Ultrasound assisted synthesis of Gd and Nd doped ceria electrolyte for solid oxide fuel cells

In this study, the ceramic powders of Ce_1?xGd_xO_2?x/2 and Ce_1?xNd_xO_2?x/2 (x=0.05, 0.10, 0.15, 0.20 and 0.25) were synthesized by ultrasound assisted co-precipitation method. The ionic conductivity was studied as a function of dopant concentration over the temperature range of 300–800 °C in air, using the impedance spectroscopy. The maximum ionic conductivity, σ_800 °C=4.01×10^?2 Scm^?1 with the activation energy, E_a=0.828 kJmol^?1 and σ_800 °C=3.80×10^?2 Scm^?1 with the activation energy, E_a=0.838 kJmol^?1 were obtained for Ce_0.90Gd_0.10O_1.95 and Ce_0.85Nd_0.15O_1.925 electrolytes, respectively. The average grain size was found to be in the range of 0.3–0.6 μm for gadolinium doped ceria and 0.2–0.4 μm for neodymium doped ceria. The uniformly fine crystallite sizes (average 12–13 nm) of the ultrasound assisted prepared powders enabled sintering of the samples into highly dense (over 95%) ceramic pellets at 1200 °C (5 °C min^?1) for 6 h.     

Effect of Nd-doping on structural,thermal and electrochemical properties of LaFe0.5Cr0.5O3 perovskites

The structural, thermal and electrochemical properties of the perovskite-type compound La_1−xNd_xFe_0.5Cr_0.5O₃ (x=0.10, 0.15, 0.20) are investigated by X-ray diffraction, thermal expansion, thermal diffusion, thermal conductivity and impedance spectroscopy measurements. Rietveld refinement shows that the compounds crystallize with orthorhombic symmetry in the space group Pbnm. The average thermal expansion coefficient decreases as the content of Nd increases. The average coefficient of thermal expansion in the temperature range of 30–850 °C is 10.12×10⁻⁶, 9.48×10⁻⁶ and 7.51×10⁻⁶ °C⁻¹ for samples with x=0.1, 0.15 and 0.2, respectively. Thermogravimetric analyses show small weight gain at high temperatures which correspond to filling up of oxygen vacancies as well as the valence change of the transition metals. The electrical conductivity measured by four-probe method shows that the conductivity increases with the content of Nd; the electrical conductivity at 520 °C is about 4.71×10⁻³, 6.59×10⁻³ and 9.62×10⁻³ S cm⁻¹ for samples with x=0.10, 0.15 and 0.20, respectively. The thermal diffusivity of the samples decreases monotonically as temperature increases. At 600 °C, the thermal diffusivity is 0.00425, 0.00455 and 0.00485 cm² s⁻¹ for samples with x=0.10, 0.15 and 0.20, respectively. Impedance measurements in symmetrical cell arrangement in air reveal that the polarization resistance decreases from 55 Ω cm⁻² to 22.5 Ω cm⁻² for increasing temperature from 800 °C to 900 °C, respectively.     

Ferroelectric properties of Pb(Zr0.52Ti0.48)O3–Bi3.25La0.75Ti3O12 ceramics

The ceramic samples of compound (1 ? x)Pb(Zr_0.52Ti_0.48)O₃–xBi_3.25La_0.75Ti₃O₁₂ (when x = 0, 0.03, 0.05, 0.07, 0.10, 0.15 and 0.20) were prepared by a solid-state mixed oxide method. X-ray diffraction analysis showed that complete solid solutions occurred for all compositions. Perovskite phase with tetragonal crystal structure and corresponding lattice distortion was observed. Scanning electron micrographs of sample surfaces showed equiaxed grains for all compositions. Ferroelectric measurements revealed that the addition of small amount of BLT (x = 0.03) showed high remanent polarization (～33.5 μC cm^?2) and low coercive field (～2.74 kV mm^?1). Further increasing BLT content could maintain ferroelectric properties of PZT–BLT ceramics. Based on this study, ferroelectric properties of this PZT–BLT ceramic system can be improved for being further used in ferroelectric memory applications.     

