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Article

Lattice Dynamics of Ni3-xCoxB2O6 Solid Solutions

by
Svetlana N. Sofronova
,
Maksim S. Pavlovskii
,
Svetlana N. Krylova
,
Alexander N. Vtyurin
and
Alexander S. Krylov
*
Kirensky Institute of Physics of the Federal Research Center “Krasnoyarsk Science Center of the Siberian Branch of the Russian Academy of Sciences”, 660036 Krasnoyarsk, Russia
*
Author to whom correspondence should be addressed.
Crystals 2024, 14(11), 994; https://doi.org/10.3390/cryst14110994
Submission received: 23 October 2024 / Revised: 8 November 2024 / Accepted: 14 November 2024 / Published: 17 November 2024
(This article belongs to the Section Inorganic Crystalline Materials)
Browse Figures
Versions Notes

Abstract

On the one hand, Ni3-xCoxB2O6 solid solutions are promising anode materials for lithium batteries, and on the other hand, they have antiferromagnetic properties. This study examines the lattice dynamics of Ni3-xCoxB2O6 solid solutions for x = 0, 1, 2, 3 by means of quantum chemistry and Raman spectroscopy. The vibrational spectra of the compound NiCo2B2O6 have been studied using the polarized Raman spectroscopy method. Good agreement was found between the theoretical and experimental results. As expected, the largest change in frequencies was observed in the modes where the vibrations of the metal ion had a large amplitude. The substitution of cobalt by nickel does not lead to the appearance of soft modes. This fact indicates that the structures of the solid solutions are stable.

1. Introduction

Oxyborates Ni3B2O6 and Co3B2O6 and solid solutions of Ni3-xCoxB2O6 were obtained in the 1990s [1,2,3,4,5]. These compounds are interesting both from the fundamental point of view and as promising anode materials for lithium-ion and sodium-ion batteries [6]. The compounds Ni3B2O6 and Co3B2O6 are antiferromagnets, but their easy axis of magnetization is different [7,8]. Mixing magnetic ions with incompatible single-ion anisotropies gives rise to what can be thought of as an atomic-level composite. This random site-dependent anisotropy in combination with the inter-species exchange interaction creates frustration in the system and may result in what is known as an oblique antiferromagnetic phase [9,10,11,12,13,14,15]. Thus, the solid solutions of Ni3-xCoxB2O6 are interesting in terms of magnetic properties, but it is not only their magnetic properties that should attract the attention of researchers. The investigation of the lattice dynamics of Ni3B2O6 shows several new phonon modes to appear at the antiferromagnetic ordering temperature [16]. In Co3B2O6, such effects are not observed [17]. To understand the mechanisms of the appearance of new modes during the antiferromagnetic phase transition, it is necessary to study the lattice dynamics of the Ni3-xCoxB2O6 solid solutions. For the practical application of new materials, in particular solid solutions, it is fundamentally important that the structures stay stable when the temperature decreases [18,19,20]. One of the implicit advantages of the density functional theory is that the modeling performs at temperatures close to zero. If unstable modes are detected as a result of the calculation, then the structure is unstable and can undergo a phase transition when the temperature decreases. In this paper, we present a theoretical study of the lattice dynamics of the Ni2CoB2O6 and Co2NiB2O6 solid solutions and an experimental study of the Raman spectra of Co2NiB2O6.

