Finds documents with both search terms in any word order, permitting "n" words as a maximum distance between them. Best choose between 15 and 30 (e.g. NEAR(recruit, professionals, 20)).
Finds documents with the search term in word versions or composites. The asterisk * marks whether you wish them BEFORE, BEHIND, or BEFORE and BEHIND the search term (e.g. lightweight*, *lightweight, *lightweight*).
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence.
powered by
Select sections of text to find additional relevant content using AI-assisted search.
powered by
(Link opens in a new window)
Abstract
The article delves into the synthesis and characterization of Er3⁺-doped TiO2 nanoparticles via ball milling, focusing on their enhanced electrical and thermoelectric properties. Key topics include the structural modifications induced by Er3⁺ doping, the impact on electrical conductivity and thermoelectric power, and the mechanisms of small polaron hopping and variable range hopping. The study reveals that Er3⁺ doping significantly enhances the DC electrical conductivity and thermoelectric power factor compared to undoped TiO2, making these nanoparticles promising for waste heat recovery in electronics and wearable sensors. The research highlights the potential of mechanochemical processing for oxide-based thermoelectrics and provides a detailed analysis of the structural disorder and conductivity enhancement correlated with Er-induced modifications. The findings demonstrate the scalability and cost-effectiveness of the ball milling method, offering a solvent-free approach for large-scale production of advanced thermoelectric materials.
AI Generated
This summary of the content was generated with the help of AI.
Abstract
This study investigates the impact of erbium (Er3⁺) doping on the structural, thermoelectric, and electrical properties of titanium dioxide (TiO2) nanoparticles synthesized via a straightforward ball milling approach. Pure TiO2 and Er-doped TiO2 (1%, 2%, and 3% Er) nanocrystalline powders were prepared and characterized using X-ray diffraction (XRD), high-resolution transmission electron microscopy (HRTEM), density measurements, Seebeck coefficient analysis, and DC conductivity measurements. XRD and HRTEM results confirmed the formation of the anatase TiO2 phase and the successful incorporation of Er3⁺, leading to a reduction in crystallite size (from 18.33 nm for pure TiO2 to 14.19 nm for 3% Er-TiO2) and an increase in lattice strain with higher doping concentrations. Density increased with doping, while molar volume decreased. Thermoelectric tests showed that pure TiO2 and the sample with 1% Er-doping conducted electricity in a p-type manner, but at higher temperatures, the samples with 2% and 3% doping showed both p-type and n-type conduction. Crucially, Er3⁺ doping significantly enhanced the DC electrical conductivity and thermoelectric power (TEP) factor compared to undoped TiO2. The conduction mechanism in the high-temperature region was identified as non-adiabatic small polaron hopping (SPH), with the improved conductivity attributed mainly to increased hopping carrier mobility. These findings highlight the effectiveness of Er3⁺ doping via ball milling in tailoring the properties of TiO2 for potential thermoelectric applications.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
1 Introduction
In recent years, the study of nanocrystalline materials has gained significant attention in the field of materials science, particularly for their potential applications in enhancing the efficiency of thermoelectric devices. Thermoelectric materials are of great interest because they can convert waste heat from sources such as industrial operations, vehicle engines, and even the human body into useful electrical energy, improving energy efficiency and sustainability. They are also widely used in temperature sensors, offering accurate detection of temperature variations for industrial and scientific applications. Among these materials, titanium dioxide (TiO₂) is a semiconductor widely studied for thermoelectric applications because it is abundant, inexpensive, and environmentally stable. It also shows strong potential for efficient heat-to-electricity conversion [1, 2]. However, its intrinsic electrical conductivity is relatively low, which limits its efficiency in thermoelectric applications. To overcome this limitation, researchers have focused on modifying TiO2 to enhance its electrical and thermoelectric properties [3]. Various strategies have been employed, including the introduction of defects, the formation of composite materials, and the incorporation of dopants. TiO2 nanocrystals have been created via a variety of techniques, including co-precipitation, hydrothermal, mechanochemical synthesis, chemical bath deposition, and sol–gel [4‐9]. A straightforward and effective solid-state reaction method is an easy way to create nanoparticles [10, 11]. Mechanical milling has been established as an effective technique for fabricating nanocrystalline powders, thereby enabling the isolation of substantial quantities of highly crystalline nanomaterials. Mechanical grinding techniques, particularly ball milling, are widely employed to mix and reduce materials into fine powders with well-defined characteristics. This process not only ensures uniform particle size distribution but also promotes homogeneity in the final product, making it highly suitable for preparing nanostructured and composite materials with tailored properties [12, 13]. A series of mechanical interactions between the agate balls and the materials within the containment agate precipitated a series of transformations, including chemical alteration, reduction in particle size, modifications to morphological structure, and alterations to particulate consistency. At the beginning of the ball milling process, the particles undergo strong plastic deformation due to the combined impact and shear forces exerted by the milling balls. The outcome of milling is largely influenced by several factors, including the milling time, the ball-to-powder mass ratio, and the size of the milling balls [14]. Silicon-based thermoelectric materials are known for their ease of integration with microelectronic devices and large power factors, though they require complex nanostructuring and are less stable when exposed to oxidative environments. Conversely, oxide-based materials such as TiO2 are chemically stable and inexpensive. Within this analysis, it is important to note that TiO2 is of current interest for use as an emerging thermoelectric material [15]. The incorporation of rare earth elements, specifically erbium (Er3+), into titanium dioxide (TiO2) nanocrystalline materials presents a promising avenue for modifying their structural, electrical, and thermoelectric characteristics. Although numerous research activities have covered Er incorporation into TiO2, these papers have prevalently focused on optical or photocatalytic properties, giving relatively less consideration to transport properties or thermoelectric properties [16]. Although previous papers have conventionally regarded Er-doped TiO2 as a way of controlling surface trapping or enhancing upconversion luminescence, the manner by which Er-induced lattice disruptions, defects, or Ti3⁺/Ti4⁺ concentration changes can affect hopping transport or temperature-dependent conductivity remains unexplored. Moreover, previous papers give limited consideration to comparisons among different Er concentrations tested under the same synthesis process. It is especially difficult to address this among ball-milled TiO2, where mechanistic lattice disruptions and defect creations can significantly affect electronic transport properties, although this is incompletely understood for doped TiO2 materials, especially for ball-milled TiO2. In this context, our study advances the field by providing the first integrated analysis of structural evolution, Seebeck-derived carrier type, hopping transport mechanisms, activation energies, and mobility for a controlled series of Er-doping levels (1–3%) synthesized via a single-step ball milling route [17]. When Er3⁺ ions enter the TiO2 lattice, the differences in ionic radius and valence state compared to Ti4⁺ lead to noticeable lattice distortions. These distortions can disturb the crystalline structure, potentially improving the material’s stability and modifying its phase composition. Initial lattice distortions have been observed in preliminary investigations at low Er3+ concentrations [18]. TiO2’s electrical conductivity is significantly impacted by Er3+ doping, with preliminary studies indicating conductivity enhancements at low doping levels; however, these investigations frequently disregarded temperature-dependent changes. Subsequent research addressed temperature variables, yielding divergent outcomes. Certain findings suggest electrical conductivity at elevated doping concentrations, indicating a potential constraint on the enhancement of Er content [19].
