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 C_αβ 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 C_αβ and also the family of material characteristics, such as Young’s modulus E, bulk modulus B, shear modulus G, Cauchy pressure P_c, 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%.

The modeling of magnetic materials at finite temperatures is an ongoing challenge in the field of theoretical physics. This field has strongly benefited from the development of computational methods, which allow to predict material’s properties and explain physical effects on the atomic scale, and are now employed to direct the design of new materials. However, simulations need to be as accurate as possible to give reliable insights into solid-state phenomena, which means that, most desirably, all competing effects occurring in a system at realistic conditions should be included. This task is particularly difficult in the modeling of magnetic materials from first principles, due to the quantum nature of magnetism and its interplay with other phenomena related to the atomic degrees of freedom. The aim of this thesis is therefore to develop methods that enable the inclusion of magnetic effects in finite temperature simulations based on density functional theory (DFT), while considering on the same footing vibrational and structural degrees of freedom,with a particular focus on the high-temperature paramagnetic phase. The type of couplings investigated in this thesis can be separated in two big categories: interplay between magnetism and structure, and between magnetism and vibrations.

Regarding the former category, I have tried to shine some light on the effect of the paramagnetic state on atomic positions in a crystal in the presence of defects or for complicated systems, as opposed to the ordered magnetic state. To model the high-temperature paramagnetic phase of magnetic materials, the disordered local moment (DLM) approach is employed in the whole work. In this framework, I have developed a method to perform local lattice relaxations in the disordered magnetic state, which consists of a step-wise partial relaxation of the atomic positions, while changing the configuration of the magnetic moments at each step of the procedure. This method has been tested on point defects in paramagnetic bcc Fe, namely the single vacancy and, separately, the C interstitial in octahedral position, and on Fe_1-xCr_x alloys, finding non-negligible effects on formation energies. In addition, the feasibility of investigating extended defects like dislocations in the paramagnetic state with this method has also been proven by studying the screw dislocation in bcc Fe. The DLM-relaxation method has then been used to investigate intrinsic and extrinsic defects in CrN, an antiferromagnetic semiconductor studied for thermoelectric applications, found in the paramagnetic state at operating temperature, and a newly synthesized compound, Fe₃CO₇, which features a complicated crystal structure and unusual electronic properties, with possible important implications for the chemistry of Earth’s mantle.

The other focus of this thesis is the coupling between magnetism and lattice vibrations. As a pre-step to perform fully coupled atomistic spin dynamics-ab initio molecular dynamics (ASD-AIMD) simulations, I have first investigated the effect of vibrations on the so called longitudinal spin fluctuations, a mechanism occurring at finite temperatures and important for itinerant electron magnetic systems. I have developed a framework to investigate the dependence of the local moment’s energy landscapes on the instantaneous positions of the atoms, testing it on Fe at different temperature and pressure conditions. This study has laid the foundation to apply machine learning techniques to the prediction of the energy landscapes during an ASD-AIMD simulation. Finally, I have investigated the phase stability of Fe at ambient pressure from the theoretical Curie temperature up to its melting point with ASD-AIMD. This task is carried out by applying a pool of thermodynamic techniques to calculate free energy differences, and therefore I have defined a strategy to discern the thermodynamic equilibrium structure in magnetic materials in the high temperature paramagnetic phase based on first principles dynamical simulations. The methodologies developed and applied in this work constitute an improvement towards the simulation of magnetic materials accounting for the coupling of all effects, and the hope is to bridge a gap between theory and experiments.