The theoretical investigation of the superconductivity mechanism of some Nb rich A15 type materials

The theoretical study of materials' structural, electronic, elastic, and vibrational properties is essential for the progress of science and technology. Detailed examination of these properties will benefit the more accurate, healthy, and efficient use of materials in technology and industry. In recent years, a theoretical method known as Density Functional Theory (DFT) has found extensive application in various fields, including physics, chemistry, geology, materials science. DFT is an effective method that allows for a detailed examination of the fundamental properties of materials. This method has garnered significant interest from researchers due to its ability to produce results consistent with experimental findings. The reason for DFT's popularity lies in its basis on first principles. As a result, the properties of the materials under investigation can be determined without the need for any experimental data. The progress in computing capabilities and computational prowess more quickly have facilitated the more widespread use of this method. To date, theoretical calculations obtained with DFT have provided results that are nearly perfect when compared with experimental data. Additionally, in situations where experimental studies cannot be conducted, this method allows for the determination of ground-state properties. Today, DFT is a powerful research method used in many scientific disciplines. This method enables researchers to determine the properties of new materials and to develop new technologies. The objective of this thesis is to examine the superconducting characteristics of niobium-based Nb3X (X: Ge, Sb, Os, Ir, Pt, Rh) compounds with a cubic A15 structure. The lattice constant was found for Nb3X compounds by geometrical optimisation. The lattice constants for the Nb3X compounds were found to be 5.169 Å for Nb3Ge, 5.301 Å for Nb3Sb, 5.17 Å for Nb3Os, 5.173 Å for Nb3Ir, 5.195 Å for Nb3Pt, and 5.174 Å for Nb3Rh. The previously reported theoretical and experimental values for Nb3X compounds in the literature are as follows: 5.151 Å and 5.152 Å for Nb3Ge, 5.294 Å and 5.262 Å for Nb3Sb, 5.16 Å and 5.14 Å for Nb3Os, 5.158 Å and 5.132 Å for Nb3Ir, 5.189 Å and 5.156 Å for Nb3Pt, and 5.182 Å and 5.115 Å for Nb3Rh. Comparing these values with our results, we found an excellent agreement. This demonstrates the validity of the selected theoretical approach and the computations conducted for the structural parameters. Calculations on elasticity show that Nb3X compounds are ductile, while electronic calculations show that they are metallic. Also the electronic properties show that the Nb 4d states play an essential role in the electronic near the Fermi level density of states. At the Fermi level (N(EF)) the density of states detected as 1.609 states/eV.atom for Nb3Ge, 0.441 states/eV.atom for Nb3Sb, 0.664 states/eV.atom for Nb3Os, 0.758 states/eV.atom for Nb3Ir, 1.032 states/eV.atom for Nb3Pt, and 0.709 states/eV.atom for Nb3Rh. The higher superconducting transition temperatures of Nb3Ge and Nb3Pt compared to the other compounds can be attributed to their higher N(EF) values. Following the evaluation of electronic properties, the stress-strain method and the Voight-Reuss-Hill (VRH) approach were utilized to ascertain the elastic constants and mechanical characteristics of the Nb3X compounds. The calculated elastic constants indicate that the Nb3X compounds with a cubic A15 crystal structure are mechanically stable according to the Born criteria. Additionally, using the obtained elastic constants, the flexibility and brittleness of the Nb3X compounds were examined through Cauchy pressure, Poisson's ratios, and BH/GH ratios. It was determined that the compounds exhibit a ductile nature. The BH/GH and Poisson's ratios for the Nb3X compounds indicate that the Nb3Ge compound has the most ductile character. Alongside investigating the structural, elastic and electronic features of Nb3X compounds, it is crucial to study their vibrational properties in detail to theoretically elucidate the source of superconductivity, which is the aim of this thesis. When the phonon