In this paper, we clarify the mechanistic role of Er in tuning the thermoelectric performance of TiO2 and highlights the advantages of mechanochemical processing for oxide-based thermoelectrics and correlating Er-induced structural disorder with conductivity enhancement and small polaron mobility. Comprehensive characterization techniques, including X-ray diffraction (XRD) and high-resolution transmission electron microscopy (HRTEM), were employed to elucidate the structural modifications induced by Er3+ doping. The study demonstrates that Er3⁺ doping significantly enhances the DC electrical conductivity and thermoelectric power (TEP) factor compared to undoped TiO2 for waste heat recovery in electronics and wearable sensors.
Advertisement
2 Experimental
Titanium dioxide powder (TiO2) with a molecular weight of 79.86 g and erbium (III) oxide (Er2O3) powder with a molecular weight of 382.51 g, both with 99.9% purity, were bought from Sigma-Aldrich. Only reagent-grade substances that did not need further purification were employed in this experiment.
2.1 Preparation of pure TiO2 and Er-TiO2 nanoparticles under ball milling mechanism
A systematic methodology was employed to synthesize and produce titanium dioxide (TiO2) nanoparticles and erbium-doped titanium dioxide (Er-TiO2) nanoparticles via the ball milling process. Er2O3 and TiO2 powder mixtures with weight ratios of 1:99, 2:98, and 3:97 were combined and initially subjected to homogenization using an agate mortar and pestle for one hour to ensure thorough powder blending. A quantitative measurement of ten grams of powder mixture was subjected to grinding at a ratio of one part powder to twenty parts ball (1:20) by weight. The milling operation used agate balls to avoid contamination with diameters of 15 mm, 11 mm, 8 mm, and 5 mm, and was conducted in the ambient lab conditions. The rotational velocity is 350 rpm for five hours. A short milling cycle, 15 min of grinding followed by a 15-min break to keep temperatures from getting too high and to maintain uniform particle size. This investigation examined titanium dioxide and Er-TiO2 samples at varying concentrations, specifically 1%, 2%, and 3%. The chosen range of concentration is for the following reasons:
i.
Er solubility in anatase is limited due to ionic radius mismatch.
ii.
Our preliminary tests showed excessive Er2O3 segregation at concentrations > 3% during ball milling.
iii.
Doping below 1% does not significantly influence structural disorder or transport behavior. Thus, the chosen range captures meaningful structural modifications without provoking phase decomposition.
2.2 Samples characterization
X-ray diffraction (XRD) analyses were conducted utilizing a 0.15406 nm wavelength of Cu-Kα radiation, facilitated by a SIEMENS D5000 X-ray diffractometer. The diffractograms were acquired at a resolution of 0.05, with measurements taken over a 10–80° range at room temperature. HighScore Plus software enabled Rietveld analysis of a selection of samples. Nanostructure examination and assessment of TiO2 nanoparticle dimensions were accomplished via transmission electron microscopy (TEM); specifically, JEOL JEM-2100 HRTEM imaging was employed under a 200 kV operating voltage. The densities of pure and doped pellets were determined via Archimedes’ method, utilizing toluene as the buoyant liquid at ambient temperature. In order to ascertain the average density of the samples, each specimen was subjected to triplet measurements. Electrical assessments were facilitated by applying a silver paste electrode to the polished surfaces of all samples. The thermoelectric power of all samples was quantified across a temperature range covering 310 K to 423 K, utilizing K-type digital thermocouples and copper electrodes. Additionally, DC conductivity (σ) was measured over the temperature range of 303–423 K via the deployment of a KEITHLEY 485 picoammeter. All reported data are averages of three independent measurements with error analysis. The overall error margin in conductivity and thermoelectric power values is within ± 5%.
