We present a theoretical study of the influence of the relativistic effects on electronic band structure and thermopower of Mg2X(X= Si, Ge, Sn) semiconductors. The full potential Korringa-Kohn-Rostoker (KKR) method is used, and the detailed compariso
n between the fully relativistic and semi-relativistic electronic structure features is done. We show that the spin-orbit (S-O) interaction splits the valence band structure at Gamma point in good agreement with the experimental data, and this effect strongly depends on X atom. The S-O modifications of the topology of the Gamma-centered hole-like Fermi surface pockets lead to a change in electron transport properties, which are investigated using the Boltzmann approach. In addition, the simple and efficient method is presented for the calculation of density of states effective mass m*, and then used to examine the impact of relativistic effects on m*. It is found that S-O coupling of the valence bands reduces effective mass and therefore significantly lowers the thermopower, primarily in Mg2Sn, but also in Mg2Ge. A detrimental influence of the S-O interaction on thermoelectric performance of p-type Mg2X is analyzed in function of temperature (10-900 K) and carrier concentration (10^18-10^22 cm-3). Interestingly, similar calculations in n-type Mg2X, show negligible effect of the S-O interaction on lowest conduction bands and consequently also on the Seebeck coefficient.
Formation energy of the sigma-phase in the Fe-V alloy system, Delta E, was computed in the full compositional range of its occurrence (34 < x < 60) using the electronic band structure calculations by means of the KKR method. Delta E-values were found
to strongly depend on the Fe concentration, also its variation with different site occupancies was characteristic of a given lattice site. Calculated magnetic and configuration entropy contributions were used to determine sublattice occupancies for various compositions and temperatures. The results agree well with those obtained from neutron diffraction measurements.
Formation energy of the $sigma$-phase in the Fe-Cr alloy system, $Delta E$, was computed versus the occupancy changes on each of the five possible lattice sites. Its dependence on a number of Fe-atoms per unit cell, $N_{Fe}$, was either monotonically
increasing or decreasing function of $N_{Fe}$, depending on the site on which Fe-occupancy was changed. Based on the calculated $Delta E$ - values, the average formation energy, $<Delta E>$, was determined as a weighted over probabilities of different atomic configurations. The latter has a minimum in the concentration range where the $sigma$-phase exists. The minimum in that range of composition was also found for the free energy calculated for 2000 K and taking only the configurational entropy into account.
Magnetic properties of a $sigma-$Fe$_{16}$Cr$_{14}$ alloy calculated with the charge and spin self- consistent Korringa-Kohn-Rostoker (KKR) and combined with coherent potential approximation (KKR-CPA) methods are reported. Non-magnetic state as well
as various magnetic orderings were considered, i.e. ferromagnetic (FM) and more complex anti-parallel (called APM) arrangements for selected sublattices, as follows from the symmetry analysis. It has been shown that the Stoner criterion applied to non-magnetic density of states at the Fermi energy, $E_F$ is satisfied for Fe atoms situated on all five lattice sites, while it is not fulfilled for all Cr atoms. In FM and APM states, the values of magnetic moments on Fe atoms occupying various sites are dispersed between 0 and 2.5 $mu_B$, and they are proportional to the number of Fe atoms in the nearest-neighbor shell. Magnetic moments of Cr atoms havin much smaller values were found to be coupled antiparallel to those of Fe atoms. The average value of the magnetic moment per atom was found to be $<mu>=0.55 mu_B$ that is by a factor of 4 larger than the experimental value found for a $sigma-$Fe$_{0.538}$Cr$_{0.462}$ sample. Conversely, admitting an anti- parallel ordering (APM model) on atoms situated on C and D sites, according to the group theory and symmetry analysis results, yielded a substantial reduction of $<mu>$ to 0.20 $mu_B$. Further diminution of $<mu>$ to 0.15 $mu_B$, which is very close to the experimental value of 0.14 $mu_B$, has been achieved with the KKR-CPA calculations by considering a chemical disorder on sites B, C and D.
