Fig. 1![\"Fig.](\"https:\/\/www.newsbeep.com\/il\/wp-content\/uploads\/2026\/08\/41598_2026_65220_Fig1_HTML.png\")
<\/p>\n
XRD patterns of xV\u2082O\u2085\u2013(40\u2009\u2212\u2009x)Cu\u2082O\u201360P\u2082O\u2085 glass\u2013ceramic nanocomposites (x\u2009=\u200910, 20, 30, and 40 mol%) after heat treatment at 873 K for 2 h. Vertical dashed lines represent standard diffraction peaks of Cu\u2082O (ICDD No. 01-078-2076) and V\u2082O\u2085 (ICDD No. 00-041-1426), confirming phase identification.<\/p>\n
As the V\u2082O\u2085 content increases (20\u201340\u00a0mol%), the intensity and sharpness of the diffraction peaks progressively increase, confirming the development of crystalline phases. The diffraction peaks observed around 2\u03b8 \u2248 29.4\u00b0, 36.2\u00b0, and 43.4\u00b0 correspond to the (110), (111), and (200) planes of cubic Cu\u2082O (ICDD No. 01-078-2076)34<\/a>. In addition, multiple peaks in the range 2\u03b8 \u2248 12\u201350\u00b0 are indexed to orthorhombic V\u2082O\u2085 (ICDD No. 00-041-1426)35<\/a>, including reflections such as (200), (101), (301), (310), and (401), as indicated in the figure. The presence of these peaks confirms the successful formation of the crystalline phases Cu\u2082O and V\u2082O\u2085 upon heat treatment. The increase in peak intensity and narrowing of peak width with increasing V\u2082O\u2085 content suggest enhanced crystallinity and the development of nanocrystalline domains. However, the persistence of the diffuse background indicates that the samples remain partially amorphous.<\/p>\n The average crystallite size (D) of the formed phases was estimated using the Scherrer equation:<\/p>\n $$D = K\\lambda \/\\beta \\cos \\theta ,$$<\/p>\n \n (10)\n <\/p>\n where K is the shape factor (\u22480.9), \u03bb is the X-ray wavelength, \u03b2 is the full width at half maximum (FWHM), and \u03b8 is the Bragg angle. The calculated crystallite sizes lie in the range of\u2009~\u200916\u201327\u00a0nm, confirming the formation of nanocrystalline phases. The ICDD reference lines shown at the bottom of the figure align well with the experimental peaks, supporting accurate phase identification. Overall, the results demonstrate that increasing V\u2082O\u2085 content promotes crystallization and phase development within the glass matrix. These structural changes are expected to influence charge transport by modifying the distribution of conduction pathways. High-resolution TEM characterization was not performed in the present study due to the current unavailability of the required facilities. TEM provides direct evidence of the crystallite size, morphology, and particle distribution, serving as an essential complement to XRD-based crystallite size estimation. These measurements will be carried out in future work.<\/p>\n The sizes of the crystallites were estimated using the strongest isolated diffraction peaks from the (111) reflection of Cu\u2082O and the (301) reflection of orthorhombic V\u2082O\u2085. Since no standard reference material was measured under the same instrumental conditions, we could not apply an instrumental broadening correction. Therefore, the calculated crystallite sizes should be seen as approximate values. Peak broadening may also result from microstrain and overlapping with the amorphous background. The estimated uncertainty in crystallite size is about\u2009\u00b1\u20092 nm.<\/p>\n DC electrical conductivity<\/p>\n Figure\u00a02<\/a> presents the temperature dependence of DC electrical conductivity (\u03c3DC) as a function of reciprocal temperature (1\/T) for xV\u2082O\u2085\u2013(40\u2009\u2212\u2009x) Cu\u2082O\u201360P\u2082O\u2085 GCN samples. The conductivity follows an Arrhenius-type behavior, described by Mott\u2019s equation36<\/a>, indicating thermally activated charge transport. The approximately linear relationship between log \u03c3DC and 1\/T suggests that charge transport is dominated by hopping mechanisms typical of transition-metal oxide-containing glass systems. Deviations from linearity at higher temperatures may reflect temperature-dependent activation energy, consistent with previous studies37<\/a>.<\/p>\n Fig. 2 Temperature dependence of DC conductivity \u03c3DC as a function of reciprocal temperature 1\/T for V2O5\u2013Cu2O\u2013P2O5 GCN.