#
The Nano-Scale Modified BaTiO_{3} Morphology Influence on Electronic Properties and Ceramics Fractal Nature Frontiers

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{7}

^{*}

## Abstract

**:**

## Featured Application

**The nano BaTiO**

_{3}modification could lead towards innovation in nanocoating of ceramic grains in function of submicron intergranular capacitors. The electronic parameters integration in the frame of microelectronics in intergranular phenomena by fractals is opening novel route in miniaturization and integrations. Fractal analysis and calculations provide necessary fractal corrections for sample synthesis.## Abstract

_{3}ceramics applications based on electronic properties have very high gradient scientific and industrial-technological interests. Our scientific research has been based on nano BaTiO

_{3}modified with Yttrium based organometallic salt (MOD-Y). The samples have been consolidated at a sintering temperature of 1350 °C. Within the study, the new frontiers for different electronic properties between the layers of BaTiO

_{3}grains have been introduced. The research target was grain boundary investigations and the influence on dielectric properties. After scanning electron microscopy and dielectric measurements, it has been established that modified BaTiO

_{3}samples with larger grains showed a better compact state that led to a higher dielectric constant value. DC bias stability was also investigated and showed a connection between the grain size and capacitance stability. Analyses of functions that could approximate experimental curves were successfully employed. Practical application of fractal corrections was performed, based on surface (α

_{s}) and pore size (α

_{p}) corrections, which resulted in obtainment of the relation between the capacitance and Curie temperature. Successful introduction of fractal corrections for capacitance-Curie temperature dependence for a set of experimental data is an important step towards further miniaturization of intergranular capacitors.

## 1. Introduction

_{3}and consequently to the decrease in the overall dielectric constant and capacitance [12]. One approach to solving the problem is doping BaTiO

_{3}with acceptors or donors, most commonly with rare-earth elements, such as Yttrium and their oxides [13,14]. After the modification, grain boundary (GB) changes, inducing changes in dielectric and ferroelectric properties, occurred [15]. By investigating the phenomena at the GB, changes in dielectric properties could be understood and controlled by changing the processing parameters [16]. It is well known that the grain size increase leads to a dielectric constant value increase but also causes higher capacitance DC bias sensitivity, that is, capacitance value decreases with the increase of applied DC voltage [9]. Finding an adequate modifier for BaTiO

_{3}that would reduce DC bias sensitivity dependence on the grain size is a real challenge, which could be easier with the use of proper theoretical models for the dielectric properties investigation at the GB, compared to the bulk sample. Dimensional and shape analysis could be achieved by using a fractal approach, giving insight into the influence on the bulk sample properties [17,18,19,20]. Fractals are irregular geometric objects with fragmented or amorphous forms that cannot be described by Euclid’s geometry [21]. The contribution of fractals correction could be observed and explained with the intergranular Heywang capacity model, Schottky barrier, Curie-Weiss law and other parameters in the field of dielectric and ferroelectric materials. Implementation of fractals correction in the Claussius-Mossotti equation could explain dimensional influence on atom polarizability, which further leads to a dielectric constant control at the grain boundary. In this manner, dielectric constant and DC bias stability could be enhanced with proper parameters during synthesis.

_{3}with rare-earth based organometallic salt (Scheme 1), in order to provide a densified compact microstructure of modified ceramic capacitor. Next to that, investigation of GB phenomena was performed using microstructural fractal analysis for the dielectric properties investigation. Obtaining intergranular microelectronic properties represents high advance in the field of electronic ceramic applications and frontiers. Modification of the grains was performed and investigated in order to obtain coated ceramics that could be implemented in an LTCC module, within the further research direction. BaTiO

_{3}was modified with Yttrium based organometallic salt, in order to obtain fine dispersion in organic solvents and to ensure uniform coating. Bilayers between grains were formed (thin films that coat grains), with as precise location control as possible in ceramic bulk.

