Role of free volume in governing electrical transport in V2O5–Cu2O–P2O5 glass ceramic nanocomposites

X-ray diffraction evaluation

X-ray diffraction (XRD) is a extensively used non-destructive approach for investigating the structural state of supplies via the interplay of X-rays with atomic planes. It offers important data concerning part composition and diploma of crystallinity. Determine 1 reveals the XRD patterns of xV₂O₅–(40 − x)Cu₂O–60P₂O₅ glass–ceramic nanocomposites (x = 10–40 mol%) after warmth remedy. The diffraction patterns reveal the coexistence of crystalline phases embedded inside an amorphous matrix. At decrease V₂O₅ content material (10 mol%), the sample is dominated by a broad background with comparatively weak diffraction peaks, indicating a predominantly amorphous construction with restricted crystallization.

XRD patterns of xV₂O₅–(40 − x)Cu₂O–60P₂O₅ glass–ceramic nanocomposites (x = 10, 20, 30, and 40 mol%) after warmth remedy at 873 Ok for two h. Vertical dashed strains characterize normal diffraction peaks of Cu₂O (ICDD No. 01-078-2076) and V₂O₅ (ICDD No. 00-041-1426), confirming part identification.

Because the V₂O₅ content material will increase (20–40 mol%), the depth and sharpness of the diffraction peaks progressively improve, confirming the event of crystalline phases. The diffraction peaks noticed round 2θ ≈ 29.4°, 36.2°, and 43.4° correspond to the (110), (111), and (200) planes of cubic Cu₂O (ICDD No. 01-078-2076)³⁴. As well as, a number of peaks within the vary 2θ ≈ 12–50° are listed to orthorhombic V₂O₅ (ICDD No. 00-041-1426)³⁵, together with reflections equivalent to (200), (101), (301), (310), and (401), as indicated within the determine. The presence of those peaks confirms the profitable formation of the crystalline phases Cu₂O and V₂O₅ upon warmth remedy. The rise in peak depth and narrowing of peak width with rising V₂O₅ content material recommend enhanced crystallinity and the event of nanocrystalline domains. Nevertheless, the persistence of the diffuse background signifies that the samples stay partially amorphous.

The typical crystallite dimension (D) of the shaped phases was estimated utilizing the Scherrer equation:

the place Ok is the form issue (≈0.9), λ is the X-ray wavelength, β is the total width at half most (FWHM), and θ is the Bragg angle. The calculated crystallite sizes lie within the vary of ~ 16–27 nm, confirming the formation of nanocrystalline phases. The ICDD reference strains proven on the backside of the determine align nicely with the experimental peaks, supporting correct part identification. Total, the outcomes show that rising V₂O₅ content material promotes crystallization and part growth throughout the glass matrix. These structural adjustments are anticipated to affect cost transport by modifying the distribution of conduction pathways. Excessive-resolution TEM characterization was not carried out within the current research as a result of present unavailability of the required services. TEM offers direct proof of the crystallite dimension, morphology, and particle distribution, serving as an important complement to XRD-based crystallite dimension estimation. These measurements will likely be carried out in future work.

The sizes of the crystallites had been estimated utilizing the strongest remoted diffraction peaks from the (111) reflection of Cu₂O and the (301) reflection of orthorhombic V₂O₅. Since no normal reference materials was measured underneath the identical instrumental circumstances, we couldn’t apply an instrumental broadening correction. Subsequently, the calculated crystallite sizes needs to be seen as approximate values. Peak broadening can also consequence from microstrain and overlapping with the amorphous background. The estimated uncertainty in crystallite dimension is about ± 2 nm.

