An investigation of local structures and EPR spectra for Cu2+ and VO2+ in biochar

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The defect structure, spin Hamiltonian parameters (SHPs: anisotropic g factors g k and g ⊥ and the hyperfine structure constants A k and A ⊥ ), and their compositional dependence of Cu 2þ in xCuO À ð68 À xÞV 2 O 5 À 32TeO 2 (x = 5, 10, 20, 30 mol%) glasses are quantitatively analyzed by using the higher-order perturbation formula of octahedral complex with tetrahedral elongation distortion. Due to the Jahn-Teller effect, the ½CuO 6 10À group is subjected to tetragonal elongation distortion of varying degrees. D q , N, ρ, κ, and H show nonlinear changes with the concentrations of Cu 2þ . When x = 10 mol% CuO, the degree of distortion (ρ ≈ 0:1%) is the smallest; when x = 30 mol% CuO, the degree of distortion (ρ ≈ 15%) is the largest, which indicates that excessive distortion leads to the appearance of Z-axis oxygen vacancies and the coordination number of copper ions from six to four. The increasing tendency of the evaluated N and H reveals decreasing covalency of the whole glass system. Present theoretical studies would be useful to the explore the structural properties and optical applications of glass with different CuO concentrations. K E Y W O R D Selectron paramagnetic resonance, local structure, xCuO À ð68 À xÞV 2 O 5 À 32TeO 2 (x = 5, 10, 20, 30 mol%)

“…The different higher‐order perturbation formulas of

{Cu}^{2 +}

with different ligand have been introduced in previous literature. [ 31 ] In Equations ()–(),

ρ

can strongly affect the cubic CF parameters and thus affect the denominator

E_{1}

and

E_{2}

of the

g

factors (the overall upward and downward trend of

\overset{g}{true}

). In Equations ()–(), the average covalent factor

N

affects the spin‐orbit coupling coefficient and the orbital shrinkage factor, thereby affecting the

g

factors.…”

Section: Discussionmentioning

confidence: 99%

“…The perturbative g factors and the hyperfine structure constants of the 3d 9 ion under the tetragonal elongated octahedral symmetry can be written as follows [30,31] :…”

Section: Theory and Formulasmentioning

confidence: 99%

Section: Theory and Formulasmentioning

confidence: 99%

“…The perturbative

g

factors and the hyperfine structure constants of the

3 {normald}^{9}

ion under the tetragonal elongated octahedral symmetry can be written as follows [ 30,31 ] :

\begin{matrix} right & left g_{‖} = g_{s} + 8 k^{'} ζ^{'} / E_{1} + k ζ^{' 2} / E_{2}^{2} + 4 k^{'} ζ ζ^{'} / (E_{1} E_{2}) \\ right & left + g_{s} ζ^{' 2} [1 / E_{1}^{2} - 1 / (2 E_{2}^{2})] \\ right & left - k^{'} ζ ζ^{' 2} (4 / E_{1} - 1 / E_{2}) / E_{2}^{2} - 2 k^{'} ζ ζ^{' 2} [2 / (E_{1} E_{2}) - 1 / E_{2}] / E_{1} \\ right & left + g_{s} ζ ζ^{' 2} [1 / (E_{1} E_{2}^{2}) - 1 / (2 E_{2}^{3})], \\ right & left g_{} \end{matrix}

…”

Section: Theory and Formulasmentioning

confidence: 99%

“…[ 36 ]

R_{⊥}

represents the

normal {Cu}^{2 +} - O^{2 -}

bond length on the plane perpendicular to the

Z

‐axis;

R_{false‖}

represents the

normal {Cu}^{2 +} - O^{2 -}

bond length parallel to the

Z

‐axis. The

normal {Cu}^{2 +} - O^{2 -}

bond length will be elongated along the

Z

‐axis (the

Z

‐axis direction is

R_{false‖}

) due to the influence of the Jahn–Teller effect, while the plane bond length (the

X

‐, the

Y

‐axis direction is

R_{⊥}

) will become shorter, so

R_{⊥}

and

R_{false‖}

can be written as follows [ 30,31 ] :

\begin{matrix} right & left R_{‖} \approx R_{0} (1 + 2 ρ), \\ right & left R_{⊥} \approx R_{0} (1 - ρ) . \end{matrix}

where the reference distance

R_{0}

is the average value of the central ion‐ligand spacing and

ρ

is the rel...…”

Section: Theory and Formulasmentioning

confidence: 99%

See 3 more Smart Citations

Investigations on the local structure and the spin Hamiltonian parameters for Cu²⁺ in xCuO−(68−x)V₂O₅−32TeO₂ glasses

Liu

Yang

et al. 2022

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A comparable study of the optical spectra and EPR parameters for 3d¹‐ and 3d⁹‐doped MgNH₄PO₄·6H₂O

Chen

Zhang²,

Li³

et al. 2022

VO2+ (3d1) and Cu2+ (3d9) are the two complementary states that usually show opposite distortions when they are doped in crystals. In this work, the optical absorption spectra (OAS), electron paramagnetic resonance (EPR) parameters, and local structure (LS) for VO2+ (and Cu2+) in MgNH4PO4·6H2O (MPPH) are uniformly investigated on the basis of the high‐order perturbation formulas for a 3d1 (and 3d9) ion in tetragonally compressed (and elongated) octahedra, respectively. In the calculated formulas, the required crystal‐field parameters can be obtained from the superposition model and reasonably linked with the LS distortion for VO2+ and Cu2+ centers. Based on the calculations, the tetragonal compressed [VO(H2O)5]2+ cluster (and tetragonal elongated [Cu(H2O)6]2+ cluster) is found to suffer tetragonal compression ratio of 1.65% and tetragonal elongation ratio of 3.8% along C4‐axis, respectively, due to the Jahn–Teller (JT) effect. The theoretical EPR parameters based on the above lattice distortions agree well with the experimental data, and the LS of the VO2+ and Cu2+ centers in MPPH is discussed.

Theoretical studies on the local structure and spin Hamiltonian parameters for Cu²⁺ ions in LiTaO₃ crystal

Chen,

Tang,

Cai

et al. 2023

The local structure and spin Hamiltonian parameters (SHPs) g factors (gx, gy, gz) and the hyperfine structure constants (Ax, Ay, Az) for Cu2+ doped in the LiTaO3 crystal are theoretically investigated by the perturbation formulas for a 3d9 ion under rhombically elongated octahedral based on the cluster approach. The impurity Cu2+ was assumed to occupy the host trigonally‐distorted octahedral Li+ site and experience the Jahn–Teller (JT) distortion from the host trigonal octahedral [TaO6]10− to the impurity rhombically elongated octahedral [CuO6]10−. Based on the calculations, the impurity‐ligand bond lengths parallel and perpendicular to the C2‐axis are found to be R||(≈ 2.305 Å) and R⊥ (≈ 2.112 Å) for the studied [CuO6]10− cluster, with the planar bond angle θ (≈ 78.2°). Meanwhile, the ground‐state wave function for Cu2+ center in LiTaO3 was also obtained. The calculated SHPs based on the above local lattice distortions agree well with the experimental data, and the results are discussed.