2. The Crystal Structure

The crystal structure of Ni3-xCoxB2O6 is classified as the kotoite structure and belongs to the space symmetry group Pnnm (58) (Figure 1). The unit cell of kotoite contains six transition metal atoms occupying two crystallographic positions 2a and 4f. The transition metal atoms are located in oxygen octahedra, which are strongly distorted. Boron and oxygen ions form the BO3 group. In the solid solutions Ni2CoB2O6 and NiCo2B2O6, nickel and cobalt ions can randomly occupy both positions (2a and 4f). Lattice dynamics have been calculated for the cation ordered state. In Ni2CoB2O6, the cobalt ions occupy the 2a crystallographic position, while the nickel ions occupy the 4f position. In NiCo2B2O6, the cobalt ions occupy the 4f crystallographic position, while the nickel ions occupy the 2a position.
The first-principles calculations were carried out using the projector-augmented wave (PAW) method [21] within the density functional theory (DFT), as implemented in the VASP code [22,23]. We used the generalized gradient approximation (GGA) functional with Perdew–Burke–Ernzerhof (PBE) parametrization [24]. Electronic configurations were chosen as follows: Ni, 3d94s1; Co, 3d84s1; B, 2s22p1; and O, 2s22p4. The plane-wave cutoff was set at 400 eV. The size of the k-point mesh for the Brillouin zone, based on the Monkhorst–Pack scheme [25], was 7 × 5 × 9. The GGA+U calculations within the Dudarev’s approach were performed by applying a Hubbard-like potential for d states of Fe [26].
The lattice parameters and ion coordinates were optimized until the residual forces acting on the ions became less than 0.02 eV/Å. In this case, the lattice parameters are determined with an accuracy of 10−5 and the coordinates of atoms up to 10−6. The optimized lattice parameters for Ni3-xCoxB2O6 (x = 0, 1, 2, 3) are presented in Table 1. Here, good agreement with the experimental data is observed with the difference being less than 2 percent.

3. The Lattice Dynamics Calculations

The phonons were calculated by constructing a supercell (2 × 2 × 2) and calculating the force constants using the small displacement method implemented in PHONOPY [24]. The decomposition of the complete vibrational representation into irreducible representations at the center of the Brillouin zone has the following form [16]:
Г = 8Ag + 8B1g + 7B2g + 7B3g + 7Au + 7B1u + 11B2u + 11B3u, including acoustic modes B1u + B2u + B3u.
The calculated phonon frequencies for Ni3-xCoxB2O6 (x = 0, 1, 2, 3) are presented in Table 2 and Table 3. The experimental phonon frequencies of Ni3B2O6 and Co3B2O6 from [16,17] are also given in the tables for comparison.
The crystal structure of the kotoite contains triangle BO3 groups. The frequencies of normal vibrations for an isolated [BO3]3− anion are 672 cm−1, 765 cm−1, 939 cm−1 and 1260 cm−1 [27]. In [15], the correlational analysis was carried out, showing that each Raman-active vibration of the free BO3 group generates a Raman combination of mode in the crystal, either (Ag + B1g) or (B2g + B3g), but each IR-active vibration transforms into either a combination mode (B2u + B3u) or a simple mode B1u in the infrared spectrum of the crystal [28]. The IR spectrum data of Co2Ni(BO3)2 and CoNi2(BO3)2 are presented in [4,5]. The comparison of the IR spectrum data [4,5] with the calculated frequencies of Co2Ni(BO3)2 and CoNi2(BO3)2 are shown in Table 4. The experimental and calculated frequencies are shown to be in good agreement.
As one can see from Table 1 and Table 2, some frequencies are similar in all the compounds, while other frequencies differ by more than 40 cm−1. The vibration frequencies associated with the movement of metal ions undergo the greatest changes. In Table 5, a part of the eigenvector of the B2u mode is presented. As is shown in the table, the direction and amplitude of vibration are changed.
Figure 2 shows the dispersion curves of frequencies for Co2Ni(BO3)2 (a) and CoNi2(BO3)2 (b). In both compounds, there are no “soft” modes. The crystal structures of Co2Ni(BO3)2 and CoNi2(BO3)2 are stable. The cause of appearance of new modes is not a structural phase transition.

