Insights into the Microstructure and Transition Mechanism for Nd3+-

18 hours ago - Due to its unusual optical properties, neodymium ion (Nd3+)-doped bismuth silicate (Bi4Si3O12, BSO) is widely used for its excellent me...
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Insights into the Microstructure and Transition Mechanism for Nd3+Doped Bi4Si3O12: A Promising Near-Infrared Laser Material Feiyang Chen,† Meng Ju,† Xiaoyu Kuang,*,† and Yauyuen Yeung*,‡ †

Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China Department of Science and Environmental Studies, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, NT, Hong Kong China

‡

S Supporting Information *

ABSTRACT: Due to its unusual optical properties, neodymium ion (Nd3+)-doped bismuth silicate (Bi4Si3O12, BSO) is widely used for its excellent medium laser amplification in physics, chemistry, biomedicine, and other research fields. Although the spectral transitions and luminescent mechanisms of Nd3+-doped BSO have been investigated experimentally, theoretical research is severely limited due to the lack of detailed information about the microstructure and the doping site of Nd3+-doped BSO, as well as the electric and magnetic dipole transition mechanisms. Herein, we systematically study the microstructure and doping site of Nd3+-doped BSO using an unbiased CALYPSO structure search method in conjunction with first-principles calculations. The result indicates that the Nd3+ ion impurity occupies the host Bi3+ ion site with trigonal symmetry, forming a unique semiconducting phase. Based on our newly developed WEPMD method, the electric dipole and magnetic dipole transition lines, including a large number of absorption and emission lines, in the region of visible and near-infrared spectra of Nd3+-doped BSO are calculated. It is found that the 4 G5/2 → 4I9/2, 2H9/2 → 4I9/2, and 4F3/2 → 4I11/2 channels are promising laser actions of Nd3+-doped BSO. These findings indicate that Nd3+-doped BSO crystals can serve as a promising multifunctional material for optical laser devices.

1. INTRODUCTION

BGO is expensive due to the use of high-purity GeO2 and has a long decay time in many applications.13 Trivalent rare-earth-doped (BSO) presents an effective means to change the characteristics of the pure BSO structure in many respects, such as the shifts of the absorption edge of the transmission spectrum or the light output, the generation and transfer of photoinduced charge carriers, and the full-widthat-half-maximum (fwhm) energy resolutions.14 In particular, Nd3+ doped BSO exhibits excellent optical transmittance between the visible and NIR regions, making it a more attractive candidate for diode-pumped microchip lasers.15 Nd3+doped BSO crystals have been widely studied in several investigations. For the first time, Senguttuvan et al.16 grew single crystals of Nd3+-doped BSO with different doping concentrations (0.5, 1.5, 2.5, 5.0, 7.5, and 10.0 at%) using the vertical Bridgman method. They obtained high quality crystals with Nd concentrations as high as 5.0 at%. Moreover, they found that the absorption coefficient of α increased steadily with an increase in the Nd concentration and when Nd3+ was inserted into BSO with a doping concentration of 5.0 at%. The absorption coefficients are approximately 34 and 19 cm−1, corresponding to the peak absorption wavelengths of 743 and 809 nm. In addition, Kaminskii et al.10 investigated the laser action and made precise measurements of Nd3+-doped BSO by stimulated emission (SE) and stimulated Raman scattering

Recently, rare-earth-ion-doped crystals have gained significant attention because of their potential optical applications for fabricating high-power fiber lasers, and magnetic resonance (MR) bioimaging well as for achieving giant optical gain.1−4 Among the various rare-earth elements, Nd3+, a promising laser ion, has been studied in various materials due to its unique luminescent properties in the visible and near-infrared regions, such as intense absorption band, high quantum efficiency, spectral sharpness, and photostability.5−8 In the wavelength range of 1.0−1.1 μm, in particular, it exhibits excellent medium laser amplification characteristics attributed to its high quantum yield photoluminescence (PL) and large absorption cross section.9,10 These features give Nd3+-doped crystals the potential to serve as lanthanide-based near-infrared (NIR) emitters.11,12 Bismuth silicate (Bi4Si3O12, BSO) is a perfect host material with a large of number of scintillation detector applications in nuclear and high-energy physics experiments owing to its remarkable characteristics such as high radiation hardness, large absorption and light out, and fast luminescent decay constant. BSO and bismuth germanate (Bi4Ge3O12, BGO) are technologically groundbreaking scintillating materials with the same cubic structure of eulytite. However, BSO crystal materials are thought to be more suitable candidates than BGO scintillating materials because BSO has a faster decay time, lower raw material cost, and lower light output than BGO. In contrast, © XXXX American Chemical Society

