Simulation and Experimental Study on Properties of Ag / SnO 2 Contact Materials Doped with Different Ratios of Ce

SnO2 in the Ag/SnO2 contact material is a kind of high hardness and almost insulated wide bandgap semiconductor material. In the process of use, the contact resistance is larger and the temperature rise is higher, which reduces the reliability of contacts and shortens the electrical life. In order to improve the properties of Ag/SnO2 contact materials, based on the first principle of density functional theory, this paper presents a method of doping SnO2 with the calculation of different proportions of rare earth Ce electrical and mechanical properties. .e results of energy band, density of state, and elastic constant show that when the doping ratio of Ce is 0.125, the electronmobility is the highest, the conductivity is the best; the hardness decreases, and the universal elastic anisotropy index is the smallest. Finally, in the experiment, SnO2 powders with different doping ratios are prepared by the sol-gel method, and Ag/SnO2 contacts with different doping proportions are prepared by powder metallurgy. Arc energy, contact resistance, and hardness are measured; scanning electron microscopy was used to observe and analyze the surface morphology. .e final simulation and experimental results are well matched.


Introduction
e contact resistance and the temperature rise in the process of using automotive relay contacts are increased, making life expectancy to decrease [1][2][3].is is because SnO 2 in Ag/SnO 2 contact material is a kind of wide bandgap semiconductor material, which is almost insulator [4].At the same time, SnO 2 is a high hardness brittle reinforcing phase, making contact material processing and composite molding extremely difficult.e study shows that the doping modification of Ag/SnO 2 with rare earth materials is a good method to solve the above problems [5].
For now, improving the performance of Ag/SnO 2 contact materials by doping is still in the experimental stage.How to get the best performance by doping with the proper amount of rare earth elements depends on the original experiments and experience, and there are some difficulties in the preparation of samples and the accuracy of experimental equipment, which restrict the development of Ag/SnO 2 materials.
Zhu Yancai and others in the study on new type of Ag/SnO 2 /CeO 2 electrical contact material preparation and electrical properties found that CeO 2 -doped Ag/SnO 2 improved electrical performance [6].From the experimental point of view, they had only selected a single ratio of doping, not knowing the best proportion of doping to get better performance.In the study of the structure and optical properties of Ce-doped SnO 2 , Shan Linting et al found that the Ce-doped SnO 2 makes conduction band bottom to move toward the low-energy side, the bandgap becomes smaller, and the conductivity increases [7].e conductivity was only studied by simulation calculations.
Wang Qingwei et al found that CeO 2 -doped SnO 2 when doping too little is not conducive to the sintering and growth of tin oxide crystals, while excessive doping will prevent the lattice growth and affects the stability of the lattice, easily leading to serious cracking of the product [8,9].So, the doping amount of CeO 2 should be controlled.
It is of great significance to understand the basic properties of Ag/SnO 2 contact material.In this paper, based on the first-principles calculation of density functional theory [10], different proportions of rare earth Ce are doped into the contact material of SnO 2 , conducting geometric optimization, energy band, density of states and elastic constant, and then analyzing the conductivity and hardness to theoretical study the electronic structure and mechanical properties.

Cell Model and Calculation Method
2.1.Cell Model.In this paper, we had constructed a SnO 2 primary cell model, as shown in Figure 1(a).SnO 2 (cassiterite) has the rutile structure space group P42/mnm [11].Each SnO 2 contains 2 Sn atoms and 4 O atoms.e atomic substitution method was used to construct the supercell model Sn 1−x Ce x O 2 (x � 0, 0.083, 0.125, and 0.167).Table 1 shows the relationship between the doping ratio and the supercell.Taking the doping ratio of 0.125 as an example, the 1 × 2 × 2 supercell model of SnO 2 is established and one of the Sn atoms is replaced by a rare earth atom Ce, as shown in Figure 1(b).

Calculation Method.
In this article, we used Materials Studio software and completed the calculation by using the CASTEP module.
e calculation process uses periodic boundary conditions based on DFT [12].Since generalized gradient approximation (GGA) considers the effect of charge density near a certain location on the exchangecorrelation energy, for example, taking into account the effect of the first-order gradient of density to correct local variations, it is possible to properly correct the effects of charge density regions exponential form; in the geometric optimization, energy band and density of state calculations have achieved good results [13].
e local density approximation (LDA) assumes that the nucleus spacing in the system is far apart, and the motion of electrons in its lattice background can be approximated as a behavior in a uniform field.It is suitable for the calculation of the ground state properties of various systems, and very good results are achieved when calculating the elastic properties of the system [14].
erefore, the geometric optimization process uses the PBE method under GGA; the CA-PZ method under LDA is used to calculate the elastic constants in the mechanical properties on the basis of optimization.For geometric optimization, energy band, density of states, and elastic constants are calculated adopting the plane wave ultrasoft pseudopotential (Ultrasoft) method.
In order to compare the calculated results of SnO 2 doped with different proportions of Ce, the parameters of software simulation are set to be consistent.e calculated parameters are as follows: the cutoff energy of the plane wave is 370 eV, the SCF tolerance is 1.0 × 10 −6 eV/atom, and the K point in the Brillouin region is 5 × 5 × 8. e calculation process is carried out in the reciprocal space.

