The investigation of mechanical and dielectric properties of Samarium doped ZnO nanoparticles

Figure 1 reveals the XRD patterns of Zn_1−xSm_xO for x = 0.00, 0.04 and 0.10. The observed peaks match with those of wurtzite hexagonal structure ZnO (JCPDS card No. 36–1451, a = b = 3.249 Å, c = 5.206 Å) with the preferred orientation of (101) planes. There are no indications for secondary phases for all prepared samples, indicating the high purity and the complete solubility of Sm on Zn location. The crystalline size and the lattice parameters, listed in table 1, were calculated by using Scherrer's equation and Bragg's equation respectively [26]. The crystalline size, calculated from XRD, was found to decrease with the increase of Sm doping which can be attributedto the distortion of the crystal lattice due to substitution of larger ionic radii of Sm³⁺ ions (0.95 Å) compared to Zn²⁺ ions (0.74 Å) [26]. The values of the lattice parameters a and c varied with the increase of Sm doping, revealing that the ZnO structure was disturbed by the doping of Sm. In table 1, the values of a and c of Zn_1−xSm_xO nanoparticles, with 0.00 ≤ x ≤ 0.10, were greater than those of pure ZnO for x = 0.02, 0.04, and 0.10. However, the lattice constants decreased for x = 0.01, 0.06, and 0.08 with respect to pure ZnO. Decrease in lattice parameters is expected when Sm substitutes Zn while the lattice parameter will increase when Sm occupies interstitial sites [26, 28].

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Figures 2 (a) and (b) show the TEM images of Zn_1−xSm_xO for x = 0.00 and 0.10, respectively. The computed size from TEM is in good agreement with those calculated from XRD as shown in table 1. Figure 2(b) clearly shows an agglomeration of the prepared nanoparticles for a high doping level of Samarium with x = 0.10 [26].

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The SEM micrographs of Zn_1−xSm_xO nanoparticles with x = 0.00, 0.04 and 0.10 are shown in figure 3. Figure 3(a) reveals that the nanoparticles were distributed in homogenous and uniform shape manner. It possesseswell defined grain boundaries and pores. From figures 3(b) and (c), it is noticed that doping ZnO with Sm has influenced the surface morphology and the size of the particles which reveals the good consistency between the SEM results with our published data regarding the decrease of crystalline size with further increase of Sm concentrations [26]. Upon doping, the surface becomes more rough and the particles denser and smaller; consequently, the agglomeration of nanoparticles with each other may be attributed to the higher relative surface to volume ratio causing an increase in the attractive forces among the nanoparticles [29, 30]. The schematic diagram represented in figure 4 shows the morphological changes and the growth mechanism of agglomeration process especially at high doping concentrations of Sm.

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Figure 5 shows the H_v values, calculated using equation (1), as a function of F at loading time t = 60 s for Zn_1−xSm_xO with x = 0.00, 0.01, 0.02, 0.04, 0.06 and 0.10. For F ≤ 5 N, H_v increases non-linearly along with the applied load; however, a plateau regime exists for F > 5 N, revealing a reverse indentation size effect (RISE). Li and Bradt [31] investigated the RISE behavior by IIC model, where the applied load is balanced in the maximum depth by the total sample resistance. According to this model, the ISE behavior explains friction (slip) and elastic effects. On the other hand, indentation cracking in the samples will lead to the RISE behavior. To investigate the best fit model regarding our obtained experimental H_v results, Meyer's law (equation (5)) together with HK (equation (6)), EPD (equation (7)), PSR (equation (8)) and IIC (equation (9)) models are analyzed using:

$$\begin{eqnarray}&&F=A{d}^{n}\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&F=W+\,{A}_{1}{d}^{2}\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&F=\,{A}_{2}{\left(d+{d}_{0}\right)}^{2}\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&F=\alpha d+\beta {d}^{2}\end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray}&&{H}_{v}={\lambda }_{1}{k}_{1}\left(\displaystyle \frac{F}{{d}^{2}}\right)+{k}_{2}\left(\displaystyle \frac{{F}^{\tfrac{5}{3}}}{{d}^{3}}\right),\end{eqnarray} \tag{ 9 }$$

