Phonon and thermodynamic properties of bcc transition metals using MEAM potentials

Thermal equation of states for body-centered cubic tungsten using extended analytic embedded-atom model

“…In the EAM, the total energy expression with the correction term for the atomic system is as the following [13][14][15][16][17][18][19][20][21][22]:…”

“…where E tot is the total energy of the system, ρ i is the electron density at the position of the ith atom contributed from the remaining atoms in the system, r ij is the distance between the ith atom and the jth atom, P i is the correction term variable related to the ith atom, F (ρ i ) is the embedding energy necessary to embed an atom into the host with electron density ρ i , φ(r ij ) is the pair interaction energy between the atoms i and j with the distance r ij , and M (P i ) is the energy correction in terms of P i . ρ i and P i are expressed by f (r ij ), the atomic electron density of atom j at site of atom i, as the following [15][16][17][18][19][20][21][22]:…”

“…Zhang et al [15] proposed the modified analytic embedded atom method (MAEAM) by adding an analytic correction term to the total energy expression to represent the difference between the actual total energy of a system of atoms and that calculated from the original EAM in a similar way to Pasianot et al [13] and adopting the analytic forms of the pair potential and the atomic electron density function in a similar way to Johnson [4]. MAEAM has been applied to many physical properties such as structure stability, point-defect, vibration and thermodynamics of metals [15][16][17][18][19][20][21][22].…”

“…Though many efforts were exerted to improve the model, the functions employed in AEAM/MAEAM [4][5][6][15][16][17][18][19][20][21][22] still show some drawbacks. The electron density function never considers the change of the atomic electron density distribution with respect to the distance between the neighboring atoms in the crystal or the volume occupied by an atom in the crystal.…”

“…Getting a better knowledge of the thermal equation of states (EOS), volume-pressure-temperature relations, of this metal is the basis of practical applications. Many theoretical and experimental studies on the thermal EOS of tungsten have been carried out, but the AEAM/MAEAM formalism [4][5][6][15][16][17][18][19][20][21][22] has not been applied to that because it does not guarantee the reliability of the results for physical behaviors under high pressure and high temperature, due to the nonphysical tendencies of the electron density function and embedding energy function far from the equilibrium state.…”