No Arabic abstract
Using the density functional theory (DFT) formulated within the framework of the plane-wave basis projector augmented wave (PAW) method, the temperature-dependent elastic properties of MgRE (RE=Y, Dy, Pr, Sc, Tb) intermetallics with B2-type structure are presented from first-principles. Our calculations are based on the fact that the elastic moduli as a function of temperature mainly results from thermal expansion. The comparison between the predicted results and the available experimental data for a benchmark material NiAl provides good agreements. At $T=0K$, our calculated values of lattice parameter and elastic moduli for MgRE intermetallics show excellent agreement with previous theoretical results and experimental data. While temperature increases, we find that the elastic constants decrease and approach linearity at higher temperature and zero slope around zero temperature.
We have investigated the finite temperature elastic properties of AlRE (RE=Y, Tb, Pr, Nd, Dy) with B2-type structures from first principles. The phonon free energy and thermal expansion is obtained from the quasiharmonic approach based on density-functional perturbation theory. The static volume-dependent elastic constants are obtained from energy-strain functions by using the first-principles total-energy method. The comparison between our predicted results and the ultrasonic experimental data for a benchmark material Al provides excellent agreements. At T = 0K, our calculated values of lattice equilibrium volume and elastic moduli of our calculated AlRE (RE=Y, Tb, Pr, Nd, Dy) intermetallics agree well with the previous theoretical results. The temperature dependent elastic constants exhibit a normal behavior with temperature, i.e., decrease and approach linearity at higher temperature and zero slope around zero temperature. Furthermore, the anisotropy ratio and sound velocities as a function of temperature has also been discussed.
The phonon and thermodynamic properties of rare-earth-aluminum intermetallics AlRE (RE=Y, Gd, Pr, Yb) with B2-type structure are investigated by performing density functional theory and density functional perturbation theory within the quasiharmonic approximation. The phonon spectra and phonon density of states, including the phonon partial density of states and total density of states, have been discussed. Our results demonstrate that the density of states is mostly composed of Al states at the high frequency. The temperature dependence of various quantities such as the thermal expansions, the heat capacities at constant volume and constant pressure, the isothermal bulk modulus, and the entropy are obtained. The electronic contribution to the specific heat is discussed, and the presented results show that the thermal electronic excitation affecting the thermal properties is inessential.
Using first-principles calculations within the generalized gradient approximation, we predicted the lattice parameters, elastic constants, vibrational properties, and electronic structure of cementite (Fe3C). Its nine single-crystal elastic constants were obtained by computing total energies or stresses as a function of applied strain. Furthermore, six of them were determined from the initial slopes of the calculated longitudinal and transverse acoustic phonon branches along the [100], [010] and [001] directions. The three methods agree well with each other, the calculated polycrystalline elastic moduli are also in good overall agreement with experiments. Our calculations indicate that Fe3C is mechanically stable. The experimentally observed high elastic anisotropy of Fe3C is also confirmed by our study. Based on electronic density of states and charge density distribution, the chemical bonding in Fe3C was analyzed and was found to exhibit a complex mixture of metallic, covalent, and ionic characters.
We present a tutorial on the principles of crystal growth of intermetallic and oxide compounds from molten solutions, with an emphasis on the fundamental principles governing the underlying phase equilibria and phase diagrams of multicomponent systems.
First-principles based on density functional theory is used to study the phase stability, elastic, magnetic, and electronic properties of cubic (c)-Fe$_4$C. Our results show that c-Fe$_{4}$C has a ferromagnetic (FM) ground state structure compared with antiferromagnetic (AFM) and nonmagnetic (NM)states. To study the phase stability of c-Fe$_4$C, BCC Fe$_4$C, FCC Fe$_4$C, and BCC Fe$_{16}$C, where C is considered at tetrahedral and octahedral interstitial sites, are also considered. Although, the formation energy of c-Fe$_4$C is smaller than BCC Fe$_4$C, but the shear moduli of c-Fe$_4$C is negative in the FM and AFM states indicating that c-Fe$_4$C is dynamically not stable in the magnetic (FM/AFM) states. However, NM state has positive shear moduli which illustrates that instability in c-Fe$_4$C is due to magnetism and can lead to soft phonon modes. The calculated formation energy also shows that c-Fe$_4$C has higher formation energy compared with the FCC Fe$_4$C indicating no possibility of c-Fe$_4$C in low carbon steels at low temperature. The magnetic moment of Fe in c-Fe$_4$C is also sensitive to lattice deformation. The electronic structure reveals the itinerant nature of electrons responsible for metallic behavior of c-Fe$_4$C.