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FIRST PRINCIPLES ANALYSIS OF MECHANICAL STABILITY OF SOLID CRYSTALS
Řehák, Petr ; Buršík, Jiří (referee) ; Šob, Mojmír (referee) ; Černý, Miroslav (advisor)
The aim of the author’s research in the period of his PhD study was the analysis of mechanical stability of cubic crystals under external loading. This work demonstrates several methods used for a study of mechanical stability of fcc crystals (C, Al, Ir, Pt, Au) during isotropic (hydrostatic) tensile loading. Ab initio methods were used for this purpose. Studied crystals were subjected to simulated isotropic tensile deformation and an analysis of elastic stability was performed. This analysis shows that first elastic instability in Al, Pt and Au crystals corresponds to vanishing of the trigonal shear modulus and diamond, Ir remains stable up to the state of maximum isotropic stress. According to the calculated band structure diamond crystal preserves his insulating character up to the onset of instability. Consequently, phonon spectra of all crystals were calculated using the linear response method and their dynamic stability was assessed. Obtained results reveal soft phonon modes in Al, Pt and Ir before an occurrence of elastic instability. Selected short-wavelength instabilities are confirmed using models of microscopic deformation and also using dispersion curves obtained by a supercell method. The observed instabilities lower critical strains related to the volumetric instability up to 40 % whereas the reduction of critical stress is by 20 % at the most.
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Magnetic shape memory alloys - ab initio approach
Heczko, Martin ; Šesták, Petr (referee) ; Zelený, Martin (advisor)
This Bachelor’s thesis is focused on theoretical study of magnetic shape memory alloys based on Ni2MnGa using ab initio calculations of electronic structure within the projector augmented wave method. In particular, the effect of increasing concertation of manganese instead of gallium was studied on total-energy and magnetic moment profiles along the tetragonal deformation path between austenite phase with cubic L21 structure and phase of nonmodulated martensite. Further, the effect of manganese atoms distribution within the gallium sublattice was studied as well as changes of this distribution under applied tetragonal deformation. At last but not at least, the elastic constants for austenitic and martensitic structures of studied alloys were calculated. The results show that the non-modulated martensite stabilized with increasing concentration of manganese, because its total energy decreased. The energetic barrier between austenitic and martensitic structures also decreased, which means the metastable austenite will change to unstable.
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Computer modeling of twin-boundaries in shape memory alloys
Heczko, Martin ; Pokluda, Jaroslav (referee) ; Zelený, Martin (advisor)
This Master‘s thesis is focused on theoretical study of twinning in magnetic shape memory alloys based on Ni2MnGa using ab initio calculations of electronic structure within the projector augmented wave method. In particular, the effect of increasing concentration of manganese at the expense of gallium was studied on total energy and stress profiles along different deformation paths in the (10-1)[101] shear system of non-modulated martensite. Further, this work deals with the effect of the concentration of manganese on the energy of planar fault caused by presence of partial dislocation due to motion of twin boundary. The results show that the shear modulus in studied shear system increases with the increasing concentration of manganese as well as energy barrier and deformation characteristics along shear deformation paths increases, which makes the shear more difficult in Mn-rich alloys. Increasing concentration of manganese also leads to rising the planar fault energy. All these effects can be responsible for lower mobility of twin boundaries in alloys with higher concentration of manganese.
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Computer modeling of high-entropy alloys
Papež, Pavel ; Jan, Vít (referee) ; Zelený, Martin (advisor)
This Master’s thesis is focused on theoretical study of the high entropy alloy CoCrNi using ab initio calculations. The focus was on the effect of short range order on the relative stability of FCC and HCP structures and the value of stacking fault energy.The results show increase of stability in both types of structures wtih decreasing number of Cr-Cr nearest neighbours. The effect of the number of Cr-Cr nearest neighbours on the stacking fault energy previously shown in literature was not observed. However the strong dependency was found on the change of short range order caused by the shift of (1 1 1) planes after the transformation from the FCC to HCP structure. The effect of interstitial atoms C a N was also studied. Both these interstitials stabilise FCC structure and thus cause the increase of stacking fault energy. Both interstitials prefer octahedral positions with higher amount of Cr in their nearest neighbour shell.
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Stability of crystalline solids from first principles
Řehák, Petr ; Šob, Mojmír (referee) ; Černý, Miroslav (advisor)
This work deals with study of stability of solid crystals under isotropic loading. Ab initio methods were used for this purpose. Crystals of four fcc metals (Al, Cu, Ir, Au) and diamond were subjected to simulated isotropic tensile deformation and maximum value of isotropic stress was evaluated for them. Consequently, phonon spectra were calculated for several strain values in order to assess crystal stability. Phonon instabilities in dispersion curves of diamond, Al, Ir and Au appeared at strains lower than those corresponding to their decohesion. This appearance of instability determinates the value of ideal strength. However, significant reduction (by about 20%) was found only in the cases of Au and Ir.
