Nd-substituted Bi<InlineEquation ID="IEq11"> <EquationSource Format="TEX">$_{1-x}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn>1</mn> <mo>-</mo> <mi>x</mi> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>Nd<InlineEquation ID="IEq12"> <EquationSource Format="TEX">$_x$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mi>x</mi> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>FeO<InlineEquation ID="IEq13"> <EquationSource Format="TEX">$_3$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>3</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> ceramics, (<InlineEquation ID="IEq14"> <EquationSource Format="TEX">$x = 0.00$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>x</mi> <mo>=</mo> <mn>0.00</mn> </mrow> </math></EquationSource> </InlineEquation>–0.10) were synthesized to investigate dielectric and impedance behavior at elevated temperatures (280–380 °C) in the frequency range of 100 Hz–1 MHz. The rhombohedral structure with space group of R3c is confirmed using XRD analysis, where the peak shifts toward higher (2<InlineEquation ID="IEq16"> <EquationSource Format="TEX">$\theta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation>) angles (lattice contraction) confirms the successful Nd substitution in BiFeO<InlineEquation ID="IEq17"> <EquationSource Format="TEX">$_3$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>3</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>. Rietveld refinement reveals the reduction in the c-lattice parameter from 13.8776 Å (<InlineEquation ID="IEq18"> <EquationSource Format="TEX">$x=0.00$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>x</mi> <mo>=</mo> <mn>0.00</mn> </mrow> </math></EquationSource> </InlineEquation>) to 13.8011 Å (<InlineEquation ID="IEq19"> <EquationSource Format="TEX">$x=0.10$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>x</mi> <mo>=</mo> <mn>0.10</mn> </mrow> </math></EquationSource> </InlineEquation>), consistent with the observed cell volume shrinkage. FE-SEM analysis shows the grain size reduction (11.54−4.52 µm), confirming the grain growth inhibition due to Nd-doping. FTIR and Raman spectroscopy show structural changes, with shifts in Fe–O bond vibrations indicating enhanced symmetry and structural stability. XPS analysis confirms the stabilization of Fe<InlineEquation ID="IEq20"> <EquationSource Format="TEX">$^{3+}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn>3</mn> <mo>+</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation> states with an increased Fe<InlineEquation ID="IEq21"> <EquationSource Format="TEX">$^{3+}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn>3</mn> <mo>+</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation>/Fe<InlineEquation ID="IEq22"> <EquationSource Format="TEX">$^{2+}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn>2</mn> <mo>+</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation> ratio (1.56–1.68), linked to reduced oxygen-vacancy conduction. Frequency and temperature-dependent investigations show that the variation in dielectric properties is attributed to reduced oxygen vacancies. The maximum dielectric constant of <InlineEquation ID="IEq23"> <EquationSource Format="TEX">$\approx $</EquationSource> <EquationSource Format="MATHML"><math> <mo>≈</mo> </math></EquationSource> </InlineEquation>1300 at 380 °C with <InlineEquation ID="IEq25"> <EquationSource Format="TEX">$\tan \delta \approx 335$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>tan</mo> <mi>δ</mi> <mo>≈</mo> <mn>335</mn> </mrow> </math></EquationSource> </InlineEquation> at 100 Hz is obtained for the <InlineEquation ID="IEq26"> <EquationSource Format="TEX">$x=0.08$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>x</mi> <mo>=</mo> <mn>0.08</mn> </mrow> </math></EquationSource> </InlineEquation> sample. AC conductivity follows Jonscher’s law, with activation energies ranging from 1.08 to 1.93 eV. Impedance and modulus analysis confirm an increase in thermally activated charge carrier mobility and relaxation. Overall, the conduction mechanism is mainly dominated by the short-range mobility of thermally activated charge carriers, resulting in BiFeO<InlineEquation ID="IEq27"> <EquationSource Format="TEX">$_3$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>3</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> being lossy at low frequencies and elevated temperatures.

Impedance characteristics of lossy Bi_1−xNd_xFeO₃ (x = 0.00–0.10) ceramics at elevated temperatures (280–380 °C)

期刊论文
发表日期：

2026年3月12日

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Sujeet Kumar,
Mohd. Fahad,
P. M. Sarun

摘要

Nd-substituted Bi $_{1-x}$ $_{1 - x}$ Nd $_x$ $_{x}$ FeO $_3$ $_{3}$ ceramics, ( $x = 0.00$ $x = 0.00$ –0.10) were synthesized to investigate dielectric and impedance behavior at elevated temperatures (280–380 °C) in the frequency range of 100 Hz–1 MHz. The rhombohedral structure with space group of R3c is confirmed using XRD analysis, where the peak shifts toward higher (2 $\theta $ $θ$ ) angles (lattice contraction) confirms the successful Nd substitution in BiFeO $_3$ $_{3}$ . Rietveld refinement reveals the reduction in the c-lattice parameter from 13.8776 Å ( $x=0.00$ $x = 0.00$ ) to 13.8011 Å ( $x=0.10$ $x = 0.10$ ), consistent with the observed cell volume shrinkage. FE-SEM analysis shows the grain size reduction (11.54−4.52 µm), confirming the grain growth inhibition due to Nd-doping. FTIR and Raman spectroscopy show structural changes, with shifts in Fe–O bond vibrations indicating enhanced symmetry and structural stability. XPS analysis confirms the stabilization of Fe $^{3+}$ $^{3 +}$ states with an increased Fe $^{3+}$ $^{3 +}$ /Fe $^{2+}$ $^{2 +}$ ratio (1.56–1.68), linked to reduced oxygen-vacancy conduction. Frequency and temperature-dependent investigations show that the variation in dielectric properties is attributed to reduced oxygen vacancies. The maximum dielectric constant of $\approx $ $\approx$ 1300 at 380 °C with $\tan \delta \approx 335$ $tan δ \approx 335$ at 100 Hz is obtained for the $x=0.08$ $x = 0.08$ sample. AC conductivity follows Jonscher’s law, with activation energies ranging from 1.08 to 1.93 eV. Impedance and modulus analysis confirm an increase in thermally activated charge carrier mobility and relaxation. Overall, the conduction mechanism is mainly dominated by the short-range mobility of thermally activated charge carriers, resulting in BiFeO $_3$ $_{3}$ being lossy at low frequencies and elevated temperatures.

Impedance characteristics of lossy Bi1−xNdxFeO3 (x = 0.00–0.10) ceramics at elevated temperatures (280–380 °C)

摘要

Impedance characteristics of lossy Bi_1−xNd_xFeO₃ (x = 0.00–0.10) ceramics at elevated temperatures (280–380 °C)