Modeling of Cr3+ doped Cassiterite (SnO2) Single Crystals
Biostatistics Molecular BiologyReceived 10 Jun 2024 Accepted 27 Jun 2024 Published online 28 Jun 2024
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Received 10 Jun 2024 Accepted 27 Jun 2024 Published online 28 Jun 2024
Using the superposition model, the crystal field and zero-field splitting parameters of Cr^{3+} doped cassiterite (tin oxide), SnO_{2} single crystals are computed. For calculations, the appropriate locations for Cr^{3+} ions in SnO_{2} with distortion are taken into account. The experimental values and the zero-field splitting parameters in theory with local distortion agree fairly well. Using the Crystal Field Analysis Program and crystal field parameters, the optical energy bands for Cr^{3+} in SnO_{2} are calculated. The findings indicate that in SnO_{2} single crystals, one of the Sn^{4+} ions is replaced by Cr^{3+} ions.
When examining the local symmetry of transition ions in crystals, electron paramagnetic resonance, or EPR, is thought to be a crucial tool. The Cr^{3+} ion introduced into different crystals provides good information about the Crystal Field (CF) and zero field splitting (ZFS) parameters [1-4]. When divalent or trivalent impurities are used in place of monovalent ions, it is crucial to compensate for the charge imbalance. In such systems positive ion vacancies fulfill the charge compensation [5]. The optical characteristics of the crystal are impacted by substituted impurities that cause very little structural change. The Superposition Model (SPM) is mostly used for the theoretical estimation of ZFS and CF parameters [6-8]. It is worth mentioning various semiempirical approaches developed for modeling CF parameters (CFPs) based on crystal structure data. Apart from the historically first, Point Charge Model (PCM), other CFP modeling approaches are Superposition Model (SPM), Angular Overlap Model (AOM), and Simple Overlap Model (SOM). These approaches may yield varying results even using the same crystallographic data as input. Various modeling techniques for the analysis and interpretation of EMR data for transition ions at low symmetry sites in crystals have been reviewed [8]. The superposition model was originally developed and applied first to CFPs for lanthanide ions in various crystals and later to CFPs for transition metal ions. Subsequently, its applications have been extended to the semi-empirical parameterization of Zero-Field Splitting Parameters (ZFSPs) and interpretation of EPR spectra for the S-state 3d^{5} and 4f7 transition ions. It should be emphasized that out of the semi-empirical approaches applicable for CFPs: PCM, SPM, AOM, and SOM, only SPM is also applicable to ZFSPs. In fact, SPM may be employed independently for modeling both CFPs and ZFSPs, whereas attempts to use PCM for ZFSPs occasionally appear in EMR literature. SPM calculations of CFPs and those of ZFSPs utilize the same mathematical framework [8]. Accurate interpretation of EMR experimental spectra and modeling of ZFSPs is important for proper understanding of spectroscopic and magnetic properties of crystals containing 4f^{N} and 3d^{N} ions. SPM yields calculable predictions for EMR experiments in which transition ions are used as probes to investigate the structure and nature of paramagnetic centers. Modeling using SPM may also help predict characteristics important for potential applications. Hence, SPM calculations of ZFS parameters are of prime importance.
SnO_{2} is one of the important semiconducting oxides having desirable qualities such as optical transmittance, mechanical hardness, low resistivity, stability under heat treatment, uniformity, and piezoelectric behavior. This semiconductor, which is of the n-type and has a wide band gap of 3.6 eV at 300 K, is highly iconic and has a wide range of uses. Some of these uses include gas sensors, catalyst supports, dye-sensitized solar cells, supercapacitors, and transparent conducting electrodes [9-13]. Recently, some researchers have added metal or halogen ions to SnO_{2} as impurities, changing its surface states, electronic structure, and optical characteristics in the process, which has improved the material’s qualities and potential applications [10,14,15]. Moreover, the Cr^{3+}-doped SnO_{2} materials are useful in solid-state lighting [16].
EPR study for Cr^{3+} ions in SnO_{2} was performed and spin Hamiltonian parameters were evaluated [17]. Sn^{4+} ions have an ionic radius of 0.069 nm, which is marginally greater than Cr^{3+} ions’ ionic radius of 0.0615 nm. Hence Cr^{3+} substitutes for one of the Sn^{4+} ions as discussed in [17].