where A is the standard hardness constant, n is Meyer's index, A₁is a load independent constant, W is the minimum applied load needed to start an indentation, A₂ is a constant, d₀ is related to the plastic deformation, $\beta$ is a constant related to plastic properties, $\alpha$ represents the surface energy and λ₁, K₁, K₂ are constants.

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To ensure the RISE behavior of the samples, Meyer's law was applied. The plot of ln(F) against ln(d), shown in figure 6, reveals the linear dependence from which A and n are calculated and listed in table 2. It is noticed that the samples displays RISE behavior since the values of slope (n) are greater than 2. The parameters obtained from the above mentioned models are listed in table 2. Negative values of W, d₀ and α obtained from HK, EPD and PSR models, respectively, reveal the RISE behavior indicating that the applied load is adequate to explain only the plastic deformation for all samples [20, 32].

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The theoretical values of Vickers microhardness are calculated using the following relations [27, 33]:

$$\begin{eqnarray}&&{{\rm{H}}}_{{\rm{HK}}}=1854.4\times {A}_{1}\end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray}&&{{\rm{H}}}_{{\rm{EPD}}}=1854.4\times {A}_{2}\end{eqnarray} \tag{ 11 }$$

$$\begin{eqnarray}&&{{\rm{H}}}_{{\rm{PSR}}}=1854.4\times \beta \end{eqnarray} \tag{ 12 }$$

$$\begin{eqnarray}&&{{\rm{H}}}_{{\rm{IIC}}}=k{\left(\displaystyle \frac{{F}^{5/3}}{{d}^{3}}\right)}^{m},\end{eqnarray} \tag{ 13 }$$

where $k$ and m are constants that are load independent.

The indentation-induced cracking (IIC) model explains the RISE behavior. From equation (13), the values of k and m are obtained from the plot of ln(H_v) versus ln($\tfrac{{F}^{5/3}}{{d}^{3}}$). The values of m, listed in table 2, are smaller than 0.6 showing that the samples follow the RISE mode where no elastic deformation is observed [33, 34].

Figures 7(a) and (b) display the variation of measured H_v (experimental) and calculated H_v (theoretical) as function of F for Zn_1−xSm_xO with x = 0.00 and 0.04, respectively. It is clearly shown that IIC model matches our experimental results with a deviation about 5%.

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The mechanical parameters (E, Y, K and B) are calculated using equations (14)–(17) and recorded in table 3 together with the measured microhardness values of Zn_1−xSm_xO samples.