4. Raman Spectra of Co2NiB2O6

A sample for the experimental study of polarized Raman spectra was grown using the “flux” method by E. Moshkina in the L. V. Kirensky Institute of Physics SB RAS. The technique was described in [29]. A single crystal of Co2NiB2O6 is shown in Figure 3. The plane of the figure corresponds to the (110) crystallographic plane.
Polarized Raman spectra were obtained in backscattering geometry using a Horiba Jobin-Yvon T64000 triple spectrometer (Horiba, France) operating in the dispersion subtraction mode. The Spectra-Physics Excelsior-532-300-CDRH (Albany, NY, USA) 532 nm diode-pumped visible CW solid-state single-mode laser with a power of 3 mW applied to the sample was used as the excitation light source. The Raman spectra resolution using gratings with 1800 mm−1 grooves and 100 m slits was about 2 cm−1. The micro-Raman system based on an Olympus BX41 microscope with a 50× objective lens f = 1.2 mm with the numerical aperture N.A. = 0.75 provides a focal spot 4 lm in diameter on the sample. The sample under investigation was a single crystal, approximately 3 mm in size, of optical quality with natural faceting that was free from defects or visible inclusions under the microscope (Figure 3).
Two series of experiments were performed with parallel and cross-(parallel) polarization of the incident and scattered beams to study the angular dependence of the intensities of Raman spectra, using the backscattering geometry. The shift of the incidence point of exciting radiation was no more than 2 µm in a complete 2π revolution.
The angular dependences of the Raman spectra of the unoriented sample make it possible to assign the lines to irreducible representations of the corresponding space group. Different representations have different values of the observed maximum, and they are possible at various rotations angles of the angular dependences on the intensities of the Raman spectra (see Figure 4). A detailed description of the experimental technique is provided in [30,31,32]. The angular dependences allow observing all the lines in the spectra, including very closely located ones, especially if they have the intensity maximum at different angles. Figure 4a,b present two regions of the angular dependence of Raman spectra of Co2NiB2O6.
The strong modes are located near 400 cm−1 and 900 cm−1 (Figure 4). According to the calculation, two modes of different symmetry (B1g, B2g) were calculated in the 400 cm−1 region (Table 2). The calculation showed that in the 900 cm−1 region, there are also two modes of different symmetry (Ag, B1g).
Figure 5 shows the calculated modes of the vibrational spectrum at 400 and 900 cm−1 for the Co3B2O6 crystal. Blue arrows indicate the vibrational directions. Oxygen atoms are shown in red, cobalt atoms in dark pink and boron in light pink. In the 400 cm−1 region, deformation modes were obtained in BO3 where oxygen and boron atoms vibrate (Figure 5a). In Figure 5b, vibrations of cobalt atoms are added to the BO3 deformations. This vibrational mode can change when the cobalt atoms are replaced by nickel and changes during the magnetic transition. Stretching modes are observed in BO3 around 900 cm−1. Figure 5d shows how oxygen atoms are displaced toward boron atoms.
The comparison of the experimental Raman spectra of Ni3B2O6 and Co2NiB2O6 in the parallel polarizer–analyzer configuration is presented in Figure 6. Here, the angle 0° denotes the initial position of the crystal and that of 90° denotes the position where the crystal is rotated by 90° around the axis of the incident light direction.
The spectra of the compounds Ni3B2O6 and Co2NiB2O6 are very similar. The vibrations of 916 cm−1, corresponding to B-O stretching, are almost identical (Figure 6b), but the deformation of BO3 with B in the plane demonstrates a slight difference (Figure 6a). In Ni3B2O6 the lengths of the B-O bonds are 1.35, 1.39 and 1.39 Å, while in Co2NiB2O6, all the B-O bonds are almost equal: 1.38, 1.39 and 1.39 Å. In Co3B2O6, the BO3 group is more distorted. The lengths of the B-O bonds are 1.41, 1.36 and 1.36 Å. The comparison of the measured Raman spectrum data [4,5] with the calculated frequencies of Co2Ni(BO3)2 is presented in Table 6. One can observe good agreement between the theoretical and experimental data for both IR and Raman spectra.
In the low-wavelength region, we observe significant differences in the positions of the Raman lines (Figure 6a). This is due to the metal ions being involved in these vibrations. The black dashed line in Figure 6 denotes the calculated frequencies of Co2NiB2O6. Here, good agreement between the theoretical and experimental results is observed.

