3.1. Characterization of Specimens
Ag has a higher reduction potential than Cu, and Ag
+ ions are reduced into Ag atoms by transforming Cu atoms into Cu
2+. However, Ag
+ ions are present in a glucose-rich alkaline solution. There is a direct reduction reaction of Ag
+ ions, which is called a “replacement-reduction” method. The chemical equations for silver ammonia solution and silver deposition are as follows [
16,
17]:
Cu and Ag are almost immiscible at room temperature, but Cu is the faster diffusion species in the Cu/Ag diffusion couple. Cu atoms at the Cu/Ag interface diffuse to the Ag surface and exchange with Ag
+ ions by leaving vacancies at the interface as a result of the Kirkendall effect. In this paper, the key to inhibit the Kirkendall effect is to add 5% dilute ammonia to inhibit the displacement reaction. Since the [Cu(NH
3)
4]
2+ ion is generated, the Equation (3) is inhibited during the coating process.
The Cu/Ag core-shell composite replicate the spherical structure of the Cu particles (
Figure 1a,b), while the particle size distribution of specimens show that the two materials have similar average particle sizes (227.17 nm for Cu, 234.96 nm for Cu/Ag core-shell composite), but the size of Cu/Ag core-shell composite is slightly larger than the Cu particles (
Figure 1i). Considering the agglomeration properties of the nanoparticles, for each sample, a large number of SEM images were measured, then 2000 particles were randomly selected for measurement and statistics, and the particle size distribution map was finally drafted. This phenomenon proves once again that Equation (3) is effectively inhibited, and the reduction reaction of Ag
+ ions mainly occurs in the solution. X-ray diffraction (XRD) measurements were made on the specimens to assess the structure and phase purity. The diffraction peaks can be indexed to a Copper, syn structure of Cu, Copper, syn, and Silver-3C, syn structure of Cu/Ag core-shell composite, as shown in
Figure 1c. No diffraction peaks from impurities were found in the specimens. These results provide parameters for the simulations below. However, the peaks of the Cu/Ag core-shell composite are significantly broadened, demonstrating that the crystallinity of the material deteriorated. To ascertain the core-shell structure, the TEM and SEM-EDS cross-sectional images are presented in
Figure 1g. In
Figure 1e,f, the TEM image of the specimen confirms that it is indeed a core-shell structure, and the average thickness of the shell layer is about 40 nm. The SAED and EDS patterns further confirm the core-shell structure and the components. In
Figure 1g, there is a strong intensity of copper on the core and a weak intensity of silver on the shell, and the composites contain 21.86 wt.% of Ag, 78.14 wt.% of Cu. (The background value of the epoxy resin has been removed). The above characterization results are similar to those in the literature, proving that the material synthesis is successful [
13].
For low-dimensional Cu/Ag core-shell structures, there are three heteroepitaxial growth modes of Ag coating, namely the Frank–Van der Merwe (FM) mode, the Volmer–Weber (VW) mode, and Stranski–Krastanow (SK) mode. In this work, Ag grows in a three-dimensional space, so whether the growth of Ag proceeds in the SK mode remains to be verified. The schematic diagram of SK growth mode is shown in
Figure 1h. The growth mode of the epitaxial layer depends on the free energy of the system, and also reflects the competitive balance between strain energy and surface energy and interface energy. Therefore, the experimental conclusion can be verified by calculating the energy relationship of the interface system by the first principles [
18].
3.2. Geometric Optimization
Based on the speculation obtained above, a Cu/Ag interface model was established to calculate interface properties and verify the growth mode. As the modeling method of the Cu/Ag core-shell system is seldom reported in the literature, in order to ensure that the simulation calculation is closer to the actual situation and the calculation result can be applied to a larger scale, a vacuum slab model is used. This does not change the periodicity of Cu and Ag, and does not limit the physical size of the material, making the calculation more convincing and universal.
For the choice of atomic layers, it is necessary to satisfy that the atoms in the depth of the surface have bulk atomic characteristics. On the other hand, with the increase in atomic layers, the computational time will increase. Therefore, the number of atomic layers in each surface model is taken as 5 layers. Since the spherical particles grow in all directions of space, one-dimensional, two-dimensional, and three-dimensional directions are selected separately when the model is built. Establishing representative (111), (110), and (100) surface models in the [111], [110], and [100] directions can be closer to the actual situation. The surface energy is calculated after geometric optimization, which is shown in
Table 1. In density functional theory, surface energy can be calculated from the following expression [
19]:
where
Eslab is the total energy of surface slab obtained using density functional theory. n is the number of atoms in the surface slab.
Ebulk is the bulk energy per atom.
A is the surface area. For a slab, we have two surfaces and they are of the same type, which is reflected by the number 2 in the denominator.
Figure 2 displays the interface models and evaluating the relatively stable interface model by calculating the interface binding energy, the density of states and population. For each set of images, the model below is the geometric optimization result of the above. For Cu(111), Cu(110), and Cu(100), their surface energy varies considerably, which proves that the active sites on the surface of Cu particles are unevenly distributed. This difference in activity influences the rate of reaction, resulting in vacancies on the surface.
The stability and combination of the interface are usually expressed by the interface energy, as given in Equation (7) [
20].
where
EAg and
ECu denote the total energies of the Ag(hkl) slab and the Cu(hkl) slab with five atomic layers, respectively,
ECu/Ag is the total energies of Cu/Ag slab, and A is the interface area.