$$\begin{eqnarray}&&E=81.9635\times {H}_{v}\end{eqnarray} \tag{ 14 }$$

$$\begin{eqnarray}&&Y=\displaystyle \frac{{H}_{v}}{3}\end{eqnarray} \tag{ 15 }$$

$$\begin{eqnarray}&&K=\sqrt{2E\alpha }\end{eqnarray} \tag{ 16 }$$

$$\begin{eqnarray}&&B=\displaystyle \frac{{H}_{v}}{K}\end{eqnarray} \tag{ 17 }$$

The proportionality between the young's modulus (E) and the yield strength (Y) with the hardness explains the same trend in variation of their values as given in table 3. Their values decrease initially when the Sm concentration is up to x = 0.02, then rise with increasing Sm content and exceed the original values of the pure ZnO sample, when the Samarium dopant is at x = 0.10. The decrease in H_v for doped samples with x = 0.01 and x = 0.02 relative to the undoped sample is related to the decrease of crystalline size from 54.4 nm to 36.2 nm. When the size of the particles decreases, porosity of the samples increases. Hence, the hardness of the doped samples decreases [20]. Therefore, increasing the porosity results in decreased mechanical properties; however, the majority of applications involving porous ceramics require excellent mechanical properties [35–37]. The increase of the hardness with the further increase in the Sm doping above x = 0.02 may be attributed to the substitution of Zn²⁺ ions by Sm³⁺ ions in the crystal lattice which decrease the weak lattice stresses on the surface by removing the defect centers [38]. The increase in microhardness can be also ascribed to the impedance to crack propagation among the grains and the enhancement of grain connectivity with Sm-substitution. For Co and Al co-doped nano-crystalline ZnO samples, Siddheswaran et al [39] describes that Vickers microhardness depends on the dopant concentrations, as it increases with Co and decreases with Al content. E and Y values change in the same manner due to their relation to the hardness. The higher value of E and thus Y of a sample, the stronger the bond between the atoms or molecules in materials. The values of the fracture toughness and brittleness fluctuate with the Samarium concentration.

ZnO is considered to be relatively 'soft' material compared to other ceramics [40] and the hardness values of ZnO vary between 0.0105 GPa and 6 GPa as reported by Kaya et al [41] and Keyan et al [42], respectively. The hardness of our synthesized Zn_1−xSm_xO nanoparticles is equal to 0.845 GPa for x = 0.00 which lies in the above-mentioned range.

For pure and Sm-doped ZnO samples, the dielectric constants (ε' and ε''), dielectric loss (tan δ) and ac conductivity (σ_ac) are measured by changing the frequency at a specific temperature. The reliance of dielectric parameters on frequency and temperature is useful in structural changes, transport mechanism and defect behavior of a solid [43]. The polar molecule ZnO, exhibiting a permanent dipole moment, is sensitive to external ac electric filed. Upon doping ZnO with Samarium, persistent electric dipoles arise due to hopping between Zn²⁺ and Sm³⁺ ions [44].

Figures 8(a)–(d) and 9(a)–(d) display the variation of ε', ε'', tan δ and σ_ac as function of frequency for Zn_1−xSm_xO (x = 0.01, 0.02, 0.06 and 0.10) at 300 and 773 K, respectively. The insets of the figures represent the dependence of ε', ε'', tan δ and σ_ac on the frequency for x = 0.00. It is clearly noticed that the dielectric constants and dielectric loss achieve high values at lower frequencies and then they decrease exponentially with increasing frequency, where they reach constant values at higher frequencies. The predominance of the four polarizations (space charge, orientational, electronic and ionic) and the existence of space charge polarization near the grain boundary interfaces in the low frequency zone explain the higher values of dielectric constants and dielectric loss [45, 46]. The reduction in the values of dielectric constant and dielectric loss at higher frequencies may be attributed to the drop in the importance of these polarizations together with the lack of charge polarization near the grain boundary interface [47], leading to the contribution of the prepared samples in nonlinear optical (NLO) applications because of high optical quality of the crystal with minor defects [48, 49]. The observed frequency dependent dielectric behavior can be explained by Maxwell-Wagner type relaxation [50]. Materials with structural in-homogeneity are formed of well conducting grains that are separated by insulating grain boundaries. Upon applying external electric field, the space charge carriers can easily move into the grains where they gather and become trapped through the defects at the interfaces leading to the formation and alignment of dipole moments. At low frequencies, the high values of dielectric constants may be ascribed to charged defects, interfacial dislocations, grain boundaries effect, oxygen vacancies, micro-pores, dangling bonds and interfacial/space charge polarization because of heterogeneous dielectric structure. Above a certain frequency of the external electric field where the orientation polarization is dominant [51, 52], the hopping between different metal ions cannot follow the alternating field. The probable origin of orientation polarization is the presence of oxygen vacancies and zinc interstitials in the nano-sized ZnO [53]. The polarizability of metal ions lags behind the external electric field at higher frequencies where the dielectric constants attain constant values. The dielectric loss (tan δ) values decrease with increasing frequency and become almost frequency independent at high frequency zones because the motion of domain walls is inhibited and magnetization is forced to change rotation, revealing the application of these materials in high frequency devices [54]. Materials with high dielectric constants along with low dielectric loss have received exceptional recognition in various applications [55, 56]. The dielectric constants and dielectric loss are also influenced by the Samarium doping. It is noticed that these parameters decline with the increase in the concentration of Sm for the same frequency that may be explained by the effect of Sm³⁺ on the polarizability of ZnO [57].