<\/p>\n A systematic increase in \u03c3DC with increasing V\u2082O\u2085 concentration was observed. Instead of specifying the valence states, the increase in conductivity is ascribed to the overall contribution of the vanadium-related electronic states to the hopping conduction. The addition of V\u2082O\u2085 also causes changes to the phosphate network, including the generation of non-bridging oxygens (NBOs), which contribute to the mobility of the charge carriers and the increase in the density of the hopping states38<\/a>. The conductivity increase for the heat-treated glasses is four orders of magnitude higher than that of the as-prepared glasses10<\/a>. The increase in conductivity is primarily attributed to compositional effects, particularly the increased vanadium ion concentration and reduced interionic distance, while nanocrystalline phase formation provides a secondary structural contribution. As shown in Fig.\u00a03<\/a>, the values of the electrical conductivity at constant temperatures (400 and 450\u00a0K) increase with increasing vanadium concentration. This trend underlines the importance of the role played by vanadium oxide (V\u2082O\u2085) as a charge transporter. The combined addition of V\u2082O\u2085 and Cu2O considerably changes the glass structure, and the interaction with the phosphate network is important for the observed electrical properties.<\/p>\n Fig. 3 Effect of V2O5 content on DC conductivity at T\u2009=\u2009400 and 450\u00a0K for V2O5\u2013Cu2O\u2013P2O5 GCN.<\/p>\n The conductivity values obtained are similar to those reported for transition-metal phosphate glass ceramics. However, they are lower than those of highly crystalline V\u2082O\u2085 because the partially amorphous matrix leads to more carrier localization. Despite this, the observed four-order-of-magnitude increase in conductivity shows that nanocrystallization combined with higher vanadium concentration is effective.<\/p>\n Activation energy and structural effects<\/p>\n The activation energy for DC conduction is observed to decrease systematically with increasing V\u2082O\u2085 concentration [Fig.\u00a04<\/a>], signifying less resistance for charge carriers. This is related to increasing electronic state density and structural relaxation effects due to vanadium incorporation and heat treatment. As V\u2082O\u2085 is known for its network-modifying and electronic transport facilitation properties, its increasing concentration is observed to increase connectivity between localized states, as is typical for small polaron hopping mechanisms of transition metal phosphate glasses39<\/a>,40<\/a>.<\/p>\n Fig. 4 Effect of V2O5 content on activation energy W for V2O5-Cu2O\u2013P2O5 GCN. The line is drawn to guide the eye. The errors are within the size of the symbol.<\/p>\n Density and oxygen molar volume<\/p>\n Figure\u00a05<\/a> shows the variation of density (d) and oxygen molar volume (Vm) as a function of V\u2082O\u2085 concentration for the xV\u2082O\u2085\u2013(40\u2013x)Cu\u2082O\u201360P\u2082O\u2085 glass\u2013ceramic nanocomposites. The results indicate a gradual decrease in density with increasing V\u2082O\u2085 content. This behaviour can be attributed to structural modifications occurring within the phosphate glass network. As V\u2082O\u2085 replaces Cu\u2082O in the composition, the glass structure becomes less densely packed due to changes in the coordination environment of the network-forming units. These structural rearrangements lead to an expansion of the glass network and a corresponding reduction in density. At the same time, the oxygen molar volume (Vm) shows a systematic increase with increasing V\u2082O\u2085 concentration. The increase in Vm suggests a decrease in the packing efficiency of the glass network and indicates the presence of larger interstitial spaces or free-volume regions within the structure. This behaviour can be explained in terms of the polarizing power of the constituent cations, which is defined as the ratio of ionic charge to ionic radius. Vanadium cations possess a higher polarizing power compared with copper cations, resulting in stronger interactions with surrounding oxygen ions. This interaction modifies the local structural arrangement and causes a redistribution of oxygen ions within the glass network. The incorporation of vanadium oxide also leads to the formation of different structural units, such as VO\u2084 and VO\u2085 polyhedra, which influence the connectivity of the phosphate network. These structural units can distort the local bonding environment and contribute to an expansion of the glass structure, thereby increasing the oxygen molar volume.