First-principles study of stability and electronic structural properties of Ag/Au/M (Cu, Ni) interface

This study investigated the interface energy, work of adhesion, and electronic structural properties at the Ag/Au/M(Cu,Ni) interface, employing the first-principles method based on density functional theory. First, the structures of various binary and ternary interfaces were optimized. Subsequently, the total density of states (TDOS), partial density of states (PDOS), charge distribution, and bonding characteristics of these interfaces were investigated. Additionally, the interface energy and work of adhesion of these interfaces were calculated. The results indicated that the Ag/Au/Ni interface exhibited higher stability and bonding strength compared to the Ag/Au/Cu interface. The contribution of the PDOS of atoms at the Ag/Au/M(Cu,Ni) interface to the TDOS can be primarily attributed to d-orbital electrons, while s- and p-orbit electrons had minimal influence on PDOS.Notably, d-d orbital hybridization emerged between the d-orbit electrons in Cu and Ni atoms and those in Ag and Au atoms, enhancing structural stability. Two distinct peaks in the TDOS of Ag/Ni, Au/Ni, and Ag/Au/Ni interfaces appeared near the Fermi level, corresponding to d-d orbital hybridization involving Ni, Ag, and Au atoms. At the Ag/Au/Cu and Ag/Au/Ni interfaces, resonance peaks corresponding to the s and p orbits of Ag and the s and p orbits of Au, as well as the d orbits of Ag and Au, indicated the presence of a relatively strong metallic bond between Ag and Au atoms. Furthermore, the Ag/Ni and Au/Ni systems exhibited greater average electron transfer compared to the Ag/Cu and Au/Cu systems. Moreover, atomic bond lengths at the Ag/Au/Ni interface were significantly less than those at the Ag/Au/Cu interface, indicating higher stability of the Ag/Au/Ni interface compared to the Ag/Au/Cu interface.


Introduction
Electrical contact materials made fromprecious metals exhibit high electrical conductivity, thermal conductivity, chemical stability, and resistance to welding and arc erosion.These materials have attracted attention owing to their ability to provide reliable electrical contact and maintain low, stable contact resistance, making them ideal for connecting and disconnecting devices [1-3].In the development of multilayer metal composite electrical contacts, precious metals are typically incorporated into the contact surface or transition layer, which not only enhances performance but also reduces costs [4,5].Conventionally, laminated composite electrical contacts are primarily composed of Ag/Cu, Au/Ag/Cu, M(Ag,Ni)/Cu, M(Ag,Ni)/Ni/M(Cu,Ni), and Au/M(Ag,Cu,Ni)/M(Cu,Ni) [6][7][8].However, few theoretical studies have investigated the stability and bonding strength of these composite interfaces [9,10].In this study, we evaluated interface energy and lattice matching for Au, Ag, and Au-Ag composites.Specifically, we constructed interface models for Au, Ag, and Au-Ag alloys with Cu and Ni substrates.Through first-principles calculations, we determined the interface energy and the degree of lattice matching for various interface combinations and optimized these combinations based on the results.
The calculations were performed using the CASTEP module in Materials Studio, employing ultrasoft pseudopotentials to describe electron-ion core interactions [12].The truncation energy was set at 400 eV, and the exchange-correlation potential used was GGA-PBEsol, with the minimization algorithm being BFGS.For the Monkhorst-Pack method in the Brillouin zone, we employed a K-point grid of 7 × 7 × 1, with the Γ-point serving as the origin of K-space, and configured the fast Fourier grid as 60 × 60 × 360.The convergence criteria for geometry optimization included: force per atom 0.03 eV Å, internal stress 0.05 GPa, atomic displacement 1 × 10 −3 Å, and system TDOS change 1 × 10 −5 eV per atom.Furthermore, the self-consistent field convergence value was set at 1 × 10 −6 eV/atom.
We optimized the bulk phase structures of pure metals Au, Ag, Cu, and Ni, all of which possess face-centered cubic (fcc) structures.Subsequently, surface relaxation calculations were performed on the (110) crystal plane of pure metals and the (100) crystal plane of Ag/Au using a slab model containing 12 atomic layers.These two slabs were then combined to construct heterogeneous interface models.To prevent interactions between identical slabs, a vacuum layer with a thickness of 20 Å was introduced between them.To simulate the effects of the bulk phase on the surface or interfacial zone, we constrained six atomic layers within the slab model.Figure 1(a) illustrates theinterface models for Ag/Cu, Ag/Ni, Au/Cu, and Au/Ni, while figure 1(b) displays the interface models for Ag/Au/Cu and Ag/Au/Ni.