## 2. Materials and Methods

#### 2.1. Materials and Sample Preparation

_{3}nanopowders were purchased from SAKAI CHEMICAL INDUSTRY CO. LTD., Sakai, Osaka, Japan. Nanoparticles with average diameters of around 40 nm and 112 nm were denoted KZM100 and BT02, respectively. Modified BaTiO

_{3}samples were prepared using solvent mixture Ethanol/Toluene/n-Butanol. Pure BaTiO

_{3}nano-structured powders were treated with additive metal-organic yttrium salt MOD-Y, where BaTiO

_{3}: MOD-Y mol ratio was 3:97. This molar ratio has been chosen as the best after a series of experiments with different ratios. After the mixing, ball milling was performed for 24 h, followed by tape casting, process of lamination and sintering, where, as a result, thin films were produced. The consolidation process was carried out according to Scheme 2. All of these have been prepared by the specific and protected ITRI procedure. The sintering was performed for one hour at 1350 °C in the reducing atmosphere 5% H

_{2}/N

_{2}.

#### 2.2. Characterization of Samples

_{3}was successful. Morphology of un-sintered and sintered ceramics was investigated via scanning electron microscopy (SEM) (EmCraft cube 2). The composition and homogeneity of the samples was investigated with energy dispersive X-ray analysis (EDX) using Cliff-Lorimer method with all the elements analyzed (Normalized). Distribution of BaTiO

_{3}size was obtained using Nicomp 380 DLS/ZLS Dynamic Light Scattering and Zeta Potential. Dielectric properties were measured on Microtest LCR Meter 6377@1KHz and KEITHLEY 2400 SourceMeter. Sample’s dimensions were round shaped films with a 3 mm diameter and a thickness of 0.75 mm. All the measurements were performed at room temperature (25 °C)

#### 2.3. Fractal Analysis

_{H}(Figure 2) and fractal correction α

_{s}based on grain surface influence [22,23]. Figure 2 shows the dependence of number of boxes, N, that cover the surface, on a box of size h. This dependence is shown on a logarithmic scale.

_{H}and corresponding fractal correction α

_{p}based on pore shape influence [22,23]. Figure 4 shows contour length (L) dependence on ruler size (r) on a logarithmic scale.

_{M}, it is neglected.

_{3}with different additives) which are natural data confirming this approach with additional microstructural analysis and characterization concretely on the surface of the grains and pores. As we explained earlier, here we did not include the influence of particles’ Brownian motion because this phenomenon is not dominant in ferroelectrics and dielectric materials and processes. Regarding the influence of grain and pore surfaces, it is definitely clear that this fractal level of microstructure characteristics directly and more precisely extend the structure influence on electrophysical properties, in this paper, specifically, ferroelectric and dielectric properties. Here, in this paper we applied previous knowledge to samples based on BaTiO

_{3}with Ytrium additives. Fractal correction is based on grains’ and pores’ surfaces fractal dimension which has been calculated by using well known methods of Richardson plot and box-counting (Figure 2 and Figure 4).

_{H}and problems related to it. As this is not the main topic of this paper, we can analyze this problems in future research in which results from this paper could be a contribution to further research and further clarification of this matter.

## 3. Results and Discussion

#### 3.1. Microstructural Analysis

#### 3.1.1. STEM-EDX

_{3}, leading to a conclusion that the used modification method with Yttrium organic salt was successful.

_{3}phase during high temperature modification of grains.

^{4+}with rare earth element.

#### 3.1.2. FESEM Analysis

#### 3.2. Dielectric Properties

_{3}have a high dielectric constant (D

_{k}) and therefore capacitance value but as D

_{k}increases, they show increased sensitivity to DC bias. It is known that up to 1 µm, D

_{k}sharply increases with the grain size [25]. BT02-MOD-Y showed by the order of magnitude higher dielectric constant value (2132), compared to KZM100-MOD-Y (182). However, consequently, it has the highest capacitance value decrease with DC bias. Figure 9 and Figure 10 show the capacitance drop with DC bias for KZM100-MOD-Y and BT02-MOD-Y respectively. Capacitance of KZM100-MOD-Y remained stable, with negligible decrease up to 73 V, where a slow drop can be observed to 67% at 96 V.

_{3}after the modification.

#### 3.3. Dielectric Constant Fractal Correction

_{M}, is not included in this analysis because of its minor influence (in comparison to α

_{S}and α

_{P}) and to provide less complicated further analysis.

_{s}(grain surface) and α

_{p}(inside pore surface) to Curie-Weiss law, introduced in References [22,23].

_{c}~10

^{5}.