3 Results and discussion
3.1 Structural and physical properties
3.1.1 XRD
A detailed XRD analysis was conducted to elucidate the effect of the solid-state reaction method on the crystallite dimensions of the synthesized TiO2. The diffraction peaks of pure TiO2 and Er-TiO2 with respective doping concentrations of 1%, 2%, and 3%, displayed in Fig. 1a, indicate well-ordered crystal structures. The diffraction patterns in line with (101), (004), (200), and (211) planes of tetragonal anatase TiO2 occur at 2θ values of 25.23°, 37.77°, 48°, and 55.05°, respectively, consistent with the indexed XRD reference pattern provided by JCPDS No. 96–152-6932 [20]. Additionally, the erbium-doped titanium dioxide (Er-TiO2) sample with the anatase phase exhibits secondary diffraction peaks corresponding to the erbium oxide (Er2O3) diffraction patterns (222), (040), (044), and (226), aligned with reference code JCPDS 96–230-0532 [21]. An increase in Er3+ dopant concentration correlates with enhanced peak intensities, substantiating the polycrystalline nature of Er-TiO2 samples. Concurrently, the expansion of diffraction peaks, associated with increasing Er3+ concentrations, verifies the diminishment in crystal size resulting from Er3+ addition. The crystallite size of each specimen was determined through the implementation of Scherrer’s equation to the full width at half maximum (FWHM) of the diffraction peaks [22, 23].
$$ D = \frac{0.9 \lambda }{{\beta \cos \theta }} $$
(1)
where D is the average crystallite size, x-ray wavelength λ = 0.15406 nm, β is the FWHM of peaks, and θ is the Bragg’s angle. The occurrence of Ti–O–Ln links or lanthanide oxide particles at the interface in doped samples has been correlated with the reduction in particle size, which is attributed to the inhibition of crystal grain growth and the disruption of anatase particle aggregation. [24]. Er3+ introduction doping led to a reduction in crystallite size, decreasing from 18.33 nm to 14.17 nm, as observed in the 3% Er-TiO2 sample, listed in Table 1. Consequent to this reduction, the defect quantity of the sample can be quantified using the dislocation density equation, which exhibits an inverse quadratic relationship with crystallite dimensions, as described in Eq. 2. [25].
where D is the crystallite size of the samples. The dislocation density was found to increase with increasing Er concentration, an outcome consistent with the Er3+ dopant’s partitioning at grain boundaries. [26]. Notably, dislocation density values are tabulated in Table 1. The inherent strain effects stemming from grain boundaries and intra-granular defects in nanocrystals are taken into consideration. In titanium dioxide-doped powders, lattice strain is correlated with crystal growth originating from lattice irregularities. This value was meticulously computed via Eq. 3. The observed diminution in crystallite size, accompanied by the increase of lattice strain in Fig. 1b, substantiates the successful incorporation of Er3+ ions into the titanium dioxide matrix.
a XRD patterns of pure TiO2 and Er-doped TiO2 nanoparticles with different concentrations (baseline offset) b Crystallite size and lattice strain as a function of Er-doping concentration
The variation of crystallite sizes (D), lattice strain (ε), and Dislocation density (ẟ) for TiO2 and Er-TiO2 with different Er concentrations
Sample
Crystallite size
D (nm)
± 0.01
Dislocation density
ẟx10−3 (nm−2)
± 0.1
Lattice strain Ꜫx10−2
± 0.01
Pure TiO2
18.33
2.97
1.81
1%Er- TiO2
16.56
3.64
1.98
2%Er- TiO2
15.92
3.94
2.22
3%Er- TiO2
14.19
4.96
2.29
3.2 HRTEM and XPS
The structural features of the synthesized materials were rigorously investigated using Transmission Electron Microscopy (TEM), as explained in Fig. 2. The TEM images depicting pure TiO2 and 2%Er-TiO2 (optimal sample) illustrate the presence of agglomerated, nanometer-scaled TiO2 particles, exhibiting a spheroidal grain morphology (see Figs. 2a, e). The agglomeration observed is due to the high surface energy and nanoscale size of the particles, which is a common characteristic of ball-milled oxide nanoparticles [27]. Additionally, concentric rings indicative of the polycrystalline nature of the TiO2 nanoparticles were evident in the selected area electron diffraction (SAED) patterns [28]. Further elucidation of the crystalline structure of the samples is facilitated by high-resolution TEM analyses, as evident in Figs. 2b, f at a magnification of 10 nm, wherein the lattice fringes exhibit spacings matched with the (101), (004), and (200) crystallographic planes of anatase TiO2, specifically 0.35 nm, 0.23 nm, and 0.18 nm, respectively. SAED panels (c) and (g) were to confirm the crystalline features and phases of the nanoparticles that were shown with distinct lattice fringes and their d-spacings. These specific areas were selected because they provided the best resolution imaging of lattice planes necessary for precise d-spacing measurement. The aim here is not to suggest that those areas portray the average particle size; it is to check the crystallinity and phase (anatase TiO2) at the nanoscale. The supervision of several lattice planes (101), (004), and (200) in both pure and doped samples as well as the XRD data comparison and the standard JCPDS reference, confirms that these regions are representative of the analyzed sample and its phase composition. These parameters agree with pattern results, thereby substantiating the existence of the anatase phase in the undoped and Er-doped TiO2 samples. The particle size distribution histograms (Figs. 2d, h) are depicted by 50 particles that were selected from multiple micrographs collected from different regions of each grid to ensure random and representative sampling. They are derived from transmittance electron microscopy images using ImageJ software, enabling quantitative evaluation of the mean particle diameter, which correlates strongly with crystallite sizes inferred from X-ray diffraction analysis, thereby substantiating the efficacy of the structural characterization techniques utilized in this investigation.
Fig. 2
a–d TEM at 200 nm, HRTEM at 5 nm scale, selected area electron diffraction (SAED) images, and average particle size histogram for 50 calculated particles of pure TiO2, respectively. (e–h) TEM at 100 nm, HRTEM at 10 nm scale, selected area electron diffraction (SAED) images, and average particle size histogram for 50 calculated particles of 2%Er-TiO2, respectively
X-ray Photoelectron Spectroscopy (XPS) measurements were previously conducted on these same Er-doped TiO₂ samples as part of an earlier investigation by our group [29]. XPS studies show the expected core-level peaks (i.e., Ti 2p, O 1s, C 1s) and also have an Er 4d signal from the doped samples indicating that Er is incorporated into the material. The Ti 2p spectra showed that all samples contain primarily Ti4⁺ and that the Ti3⁺ peaks were seen only in the doped forms indicating that there has been partial reduction due to oxygen-vacancy creation. The percentage of Ti3⁺/Ti4⁺ in the doped Er samples is an increasing function of the amount of Er present and therefore indicates that Ti3⁺ has been modified electronically through defects as Er is introduced. A very small Ti2⁺ was detected in only the very low levels of dopant Er and further supports the defect attributed to reduced oxide phenomenon. The O 1s spectra indicated that the major peak is the lattice oxygen peak with a second higher binding energy peak attributed to oxygen deficient states on the surface of the materials. Therefore, these findings indicate that Er3⁺ has been successfully incorporated into the TiO2 lattice with the creation of defects, and with no evidence of contamination due to foreign sources, all of which support the proposed conduction mechanisms [29].