Received: February 5, 2018

A

DOI: 10.1021/acs.inorgchem.8b00316 Inorg. Chem. XXXX, XXX, XXX−XXX

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To further explore the promising application in laser materials, we adopt our developed WEPMD method to analyze the f-shell energy level of Nd3+-doped BSO. The method is presented as a new userfriendly computer package for spectroscopic property analysis of lanthanide ions with the inclusion of spin−spin interactions, different types of correlation crystal fields, and irreducible representations of individual energy levels, which has been significantly improved and has had great success in different lanthanide systems by removing the errors in the reduced matrix elements and introducing a new parameter called the strength of the normalized electrostatic repulsion.26−31 Additionally, this method yields new findings in nephelauxetic effects,27 configuration interactions for four isoelectronic 4f2 systems,31 and trends in atomic parameters for crystals and free ions across the lanthanide series.26,29 According to the above theoretical methods, the atomic energy structure for the 4f 3 configuration (Nd3+) can be most accurately described by the isolated free ion HA:26,27,29,39,40

(SRS) spectroscopy. They determined absorption and luminescence intensity characteristics such as the spectroscopic quality parameter and the effective cross sections for two interStark laser transitions of the 4F3/2 → 4I11/2 and 4F3/2 → 4I13/2 channels. Very recently, Isber et al.14 studied the magnetization, electron paramagnetic resonance (EPR) properties, and crystalfield effects of Bi4(1−x)Nd4xSi3O12 (x = 0.5%, 1.5%, 2.5%, 3.5%, and 5%). In particular, the site symmetry and the g-factors of Nd3+-doped BSO were determined by measuring the X-band EPR. On the theoretical side, the local geometrical structure and EPR parameters of BGO doped with Nd3+ ions have been studied.17,18 However, no theoretical study has reported the microstructure and location site of Nd3+-doped BSO. To address these unanswered questions, we systematically study detailed information about the microstructure and location site of Nd3+-doped BSO. In particular, the knowledge of the electric and magnetic dipole transitions mechanisms has significant research value in terms of the luminescent properties of the laser materials. In this paper, we first perform an extensive structure search by combining the Crystal structure AnaLYsis by Particle Swarm Optimization19−25 (CALYPSO) code with first-principles calculations to obtain the ground-state structures of the global minimum geometries and explore their respective microstructures and electronic structure properties. Next, we determine the energy levels of Nd3+-doped BSO and probe the physical origin of the electric and magnetic dipole transition mechanisms using our newly developed Well-Established Parametrization Matrix Diagonalization (WEPMD) method.26−31 Our computational details are described in section 2. The discussion and results are presented in section 3. Finally, a summary is given in section 4.

HA = EAVG +

∑ F kfk

+ ζ4f ASO + HADD

(1)

k

where: HADD = αL(L + 1) + βG(G2) + γG(R 7) +

∑ T iti + ∑ P jpj i

+

j

n

∑ M mn

(2)

n

where k = 2, 4, 6; i = 2−4, 6−8; j = 2, 4, 6; and n = 0, 2, 4. The first term, EAVG, donates the barycenter energy of the 4f3 configuration. The parameters Fk, α, β, γ, and Ti, ζ4f, Mn, and Pj account for two-body electrostatic repulsion, two-body configuration, three-body configuration, spin−orbit, spin-other-orbit and electrostatically correlated spin−orbit interactions, respectively. In addition, the angular parts of the electrostatic, spin−orbit, and intra-atomic magnetic interactions are described by the tensor operators fk, ASO, ti, pj, and mn. G(G2) and R(R7) are the Casimir’s operators for groups G2 and R7, and L represents the total orbital momentum. In Nd3+ doped BSO, the optically active Nd3+ ion occupies a site with C3 point group symmetry, and the crystal-field interaction Hamiltonian HCF has been determined by Loro et al.39 Moreover, the crystal-field parameters (CFPs) ImB36 and ImB66 are set to zero when we adopt the approximate C3v site symmetry for the local unit [NdO6]9−. Therefore, the crystal-field interaction Hamiltonian HCF can be simplified to

