Dear MD society,

I have a question regarding the calculation of embedding energy of the EAM (**E**mbedded **A**tom **M**ethod potential) potential type. In the paper of “Phase stability in the Fe-Ni system: Investigation by first-principles calculations and atomistic simulations (as attached)”, it is stated that the embedding energy is calculated by inverting the universal equation of state (shown as in the picture below, **E(a)** is the crystal energy per atom relative to a set of isolated atoms, ** E_{0}** is the equilibrium cohesive energy (minimum energy of

**E(a)**),

*is the cubic lattice parameter,*

**a****is the equilibrium value of**

*a*0**,**

*a***is the equilibrium atomic volume,**

*Omega*_{0}_{}**is the bulk modulus, and**

*B***is just a parameter). I have three questions regarding this calculation:**

*beta*(1) This universal equation of state (equation 9 as shown below) is independent of electron density, but an equation of cubic lattice constant * a*, while the embedding energy

*F*should be an equation of electron density (\rho).

**Then how the equation 9 relates to the electron density?**

(2) **How the equilibrium atomic volume Omega_{0} is calculated?** Using 4/3

*pi*r^3 (r is the atomic radius =

**sqrt(2)**in fcc lattice), or

*a*/4**^3/4 (**

*a*_{0}**is the equilibrium value of**

*a*_{0}**in equation 9, this is from the paper: Atomistic modeling of the γ and γ’-phases of the Ni–Al system)?**

*a*(3) **What does the “inverting” mean here?** The embedding energy = 1 / EOS (equation of state)?

Really appreciate if anyone can provide some information here! Thanks a lot!

Best,

Jiaqi

EAM_Ni potential.pdf (332 KB)