# Theoretical description of Ti and Ti alloys from first principles

Sammanfattning: Modern world is known for many advanced technologies and solutions to complex problems. Technical progress runs at high speed. In order to most effectively use materials, given to us by Nature, it is important to know their properties. To do laboratory experiments is often too expensive and time consuming. Therefore, it is very important to possess the knowledge and capabilities of studying materials properties without actual experiments. I use different methods based on the laws of Quantum mechanics to conduct my investigations. In this work I studied from first principles properties of titanium and titanium alloys that are of potential interest for various applications. Titanium was chosen because of its unique properties, which are both useful and reveal interesting physics. First, I investigated elastic properties using density functional theory (DFT) in different implementations, such as the projector augmented wave (PAW) and the exact muffin-tin orbitals (EMTO) methods. The single crystal’s elastic constants Cαβ of pure Ti, Ti-V, and Ti-Ni-Al alloys were obtained by calculating the total energy as a function of appropriate strains or stress-strain relations. Disordered substitutional alloys were modeled using a special quasi-random structure (SQS) technique combined with PAW as well as the coherent potential approximation (CPA) combined with EMTO. The concentration dependence of Cαβ and also the family of material characteristics, such as Young’s modulus E, bulk modulus B, shear modulus G, Cauchy pressure Pc, Pugh’s coefficient k, and Poisson’s coefficient ν for the TiV system were estimated and discussed. The elastic properties of alloys in the Ni-Al- Ti system were also calculated and analyzed, as well as the temperaturedependent elastic constants of pure Ti. The influence of the amount of V on the mechanical phases stability of body-centered cubic (bcc) Ti-V alloys was studied. It was found that Ti-rich Ti-V alloys are mechanically unstable in the bcc phase, but at higher concentration of V in the system the mechanical stability is increased. It was found that the Ni-Al-Ti system is mechanically stable in accordance with the requirements of mechanical stability for a cubic crystal. The first-principles calculations yielded solution enthalpies for B2 and bcc solid solution alloys. The enthalpies of bcc Ti-V alloys were calculated from first principles at 0 and 1300 K as a function of concentration using static and molecular dynamics simulations. The enthalpy curves for the B2 Ti-V alloys were described as a function of the V concentration by using the calculated solution enthalpies. The enthalpies of the β-phase Ti-V alloys decrease with increasing concentration of vanadium in the range from 0 to 1. Next, selfdiffusion in pure Ti was studied at high temperature using classical and ab initio molecular dynamics. We reveled a physical mechanism entailing a rapid collective movement of numerous (from two to dozens) neighboring titanium atoms along tangled closed-loop paths in defectfree crystal regions. Further, we addressed the effect of atomic relaxations on the formation enthalpy and the size of the tetra and octa voids in the body-centered cubic (bcc) high entropy alloys (HEA), where one of the principal elements is Ti. These are the alloys with 5 different components in equal proportions, which recently become the objects of extensive research due to their interesting properties, such as, for example, combined toughness and plasticity as well as corrosion resistance. We found that the relaxations are crucial and can change the energetically preferable distribution of elements in the periodic bcc lattice from segregated to random-alloy-like. The tetra and octa voids in HEAs can accommodate interstitial impurities that can be of interest to improve the alloy properties. We found that the distribution of void volumes due to atomic relaxations can be described by a set of Gaussians, whose number depends on the type of the void and the atomic distribution (random vs segregated). It could also be important that the largest volumes of the voids due to atomic relaxations are increased by nearly 25%.

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