2. COMPUTATIONAL METHODS Our structural prediction identifying the ground-state structure is based on a global minimum search of free energy surfaces obtained by ab initio total-energy calculations using the PSO technique as implemented in the CALYPSO code.19−25 The significant feature of CALYPSO is that it is designed to predict truly stable structures, requiring the only chemical composition of a given compound and the external conditions. This method has achieved great success in predicting the structure of many systems ranging from elemental solids to binary and ternary compounds, several of which have subsequently been confirmed by independent experiments.32,33 The evolutionary variable-cell structure predictions are performed with 1 to 4 formula units (f.u.) per simulation cell under ambient pressure conditions. Each generation contains 50 structures, 60% of which are generated by particle swarm optimization, while the other 40% of the new structures are generated randomly. We followed 30 generations until converged structures are obtained. Among the 1000−1500 structures, we collect the top 50 lowest lying structures as candidates for the lowest energy structure. The underlying structural relaxations and electronic structure calculations are performed using DFT within both the generalized gradient approximation (GGA) and local density approximation (LDA), as implemented in the Vienna Ab Initio Simulation Package (VASP) code.34−36 A kinetic energy cutoff of 500 eV for the plane-wave basis set and fine Monkhorst−Pack k meshes are chosen to ensure that all the enthalpy calculations are well converged to less than 1 meV per atom. It is well-known that 4f3 configuration Nd3+ systems are strongly correlated. Thus, we must consider the electronic correlations in the total-energy calculations and explore the influence beyond GGA or LDA by including an on-site Coulomb repulsion parameter U within the LDA+U approach. To denote the on-site repulsive Coulomb potential of the Nd 4f-electrons in our calculation, we adopt the value of U = 6.5 eV, which was precisely measured by Wang et al.37 and Herbst et al.38

HCF = B20 C 20 + B40 C40 + B60 C60 + ReB43(C43 − C4−3) + ReB63(C63 − C6−3) + ReB66 (C66 + C6−6)

(3)

The description and significance of the parameters were taken from Yeung et al.26 and Loro et al.39 To account for correlation effects (i.e., two-particle crystal field), it is necessary to introduce orthogonal correlation CF operators (OCCF).41 These operators may represent an effective means to address the anomalous splitting of the 2H11/2 Jmultiplet of the Nd3+ ion. The orthogonal correlation CF operators (OCCF) can be written as41

HOCCF =

∑ Gik, qgik, q i,k ,q

(4)

k

where g i,q are the OCCF operators of type i, rank k, and component q, and Gki,q are the corresponding parameters; k runs through the even integers from 0 to 12; q is restricted by symmetry; and the number of operators varies with k. Previous research findings42,43 on Nd3+ ion doped in various host crystals revealed that the OCCF operators better describe the notorious splitting of the 2H11/2 multiplet when they are restricted to types labeled i = 2, 10A, and 10B.

3. RESULTS AND DISCUSSION We first applied the structure search to predict the ground-state structure of BSO via the CALYPSO code. As expected, the designed PSO algorithm successfully reproduced the experB

DOI: 10.1021/acs.inorgchem.8b00316 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry imentally known I43̅ d structure under ambient conditions for the chemical composition of Bi:Si:O = 4:3:12. To further explore the structure of Nd3+-doped BSO at the nominal concentration, we assumed an ambient pressure of 0.0001 GPa and a chemical composition of Nd:Bi:Si:O = 1:15:12:48 and performed the evolutionary variable-cell structure prediction with simulation sizes up to 76 atoms/cell. Interestingly, we uncovered a novel phase transition with a R3 structure when an Nd3+ ion is doped into the BSO crystal, where the Nd3+ ion impurity naturally substitutes the host Bi3+ ion site with trigonal symmetry. By combining our CALYPSO and VASP codes, we obtained a large number candidate structures, including the lowest energy structures of pure BSO and Nd3+ doped BSO as shown in Figure 1. In pure BSO, the local [BiO6] unit is

