The effect of scandium doping on the structural, electronic, optical, and thermodynamic properties of scandium-doped zirconia (Zr_0.875Sc_0.125 O_1.9375) was investigated by first-principles calculations. The results of electronic property calculation show that the incorporation of scandium (Sc³⁺) in ZrO₂ has reduced its bandgap due to the formation of scandium 3d states in the conduction band. The analysis of optical properties shows that scandium doping in ZrO₂ improves the real (ε₁) and imaginary dielectric functions (ε₂), extinction coefficient (k), refractive index (n), reflectivity (R), and absorption coefficient (α) properties thereby enhancing its photocatalytic and optical activities. The heat capacities of ZrO₂ and Sc-ZrO₂ calculated at temperature of 800 K are 74.27 and 77.98 J/K/Nmol, respectively. The result of thermodynamic properties calculations show that doping scandium in zirconia enhances its entropy and specific heat capacity thereby allowing it to be thermodynamically stable for a wide range of electronic applications.

1. Introduction

The biological inertness, biocompatibility, and high impact toughness and strength of zirconia (ZrO₂) make it a popular material for use in the production of medical equipment [1, 2]. The optical characteristics of single crystals based on zirconia have significant potential for application in the field of gate dielectrics, photonics, and micro- and nanoelectronics [3, 4]. Researchers were interested in ZrO₂ because of its many uses in solid oxide fuel cells, thermal coatings, resistive switching devices, gas sensors, and medicine [5]. Zirconia is an indispensable element in active electro-optical devices, broadband interference filters, and high-refractive mirrors because of its remarkable optical properties, which include a high refractive index, a wide optical bandgap, low optical loss, and high transparency in the visible and near-infrared regions [6]. At room temperature, pure ZrO₂ lacks a cubic fluorite structure [7, 8]. On the other hand, adding tri- or divalent ions to zirconia can stabilize its cubic fluorite structure and produce oxygen vacancies, which will increase the compound’s ionic conductivity [7, 9, 10].

Due to its sufficiently high ionic conductivity at high temperatures (1,000°C), yttrium stabilized zirconia (YSZ) is the most commonly used electrolyte for solid oxide fuels cell (SOFC) [11, 12]. Unfortunately, the ionic conductivity of YSZ is insufficient at operating temperatures of 500–600°C (intermediate temperature operation) [13]. In contrast, scandium-doped zirconia (Sc-ZrO₂) is considered as the best material at intermediate temperatures (IT) because it has two orders of magnitude higher ionic conductivity than yttrium-doped zirconia [14, 15, 16, 17]. The ionic radii of Zr⁴⁺ is 0.84 Å, whereas the dopant ions are 0.87 Å for Sc³⁺ and 0.94 Å for Y³⁺, respectively. Sc³⁺ has nearer ionic radii to that of Zr⁴⁺, which reduces the steric-blocking effect during oxygen ion transport. Therefore, Sc-ZrO₂ has higher ionic conductivity than YSZ as a result of small ionic radii difference between the host (Zr⁴⁺) and dopant ions (Y ³⁺, Sc³⁺) [10, 18, 19]. Scandium-doped zirconia achieves a stable cubic phase when the scandium concentration is x > 0.18 [7, 20, 21]. The substitution of scandium into zirconia increases its conductivity and decreases its high-temperature activation energy [22]. Moreover, doping scandium enhances the mechanical strength of zirconia [23]. The small difference in ionic radii of zirconium and scandium ions is the reason for the higher conductivity of scandium-stabilized zirconia [19, 24, 25, 26]. Further research is needed to explore the properties of scandium-doped zirconia for a wide range of applications in order to better understand the effect of this doping in zirconia. Therefore, the purpose of this work is to use first the principle density functional theory (DFT) to examine how scandium doping affects the structural, electronic, optical, and thermodynamic properties of ZrO₂.