5. Conclusions

The theoretical study of the lattice dynamics of the Ni3-xCoxB2O6 solid solutions for x = 0, 1, 2, 3 was carried out in the VASP code. The experimental Raman spectra at the center of the Brillouin zone for Co2NiB2O6 were obtained. The theoretical and experimental data are observed to be in good agreement. The spectra of the compounds Ni3B2O6, Co3B2O6, Ni2CoB2O6 and Co2NiB2O6 are very similar. The phonon spectra contain the modes which correspond to the BO3 vibration group with the calculated and experimental (IR and Raman) modes being in good agreement. The most significant differences in the positions of the Raman lines are observed in the low-wavelength region, where the vibrations involve transition metal ions. The simulation of the lattice dynamics of the solid solutions showed the decreasing temperature; these compounds should not experience phase transitions, because unstable modes (soft modes) were not obtained.
The study of the lattice dynamics of the four compounds helped us to establish that the solid solution structures are stable and to determine the general trends in the substitution of nickel for cobalt. However, in order to understand the processes in the antiferromagnetic transition, low-temperature studies should be carried out. Therefore, we plan to perform low temperature Raman studies of the oxyborates and evaluate the effect of nickel substitution for cobalt on the antiferromagnetic transition.

Author Contributions

Conceptualization, S.N.S. and A.S.K.; methodology, A.S.K., M.S.P. and S.N.K.; funding, S.N.S.; writing draft, S.N.S. and A.S.K.; writing, A.N.V. and S.N.K.; software S.N.K., A.N.V. and M.S.P.; formal analysis, S.N.S. and M.S.P.; investigation, A.S.K.; data curation, S.N.K. and A.N.V.; writing—review and editing, A.S.K. and S.N.K.; visualization, S.N.S., S.N.K. and A.S.K.; supervision, S.N.S.; project administration, S.N.S. All authors have read and agreed to the published version of the manuscript.

Funding

The research was supported by Russian Science Foundation and Krasnoyarsk Regional Science Foundation, project № 23-12-20012 (https://rscf.ru/en/project/23-12-20012/, accessed on 13 November 2024).

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors on request.

Acknowledgments

The experimental investigations were carried out in the Center for Collective Use of the Krasnoyarsk Regional Center of Research Equipment of Federal Research Center “Krasnoyarsk Science Center SB RAS”.

Conflicts of Interest

The authors declare no conflicts of interest.

