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Vol. 9. Issue 1.
Pages 413-420 (January - February 2020)
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Vol. 9. Issue 1.
Pages 413-420 (January - February 2020)
Original Article
DOI: 10.1016/j.jmrt.2019.10.070
Open Access
Electronic and optical properties of Tl4GeX3 (X=S, Se and Te) compounds for optoelectronics applications: insights from DFT-computations
Shah Khalida,b,c, Yue Maa,b, Xiaoliang Suna,b, Guanggang Zhouc, Haicheng Wuc,
Corresponding author

Corresponding authors.
, Guiwu Lub,c,
Corresponding author

Corresponding authors.
, Zhenqing Yangc, Junaid Khand, Rabah Khenatae, Abdelmadjid Bouhemadouf
a Institute of New Energy and Materials, China University of Petroleum, Beijing 102249, PR China
b State Key Laboratory for Heavy Oil Processing, China University of Petroleum, Beijing 102249, PR China
c Beijing Key Laboratory of Optical Detection Technology for Oil and Gas, and College of Science, China University of Petroleum, Beijing 102249, PR China
d Department of Physics, Khushal Khan Khattak University, Karak, Pakistan
e Laboratoire de Physique Quantique de la Matière et de Modélisation Mathématique (LPQ3M), Université de Mascara, 29000 Mascara, Algeria
f Laboratory for Developing New Materials and Their Characterization, University of Setif 1, 19000 Setif, Algeria
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Tables (2)
Table 1. The lattice parameters of Tl4GeS3, Tl4GeSe3, and Tl4GeTe3 compounds.
Table 2. The band values of Tl4GeS3, Tl4GeSe3, and Tl4GeTe3.
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In this work, first-principles computational study on the structural, electronic and optical properties of Tl4GeS3, Tl4GeSe3 and Tl4GeTe3 ternary compounds are presented. The computations are performed with pseudopotential plane wave method based on density functional theory with the generalized gradient approximation of Perdew–Burke and Enzerhof (PBE-GGA). The calculated structural, electronic and optical parameters are consistent with the available experimental results. The computed electronic band structures confirm the semiconducting nature for these compounds with direct band gaps of 0.17eV, 0.085eV and 0.015eV for Tl4GeS3, Tl4GeSe3 and Tl4GeTe3, respectively. Furthermore, the electron charge density distribution indicated that the nature of bonds between Ge and S/Se/Te are covalent nature, whereas Ge and S/Se/Te anions formed ionic bonds. The optical parameters revealed that Tl4GeS3, Tl4GeSe3 and Tl4GeTe3 are highly dielectric materials and has the potential to be beneficial in the optoelectronic device applications.

Band gap
Density of states
Optical properties
Density functional theory
Full Text

The rapid advancement of novel technologies open up new avenues to search for advanced functional-materials (FM). The desirable chemical and physical properties of such materials rely on the chemical composition depending on the crystal structure and atomic positions. The tuning of structural parameters can bring out huge modification in the electronic structure. In recent studies the attempts are made to developed potential semiconductor materials from single and poly-crystal to meet the specific requirements for technological applications. The prime purpose of this paper is to model and investigate the structural, electrical, and optical properties of three narrow band gap Tl4GeX3 (X=S, Se and Te) semiconductors by using the quantum mechanical first principles calculations [1–7].

Such investigations can help in analyzing the experimental data and as well as design a series of novel materials that may paved a path for the production of new optoelectronic devices [8–10]. The interesting features that can be seen in halides and chalcogenides compounds have a great impact, including little anisotropy, non-linear optical properties and piezoelectric properties [11,12]. The fluorooxoborates materials such as LiB6O9F, Li2B6O9F2 and Li2B3O4F3 are investigated with the help of first-principles methods study for their nonlinear optical performance and structural features. The nonlinear optical materials played a very important role in solid state laser. A tunable, compact and deep-ultraviolet (wavelength less than 200nm) laser source could be utilized in large scale in advanced photonic technology [13,14].

