Meso-kinetics of one time relaxation electrical processes in BaTiO₃ ceramics—modified Boltzmann-Poisson model

References

• M. Grundmann, The Physics of Semiconductors (Springer International Publishing Switzerland, Heidelberg 2016).
   Google Scholar
• P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physic (Cambridge University Press, Cambridge 1995).
   Google Scholar
• D. A. McQuarrie, Statistical Mechanics (Harper & Row, New York 1976).
   Google Scholar
• Z. Li-Zhi and W. Zheng-Chuan, Analytical solution to the boltzmann-poisson equation and its application to MIS tunneling junctions, Chinese Phys. B. 18 (2), 2975–80 (2009). doi:10.1088/1674-1056/18/7/059.
   Google Scholar
• W. Heywang, Resistivity anomaly in doped barium titanate, J. Am. Ceram. Soc. 47 (10), 484–90 (1964). doi:10.1111/j.1151-2916.1964.tb13795.x.
   Web of Science ®Google Scholar
• W. Heywang, Semiconducting barium titanate, J. Mat. Sci. 6, 1214–26 (1971). doi:10.1007/BF00550094.
   Web of Science ®Google Scholar
• W. Heywang and W. Wersing, Anomalous temperature resistance characteristic of highly acceptor doped BaTiO3 PTC resistors, Ferroelectrics 7 (1), 361–3 (1974). doi:10.1080/00150197408238047.
   Web of Science ®Google Scholar
• Y. L. Chen and S. F. Yang, The PTCR effect in donor-doped barium titanate: Review of compositions, microstructures, processing and properties, Adv. Appl. Ceram. 110 (5), 257–69 (2011). doi:10.1179/1743676111Y.0000000001.
   Web of Science ®Google Scholar
• S. H. Cho, Theoretical aspects of PTC thermistors, J. Korean Ceram. Soc. 43 (11), 673–9 (2006). doi:10.4191/KCERS.2006.43.11.673.
   Google Scholar
• V. Paunović et al., Ho2O3 additive effects on BaTiO3 ceramics microstructure and dielectric properties, Sci. of Sint. 44, 223–33 (2012). doi:10.2298/SOS1202223P.
   Web of Science ®Google Scholar
• V. V. Mitić, V. V. Paunović and L. Kocić, Dielectric properties of BaTiO3 ceramics and curie-weiss and modified curie-weiss affected by fractal morphology, in Advanced Processing and Manyfacturing Technologies for Nanostructured and Multifunctional Materials, edited by T. Ohji, M. Singh, and S. Mathur (Ceramic Engineering and Science Proceedings, Hoboken, New Jersey), Vol. 35, no. 6, pp. 123–33.
   Google Scholar
• V. V. Uchaikin, Fractional Derivatives for Physicists and Engineers: Volume I Background and Theory (Springer-Higher Education Press, Berlin-Beijing 2013).
   Google Scholar
• S. Wang and G. O. Dayton, Dielectric properties of fine-grained barium titanate based X7R materials, J. Am. Ceram. Soc. 82 (10), 2677–82 (1999). doi:10.1111/j.1151-2916.1999.tb02141.x.
   Web of Science ®Google Scholar
• C. Pithan, D. Hennings, and R. Waser, Progress in the synthesis of nanocrystalline BaTiO3 powders for MLCC, Int J Appl Ceram Tec. 2 (1), 1–14 (2015). doi:10.1111/j.1744-7402.2005.02008.x.
   Web of Science ®Google Scholar
• P. Kumar et al., Influence of calcium substitution on structural and electrical properties of substituted barium titanate, Ceram Int. 37, 1697–700 (2011). doi:10.1016/j.ceramint.2011.01.022.
   Web of Science ®Google Scholar
• Z. C. Li and B. Bergman, Electrical properties and ageing characteristics of BaTiO3 ceramics doped by single dopants, J. E. Ceram. Soc. 25, 441–5 (2005). doi:10.1016/j.jeurceramsoc.2004.03.012.
   Web of Science ®Google Scholar
• V. V. Mitic et al., Influence of Yb2O3 and Er2O3 on BaTiO3 ceramics microstructure and corresponding electrical properties, Dev. Strategic Mater. 29 (10), 231–6 (2008).
   Google Scholar
• V. Mitic et al., Dielectric properties of BaTiO3 doped with Er2O3, Yb2O3 based on intergranular contacts model, Adv. Electroceram. Mater. Ceram. Trans. 204, 137–44 (2009). doi:10.1002/9780470528990.ch16.
   Google Scholar
• V. V. Mitic, V. Paunovic, and V. Pavlovic, Microstructure and dielectric properties of rare-earth doped BaTiO3 ceramics, Ferroelectrics 470 (1), 159–67 (2014). doi:10.1080/00150193.2014.923229.
   Web of Science ®Google Scholar
• V. V. Mitić et al., Kinetics of one-time relaxation electrical processes in BaTiO3 ceramics with constitutive relation – generalized Lorentz model, Cermodel 2017conference, July 28-28, Trento, Italy 2017.
   Google Scholar
• V. V. Mitić et al., Meso-Kinetics of One Time Relaxation Electrical Processes in BaTiO₃ Ceramics – Boltzmann-Poisson model (IMF, San Antonio, USA September 4–8, 2017).
   Google Scholar
• B. R. Sontakke and A. S. Shaikh, Properties of caputo operator and its applications to linear fractional differential equations, B. R. Sontakke Int. J. Eng. Res. Appl. 5 (5), 22–27 (2015).
   Google Scholar
• B. McGonegal, Fractional brownian motion and the fractional stochastic calculus. arXiv:1401.2752 [math.PR].
   Google Scholar
• T. Sandev, R. Metzler, and Z. Tomovski, Correlation functions for the fractional generalized Langevin equation in the presence of internal and external noise, JMP 55, 023301 (2014). doi:10.1063/1.4863478.
   Web of Science ®Google Scholar
• M. D. Ortigueira and A. G. Batista, On the relation between the fractional Brownian motion and the fractional derivatives, Phys. Lett. A. 372, 958–68 (2008). doi:10.1016/j.physleta.2007.08.062.
   Web of Science ®Google Scholar
• V. V. Uchaikin, Fractional Derivatives for Physicists and Engineers, Volume II Applications (Springer-Higher Education Press, Berlin-Beijing 2013).
   Google Scholar