Miedema's semi-empirical calculation for enthalpy of alloys

Binary system: 

  Solute Ag Al As Au B Ba Be Bi C Ca Cd Ce4+ Ce3+ Co Cr Cs Cu Dy Er Eu2+ Eu3+ Fe Ga Gd Ge H Hf Hg Ho In Ir K La Li Lu Mg Mn Mo N Na Nb Nd Ni Os P Pb Pd Pm Pr Pt Pu Rb Re Rh Ru Sb Sc Si Sm Sn Sr Ta Tb Tc Th Ti Tl Tm U V W Y Yb2+ Yb3+ Zn Zr mole Solvent Ag Al As Au B Ba Be Bi C Ca Cd Ce4+ Ce3+ Co Cr Cs Cu Dy Er Eu2+ Eu3+ Fe Ga Gd Ge H Hf Hg Ho In Ir K La Li Lu Mg Mn Mo N Na Nb Nd Ni Os P Pb Pd Pm Pr Pt Pu Rb Re Rh Ru Sb Sc Si Sm Sn Sr Ta Tb Tc Th Ti Tl Tm U V W Y Yb2+ Yb3+ Zn Zr mole      

 Interfacial energy:

binary alloy delta H =  kJ/mole

Ternary system: 

  Element A Ag Al As Au B Ba Be Bi C Ca Cd Ce4+ Ce3+ Co Cr Cs Cu Dy Er Eu2+ Eu3+ Fe Ga Gd Ge H Hf Hg Ho In Ir K La Li Lu Mg Mn Mo N Na Nb Nd Ni Os P Pb Pd Pm Pr Pt Pu Rb Re Rh Ru Sb Sc Si Sm Sn Sr Ta Tb Tc Th Ti Tl Tm U V W Y Yb2+ Yb3+ Zn Zr mole Element B Ag Al As Au B Ba Be Bi C Ca Cd Ce4+ Ce3+ Co Cr Cs Cu Dy Er Eu2+ Eu3+ Fe Ga Gd Ge H Hf Hg Ho In Ir K La Li Lu Mg Mn Mo N Na Nb Nd Ni Os P Pb Pd Pm Pr Pt Pu Rb Re Rh Ru Sb Sc Si Sm Sn Sr Ta Tb Tc Th Ti Tl Tm U V W Y Yb2+ Yb3+ Zn Zr mole     Element C Ag Al As Au B Ba Be Bi C Ca Cd Ce4+ Ce3+ Co Cr Cs Cu Dy Er Eu2+ Eu3+ Fe Ga Gd Ge H Hf Hg Ho In Ir K La Li Lu Mg Mn Mo N Na Nb Nd Ni Os P Pb Pd Pm Pr Pt Pu Rb Re Rh Ru Sb Sc Si Sm Sn Sr Ta Tb Tc Th Ti Tl Tm U V W Y Yb2+ Yb3+ Zn Zr mole

  Interfacial energy:  A (solute) in B (solvent) :

                                A (solute) in C (solvent) :

                                B (solute) in C (solvent) :           

ternary alloy delta H =  kJ/mole       

Empirical approximation of ternary alloy enthalpy from three binary alloy enthalpies

formation enthalpy of A-B =    kJ/mole         Amount :   A= mole

                                 B-C =    kJ/mole                          B= mole    

                                 A-C =    kJ/mole                          C= mole

formation enthalpy of A-B-C =   kJ/mole  (Toop's method 1965)

                                                  kJ/mole  (Kohler's method 1960)

                                                  kJ/mole  (bonnier's method)