The complex-chalcogenides having general formula Tl-BIV,V-CVI, where B is Sn, Ge having d-block element, are of great interest due to their capacity to solve numerous technological issues. Due to the exceptional chemical and physical properties, these compounds are suitable for use as advanced light-emitting diodes (LED), infrared optoelectronics and photo-detectors working in far and mean spectral infrared regions (SIR) and photo-voltaic systems [15–18]. Tl4XB3 (X=Pb, Sn and B=S, Se and Te) (having space group P4/ncc) are ternary semiconductors-chalcogenides with unique properties of excellent thermo-electric features distinguished by low-phonon thermal conductivity [19–24]. The specific importance for the generation of remarkable optical feature is due to the presence of thallium cations, which give attraction to anion co-ordination in a way that ensures the co-existence of covalence and ionic bonds [25–30].

The phase relation in Tl4SeSnS was studied [31,32]. The polymorphic transformation (PT) of Tl4SnS3 compounds is seen at 600K [33]. The Tl4Sn2S3 have monoclinic symmetry, a=13.78Å, b=7.732Å, c=7.266Å, (space group 2/c and β=105.3°) [34]. SnTe-Tl2Te and intermediate phase of Tl4SnTe3 have been synthesized and melts at 817K [35]. An infinite solid solution is made of tetragonal phase between Tl2Te and Tl4SnTe3 (concentration range 60–100mole% of Tl2Se) [36–42].

It is instructive to search for materials of similar nature that can be applied in optoelectronic applications. In this work, the structural, electronic and optical properties of Tl4GeS3, Tl4GeSe3, and Tl4GeTe3 chalcogenides are investigated using the density functional theory. The next section presents the computational methods that are used in the present study.

2Computational method

The generalized-gradient approximation of Perdew–Burke and Enzerhof (GGA-PBE) is used for all the calculations presented herein. The exchange-correlation function (ECF) through DFT is used in CASTEP method (material studio package) [43,44]. The cut-off energy of the plane wave is fixed at 330eV. In all processes, the ultra-soft pseudo-potentials are used. The parameters of energy convergence are fixed as the maximum force accuracy is 0.02eV/Å, the maximum stress component is 0.03GPa, the total energy accuracy is 6×10−5eV/atom and the maximum atomic displacement is 5×10−4Å. The k points of the Brillouin zone are chosen as 5×5×3 for Tl4GeS3, Tl4GeSe3, and Tl4GeTe3. For fast calculations, the primitive cells are chosen. The electronic configurations are 5d106s26p1 for Tl, 4s24p2 for Ge, 3s24s4 for S, 4s24p4 for Se, and 5s25p4 for Te, respectively.

3Results and discussions3.1Structural properties

Tl4GeS3, Tl4GeSe3, and Tl4GeTe3 compounds are body-centered tetragonal with space group 4/mmm. The crystal unit cell structures of all three compounds are presented in Fig. 1. The Brich–Murnaghan equation of state was used to investigate the ground state structural parameters of chalcogenides compounds under study. Our optimized ground states structural parameters are listed in Table 1. The lattice parameters for Tl4GeS3, Tl4GeSe3, and Tl4GeTe3 are a=8.303Å, and b=12.96Å, for Tl4GeSe3, a=8.836Å and b=12.57Å for Tl4GeTe3, a=8.863Å and b=12.96Å respectively, while other calculated values are a=8.314Å where b=12.647Å, while Tl4GeSe3 are a=8.819Å, b=64Å, respectively. The previously obtained results and our calculated results showed a closed agreement.

Fig. 1.

Crystal structure of Tl4GeX3 (X=S, Se and Te) compounds.

Table 1.

The lattice parameters of Tl4GeS3, Tl4GeSe3, and Tl4GeTe3 compounds.