_{3}-ceramics must be influenced by three factors forming fractal corrective factor α

_{f}, making the real ceramic temperature T

_{f}, which is a corrected T; the two temperatures are connected using equation T

_{f}= α

_{f}*T and α

_{f}is a complex fractal correction.

_{f}will be temperature fractal correction that is, T

_{f}= α

_{f}*T. In this case, the microfractality and associate complex fractal correction α

_{f}have very important role on that submicrolevel and also influence on local and in summary the samples thermal effects.

_{M}, total fractality impact is equally distributed over α

_{s}and α

_{p}

_{r}can be presented with equation:

_{0}stands for absolute dielectric constant, S is the sample surface and d represents sample thickness. Including values for T

_{f}(25 °C), S (3 mm) and d (0.75 mm), a function showing relation between capacitance (C) and T

_{c}can be obtained for our experimental data:

_{c}change, which is very important for the investigation of capacitor stability under different operational conditions. According to the literature, C

_{c}of pure BaTiO

_{3}is the order of magnitude 10

^{5}, so it can be assumed that modified BaTiO

_{3}could have the similar values, obtaining the dependence [27]:

## 4. Conclusions

_{3}ceramics for different grain sizes (40 nm and 112 nm). Modification was performed by a chemical solvent coating method, using metal-organic Yttrium salt in the mixture of organic solvents, in order to obtain uniformly modified samples. Microanalysis revealed the formation of ultra-thin second phase, which allowed effective consolidation during sintering. By using fractal analysis, successful reconstruction of grains and pore shapes was performed, which is important for the prediction and design of microstructure. Samples with higher grain size showed better compact state that led to a higher dielectric constant value. BT02-MOD-Y showed an excellent dielectric constant, over 2000, with a low dielectric loss of <1%. However, DC bias stability of smaller grain samples was significantly higher. BT02-MOD-Y showed sharp drop below 4 V, while KZM100-MOD-Y remained stable up to 80 V, with a slow drop to around 33% at 98 V. Adequate analyses of possible functions that can make an approximation of experimental curves in the best manner were successfully used, providing scaled reliability functions for capacitance change with DC bias. The practical application of fractal corrections based on α