Electrocaloric effect and pyroelectric energy harvesting of (0.94 − x)Na0.5Bi0.5TiO3-0.06BaTiO3-xSrTiO3 ceramics

Ceramics with the composition (0.94 − x)Na_0.5Bi_0.5TiO₃–0.06BaTiO₃–xSrTiO₃ (NBBSTx) where x = 0.10, 0.15, 0.20, and 0.25 were synthesized by a conventional solid-state reaction method to investigate their electrocaloric effect (ECE) and pyroelectric energy harvesting (PEH) properties. The ferroelectric, dielectric, and pyroelectric properties of the prepared ceramics were measured and discussed. It is found that the strontium titanate (ST) content and bias field greatly affect the ferroelectric–relaxor transition. Increasing ST content lowers the depolarization temperature of the ceramics, and both the ECE and PEH behavior of the ceramics strongly depend on their ST content because of the composition-induced decrease of the ferroelectric–relaxor transition temperature. The present investigation demonstrates that the ECE and PEH properties of NBBSTx ceramics can be tuned by introducing ST. Furthermore, a high PEH density of 425 kJ/m³ is obtained for NBBST0.20, which is much higher than those of conventional Pb-based ferroelectrics.     

Enhanced electrical properties in lead-free NBT–BT ceramics by series ST substitution

Comprehensive electrical properties of 0.94(Na_1/2Bi_1/2)TiO₃–0.06BaTiO₃ lead-free ceramics by doping series SrTiO₃ were investigated. High piezoelectric constant of 205 pC/N and electromechanical coupling factor of 0.34 were obtained due to the forming of the rhombohedral–tetragonal morphotropic phase boundary at x=0.02–0.06. Very large recoverable strain of 0.34% was obtained at x=0.10 due to the coexistence of ferroelectric and relaxor pseudocubic phases. A large electrocaloric effect (ΔT_max=1.71 K and ΔT/ΔE=0.34 K mm kV⁻¹ at 50 kV cm⁻¹) which determined by indirect measurements method was obtained at 120 °C at x=0.02, which is significantly higher than that of lead-free ferroelectric ceramics reported so far. Moreover, lower operating temperatures of 50 °C and 30 °C were proposed when x=0.10 and 0.20 with ΔT_max=0.79 K and 0.6 K, respectively. These properties added together indicate a promising material for applications in cooling systems and actuators.     

Microstructural characterization and crystallization kinetics of (1 − x)TeO2–xK2O (x = 0.05, 0.10, 0.15, 0.20 mol) glasses

Microstructural characterization and crystallization kinetics of (1 − x)TeO₂–xK₂O (x = 0.05, 0.10, 0.15, and 0.20 in molar ratio) glasses were investigated using DTA, XRD, Raman spectroscopy, optical microscopy and SEM techniques. Whereas only one exothermic peak was observed for the 0.95TeO₂–0.05K₂O and 0.90TeO₂–0.10K₂O glasses, two crystallization peaks were present on the DTA plots of the 0.85TeO₂–0.15K₂O and 0.80TeO₂–0.20K₂O glasses. On the basis of the XRD and Raman spectrophometry investigations, α-TeO₂, γ-TeO₂ and K₂Te₄O₉ crystal phases were present in the (1 − x)TeO₂–xK₂O (x = 0.05, 0.10, 0.15, and 0.20 in molar ratio) glass samples heated above the peak crystallization temperatures, T_p. SEM/EDS investigations of (1 − x)TeO₂–xK₂O (x = 0.05, 0.10, 0.15, and 0.20 in molar ratio) glasses heated above T_p revealed the presence of distinct TeO₂-rich and K₂Te₄O₉ in the 0.95TeO₂–0.05K₂O and triangular wedge-shaped crystalline regions in the 0.90TeO₂–0.10K₂O, 0.85TeO₂–0.15K₂O and 0.80TeO₂–0.20K₂O glasses. DTA analyses were carried out at different heating rates and the Avrami constant for the 0.95TeO₂–0.05K₂O glass was calculated as 0.94, an indication of surface crystallization also confirming SEM results. On the other hand, the n values were between 1.7 and 1.87 for the exothermic peaks of the 0.80TeO₂–0.10K₂O, 0.85TeO₂–0.15K₂O and 0.80TeO₂–0.20K₂O glasses, indicating one-dimensional crystalline growth mechanisms for these glasses. Activation energies for one-dimensional crystal growth mechanisms in these crystals determined from the modified Kissinger plots were found to vary between 550 and 650 kJ/mol.     