dispersion graphs of Nb3X compounds are examined, the absence of a negative phonon mode indicates that the A15 crystal structure of the compounds is dynamically stable. The dynamic properties reveal that the phonon dispersion curves calculated for Nb3X compounds do not contain any gaps despite the significant mass differences between Nb and X atoms. It is noteworthy the way in which the vibrations of Nb atoms are crucial in shaping the peak optical phonon mode in Nb3X compounds. The calculated phonon modes for Nb3X closely match the experimental results, further proving the accuracy for our calculations. Additionally, it was determined that the low-frequency phonon modes significantly influence the electron phonon coupling parameter. Phonon density of state plots of Nb3X were analyzed and it was concluded that the largest contribution phonon modes for all compounds come from Nb atoms in the region outside a very small frequency range for Nb3Ge and in the region above 4.2 THz and 3THz for Nb3Os and Nb3Pt, respectively. This result demonstrates that Nb atoms appear to play a predominant role in the superconductivity of these compounds. Subsequently, parameters related to superconductivity were obtained utilizing electronic and phonon features. Electron phonon coupling parameters for Nb3X compounds were determined as follows: 2.056 for Nb3Ge, 0.387 for Nb3Sb, 0.41 for Nb3Os, 0.51 for Nb3Ir, 1.253 for Nb3Pt, and 0.571 for Nb3Rh. When these values are ordered from largest to smallest, it is evident that Nb3Ge has the highest electron-phonon interaction parameter, followed by Nb3Pt, with the other compounds having significantly lower values. This dramatic difference helps explain why the superconducting temperatures of Nb3Ge and Nb3Pt differ so much from those of the other compounds, in addition to the N(EF) factor. Furthermore, the logarithmic average phonon frequencies (ω_ln) for the Nb3X compounds were determined to be 170.58 K for Nb3Ge, 219.73 K for Nb3Sb, 222.97 K for Nb3Os, 222.05 K for Nb3Ir, 128.49 K for Nb3Pt, and 201.93 K for Nb3Rh. Using these values, the estimated superconducting transition temperatures (Tc) were found to be 23.37 K for Nb3Ge, 0.31 K for Nb3Sb, 1.05 K for Nb3Os, 1.8 K for Nb3Ir, 10.82 K for Nb3Pt, and 2.68 K for Nb3Rh. The Tc values reported in the literature for Nb3X compounds are 23.2 K for Nb3Ge, 0.20 K for Nb3Sb, 1.05 K and 0.943 K for Nb3Os, 1.7 K for Nb3Ir, 10.9 K for Nb3Pt, and 2.64 K for Nb3Rh. These experimental values show excellent agreement with our results. The theoretical investigation of the superconductivity mechanism of some nb-rich A15 type materials is aimed to understand the superconductivity mechanism of these niobium-based compounds in the cubic A15 structure with these parameters calculated as a result of the study. The structural parameters are in agreement with previous experimental values. The electronic structure parameters suggest a 3D metallic character for these materials. Using the calculated elastic constants and Born criteria for Nb3X compounds, it is found that Nb3X compounds are mechanically stable in the cubic A15 crystal structure. The order of BH/GH and Poisson ratios is Nb3Ge>Nb3Os>Nb3Pt>Nb3Rh>Nb3Ir>Nb3Sb. The absence of a negative phonon mode in the phonon dispersion graphs of the studied compounds showed that the A15 crystal structure of the compounds is dynamically stable. Moreover, the calculated phonon modes for Nb3X compounds showed high agreement with the previous experimental results and proved the accuracy of our calculations. It is found that low-frequency phonon modes contribute more to the electron-phonon interaction parameter and Nb atoms play a dominant role in the superconductivity formation for all Nb3X compounds. The largest electron-phonon interaction parameter was found to be first for Nb3Ge and then for Nb3Pt, with the other compounds taking much smaller values compared to these two. The difference between the electron-phonon interaction parameter and N(EF) values reveals why the superconductivity temperatures between Nb3Ge and Nb3Pt and other compounds are very different. The Tc values of Nb3X compounds were obtained and found to be in excellent agreement with the experimental values.