_{s}(grain surface) and α

_{p}(inside pore surface), with the idea of establishing the relationship between the capacity and Curie temperature, was performed. The fractal characterization of grains and pores surfaces is important, because contacts between the grains and pores, considering the roughness of the surfaces, can influence the specific integranular relations and characteristics. This is especially important due to sensitive dielectric and ferroelectric characteristics that have influence in the field of further submicron parameters integrations, which represents the possible future research of deep level miniaturization. In this sense, surface fractal characterizations give more advanced details within this matter. In all of our previous research, the basic element is a practically existing intergranular fractal capacitor that is, capacity. This model already included the granular and pores’ surface effects integrated as intergranular capacity. Our results based on introduced complex fractal correction do not involve other possible factors, like grain size. For future research, we plan to extend all of these analyses and models with a goal to integrate, besides the surface and intergranular relations, the grain size and distribution phenomena.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Slimani, Y.; Unal, B.; Hannachi, E.; Selmi, A.; Almessiere, M.A.; Nawaz, M.; Baykal, A.; Ercan, I.; Yildiz, M. Frequency and dc bias voltage dependent dielectric properties and electrical conductivity of BaTiO
_{3}–SrTiO_{3}/(SiO_{2})_{x}nanocomposites. Ceram. Int.**2019**, 45, 11989–12000. [Google Scholar] [CrossRef] - Beuerlein, M.A.; Kumar, N.; Usher, T.M.; Brown-Shaklee, H.J.; Raengthon, N.; Reaney, I.M.; Cann, D.P.; Jones, J.L.; Brennecka, G.L. Current understanding of structure–processing–property relationships in BaTiO
_{3}–Bi(M)O_{3}Dielectrics. J. Am. Ceram. Soc.**2016**, 99, 2849–2870. [Google Scholar] [CrossRef][Green Version] - Hou, Y.; Xie, C.; Radmilovic, V.V.; Puscher, B.; Wu, M.; Heumüller, T.; Karl, A.; Li, N.; Tang, X.; Meng, W.; et al. Assembling mesoscale-structured organic interfaces in perovskite photovoltaics. Adv. Mater.
**2019**, 31, 1–8. [Google Scholar] [CrossRef] [PubMed] - Jeangros, Q.; Duchamp, M.; Werner, J.; Kruth, M.; Dunin-Borkowski, R.E.; Niesen, B.; Ballif, C.; Hessler-Wyser, A. In situ TEM analysis of organic-inorganic metal-halide perovskite solar cells under electrical bias. Nano Lett.
**2016**, 16, 7013–7018. [Google Scholar] [CrossRef] - Ihlefeld, J.F.; Harris, D.T.; Keech, R.; Jones, J.L.; Maria, J.P.; Trolier-McKinstry, S. Scaling effects in perovskite ferroelectrics: Fundamental limits and process-structure-property relations. J. Am. Ceram. Soc.
**2016**, 99, 2537–2557. [Google Scholar] [CrossRef] - Wang, S.F.; Hsu, Y.F.; Hung, Y.W.; Liu, Y.X. Effect of Ta
_{2}O_{5}and Nb_{2}O_{5}dopants on the stable dielectric properties of BaTiO_{3}-(Bi_{0.5}Na_{0.5})TiO_{3}-based materials. Appl. Sci.**2015**, 5, 1221–1234. [Google Scholar] [CrossRef][Green Version] - Guzu, A.; Ciomaga, C.E.; Airimioaei, M.; Padurariu, L.; Curecheriu, L.P.; Dumitru, I.; Gheorghiu, F.; Stoian, G.; Grigoras, M.; Lupu, N.; et al. Functional properties of randomly mixed and layered BaTiO
_{3}—CoFe_{2}O_{4}ceramic composites close to the percolation limit. J. Alloys Compd.**2019**, 796, 55–64. [Google Scholar] [CrossRef] - Sato, Y.; Aoki, M.; Teranishi, R.; Kaneko, K.; Takesada, M.; Moriwake, H.; Takashima, H.; Hakuta, Y. Atomic-scale observation of titanium-ion shifts in barium titanate nanoparticles: Implications for ferroelectric applications. ACS Appl. Nano Mater.