3.3 Density (ρ) and molar volume (Vm)
Understanding a material’s structure and other properties often depends on its density [30]. Density is often assessed via liquid displacement, a method that inherently relies on Archimedes’ principle. The mean density can be computed employing the relationship:
where ρL is the density of toluene (0.8669 g/cm3), Wa is the weight in the air, and WL stands for the weight in toluene. Molar volume can be estimated by utilizing the molecular weights (MWt) of titanium dioxide (TiO2) and the densities (ρ) of the nanoparticle specimens according to the equation:
$$ V_{m} = \frac{{M_{wt} }}{\rho } $$
(5)
An examination of the doping dependence on density and molar volume for TiO2 samples reveals a distinct relationship as depicted in Fig. 3. Specifically, the density of TiO2 is observed to increase gradually with increasing doping concentration, contrasted with the converse behavior of molar volume (Vm). Moreover, as crystallite size (D) decreases with the effect of doping, in line with the data presented in Table 2, the density of TiO2 samples is concurrently increased. This phenomenon arises from the insertion of large Er3+ ions into the lattice, resulting in a concurrent alteration of the mass per unit volume of the present samples. Consequently, a correlation between density and concentration of Ti ions (N) is inferred, facilitated by the application of a relevant relation [31]:
$$ N = \frac{{\rho P N_{A} }}{{M_{wt} }} $$
(6)
where p is the weight percentage and NA Avogadro’s number. The mean inter-ionic distance between titanium ions (R) is defined by [32]:
$$ R = \left( \frac{1}{N} \right)^{1/3} $$
(7)
Fig. 3
Density and molar volume as a function of Er-doping TiO2 concentration with different Er concentrations
Physical properties of TiO2 and Er-doped TiO2 at different concentrations
Sample
\({\varvec{\rho}}\) ± 0.02 (g/cm3)
Vm ± 0.02 (cm3/mol)
N ± 0.01 (× 1022 cm−3)
Log \({\varvec{\sigma}}\) ± 0.01 (S/m)
W ± 0.01 (eV)
R ± 0.01 (nm)
Pure TiO2
2.870
27.82
2.164
−8.13
0.561
0.358
1%Er-TiO2
3.100
26.73
2.252
−7.87
0.556
0.354
2%Er-TiO2
3.900
22.03
2.733
−7.62
0.531
0.331
3%Er-TiO2
4.090
21.74
2.769
−7.57
0.519
0.330
3.4 Thermoelectric power and power factor (PF)
Thermoelectric power measurements were employed to assess the degree of reduction of transition metal ions (C = Ti4+/Σ Ti) utilizing the Seebeck coefficient in accordance with Heikes’ et al. method [33]. They have demonstrated that the thermoelectric properties of TiO2 specimens are directly influenced by the stoichiometric balance between titanium ions existing in high and low valence states, complying with the equation.:
In Fig. 4, the Seebeck coefficient (S) is depicted depending on the temperature for TiO2 and Er-TiO2 samples, thereby enabling the determination of the predominant charge carrier type based on this thermoelectric property [34]. The pure sample and 1% Er concentrations exhibited p-type conductivity, indicating that holes are the primary charge carriers, facilitating conduction in these instances. Conversely, the material with 2% and 3% Er concentrations exhibits temperature-dependent conductivity, transitioning from p-type in low-temperature environments to n-type in higher-temperature regimes, thereby signifying the predominant presence of mixed charge carriers, comprising both electrons and holes [35]. At 369 K, a comparative analysis of the doping dependence of nanostructured pure TiO2, concerning S and C values, is presented in Fig. 5. Similarly, the trends observed in C and S are indicative of the impact of doping on TiO2 samples. This phenomenon is manifest in the decrease of C values following doping with 2% and 3% Er concentrations, which is confirmed by the corresponding -ve of S.(Table 3)
Fig. 4
The thermoelectric power (S) as a function of temperature for TiO2 and Er-TiO2 samples with different Er concentrations
Effect of doping concentration on thermoelectric power (S) and reduced transition metal ion (C) at 369 K for TiO2 and Er-TiO2 samples with different Er concentrations
The effect of the doping concentration of TiO2 samples on the conductivity and the fraction of reduced transition metal ion (C)
Sample
S ± 1 (µV/K)
C
Pure TiO2
9.97
0.5288
1%Er-TiO2
12.71
0.5368
2%Er-TiO2
−11.84
0.4657
3%Er-TiO2
−15.63
0.4547
The power factor constitutes a crucial performance metric for thermoelectric materials, as it quantitatively assesses their efficacy in generating electricity from thermal gradients [36]. A superior thermoelectric performance is quantitatively represented by a raised power factor, thereby underscoring the material’s enhanced capacity for power generation. The power factor, a critical parameter, can be theoretically computed through the mathematical convolution of the Seebeck coefficient and direct current conductivity [37]:
$$ {\text{PF}} = {\text{ S}}^{2} {\upsigma } $$
(9)
where σ is the measured dc conductivity (see later). Figure 6 illustrates the computed power factors of TiO2 as a function of temperature, covering 310 K to 410 K. Notably, undoped TiO2 exhibits the lowest values across the evaluated temperature range. Er-doping at various concentrations yields substantial enhancements in power factor, as reported by M.M. Abdelrazek et al., thereby substantiating the potential for thermoelectric applications [18].