The crystallographic axes (a, b, and c) and the laboratory axes (x, y, and z) are chosen in parallel. The symmetry-adopted axes (magnetic axes) have labels (X, Y, Z). The crystallographic c axis is found to correspond with the principal Z axis of the g and D tensors of Cr^{3+} ions.
The superposition model (SPM) analysis of the ZFS and CF parameters for Cr^{3+} ions in SnO_{2} single crystal is presented in the current work. Investigating the ZFS parameters, the CF parameters, and the lattice distortion for the Cr^{3+} ions in SnO_{2} at octahedral sites is the goal. The Crystal Field Analysis (CFA) computer program and CF parameters are used to determine the optical energy bands for Cr^{3+} ions in SnO_{2}. The estimated CF and ZFS parameters could both be helpful in later research for obtaining crystals of various scientific and industrial applications.
SnO_{2} belongs to the TiO_{2} (Rutile) crystal class, which crystallizes in a space group P42 21/n 2/m-D4h14 tetragonal crystal system [18]. The unit cell has the following parameters: a = 0.4737 nm, b = 0.4737 nm, and c = 0.3185 nm. Two nonequivalent Sn^{4+} sites make up the unit cell, and they can be converted into one another by rotating 900 around the c-axis. Due to a slight deformation of the SnO_{6} octahedra, an orthorhombic local symmetry D_{2h} is formed around the Sn^{4+} site. Figure 1 shows the SnO_{2} crystal structure with the Symmetry-Adopted Axis System (SAAS).
The directions of metal-ligand bonds that are mutually perpendicular are the symmetry adopted axes (SAA) or local site symmetry axes. For centers I, the two other axes (X, Y) are perpendicular to the Z axis of SAAS, which is along the metal-ligand bond Sn-O (crystal c-axis) (Figure 1). This suggests that in the SnO_{2} crystal, Cr^{3+} takes the place of Sn^{4+} with approximately orthorhombic symmetry. The ionic radius of Cr^{3+} ions (0.0615 nm) is slightly less than that of Sn^{4+} ions (0.069 nm), suggesting that Cr^{3+} ions can, with some distortion, occupy the position of Sn^{4+} ions. The ligands’ spherical polar coordinates and the position of the Cr^{3+} ion for center I in SnO_{2} are shown in Table 1 [18]. These specifics are employed for Cr^{3+} ion CF and ZFS computations in SnO_{2}.
The energy levels of Cr^{3+} ions in crystals are found using the spin Hamiltonian [19-21]:
ℋ = ℋZe+ ℋZFS ${\text{H}}_{\text{ZFS}}={B}_{2}^{0}O{}_{2}{}^{0}+{B}_{2}^{2}{O}_{2}^{2}=\frac{1}{3}{b}_{2}^{0}{O}_{2}^{0}+\frac{1}{3}{b}_{2}^{2}{O}_{2}^{2}=D({S}_{z}^{2}-\frac{1}{3}S(S+1))+E({S}_{x}^{2}-{S}_{y}^{2})$ (1)
Where spectroscopic splitting factor, Bohr magneton, and steady magnetic field are represented by g, µB, and B, respectively. S represents the effective spin operator and ${O}_{k}^{q}({S}_{x},{S}_{y},{S}_{z})$ are the extended Stevens operators (ESO) [22,23]; and are the parameters of ZFS, ƒk = 1/3 and 1/60 give the scaling factors for k = 2 and 4, respectively. At orthorhombic symmetry sites, the ZFS terms in (1) for the Cr^{3+} ion (S = 3/2) are evaluated as [24,25]:
HZFS $={B}_{2}^{0}O{}_{2}{}^{0}+{B}_{2}^{2}{O}_{2}^{2}=\frac{1}{3}{b}_{2}^{0}{O}_{2}^{0}+\frac{1}{3}{b}_{2}^{2}{O}_{2}^{2}=D({S}_{z}^{2}-\frac{1}{3}S(S+1))+E({S}_{x}^{2}-{S}_{y}^{2})$ , (2)
The traditional orthorhombic ZFS parameters D, E and ${B}_{k}^{q}$ ${b}_{k}^{q}$
, have relations :${b}_{2}^{0}=D=3{B}_{2}^{0},{b}_{2}^{2}=3E={B}_{2}^{2}$ (3)
In ESO notation, the parameters of ZFS for any symmetry utilizing SPM [24,25] are obtained as:
$b\frac{q}{k}={\displaystyle \sum _{i}{\stackrel{-}{b}}_{k}}\left({R}_{0}\right){\left(\frac{{R}_{0}}{{R}_{1}}\right)}^{{t}_{k}}{K}_{k}^{q}\left({\theta}_{i},{\phi}_{i}\right)$ (4)
Where (R_{i}, θ_{I}, ϕ_{i}) present the spherical polar coordinates of the i-th ligand. The intrinsic parameters $\overline{b}k$ represent the magnitude of a ligand’s k-th rank ZFS contribution at a distance R_{i} and the coordination factors ${K}_{k}^{q}$ provide the geometrical data. ${K}_{k}^{q}$ for k=1 to 6 in ESO notation [26] are given in Appendix A1 of [27].