Effect of two different dopants (Mg2+ and Ca2+) and processing parameters on γ-phase stabilization and conductivity of Bi4V2O11−δ

Mg²⁺ and Ca²⁺ doped Bi₄V₂O_11−δ systems are synthesized by a melt quench technique followed by heat treatment. The Ca²⁺ doped samples show higher density than Mg²⁺ doped samples. All the quenched samples show γ-phase stabilization irrespective of dopants and their concentration. The γ-phase stabilization takes place at lower dopant concentration than earlier reported systems. The conversion of γ-phase to ordered β-phase is observed with heat treatment for Bi₄V_2−xMg_xO_11−δ (x=0.05, 0.10 and 0.20) and Bi₄V_2−xCa_xO_11−δ (x=0.05 and 0.10). Ca²⁺ doped system, particularly high concentration (x=0.15 and 0.20) did not show γ→γ׳ phase transition. The lowest activation energy; E_a is observed for Bi₄Mg_0.15V_1.85O_11−δ sample ~0.74 eV in the temperature range 570–750 °C.     

Dielectric,ferroelectric and field-induced strain behavior of K0.5Na0.5NbO3-modified Bi0.5(Na0.78K0.22)0.5TiO3 lead-free ceramics

Lead-free piezoelectric (1 ? x)Bi_0.5(Na_0.78K_0.22)_0.5TiO₃–xK_0.5Na_0.5NbO₃ (BNKT–xKNN, x = 0–0.10) ceramics were synthesized using a conventional, solid-state reaction method. The effect of KNN addition on BNKT ceramics was investigated through X-ray diffraction (XRD), dielectric, ferroelectric and electric field-induced strain characterizations. XRD revealed a pure perovskite phase with tetragonal symmetry in the studied composition range. As the KNN content increased, the depolarization temperature (T_d) as well as maximum dielectric constant (?_m) decreased. The addition of KNN destabilized the ferroelectric order of BNKT ceramics exhibiting a pinched-type hysteresis loop with low remnant polarization (11 μC/cm²) and small piezoelectric constant (27 pC/N) at 3 mol% KNN. As a result, at x = 0.03 a significant enhancement of 0.22% was observed in the electric field-induced strain, which corresponds to a normalized strain (S_max/E_max) of ～434 pm/V. This enhancement is attributed to the coexistence of ferroelectric and non-polar phases at room temperature.     

Compositional range and electrical properties of the morphotropic phase boundary in the Na0.5Bi0.5TiO3–K0.5Bi0.5TiO3 system

We have investigated the Na_0.5Bi_0.5TiO₃–K_0.5Bi_0.5TiO₃ (NBT–KBT) system, with its complex perovskite structure, as a promising material for piezoelectric applications. The NBT–KBT samples were synthesized using a solid-state reaction method and characterized with XRD and SEM. Room-temperature XRD showed a gradual change in the crystal structure from tetragonal in the KBT to rhombohedral in the NBT, with the presence of an intermediate morphotropic region in the samples with a compositional fraction x between 0.17 and 0.25. The fitted perovskite lattice parameters confirmed an increase in the size of the crystal lattice from NBT towards KBT, which coincides with an increase in the ionic radii. Electrical measurements on the samples showed that the maximum values of the dielectric constant, the remanent polarization and the piezoelectric coefficient are reached at the morphotropic phase boundary (MPB) (? = 1140 at 1 MHz; P_r = 40 μC/cm²; d₃₃ = 134 pC/N).     

A correlation between piezoelectric response and crystallographic structural parameter observed in lead-free (1-x)(Bi0.5Na0.5)TiO3–xSrTiO3 piezoelectrics

The structure of lead-free (1-x)(Bi_0.5Na_0.5)TiO₃-xSrTiO₃ (BNT-STx) ceramics was analyzed by the Rietveld method, using X-ray diffraction and neutron scattering data. The structural refinement results suggest that the crystal structure successively changes with SrTiO₃ concentration, x, from the rhombohedral phase (x = 0.00) to rhombohedral and tetragonal (x = 0.10–0.30), tetragonal and cubic (x = 0.40–0.60), and finally cubic (x = 0.80–1.00) phases. Correlation between the charge sensor constant (d₃₃) and the weighted off-center value (d_w) was observed, which may be attributed to the increased dipole motion in the unit cell due to an increased tendency to respond to external stimulation. Furthermore, an improved charge sensor constant (d₃₃) of 140 pC/N was observed for BNT-ST0.20, and a large strain of 0.25% and a d₃₃^* value of 443 pm/V were observed from x = 0.30.     