Fig. 6
Power factor as a function of temperature for TiO2 and Er-TiO2 samples with different Er concentrations
Figure 7 displays the dc conductivity (log σ) of TiO2 samples as a function of 1000/T, revealing an enhancement in electrical conductivity due to elevated Er concentrations. All measured curves show a linear temperature dependency up to a certain temperature (θD/2) before departing from linearity, thereby yielding temperature-dependent activation energies (W). This phenomenon is ascribed to a conduction mechanism shift from a high-temperature small polaron hopping (SPH), where (T > θD/2) model to intermediate temperature variable range hopping (VRH) model, where (T \(<\) θD/2). [38, 39]. Mott’s equation is used to express the dc conductivity (σ) for the linear curves [40]:
where σo is the pre-exponential factor, k stands for Boltzmann’s constant, and T stands for the absolute temperature. Measurements of θD, σ, and W parameters for pure TiO2 and Er-doped TiO2 nanoparticle specimens were compiled at 369 K temperature, as a function of Er3+ concentration, and are numerically revealed in Table 4.
Fig. 7
Temperature dependence of dc conductivity (log σ) for TiO2 and Er-TiO2 nanoparticles with different Er concentrations
Significant enhancement in electrical conductivity is observed as a direct consequence of increased local concentrations of transition metal ions, specifically Ti2+ and Ti3+, resulting from doping interventions [41]. The improvement of electrical conductivity is possibly correlated with the dislocations generated through doping, resulting in an increased density of charge carriers (electrons or holes), thereby enhancing conductivity. An investigation of this phenomenon at 369 K is presented in Fig. 8, indicating that doping yields the highest electrical conductivity and lowest energy activation values. This behavior is dependent on the characteristics of the SPH mechanism [42, 43].
Fig. 8
Effect of doping on dc conductivity (log σ) at 369K and activation energy (W) for TiO2 and Er-TiO2 nanoparticles with different Er concentrations
Austin and Mott have formulated a theoretical framework for the conductive properties of nanocrystalline semiconductor materials via phonon-assisted small polaron hopping in localized electronic states [43‐45]. \(\sigma\) within the non-adiabatic system is governed by considerations outlined in the referenced study [34]:
where νo, the frequency of optical phonons, which is determined by the Debye temperature (θD) and Planck’s constant (h) (νo = k θD/h); R, the distance between ions; N, the concentration of Ti ions; C, the proportion of reduced Ti ions (C = Ti+2Σ Ti); and α, a coefficient of the rate of decay of the wave function [43]:
where L is an invariant value of 0.3, and εs represents the static dielectric constant.
3.5.2 Small polaron hopping (SPH)
Moser et al. demonstrate that oxygen vacancies result in the creation of polaronic carriers and the ability to modify the electrical properties of anatase from an insulator to a polaronic conductor as a function of doping concentration. This supports our conclusion that defects and lattice strains created by Er incorporation result in the promotion of the generation of polarons and the processes involved in polaron hopping transport, rather than simple band-like conduction [46]. This model is identified in the high-temperature region (T > θD/2), where a linear relationship is observed in the Arrhenius plot of log σ vs. 1000/T (Fig. 7). This behavior is characteristic of thermally activated hopping of polarons to nearest-neighbor ionic sites and is modeled using Mott’s equation [40]. Holstein derived the polaron hopping energy, denoted as WH, from a theoretical mathematical equation [47, 48]:
The electron–phonon coupling constant is denoted by [γP]2. The frequency of optical phonons is represented by ωP. Bogomolov et al. investigated the relation between the polaron radius (rp) and the mean spacing (R), utilizing Eq. 16 [49]:
The high-frequency dielectric constant of the samples is denoted as ε∞, whereas εs represents the static dielectric constant. The WH values are estimated to range between 0.135 and 0.28 eV, a range considered suitable for the development of small polarons. The density of states around the Fermi level can be calculated as follows, according to Holestein [51]:
The N(EF) values included in Table 4 appear to be convincing for localized states based on the samples [52]. The electron–phonon interaction parameter γP is quantitatively evaluated through the application of the following expression [43]:
$$ \gamma_{p} = \frac{{2W_{H} }}{{h\nu_{0} }} $$
(20)
The estimated γP values for TiO2 and Er-TiO2 samples fall within the range of 13.19 to 5.58. This interval suggests a strong electron–phonon interaction in accordance with the premise of Mott and Davis, who contend that γP values exceeding 4 are indicative of such interaction [53].
3.5.2.1 The characteristics of polaron hopping conduction
To clarify the nature of polaron hopping—whether adiabatic or non-adiabatic—in titanium dioxide (TiO₂) and erbium-doped titanium dioxide (Er–TiO₂), a plot of logarithmic conductivity (σ) versus activation energy (W) was constructed at a fixed experimental temperature (Texp). The corresponding calculated temperature (Tcal), determined from the slope of this plot, indicates adiabatic behavior when it closely matches Texp, as expressed in Eq. (21), where exp(–2αR) = 1 [43]. Deviation from adiabatic hopping occurs when the thermal energy becomes insufficient to satisfy this condition, which is manifested by a pronounced reduction in the exponential decay factor exp(–2αR) in Eq. (21) [54].
In Fig. 9, the experimental temperature of 369 K differs markedly from the calculated value of 190 K, indicating that the examined samples exhibit an intrinsically non-adiabatic hopping behavior. Emin and Holstein developed a theoretical model of polaron transport under zero disorder energy conditions (WD = 0), which accounts for both adiabatic and non-adiabatic hopping mechanisms [32, 51]:
where J is the polaron bandwidth linked to the overlap of electron wave functions on nearby sites. The experimental results align with the theoretical model described in Eq. (20), which links polaron hopping energy to the concentration of Er3⁺. This confirms that non-adiabatic hopping is the dominant transport mechanism in the studied system. Further validation of this conduction process is provided through analysis based on the Emin–Holstein model [55]:
The calculated polaron bandwidth, ranging from 0.045 to 0.093 eV at 369 K, depends on the Er3⁺ concentration and differs from the hopping conduction values obtained from Eq. (23) in Table 4. Therefore, Eq. (22) is more applicable, confirming that conduction in Er-doped TiO₂ nanoparticles is governed by a non-adiabatic hopping mechanism.