Eq. (4), in terms of the intrinsic parameters $\overline{b}k$ , the power-law exponents t_{k} and the reference distance R_{0}, provide traditional ZFS parameters, D and E as given below[27,28-30]:
${b}_{2}^{0}=D=\frac{{\stackrel{-}{b}}_{2}\left({R}_{0}\right)}{2}\left[{\left(\frac{{R}_{0}}{{R}_{1}}\right)}^{{t}_{2}}{\displaystyle \sum _{i}\left(3{\mathrm{cos}}^{2}{\theta}_{i}-1\right)}\right]$ (5)
${b}_{2}^{2}=3E=\frac{{b}_{2}^{2}}{3}\frac{{\stackrel{-}{b}}_{2}\left({R}_{0}\right)}{2}\left[{\left(\frac{{R}_{0}}{{R}_{1}}\right)}^{{t}_{2}}{\displaystyle \sum _{i}{\mathrm{sin}}^{2}{\theta}_{i}\mathrm{cos}2{\phi}_{i}}\right]$
The Sn^{4+} ion site and the interstitial site with a comparable ligand environment are expected to be substituted by the Cr^{3+} ion in SnO_{2}. The Cr^{3+} ion’s local symmetry is orthorhombic. In LiNbO_{3} having octahedral coordination of Cr^{3+} ion with Cr^{3+}-O_{2}- bond, t2 = -0.12 and = ${\overline{b}}_{2}({R}_{0})$ 2.34 cm^{-1} [31] were taken to compute ${b}_{2}^{0}$ and ${b}_{2}^{2}$ . Since oxygen serves as a ligand and the Cr^{3+} ion in SnO_{2} has distorted octahedral coordination (Figure 1), ${b}_{K}^{q}$ the in the current study is established using ${\overline{b}}_{2}({R}_{0})$ = 2.34 cm^{-1} and t2 = -4.173 for the center I.
The spherical polar coordinates of ligands and the Cr^{3+} ion’s location as shown in Table 1 are considered for computation. The traditional ZFS parameters, D and E of Cr^{3+} ion in a single crystal of SnO_{2} are calculated using Eq. (5). The reference distance R_{0} = 0.200 nm is used [32] to find the ZFS parameters, and the values are: |D| = 2395.2 × 10^{-4} cm^{-1}and |E| = 4.2E-13 × 10^{-4} cm^{-1} for center I. For symmetry that is orthorhombic, the ratio ${b}_{2}^{2}/{b}_{2}^{0}$ should fall between 0 and 1 [33]. In the current calculation, the ratio $\left|{b}_{2}^{2}\right|/\left|{b}_{2}^{0}\right|$ = 5.2E-16 and |E| / |D| = 1.74E-16 for the center I. It is seen that the calculated values of |D| and |E| do not match with the experimental ones though $\left|{b}_{2}^{2}\right|/\left|{b}_{2}^{0}\right|$ falls in the specified range [33]. Therefore, with the above t2 and reference distance R_{0}, the ZFS parameters |D| and |E| are calculated for Cr^{3+} at the Sn^{4+} site with distortion having position Sn^{4+} (-0.1662, -0.1185, -0.0022) for center I. The local environment about Cr^{3+} is shown in Figure 2. The traditional ZFS parameters obtained now are |D| = 5778.1 × 10^{-4} cm^{-1}, |E| = 953.6 × 10^{-4} cm^{-1}for center I, which are matching fairly well with the values found from the experiment. The ratio $\left|{b}_{2}^{2}\right|/\left|{b}_{2}^{0}\right|$ = 0.495 and |E| / |D| = 0.165 for the center I are in the specified range [34]. Further, with the above t2 and reference distance R0, the ZFS parameters |D| and |E| are calculated for Cr^{3+} at the interstitial site but the values discovered differ significantly from the experimental ones. For this reason, they are not included here.
