BaTiO grain size

Fig. 8. Dielectric constant (1 kHz) vs temperature for BaTiO ceramics of A, l-)Tm grain size, and B, 50-)Tm grain size.

Offer outline explanations of why the permittivity of polycrystalline BaTiOs increases with decreasing grain size. Show that the 90° domain wall area is proportional to (grain size)5/2 and that the domain wall area per unit volume is approximately 5 x 103g-1/2. Numerical data can be found in Section 5.7.1. 

Tsunekawa S, Ito S, More T, Ishikawa K, Li Z-Q, Kawazoe Y (2000a) Critical size and anomalous lattice expansion in nanocrystalline BaTiOs particles. Phys Rev B 62 3065-3070 Tsunekawa S, Ishikawa K, Li Z-Q, Kawazoe Y, Kasuya A (2000b) Origin of anomalous lattice expansion in oxide nanoparticles. Phys Rev Letters 85 3440-3443 Turkovic A, Ivanda M, Popovic S, Tonejc A, Gotic M, Dubcek P, Music S (1997) Comparative Raman, XRD, HREM and SAXS studies of grain sizes in nanophase Ti02. J Molec Struct 410/411 271-273 ten Wolde PR, Frenkel D (1997) Enhancement of protein crystal nucleation by critical density fluctuations. Science 277 1975-1978... 

Figure 15.17 Effect of grain size on pemiittivity of BaTiO. ...

A co-extrusion technique was also applied by Beeaff and Ifilmas to produce a BaTiOs multilayer capacitor with nickel electrodes [Bee 02], Polyethylene co-butyl acrylate was used as the major binder component. The minor binder, plasticizer and surfactants used were polyethylene ethyl acetate, microcrystalline wax, mineral oil and PEG. With this binder system it was possible to produce multilayer capacitors with 10 im thick Ni electrode layers by co-extrusion. The limitation was given by the grain size of the ceramic powder used and not by the processing technique. 

Avila HA, Ramajo LA, Reboredo MM, Castro MS, Parra R (2011) Hydrothermal s5mthesis of BaTiOs from different Ti-precursors and microstructural and electrical properties of sintered samples with submicrometric grain size. Ceram Int 37 2383-2390... 

Fig. 2.4 The grain size dependences of BaTiOs room temperature properties the tetragonality (A), the specific heat of tetragonal-cubic (o) and orthorhombic-tetragonal ( ) phase transitions. The calculated transition specific heat ( ) [19]...

Zhao, Z., Buscaglia, V., Viviani, M., Buscaglia, M.T., Mitoseriu, L., Testino, A., Nygren, M., Johnsson, M., Nanni, R Grain-size effects on the ferroelectric behavior of dense nanocrystalline BaTiOs ceramics. Phys. Rev. B 70, 024107(8) (2004)... 

Table 3.1 Experimental data and parameters of grain size distribution function, extracted from observed specific heat temperature dependence for BaTiOs nanogranular ceramics...

Fig. 3.26 The dependence of ferroelectric phase transition temperature on inverse mean grain size for nanogranular BaTiOs ceramics. Solid line is theory, the open squares are experimental points [95]...

Fig. 3.27 Specific heat temperature dependence of BaTiOs film with 500 nm thickness and different grain sizes, calculated with the help of Eqs, (3.89) and (3.92) solid lines) and experimental data (symbols) [95] for the following grain sizes 35 nm (o), 65 nm (x), 90 nm ( ), 165 nm (0)...

Strukov, B., Davitadze, S.T., Shulman, S.G., Goltzman, B.M., Lemanov, V.V. Classification of size effects in polycrystalline BaTiOs thin films by means of the specific heat measurements grain size or film thickness cond-mat/0405224 (6) (2004)... 

Fig. 2. (a) XRD patterns of BaTiOs ceramics with different grain size, (b) Detailed diffraction profiles around 20 = 45° for different grain size BaTiOs ceramics. Dashed lines are obtained by the best fit to a mixed Gaussian-Lorentzian distribution, and solid lines are their measured data. 

Raman Vibrational Characteristics of BaTiOa Ceramics. The assignments, both the symmetry and the nature of the observed Raman and infrared frequencies, have remained somewhat controversial in early studies [14,15]. The Raman spectra of BaTiOs samples with various grain sizes at room temperature are shown in Fig. 3. 

Fig. 3. Raman spectra of BaTiOs ceramics with different grain sizes at room temperature (a) 3000 (b) 100 (c) 80 (d) 50 and (e) 20 nm.

From Fig. 3 it is obvious that the grain size has a significant effect on the Raman vibrational modes. The soft mode Al(TOi) of nanograin BaTiOs ceramics shifts upward to high frequency compared with the coarse sample, which is different from the research of PLT [16], Further studies are necessary to clarify this issue. With a decrease in GS, the A1(L03) phonon mode at 715 cm and the sharp peak of E(TO) at 306 cm remain at the same frequency position and gradually weaken, but still exist in nanocrystalline BaTiOs ceramics below 100 nm. According to Ref [17], these bands should become Raman inactive in the cubic phase. Thus, unlike normal XRD we find that small grain size, even in 15 nm BaTiOs ceramics does not have perfect cubic symmetry but has some disorder, which breaks the symmetry. 

Temperature dependent dielectrics of Nanocrystalline BaTiOa Ceramics. The dielectric properties with different frequencies for nanocrystalline BaTiOs samples are shown in Figure 6. In the temperature (T) spectra of relative dielectric constant (K) all the samples showed a discernible eubie (C) to T transition. In eomparison, the low temperature transitions were much weaker and broader. At smaller grain size 20 nm, they appeared as diffuse humps on a positively sloping background that is part of the low-temperature tail of the C/T transition. In the range of 20-100 nm, the transition temperatures thus determined show a steady decrease for the C/T transition, in contrast to a steady increase for the T/0 transition and for the 0/R transition. However, even the maximum value of K for 20 nm BaTiOs is only about 930 at IkHz, it still exhibits a broadening and... 

Fig. 3. Cumulative grain size distribution curves for doped BaTiOs with a) 0.5 wt% Er203, and b) 0.5 wt% YbjOj,...

Table 8.2 Dependence of the properties of BaTiOs on the grain size ...

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