**2019**, 2, 5761–5768. [Google Scholar] [CrossRef] - Shen, Z.; Wang, X.; Gong, H.; Wu, L.; Li, L. Effect of MnO
_{2}on the electrical and dielectric properties of Y-doped Ba_{0.95}Ca_{0.05}Ti_{0.85}Zr_{0.15}O_{3}ceramics in reducing atmosphere. Ceram. Int.**2014**, 40, 13833–13839. [Google Scholar] [CrossRef] - Zhang, M.; Zhai, J.; Xin, L.; Yao, X. Effect of biased electric field on the properties of ferroelectric-dielectric composite ceramics with different phase-distribution patterns. Mater. Chem. Phys.
**2017**, 197, 36–46. [Google Scholar] [CrossRef] - Yu, Z.; Ang, C.; Guo, R.; Bhalla, A.S. Dielectric properties and high tunability of Ba(Ti
_{0.7}Zr_{0.3})O_{3}ceramics under dc electric field. Appl. Phys. Lett.**2002**, 81, 1285–1287. [Google Scholar] [CrossRef] - Gong, H.; Wang, X.; Zhang, S.; Li, L. Synergistic effect of rare-earth elements on the dielectric properties and reliability of BaTiO
_{3}-based ceramics for multilayer ceramic capacitors. Mater. Res. Bull.**2016**, 73, 233–239. [Google Scholar] [CrossRef] - Daniels, J. Defect chemistry and electrical-conductivity of doped barium-titanate ceramics 2. Defect equilibria in acceptor-doped barium-titanate. Philips Res. Rep.
**1976**, 31, 505–515. [Google Scholar] - Hennings, D.F.K. Dielectric materials for sintering in reducing atmospheres. J. Eur. Ceram. Soc.
**2001**, 21, 1637–1642. [Google Scholar] [CrossRef] - Boonlakhorn, J.; Putasaeng, B.; Thongbai, P. Origin of significantly enhanced dielectric response and nonlinear electrical behavior in Ni
^{2+}-doped CaCu_{3}Ti_{4}O_{12}: Influence of DC bias on electrical properties of grain boundary and associated giant dielectric properties. Ceram. Int.**2019**, 45, 6944–6949. [Google Scholar] [CrossRef] - Mitrovic, I.; Mitic, V.V. BaTiO
_{3}-ceramics electrical model based on intergranular contacts. J. Eur. Ceram. Soc.**2001**, 21, 2771–2775. [Google Scholar] [CrossRef] - Mitic, V.V.; Nikolic, Z.S.; Pavlovic, V.B.; Paunovic, V.; Miljkovic, M.; Jordovic, B.; Zivkovic, L. Influence of rare-earth dopants on barium titanate ceramics microstructure and corresponding electrical properties. J. Am. Ceram. Soc.
**2010**, 93, 132–137. [Google Scholar] [CrossRef] - Mandelbrot, B.B. The Fractal Geometry of Nature, 1st ed.; W. H. Freeman and Company: San Francisco, CA, USA, 1982. [Google Scholar]
- Barnsley, M.F. Fractals Everywhere, 2nd ed.; Morgan Kaufmann: Burlington, MA, USA, 1993. [Google Scholar]
- Even, U.; Rademann, K.; Jortner, J.; Manor, N.; Reisfeld, R. Direct electronic energy transfer on fractals. J. Lumin.
**1984**, 31, 634–638. [Google Scholar] [CrossRef] - Falconer, K. Fractal Geometry: Mathematical Foundations and Applications, 2nd ed.; Wiley: Hoboken, NJ, USA, 2003. [Google Scholar]
- Mitic, V.V.; Kocic, L.; Paunovic, V.; Lazović, G.; Miljkovic, M. Fractal nature structure reconstruction method in designing microstructure properties. Mater. Res. Bull.
**2018**, 101, 175–183. [Google Scholar] [CrossRef] - Mitic, V.V.; Paunović, V.; Lazovic, G.; Kocic, L.; Vlahovic, B. Clausius–Mossotti relation fractal modification. Ferroelectrics
**2018**, 536, 60–76. [Google Scholar] [CrossRef] - Mitic, V.V.; Lazovic, G.; Paunovic, V.; Cvetkovic, N.; Jovanovic, D.; Veljkovic, S.; Randjelovic, B.; Vlahovic, B. Fractal frontiers in microelectronic ceramic materials. Ceram. Int.
**2019**, 45, 9679–9685. [Google Scholar] [CrossRef] - Gong, H.; Wang, X.; Zhang, S.; Wen, H.; Li, L. Grain size effect on electrical and reliability characteristics of modified fine-grained BaTiO
_{3}ceramics for MLCCs. J. Eur. Ceram.**2014**, 34, 1733–1739. [Google Scholar] [CrossRef] - Li, Y.; Li, W.; Du, G.; Chen, N. Low temperature preparation of CaCu
_{3}Ti_{4}O_{12}ceramics with high permittivity and low dielectric loss. Ceram. Int.**2017**, 43, 9178–9183. [Google Scholar] [CrossRef] - Zhao, Z.; Buscaglia, V.; Viviani, M.; Buscaglia, M.T.; Mitoseriu, L.; Testino, A.; Nygren, M.; Johnsson, M.; Nanni, P. Grain-size effects on the ferroelectric behavior of dense nanocrystalline BaTiO
_{3}ceramics. Phys. Rev. B Cond. Matter**2004**, 70, 024107. [Google Scholar] [CrossRef]