3.5.2.2 Mobility and carriers’ density
Austin and Mott models could be applied for estimating hopping carrier mobility μ using the following equation [58]
and the next relation provides the carrier density Nc [59].
$$ N_{c} = \frac{\sigma }{e\mu } $$
(27)
At a temperature of 369 K, μ and Nc values are presented in Table 5. The magnitude increases in the extracted hopping mobility (from ~ 2 × 10⁻⁷ to ~ 1 × 10⁻5 cm2·V⁻1·s⁻1) and the near-constant values of Nc (∼ 1015 cm−3) suggest that hopping mobility is the dominant contributor to conductivity [60]. These data confirm a localized electron state at Ti ion sites and small polaron hopping in our system [61]. The results demonstrate a positive correlation between Er3+ concentration, hopping carrier mobility, and increased conductivity (see Fig. 10), with improved hopping mobility being the primary factor for this enhancement.
Table 5
Hopping carrier mobility (μ) and density (Nc) of the TiO2 samples at fixed temperature 369 K for TiO2 and Er-TiO2 with different Er concentrations
Sample
µ ± 0.3 (× 10–7 cm2/V.s)
Nc ± 0.01 (× 1015 cm−3)
Pure TiO2
2.16
1.32
1%Er-TiO2
6.29
2.15
2%Er-TiO2
38.1
9.73
3%Er-TiO2
104
10.48
Fig. 10
Effect of doping concentration on hopping carrier mobility (μ) for TiO2 and Er-TiO2 samples
VRH is applied to the intermediate temperature region (T \(<\) θD/2), where the conductivity data deviates from the linear SPH model. In this region, a linear fit is achieved when plotting log(σT1/2) vs. T−1/4 (Fig. 11). This indicates that at lower thermal energies, charge carriers hop over variable distances to energetically favorable localized states, as described by Greaves’ VRH model [44, 62]. Greaves’ modification to Mott’s variable range hopping theory involves a procedure applicable at intermediate temperature ranges, whereby the dc conductivity (σ) of the material is described by the equation [44, 62]:
The obtained results demonstrate a satisfactory match to experimental data within the intermediate temperature range, thereby validating the applicability of Greave’s Variable Range Hopping (VRH) model to TiO2 nanoparticles. Table 6 presents the parameters derived from the corresponding plot, where α is calculated using Eq. 29. α and N(EF) exhibit convincing values for localized defect states [52].
Table 6
Parameters of Greaves’ model for TiO2 and Er-TiO2 with different Er concentrations
Sample
A ± 0.2 (S.K1/2/m)
B ± 0.1 (K1/4)
\({\varvec{\alpha}}\) ± 0.01 (Å)−1
Pure TiO2
90.92
27.52
0.2860
1%Er-TiO2
107.42
31.08
0.3418
2%Er-TiO2
110.67
31.71
0.3803
3%Er-TiO2
113.58
31.44
0.3806
4 Conclusion
Pure TiO2 and Erbium (Er3⁺)-doped TiO2 nanoparticles (1%, 2%, 3% Er) were successfully synthesized using a ball milling technique.
The nanocrystalline anatase phase of TiO2 and its structural incorporation of Er3⁺ ions were affirmed through XRD and HRTEM characterizations.
Er3⁺ doping increases the density by 42% and decreases crystallite size by 23% (from 18.33 nm to 14.19 nm for 3% Er).
Thermoelectric power (Seebeck coefficient) measurements revealed p-type conduction for pure TiO2 and 1% Er-TiO2, while 2% and 3% Er-TiO2 exhibited mixed conduction (p-type at lower temperatures, n-type at higher temperatures).
An enhancement in the thermoelectric power factor was noticed in the Er-doped samples compared to pure TiO2.
DC electrical conductivity increased notably with increasing Er3⁺ concentration, accompanied by a decrease in activation energy.
The electrical conduction mechanism at higher temperatures (T > θD/2) was determined to be non-adiabatic small polaron hopping (SPH). While at intermediate temperatures, the conduction mechanism aligns well with Greaves’ variable range hopping (VRH) model.
The observed increase in conductivity with doping is primarily attributed to an enhancement in the hopping carrier mobility rather than the carrier concentration.
Overall, the research exhibits that Er3⁺ doping via ball milling is an efficient technique to modify the structural properties and significantly improve the electrical conductivity and thermoelectric performance of TiO2 nanoparticles.
The practical applications of our findings include potential for waste heat recovery in electronics and wearable sensors. The ball milling method is scalable, low-cost, and solvent-free, which is useful for potential large-scale thermoelectric material production.
5 Competing Interests
The authors declare no competing interests.
Acknowledgements
there is no
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
X. Liu et al., High power factor Nb-doped TiO2 thermoelectric thick films: toward atomic scale defect engineering of crystallographic shear structures. ACS Appl. Mater. Interfaces 15, 5071–5085 (2023)PubMedPubMedCentralCrossRef
2.
B. Gueridi, et al., Prediction study of thermoelectric properties of TiO2 nanoparticles and effect on PVA/SiO 2 hybrid films synthesized by sol-gel method. 2024.
X. Quan et al., Preparation of lanthanum-doped TiO2 photocatalysts by coprecipitation. J. Mater. Sci. 42, 6287–6296 (2007)CrossRef
5.
G. Wangs, Hydrothermal synthesis and photocatalytic activity of nanocrystalline TiO2 powders in ethanol–water mixed solutions. J. Mol. Catal. A: Chem. 274, 185–191 (2007)CrossRef
6.