Compounds  Present work  Other works [45–47] 
Tl4GeS3  a=8.303Å, c=12.96Å, V=879.2923  a=8.314Å, c=12.647, V=874.1953 
Tl4GeSe3  a=8.836Å, c=12.57Å, V=875.1129 Å3  a=8.819Å, c=12.64Å, V=872.301 Å3 
Tl4GeTe3  a=8.863Å, c=12.965Å, V=1014.4433  a=8.822Å, c=13.03Å, V=1012.0833 
3.2Electronic properties

To understand the nature of materials, the band gap is very important for electromagnetic, optical, and other physical properties. The structural properties of the three compounds are optimized by the procedure mention above. The electronic and optical properties are calculated by using GGA-PBE approximation. The Tl4GeS3, Tl4GeSe3, and Tl4GeTe3 ternary compounds show their narrow band gaps. Their direct band energies are 0.170eV, 0.085eV and 0.015eV, respectively, as shown in Table 1. The optimized band structures are shown in Fig. 2(a–c). The conduction band minimum (CBM) and the valence band maximum (VBM) are symmetric and are shown at the vicinity of X and Γ symmetry points for Tl4GeX3 (X=S, Se and Te) compounds in the first Brillouin zone as presented in Fig. 2(a–c). As no experimental work has been done on our compounds yet, we will compare the results to similar compounds of the same group like Tl4SnX3 (X=S, Te); their indirect band gaps are 0.708eV and 0.027eV [34]. Our results are closely matched with these compounds. The good point is that the band gaps obtained here are narrow direct band gaps, so the device that will be manufactured from it will be operated by the very low cost of energy. It can be seen from Table 2 that the value of band gaps becomes smaller and smaller and the valance band and the conduction band comes closer and closer to the Fermi level as we doped S, Se and Te in Tl4GeX3, i.e. for Tl4GeS3 it is 0.170eV, for Tl4GeSe3 it is 0.085eV and for Tl4GeTe3 it is 0.015eV. This is because the conductivity of the elements is enhancing as we go down in groups of periodic table so tellurium has more electrons than selenium and selenium has more electrons than sulfur available for conduction as shown in Fig. 2(d). From all the above discussion, it can be figured out that our calculations have good agreement with the other calculations, so our methodology is reasonable.

Fig. 2.

(a) The band gap of Tl4GeS3; (b) the band gap of Tl4GeSe3; (c) the band gap of Tl4GeTe3; (d) the band gap versus composition of Tl4GeX3 (X=S, Se, Te).

Table 2.

The band values of Tl4GeS3, Tl4GeSe3, and Tl4GeTe3.

Compounds  Our proposed (GGA)  Refs. 
Tl4GeS3  0.17eV  0.103eV [45] 
Tl4GeSe3  0.085eV   
Tl4GeTe3  0.015eV  0.027eV [45] 

The electronic density of states (DOS) investigation is really important for the analysis of physical features of Tl4GeX3 (X=S, Se, Te) semiconductors. To figure out the detail bonding nature of Tl4GeS3, Tl4GeSe3 and Tl4GeTe3 ternary compounds, we have calculated the partial and total densities states (PDOS and TDOS) as shown in Fig. 2(a–c). For Tl4GeS3, as in Fig. 3(a), the valance band is originated dominantly from the Tl-5d, Ge-4p, and S-3sp bonding orbitals. However, Tl-5d, Ge-4s, Ge-4p states contribute more than the S-3p states. The atomic orbitals Ge-4p, Tl-6p and S-3p constituted the conduction band. Moreover, the lower part of the conduction band is formed by Tl-6p and S-3p and the upper part is formed by the Ge-4p states. The compound Tl4GeS3 has a narrow energy gap which is 0.17eV due to the involvement of 5d orbitals of Tl and 4p orbitals Ge during the band formation. In the case of Tl4GeSe3 in Fig. 3(b), the valance band is formed by Tl-5d, Se-4sp Ge-4s, and Ge-4p bonding orbitals but the Se-4sp and Tl-4d give large contribution compared to Ge-4s and Ge-4p. In the conduction band, the Ge-4p, Se-4p and Tl-6p states are contributing. Here we see that the main contributions are due to Ge-4p and the minor contributions are due to Tl-6p and Se-4p orbitals. The small band gap energy of 0.085eV is due to the inclusion 5d orbital of Tl and 4p orbitals of Ge and Se during band construction.

