First-principles calculations of pure elements: Equations of state and elastic stiffness constants

Effects of Alloying Elements on Elastic, Stacking Fault and Diffusion Properties of Fcc Ni from First-principles: Implications for Tailoring the Creep Rate of Ni-base Superalloys

“…It can be seen that the shear modulus decreases with increasing equilibrium volume, agreeing with the general trend observed for elastic properties relating moduli and equilibrium volume [9]. The shear modulus values of Ni 31 X alloys are affected greatly by the properties of the respective alloying element, such as, the larger shear moduli of Ni 31 Ru and Ni 31 Os are mainly caused by the larger shear moduli of pure elements Ru and Os compared to Ni [9]. Among all of the 26 alloying elements, the largest decrease of elastic properties of Ni is due to element Y, followed by Zr and Sc.…”

Effects of Alloying Elements on Stacking Fault Energies and Electronic Structures of Binary Mg Alloys: A First-Principles Study

“…The different concentration of alloying elements is likely the reason for the discrepancy in reported data from Muzyk et al [23] and Zhang et al [22,24] Since the local chemical environments for alloying elements in I1 (ABC), I2 (ACB), and EF (ACB) are similar to that of FCC, the calculated stacking fault energies and the Mg-X supercell volumes are plotted in Figure 3 with respect to the volume of each individual alloying element X in the FCC structure. [31,38] It can be seen that the equilibrium volumes of Mg-X supercells increase almost linearly with the volume of alloying element X in the FCC structure. Consequently, it is plausible to select two alloying elements, both decreasing the stacking fault energy but changing the equilibrium volume in opposite way so that their co-segregation will be more energetically favorable due to the minimization of elastic lattice strain.…”

“…[37] The total energies of I1, I2, and EF structures as a function of volume are fitted by a four parameters Birch-Murnaghan equation of state. [38] From previously examined results looking at the effects of supercell size (on the [0001] direction), [39] it was seen that the difference between three and seven atomic layers separating the stacking faults (I1, I2 and EF) is less than 3%. The deformation electron density, [16] ρ, is calculated using the Harris-Foulkes functional, [40,41] also known as the reference state in the independent atom model.…”

“…Through the four parameters Birch-Murnaghan equation of state, [38] the total energies of I1, I2, and EF structures at equilibrium volume are obtained and [30] summarized in Table 1 along with various computational data in the literature with the majority of data for I1 from Zhang et al [22] and those of I2 from Zhang et al [24] and Muzyk et al [23] Correspondingly, the segregation behavior of the alloying element in stacking faults are obtained and shown in Figure 2. According to the crystal structures of each individual solute atom at room temperature, it can be seen that some alloying elements with HCP and FCC structures reduce the stacking fault energies the most.…”

Structural and elastic properties of TiN and AlN compounds: first-principles study

“…To calculate the elastic constants, we have used two different methods, Mehl method, [20] for the cubic system and the method developed by Shang et al [21], for the hexagonal system, with deformation δ = 0.01. Materials with cubic symmetry have only three independent elastic moduli C 11 , C 12 and C 44 .…”