A theoretical study of the stability of Zr-Al-C and Ti-Al-C MAX phases

Abstract

MAX phases have garnered considerable research attention due to their unusual combination of metallic and ceramic properties that make them desirable materials especially in applications requiring extreme operating conditions. Zr-Al-C MAX phases specifically, are of particular interest in the nuclear industry where their low neutron absorption make them compelling candidates for fuel cladding materials. The synthesis of Zr-Al-C MAX phases, however, has been challenging, with the presence of impurities suggested as necessary to stabilise them [1, 2, 3] and secondary phases considered unavoidable in the reported successful synthesis of Zr$_2$AlC [4] and Zr$_3$AlC$_2$ [5]. This has led to questions as to whether the composition of MAX phases in this system is likely to change when in service. Addressing these uncertainties has been the main objective of this thesis, making the theoretical study of the thermodynamic stability of Zr$_{n+1}$AlC$_n$ of central importance. The stability of the Zr$_{n+1}$AlC$_n$ and closely related Ti$_{n+1}$AlC$_n$ MAX phases in the context of the M-A-X ternary phase diagrams and competing binary and ternary compounds, as a function of temperature, was calculated by applying density functional theory (DFT) within the quasiharmonic approximation. We found that the Zr-based MAX phases are thermodynamically unstable at room temperature, although Zr$_3$AlC$_2$ becomes stable above 500 K. Ti-based MAX phases on the other hand, show higher thermodynamic stability, with Ti$_2$AlC in particular, having the lowest formation energy of the MAX phases on the Ti-Al-C convex hull and appearing stable at all temperatures, in agreement with its reported success in synthesis. In the course of this work we also attempted to identify trends and similarities in predicted structural, elastic, thermophysical and electronic properties as well as the chemical bonding within the MAX phases in the two systems. Chemical bonding differences between the two systems, though, were not found to explain their differences in stability. Based on phonon calculations, Raman-active mode frequencies of Zr-based MAX phases and their most competing phases were also predicted, to assist in identifying phases present in a Zr$_3$AlC$_2$ synthesised sample [6]. Our predicted Zr$_3$AlC$_2$ frequencies of Raman-active modes were within 2% of peaks in the experimental Raman spectra recently measured by Lyons [6].