Fig. 3.

(a) Total and partial densities of states of Tl4GeS3. (b) Total and partial densities of states of Tl4GeSe3. (c) Total and partial densities of states of Tl4GeTe3.


In the case of the Tl4GeTe3 compound, as presented in Fig. 3(c), the valance band is formed by Te-5p, Tl-5d, and Ge-4s bonding orbitals. The conduction band is comprised of Ge-4p, Tl-6p, and Te-5p. We can see that the large part is given by Ge-4p states and a small part is given by Te-5p state. The energy gap of Tl4GeTe3 is very small (0.015eV) due to the 5p and 5d bonding orbital contributions of Te and Tl atoms in bond formation.

Furthermore, to know about the bonding character clearly, the 2D charge density distribution of Tl4GeS3, Tl4GeSe3, Tl4GeTe3 compounds have been calculated and plotted in Fig. 4. It is revealed from the charge density calculations that these materials have similar bond characteristics. One can observe from charge distribution maps that there are covalent chemical bonds between Ge and S/Se/Te anions and there are ionic bonds between Tl and S/Se/Te. Obviously, these compounds consist of a mixture of covalent and ionic characters. The various charge densities of space hybridizations are due to the geometrical structure of the compounds under consideration. The space hybridization degree is a good technique for the mobility charge detection mainly made by p S/Se/Te holes in the valence band and s, d cationic electron in conduction band near the Fermi level.

Fig. 4.

The charge densities of states for Tl4GeS3 (a), Tl4GeSe3 (b) and Tl4GeTe3 (c).

3.3Optical properties

A comprehensive understanding of the basic optical characteristics, i.e., photonics, and optoelectronics of a compound is of great interest. We should mention in this section that the studied compounds have tetragonal structure, hence we need to calculate two non-zero independent components of the dielectric tensors, namely, εxx=εyy, and εzz to completely characterize their linear optical properties. These components, i.e., εxx and εzz, corresponds to incident radiations with electric field vector E→ polarized parallel to x- and z-axes ([100] and [001] directions), respectively. We find that the calculated components ε2xx(ω) and ε2zz(ω) spectra of each studied compound overlap perfectly. This indicates that the optical properties of the title compounds are perfectly isotropic, i.e. they are independent of the crystallographic direction. The frequency-dependent dielectric function (DF) ε(ω)=ε1(ω)+iε2(ω) is used to figure out the optical properties of Tl4GeS3, Tl4GeSe3, and Tl4GeTe3 ternary compounds. The ε1(ω) and ε2(ω) are the two parts of the dielectric function (DF). Where ε1(ω) is the real part of DF and ε2(ω) is the imaginary part of DF. The imaginary part can be derived from the momentum matrix elements (MME) of filled and unfilled bonding orbitals by applying the following equation:

where u represents the incident electric field polarization, ω is the frequency of light, e defines the electron charge, ψkc and ψkv denotes the conduction and valance band wave functions at a particular k, respectively.

Reflectivity is an optical parameter that characterizes the optical response of the surface of the material. From Fig. 5(a), it is seen that the reflectivity spectra of Tl4GeX3 (X=S, Se and Te) compounds show similar characteristics. The reflectivity of Tl4GeS3 gets to a maximum value of 4.1. On the other hand, the reflectivity of Tl4GeSe3 begins at 4.6, goes up and gets to a maximum value of ∼4.8 in the energy range from 0 to 15eV. For the Tl4GeTe3 compound, the reflectivity starts at 5.3 and get to the highest value of 5.8. It can be noted that all three compounds have similar same spectra and show good characteristics of coating materials. Next, the absorption parameter that shows the depth light of specific photon (energy) or wavelength which can go into the material before being fully absorbed. Fig. 5(b) shows the absorption-spectra of Tl4GeS3, Tl4GeSe3, and Tl4GeTe3 compounds showing that these compounds have semiconducting nature. The absorption spectra of these compounds grow sharply close to 5.8eV. On the other hand, for polarization direction [100], the maximum peaks have an appearance at 6.3eV, after this it undergoes drastic decrement at about 13.6eV. The real parts of refractive-indices of Tl4GeX3 (X=S, Se and Te) compounds are depicted in Fig. 5(c). The refractive indices of the compounds under investigation are about 3.6, 4.2 and 4.8 respectively. These materials are, therefore, suitable for applications where large refractive indices are prerequisites. It can be noted from the refractive indices spectra that they are high in infrared (IR) region, then slowly decrease in the visible and then in the ultraviolet (UV) regions. The results also illustrate that the refractive indices have an inverse relation with the band gaps of the compounds under consideration. It can be observed that the refractive indices are increasing as the bang gap decreasing. From this observation, it can be claimed that our calculations, methodology, and results are reasonable.