Table 2 gives the experimental and calculated ZFS parameters of the Cr^{3+} ion in SnO_{2}. It shows that the ZFS parameters |D| and |E| are in fair agreement with the values of the experiment [17] when the distortion is introduced into the calculation.
The transition ion CF energy states in crystals [34-37] can be obtained using Wybourne operators as follows [19,38,39]:
${H}_{\text{CF}}={\displaystyle \sum _{kq}{B}_{kq}{C}_{q}^{\left(k\right)}}$ (6)
Where HCF is CF Hamiltonian. The metal-ligand complex’s CF parameters in equation (6) are found using SPM [24,25] as follows:
${\mathcal{B}}_{\text{kq}}={\displaystyle \sum _{i}{}_{\stackrel{-}{A}k}}{\left(\frac{{R}_{0}}{Ri}\right)}^{{t}_{k}}{K}_{kq}\left({\theta}_{i},{\phi}_{i}\right)$ (7)
R_{0} denotes the reference distance, R_{i}, θ_{i}, φ_{i} provide the ith ligand spherical polar coordinates and K_{kq} are the coordination factors [34]. = 40, 400 cm^{-1}, t_{2} = 1.3, =11, 700 cm^{-1} and t_{4} = 3.4 are used to find B_{kg} (k = 2, 4; q = 0, 2, 4) [34]. Table 3 contains a list of the calculated B_{kq} parameters. The ratio |B22|/|B20| = 0.091 for the center I, which suggests that B_{kq} parameters established are standardized [33]. In order to analyze the optical spectroscopy data using the crystal-field approach, an efficient computer program for diagonalization of a complete Hamiltonian (including electrostatic terms, Trees correction, spin-orbit interaction, and crystal-field) within the 3d^{N} configuration (N = 2 to 8) is essential. Yeung and Rudowicz [35,36] recently developed a computer program CFA for 3d^{N} configuration (N = 2 to 8) and for symmetry as low as orthorhombic. The CF analysis computer program is suitable for orthorhombic symmetry, tetragonal symmetry, cubic symmetry, trigonal symmetry, and hexagonal symmetry. Monoclinic and triclinic as well as trigonal and tetragonal symmetry cases involving “imaginary” CF terms are also included. Note that in the latter cases, the complex CF parameter can be made real by an appropriate rotation around the z-axis. Other low-spin states, e.g. S = 1, 0, for 3d^{4} and 3d^{6} ions and S = 3/2, l/2 for 3d^{5} ions, arising at strong ligand fields, as well as the low spin to high spin transition can also be studied using the package. The Hamiltonian for a 3d^{N} ion in crystals can be written as the sum of the free-ion Hamiltonian, the spin-orbit interaction, and the Trees correction describing the two body orbit-orbit polarization. The crystal (ligand) field Hamiltonian in the equation in Wybourne’s notation is taken in terms of the crystal field parameters B_{kq} and the renormalized spherical tensor operators. Since the ligand field is in the weak to intermediate range for most of the 3d transition metal ions in crystals, the basis of states in the LS coupling scheme can be taken. The Slater integrals F^{k} (k = 0, 2, and 4) are related to the Racah parameters A, B, and C as follows:
A = F_{0} - 49FF_{4}
B = F_{2} - 5FF_{4}
C = 35F_{4}
And F_{0} = F^{0}, F_{2} = F^{2}/49, F_{4} = F^{4}/441. Usually, we set A = 0 since it will cause no energy
Level splittings apart from shifting the center of the whole spectrum. Racah parameters A, B, C, Tree’s correction and spin-orbit coupling, and the CF parameters B_{kq} are taken as input parameters.
The total Hamiltonian is diagonalized to calculate the CF energy levels of the Cr^{3+} ion in SnO_{2} single crystals using the B_{kq} parameters in Table 3 and the CFA computer program [35,36]. Table 4 shows the energy values that were calculated. The calculated and experimental energy values for Cr^{3+}: Cassiterite (SnO_{2}) [40] are contrasted. The experimental and theoretical energy values seem to be reasonably in agreement based on Table 4. Therefore, the experimental findings are supported by examining Cr^{3+} ions at Sn^{4+} sites in SnO_{2} theoretically [17,40].