Crystal Structure.
e crystal parameters of geometry optimization and experimentation of SnO 2 doped with different proportions of Ce are optimized, and the parameters after optimization are shown in Table 2.
According to the optimization results, the experimental values and calculated values of the lattice parameters of Cedoped SnO 2 with different proportions are not much different.e lattice constant and volume of SnO 2 after doping have different growth degrees compared with SnO 2 , which is consistent with Vegard's law [15], indicating that the calculation results are reliable.is shows that doping Ce can cause slight distortion of the crystal structure and thus can adjust the structural parameters of SnO 2 , thereby improving the performance of SnO 2 .

Density of States and Electron Concentration.
e density of states of SnO 2 and SnO 2 doped with different proportions of rare earth Ce is shown in Figure 2. Figure 2(a) shows the density of states of SnO 2 , and Figures 2(b)-2(d) show the density of states of SnO 2 with the Ce doping ratios of 16.7%, 12.5%, and 8.34%, respectively.e Fermi level is chosen to be zero of the energy scale.e energy level above the Fermi surface (0 eV) is the conduction band, and the energy level below the Fermi surface is the valence band.
It can be seen from Figure 2 that the density of states undoped and doped with different ratios of Ce shows that the Fermi surface of the SnO 2 supercell after doping moves to the valence band in different degrees, while the conduction band of undoped SnO 2 is about 0 eV-20 eV, and the conduction band of SnO 2 is about 0 eV-7 eV after doping.
e conduction band is narrowed, which indicates that the SnO 2 model after different ratios of doping enhances the electronic state near the Fermi level, and more partial waves cross the Fermi level, the interaction between electrons is enhanced, and the conductivity is enhanced.
e Fermi surface of the Ce-doped SnO2 supercell with different ratios of rare earth elements enters the conduction band to a different extent, which indicates that the relative electron concentration entering the conduction band of SnO2 supercell is different.e relative number of electrons entering the conduction band can be obtained by integrating the density of states of Figures 2(a 3.
As can be seen from Table 3, the higher the doping concentration, the higher the relative electron number into the conduction band and the higher the concentration of relative electron.
e conductive performance of the material can be expressed by the conductivity δ i .e conductivity of the material by semiconductor physics theory is [16] where q is the electron charge constant, and the conductivity is proportional to the electron concentration n i and the electron mobility μ i , which can be obtained from the above formula.
In addition to being affected by the relative number of electrons, the conductivity is also affected by the electron 2 Advances in Materials Science and Engineering mobility.According to the characteristics of the CASTEP software.When applying the first-principles study, the software sets the temperature to a low temperature of 0 K.According to semiconductor theory, the crystal scattering is dominated by ionized impurities.erefore, it is necessary to fully consider the influence of the relative electron number and electron mobility into the conduction band on the conductivity of SnO 2 to obtain a correct conclusion.

Band and Electronic Effective Mass.
e band structure of SnO 2 and different ratios of Ce-doped SnO 2 shown in Figure 3(a) is the band of SnO 2 , and Figures 3(b)-3(d) are the band of SnO 2 with the Ce doping ratios of 16.7%, 12.5%, and 8.34%, respectively.
From Figure 3, the bandgap decreases after doping.e band of SnO 2 after doping is introduced in the region of −35 eV∼−30 eV new energy level, but this energy level is in the deep-rail region and has little effect on the conductivity.erefore, we do not consider it.At the same time, new energy levels appear in the doping system near −15 eV and the distribution of electrons increases, providing more electronic states, and the valence band to the conduction band energy level jump probability is greatly increased.Band fluctuations become gentle, indicating that the doping of the electronic locality enhancement.Hence, when SnO 2 is doped with Ce, it makes metal properties to enhance to increase the conductivity of the material.e electron mobility is inversely proportional to the effective electron mass, and the data derived from two derivation of the band by software are shown in Table 4.
e formula for the effective electron mass is as follows: where h is the Planck constant, k is the wave vector, and E is the electron energy at the wave vector.

