The room temperature XRD patterns of La2Ti2 − xNbxO7 (LTO) ceramics are shown in Fig. 2(a). The patterns are indexed to a La2Ti2O7 monoclinic structure ceramic (space group, P21) with the lattice constant a = 7.80896(10) Å, b = 5.54608(7) Å, and c = 13.01425(22) Å,  consistent with those reported in the literature [14, 15]. No secondary phases were detected in any of the compositions within the detection limit of the diffractometer, and the peaks were sharp, suggesting a large particle size according to the Scherrer formula . The bulk and relative density of all compositions for different Nb concentrations are plotted in Fig. 2(b). The relative density of all compositions varied progressively from 84% to 93%. This implies the bulk density increased with increase in Nb concentration with x = 0.25 showing the maximum sintering density of 5.38 g/cm3 (93% of theoretical density, 5.789 g/cm3) .
The SEM images of the 5%H2/N2 sintered, thermally etched and carbon coated surfaces for La2Ti2 − xNbxO7; 0.00 ≤ x ≤ 0.25 ceramics are shown in Fig. 3. The SEM images revealed homogenous and porous structures consistent with their low relative density of ≤ 93% and average grain size of ≤ 2 µm. The effect of porosity on the thermoelectric performance of these compositions is unclear. However, some authors have suggested the presence of porosity in the lattice creates discontinuities which act as scattering centres thereby restricting carrier mobility and enhancing phonon scattering [21, 23, 24]. As a result, both electrical conductivity, σ and thermal conductivity, k is reduced.
Figures 4 and 5 show the temperature dependence of the electrical conductivity (σ), absolute Seebeck coefficient (│S│, power factor (PF), respectively for La2Ti2-xNbxO7 ceramic compositions. x = 0.00 (undoped La2Ti2O7) exhibited the lowest σ in all the measured temperature range, consistent with its lowest density (Figure 2b). The low σ obtained in x = 0.00 showed that carrier mobility was restricted probably by the inherent heavy pores in the grains. The electrical conductivity increased with Nb doping but inconsistent with dopant (Nb) concentration. x = 0.10 showed the highest σ in all the measured temperature range (Figure 4a), reaching a maximum of ~ 2.0 S/cm (200 S/m) at 873 K. This increase in electrical conductivity is attributed to the increase in carrier (electron) concentration due to the substitution of Nb5+ for Ti4+ which produces electrons. Moreover, oxygen vacancy, VO introduced by processing in reducing atmosphere increases the carrier concentration, thereby increasing σ [25, 26]. Some authors have also suggested the effect of grain size as a contributory factor to the enhanced σ. Doping has generally been observed to increase grain size, resulting in a reduced grain boundary area and scattering which may enhance the conduction [25-27]. The highest σ (200 S/m) at 873 K for La2Ti1.9Nb0.1O7 obtained in this study is higher than the maximum σ (0.5 S/m) reported in the literature for La1.6Sr0.4Ti2O6.8±δ ceramic at 573 K .
Figure 4(b) shows the Seebeck coefficient, │S│ of La2Ti2-xNbxO7 sample as a function of temperature. S of all ceramics are negative, indicating that electrons are the dominant carriers [26, 28-30]. S increased monotonically with increasing temperature in all the measured temperature range. However, the behaviour of S of the sample is inconsistent with Ioffe theory  (except x = 0.00 at 973 K). The relationship between S and carrier concentration is given by the following equation :
where ϒ and n are the scattering factor and the carrier concentration, respectively. S is inversely proportional to the carrier concentration. This implies that x = 0.00 with the lowest σ (lowest carrier concentration) is expected to show the highest S in all temperatures while x = 0.10 should likewise exhibit the lowest S as a result its high σ in obedience with Ioffe’s theory. At the maximum measured temperature (973 K), x = 0.00 as expected exhibited the highest absolute Seebeck coefficient value of ~ 389 µV/K. This value is larger than values obtainable in most doped SrTiO3 ceramics in the literature [28, 32–35].