2. Computational Methods

DFT, as implemented in open source Quantum Espresso software package within general gradient approximation function (GGA), was used to calculate the structural, electronic, optical, and thermodynamic properties of pure ZrO₂ and Sc-ZrO₂. First, a 2 × 2 × 2 supercell consisting of 32-zirconium atoms and 64 oxygen atoms was created using crystal maker. The doping process was performed using VESTA software to replace 4Zr ⁴⁺ atoms by 4Sc³⁺ atoms corresponding to a dopant concentration of 0.125 (12.5%). During the doping process, two oxygen atoms are removed, leaving two vacancies in their place to maintain stoichiometry and charge neutrality. This resulted in 28Zr, 4Sc, and 62O atoms constituting a total of 94 atoms and two oxygen vacancies in the simulation cell. The ultra-soft pseudopotentials were used to treat the interaction of the electrons with the ion cores, where Zr (4d, 5 s), O (2 s, 2p), and Sc (3d, 4 s) electrons were treated as valence states. To improve the precision of calculation, convergence of cutoff energy, k-point grid, and lattice parameter were employed separately for pure ZrO₂ and Sc-ZrO₂. Convergence testing of total minimum energy as a function of cutoff energy is performed with an increase of 5 Ry in the range of 30–100 Ry. In this calculation, energy threshold convergence of both compounds was achieved at 75 Ry. The convergence test for total minimum energy versus k-point sampling was employed from 2 × 2×2 to 10 × 10 × 10 and achieved at 6 × 6 × 6 k-point grid for both pure ZrO₂ and Sc-ZrO₂. The optimization of lattice parameter was performed for each compound keeping optimized cutoff energy and k-point. The optimized structural parameters of ZrO₂ and Sc-ZrO₂ were used for subsequent computations to investigate their electronic, optical, and thermodynamics properties.

3. Result and Discussions

3.1. Structural Optimization of Zirconia and Scandium-Doped Zirconia

The crystal structure of pure ZrO₂ and Sc-ZrO₂ compounds is studied using DFT calculations. The unit cell of pure ZrO₂ and Sc-ZrO₂ was described in Figures 1(a) and 1(b), respectively.

Details are in the caption following the image — **Figure 1 (a)**
Open in figure viewer PowerPoint

Crystal structure of (a) ZrO₂ and (b) Sc-ZrO₂. Green color = Zr, red color = O, and violet color = Sc.

In order to achieve the equilibrium structure, one has to calculate the lattice parameter that minimizes the DFT total energy.

Figure 2 depicts the calculated lattice parameter of ZrO₂ and Sc-ZrO₂. The calculated lattice parameter that minimizes the DFT of total energy is achieved at 9.8 bohr (5.194 Å) for Sc-ZrO₂ and 9.7 bohr (5.14 Å) for ZrO₂ which is in better agreement with the experimental value of ZrO₂ (5.135 Å) [27, 28]. Thus, the computational result indicates that doping Sc³⁺ raises the lattice parameter of zirconia (ZrO₂), which in turn raises its volume.

3.2. Electronic Properties of Zirconia and Scandium-Doped Zirconia

3.2.1. Density of States

Figure 3 shows the electronic density of states (DoS) for ZrO₂ and Sc-ZrO₂, respectively. As can be seen in Figure 3, the upper valence band energy ranges from −7.27 to −1.82 eV are essentially dominated by O-2p states, with a minor presence of Zr-d states from the hybridization with O-2p for ZrO₂. Furthermore, the result shows that the Zr-d valence band is partially occupied indicating a partial Zr–O covalent interaction. The unoccupied conduction band, which is separated from the valence band essentially dominated by Zr-d states for pure ZrO₂.

As depicted in Figure 3, the Sc-ZrO₂ band located at the range −17.58 to −15.20 eV originates with Sc 2s states. The band at −6.42-0.−1.48 eV originates with the hybrid of Sc2p orbital, Zr4d and Zr4p orbitals. This state contributes to the formation of covalent bond between Sc, Zr, and oxygen. The lower unoccupied conduction band originates with hybrid Sc (3d) and Zr (4d) states. Figure 3 shows that introducing Sc³⁺ contents (12.5%) into ZrO₂ reduced the width of bandgap between the conduction and valence bands.

3.2.2. Band Structure of Zirconia and Scandium-Doped Zirconia

The distance between a material’s valence and conduction bands is known as its optical bandgap. A material’s optical bandgap (Eg) is correlated with its absorption(α) [29].

Figures 4(a) and 4(b), respectively, show the band structure of ZrO₂ and Sc-ZrO₂, which were calculated along the Brillion zone’s high symmetry direction. In this study, the calculated bandgap of Sc-ZrO₂ and pure ZrO₂ are 3.8 and 4.9 eV, respectively. This value is smaller than the experimental value reported for Sc-ZrO₂ (3.8–5.25 eV) and ZrO₂ (3.85–5.65 eV) [21]. Therefore, the incorporation of Sc³⁺ decreases the bandgap of ZrO₂ due to increased Sc3d states in the conduction band which is the core reason for enhancing the photocatalytic and optical activities of scandium-doped zirconia (Sc-ZrO₂).