DC electrical conductivity

Determine 2 presents the temperature dependence of DC electrical conductivity (σ_DC) as a operate of reciprocal temperature (1/T) for xV₂O₅–(40 − x) Cu₂O–60P₂O₅ GCN samples. The conductivity follows an Arrhenius-type conduct, described by Mott’s equation³⁶, indicating thermally activated cost transport. The roughly linear relationship between log σ_DC and 1/T means that cost transport is dominated by hopping mechanisms typical of transition-metal oxide-containing glass methods. Deviations from linearity at increased temperatures might mirror temperature-dependent activation vitality, in keeping with earlier research³⁷.

Temperature dependence of DC conductivity σ_DC as a operate of reciprocal temperature 1/T for V₂O₅–Cu₂O–P₂O₅ GCN.

A scientific improve in σ_DC with rising V₂O₅ focus was noticed. As an alternative of specifying the valence states, the rise in conductivity is ascribed to the general contribution of the vanadium-related digital states to the hopping conduction. The addition of V₂O₅ additionally causes adjustments to the phosphate community, together with the technology of non-bridging oxygens (NBOs), which contribute to the mobility of the cost carriers and the rise within the density of the hopping states³⁸. The conductivity improve for the heat-treated glasses is 4 orders of magnitude increased than that of the as-prepared glasses¹⁰. The rise in conductivity is primarily attributed to compositional results, significantly the elevated vanadium ion focus and lowered interionic distance, whereas nanocrystalline part formation offers a secondary structural contribution. As proven in Fig. 3, the values of {the electrical} conductivity at fixed temperatures (400 and 450 Ok) improve with rising vanadium focus. This pattern underlines the significance of the position performed by vanadium oxide (V₂O₅) as a cost transporter. The mixed addition of V₂O₅ and Cu₂O significantly adjustments the glass construction, and the interplay with the phosphate community is necessary for the noticed electrical properties.

Impact of V₂O₅ content material on DC conductivity at T = 400 and 450 Ok for V₂O₅–Cu₂O–P₂O₅ GCN.

The conductivity values obtained are just like these reported for transition-metal phosphate glass ceramics. Nevertheless, they’re decrease than these of extremely crystalline V₂O₅ as a result of the partially amorphous matrix results in extra provider localization. Regardless of this, the noticed four-order-of-magnitude improve in conductivity reveals that nanocrystallization mixed with increased vanadium focus is efficient.

Activation vitality and structural results

The activation vitality for DC conduction is noticed to lower systematically with rising V₂O₅ focus [Fig. 4], signifying much less resistance for cost carriers. That is associated to rising digital state density and structural rest results because of vanadium incorporation and warmth remedy. As V₂O₅ is understood for its network-modifying and digital transport facilitation properties, its rising focus is noticed to extend connectivity between localized states, as is typical for small polaron hopping mechanisms of transition steel phosphate glasses^39,40.

Impact of V₂O₅ content material on activation vitality W for V₂O₅-Cu₂O–P₂O₅ GCN. The road is drawn to information the attention. The errors are throughout the dimension of the image.

Density and oxygen molar quantity

Determine 5 reveals the variation of density (d) and oxygen molar quantity (V_m) as a operate of V₂O₅ focus for the xV₂O₅–(40–x)Cu₂O–60P₂O₅ glass–ceramic nanocomposites. The outcomes point out a gradual lower in density with rising V₂O₅ content material. This behaviour may be attributed to structural modifications occurring throughout the phosphate glass community. As V₂O₅ replaces Cu₂O within the composition, the glass construction turns into much less densely packed because of adjustments within the coordination surroundings of the network-forming models. These structural rearrangements result in an enlargement of the glass community and a corresponding discount in density. On the identical time, the oxygen molar quantity (V_m) reveals a scientific improve with rising V₂O₅ focus. The rise in V_m suggests a lower within the packing effectivity of the glass community and signifies the presence of bigger interstitial areas or free-volume areas throughout the construction. This behaviour may be defined when it comes to the polarizing energy of the constituent cations, which is outlined because the ratio of ionic cost to ionic radius. Vanadium cations possess the next polarizing energy in contrast with copper cations, leading to stronger interactions with surrounding oxygen ions. This interplay modifies the native structural association and causes a redistribution of oxygen ions throughout the glass community. The incorporation of vanadium oxide additionally results in the formation of various structural models, equivalent to VO₄ and VO₅ polyhedra, which affect the connectivity of the phosphate community. These structural models can distort the native bonding surroundings and contribute to an enlargement of the glass construction, thereby rising the oxygen molar quantity.

