Vibrations in solids : From first principles lattice dynamics to high temperature phase stability

Abstract

In this thesis I introduce a new method for calculating the temperature dependent vibrational contribution to the free energy of a substitutionally disordered alloy that accounts for anharmonicity at high temperatures. This method exploits the underlying crystal symmetries in an alloy to make the calculations tractable. The validity of this approach is demonstrated by constructing the phase diagram via direct minimization of the Gibbs free energy of a notoriously awkward and technologically important system, Ti 1-x Al x N. The vibrational entropy including anharmonic effects is shown to be large and comparable to the configurational entropy at high temperatures, and with its inclusion, the theoretical miscibility gap of Ti 1-x Al x N is reduced from 6560 K to 2860 K, in line with atom probe experiments. A similar treatment of Zr 1-x Al x N and Hf 1-x Al x N alloys suggests that mass disorder has a minimal effect on phase stability compared with chemical ordering. My method is also capable of demonstrating that Hf 1-x Al x N, which is dynamically unstable at room temperature, is stabilised at high temperatures. Moreover I develop a new method of computing temperature dependent elastic constants for alloys from their phonon spectra, and show that for Ti 1-x Al x N, the elastic anisotropy is found to increase with temperature, helping to explain the spinodal decomposition.The effects of lattice dynamics on phase stability, mechanical, magnetic and transport properties on other materials are also examined. Four specific systems are discussed in detail. Firstly, in the case of CrN, lattice vibrations are shown to decrease the antiferromagnetic to paramagnetic phase transition temperature from 500 K to 380 K, in line with experimental evidence. Secondly, a temperature/pressure induced phase transition in AlN becomes much more facile than in the quasiharmonic approximation, and the thermal conductivity of the rocksalt phase is shown to be much lower than that of the wurtzite phase, as a result of the increased anharmonicity in the rocksalt structure. Thirdly, the temperature dependence of elastic constants of TiN becomes more isotropic as the temperature increases. Finally, iron carbides are evaluated as potentially important phases at the Earth's core; specifically, calculating the Gibbs free energy of a recently discovered orthorhombic phase of Fe 7 C 3 demonstrates that it is not stable relative to the known hexagonal phase at extreme pressure and temperatures.V Popular science summary Solid materials can be described using a simple mathematical model from the theory of lattice dynamics. In a solid, atoms are arranged in a regular and repeating structure (a lattice), and the forces between them can essentially be modelled as springs. Despite the simplicity of this model, it is possible to derive a surprising amount of information on materials from it. One can determine which arrangements of atoms, or phases, form the stable microscopic structures that we encounter in the real world, their mechanical properti...

Thermal and mechanical stability of wurtzite-ZrAlN/cubic-TiN and wurtzite-ZrAlN/cubic-ZrN multilayers

“…At even higher temperatures this alloy further decomposes into its thermodynamically stable phases c-TiN and wurtzite (w-) AlN [9] that deteriorates the mechanical properties [10,11]. The related Zr 1-x Al x N alloys display characteristics similar to Ti 1-x Al x N with a miscibility gap for cubic solid solutions and a higher driving force for decomposition compared to Ti 1-x Al x N [12,13] resulting in promising mechanical properties [14][15][16][17][18] at high temperature. In addition to cubic solid solutions, wurtzite structured Zr 1-x Al x N solid solutions have high thermal stability when the Al content is higher than ~70% [13].…”

Temperature-dependent elastic properties of Ti1−xAlxN alloys

“…Using the temperature dependent effective potential (TDEP) method, [18][19][20] one can calculate the finite temperature phonon spectra, which implicitly include renormalization to all orders of anharmonicity, and thus derive the force constants, which we use to obtain the elastic constants from Eq. (2).…”

Density Functional Studies of Electronic Structure, Chemical Bonding and Thermodynamic Properties of Ternary Lanthanum-Gold-Cadmium Inorganic Materials

“…This is due to the fact that as pressure increases, the volume of unit cell decreases, results smaller space for energies of the particles. So they are less spread out and hence entropy decreases [23].…”