Fig. 5.

(a–c) The reflectivity, absorption and refractive index for Tl4GeS3, Tl4GeSe3, and Tl4GeTe3. (d–f) The dielectric function, conductivity and loss function for Tl4GeS3, Tl4GeSe3, and Tl4GeTe3.


Fig. 5(d) shows the DF that is the basic optical parameter for the description of polarization and absorption feature of materials. It is clear from Fig. 5(d), that the imaginary part of dielectric function is zero near 9.2eV for Tl4GeS3, 9.8eV for Tl4GeSe3 and 10.2eV for Tl4GeTe3. The materials are transparent above this energy. The non-zero portion of the imaginary part indicates that absorption occurs in this range of energy. These calculated results by DFT for the three compounds are aligned with the band structure results, showing that these materials have good absorption quality. Dielectric materials with value of dielectric constant k×8.854F/cm greater than that of silicon nitride (k>7) are categorized as high dielectric materials and that materials having k values less than the dielectric constant of silicon dioxide (k<3.9) are categorized as low dielectric materials. So, by comparing the k values of the materials under study with the above-mentioned reference values, we found that our materials have k value more than 7 and could be classified as high dielectric materials and they may have applications in optoelectronics such as memory cell dielectrics, gate dielectrics and passive components [47].

Moreover, the photoconductivity is an optical phenomenon that illustrates that the conductivity of the material goes up due to the absorption of radiation or light energy. Fig. 5(e) shows the photoconductivity of Tl4GeS3, Tl4GeSe3, and Tl4GeTe3 begins at 0.05eV. These materials are significantly electrically conductive for the incident photon energy in the range between 1.3 and 3.8eV. The conductivity becomes small in the energy range 12.2–14.3eV. For energies higher than 15eV, there is no photoconductivity at all. The energy loss function is presented in Fig. 5(f). This shows the energy loss of an electron passing through the materials. It can be seen from the energy loss function that effective plasma frequencies reside within an energy range of 12.5–13.6eV. Also, the compounds are transparent when the frequency of the incident photon energy is larger than the plasma frequency.


In this study, we find out the structural, electronic and optical properties of Tl4GeS3, Tl4GeSe3 and Tl4GeTe3 compounds by using the GGA-PBE approach. All three compounds are narrow band gap semiconductors with band gap energies of 0.170eV for Tl4GeS3, 0.085eV for Tl4GeSe3 and 0.015eV for Tl4GeTe3. The calculation of band gaps, densities of states and optical features of Tl4GeS3, Tl4GeSe3, and Tl4GeTe3 semiconductors showed good alliance with each other and other related calculations. The DOS calculations showed that the maximum contribution near the Fermi level is due to Tl-d, Ge-p, Se-p, and Te-p bonding orbitals. It can be seen from charge distribution maps that the compounds under study have covalent bonds between Ge and S/Se/Te anions and there are ionic bonds between Tl and S/Se/Te. One can clearly see a mixture of covalent and ionic character in these compounds. The optical properties, such as the reflectivity, absorption, refractive index, dielectric function, conductivity and loss function of materials revealed that our materials may have optoelectronic applications. As it is the first time that we have figured out the physical features of Tl4GeS3, Tl4GeSe3 and Tl4GeTe3 compounds, confirmation with experimental results are expected in the future. It is hoped that our findings will open new gateways in this advanced field of research.