<\/p>\n Fig. 5 Composition dependence of density d and oxygen molar volume Vm for V2O5\u2013Cu2O\u2013P2O5 GCN. The lines are drawn to guide the eye.<\/p>\n Overall, the observed decrease in density and increase in oxygen molar volume with increasing V\u2082O\u2085 concentration indicate a progressive modification of the glass network structure. These changes are associated with variations in cation\u2013oxygen interactions, ionic size effects, and the redistribution of structural units within the V\u2082O\u2085\u2013Cu\u2082O\u2013P\u2082O\u2085 glass\u2013ceramic system, consistent with similar observations reported in related phosphate glass systems41<\/a>.<\/p>\n Electrical transport mechanism<\/p>\n In vanadium-containing phosphate glass\u2013ceramic nanocomposites, DC electrical conductivity is predominantly governed by small-polaron hopping between mixed-valence vanadium ions (V4\u207a\/V5\u207a). This conduction mechanism is highly sensitive to the spatial distribution and separation between vanadium ions within the glass network. The electrical conduction does not occur exclusively through interconnected V\u2082O\u2085 nanocrystals. Instead, electron transport proceeds through small-polaron hopping involving both vanadium ions remaining in the partially amorphous phosphate matrix and those located inside the nanocrystalline regions. Therefore, the nanocrystals act as highly conductive local domains, whereas the surrounding amorphous matrix still contributes to the overall hopping network. Cu\u2082O mainly acts as a network modifier by generating non-bridging oxygen sites and altering the local phosphate structure. Consequently, its contribution to electrical conductivity is primarily indirect through structural modification rather than direct electronic conduction. XRD confirms that the glass matrix remains partially amorphous after heat treatment. Consequently, charge transport results from the coexistence of crystalline V\u2082O\u2085 domains embedded within an electrically active amorphous matrix.<\/p>\n The average interionic distance (Aid) between vanadium ions was calculated using the relation: Aid\u2009=\u2009(1\/N)1\/3, where N is the vanadium ion concentration per unit volume, determined from the experimentally measured density and glass composition. The calculated values of density (d), molecular weight (Mw), vanadium ion concentration (N), and interionic distance (Aid) are listed in Table 1<\/a>. In addition, the polaron hopping distance rp was estimated from the average interionic distance Aid using:<\/p>\n $${r}_{\\text{p}}={\\left(\\frac{\\pi }{6}\\right)}^{1\/3}\\frac{{A}_{id}}{2},$$<\/p>\n \n (11)\n <\/p>\n and also listed in Table 1<\/a>. The results show that the hopping distance decreases with increasing V\u2082O\u2085 content. This reduction indicates that the separation between adjacent vanadium ions becomes smaller, thereby facilitating electron hopping and enhancing electrical conductivity. Furthermore, the values of the localization parameter \u03b1Aid, which is used to represent the localization of charge carriers, are determined to be higher than unity, confirming the small polaron hopping conduction mechanism.<\/p>\n Table 1 Chemical composition and physical properties of V2O5\u2013Cu2O\u2013P2O5 GCN.<\/p>\n It should be emphasized that Aid and rp represent effective bulk-average parameters derived from the overall vanadium concentration. Because the present material consists of V\u2082O\u2085 nanocrystals dispersed within a partially amorphous matrix, these parameters do not represent the exact V\u2013V distances inside individual nanocrystals. They should therefore be interpreted as average transport descriptors useful for discussing composition-dependent conductivity trends.