S1 (see Supporting Information), the optimized lattice parameters of pure BSO are a = b = c = 10.405 Å with Bi at the Wyckoff 16c (0.083, 0.083, 0.083), Si at the 12a (0.375, 0.00, 0.250), and O at 48e (0.60, 0.131, 0.289) position, respectively. These parameters are in good agreement with experimental measurements, which validates the application of our methods to BSO and provides significant support for the search of Nd3+-doped BSO. We then simulated the X-ray diffraction (XRD) patterns of the ground-state structures and compared them with available experimental data, as shown in Figure 2. In the 2θ range of 20◦ to 70◦, we can clearly see that

Figure 2. E experimental XRD patterns of (a) BSO and the simulated patterns of (b) BSO and (c) Nd3+-doped BSO.

the simulated XRD spectrum of pure BSO is extremely similar to the experimental data.44 This result indicates that the XRD data of pure BSO is best matched by our identified ground-state structure and further validates the reliability of our structure search. No extra diffraction peaks are detected when the Nd3+ ion impurity is doped into BSO. The XRD pattern of Nd3+doped BSO, however, shows a slight shift in the relative intensities at 43◦ and 44◦ compared to the XRD pattern of pure BSO. Obviously, the presence of the Nd3+ ion impurity causes a slight difference in the relative intensities in the local XRD pattern. In addition, we can see clearly that all the diffraction peaks of Nd3+-doped BSO slightly shifted to small diffraction angles compared to the XRD pattern of experimental and simulated BSO. According to the conclusion of our previous structure searching, when the slightly larger ionic radius of Nd3+ (ionic radius = 1.04 Å for Nd3+) occupies the position of Bi3+ with a smaller ionic radius (ionic radius = 0.96 Å for Bi3+), it will cause a slight increase of the unit cell volume. Therefore, it is known from Bragg’s law:

Figure 1. Optimized coordination structures of BSO and Nd3+-doepd BSO. The red, yellow, blue, and green spheres represent O, Si, Bi, and Nd atoms, respectively.

identified to have C3 point group symmetry. We can clearly see that each Bi atom forms a strongly distorted octahedron with six oxygen ligands, in which three of them are situated closer to the Bi atom than the other three oxygen atoms, as shown by the two different bond distances of 2.216 and 2.604 Å. For Nd3+doped BSO, there is no obvious structural distortion, although 6.25% (1/16) of the Bi3+ ion sites are occupied by Nd3+ ions. The point group symmetry of the local [NdO6] unit is the same as that of the [BiO6] unit, and the Nd−O bonds also have two different bond distances of 2.322 and 2.525 Å. In addition, the O−Nd−O and O−Bi−O bond angles are also quantitatively similar. Interestingly, we can see a slight deviation between the Bi−O and Nd−O bond lengths, and a slight deviation between O−Nd−O and O−Bi−O bond angles. This may be because Bi3+ ions have a slightly smaller ionic radius than Nd3+ ions (ionic radius = 1.04 Å for Nd3+ and 0.96 Å for Bi3+). In Table

sin θ = n

λ 2d

(5)

where the wavelength of the incident X-way beam λ and the integer n are constant. The Bragg angle θ between the scattering planes and the incident X-ray decreases when the distance d between the planes in the atomic lattice increases (increase of the unit cell volume). In other words, because the unit cell volume of Nd3+-doped BSO increases slightly, the diffraction peak is slightly shifted to a small angle. In fact, a C

DOI: 10.1021/acs.inorgchem.8b00316 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