Conflicts of interest

The authors declare no conflicts of interest.


We acknowledge financial support from the National Natural Science Foundation of China (Grant no. 11405272), and outstanding young teachers’ research projects of China University of Petroleum-Beijing (Grant no. 2462015YQ0603). Author (R.K.) would like to acknowledge the help of Prof. Saleh. H. Naqib from the University of Rajshahi, Bangladesh and Prof. Hamad R. Jappor from University of Babylon, Iraq, for their careful reading of the paper.

O.Y. Khyzhun, M. Piasecki, I.V. Kityk, I. Luzhnyi, A.O. Fedorchuk, P.M. Fochuk, et al.
J Solid State Chem, 242 (2016), pp. 193-198
O.Y. Khyzhun, P.M. Fochuk, I.V. Kityk, M. Piasecki, S.I. Levkovets, A.O. Fedorchuk, et al.
Mater Chem Phys, 172 (2016), pp. 165-172
A.H. Reshak, V.V. Atuchin, S. Auluck, I.V. Kityk.
J Phys Condens Matter, 20 (2008), pp. 325234
V.L. Bekenev, O.Y. Khyzhun, V.V. Atuchin.
J Alloys Compd, 485 (2009), pp. 51-58
A.H. Reshak, X. Chen, S. Auluck, H. Kamarudin, J. Chysky, A. Wojciechowski, et al.
J Phys Chem B, 117 (2013), pp. 14141-14150
E. Rossinyol, A. Prim, E. Pellicer, A. Cornet, J.R. Morante, L.A. Solovyov, et al.
Adv Funct Mater, 17 (2007), pp. 1801-1806
M. Brik, M. Piasecki, I. Kityk.
Inorg Chem, 53 (2014), pp. 2645-2651
A.H. Reshak, Z.A. Alahmed, J. Bila, V. Victor, G. Atuchin, O.D. Bazarov, et al.
J Phys Chem C, 120 (2016), pp. 10559-10568
M. Piasecki, M.G. Brik, I.V. Kityk.
Mater Chem Phys, 163 (2015), pp. 562-568
M.B. Babanly, V.P. Zlomanov, F.N. Guseinov, G.B. Dashdyeva.
J Inorg Chem, 56 (2011), pp. 1981-1987
A.A. Lavrentyev, B.V. Gabrelian, T.V. Vu, P.N. Shkumat, P.M. Fochuk, O.V. Parasyuk, et al.
Inorg Chem, 55 (2016), pp. 10547-10557
Q. Guo, A. Assoud, H. Kleinke.
Adv Energy Mater, 4 (2014), pp. 140-0348
B. Zhang, G. Shi, Z. Yang, F. Zhang, S. Pan.
Angew Chem Int Ed, 56 (2017), pp. 3916-3919
G. Shi, Y. Wang, F. Zhang, B. Zhang, Z. Yang, X. Hou, et al.
J Am Chem Soc, 139 (2017), pp. 10645-10648
E. Rogacheva, O. Vodorez, O. Nashchekina, A. Sipatov, A. Fedoeov, S. Olkhovskaya, et al.
J Elect Mater, 39 (2010), pp. 2085-2091
M.G. Kanatzidis.
Semicond Semimet, 69 (2001), pp. 51-100
A.H. Reshak, S.A. Khan.
Mater Res Bull, 48 (2013), pp. 4555-4564
L.E. Shelimova, O.G. Karpinskii, T.E. Svechnikova, E.S. Avilov, M.A. Kretova, V.S. Zemskov.
Inorg Mater, 40 (2004), pp. 1264-1270
I. Khan, I. Ahmad, D. Zhang, H.A.R. Aliabad, S.J. Asadabadi.
J Phys Chem, 74 (2013), pp. 181-188
M.A. Mcguire, T.K. Reynolds, F.J. DiSalvo.