Work of adhesion and interface energy of different interfaces
Firstly, the lattice parameters of Au, Ag, Cu and Ni are listed and compared with experimental data in table 1.The calculated lattice parameter of Au is found to be 2.923 Å, which is 0.8% less than the corresponding experimental value.And for Ag, the calculated lattice parameters match fairly well with the experimental ones (the error less than 0.02%).The calculated lattice constant of Cu is 2.5175 Å which is in good agreement with  that of the experimental value of 2.573 Å.And for Ni, the calculated lattice parameters match fairly well with the experimental ones (the error less than 0.9%).
In the context of composite interfacial structures, the bonding strength of an interface can be quantified using two key metrics: work of adhesion (W ad ) and interface energy (E int ) [13,14].Work of adhesion represents the energy required to separate the interface into two free surfaces per unit area.The higher the work of adhesion, the stronger the mechanical integrity of the interface [15].For the Ag/Ni interface, W ad can be calculated as follows [16]: where E Ag Ni / is the total energy of the Ag/Ni composite interface, E Ag and E Ni correspond to the free energy of the individual silver and nickel layers, respectively, forming the interface, and A represents the interface area.When Ag/Au is considered as a solid solution in the construction of interface models for Ag/Au/Cu and Ag/ Au/Ni, it simplifies the calculation of the work of adhesion, which is similar to that of binary interfaces.A comparison between the Ag/Ni and Ag/Cu interfaces reveals that the former exhibits higher work of adhesion, indicating superior bonding strength.Similarly, Au/Ni demonstrates higher bonding strength than Au/Cu.Therefore, the Ag/Au/Ni interface outperforms Ag/Au/Cu in terms of bonding strength.
Interface energy reflects the energy difference per unit surface area between two free surfaces after the formation of a complete interface [17].This energy difference is attributable to atomic distortion at the interface, changes in chemical bonding, and structural strain-induced energy differences.A higher interface energy suggests a greater energy requirement for interface formation [18].Conversely, lower interface energy facilitates interface formation and enhances stability in composite interfacial bonding.For a Ag/Ni interface, the formula for interface energy (E int ) can be expressed as follows [19]: where E surface Ag , and E surface Ni , represent the surface energy of Ag and Ni free surfaces respectively.E surface can be derived as follows [20]: where E tot surface and E tot bulk represent the total energy of the surface and bulk phases, respectively, and A denotes the interface area.Table 2 summarizes the work of adhesion and interface energy for various interfaces.Notably, interface energy exhibits a negative correlation with separation work, facilitating interface formation and enhancing bonding stability.Calculations of work of adhesion and interface energy revealed the superior stability and bonding strength of the Ag/Au/Ni interface compared to Ag/Au/Cu.Remarkably, the Au/Ni interface exhibited the highest stability and bonding strength among the interfaces.

Analysis of density of states
The density of states (DOS) provides insights into the energy state contributions of interfacial atoms.Figures 2(a) to 2(f) illustrate the DOS models for Ag/Cu, Ag/Ni, Au/Cu, Au/Ni, AgAu/Cu, and AgAu/Ni interfaces.Across all interfaces, the energies contributing to bonding are predominantly concentrated within the −13 to −25 eV range.The contribution of the partial density of states (PDOS) to the total density of states (TDOS) can be attributed to the presence of d-orbital electrons.In the lower energy range (−7 to 0 eV), the TDOS is primarily influenced by the d-orbital electrons of Cu and Ni, as well as a limited number of d-orbit electrons from Ag and Au.In the higher energy range (−1 to 20 eV), the s-and p-orbital electrons of Ag, Au, Cu, and Ni atoms contribute to the TDOS.
In the DOS of the Ag/Cu interface (figure 2

Charge transfer analysis
To determine the electron gain/loss of each atom and interatomic bonding strength at the interfaces, we calculated charge distribution and bond population (refer to table 3 and table 4).Additionally, we computed the average charge transfer.Ag donates electrons at the binary Ag/Cu and Ag/Ni interfaces, resulting in a positive charge, while Cu and Ni accept electrons, bearing negative charges.Conversely, at the binary Au/Cu and Au/Ni interfaces, Au accumulates electrons, leading to a negative charge, while Cu and Ni relinquish electrons and exhibit positive charge.These observations indicate the tendency of Ag and Cu to lose and gain electrons, respectively.The average charge transfer is greater in the Ag/Ni and Au/Ni systems compared to the Ag/Cu and Au/Cu systems.This trend aligns with the enhanced bonding stability revealed by the calculations of interface energy and work of adhesion.In the ternary Ag/Au/Cu and Ag/Au/Ni interfaces, Ag exhibits a positive charge resulting from electron loss, while Au carries a negative charge due to electron gain, facilitating a strong bonding tendency between Ag and Au, as indicated by the DOS analysis results.