conduction band from 3.9 to 5.0 eV are dominated by the p state, where the s state only weakly contributes to the partial DOS and the DOS of the d and f states are almost equal to zero. However, it is well-known that standard DFT calculations using LDA or GGA may largely underestimate the band gap. This is the primary reason why the LDA or GGA method cannot accurately describe localized f states. To improve the description of the Nd3+ 4f shell with strongly correlated electron potentials, we adopt the LDA+U approach, including spin−orbit effects, to obtain the DOS, shown in Figure 3(b), and band structure, shown in Figure S3(b) (see Supporting Information), for Nd3+-doped BSO. The LDA+U approach yields a small band gap of approximately 1.362 eV for Nd3+doped BSO, as shown in Figure S3(b). In Figure 3(b), we can clearly see that the spin-down component of the f orbital is almost empty from the partial DOS of Nd3+-doped BSO, indicating that the carriers of the magnetic moment are mainly Nd atoms. In addition, the occupied states between the Fermi level and the bottom of the conduction band draw their contribution almost completely from the 4f orbital of the Nd3+ ion impurity, as determined by comparing the total DOS of pure BSO with that of Nd3+-doped BSO. These facts indicate that the presence of the Nd3+ ion impurity imparts semiconducting behavior. To more further describe the local magnetic field of the ground-state structure of Nd3+-doped BSO, the CFPs and atom energy levels of the [NdO6]9− local unit are calculated using our the WEPMD method, which is based on crystal-field theory. When considering the crystal-field interaction of the ligand complex [NdO6]9−, the energy levels will split into many Stark levels. According to our results of the structural search and optimization, C3 point group symmetry of the local unit [NdO6]9− is employed to fit the CFPs and free-ion parameters. As a first step, the experimental data given in other works39 are used as the starting set of parameters to reproduce the energy levels, free-ion parameters, and CFPs. To further reduce the rms deviation of the fit for Nd3+-doped BSO, we fix the values of α, β, and γ for the 20 free-ion parameters and 8 CFPs to the values shown in Table 1. Here, the ratios of the intra-atomic magnetic parameters M0:M2:M4 = 1.00:0.56:0.38 and P2:P4:P6 = 1.000:0.672:0.495 are fixed as followed from Crosswhite et al.46 By an iterative process, a reasonable fitting result with a minimum standard deviation of 20.7 cm−1 is obtained in fit 1 with 21 free parameters and 109 newly determined levels. Before our work, the best results for Nd3+-doped BSO were calculated by Loro et al.39 in 2007, with an rms deviation of 24 cm−1. Obviously, our fit 1 lead to a significant reduction of the rms deviation using our WEPMD method, which is smaller than previous results reported by Kumar et al.47 and Loro et al.39 Additionally, we predict the energy levels Efit1 in Table S3 (see Supporting Information) in which most of the fitted parameters are in good agreement with the experimental energy levels. However, the 2H11/2 multiplet shows a very large discrepancy between the calculated and experimental energy levels, in particular for the level numbers 48, 49, 52, and 53. As discussed in a previous report,42,48,49 the well-known deviance of the 2H11/2 multiplet for Nd3+ in various host crystals proved to be difficult to fit with satisfactory accuracy and so these energy levels are often withheld from the fitting process when only the one-electron crystal field is considered. To improve the fit for the anomalous 2H11/2 multiplet and further reduce the rms deviation, we tested different kinds of correlation crystal fields in the fitting process. As the most accurate and

large number of candidate structures were carefully selected and optimized by combining our structure search method with density functional theory. Following the order of energy from low to high, we list the ground-state and first four metastable structures in Table S2 (see Supporting Information). For simplicity, we have just listed several metastable structures and compared with the ground-state structure for XRD data, as shown in Figure S2. We can clearly see that the first four lowlying structures (a), (b), (c), (d) and the ground-state structure of XRD patterns have a similar distribution of peaks and similar overall intensities. Surprisingly, four candidate structures are also identified to have an R3 space group structure; furthermore, their total-energy values are very close, and their structural parameters are almost the same. Thus, the XRD patterns of the candidates have almost no difference although the positions that Nd3+ occupy in BSO are different, as shown in Figure S1 (see Supporting Information). Undoubtedly, the perfect ground-state structure is easily determined because the total-energy of the ground-state (approximately −531.376 eV) is much lower than the energy of the other metastable structures. In the following, we present calculations of the band structures and the total and partial electronic density of states (DOS) of the pure and Nd3+-doped BSO structures using some of the most accurate theoretical tools, i.e., the GGA and LDA +U method. As shown in Figure S3(a) (see Supporting Information), the GGA calculation shows that pure BSO has a band gap of 3.925 eV, which matches well with the experimental value of 4.34 eV.45 In Figure 3(a), the partial DOS of the valence band in the range of −2.0 to 0 eV and the

Figure 3. Calculated total and partial DOS of (a) BSO and (b) Nd3+doped BSO using the LDA+U method (including spin−orbit effects). The Fermi level is indicated by the vertical dotted lines. D

DOI: 10.1021/acs.inorgchem.8b00316 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Table 1. Fitted Values of the Free-Ion and Crystal-Field Parameters of Nd3+-Doped BSOa Param.