Conductivity Analysis.
e following equation is the relationship between the electron mobility μ i , the doping concentration N i , and the electron effective mass m * e : e following equation is derived from the formulas (1)-( 3), and the conductivity is proportional to the relative electron concentration and inversely proportional to the doping concentration and the electron effective mass [17]: Table 1: Doping ratio and supercell correspondence.
e doping ratio of 12.5% is used as a reference to get the relative conductivity, as shown in Table 5.
It can be seen from Table 5 that the conductivity of SnO 2 with the Ce doping ratio of 12.5% is the highest.

3.3.1.
e Formula for the Elastic Constant.For polycrystalline systems, Hill proved that VRH (Voigt-Reuss-Hill) is closer to the experimental results [18].e formula for bulk modulus (B) and shear modulus (G) is as follows: where B V and G V are the elastic modulus and shear modulus of the Voigt model, respectively, and B R and G R are the elastic modulus and shear modulus of the Reuss model, respectively.e formula between bulk modulus, shear modulus, and elastic constant C ij (i, j 1∼6) under the Voigt and Reuss model is as follows [19,20]:

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Poisson's ratio (σ) is related to the bulk modulus and the shear modulus as calculated by Hill as follows: When studying the mechanical properties of materials, we usually consider the effects of microcracks and lattice distortion on the mechanical properties of materials, and the universal elastic anisotropy index A U is usually the determinant of microcracks and lattice distortion [21]: e Vickers hardness in GPa is evaluated based on the empirical formula of Tian (2012).When the hardness is greater than 5 GPa, the correlation between the empirical formula and the experimentally measured hardness value is quite good.e formula is as follows [22]: where k � G/B.

Calculation and Analysis of Elastic Constants.
In order to study the dynamic stability of the doped system, the corresponding relationship between the elastic constants (C ij (GPa)) of SnO 2 and different ratios of Ce-doped SnO 2 is given in Table 6.
For tetragonal systems, if the dynamics are stable, the elastic constants satisfy the following requirements [23]: e elastic constants of SnO 2 and different ratios of Cedoped SnO 2 in Table 6 are calculated, and all satisfy the stability criterion.erefore, SnO 2 and different ratios of Cedoped SnO 2 are stable in dynamics.
In order to further predict theoretically the mechanical properties such as hardness (H V ) and crack, the bulk modulus (B), shear modulus (G), hardness (H V ), and universal elastic anisotropy index (A U ) values are shown in Table 7.
According to the Pugh criterion, it is generally considered that solid materials with G/B > 0.57 are brittle; if they are less than 0.57, it exhibits toughness [24].From Table 7, the order of G/B values is SnO 2 > Sn 0.9166 Ce 0.0834 O 2 > Sn 0.875 Ce 0.125 O 2 > Sn 0.833 Ce 0.167 O 2 , which indicates that doping can change the brittleness of the material, and the more the rare earth element Ce, the more obvious the improvement.
Covalent bond orientation directly affects the ability of the material to resist shear strain.Poisson's ratio can reflect the covalent bond orientation problem of internal structure of the material, the lower the value of the former, the stronger the ability of material to resist shear strain.Table 7 shows that Poisson's ratio becomes smaller after doping, indicating that their ability to resist shear strain is enhanced.SnO 2 with the Ce doping ratio of 12.5% has the smaller Poisson's ratio and the best ability to resist shear strain.e index of pervasive elastic anisotropy, A U , is often the decisive factor in the production of cracks.As can be seen from Table 7, the A U values of SnO 2 after doping are smaller and closer than those of SnO 2 , indicating that doping has an important effect on improving microcracks.e traditional powder metallurgy method only mixes the doping element powder, SnO 2 powder, and silver powder, which makes it difficult for the doping element to enter the SnO 2 crystal.In order to be consistent with the theoretical calculation model of this paper, the sol-gelation method was used to first prepare different proportions of Ce-doped SnO 2 powder.

Experimental Preparation of Ag/SnO
en, Ag/SnO 2 and Ce-doped Ag/SnO 2 contact materials were prepared by the powder metallurgy method.
e proportion of silver base in each sample was 88%.

Test of Contact Resistance and Arcing
Energy.e electrical contact properties of test materials were tested by using the JF04C electrical contact material tester.25000 onoff tests were conducted using each pair of contacts.e contact resistance and arcing energy measurement were done every 100 cycles under load 24 V, 13 A, and contact pressure was 86 cN for the on-off period of 0.4 seconds.Finally, the conductivity of the test material is evaluated by the contact resistance and the arcing energy.e arc energy and contact resistance of Ag/SnO 2 doped with different proportions of rare earth elements Ce are shown in Table 8.
Because the rare earth elements easily lose the outermost electrons to form a stable structure with a high melting point, they are not easily decomposed under the action of the arc but accumulate on the surface of the contact, thereby reducing the ablation of the contacts by the arc and reducing the arcing energy.
From Table 8, when the doping ratio is 12.5%, the arcing energy has the smallest variation range, average arcing It is proved that when the rare earth element Ce doping ratio is 12.5%, the electrical properties of the Ag/SnO 2 contact material are the best under the applied test conditions here.