Crystal structure,microstructure and electrical properties of (1−x−y)Bi0.5Na0.5TiO3–xBi0.5K0.5TiO3–yBiFeO3 ceramics near MPB prepared via the combustion technique

(1?x?y)Bi_0.5Na_0.5TiO₃–xBi_0.5K_0.5TiO₃–yBiFeO₃ (BNKFT-x/y with 0.12≤x≤0.24, 0≤y≤0.07) lead-free piezoelectric ceramics have been prepared by the combustion technique. The effects of amounts of x and y on structures and electrical properties were examined. Powders and ceramics can be well calcined and sintered at 750 °C for 2 h and 1025–1050 °C, respectively. The results indicated that the crystalline structure and microstructure changed with the increase of x and y concentrations. XRD results of BNKFT-x/0.03 and BNKFT-0.18/y ceramics with 0.12≤x≤0.24 and 0≤y≤0.07 showed the rhombohedral–tetragonal morphotropic phase boundary (MPB). The addition of y caused a promoted grain growth while the addition of x suppressed the grain growth. The highest density (ρ=5.85 g/cm³), superior dielectric properties at T_c (ε_r=7846 and tan δ=0.02), remnant polarization measured at 40 kV/cm (P_r = 20.1 μC/cm²) and piezoelectric coefficient (d₃₃=213 pC/N) were obtained for x=0.18 and y=0.03.     

High recoverable energy storage density and large piezoelectric response in (Bi0.5Na0.5)TiO3-PbTiO3 thin films prepared by a sol-gel method

Low-lead-content (1-x)(Bi_0.5Na_0.5)TiO₃-xPbTiO₃ (x = 0, 0.05, 0.10, 0.15, 0.25) (hereafter abbreviated as BNT-xPT) thin films were prepared by a sol-gel method, and their crystal structure, dielectric properties, recoverable energy-storage density and piezoelectric response were investigated as a function of PT concentration. Combining the XRD patterns and Raman spectroscopy indicate the phase structures go through rhombohedral (R) – rhombohedral + tetragonal (R + T) – tetragonal (T) evolution with increasing of PT content. A high recoverable energy storage density of 13.02 ± 0.39 J/cm³ was achieved in the BNT-0.10PT thin films due to the high field endurance and significantly enhanced polarizability. Moreover, a superior piezoelectric response (d₃₃^* = 120 ± 5 pm/V) was also obtained in the 10% PT-modified BNT films, which can be attributed to easy polarization rotation due to low polarization anisotropy on the R-T phase boundary. These properties indicate that BNT-0.10PT films might be promising multifunctional materials for piezoelectric micro-actuator and energy storage embedded capacitor applications.     

Piezoelectric and ferroelectric properties of lead-free [Bi1−y(Na1−x−yLix)]0.5BayTiO3 ceramics

Lead-free [Bi_1−y(Na_1−x−yLi_x)]_0.5Ba_yTiO₃ (BNLB-x/y) piezoelectric ceramics were prepared by sintering the constituent oxides, and their piezoelectric and ferroelectric properties studied. The results of X-ray diffraction (XRD) suggest that Li⁺ and Ba²⁺ diffuse into the Bi_0.5Na_0.5TiO₃ (BNT) lattices to form a solid solution with a single-phase perovskite structure. The ceramics can be well sintered at 1100–1150 °C. The introduction of Li⁺ and Ba²⁺ into Bi_0.5Na_0.5TiO₃ significantly decreases the coercive field, E_c but maintains the large remanent polarization, P_r of the materials. The ceramics exhibit relatively good piezoelectric properties and very strong ferroelectricity: piezoelectric constant, d₃₃ = 208 pC/N, planar electromechanical coupling factor, k_p = 37.0%, remanent polarization, P_r = 38.5 μC/cm², coercive field, E_c = 3.27 kV/mm. The depolarization temperature, T_d of BNLB-0.075/0.04 ceramics is about 190 °C.     