Fit 1

Error

Fit 2

Error

Eav F2 F4 F6 ζ α β γ T2 T3 T4 T6 T7 T8 M0 P2 B02 B04 ReB34 B06 ReB36 ImB36 ReB66 ImB66 G210B,0 G410B,0 Reg34 G610B,0 Reg36 Reg66 Nexp Np σ

23864.4 67565.3 50016.4 36229.2 878.6 [22.1] [-648.3] [1719.9] 1474 41.9 51.1 −457.7 813.4 1273.9 1.6 154.4 −856.4 −485.3 1773.7 287.1 −298.1 69.6 793.7 298.2 [0] [0] [0] [0] [0] [0] 99 21 20.7

49.8 747.5 317.8 324.2 0.9

23912.8 68275.1 50161 36180.9 873.7 [22.1] [-648.3] [1719.9] 1292.2 42.1 63.3 −416.9 740.5 1147.3 1.4 204.7 −880.3 −682.6 1797.5 199.9 −288.7 [0] 823 [0] −15.7 157.7 −576.3 302.3 −313.9 835.8 99 22 17.2

64.4 976.5 454.8 452.7 1

216.9 0.7 3.6 31 86 199.8 0.1 24.7 13.5 33 19.4 27.5 22.1 61.3 26.5 85.5

290.8 0.6 3.5 39.6 113.9 263.1 0.1 19.4 10.2 21.6 13 17.2 16.8 10.5 52.7 12.7 46.2 28.6 29.7 79.1

Other39

Other47

71776.1 51928.3 34545.5 874.5 [22.1] [-648.3] [1719.9] 236.6 41 41.2 −280 318.8 187.2 1.68 247.8 −849.4 −454.4 1760.2 293.3 −302.3 77.6 800.5 284.5 [0] [0] [0] [0] [0] [0] 99 24 24

24968 [79338] [44507] [46394] [869] [20.7] [-598] [1524] [380] [39] [62] [-290] [352] [363] [1.83] [256] 824 −169 ±2067 335 ±42 [0] 468 [0] [0] [0] [0] [0] [0] [0] 27 6 ±41

a The parameter values in square brackets are fixed in the fitting calculations. All values are in cm−1. Nexp refers to the number of experimental energy levels used in the fit. Np refers to the total number of freely varying parameters. σ refers to the rms deviation between the experimental and calculated energies.

As a further test of the validity of the new fit 2, the Zeeman splitting g-factors were calculated and are shown in Table 2. In

efficient methods, a specific type of orthogonal correlation crystal field in eq 4 can be incorporated into the conventional crystal-field parametrization by introducing the orthogonal operators. In Table 1, we can clearly see that the rms deviation of new set of fitted parameters (fit 2) is significantly reduced from 20.7 to 17.2 cm−1. To limit the number of freely varying parameters in fit 2, we purposely set ImB36 = 0 and ImB66 = 0 and linked ReGkq with Gki,0 through a fixed ratio for the corresponding CFPs, i.e., ReBqk/B0k. Here, the OCCF of type i = 10B is the most effective to improve the rms deviation, although the type i = 2, 10A, and 10B can describe the notorious 2H11/2 multiplet found for the Nd3+-doped BSO. In addition, we adopt a higher symmetry C3v crystal site for the fit to avoid the poor fitted values caused by too many freely varying parameters; thus, the imaginary components of the CFP and OCCF are set to zero. Notably, the calculated energy levels of the 2H11/2 multiplet (levels 48, 49, 52, and 53) based on fit 2 are much closer to the experimental values than those baesd on fit 1. This finding indicates that the specific type of correlation crystal-field OCCF perfectly addresses the notorious splitting of the 2H11/2 multiplet and further reduces the rms deviation.

Table 2. Experimental and Calculated Values of the Zeeman Splitting g-Factors g∥ and g⊥ and Their Average Value g ̅ for Nd3+-Doped BSO Present calculation g-factor g∥ g⊥ g̅

Expt.