Chem Mater, 17 (2005), pp. 2875-2884
P. Spitzer.
J Phys Chem Solids, 31 (1970), pp. 19-40
F. Bertolotti, L. Protesescu, M. Kovalenko, S. Yakunin, A. Cervellino, S.J. Billinge, et al.
ACS Nano, 11 (2017), pp. 3819-3831
J. Xu, A. Assoud, Y. Cui, H. Kleinke.
Solid State Sci, 10 (2008), pp. 1159-1165
C.R. Sankar, S. Bangarigadu-Sanasy, H. Kleinke.
J Electron Mater, 41 (2012), pp. 1662-1666
Q. Guo, A. Assoud, H. Kleinke.
Adv Energy Mater, 4 (2014), pp. 1400-2348
V.L. Bekenev, O.Yu. Khyzhun, A.K. Sinelnichenko, V.V. Atuchin, O.V. Parasyuk, O.M. Yurchenko.
Chem Phys, 72 (2011), pp. 705-713
S.V. Borisov, A. Magarill, V. Pervukhin.
J Struct Chem, 57 (2016), pp. 512-528
O.V. Parasyuk, O.Y. Khyzhun, M. Piasecki, I.V. Kityk, G. Lakshminarayana, P.M. Fochuk, et al.
Mater Chem Phys, 187 (2017), pp. 156-163
A.Y. Tarasova, L.I. Isaenko, V.G. Kesler, V.M. Pashkov, A.P. Yelisseyev, N.M. Denysyuk, et al.
J Phys Chem Solids, 73 (2012), pp. 674-682
D.P. Weller, G.E. Kunkel, A.M. Ochs, D.T. Morelli, M.E. Anderson.
Mater Today Phys, 7 (2018), pp. 1-6
S.K. Matta, C. Zhang, Y. Jiao, A. Mullane, A. Du.
Beilstein J Nanotechnol, 9 (2018), pp. 1247-1253
T.A.M. Rosokha, M.Y. Sabov, I.E. Barc, E.Y. Peresh.
Russ J Inorg Chem, 56 (2011), pp. 118-123
Y. Pei, H. Wang, G.J. Snyder.
Adv Mater, 24 (2012), pp. 6125-6135
M. Piasecki, M.G. Brik, I.E. Barchiy, K. Ozga, I.V. Kityk, A.M.E. l-Naggar, et al.
J Alloys Compd, 710 (2017), pp. 600-607
P. Zeng, J. Cadusch, D. Chakraborty, T.A. Smith, A. Roberts, J.E. Sader, et al.
Nano Lett, 16 (2016), pp. 43
M. Haixia Ma, W. Zhang.
Optik, 182 (2019), pp. 233-240
G. Oskam, J.G. Long, A. Natarajan, P.C. Searson.
J Phys D: Appl Phys, 31 (1998), pp. 16
A.A. Gotuk, M.B. Babanly, A.A. Kuliev.
Zh Neorg Mater, 14 (1978), pp. 587-589
T.A. Rosokha, M.Y. Sabov, I.E. Barchiі, E.Y. Peresh.
J Mater Chem, 75 (2009), pp. 89-91
K. Momma, F. Izumi.
J Appl Crystallogr, 44 (2011), pp. 1272
T.J.B. Holland, S.A.T. Redfern.
Miner Mag, 61 (1997), pp. 65-77
S.J. Clark, M.D. Segall, C.J. Pickard, P.J. Hasnip, M.J. Probert, K. Refson, et al.
Z Kristallogr, 220 (2005), pp. 567-570
H.J. Monkhorst, J.D. Pack.
Phys Rev B, 13 (1976), pp. 5188
J.P. Perdew, K. Burke, M. Ernzerhof.
Phys Rev Lett, 77 (1996), pp. 3865
K. Momma, F. Izumi.
J Appl Cryst, 44 (2011), pp. 1272-1276
T. Holland, S. Redfern.
Miner Mag, 61 (1997), pp. 65-77
R. Kyoung, K. Sojin, J.H. Koo.
J Am Ceram Soc, 81 (1998), pp. 2998
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