The interface energy is shown in
Table 2. In the absence of special instructions, the comparison between energy does not take into account the sign. The order of the absolute values of interface energy indicates that the Ag(100)/Cu(100) interface is the most stable structure.
The total free energy of the model determines the growth pattern of the Ag coating, usually represented by Equation (8) [
21]. However, the correspondence between the growth mode and the free energy of the model is not clear, and the calculation of strain energy is difficult. Therefore, the growth mode of the coating is determined by calculating the energy relationship between the substrate, the coating, and the interface.
where
F denotes the total free energy of the model,
Estrain is the strain energy of the model,
σ is the surface energy of the model, and
γint is the interface energy of the model.
According to the data in
Table 2, the energy relationship between the substrate, the coating, and the interface can be obtained, which is presented in
Table 3. The surface energy of the substrate (σ
Cu) is greater than the sum of the surface energy of the coating (σ
Ag) and the interface energy (
γint). It is found that the interface energy is small, and the epitaxial material atoms are distributed on the substrate, and a thin strain layer is formed on the surface in the pre-stage. As the epitaxial growth progresses, the elastic strain in the epitaxial layer increases as the layer thickness increases. When the thickness of the epitaxial layer is raised to a certain value, the strain energy accumulated in the strained layer is released by redistributing the atoms reaching the surface to form a three-dimensional island. It is pointed out that although the formation of the island increases the surface energy, but reduces the total energy of the epitaxial layer. The surface energy of slab models is shown in
Table 4 and the positive and negative of energy is not considered. It is noted that the surface energy of the slab models is indeed reduced, as in the conclusions of the literature [
22].
3.4. Electronic Structure Analysis of Interface
To investigate the differences in bonding ability, the density of states is calculated where the Fermi level
EF is set at the position of energy
E = 0 eV, as shown in
Figure 3. The
EF of DOS for each model is larger than 0, indicating that both the Ag and Cu slab in the interface system maintain the metallic characteristic. The DOS of the Ag atoms is mainly contributed by the valence electrons of Ag 4d and a small amount of Ag 4p, Ag 5s orbitals, and the DOS of the Cu atoms is mainly contributed by the valence electrons of Cu 3d and a small amount of Cu 3p, Cu 4s orbitals. Except for peak and peak shapes, the density of states of different models is comparable, and the d orbital of the Cu atom overlaps with the d orbital of the Ag atom, resulting in hybridization and a strong interaction.
Figure 3d shows the density of states of Cu and Ag atoms in the Ag(100)/Cu(100) model, and the density of states of the Cu and Ag atoms in other interfaces is not given because the stability of Ag(100)/Cu(100) is the highest and the peak is more obvious. It is exhibited that the p orbital of the Cu atom also overlaps with the d orbital of the Ag atom but it is not obvious. Moreover, the charge density distribution and the difference charge density distribution of the interface can show the electron transfer and electron density of interfaces more intuitively. The unit of the values in
Figure 4 is all electrons/Å
3. There is a phenomenon of charge accumulation and electron transfer between Cu and Ag, indicating that they are connected by ionic bonds with covalent properties. For the Ag(111)/Cu(111) model, although Cu and Ag in the vicinity of the interface have common electrons, the density is extremely low, and mainly free electrons are present. Therefore, there is a strong metal bond between Cu and Ag. For the Ag(110)/Cu(110) and Ag(100)/Cu(100) models, the latter exhibits more common electrons and strong covalent bonds. However, the mismatch of the Cu/Ag interface is large (more than 15%), so there are non-bonding forces and strain at the interface, which requires further calculations.
3.5. Force Analysis of Interface
To further describe the forces between Cu and Ag, the radial distribution function is calculated, as shown in
Figure 5. In all models, there is a maximum in the range of
r < 2.6 Å, indicating that the bond is the main force that constitutes the interface. However, for the Ag(100)/Cu(100), there also peaks with high peaks in the range of 2.6–3.1 Å, indicating that there are strong hydrogen bonds in the interface. Besides, there are also peaks in the range of
r > 3.1 Å, exhibiting Van der Waals force [
23].
According to the above conclusion, the growth mode of the Ag coating can be inferred, and the three-dimensional schematic diagram is also as shown in
Figure 5. The growth of the Ag coating is mainly composed of three stages.
Pre-stage: The displacement reaction and the direct reduction reaction occur simultaneously in the solution, but since the surface energy of each surface of Cu differs, the reactivity of each surface also differs, resulting in the formation of vacancies and a thin layer of Ag on the Cu surface.
Min-stage: As the direct reaction of Ag continues, the Cu surface is covered by Ag and the vacancies disappear. When the coating reaches a certain thickness, the strain energy of each surface is released outward, resulting in irregular protrusions on the surface of the composite.
Post-stage: As the reaction progresses, the Ag+ ion concentration in the solution gradually decreases, the reaction reaches equilibrium, and the growth of the Ag coating stops.
Regarding the core of a regular geometry, especially two elements (such as Pb and Pt) that differ by one period from the periodic table, the conclusions reached are similar. The growth of the shell is divided into two stages, that is, the shell grows epitaxially, and then the island grows. The difference is that the simulation calculation and characterization of core-shell particles with a spherical structure are more complex, and are easily affected by external factors during the synthesis [
24]. In this paper, calculations and characterizations confirm each other, indicating that the method is credible.