Composition dependence of density d and oxygen molar quantity V_m for V₂O₅–Cu₂O–P₂O₅ GCN. The strains are drawn to information the attention.

Total, the noticed lower in density and improve in oxygen molar quantity with rising V₂O₅ focus point out a progressive modification of the glass community construction. These adjustments are related to variations in cation–oxygen interactions, ionic dimension results, and the redistribution of structural models throughout the V₂O₅–Cu₂O–P₂O₅ glass–ceramic system, in keeping with related observations reported in associated phosphate glass methods⁴¹.

Electrical transport mechanism

In vanadium-containing phosphate glass–ceramic nanocomposites, DC electrical conductivity is predominantly ruled by small-polaron hopping between mixed-valence vanadium ions (V⁴⁺/V⁵⁺). This conduction mechanism is extremely delicate to the spatial distribution and separation between vanadium ions throughout the glass community. {The electrical} conduction doesn’t happen completely via interconnected V₂O₅ nanocrystals. As an alternative, electron transport proceeds via small-polaron hopping involving each vanadium ions remaining within the partially amorphous phosphate matrix and people situated contained in the nanocrystalline areas. Subsequently, the nanocrystals act as extremely conductive native domains, whereas the encompassing amorphous matrix nonetheless contributes to the general hopping community. Cu₂O primarily acts as a community modifier by producing non-bridging oxygen websites and altering the native phosphate construction. Consequently, its contribution to electrical conductivity is primarily oblique via structural modification fairly than direct digital conduction. XRD confirms that the glass matrix stays partially amorphous after warmth remedy. Consequently, cost transport outcomes from the coexistence of crystalline V₂O₅ domains embedded inside an electrically energetic amorphous matrix.

The typical interionic distance (A_id) between vanadium ions was calculated utilizing the relation: A_id = (1/N)^1/3, the place N is the vanadium ion focus per unit quantity, decided from the experimentally measured density and glass composition. The calculated values of density (d), molecular weight (M_w), vanadium ion focus (N), and interionic distance (A_id) are listed in Desk 1. As well as, the polaron hopping distance r_p was estimated from the common interionic distance A_id utilizing:

and likewise listed in Desk 1. The outcomes present that the hopping distance decreases with rising V₂O₅ content material. This discount signifies that the separation between adjoining vanadium ions turns into smaller, thereby facilitating electron hopping and enhancing electrical conductivity. Moreover, the values of the localization parameter αA_id, which is used to characterize the localization of cost carriers, are decided to be increased than unity, confirming the small polaron hopping conduction mechanism.

It needs to be emphasised that A_id and r_p characterize efficient bulk-average parameters derived from the general vanadium focus. As a result of the current materials consists of V₂O₅ nanocrystals dispersed inside {a partially} amorphous matrix, these parameters don’t characterize the precise V–V distances inside particular person nanocrystals. They need to subsequently be interpreted as common transport descriptors helpful for discussing composition-dependent conductivity traits.

The density of localized states close to the Fermi degree, N(E_F), was estimated utilizing the expression proposed by Emin and Holstein⁴²:

The calculated values of N(E_F) are additionally listed in Desk 1. The obtained values fall throughout the typical vary reported for disordered transition steel oxide glasses and are attribute of localized digital states related to polaronic conduction. Furthermore, the gradual improve in N(E_F) with rising V₂O₅ focus signifies the next density of localized states out there for electron hopping, which additional contributes to the enhancement {of electrical} conductivity within the investigated glass ceramic nanocomposites.