14

1.15 2.47 2.03

Previous calculation

Fit 1

Fit 2

Calc.a

Calc.b

Calc.c

0.523 0.965 0.818

0.653 2.585 1.941

0.556 0.980 0.839

0.63 2.78 2.03

2.15 1.92 2.00

Using the original crystal field parameters from Loro et al.39 bB06 was arbitrarily changed to fit the observed g values from Loro et al.39 c Calculated by Isber et al.14 a

all calculations of the g-factors, we can clearly see that the calculated values based on fit 2 are the closest to the experimental values reported by Isber et al.14 Notably, if we use the initial parameters reported by Loro et al.39 to calculate the g-factors, we obtain much lower values than the experimental results (see calca in Table 2). On the other hand, several attempts have been made by previous researchers E

DOI: 10.1021/acs.inorgchem.8b00316 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry to calculate the g-factors, in which B06 was arbitrarily changed to yield better match with the observed g values (see calcb and calcc in Table 2), but the reliability of these results is questionable. The main concern is that they performed two separate fittings instead of one, leading to two different sets of CFPs. This is a problematic fit because the fitted values of the parameters could not provide a set of consistent results for both the optical and EPR data. Similar calculations have been demonstrated by Chen et al.50 for the Nd3+-doped BGO system. To probe the light−matter interactions and luminescent properties of Nd3+-doped BSO, we employed Judd-Ofelt theory to calculate the electric dipole (ED) and magnetic dipole (MD) transitions based on the free-ion parameters and CFPs obtained from our fit 2 with the minimum rms deviation. Judd-Ofelt theory, introduced by B. R. Judd51 and G. S. Ofelt,52 has been widely used and has achieved great success in the study of the intra4fn optical transitions in trivalent lanthanides. To calculate the ED transitions, we employed the Judd-Ofelt intensity parameters taken from the extremely similar Nd3+-doped BGO system reported by Chen et al.50 and the refractive index n = 1.96 reported by Kumar et al.47 as the initial input parameters; the corresponding method and equations for the calculations are given in the Supporting Information. We first calculated the ED (AED) radiative decay rates, branching ratios (β), and radiative lifetimes (τ) for the spontaneous emission transitions between all J-multiplets; Table S4 in the Supporting Information only shows part of the typical ED transition lines. The branching ratios β of the lines in the 4F3/2 → 4 I9/2−15/2 transition are equal to 0.421, 0.482, 0.092, and 0.005, respectively. These values are very close to the experimentally measured values reported by Kaminskii et al.,10 i.e., βJ−9/2 = 0.338, βJ−11/2 = 0.538, βJ−13/2 = 0.118, and βJ−15/2 = 0.006, which provides great evidence for the reliability of our prediction for other ED transition lines. Interestingly, among all spontaneous emission transitions, the metastable states 4 I11/2, 4I13/2, and 4I15/2 have very long radiative lifetimes of 73096.9, 20987.2, and 17987.0 μs, respectively. The long radiative lifetimes of these metastable states (4I11/2, 4I13/2, and 4 I15/2) are longer than those of the others, indicating that a favorable particle number inversion may be easily achieved. Furthermore, the 4G5/2 → 4I9/2 transition is the most promising candidate for laser output because of its large branching ratio, β = 0.727, as well as the occurrence of the spontaneous emission transition 4G5/2 → 4I9/2, which shows the strongest ED transition intensity of 11649.0 s−1 at 592.2 nm. The large branching ratio and high ED oscillator strength may create conditions that are beneficial for potential laser action. By comparison, we can clearly see that most of the MD transition intensities are extremely weak, but the transition 2H9/2 → 4I9/2 (804.9 nm) has rather strong transition intensities (radiative decay rates AMD) compared with other transitions. In particular, the large MD contribution of the 2H9/2 → 4I9/2 transition line to the overall decay will be helpful to guide the study of the magnetic light−matter interactions for Nd3+ ions doped in the BSO crystal. To clearly show the difference of the two transitions 4G5/2 → 4I9/2 and 2H9/2 → 4I9/2, we present their respective transition diagrams with green and violet lines, respectively, in Figure 4. Although the contributions of the MD transition rates and oscillator strengths are negligible compared to the ED transition, the well-known inter-Stark laser transition 4F3/2 →

Figure 4. Energy level diagrams for a Nd3+ ion in the BSO crystal. The ED transitions 4G5/2 → 4I9/2 and 2H9/2 → 4I9/2 and the MD transitions 4 F3/2 → 4I11/2 of Nd3+-doped BSO are shown. 4