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Crystals 14 00994 g001
Figure 1. The crystal structure of kotoite. The 2a and 4f crystallographic positions of the transition metal ions are shown by different colors.
Figure 1. The crystal structure of kotoite. The 2a and 4f crystallographic positions of the transition metal ions are shown by different colors.
Crystals 14 00994 g001
Crystals 14 00994 g002aCrystals 14 00994 g002b
Figure 2. The dispersion curves of frequencies for Co2Ni(BO3)2 (a) and CoNi2(BO3)2 (b).
Figure 2. The dispersion curves of frequencies for Co2Ni(BO3)2 (a) and CoNi2(BO3)2 (b).
Crystals 14 00994 g002aCrystals 14 00994 g002b
Crystals 14 00994 g003
Figure 3. A single crystal of Co2NiB2O6.
Figure 3. A single crystal of Co2NiB2O6.
Crystals 14 00994 g003
Crystals 14 00994 g004
Figure 4. The angular dependence of the Raman spectra of Co2NiB2O6 (a) low-wavenubers region (b) high-wavenumbers region.
Figure 4. The angular dependence of the Raman spectra of Co2NiB2O6 (a) low-wavenubers region (b) high-wavenumbers region.
Crystals 14 00994 g004
Crystals 14 00994 g005
Figure 5. The forms of the vibrational modes of the Co3B2O6 crystal near 400 and 900 cm−1. (a) mode B1g 396.3 cm−1; (b) mode B2g 396.4 cm−1; (c) mode B1g 898.2 cm−1; (d) mode A1g 897.4 cm−1.
Figure 5. The forms of the vibrational modes of the Co3B2O6 crystal near 400 and 900 cm−1. (a) mode B1g 396.3 cm−1; (b) mode B2g 396.4 cm−1; (c) mode B1g 898.2 cm−1; (d) mode A1g 897.4 cm−1.
Crystals 14 00994 g005
Crystals 14 00994 g006
Figure 6. The comparison of the experimental Raman spectra of Ni3B2O6 and Co2NiB2O6 in the parallel polarizer–analyzer configuration. (a) 100–500 cm−1, (b) 500–1300 cm−1. The angle 0° denotes the initial position and 90° denotes the position of the crystal rotated by 90° to the incident light polarization.
Figure 6. The comparison of the experimental Raman spectra of Ni3B2O6 and Co2NiB2O6 in the parallel polarizer–analyzer configuration. (a) 100–500 cm−1, (b) 500–1300 cm−1. The angle 0° denotes the initial position and 90° denotes the position of the crystal rotated by 90° to the incident light polarization.
Crystals 14 00994 g006
Table 1. The calculated lattice parameters in comparison with the experimental data.
Table 1. The calculated lattice parameters in comparison with the experimental data.
Compounds a (Å)b (Å)c (Å)
Co3B2O6exp. [16]4.52905.46208.4360
calc.4.49565.45948.4071
NiCo2B2O6exp. [4]4.504 (1)5.444 (8)8.404 (0)
calc.4.48145.39468.4098
Ni2CoB2O6exp. [5]4.478 (8) 5.419 (9)8.352 (0)
calc.4.49055.36868.2444
Ni3B2O6exp. [15]4.4595.3968.297
calc.4.44805.34848.2667
Table 2. The calculated phonon frequencies (g-symmetry) for Ni3-xCoxB2O6 (x = 0, 1, 2, 3). The experimentally measured frequencies are presented for comparison.
Table 2. The calculated phonon frequencies (g-symmetry) for Ni3-xCoxB2O6 (x = 0, 1, 2, 3). The experimentally measured frequencies are presented for comparison.
ModeCo3B2O6Co2NiB2O6Ni2CoB2O6Ni3B2O6
calc.exp. [17]calc.calc.calc.exp. [16]
Ag218.823205.6220.277233.985234.541238
246.300248.4257.783258.942271.995278
314.787304.8329.223337.229351.245351
378.206382.4422.192397.743401.149403
647.449661.7630.713655.072662.172681
715.109766690.641719.200717.404766
897.375912.1890.618898.151896.602912
1233.7941233.61243.9231224.7071235.2021238
B1g266.622 271.890276.774279.385283
276.010275.2285.502295.481305.040310
349.905291.5360.570361.562372.938372
396.303335.2403.110410.896412.032415
654.899 663.616661.465667.399690
717.897669.3720.375721.263719.727777
898.160777894.392899.595898.444915
1249.602 1248.0001244.9901255.1201256
B2g132.321 131.920139.540145.820158
172.158160.9173.819191.752192.945205
193.600 213.262219.947236.276287
291.116 297.232317.036325.069337
396.421384.0408.239417.038423.669400
560.903569.7557.106568.877566.685553
1126.3151147.01123.9311138.1001127.1221142
B3g143.602136.4142.851157.678159.502151
176.230187.6175.470200.386202.162189