<\/p>\n The density of localized states near the Fermi level, N(EF), was estimated using the expression proposed by Emin and Holstein42<\/a>:<\/p>\n $$\\it N\\left({E}_{f}\\right)=\\frac{3}{4 \\uppi {Aid}^{3 }\\text{W}}$$<\/p>\n \n (12)\n <\/p>\n The calculated values of N(EF) are also listed in Table 1<\/a>. The obtained values fall within the typical range reported for disordered transition metal oxide glasses and are characteristic of localized electronic states associated with polaronic conduction. Moreover, the gradual increase in N(EF) with increasing V2O5 concentration indicates a higher density of localized states available for electron hopping, which further contributes to the enhancement of electrical conductivity in the investigated glass ceramic nanocomposites.<\/p>\n As the concentration of V\u2082O\u2085 is increased from 10 to 40 mol%, the concentration of vanadium ions (N) also increases significantly, resulting in a corresponding decrease in interionic distance (Aid) and polaron hopping distance (rp). This helps in the overlapping of orbitals between the vanadium ions, resulting in increased electron hopping and hence the conductivity. Simultaneously, the activation energy (W), obtained from Arrhenius analysis (Section “Activation energy and structural effects<\/a>“), decreases with decreasing interionic distance, as shown in Fig.\u00a06<\/a>. This inverse relationship indicates that shorter hopping distances reduce the energy barrier for charge transport. These results clearly demonstrate that the electrical conduction in the present glass\u2013ceramic nanocomposites occurs via a thermally activated small-polaron hopping mechanism, and that increasing V\u2082O\u2085 content enhances electrical transport by reducing hopping distance and activation energy. These findings are consistent with previous reports by Sayer and Mansingh43<\/a> and El-Desoky44<\/a>, who demonstrated that increased V\u2013O\u2013V separation leads to higher hopping activation energies. On the other hand, the increase in conductivity is mainly attributed to the reduction in interionic distance between vanadium ions (V4\u207a\/V5\u207a pairs). As the V\u2082O\u2085 content increases, the vanadium ion concentration rises, leading to a decrease in both the average interionic distance (Aid) and polaron hopping distance (rp). This enhances the probability of small-polaron hopping and reduces the activation energy for conduction.<\/p>\n Fig. 6 Variation of average interionic distance Aid, and the high-temperature activation energy, W, for V2O5\u2013Cu2O\u2013P2O5 GCN. The line is drawn to guide the eye.<\/p>\n PAL analysis<\/p>\n In the present study, the term \u2018defects\u2019 refers primarily to free-volume (vacancy-type) sites within the glass network, as probed by PAL spectroscopy. These defects correspond to open-volume cavities associated with local structural disorder rather than crystallographic defects. The PAL spectra of the xV\u2082O\u2085\u2013(40\u2013x)Cu\u2082O\u201360P\u2082O\u2085 glass\u2013ceramic nanocomposites (GCN), where x\u2009=\u200910, 20, 30, and 40 mol%, were analysed by decomposing the spectra into three lifetime components (\u03c4\u2081, \u03c4\u2082, and \u03c4\u2083) using the PALSfit and LT10 analysis programs. The PAL parameters obtained from both fitting procedures showed close agreement, confirming the reliability of the lifetime analysis. In disordered systems such as oxide glasses and glass\u2013ceramic nanocomposites, three lifetime components are typically observed. The shortest lifetime component (\u03c4\u2081) corresponds to the annihilation of free positrons in defect-free regions of the matrix or shallow trapping sites. The intermediate lifetime component (\u03c4\u2082) is generally associated with positrons trapped at vacancy-type defects or structural imperfections within the amorphous network. The longest lifetime component (\u03c4\u2083) is attributed to the annihilation of ortho-positronium (o-Ps) formed in free-volume cavities or nano-voids in the glass structure45<\/a>,46<\/a>.