**Figure 1.**Grains surface reconstruction based on scanning electron microscopy (SEM) and scanning transmission electron microscopy (STEM) microstructure characterization under 60 k times magnification.

Spectrum | In Stats. | O | Si | Ti | Y | Ba | Total |
---|---|---|---|---|---|---|---|

Spectrum 1 | Yes | 18.12 | 0.18 | 18.30 | 0.38 | 63.01 | 100.00 |

Spectrum 2 | Yes | 18.17 | −0.24 | 18.36 | 0.77 | 62.96 | 100.00 |

Spectrum 3 | Yes | 16.43 | 0.32 | 19.61 | 1.55 | 62.09 | 100.00 |

Spectrum 4 | Yes | 16.61 | 0.28 | 17.64 | 1.21 | 64.26 | 100.00 |

Spectrum 5 | Yes | 19.38 | 0.00 | 17.68 | 1.63 | 61.32 | 100.00 |

Spectrum 6 | Yes | 15.80 | 0.02 | 16.92 | 1.01 | 66.26 | 100.00 |

Spectrum 7 | Yes | 17.35 | −0.07 | 18.14 | 0.95 | 63.63 | 100.00 |

Mean | 17.41 | 0.07 | 18.09 | 1.07 | 63.36 | 100.00 | |

Std. deviation | 1.24 | 0.20 | 0.83 | 0.44 | 1.60 | ||

Max. | 19.38 | 0.32 | 19.61 | 1.63 | 66.26 | ||

Min. | 15.80 | −0.24 | 16.92 | 0.38 | 61.32 |

Spectrum | In Stats. | O | Si | Ti | Y | Ba | Total |
---|---|---|---|---|---|---|---|

Spectrum 1 | Yes | 9.49 | 0.15 | 17.30 | 2.25 | 63.60 | 100.00 |

Spectrum 2 | Yes | 10.67 | 0.11 | 17.66 | 2.02 | 63.16 | 100.00 |

Spectrum 3 | Yes | 11.89 | 0.16 | 17.46 | 2.68 | 61.16 | 100.00 |

Spectrum 4 | Yes | 13.29 | −0.10 | 15.76 | 2.37 | 62.73 | 100.00 |

Spectrum 5 | Yes | 12.19 | −0.02 | 17.11 | 2.32 | 61.51 | 100.00 |

Spectrum 6 | Yes | 12.56 | 0.02 | 18.12 | 2.12 | 60.38 | 100.00 |

Spectrum 7 | Yes | 11.37 | 0.06 | 18.46 | 2.51 | 60.84 | 100.00 |

Mean | 12.46 | 0.05 | 18.65 | 2.49 | 66.32 | 100.00 | |

Std. deviation | 1.26 | 0.09 | 0.87 | 0.23 | 1.25 | ||

Max. | 13.29 | 0.16 | 18.46 | 2.68 | 63.60 | ||

Min. | 9.49 | −0.10 | 15.76 | 2.02 | 60.38 |

C change, % | 100 | 100.32 | 101.28 | 100.97 | 100.64 | 100.64 | 100.32 | 100.16 | 93.13 | 78.90 | 0 |

DC bias, V | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |

C change, % | 100.16 | 100.01 | 98.76 | 97.50 | 95.49 | 93.13 | 90.94 | 88.44 | 86.25 | 83.43 | 78.90 | 74.21 | 70.78 | 67.17 | 33.70 |

DC bias, V | 70 | 72 | 74 | 76 | 78 | 80 | 82 | 84 | 86 | 88 | 90 | 92 | 94 | 96 | 98 |

C change, % | 100 | 106.90 | 108.14 | 108.14 | 0 |

DC bias, V | 0 | 1 | 2 | 3 | 3.83 |

C change, % | 100 | 101.28 | 103.14 | 104.40 | 105.64 | 106.90 | 107.21 | 107.52 | 108.14 | 108.14 | 108.14 |

DC bias, V | 0 | 0.2 | 0.4 | 0.6 | 0.8 | 1 | 1.2 | 1.4 | 1.6 | 1.8 | 2 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mitic, V.V.; Lazovic, G.; Lu, C.-A.; Paunovic, V.; Radovic, I.; Stajcic, A.; Vlahovic, B.
The Nano-Scale Modified BaTiO_{3} Morphology Influence on Electronic Properties and Ceramics Fractal Nature Frontiers. *Appl. Sci.* **2020**, *10*, 3485.
https://doi.org/10.3390/app10103485

**AMA Style**

Mitic VV, Lazovic G, Lu C-A, Paunovic V, Radovic I, Stajcic A, Vlahovic B.
The Nano-Scale Modified BaTiO_{3} Morphology Influence on Electronic Properties and Ceramics Fractal Nature Frontiers. *Applied Sciences*. 2020; 10(10):3485.
https://doi.org/10.3390/app10103485

**Chicago/Turabian Style**

Mitic, Vojislav V., Goran Lazovic, Chun-An Lu, Vesna Paunovic, Ivana Radovic, Aleksandar Stajcic, and Branislav Vlahovic.
2020. "The Nano-Scale Modified BaTiO_{3} Morphology Influence on Electronic Properties and Ceramics Fractal Nature Frontiers" *Applied Sciences* 10, no. 10: 3485.
https://doi.org/10.3390/app10103485