3.3. Optical Properties of Zirconia and Scandium-Doped Zirconia

It is well-known that the strong light absorption is an indication of a high-efficiency photocatalyst. Moreover, it is known that the optical properties of compounds give useful information about their internal structure and can be described from the dielectric function that gives the linear response of an electronic system submitted to an applied external electric field [30]. The electronic response of a material toward an incident photon can be described from its complex dielectric function ε(ω) = ε₁(ω) + iε₂(ω). Generally, the real part ε₁(ω) represents the phase lag between the incident field and induced field due to polarization and the imaginary part iε₂(ω) represents the measure of energy loss [31].

The optical properties ε₁(ω), ε₂(ω), n(ω), κ(ω), R(ω), and α(ω) is given by the following equation [32]:

(1)

(2)

(3)

(4)

(5)

(6)

where P is the integral, M is a dipole matrix, i and j are the initial and final states, respectively, f_i is the Fermi distribution function for the initial state, E_i is the energy of an electron in the initial state, and ω is the frequency of the photon. The optical properties of ZrO₂ and Sc-ZrO₂ crystals were calculated at equilibrium lattice parameters using GGA approximation in the photon energy range 0–25 eV.

Figure 5 illustrates how the real part of the dielectric function ε₁ (ω), which describes the material’s electronic polarization, varies with incident photon energy up to 25 eV. The first peak observed (23.22) is at 1.759 eV for Sc-ZrO₂ and 15.04 at 4.69 eV for ZrO₂ corresponding to the experimental value 3.9 eV. The second peak 12.68 is at 2.98 eV for Sc-ZrO₂ and 12.16 at 5.67 eV for ZrO₂. As shown in Figure 5, the static dielectric constant around zero frequency limit ε₁(0) is 16.25 for Sc-ZrO₂ and 9.348 for ZrO₂, respectively. The real part of the dielectric function decreases with increasing frequency for both Sc-ZrO₂ and ZrO₂. It also reaches negative value for ZrO₂, which is a characteristic of instability. On the other hand, the real dielectric function of Sc-ZrO₂ is positive confirming scandium doping in zirconia stabilizes its structure.

The imaginary part of the frequency-dependent dielectric function ε₂ (ω) gives the information about the absorption properties of compounds. Figure 6 shows the imaginary part of the dielectric function of zirconia (ZrO₂) and scandium-doped zirconia (Sc-ZrO₂). As shown in Figure 6, the first imaginary dielectric function peak of Sc-ZrO₂ is 17.24 at 2.004 eV and 10.73 at 5.95 eV for ZrO₂. The second peaks are 10.8 at 2.249 eV for Sc-ZrO₂ and 17.72 at 11.79 eV for ZrO₂, respectively.

Among them, peaks 1 and 2 mainly originate from the electronic intraband transition of impurity Sc 3d states and Zr 4d states in the conduction band, where the shift of the position corresponds to the localized degree of the scandium band.

The incorporation of scandium atom causes a slight shift in the energy band, which also causes peak 1 to shift toward lower energy. That is, the absorption edge of the imaginary part of the dielectric function of Sc-ZrO₂ is red-shifted compared to ZrO₂. This corresponds with the preceding calculation, which confirmed that the bandgap become narrower after doping ZrO₂ with scandium. Table 1 presents the real and imaginary dielectric functions of ZrO₂ and Sc-ZrO₂.

Table 1. Real and imaginary dielectric function of ZrO₂ and Sc-ZrO₂.

Compound	ε₁				ε₂
Compound	Peak 1	Energy (eV)	Peak 2	Energy (eV)	Peak 1	Energy (eV)	Peak 2	Energy (eV)
ZrO₂	15.04	4.69	12.16	5.67	10.73	5.95	17.72	11.79
Sc-ZrO₂	23.22	1.759	12.68	2.98	17.24	2.00	10.8	2.24

The optical properties explained by real and imaginary dielectric functions can also be described by the refractive index n (ω) and the extinction coefficient k (ω) [30]. Figure 7 shows the calculated value of n (ω) of each ZrO₂ and Sc-ZrO₂. Relating Figures 5 and 7, the refractive index n (ω) of both Sc-ZrO₂ and ZrO₂ have nearly identical characteristics with their respective real dielectric function ε₁ (ω). As can be seen in Figure 7, the largest refractive index peak is 15.48 at 1.759 eV for Sc-ZrO₂ and 4.01 at 10.81 eV for ZrO₂. The refractive index of Sc-ZrO₂ and ZrO₂ at about zero frequency limit n (0) are 10.83 and 3.05, respectively. In this study, the zero frequency refractive index (n = 3.05) of ZrO₂ calculated is higher than previously reported result(n = 2.15) [33]. As shown in Figure 7, the refractive index of both Sc-ZrO₂ and ZrO₂ decreases as frequency or energy increases. The peaks in ε₁ (ω) and n (ω) are due to the interband electronic transitions.