Conclusions
(1) Our calculations of interface energy and work of adhesion revealed that the Ag/Au/Ni interface exhibits superior stability and greater bonding strength compared to the Ag/Au/Cu interface.Notably, the Au/Ni interface exhibited the highest stability, corresponding to the highest atomic bonding strength.
( (3) The average electron transfer was more pronounced in the Ag/Ni and Au/Ni systems than in the Ag/Cu and Au/Cu systems, indicating higher bonding stability.Additionally, in the ternary Ag/Au/Cu and Ag/ Au/Ni interfaces, Ag exhibited a positive charge due to electron loss, while Au exhibited a negative charge due to electron gain.Thus, Ag and Au tend to form strong bonds, as indicated by the DOS analysis results.
(4) The analysis of bond lengths at the interface within the Ag/Au/Ni system revealed substantially smaller bond lengths than the Ag/Au/Cu system, indicating the high stability of the Ag/Au/Ni interface and confirming our interface energy and work of adhesion calculations.Furthermore, the bonding mode of the interface atoms with non-zero bond populations indicatedcovalent bonding in binary interfaces, while the ternary interfaces exhibited metallic bonding.
(a)), a pronounced DOS peak appeared within the −3 to −1 eV range, corresponding to the d-orbitals of Cu atoms.Furthermore, s-and p-orbital hybridization occurs between Ag and Cu in the −10 to 20 eV range, along with d-orbit hybridization between Ag and Cu atoms within the −5 to 0 eV range, indicating the formation of relatively strong covalent bonds at the Ag/Cu interface.The DOS of the Ag/Ni interface (figure 2(b)) resembles that of the Ag/Cu interface, resulting in a d-orbit peak for Ni at the

Fermi
level.Two distinct peaks in the TDOS at −4 eV and near the Fermi level indicate enhanced bonding strength in the Ag-Ni interface.For the Au/Cu interface (figure 2(c)), a pronounced TDOS peak was observed at −2.5 eV corresponding to the d-orbital electrons of Au and Cu.Additionally, d-orbital hybridization between Au and Cu occurred within the −5 to −1 eV range owing to covalent bonding between the two elements at the interface.Two distinct peaks in the TDOS at −3 eV and near the Fermi level further confirmed strong bonding.Moreover, peaks corresponding to s-s and p-p orbital hybridization of Au and Ni were observed within the range from −10 to 22 eV, and those corresponding to the hybridization of d-orbit of Au atoms with d-orbit of Ni atoms were observed within the range from −5 to 0 eV.Figures 2(e) and 2(f) display the DOS of Ag/Au/Cu and Ag/Au/Ni, respectively.Resonance peaks corresponding to the s and p orbits of Ag and the s and p orbits of Au appeared within the range from −10 to 20 eV, and those corresponding to the d-orbit of Ag and Au appeared within the range from −7 to 2 eV, indicating a strong metallic bonding between the Ag and Au atoms.The TDOS of the Ag/Au/Cu interface exhibited a distinct peak near −3 eV (figure 2(e)), indicating the co-hybridization of the d-orbital of Cu, Ag, and Au.Similarly, the TDOS of the Ag/Au/Ni interface exhibited two distinct peaks at −2.5 eV and near the Fermi level, corresponding to the co-hybridization of the d-orbital of Ni, Ag, and Au (figure 2(f)).

)
The bonding energy distribution indicated a concentration in the range of −13 to −25 eV at the interfaces.Furthermore, the PDOS of the d-orbital electrons dominated the TDOS.In particular, the hybridization of Cu and Ni d-orbital electrons with those of Ag and Au resulted in stable material structures.Significantly, the TDOS plots of Ag/Ni, Au/Ni, and Ag/Au/Ni interfaces comprised two distinct peaks near the Fermi level, indicating co-hybridization of Ni, Ag, and Au d-orbitals.For the Ag/Au/Cu and Ag/Au/Ni interfaces, resonance peaks were observed between the s-and p-orbitals of Ag and Au, along with d-orbital hybridization between Ag and Au, confirming the formation of strong metallic bonds between Ag and Au atoms.

Table 2 .
Total energy of different interfaces, the free energy of two free surfaces, work of adhesion, and interface energy.
[24]e 4presents data on bond lengths and populations, exclusively analyzing bond lengths at the interfaces.Typically, stronger bonds are associated with shorter bond lengths and a higher number of chemical bonds between atoms[24].Shorter bond lengths indicate higher bond energy and material stability.As shown in table4, bonds between different atoms at the Ag/Ni interface are significantly shorter than those at the Ag/Cu interface, indicating superior stability in the Ag/Ni interface.Similarly, bonds at the Au/Ni interface are shorter than those at the Au/Cu interface.Furthermore, comparing bond lengths between atoms at the ternary Ag/Au/ Cu and Ag/Au/Ni interfaces revealed that the Ag/Au/Ni interface is more stable than Ag/Au/Cu, consistent with the results of interface energy and work of adhesion calculations.Notably, interfaces with non-zero bond populations exhibit covalent bonding, with binary interfaces predominantly exhibiting covalent bonds and ternary interfaces featuring metallic bonding.

Table 3 .
Charge distribution and average charge transfer between atoms at different interfaces.