<\/p>\n The corresponding intensities (I\u2081, I\u2082, and I\u2083) represent the probabilities of positron annihilation through these channels. The variations of these parameters with V\u2082O\u2085 concentration are presented in Fig.\u00a07<\/a>. These variations reflect modifications in the defect structure and free-volume distribution of the glass\u2013ceramic matrix caused by the incorporation of vanadium oxide. The intermediate lifetime component \u03c4\u2082 was found to lie in the range 0.38\u20130.53 ns, which is characteristic of positron trapping at vacancy-type defects in oxide glasses. The presence of such defects may arise from structural disorder, non-stoichiometric bonding configurations, or local distortions within the phosphate glass network. The gradual change in \u03c4\u2082 with increasing V\u2082O\u2085 concentration indicates that the incorporation of vanadium ions modifies the local defect environment of the glass matrix. The longest lifetime component \u03c4\u2083 corresponds to the annihilation of ortho-positronium atoms in free-volume holes within the glass structure. The variation of \u03c4\u2083 and its intensity I\u2083 provides important information about the size and concentration of these free-volume cavities. The observed decrease of \u03c4\u2083 with increasing V\u2082O\u2085 concentration suggests that the average size of free-volume holes decreases as vanadium oxide is incorporated into the glass network. This behaviour indicates a gradual compaction of the glass structure and a redistribution of free-volume sites.<\/p>\n Fig. 7 The three lifetimes\u2019 components (\u03c41, \u03c42, and \u03c43) and their intensities (I1, I2, and I3) for xV2O5\u2013(40\u2212x)Cu2O\u201360P2O5 GCN with different concentrations of V2O5. The lines are drawn to guide the eye.<\/p>\n According to the two-state positron trapping model proposed by Shpotyuk et al.47<\/a> and \u0160ediv\u00fd et al.48<\/a>, positrons may become trapped at different defect sites within the material. In this model, positron annihilation occurs either in defect-free regions or in trapping centres such as vacancies or free-volume holes. Although the two-state model does not explicitly distinguish between different types of defects associated with multiple lifetime components, it provides a useful framework for estimating the positron trapping rates. The trapping rates for positrons at different defect sites were calculated using the relations:<\/p>\n $${K}_{d1}={I}_{2}\\left(\\frac{1}{{\\tau}_{1}}-\\frac{1}{{\\tau}_{2}}\\right),$$<\/p>\n \n (13)\n <\/p>\n $${K}_{d2}={I}_{3}\\left(\\frac{1}{{\\tau}_{1}}-\\frac{1}{{\\tau}_{3}}\\right).$$<\/p>\n \n (14)\n <\/p>\n where Kd1 represents the trapping rate associated with vacancy-type defects, and Kd2 corresponds to trapping related to free-volume sites where positronium formation occurs. The variation of Kd1 and Kd2 as a function of V\u2082O\u2085 concentration is shown in Fig.\u00a08<\/a>a, b. The opposite trends observed for these parameters indicate that the addition of V\u2082O\u2085 significantly influences the defect structure of the glass\u2013ceramic nanocomposites. As the vanadium content increases, the trapping rate associated with vacancy-type defects decreases, suggesting a reduction in the concentration of these defects within the glass network.<\/p>\n Fig. 8 Variation of (a) Kd1, (b) Kd2, (c) \u03c4mean, (d) \u03c4bulk, (e) V+, and (f) Vd for xV2O5\u2013(40-x)Cu2O\u201360P2O5 GCN with different concentrations of V2O5. The lines are drawn to guide the eye and the errors are within the size of the symbols.<\/p>\n The mean positron lifetime (\u03c4mean), which reflects the overall defect structure of the samples, was calculated using49<\/a>,50<\/a>:<\/p>\n $${\\uptau}_{\\text{m}\\text{e}\\text{a}\\text{n}}=\\frac{{\\uptau}_{1}{I}_{1}+ {\\uptau}_{2}{I}_{2}+ {\\uptau}_{3}{I}_{3} }{{I}_{1}+{I}_{2}+{I}_{3} },$$<\/p>\n \n (15)\n <\/p>\n The variation of \u03c4mean with V\u2082O\u2085 concentration is shown in Fig.