259.677 278.456273.387291.196231
319.456 320.319333.151337.236311
357.962346.3379.684394.317399.470421
531.206 526.714537.991538.014584
1144.0211164.81139.6381153.1401141.8051128
Table 3. The calculated phonon frequencies (u-symmetry) for Ni3-xCoxB2O6 (x = 0, 1, 2, 3). The experimentally measured frequencies are presented for comparison.
Table 3. The calculated phonon frequencies (u-symmetry) for Ni3-xCoxB2O6 (x = 0, 1, 2, 3). The experimentally measured frequencies are presented for comparison.
Co3B2O6Co2NiB2O6Ni2CoB2O6Ni3B2O6
calc.exp. [17]calc.calc.calc.exp. [16]
Au136.525 151.267135.729157.822
193.487 197.641203.412206.968
287.366 283.441310.643315.534
331.036 344.134344.019360.098
429.832 446.587446.064456.276
567.895 564.034570.299569.288
1251.491 1244.4831259.3581243.797
B1u173.946190.8196.489171.755201.160200
301.179256316.769328.449341.500340
335.321331.4338.665344.310350.869354
492.831480505.480503.554509.944513
574.690591.5568.443586.237584.770603
1142.89112251134.2541158.1111146.2981146
B2u132.186 135.920143.068147.366132
182.147136.1188.568197.522203.151208
223.536173.7225.049247.549250.657245
286.862236.4309.861321.309331.670342
360.533305362.851367.989375.145372
367.425375383.006395.053390.782420
586.068419.2587.511580.977581.661575
658.254633.3661.597667.164668.771691
878.269735.6875.944882.204880.292896
1254.988 1252.4571243.5101249.6991244
B3u118.508116122.188128.424130.064149
177.081180191.195193.158205.371202
230.118224.4233.636240.343246.192255
306.416314.5330.273342.077341.825327
350.095352354.441363.642372.059375
391.129411401.574417.168416.259396
582.917620585.225582.322583.819611
653.186681.6657.250658.940660.475696
879.610898.9877.406880.845878.720
1235.50012781233.2601232.0421239.3591252
Table 4. The comparison of the IR spectrum data [4,5] with the calculated frequencies of Co2Ni(BO3)2 and CoNi2(BO3)2.
Table 4. The comparison of the IR spectrum data [4,5] with the calculated frequencies of Co2Ni(BO3)2 and CoNi2(BO3)2.
The Vibrations of BO3 GroupCo2Ni(BO3)2CoNi2(BO3)2
exp. [4]calc.exp. [5]calc.
υ3(BO3)12551233,312531232.0
υ3(BO3)11701134,311801158.1
υ2(BO3)707661,6712667.2
υ2(BO3)668657,3688658.9
υ4(BO3)615585,2622582.3
Table 5. A part of the eigenvector of the B2u mode.
Table 5. A part of the eigenvector of the B2u mode.
PositionIonsThe Eigenvector of B2u Mode
Co3B2O6Ni3B2O6
B2u (cm−1)286.8331.6
2aCo/Ni(0.42  0  0.04)(0.34  0  0.09)
Co/Ni(0.42  0 −0.04)(0.34  0 −0.09)
4fCo/Ni(0.10  0 −0.06)(0.16  0 −0.05)
Co/Ni(0.10  0  0.06)(0.16  0  0.05)
Co/Ni(0.10  0 −0.06)(0.16  0 −0.05)
Co/Ni(0.10  0  0.06)(0.16  0  0.05)
Table 6. The comparison of the Raman spectrum data [4,5] with the calculated frequencies of Co2Ni(BO3)2.
Table 6. The comparison of the Raman spectrum data [4,5] with the calculated frequencies of Co2Ni(BO3)2.
The Vibrations of BO3 GroupCo2Ni(BO3)2
exp.calc.
υ1(BO3)916890.6
υ1(BO3)912894.4
υ2(BO3)767690.6
υ2(BO3)779720.4
υ3(BO3)11301123.9
υ3(BO3)11551139.6
υ3(BO3)12381243.9
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Sofronova, S.N.; Pavlovskii, M.S.; Krylova, S.N.; Vtyurin, A.N.; Krylov, A.S. Lattice Dynamics of Ni3-xCoxB2O6 Solid Solutions. Crystals 2024, 14, 994. https://doi.org/10.3390/cryst14110994

AMA Style

Sofronova SN, Pavlovskii MS, Krylova SN, Vtyurin AN, Krylov AS. Lattice Dynamics of Ni3-xCoxB2O6 Solid Solutions. Crystals. 2024; 14(11):994. https://doi.org/10.3390/cryst14110994

Chicago/Turabian Style

Sofronova, Svetlana N., Maksim S. Pavlovskii, Svetlana N. Krylova, Alexander N. Vtyurin, and Alexander S. Krylov. 2024. "Lattice Dynamics of Ni3-xCoxB2O6 Solid Solutions" Crystals 14, no. 11: 994. https://doi.org/10.3390/cryst14110994

APA Style

Sofronova, S. N., Pavlovskii, M. S., Krylova, S. N., Vtyurin, A. N., & Krylov, A. S. (2024). Lattice Dynamics of Ni3-xCoxB2O6 Solid Solutions. Crystals, 14(11), 994. https://doi.org/10.3390/cryst14110994

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