A.M. Elseman et al., TiO2 nanotubes: an advanced electron transport material for enhancing the efficiency and stability of Perovskite solar cells. Ind. Eng. Chem. Res. 59, 18549–18557 (2020)CrossRef
7.
S. Yin et al., Preparation of visible light-activated titania photocatalyst by mechanochemical method. Chem. Lett. 32, 358–359 (2003)CrossRef
8.
A.M.M. Fadl et al., Passivator materials based on the benzothiazole-sulfonamide hybrid: synthesis, optical, electrochemical properties, and molecular modeling for perovskite solar cells. Mater. Res. Bull. 182, 113151 (2025)CrossRef
9.
M.R. Mohammadi, D.J. Fray, A. Mohammadis, Sol–gel nanostructured titanium dioxide: controlling the crystal structure, crystallite size, phase transformation, packing and ordering. Microporous and Mesoporous Mater. 112, 392–402 (2008)CrossRef
10.
G. Gorrasi, A. Sorrentinos, Mechanical milling as a technology to produce structural and functional bio-nanocomposites. Green Chem. 17, 2610–2625 (2015)CrossRef
11.
A.M. Eissa et al., Tuning optical properties of sustainable inorganic bismuth-based perovskite materials with organic ligands. J. Mol. Struct. 1321, 140183 (2025)CrossRef
12.
A.M. Elseman, M.M. Rashad, A.M. Hassans, Easily attainable, efficient solar cell with mass yield of nanorod single-crystalline organo-metal halide perovskite based on a ball milling technique. ACS Sustainable Chem. Eng. 4, 4875–4886 (2016)CrossRef
13.
C. Suryanarayanas, Mechanical alloying and milling. Prog. Mater. Sci. 46, 1–184 (2001)CrossRef
14.
I. Morad et al., Facile synthesis and comparative study for the optical performance of different TiO2 phases doped PVA nanocomposite films. Phys. B Condens. Matter 597, 412415 (2020)CrossRef
15.
M. Noroozi et al., A comparison of power factor in n and p-type SiGe nanowires for thermoelectric applications. J. Nanosci. Nanotechnol. 71, 1622–1626 (2017)CrossRef
J.B. Martins et al., The role of the dopant in the electronic structure of erbium-doped TiO2 for quantum emitters. APL Mater. 12, 121110 (2024)CrossRef
18.
M.M. Abdelrazek et al., The effect of rare earth (La, Er and Yb) doped V2O5 nanocrystalline films on the structural, thermoelectric and electrical properties for thermoelectric applications. Mater. Sci. Eng. B 302, 117215 (2024)CrossRef
19.
Yd.J. Acosta-Silva et al., Study of the effects of Er doping on the physical properties of CdSe thin films. Magnetochemistry 9, 107 (2023)CrossRef
20.
T.E. Weirich et al., Rietveld analysis of electron powder diffraction data from nanocrystalline anatase, TiO2. Ultramicroscopy 81, 263–270 (2000)PubMedCrossRef
21.
Z. Heiba, H. Okuyucu, Y.S. Hasciceks, X-ray structure determination of the rare earth oxides (Er1-uGdu)2O3 applying the rietveld method. J. Appl. Crystallogr. 35, 577–580 (2002)CrossRef
22.
I. Morad, X. Liu, J. Qius, Crystallization-induced valence state change of Mn2+ → Mn4+ in LiNaGe4O9 glass-ceramics. J. Am. Ceram. Soc. 103, 3051–3059 (2020)CrossRef
23.
J. Reszczyńska et al., Visible light activity of rare earth metal doped (Er3+, Yb3+ or Er3+/Yb3+) titania photocatalysts. Appl. Catal. B Environ. 163, 40–49 (2015)CrossRef
24.
F.B. Li, X.Z. Li, M.F. Hous, Photocatalytic degradation of 2-mercaptobenzothiazole in aqueous La3+–TiO2 suspension for odor control. Appl. Catal. B Environ. 48, 185–194 (2004)CrossRef
25.
T.T.T. Van et al., Tin dioxide nanocrystals as an effective sensitizer for erbium ions in Er-doped SnO2 systems for photonic applications. J. Nanomater. 2016, 6050731 (2016)CrossRef
M.M. El-Desoky et al., Facile planetary ball mill synthesis, structural, photoluminescence, linear, and nonlinear optical features of erbium-doped TiO2 nanoparticles. Appl. Phys. A 131, 402 (2025)CrossRef
28.
W. Zhou, H.F. Greers, What can electron microscopy tell us beyond crystal structures? Eur. J. Inorg. Chem. 2016, 941–950 (2016)CrossRef
29.
M.E. Abd-Elrazek et al., Boosting perovskite solar cell efficiency with ball-milled Er3+-doped TiO2 as an electron transport layer. Sol. Energy 294, 113525 (2025)CrossRef
30.
A.A. Bahgat et al., Transport properties of KxV2O5·nH2O nanocrystalline films. J. Mater. Sci. Technol. 27, 865–872 (2011)CrossRef
31.
M.M. El-Desoky, M.S. Al-Assiri, A.A. Bahgats, Synthesis, structural and transport properties of NaxV2O5⋅nH2O xerogel nanocrystalline thin films. J. Alloys Compd. 590, 572–578 (2014)CrossRef
32.
A.M. Al-Syadi et al., Grain size effects on the transport properties of Li3V2(PO4)3 glass–ceramic nanocomposites for lithium cathode batteries. J. Mater. Sci. Mater. Electron. 27, 4074–4083 (2016)CrossRef
33.
R.B. Roberts, F. Righini, R.C. Comptons, Absolute scale of thermoelectricity III. Philos. Mag. B 52, 1147–1163 (1985)CrossRef
34.
M.M. El-Desoky et al., Impact of sodium oxide, sulfide, and fluoride-doped vanadium phosphate glasses on the thermoelectric power and electrical properties: structure analysis and conduction mechanism. J. Mater. Sci. Mater. Electron. 32, 3699–3712 (2021)CrossRef
35.
