This study explores the structural and thermal optimization of CoFe2O4 spinel nanoparticles synthesized via the Pechini method and calcined at 450<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$^{\circ }$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>∘</mo> </mmultiscripts> </math></EquationSource> </InlineEquation>C and 650<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$^{\circ }$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>∘</mo> </mmultiscripts> </math></EquationSource> </InlineEquation>C. X-ray diffraction and Rietveld refinement confirm a single-phase cubic spinel (Fd<InlineEquation ID="IEq3"> <EquationSource Format="TEX">${\bar{3}}$</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mrow> <mn>3</mn> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> </math></EquationSource> </InlineEquation>m) with high thermal stability and controlled lattice dynamics. Increasing the calcination temperature induces a slight lattice contraction (8.3877(16) Å to 8.3795(6) Å), while the microstrain remains relatively stable (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\epsilon$</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϵ</mi> </math></EquationSource> </InlineEquation> from 0.18 (6)% to 0.239 (23)%). Heat-capacity data (2–210 K) reveal dual phonon behavior: a low Debye temperature (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\Theta$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Θ</mi> </math></EquationSource> </InlineEquation>D=396.47 K) reflecting global phononic softening, and a high Einstein temperature (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\Theta$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Θ</mi> </math></EquationSource> </InlineEquation>E=683.34 K) indicating local rigidity from Co–O and Fe–O bonds. FTIR analysis suggests cation redistribution between A and B sites, increasing Fe–O stiffness (FCO from 124 to 128 N·m−1) and slightly relaxing tetrahedral bonds (FCT from 223 to 218 N·m−1), thus preserving the spinel framework. These phononic adjustments enhance lattice flexibility and yield a direct band gap of 1.92 eV suitable for visible-light absorption. CoFe2O4 exhibits visible-light photocatalytic activity with negative Gibbs free energy (G298.15=−10,432 J mol−1), supporting effective electron–hole separation. The interplay of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\Theta _D$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="normal">Θ</mi> <mi>D</mi> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$\Theta _E$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="normal">Θ</mi> <mi>E</mi> </msub> </math></EquationSource> </InlineEquation> governs structural stability and charge transport, offering guidance for the design of thermally robust and efficient catalysts.

Anomalous heat-capacity reduction driven by defects and phonon confinement in inverse spinel CoFe₂O₄ nanoparticles

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2026年6月29日

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Daniel E. Bernal L.,
M. Perdomo-Gutiérrez,
Vannyla V. V. Vasconcelos,
Elaine C. Paris,
Miryam Rincón Joya

摘要

This study explores the structural and thermal optimization of CoFe₂O₄ spinel nanoparticles synthesized via the Pechini method and calcined at 450 $^{\circ }$ $^{\circ}$ C and 650 $^{\circ }$ $^{\circ}$ C. X-ray diffraction and Rietveld refinement confirm a single-phase cubic spinel (Fd ${\bar{3}}$ $\bar{3}$ m) with high thermal stability and controlled lattice dynamics. Increasing the calcination temperature induces a slight lattice contraction (8.3877(16) Å to 8.3795(6) Å), while the microstrain remains relatively stable ( $\epsilon$ $ϵ$ from 0.18 (6)% to 0.239 (23)%). Heat-capacity data (2–210 K) reveal dual phonon behavior: a low Debye temperature ( $\Theta$ $Θ$ _D=396.47 K) reflecting global phononic softening, and a high Einstein temperature ( $\Theta$ $Θ$ _E=683.34 K) indicating local rigidity from Co–O and Fe–O bonds. FTIR analysis suggests cation redistribution between A and B sites, increasing Fe–O stiffness (F_CO from 124 to 128 N·m⁻¹) and slightly relaxing tetrahedral bonds (F_CT from 223 to 218 N·m⁻¹), thus preserving the spinel framework. These phononic adjustments enhance lattice flexibility and yield a direct band gap of 1.92 eV suitable for visible-light absorption. CoFe₂O₄ exhibits visible-light photocatalytic activity with negative Gibbs free energy (G_298.15=−10,432 J mol⁻¹), supporting effective electron–hole separation. The interplay of $\Theta _D$ $Θ_{D}$ and $\Theta _E$ $Θ_{E}$ governs structural stability and charge transport, offering guidance for the design of thermally robust and efficient catalysts.

Anomalous heat-capacity reduction driven by defects and phonon confinement in inverse spinel CoFe2O4 nanoparticles

摘要

Anomalous heat-capacity reduction driven by defects and phonon confinement in inverse spinel CoFe₂O₄ nanoparticles