Microstructure Analysis of Contact Material Surface.
Scanning electron microscopy (SEM) was used to observe the arc ablation morphology of the four types of Ag/SnO 2 contact materials, and the arc erosion resistance of the four types of contact materials was analyzed.
After 25,000 electrical contact performance tests of the contact material, the photomicrographs of the contact surface magnified 1000 times are shown in Figure 4, among them Figure 4(a) shows Ag/SnO 2 and Figures 4(b)-4(d) show the Ag/SnO 2 with the Ce doping ratios of 16.7%, 12.5%, and 8.34%, respectively.e wettability between Ag and SnO 2 particles is poor, which causes the SnO 2 particles to be suspended in the liquid Ag molten pool when the Ag/SnO 2 contact material is in the arc.e surface is easy to form Ag-rich region and SnO 2 -rich region.
e formation of the Ag-rich region is likely to exacerbate the splash erosion of the contact Ag droplets, and the SnO 2 -rich region tends to increase the contact resistance of the contacts.Doping can effectively improve the wettability between Ag liquid and SnO 2 particles so that SnO 2 particles are suspended in the molten system of silver, increasing the viscosity of Ag molten pool, reducing the probability of formation of the SnO 2 polymerization zone, and thus improving the resistance to arc erosion of the Ag/SnO 2 contact material.
Comparing the surface topography of the ablation edge regions of three different proportions of doping, when the doping is 12.5%, the contact surface is flat and without pits, which was because the contact surface shows signs of fluid metal activity after slight melting, and the gap and other phenomena were improved because of the movement of the  Advances in Materials Science and Engineering flow metal.At this time, the surface is relatively flat and smooth, and the electrical properties are the best.e other two ratios are doped, the surface of the contact has holes, the surface of the molten layer exhibits a flowing state of liquid metal and a mountain pack forms after solidification, and some of the black nonconductive oxides are precipitated.

Hardness Measurement.
e hardness of the sample was measured using the HXD-1000TM digital microhardness tester [17].e test strength was selected, and the diamond was pressed into the test sample for 5 s. e two diagonal lengths of the diamond indentation on the surface of the sample were observed by a microscope.e hardness value was read, the sample position was changed, and the above process was repeated.ree measurements were made for each sample, and the average value of the hardness was calculated.e hardness values of Ag/SnO 2 and Ag/SnO 2 doped with different proportions of Ce are given in Table 9.
It can be seen from the above table that the more the doping, the lower the hardness.By comparing the theoretical and actual hardness values in Tables 7 and 9, it is found that the simulations and experiments are well matched.From the perspective of the application environment of the contact, high hardness plays an important role in improving the service life of the contact; from the perspective of the forming of the contact, high hardness affects the plasticity and reduces the yield.erefore, the hardness value must be considered comprehensively.

Conclusions
Based on the first principle of density functional theory, the calculated and analyzed results of Sn 1−x Ce x O 2 (x � 0, 0.083, 0.125, 0.167) show the following: (1) When the doping proportion of Ce is 0.125, the electron mobility is the highest, and the conductivity and the ability to resist shear strain are the best (2) When the doping is 0.834, the universal elastic anisotropy index is the smallest Compared with all performances, 0.125 is the best doping ratio.
Finally, Ag/SnO 2 contacts with different doping ratios were prepared, and arcing energy, contact resistance, and hardness were measured.e final simulation and experimental results can be well matched.
Some people study on Ce-doped Ag/SnO 2 contact material to improve the performance is still in the experimental stage, and the control of the doping amount is also based on the original experience.e innovation of this paper is to obtain the most comprehensive performance by simulating different proportions of Ce doping.A good doping ratio is then verified by experimentation.In the experiment, we not only tested the contact resistance and arc energy but also performed a scanning electron microscope experiment to observe the arc ablation morphology of the contact material.e final theoretical model is well matched to the experiment, providing a method of saving manpower, material resources, and financial resources to improve the electrical properties of Ag/SnO 2 contact materials.

Table 2 :
Doping ratio and crystal structures.

2 and Ce- Doped Ag/SnO 2 Contact Materials
4.1.Preparation of Doped SnO 2 Powder by Sol-Gel Method and Ag/SnO 2 -Ce Contact Material by Powder Metallurgy.

Table 7 :
Bulk modulus (GPa), shear modulus (GPa), Poisson's ratio, and universal elastic anisotropy index.Advances in Materials Science and Engineering energy, and the actual measured conductivity are also the smallest, indicating that Ce-doped SnO 2 has the smallest fluctuation and the most stable.

Table 8 :
Arc energy and contact resistance.