Enhanced multiferroic properties in Pr-doped BiFe0.97Mn0.03O3 films

Bi_1−xPr_xFe_0.97Mn_0.03O₃ (x=0.00, 0.05, 0.10, 0.15, 0.20) thin films were deposited on FTO/glass substrate using chemical solution deposition. The influences of Pr doping on the crystalline structure and multiferroic properties were investigated. In the X-ray diffraction and Raman spectra results, the crystal structures of Bi_1−xPr_xFe_0.97Mn_0.03O₃ films revealed a gradual transformation from the trigonal structure to the tetragonal structure. The leakage current densities of Bi_1−xPr_xFe_0.97Mn_0.03O₃ films are one order of magnitude lower than that of BiFeO₃. Compared with unsaturated polarization-electric field hysteresis loop of BiFeO₃ film, the Pr and Mn co-doped BFO films have significantly improved ferroelectric properties. The improved remnant polarization (Pr=91.3 µC/cm²) and the positive switching current (I=0.028 A) have been observed in Bi_0.85Pr_0.15Fe_0.97Mn_0.03O₃ film. The improved electrical properties are attributed to the structure transformation, increasing grain boundaries, low oxygen vacancies ratio and increasing Fe³⁺ concentration. In addition, the saturation magnetization of Bi_0.85Pr_0.15Fe_0.97Mn_0.03O₃ film is 1.81 emu/cm³, which is approximately three times higher than pure BiFeO₃ (M_s=0.67 emu/cm³).     

Phase transition behavior and electrical properties of (1 − x)Bi0.5Na0.5TiO3–x(Na0.53K0.44Li0.04)(Nb0.88Sb0.08Ta0.04)O3 lead-free ceramics

(1 ? x)Bi_0.5Na_0.5TiO₃–x(Na_0.53K_0.44Li_0.04)(Nb_0.88Sb_0.08Ta_0.04)O₃ (BNT–xNKLNST) with x = 0–0.10 lead-free piezoelectric ceramics were prepared by a solid state method, and the structure and electrical properties were investigated in this study. It is found that a morphotropic phase boundary (MPB) of rhombohedral (R) and tetragonal (T) phase exists in the range of 0.03 ≤ x ≤ 0.05 and the structure changes to paraelectric phase when x > 0.07. The samples with x = 0.05 exhibit improved electrical properties owing to the formation of MPB, which are as follows: piezoelectric constant d₃₃ = 120 pC/N, remnant polarization P_r = 39.4 μC/cm² and coercive field E_c = 3.6 kV/mm. These results indicate that the enhanced piezoelectric properties for BNT can be achieved by forming the coexistence of R and T phase.     

Improvement of structural and superconducting properties of Bi-2212 textured rods by substituting sodium

In this paper, the physical and superconducting properties of Bi₂Sr₂Ca_1−xNa_xCu₂O_8+δ with x=0.0, 0.05, 0.075, 0.1, and 0.20 textured superconducting fiber rods prepared by a laser floating zone (LFZ) technique were studied. The effects of Na⁺¹ substitution for Ca²⁺ have been investigated by X-ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDX), transport measurements, dc-magnetization, magnetic hysteresis and magnetic critical current density. The powder XRD patterns of samples have indicated that Bi-2212 phase is the major one, independently of Na content. The best critical temperature, T_C, has been found as 93.3 K from M–T data for the sample with 0.075 Na substitution. The maximum magnetic J_C value has been calculated as 1.35×10⁵ A/cm² at 10 K for the 0.10 Na sample. The maximum transport critical current density has directly been measured as 1.3×10³ A/cm² at 77 K for the 0.05Na sample.     

Piezoelectric properties and phase transition temperatures of the solid solution of (1 − x)(Bi0.5Na0.5)TiO3–xSrTiO3

The phase diagram of (1 ? x)(Bi_0.5Na_0.5)TiO₃–xSrTiO₃ was completed and investigations on polarization and strain in this system were carried out. (1 ? x)(Bi_0.5Na_0.5)TiO₃–xSrTiO₃-ceramics were prepared by conventional mixed oxide processing. The depolarization temperature (T_d), the temperature of the rhombohedral–tetragonal phase transition (T_r–t) and the Curie temperature (T_m) were determined by measuring the temperature dependence of the relative permittivity. All solid solutions of (1 ? x)(Bi_0.5Na_0.5)TiO₃–xSrTiO₃ show relaxor behavior (A-site relaxor). From XRD-measurements a broad maximum of the lattice parameter can be observed around x = 0.5 but no structural evidence for a morphotropic phase boundary was found. SEM-analysis revealed a decrease of the grain size for increasing SrTiO₃-content. At room temperature a maximum of strain of about 0.29% was found at x = 0.25 which coincides with a transition from a ferroelectric to an antiferroelectric phase. The temperature dependence of the displacement indicates an additional contribution from a structural transition (rhombohedral–tetragonal), which would be of certain relevance for the existence of a morphotropic phase boundary.     

