Study on the Melting of the Defective Interstitial Alloys TaSi and WSi with BCC Structure

Study on the Melting Temperature, the Jumps of Volume, Enthalpy and Entropy at Melting Point, and the Debye Temperature for the BCC Defective and Perfect Interstitial Alloy WSi under Pressure

“…Metals and interstitial alloys [1][2][3][4][5] have been investigated by several research groups in the last decades due to their applications in various fields [6][7][8][9]. Many theoretical and experimental studies about the mechanical and thermodynamic properties of metals and interstitial alloys gained scientific and technological attention and represent an active area of research that requires integrating modern scientific insights [10][11][12][13][14] from multiple disciplines [15][16][17][18][19].…”

“…In it, the A metal has atoms in the center and peaks of cubic, while the atoms of B are in the center of cubic. With the parameters k, γ 1 , γ 2 , γ, the cohesive energy u 0 with the sphere center at the position of B, radii r 1B and r 2B are determined as follows [1][2][3][4]29,33]:…”

“…where u iβ , n i , and r 1B = r 01B + y 0A 1 (T) are the displacements of the ith atom in the direction of β, α, β = x, y, z, α = β, the number of atoms on the ith coordination sphere with radius r i (i = 1, 2), and the nearest neighbor distance between the interstitial atom B and the main metal A in the alloy at temperature T; y 0A 1 (T) and r 01B are the displacements of atom A 1 (atom A in the body center of the cubic unit cell) from the equilibrium position at temperature T, determined from the minimum condition of the cohesive energy u 0B , and the nearest neighbor distance between the interstitial atom B and the main metal A in the alloy at temperature 0 K; ϕ AB is the interaction potential between atom A and atom B. The cohesive energy u 0 and the alloy parameters k, γ 1 , γ 2 , γ for atom A 1 (atom A in the body center of the cubic unit cell) in the approximation of three coordination spheres with the sphere center at the position of A 1 and the radius r 1A 1 of the third coordination sphere are determined as follows [1][2][3][4]29,33]:…”

“…where r 1A 1 ≈ r 1B is the nearest neighbor distance between atom A 1 and the other atoms in the alloy. The u 0 , k, γ 1 , γ 2 , γ are the cohesive energy and the alloy parameters for atom A 2 (atom A in the peaks of the cubic unit cell) in the approximation of three coordination spheres, with A 2 and radius r 1A 2 of the third coordination sphere as follows [1][2][3][4]29,33]:…”

“…where r 01A (P, 0), r 01A (P, 0), r 1A (P, T), r 01A (P, 0) and c B are the mean nearest neighbor distances between two atoms A in the clean metal A at pressure P and temperature 0 K; the region containing the interstitial atom C of the alloy at P and T = 0 K, and the concentration of the interstitial atoms B and nearest neighbor distance between two atoms A in the alloy at P and T and at P and T = 0 K. The Helmholtz free energy of the BCC perfect interstitial alloy AB with the condition c B << c A (c A , c B , respectively, are the concentrations of atoms A and B) can be calculated with the following relations [1][2][3][4]:…”