Combining the electrical conductivity and the Seebeck coefficient, the power factor (PF) of La2Ti2 − xNbxO7 sample was determined and shown in Fig. 5 as a function of temperature. Despite the high Seebeck coefficients (190–389 µV/K) exhibited by all the compositions, the PF remained very low (< 20 µW/K2.m), due to the low σ (≤ 2.0 S/cm). However, the results obtained showed that the power factors of the Nb-doped compositions (0.05 ≤ x ≤ 0.25) where higher than that of undoped composition (x = 0.00) in all the measured temperature range, due to the enhanced electrical conductivity. x = 0.10 showed a higher PF value especially at high temperatures (773–973 K) than other compositions and recorded the maximum PF value of ~ 18 µW/K2.m at 973 K.
The temperature dependence of the total thermal conductivity, k and the electronic thermal conductivity, kE of all samples are shown in Figs. 6. The thermal transport behaviour particularly k of the Nb-doped ceramics is irregular with temperature. This behaviour could be related to the complex interplay of phonon scattering including U and N-processes on the ceramic material. Since cation doping of a material increases the grain size thereby promoting carrier (electron) mobility, it could be assumed that phonon propagation as well occurs. As a result, the Nb-doped La2Ti2O7 ceramics exhibited a metallic conduction behaviour, which is evidenced in the increased σ and k, respectively.
On the other hand, undoped La2Ti2O7 showed the lowest k across the measured temperature range, with a minimum = 1.18 W/m. K at 773–873 K. The reduced relative density observed in La2Ti2O7 ceramics indicates an increase in porosity in the microstructure, which significantly affected thermal conductivity. The relation between the k and volume of pores is given in the following equation :
where kO is the thermal conductivity of the material without porosity and P is the fraction of pores in the material. The implication of Eq. 3 therefore, is that increase porosity leads to an increase in phonon scattering, resulting in reduction of k. The minimal k value (1.18 W/m.K) obtained in an undoped La2Ti2O7 is lower than the value (1.3 W/m.K at 573 K) obtained in the literature for pure La2Ti2O7  and comparable to related polycrystalline PLS compounds such as Bi4Ti3O12 (k ~ 1W/m.K) [14, 37] and Sr2Nb2O7 (k = 1.5 W/m.K) [14, 38]. For the Nb-doped La2Ti2O7 compositions reported in this study, x = 0.10 showed the highest k value (2.26 W/m. K) at 973 K, while x = 0.05 exhibited the lowest k value of 1. 49 W/m. K at 773 K, attributed to its large unit cell, large atomic mass, crystal anisotropy and complex crystal structure [37, 38].
The electronic thermal conductivity of all LTO compositions showed similar temperature dependence with σ and increased with increase in temperature as presented in Fig. 6(b). From the small kE values (≤ 0.0044 W/m. K), it is obvious to state that electronic thermal conductivity makes a very small contribution to the total thermal conductivity. This means that k comes mainly from their lattice thermal conductivity [14, 39].
The cumulative impact of the electrical and thermal transport properties on the thermoelectric performance is illustrated by the temperature dependence of the dimensionless figure of merit, ZT as shown in Fig. 7. From 573 K up to 873 K (573–873 K), x = 0.00 (pure La2Ti2O7) had the lowest ZT values (≤ 0.0045) because of the low electrical conductivity. The combination of a higher σ and S resulted in a relatively high ZT in Nb-doped La2Ti2O7 ceramics compared to undoped La2Ti2O7. This suggests that the ZT of La2Ti2O7 could be increased by a careful tuning with an appropriate dopant such as Nb. The ZT of all the compositions except x = 0.15 increased with increasing temperature within the measured temperature range. The ZT of La2Ti1.85Nb0.15O7 (x = 0.15) ceramic increased with temperature up to 873 K and decreased at 973 K. Furthermore, in all compositions, x = 0.05 and 0.10 showed a high ZT values at low temperatures (573–673 K), and beyond 673 K, x = 0.05 exhibited the highest values with a maximum ZT of 0.0084 at 973 K. The highest ZT displayed by 5 mol% Nb-doped La2Ti2O7 is traceable to the lowest k value recorded at high temperatures (773–973 K) compared to other Nb-doped La2Ti2O7 ceramics.