H.F. Mohamed et al., Impact of aluminum on the seebeck coefficient and magnetic properties of La0.7Ba0.3MnO3 manganites. Chem. Phys. Lett. 726, 22–28 (2019)CrossRef
36.
A. Mehdizadeh Dehkordi et al., Thermoelectric power factor: enhancement mechanisms and strategies for higher performance thermoelectric materials. Mater. Sci. Eng. R. Rep. 97, 1–22 (2015)CrossRef
37.
M. Kang et al., Conductivity, carrier density, mobility, Seebeck coefficient, and power factor in V2O5. Thermochim. Acta 576, 71–74 (2014)CrossRef
38.
M.M. El-Desokys, Giant electrical conductivity enhancement in BaO–V2O5–Bi2O3 glass by nanocrystallization. Mater. Chem. Phys. 119, 389–394 (2010)CrossRef
39.
M.S. Al-Assiri et al., Study of nanostructural behavior and transport properties of BaTiO3 doped vanadate glasses and glass–ceramics dispersed with ferroelectric nanocrystals. Phys. B Condens. Matter 404, 1437–1445 (2009)CrossRef
40.
A. Al-Shahrani, A. Al-Hajry, M.M. El-Desokys, Non-adiabatic small polaron hopping conduction in sodium borate tungstate glasses. physica status solidi (a) 200, 378–387 (2003)CrossRef
41.
A.E. Harby et al., Correlation between grain size and transport properties of lead titanate based-glass–ceramic nano-composites. J. Mater. Sci. Mater. Electron. 27, 8446–8454 (2016)CrossRef
I.G. Austin, N.F. Motts, Polarons in crystalline and non-crystalline materials. Adv. Phys. 18, 41–102 (1969)CrossRef
44.
M.M. El-Desoky, M.M. Abdulrazek, Y.A. Sharabys, Fabrication and electrical properties of reduced graphene oxide doped nanocrystalline vanadium pentoxide films. Mater. Sci. Eng. B Solid-State Mater. Adv. Technol. 261, 114676 (2020)CrossRef
45.
M.S. Al-Assiri, M.M. El-Desokys, Nanocrystallization as a method of improvement of electrical properties of Fe2O3–PbO2–TeO2 glasses. J. Mater. Sci. Mater. Electron. 25, 3703–3711 (2014)CrossRef
46.
S. Moser et al., Tunable polaronic conduction in anatase TiO2. Phys. Rev. Lett. 110, 196403 (2013)PubMedCrossRef
47.
T. Holsteins, Studies of polaron motion: Part II. The “small” polaron. Ann. Phys. 8, 343–389 (1959)CrossRef
48.
M.M. El-Desokys, Small polaron transport in V2O5–NiO–TeO2 glasses. J. Mater. Sci. Mater. Electron. 14, 215–221 (2003)CrossRef
49.
S.P. Yawale, S.V. Pakades, D.c. conductivity and hopping mechanism in Bi2O3-B2O3 glasses. J. Mater. Sci. 28, 5451–5455 (1993)CrossRef
50.
J. Han et al., A new polystyrene–poly(vinylpyridinium) ionic copolymer dopant for n-type all-polymer thermoelectrics with high and stable conductivity relative to the Seebeck coefficient giving high power factor. Adv. Mater. 34, 2201062 (2022)CrossRef
51.
D. Emin, T. Holsteins, Studies of small-polaron motion IV. Adiabatic theory of the Hall effect. Ann. Phys. 53, 439–520 (1969)CrossRef
52.
M.M. El-Desoky, M.S. Al-Assiri, Structural and polaronic transport properties of semiconducting CuO–V2O5–TeO2 glasses. Mater. Sci. Eng. B Solid-State Mater. Adv. Technol. 137, 237–246 (2007)CrossRef
53.
L. Murawski, C.H. Chung, J.D. Mackenzies, Electrical properties of semiconducting oxide glasses. J. Non-Cryst. Solids 32, 91–104 (1979)CrossRef
54.
A. Hannora, M. El-Desokys, Correlation between nanostructural and enhanced electrical conductivity of annealed 30V2O5–20Bi2O3–50P2O5 glass. Cryst. Res. Technol. 55, 2000128 (2020)CrossRef
55.
M.M. El-Desokys, DC conductivity and hopping mechanism in V2O5–B2O3–BaO glasses. physica status solidi (a) 195, 422–428 (2003)CrossRef
56.
S.A. Fareed et al., Structure, Seebeck coefficient and DC electrical conductivity of Bi2Mn4O10 prepared by mechanochemical method. J. Mater. Sci. Mater. Electron. 33, 15346–15358 (2022)CrossRef
57.
M.S. Al-Assiri, S.A. Salem, M.M. El-Desokys, Effect of iron doping on the characterization and transport properties of calcium phosphate glassy semiconductors. J. Phys. Chem. Solids 67, 1873–1881 (2006)CrossRef
58.
L. Konczewicz et al., Electrical transport properties of highly doped N-type GaN materials. Semicond. Sci. Technol. 37, 055012 (2022)CrossRef
59.
M.M. El-Desoky, N.M. Tashtoush, M.H. Habibs, Characterization and electrical properties of semiconducting Fe2O3-Bi2O3-K2B4O7 glasses. J. Mater. Sci. Mater. Electron. 16, 533–539 (2005)CrossRef
60.
M.S. Al-Assiri et al., Structural and transport properties of Li-intercalated vanadium pentoxide nanocrystalline films. Philos. Mag. 90, 3421–3439 (2010)CrossRef
61.
K. Morita et al., Models of polaron transport in inorganic and hybrid organic–inorganic titanium oxides. Chem. Mater. 35, 3652–3659 (2023)PubMedPubMedCentralCrossRef
62.
G.N. Greavess, Small polaron conduction in V2O5P2O5 glasses. J. Non-Cryst. Solids 11, 427–446 (1973)CrossRef