\u00a08<\/a>c. The results reveal a gradual decrease in \u03c4mean as the V\u2082O\u2085 concentration increases, indicating a reduction in the average defect size or free-volume cavities within the glass matrix. The bulk positron lifetime \u03c4bulk corresponding to annihilation in defect-free regions of the material was determined from the relation:<\/p>\n $${\\uptau}_{\\text{b}\\text{u}\\text{l}\\text{k}}= {\\left[\\frac{{I}_{1}}{{\\uptau}_{1}}+\\frac{{I}_{2}}{{\\uptau}_{2}}+\\frac{{I}_{3}}{{\\uptau}_{3}}\\right]}^{-1}$$<\/p>\n \n (16)\n <\/p>\n The calculated \u03c4bulk values are presented in Fig.\u00a08<\/a>d. A gradual decrease in \u03c4bulk with increasing V\u2082O\u2085 concentration suggests an increase in the annihilation rate of free positrons within the matrix, which may be related to structural rearrangements in the glass network.<\/p>\n The trapping rate of positrons in vacancy-type defects (V+) was estimated using the expression proposed by Shantarovich and Goldanskii51<\/a>:<\/p>\n $${V}_{+}=\\frac{3{I}_{2}\\left(\\frac{1}{\\langle {\\tau}_{b}\\rangle }-\\frac{1}{{\\tau}_{2}}\\right)}{3{I}_{1}-{I}_{3}}.$$<\/p>\n \n (17)\n <\/p>\n The obtained values of V+ are shown in Fig.\u00a08<\/a>e. The results indicate that V+ decreases with increasing V\u2082O\u2085 concentration, suggesting a reduction in the density of vacancy-type defects in the glass matrix. Similarly, the positronium trapping rate (Vd) associated with free-volume sites was calculated using52<\/a>:<\/p>\n $${V}_{d}=\\frac{4{I}_{3}\\left(\\frac{1}{\\langle {\\tau}_{b}\\rangle }-\\frac{1}{{\\tau}_{3}}\\right)}{3-4{I}_{3}-3{I}_{2}},$$<\/p>\n \n (18)\n <\/p>\n The calculated values of Vd are shown in Fig.\u00a08<\/a>f. The gradual decrease of Vd with increasing V\u2082O\u2085 concentration further supports the conclusion that the incorporation of vanadium oxide leads to a reduction in the size and concentration of free-volume cavities within the glass network.<\/p>\n The structural parameters associated with the longest lifetime component \u03c4\u2083, including the vacancy radius (Rv) and the free-volume size (Vv), were estimated using the LT10 analysis program25<\/a>,53<\/a>. The distributions of these parameters are presented in Fig.\u00a09<\/a>. The results show that both the vacancy radius and the corresponding free-volume size decrease slightly with increasing V\u2082O\u2085 concentration, indicating a gradual compaction of the glass network structure. The calculated full width at half maximum (FWHM) values of the vacancy size distribution for V\u2082O\u2085 concentrations of 10, 20, 30 and 40 mol% were 0.1040, 0.1043, 0.1064, and 0.1174 nm3, respectively. These values suggest a slight narrowing of the free-volume distribution with increasing vanadium content.<\/p>\n Fig. 9 Distribution of long lifetime \u03c43, the vacancy radius Rv, and vacancy size Vv for xV2O5\u2013(40-x)Cu2O\u201360P2O5 GCN with different concentrations of V2O5 (where x\u2009=\u200910, 20, 30, and 40 mol%) deduced using LT10 program.<\/p>\n Overall, the PAL results demonstrate that the addition of V\u2082O\u2085 significantly modifies the structural features of the xV\u2082O\u2085\u2013(40\u2013x)Cu\u2082O\u201360P\u2082O\u2085 glass\u2013ceramic nanocomposites. The observed changes in positron lifetimes, trapping rates and free-volume parameters indicate a gradual reduction in vacancy-type defects and free-volume cavities as the V\u2082O\u2085 concentration increases, reflecting the important role of vanadium oxide in controlling the structural properties of the investigated glass system. However, the positron annihilation lifetime (PAL) results indicate a reduction in vacancy-type defects and free-volume size, which reflects improved structural ordering (or structural compactness). This structural refinement reduces disorder and carrier localization, thereby facilitating more efficient electron hopping. Although free-volume (vacancy-type) defects decrease with increasing V\u2082O\u2085 content, the enhancement in conductivity is dominated by compositional effects, while defect reduction contributes indirectly by reducing carrier localization. It should be noted that the increase in oxygen molar volume observed from density measurements does not contradict the reduction in PAL-derived free-volume size and vacancy-related parameters. The oxygen molar volume reflects a macroscopic structural parameter associated with the overall rearrangement and expansion of the phosphate glass network due to the