Because the focus of V₂O₅ is elevated from 10 to 40 mol%, the focus of vanadium ions (N) additionally will increase considerably, leading to a corresponding lower in interionic distance (A_id) and polaron hopping distance (r_p). This helps within the overlapping of orbitals between the vanadium ions, leading to elevated electron hopping and therefore the conductivity. Concurrently, the activation vitality (W), obtained from Arrhenius evaluation (Part “Activation energy and structural effects“), decreases with reducing interionic distance, as proven in Fig. 6. This inverse relationship signifies that shorter hopping distances scale back the vitality barrier for cost transport. These outcomes clearly show that {the electrical} conduction within the current glass–ceramic nanocomposites happens by way of a thermally activated small-polaron hopping mechanism, and that rising V₂O₅ content material enhances electrical transport by lowering hopping distance and activation vitality. These findings are in keeping with earlier stories by Sayer and Mansingh⁴³ and El-Desoky⁴⁴, who demonstrated that elevated V–O–V separation results in increased hopping activation energies. However, the rise in conductivity is principally attributed to the discount in interionic distance between vanadium ions (V⁴⁺/V⁵⁺ pairs). Because the V₂O₅ content material will increase, the vanadium ion focus rises, resulting in a lower in each the common interionic distance (A_id) and polaron hopping distance (r_p). This enhances the likelihood of small-polaron hopping and reduces the activation vitality for conduction.

Variation of common interionic distance A_id, and the high-temperature activation vitality, W, for V₂O₅–Cu₂O–P₂O₅ GCN. The road is drawn to information the attention.

PAL evaluation

Within the current research, the time period ‘defects’ refers primarily to free-volume (vacancy-type) websites throughout the glass community, as probed by PAL spectroscopy. These defects correspond to open-volume cavities related to native structural dysfunction fairly than crystallographic defects. The PAL spectra of the xV₂O₅–(40–x)Cu₂O–60P₂O₅ glass–ceramic nanocomposites (GCN), the place x = 10, 20, 30, and 40 mol%, had been analysed by decomposing the spectra into three lifetime elements (τ₁, τ₂, and τ₃) utilizing the PALSfit and LT10 evaluation applications. The PAL parameters obtained from each becoming procedures confirmed shut settlement, confirming the reliability of the lifetime evaluation. In disordered methods equivalent to oxide glasses and glass–ceramic nanocomposites, three lifetime elements are sometimes noticed. The shortest lifetime part (τ₁) corresponds to the annihilation of free positrons in defect-free areas of the matrix or shallow trapping websites. The intermediate lifetime part (τ₂) is mostly related to positrons trapped at vacancy-type defects or structural imperfections throughout the amorphous community. The longest lifetime part (τ₃) is attributed to the annihilation of ortho-positronium (o-Ps) shaped in free-volume cavities or nano-voids within the glass construction^45,46.

The corresponding intensities (I₁, I₂, and I₃) characterize the chances of positron annihilation via these channels. The variations of those parameters with V₂O₅ focus are offered in Fig. 7. These variations mirror modifications within the defect construction and free-volume distribution of the glass–ceramic matrix attributable to the incorporation of vanadium oxide. The intermediate lifetime part τ₂ was discovered to lie within the vary 0.38–0.53 ns, which is attribute of positron trapping at vacancy-type defects in oxide glasses. The presence of such defects might come up from structural dysfunction, non-stoichiometric bonding configurations, or native distortions throughout the phosphate glass community. The gradual change in τ₂ with rising V₂O₅ focus signifies that the incorporation of vanadium ions modifies the native defect surroundings of the glass matrix. The longest lifetime part τ₃ corresponds to the annihilation of ortho-positronium atoms in free-volume holes throughout the glass construction. The variation of τ₃ and its depth I₃ offers necessary details about the scale and focus of those free-volume cavities. The noticed lower of τ₃ with rising V₂O₅ focus means that the common dimension of free-volume holes decreases as vanadium oxide is integrated into the glass community. This behaviour signifies a gradual compaction of the glass construction and a redistribution of free-volume websites.