The calculated value of the extinction coefficient k (ω) provides information about the fraction of light lost due to scattering and absorption per unit distance of the participating medium.

Figure 8 displays the reflectivity and loss function of ZrO₂ and Sc-ZrO₂ compounds in the energy range of 0–25 eV. Correlating Figures 6 and 8, the extinction coefficient k (ω) has almost the same characteristics as the corresponding ε₂ (ω). The frequency-dependent k (ω) of ZrO₂ and Sc-ZrO₂ increases with frequency at low-frequency region and reaches a maximum absorption in the medium at 9.85 at 2.00 eV for Sc-ZrO₂ and 2.64 at 12.03 eV for ZrO₂, respectively. As a conclusion, doping scandium in zirconia leads to rapid absorption of photons.

In this study, to investigate the surface behavior of ZrO₂ and Sc-ZrO₂, its reflectivity, which is the ratio of incident light intensity to reflected light intensity, is also calculated using generalized gradient approximation.

Figure 9 depicts the reflectivity R (ω) versus energy of ZrO₂ and Sc-ZrO₂. As can be seen in Figure 9, the value of reflectivity of Sc-ZrO₂ is 0.594 at 2.0 and 0.41 at 11.05 eV for ZrO₂. In addition, the reflectivity of Sc-ZrO₂ decreases with increasing frequency. This means it shows a good transparency and absorption in the visible range of electromagnetic waves. The reflectivity plot in Figure 9 shows that doping scandium in zirconia leads to a decrease in reflectivity as frequency increases.

It is well-known that the strong light absorption is an indication of highly efficient photocatalyst. Figure 10 shows the calculated absorption coefficients as function of frequency for pure ZrO₂ and Sc-ZrO₂ compounds. The maximum peaks of the absorption coefficient for Sc-ZrO₂ and pure ZrO₂ calculated by the general gradient approximations were obtained at around 17.66 and 23.04 eV, respectively. It is evident in Figure 10 that pure ZrO₂ and Sc-ZrO₂ spectrum shows a good absorption characteristics for the incident photons in the ultraviolet part of the solar irradiation, while a small component appears in the visible region. However, the absorption intensity amplitude is greater for Sc-ZrO₂ than pure ZrO₂. The correlation between the two variables shows that higher absorbance is correlated with lower reflectance or vice versa [34]. Therefore, doping scandium into zirconia enhanced the absorption and lowers the reflectivity of solar radiation.

The incorporation of scandium into the zirconia lattice leads to the formation of new energy levels in the conduction band (Sc-3d). This in turn causes a red shift of the spectra, improving the photocatalytic performance of the studied systems. Additionally, scandium-doped zirconia exhibits a good transparency in the visible range nominating this material for the optical applications. Furthermore, the absorption curve of Sc-ZrO₂ displays relatively larger absorption values than ZrO₂, indicating a good performance for solar cell applications [35].

This study demonstrated that the density functional calculation output indicated that scandium-doped zirconia had an increased refractive index and reduced extinction coefficients in a wide range of frequencies, indicating improved optical transparency [17]. Additionally, it was found that scandium-doped zirconium nanoparticles had enhanced photoluminescent properties, potentially making them suitable for optical sensing applications [36]. Overall, scandium doping has been demonstrated to enhance zirconia’s optical properties, making it a potential material for a variety of optical applications.

3.4. Thermodynamic Properties

The thermodynamic properties of compounds play a major role in their ability to be used in electronic applications. This section examined the thermodynamic properties of the compounds, including internal energy (E), Helmholtz free energy (F), entropy (S), and constant volume-specific heat capacity (C_v) as a function of temperature (T) using a generalized gradient approximation (GGA).

Figures 11 and 12, respectively, show the temperature dependence of the internal energy and Helmholtz free energy of pure ZrO₂ and Sc-ZrO₂. It is observed that the internal energy of these compounds increases with increase in temperature. However, the Helmholtz free energy of the compounds decreases with increasing temperature. At zero temperature (0 K), the calculated value of internal energy and Helmholtz free energy of ZrO₂ and Sc-ZrO₂ is 20.57 and 21.64 kJ/Nmol, respectively. The value of Helmholtz free energy and internal energy of both compounds is different from zero at a temperature of 0 K due to the presence of phonon oscillations. This indicates that doping scandium in zirconia enhanced the internal energy and Helmholtz free energy at temperature of zero (0 K). In addition, doping of scandium enhances both enthalpy and entropy of zirconia, as well as the stabilization of its cubic phase [37].