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Regarding the dependence of ac conductivity on the frequency, it is observed that σ_ac increases along with the frequency for all samples due to grain effect and increase in hopping of charge carriers as explained by Koop's theory [51]. The increase in conductivity is almost zero in low frequencies region. Above a certain characteristic frequency called the critical frequency, the conductivity increases according to the Jonscher power law relation [58] in disordered materials:

$$\begin{eqnarray}&&{\sigma }_{AC}=A{\omega }^{S}\end{eqnarray} \tag{ 18 }$$

where $\omega$ is angular frequency, A is a constant and s is a frequency exponent, generally less than or equal to 1. As stated above, ${\sigma }_{AC}$ is calculated using equation (4). The interfaces or grain boundaries present potential barriers to the movement of charge carriers that seem to be confined in a potential well. The charge carriers are free to migrate inside the grains; however, the grain boundaries pose resistance to the flow of the charge carriers that cannot move further.

At high frequencies, the charge carriers possess enough energy to overcome the potential barriers leading to the fast improvement in the conductivity, because increase in frequency intensifies the charges flow. Values of s > 1 are announced in ion conducting glasses [59] and ionic crystals [60, 61] and pointed up by Papathanassiou et al [62–64] in a new form of the universal power law, where they concluded that there is an upper frequency limit for the dispersive conductivity after which saturation is observed. The measured conductivity almost saturates in the high frequency limit as observed in some cases such as in conducting polypyrrole and polyaniline [65]. Panteny et al [66] reported that at high frequencies (>10⁷ Hz), the ac conductivity of the capacitors is much higher than that of the resistors; then, the network conductivity presents a frequency independent behavior. Vohra et al [67] announced that ${\sigma }_{{\rm{AC}}}$ gets saturated to a value approximately equal 10⁻³ Ω⁻¹cm⁻¹ near 8 GHz for As₂Se₃. In our work, the frequency limit of our instrument is 10⁶ Hz; consequently, the saturation of ac conductivity could not be detected.

For a given frequency, the conductivity decreases with the increase of Samarium doping due the reduction in the concentration of intrinsic donors leading to the cease of the hopping mechanism between Zn²⁺ and Sm³⁺; consequently, the n-type conductivity of host ZnO decreases [68].

Figures 10(a) and (b) represent the temperature dependence of dielectric constant ε' and ac conductivity σ_ac at f = 500 KHz for x = 0.01, 0.02 and 0.06. Values of ε' and σ_ac decrease as the Samarium doping content increases at all temperatures. It is noticed from figure 10 that the dielectric constant ε' decreases with the increase in measuring temperature up to 450 K and then increases with more rise in temperature. The following behavior may be ascribed to the depletion of pore space volume between the particles, when the synthesized nanoparticles are influenced by high temperature sintering that leads to a growth in the larger grains at the expense of smaller grains and decrease of the energy barrier with fast grow of the diffusion of atoms to another grain. Thus, our sintered nanoparticles reveal conductor type behavior because of the increase of conductivity with enlargement of the mobility. At T = 773 K, ε' and σ_ac attain the highest values which are attributed to structural relaxation where the polarization resulting from molecular dipoles becomes significant and adds to other contributions of polarizability [69] and the increase of the mobility of the charge carriers in accordance with the ion hopping mechanism [70], respectively.

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