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Ab-initio calculation of structures´ stability of Ni-N compounds
Šárfy, Pavlína ; Vřešťál,, Jan (referee) ; Šob,, Mojmír (advisor)
The present thesis is devoted to ab initio study of electronic structure of nickel nitrides NiN, Ni2N, Ni3N and Ni4N. The results are used to predict the most stable structures for each composition. The total energies and the electronic structures are calculated by means of the pseudopotential method implemented in the Abinit code and by full-potential linearized augmented plane wave (FLAPW) method incorporated in the Wien2K code. For the exchange-correlation energy, both the local density approximation (LDA) and generalized approximation (GGA) are employed. We predicted the face centered cubic structure B3 as the most stable modification of NiN, the primitive tetragonal structure C4 as the most stable modification of Ni2N, the hexagonal structure as the most stable modification of Ni3N (in agreement with experimental data) and the primitive cubic structure as the most stable modification of Ni4N.
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The effect of impurities on the interface cohesion in multilayers in transition metal nitrides
Češka, Jakub ; Zelený, Martin (referee) ; Černý, Miroslav (advisor)
This work deals with the study of transtition metal nitride multilayers using first-principles calculations. Objects of this study are three particular systems AlN / TiN, AlN / VN and TiN / VN. Studied systems are in the B1 structure with an interface along the (001) plane. The main goal is to unravel the effect of impurity on cohesion in these multilayers. The impurity in question is a substitutional O atom replacing N in the lattice. Preferred positions of these substitutions are predicted for three different concentrations of substitution impurity. These predictions are based on the energy balance of substitutions in different positions. Resulting preferred positions within the multilayer may differ depending on the oxygen concentration. In most cases, the preferred position is at the interface between the two nitrides. For such systems with oxygen impurity in the preferred position a cleavage energy along several (001) planes is calculated. The effect of the impurity on the value of cleavage energy depends on its concentration. In the case of AlN / TiN multilayer, a suitable concentration of the impurity may increase the cleavage energy of the weakest link in multilayer compared to clean multilayer. In other cases the presence of impurity either causes a decrease in the cleavage energy or does not significantly affect its value.
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Ab initio calculation of doping in Ni2MnGa alloy
Janovec, Jozef ; Černý, Miroslav (referee) ; Zelený, Martin (advisor)
Cieľom tejto práce je teoretické štúdium systému Ni-Mn-Ga, vykazujúceho efekt magnetickej tvarovej pamäti. Pri výpočtoch bola použitá metóda Exaktných Mufiin-Tin Orbitálov v kombinácii s aproximáciou koherentného potenciálu vrámci Korringa-Kohn-Rostoker formalizmu. Totálna energia bola spočítaná pomocou metódy úplnej nábojovej hustoty. Skúmaný bol vplyv dopovania zinkom alebo kadmiom na totálne energie pozdĺž tetragonálnej deformačnej dráhy a následne na teplotu martenzitickej premeny TM a Curieho teplotu TC. Taktiež boli skúmané nestechiometrické zliatiny prebytkom Mn na úkor Ga. Výsledky predikujú nárast TM po všetkých pozorovaných substitúciách v podmriežke Ga a pokles TM po substitúciách v podmriežke Mn. Curieho teplotu znižujú všetky študované substitúcie s výnimkou zmeny magnetického usporiadania v martensite nestechiometrickej zliatiny.
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Computational prediction of solubility limits in solid solutions
Fikar, Ondřej ; Friák, Martin (referee) ; Zelený, Martin (advisor)
This diploma thesis is focused on a theoretical study of the phase stability of solid solutions in selected aluminium and silver alloys. The ab initio calculations were performed using projected augmented waves method and the thermal dependencies of thermodynamic quantities were acquired using phonon calculations. The main focus of this work is the of aluminium-germanium alloy, while the other examined alloys (Al-Pb, Ag-Ge and Ag-Pb) serve the purpose of comparison of the solid solubility prediction and its reliability in systems with different composition. The temperatures, at which the solid solutions become stable, were evaluated using the energy difference between possible states and this evaluation was carried out for different contributions to the total energy. Also the electronic and phonon densities of states were calculated for all pure elements and solid solutions. The temperatures of solubility were compared to the experimental ones provided by the CALPHAD method and the individual contributions to the total energy were determined and depicted. The results obtained in this work tend to underestimate temperatures of solubility of individual solid solutions by hundreds of Kelvin.
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