The heat capacity, entropy, free energy, and internal energy of pure ZrO₂ and Sc-ZrO₂ were measured at temperature range of 0–800 K. Figure 13 indicates the entropy of pure ZrO₂ and Sc-ZrO₂ as a function of temperature. The entropy of both ZrO₂ and Sc-ZrO₂ gradually increases with temperature due to increase in the oscillation of phonons. It is observed in Figure 13, the entropy of Sc-ZrO₂ increases faster than that of pure ZrO₂ with temperature. Therefore, doping ZrO₂ with Sc³⁺ enhances its entropy and facilitates the stabilization of cubic phase by increasing its volume which is in agreement with the literature [37].

Figure 14 shows the temperature dependence of specific heat capacity of pure ZrO₂ and Sc-ZrO₂ at constant volume, which was calculated using the first principle investigation. As shown in Figure 14, heat capacity (C_v) values of pure ZrO₂ and Sc-ZrO₂ increase with the temperature until they reache a temperature limit (T_D) where it reaches a constant level following the Dulong–Petit law, and then it remains nearly constant with further increase in the temperature [38].

In this study, constant volume-specific heat capacity of ZrO₂ and Sc-ZrO₂ computed at a temperature of 800 K is 74.27 and 77.98 J/K/(N mol), respectively. As depicted in Figure 14, the doping of scandium into zirconia increased the heat capacity. The constant volume-specific heat capacity of ZrO₂ is consistent with the previous reported value (60 J/K/(N mol)) [39].

The overall conclusion of the thermodynamic properties calculation is that the addition of scandium to zirconia increases the entropy and the constant volume-specific heat capacity, thus contributing to its thermodynamic stability for various electronic applications. The thermodynamic properties of Sc-ZrO₂ are not compared with experimental values due to the unavailability of literatures.

4. Conclusion

First-principle calculations were employed in order to investigate the effects of scandium doping on the structural stability, electronic characteristics, optical properties, and thermodynamic properties of zirconia. The results of DFT calculations indicated that scandium-doping improved the structural stability of zirconia due to its optimal ionic radii of scandium with zirconia. The electronic analysis shows that doping scandium into zirconia results in a narrower bandgap. The examination of optical characteristics reveals that the addition of scandium doping to ZrO₂ enhances its photocatalytic and optical activities by improving its real (ε₁) and imaginary dielectric functions (ε₂), extinction coefficient (k), refractive index (n), reflectivity (R), and absorption coefficient (α). Calculations of thermodynamic properties reveal that doping zirconia with scandium increases its specific heat capacity and entropy, making it thermodynamically stable for a variety of electronic applications.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Open Research

Data Availability

All the required data are included in the manuscript.

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First Principle Study of Structural, Electronic, Optical, and Thermodynamic Properties of Scandium-Doped Zirconia (Zr_1−xSc_xO₂, x = 0.125)

Abstract

1. Introduction

2. Computational Methods

3. Result and Discussions

3.1. Structural Optimization of Zirconia and Scandium-Doped Zirconia

3.2. Electronic Properties of Zirconia and Scandium-Doped Zirconia

3.2.1. Density of States

3.2.2. Band Structure of Zirconia and Scandium-Doped Zirconia

3.3. Optical Properties of Zirconia and Scandium-Doped Zirconia

3.4. Thermodynamic Properties

4. Conclusion

Conflicts of Interest

Open Research

Data Availability

References

Figures

References

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First Principle Study of Structural, Electronic, Optical, and Thermodynamic Properties of Scandium-Doped Zirconia (Zr1−xScxO2, x = 0.125)

Abstract

1. Introduction

2. Computational Methods

3. Result and Discussions

3.1. Structural Optimization of Zirconia and Scandium-Doped Zirconia

3.2. Electronic Properties of Zirconia and Scandium-Doped Zirconia

3.2.1. Density of States

3.2.2. Band Structure of Zirconia and Scandium-Doped Zirconia

3.3. Optical Properties of Zirconia and Scandium-Doped Zirconia

3.4. Thermodynamic Properties

4. Conclusion

Conflicts of Interest

Open Research

Data Availability

References

Figures

References

Related

Information

First Principle Study of Structural, Electronic, Optical, and Thermodynamic Properties of Scandium-Doped Zirconia (Zr_1−xSc_xO₂, x = 0.125)