The quantum theory of solid-state atomic bonding

Solid-state bonding refers to the bonding of solid material A and solid material B. Numerous experimental data have shown this possibility. Neither principle nor theory at the atomic level has been reported. How is solid-state bonding possible? Fundamentally, it is possible only if materials A and B can be brought within atomic distance. Over the years, we have proposed the principle: “As A atoms and B atoms are brought within atomic distance so that they can see each other, they will bond provided that they are willing to share the outer electrons.” This is qualitative statement. In this research, we took it one step further and established a quantitative bonding theory. It has been proved that Cu, Ag, and Au atoms do share outer electrons to form molecules: Cu
₂
, Ag
₂
, Au
₂
, CuAg, AgAu, and CuAu. The binding energy, equilibrium distance, and vibrational frequency of the molecule have been measured. They are used to fit the Morse potential energy (E) vs. atomic separation S
_atm
curve. In our model, A atoms and B atoms on the bonding interface share electrons like molecules A:B, where “:” designates 2 shared electrons. The interface is emulated as 2-D array of A:B molecules. The A molecules connect to metal A represented by conventional model of ion core submerged in an electron sea. Same is true for molecules B. The breaking strength of the bonding interface is obtained by multiplying the binding force and the number of atoms per area. The Young's modulus can also be calculated. For Cu:Cu bonding, the Young's module is 261GPa. The experimental value is 110Gpa. The strength of Cu-Ag bonding interface depends on S
_atm
between Cu and Ag atoms. The maximum strength is 25.5Gpa at S
_atm
=0.283nm. The strength decreases to 2.55 GPa at 0.481nm, 255 MPa at 0.635nm, and 25.5MPa at 0.788nm. In bonding experiments, S
_atm
is determined by the bonding conditions and the surface conditions. The bonding theory allows us to estimate how close the interface atoms have to be to achieve adequate bonding strength.