The three lifetimes’ elements (τ₁, τ₂, and τ₃) and their intensities (I₁, I₂, and I₃) for xV₂O₅–(40−x)Cu₂O–60P₂O₅ GCN with completely different concentrations of V₂O₅. The strains are drawn to information the attention.

In accordance with the two-state positron trapping mannequin proposed by Shpotyuk et al.⁴⁷ and Šedivý et al.⁴⁸, positrons might grow to be trapped at completely different defect websites throughout the materials. On this mannequin, positron annihilation happens both in defect-free areas or in trapping centres equivalent to vacancies or free-volume holes. Though the two-state mannequin doesn’t explicitly distinguish between various kinds of defects related to a number of lifetime elements, it offers a helpful framework for estimating the positron trapping charges. The trapping charges for positrons at completely different defect websites had been calculated utilizing the relations:

the place Ok_d1 represents the trapping price related to vacancy-type defects, and Ok_d2 corresponds to trapping associated to free-volume websites the place positronium formation happens. The variation of Ok_d1 and Ok_d2 as a operate of V₂O₅ focus is proven in Fig. 8a, b. The other traits noticed for these parameters point out that the addition of V₂O₅ considerably influences the defect construction of the glass–ceramic nanocomposites. Because the vanadium content material will increase, the trapping price related to vacancy-type defects decreases, suggesting a discount within the focus of those defects throughout the glass community.

Variation of (a) Ok_d1, (b) Ok_d2, (c) τ_imply, (d) τ_bulk, (e) V₊, and (f) V_d for xV₂O₅–(40-x)Cu₂O–60P₂O₅ GCN with completely different concentrations of V₂O₅. The strains are drawn to information the attention and the errors are throughout the dimension of the symbols.

The imply positron lifetime (τ_imply), which displays the general defect construction of the samples, was calculated utilizing^49,50:

The variation of τ_imply with V₂O₅ focus is proven in Fig. 8c. The outcomes reveal a gradual lower in τ_imply because the V₂O₅ focus will increase, indicating a discount within the common defect dimension or free-volume cavities throughout the glass matrix. The majority positron lifetime τ_bulk comparable to annihilation in defect-free areas of the fabric was decided from the relation:

The calculated τ_bulk values are offered in Fig. 8d. A gradual lower in τ_bulk with rising V₂O₅ focus suggests a rise within the annihilation price of free positrons throughout the matrix, which can be associated to structural rearrangements within the glass community.

The trapping price of positrons in vacancy-type defects (V₊) was estimated utilizing the expression proposed by Shantarovich and Goldanskii⁵¹:

The obtained values of V₊ are proven in Fig. 8e. The outcomes point out that V₊ decreases with rising V₂O₅ focus, suggesting a discount within the density of vacancy-type defects within the glass matrix. Equally, the positronium trapping price (V_d) related to free-volume websites was calculated utilizing⁵²:

The calculated values of V_d are proven in Fig. 8f. The gradual lower of V_d with rising V₂O₅ focus additional helps the conclusion that the incorporation of vanadium oxide results in a discount within the dimension and focus of free-volume cavities throughout the glass community.

The structural parameters related to the longest lifetime part τ₃, together with the emptiness radius (Rv) and the free-volume dimension (V_v), had been estimated utilizing the LT10 evaluation program^25,53. The distributions of those parameters are offered in Fig. 9. The outcomes present that each the emptiness radius and the corresponding free-volume dimension lower barely with rising V₂O₅ focus, indicating a gradual compaction of the glass community construction. The calculated full width at half most (FWHM) values of the emptiness dimension distribution for V₂O₅ concentrations of 10, 20, 30 and 40 mol% had been 0.1040, 0.1043, 0.1064, and 0.1174 nm³, respectively. These values recommend a slight narrowing of the free-volume distribution with rising vanadium content material.

