical properties of the system. For last few decades, a thermodynamic modeling technique, known as the CALPHAD method (CALculation of PHAse Diagrams), has shown to be a reliable approach in calculating phase equilibria, stability and transformation in multicomponent system. At the same time, the first-principles calculations based on the density functional theory has demonstrated that it can predict the thermodynamic and mechanical properties comparable with experimental data. The first-principles calculation can also provide quantitative inputs in the CALPHAD modeling when the experimental thermochemical data is scarce. In this dissertation, the integrated CALPHAD and first-principles calculations approach is used to study the thermodynamic, elastic and thermal expansion properties of Ni base alloys, focusing on γ+γ phases in the Ni-Al-Cr-Hf-Pt system. The available constituent binary and ternary systems in the literature are carefully reviewed and selected to combine into the quinary system. The binary systems should be well developed since binary interactions are dominant in a higher order multicomponent system. From the review of the all constituent binary system, it is found that the Al-Pt system should be remodeled since existing thermodynamic database did not include the AlPt2 and  phases and the disordered fcc_A1 phase and the ordered fcc phase(L12-AlPt3) were modeled using two different Gibbs energy functions with a two-sublattice model for the ordered fcc phase, which is not consistent with other binary systems. In this work, the AlPt2 and  phases are added according to new experimental observations and the four-sublattice compound energy formalism is applied to describe the ordered fcc phase, which gives the consistency with other constituent binary systems. The enthalpies of mixing of the fcc, bcc, B2 and L12 phases are calculated from the first-principles calculations using special quasirandom structures (SQS) and used to evaluate model parameters of the corresponding phases since there is no available experimental data. Then, the Ni-Al-Pt ternary system is remodeled by combining the updated Al-Pt system and other two sub-binary systems (Ni-Al and Ni-Pt) from the literature. The first-principles calculations using ternary SQS are performed to calculate the enthalpies of mixing for the fcc, bcc, B2 and L12 phases, and through this approach the challenge of scarce experimental thermochemical data for the ternary solid solution phases can be overcome. The thermodynamic database of the Ni-Al-Cr-Hf-Pt system is generated by combining the remodeled Al-Pt and Ni-Al-Pt system with the other constituent binary and ternary systems in the literature. Apart from the highlighting the development of the thermodynamic database of the Ni-Al-Cr-Hf-Pt system, the dissertation also gives an understanding of the influence of alloying elements on the elastic and thermal expansion properties of Ni and Ni3Al alloys based on the first-principles calculations. The alloying element of Al, Co, Cr, Cu, Fe, Hf, Mo, Nb, Pt, Re, Ta, Ti, W, Y and Zr are considered for elastic properties of Ni alloys, and Al, Cr, Hf, Pt, Y and Zr are selected for elastic properties of Ni3Al alloys and thermal expansion properties of Ni and Ni3Al alloys. The efficient strain-stress method is used to predict the elastic properties of the Ni base alloys by the resultant change of stress due to the applied strain. The calculated elastic constants are correlated to ductility, solid solution strengthening and elastic anisotropy, thus providing a better understanding of the mechanical properties of Ni alloys with alloying elements. The effect of each element on the elastic properties is analyzed in terms of the volume change, electron density and alloying element’s elastic properties, and the elastic constant change rates of the alloying element are obtained. The first-principles quasiharmonic approach is used to investigate the effect of alloying element on the coefficients of thermal expansion (CTE) of γ-Ni and γ’-Ni3Al phases. The Helmholtz free energy as function of volume and temperature is used to estimate the finite temperature thermodynamic properties, including the 0K static energy, vibrational and thermal electronic contributions. The static energy at 0K is obtained by fitting the energy vs. volume data points with the four parameters Birch-Murnaghan equation of state. The vibrational contribution is estimated from Debye model for the sake of the efficiency and simplicity. The validity of Debye model is carefully tested for both Ni and Ni3Al by comparing the results with experiments and phonon calculation results. The change rates of the coefficients of thermal expansion due to the alloying element at elevated temperatures in γ-Ni and γ’-Ni3Al phases are obtained. By combining the obtained elastic constant and CTE change rates from the first-principles calculations with the thermodynamic properties such as mole fraction, site fraction and phase fraction of an alloy calculated from thermodynamic databases, the elastic constant and CTE for Ni base alloys consisting of γ and γ´ phases is predicted. The methodology and results presented in the dissertation provide a better understanding of the mechanical properties of γ and γ′ phases of Ni base alloys and can also be a bench mark to study the same properties not only for other phases in Ni base alloys but also for other alloy systems with different major element, for example, Al base alloys.