Morphotropic phase boundary in the BNT–BT–BKT system

Lead-free x Bi_0.5Na_0.5TiO₃–y BaTiO₃–z Bi_0.5K_0.5TiO₃ piezoelectric ceramics were synthesized by a conventional solid state reaction method. The microstructure, ferroelectric and piezoelectric properties of the ceramics were investigated. Structure measurements by X-ray diffraction with Rietveld refinement have allowed us to specify more precisely the morphotropic phase boundary (MPB) in this system. For (1 ? x) BNT–x BT solid solution ceramics, the 0.94 BNT–0.06 BT morphotropic composition shows the higher values with d₃₃ = 170 pC/N, k_p = 0.35 and k_t = 0.53. In the case of (1 ? x) BNT–x BKT compositions, the d₃₃, k_p and k_t are, respectively, 137 pC/N, 0.39 and 0.54 for the 0.80 BNT–0.20 BKT ceramic. On the other hand, the ternary 0.865 BNT–0.035 BT–0.100 BKT morphotropic composition shows high piezoelectric constant and electromechanical coupling factors (d₃₃ = 133 pC/N, k_p = 0.26 and k_t = 0.57).     

Low temperature sintering of ZnTiO3/TiO2 based dielectric with controlled temperature coefficient

Structure, microstructure and dielectric properties of ZnTiO₃ and rutile TiO₂ mixtures (ZnTiO₃ + xTiO₂ with x = 0, 0.02, 0.05, 0.1, 0.15 and 0.2) sintered using ZnO–B₂O₃ glass phase (5 wt.% added) as sintering aid have been investigated. For all compounds, the sintering temperature achieves 900 °C. The X-ray diffraction patterns indicate for x = 0.1 that the material is composed by three phases identified as ZnTiO₃ hexagonal, TiO₂ rutile and ZnO. The presence of ZnO is explained by the introduction of Ti into Zn site to form the (Zn_1−xTi_x)TiO_3+x solid solution in resulting the departure of ZnO from the ZnTiO₃ structure. The ZnTiO₃ + 0.15TiO₂ composition sintered at 900 °C with glass addition exhibits attractive dielectrics properties (ɛ_r = 23, tan(δ) < 10⁻³ and a temperature coefficient of the dielectric constant near zero (τ_ɛ = 0 ppm/°C)) at 1 MHz. It is also shown that the introduction of TiO₂ allows to tune the temperature coefficient of the permittivity. All these properties lead this system compatible to manufacture silver based electrodes multilayer dielectrics devices.     

Electrical,structural and thermal properties of nanoceramic (Bi2O3)1−x−y(Ho2O3)x(Tm2O3)y ternary system

Ho₂O₃ and Tm₂O₃ doped Bi₂O₃ composite electrolyte type materials for solid oxide fuel cells (SOFCs) operating at intermediate-temperature were investigated. The bismuth-based ceramic powders were produced by using conventional solid-state synthesis techniques. The products were characterized by means of scanning electron microscopy (SEM), X-ray powder diffraction (XRD), differential thermal analysis/thermal gravimetry (DTA/TG), and the four-point probe technique (4PPT). XRD and DTA/TG measurements indicate that all of the samples have the stable fluorite type face centered cubic (fcc) δ-phase. 4PPT measurements were performed in the temperature range 150–1000 °C in air and these measurements showed that the electrical conductivity of the samples decrease with increasing amount of Tm₂O₃. This increase in the electrical conductivity of the samples could be attributed to the increase in the numbers of highly polarizable cations and oxide ion vacancies. The highest conductivity value was found as 5.31×10^?1 Ω cm^?1 for the (Bi₂O₃)_1?x?y(Ho₂O₃)_x(Tm₂O₃)_y ternary system (for x=20 and y=5 mol%) at 1000 °C. The activation energies of the samples were calculated from log σ graphics versus 1000/T. These calculated results showed that the translation motion of the charge carriers, oxygen vacancies, and space charge polarizations are responsible for the change in activation energy as a function of temperature.