incorporation of V\u2082O\u2085 and the formation of VO\u2084\/VO\u2085 structural units. In contrast, PAL spectroscopy probes microscopic localized free-volume cavities and vacancy-type defects within the glass matrix. Therefore, although the average network structure becomes relatively more expanded at the macroscopic scale, the local structural ordering and homogenization improve simultaneously, leading to a reduction in the size and concentration of localized free-volume defects. These observations indicate that the structural evolution occurs at different length scales and collectively contributes to the observed electrical transport behavior.<\/p>\n Correlation between electrical conductivity and defect structure<\/p>\n Figure\u00a010<\/a> illustrates the relationship between DC electrical conductivity (\u03c3DC), activation energy (W), and vacancy size (Vv) obtained from PAL analysis for xV\u2082O\u2085\u2013(40\u2013x)Cu\u2082O\u201360P\u2082O\u2085 glass\u2013ceramic nanocomposites. As shown in Fig.\u00a010<\/a>A, the logarithm of DC conductivity increases with increasing vacancy size. However, although the vacancy size decreases with increasing V\u2082O\u2085 content, the conductivity enhancement is primarily governed by compositional effects, including the increased concentration of vanadium ions and the reduction in interionic and hopping distances. In this context, defect-related changes influence electrical transport indirectly by modifying the local structural environment. Figure\u00a010<\/a>B shows that the activation energy decreases with increasing vacancy size, indicating that free-volume (vacancy-type) defects can reduce the energy barrier for charge transport by facilitating thermally activated hopping. These defects correspond to free-volume cavities probed by PAL and are distinct from the crystalline features identified by XRD. Their role is mainly indirect, as they modify local atomic packing and orbital overlap between neighbouring transition-metal ions.<\/p>\n Fig. 10 (A) Log(\u03c3DC) and (B) the activation energy at high temperature for xV2O5\u2013(40-x)Cu2O\u201360P2O5 GCN with varying V2O5 concentrations (where x\u2009=\u200910, 20, 30, and 40\u00a0mol%) are correlated with the vacancy size Vv. The errors are within the size of the symbols.<\/p>\n Overall, the results indicate that electrical transport is dominated by small-polaron hopping between V4\u207a\/V5\u207a ions, controlled primarily by compositional parameters such as vanadium ion concentration and interionic distance. The reduction in free-volume defects with increasing V\u2082O\u2085 content reflects improved structural ordering, which supports charge transport by reducing carrier localization. Thus, defect evolution, network modification, and compositional effects collectively influence the transport behaviour, with composition playing the dominant role.<\/p>\n","protected":false},"excerpt":{"rendered":"X-ray diffraction analysis X-ray diffraction (XRD) is a widely used non-destructive technique for investigating the structural state of…\n","protected":false},"author":2,"featured_media":582111,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[4068,85,46,7146,4069,44650,370,141],"class_list":["post-582110","post","type-post","status-publish","format-standard","has-post-thumbnail","category-science","tag-humanities-and-social-sciences","tag-il","tag-israel","tag-materials-science","tag-multidisciplinary","tag-nanoscience-and-technology","tag-physics","tag-science"],"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/posts\/582110","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/comments?post=582110"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/posts\/582110\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/media\/582111"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/media?parent=582110"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/categories?post=582110"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/tags?post=582110"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"Fig.](\"https:\/\/www.newsbeep.com\/il\/wp-content\/uploads\/2026\/08\/41598_2026_65220_Fig2_HTML.png\")
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