IJ produces a large number of strong MD emission lines in the near-infrared range.39,47,53 Here, we first calculated the oscillator strengths for transitions from the emitting Stark levels 4F3/2(27, 28) to the Stark levels in manifolds 4I9/2, 4I11/2, 4 I13/2, and 4I15/2. As shown in Table S5 (see Supporting Information), there are many strong MD emission lines, such as 4 F3/2(28) → 4I11/2(11) (1081.2 nm), 4F3/2(27) → 4I9/2(2) (887.0 nm), 4F3/2(27) → 4I11/2(6) (1062.8 nm), 4F3/2(27) → 4 I11/2(10) (1096.1 nm), 4F3/2(28) → 4I11/2(8) (1050.6 nm), and 4F3/2(28) → 4I11/2(11) (1375.0 nm), in which the interStark laser transition 4F3/2 → 4I11/2 produced the strongest MD emission line 4F3/2(28) → 4I11/2(11), which has an oscillator strength near 1.882. Note that most of the strong MD emission lines occur between the excited state 4F3/2 and 4I11/2, corresponding to the emission wavelengths range of 1.0−1.1 μm. These strong MD transitions in the near-infrared spectrum may be beneficial for creating conditions for the design and fabrication of resonant optical antennas, plasmonic waveguides, metamaterials, and photonic crystals. In view of the importance of the inter-Stark laser transition 4F3/2 → 4I11/2 (1068.2 nm), we draw its ED transitions and associated MD transition diagrams using blue lines. Most interestingly, the transition 4 F3/2(28) → 4I11/2(11) occurs at 1081.2 nm with the strongest fluorescence intensity. It is hoped that these theoretical predictions can be used to guide further study in future experiments.

4. CONCLUSION In conclusion, we have studied the microstructure, doping site location, and luminescence properties of Nd3+-doped BSO crystal. By combining the CALYPSO method and firstprinciples calculations, a unique semiconducting phase with the R3 space group was found. The result indicated that the Nd3+ impurity occupies the host site of the Bi3+ ion. The electronic band structures and DOS of pure BSO and BSO doped with Nd3+ were calculated using the LDA+U method. Compared to pure BSO, we found the band gap is reduced to 1.362 eV after the Nd3+ impurity was inserted into the BSO host crystal, indicating the closure of the energy gap with insulating characteristics due to the contribution of the 4f F

DOI: 10.1021/acs.inorgchem.8b00316 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry orbital of the Nd3+ ion impurity. Employing our developed WEPMD method, we introduced orthogonal correlation CF operators (OCCF) to further improve the rms deviation of the fitting. The notorious splitting of the 2H11/2 multiplet is perfectly improved. Moreover, we calculated the Zeeman splitting g-factors for Nd3+-doped BSO and obtained good agreement with the experimental values, which indicates that our results are very reliable and our developed WEPMD is a superior method. Additionally, some promising ED and MD transition lines were predicted based on our new crystal-field fitting parameters. The main luminescence lines of the two channels 4G5/2 → 4I9/2 and 2H9/2 → 4I9/2, occurring at approximately 592.2 and 804.9 nm, show the strongest ED transition intensities and MD contributions, respectively. In particular, the inter-Stark laser transition of the 4F3/2 → 4I11/2 channel was determined, which has the strongest oscillator strength corresponding to emission wavelengths in the range of 1.0−1.1 μm. These results enhance our understanding of the transition mechanism and offer a useful guide of multifunctional materials for optical laser devices.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b00316. Calculated band structures of BSO and Nd3+-doped Bi 4Si 3O 12 . The atomic coordinates of metastable candidate structures, energy levels, and electric and magnetic dipole transitions of Nd3+-doped Bi4Si3O12. The method and equations for the calculations of the transition intensities. (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (X.Y.K.). *E-mail: [email protected] (Y.Y.Y). ORCID

Xiaoyu Kuang: 0000-0001-7489-9715 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported by National Natural Science Foundation of China (Nos. 11274235, 11304167, 11574220, and 21671114), Program for Science & Technology Innovation Talents in Universities of Henan Province (No. 15HASTIT020), and Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase). Funding support from the Committee on Research and Development and Dean’s Research Grants of the Faculty of Liberal Arts and Social Sciences, EdUHK is gratefully acknowledged.

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