Distribution of lengthy lifetime τ₃, the emptiness radius R_v, and emptiness dimension V_v for xV₂O₅–(40-x)Cu₂O–60P₂O₅ GCN with completely different concentrations of V₂O₅ (the place x = 10, 20, 30, and 40 mol%) deduced utilizing LT10 program.

Total, the PAL outcomes show that the addition of V₂O₅ considerably modifies the structural options of the xV₂O₅–(40–x)Cu₂O–60P₂O₅ glass–ceramic nanocomposites. The noticed adjustments in positron lifetimes, trapping charges and free-volume parameters point out a gradual discount in vacancy-type defects and free-volume cavities because the V₂O₅ focus will increase, reflecting the necessary position of vanadium oxide in controlling the structural properties of the investigated glass system. Nevertheless, the positron annihilation lifetime (PAL) outcomes point out a discount in vacancy-type defects and free-volume dimension, which displays improved structural ordering (or structural compactness). This structural refinement reduces dysfunction and provider localization, thereby facilitating extra environment friendly electron hopping. Though free-volume (vacancy-type) defects lower with rising V₂O₅ content material, the enhancement in conductivity is dominated by compositional results, whereas defect discount contributes not directly by lowering provider localization. It needs to be famous that the rise in oxygen molar quantity noticed from density measurements doesn’t contradict the discount in PAL-derived free-volume dimension and vacancy-related parameters. The oxygen molar quantity displays a macroscopic structural parameter related to the general rearrangement and enlargement of the phosphate glass community as a result of incorporation of V₂O₅ and the formation of VO₄/VO₅ structural models. In distinction, PAL spectroscopy probes microscopic localized free-volume cavities and vacancy-type defects throughout the glass matrix. Subsequently, though the common community construction turns into comparatively extra expanded on the macroscopic scale, the native structural ordering and homogenization enhance concurrently, resulting in a discount within the dimension and focus of localized free-volume defects. These observations point out that the structural evolution happens at completely different size scales and collectively contributes to the noticed electrical transport conduct.

Correlation between electrical conductivity and defect construction

Determine 10 illustrates the connection between DC electrical conductivity (σ_DC), activation vitality (W), and emptiness dimension (V_v) obtained from PAL evaluation for xV₂O₅–(40–x)Cu₂O–60P₂O₅ glass–ceramic nanocomposites. As proven in Fig. 10A, the logarithm of DC conductivity will increase with rising emptiness dimension. Nevertheless, though the emptiness dimension decreases with rising V₂O₅ content material, the conductivity enhancement is primarily ruled by compositional results, together with the elevated focus of vanadium ions and the discount in interionic and hopping distances. On this context, defect-related adjustments affect electrical transport not directly by modifying the native structural surroundings. Determine 10B reveals that the activation vitality decreases with rising emptiness dimension, indicating that free-volume (vacancy-type) defects can scale back the vitality barrier for cost transport by facilitating thermally activated hopping. These defects correspond to free-volume cavities probed by PAL and are distinct from the crystalline options recognized by XRD. Their position is principally oblique, as they modify native atomic packing and orbital overlap between neighbouring transition-metal ions.

(A) Log(σ_DC) and (B) the activation vitality at excessive temperature for xV₂O₅–(40-x)Cu₂O–60P₂O₅ GCN with various V₂O₅ concentrations (the place x = 10, 20, 30, and 40 mol%) are correlated with the emptiness dimension V_v. The errors are throughout the dimension of the symbols.

Total, the outcomes point out {that electrical} transport is dominated by small-polaron hopping between V⁴⁺/V⁵⁺ ions, managed primarily by compositional parameters equivalent to vanadium ion focus and interionic distance. The discount in free-volume defects with rising V₂O₅ content material displays improved structural ordering, which helps cost transport by lowering provider localization. Thus, defect evolution, community modification, and compositional results collectively affect the transport behaviour, with composition taking part in the dominant position.