SPM studies of 3d^{N} ions in ferroelectrics, for example, Fe^{3+} ions in PbZrO_{3}, Pb(Zr_{x}Ti_{1-x})O_{3} and PbTiO_{3} and Cr^{3+} ions in PbTiO_{3} and Ba_{x}Pb1_{-x}TiO_{3} powders, Mn^{2+} ions in BaTiO_{3} nanopowders, and other related ion-host systems as well as Fe^{3+} and Mn^{2+} in ZnO also back the experimental EPR findings [8]. The major usage of this investigation may be done in studies of Single Molecule Magnets (SMM), Single-Chain Magnets (SCM), and Single Ion Magnets (SIM) based on transition ions for computational modeling of their properties. The SMM, SCM, and SIM are formed by polynuclear clusters assembled from mononuclear coordination complexes. These systems have become a subject of large interest due to their unique magnetic properties like the phenomenon of macroscopic quantum tunneling of magnetization, as well as possible applications in high-density information storage and quantum computing [8]. Recently many novel SMM or SCM systems containing Cr^{3+} and/or Mn^{2+} ions as well as nanomagnets with elaborate coordination geometry containing Gd3+ ions have been synthesized [8].
The spectra of optical absorption of Cr^{3+}-activated phosphors are now explained using Franck-Condon analysis using the model known as configurational-coordinate (CC) [41]. The various excited state-ground state transitions in Cr^{3+} are a result of the lattice vibrations’ strong coupling (CC model) [41]. The CC model is not being utilized so there is a difference between excited-state peak energies obtained here and energies of the zero-phonon line (ZPL) discussed in [41,42]. There are two types of oxide-phosphors that are doped with Cr^{3+}: the O-Cr-A type and the O-Cr-B type. The characteristics of type O-Cr-A phosphors’ luminescence are obtained from the 2Eg-related luminescence transitions as their crystal-field strength lies in the region of Dq/B > 2.1 while type O–Cr–B phosphors have a crystal-field strength falling within the range of Dq/B < 2.1, as a result, the transitions associated with ^{4}T_{2g} are used to find their luminescence properties. SnO_{2}: Cr^{3+} is classified as an O-Cr-A type phosphor (Dq/B = 4.15, > 2.1) [42].
The Crystal Field (CF) and Zero-Field Splitting (ZFS) parameters for Cr^{3+} ions in SnO_{2} single crystals are determined using the Superposition Model (SPM). Calculations are performed using the interstitial site, distortion models, and Cr^{3+} ions in SnO_{2} crystal at Sn^{4+} ion sites. When distortion is included in the calculation, the calculated conventional ZFS values for the Cr^{3+} ion at Sn^{4+} sites in SnO_{2} single crystal give a reasonable accord with the experimental values. It is found that the Cr^{3+} ions in the SnO_{2} lattice replace the Sn^{4+} ions at those locations. The CF energy values for Cr^{3+} ions at Sn^{4+} sites calculated with CF parameters and the CFA program show an adequate degree of conformity with the experimental ones. Therefore, the theoretical inferences support the experimental result.
The modeling approach adopted in this work could prove useful in the future to find crystals for different industrial and scientific applications by correlating EPR and optical data for several other ion-host systems. The major usage of this investigation may be done in studies of Single Molecule Magnets (SMM), Single-Chain Magnets (SCM), and Single Ion Magnets (SIM) based on transition ions for computational modeling of their properties.
The CFA computer program was provided by Prof. C. Rudowicz of the Chemistry Faculty at A. Mickiewicz University in Poznan, Poland, for which the authors are grateful, and the department head of physics for the departmental facilities.
Bharati M, Singh V, Kripal R. Modeling of Cr3+ doped Cassiterite (SnO2) Single Crystals. IgMin Res. Jun 28, 2024; 2(6): 484-489. IgMin ID: igmin207; DOI:10.61927/igmin207; Available at: igmin.link/p207
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^{1}Department of Physics, Nehru Gram Bharti (DU), Jamunipur, Prayagraj, India
^{1}Department of Physics, Nehru Gram Bharti (DU), Jamunipur, Prayagraj, India
^{2}EPR Laboratory, Department of Physics, University of Allahabad, Prayagraj-211002, India
Address Correspondence:
Ram Kripal, EPR Laboratory, Department of Physics, University of Allahabad, Prayagraj-211002, India, Email: [email protected]
How to cite this article:
Bharati M, Singh V, Kripal R. Modeling of Cr3+ doped Cassiterite (SnO2) Single Crystals. IgMin Res. Jun 28, 2024; 2(6): 484-489. IgMin ID: igmin207; DOI:10.61927/igmin207; Available at: igmin.link/p207
Copyright: © 2024 Bharati M, et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.