4.1 Results of the SEM patterns
BaTiO3 nanoparticles shown in FESEM micrographs of Fig. 4.1 have low aggregation and narrow size distribution with mean diameters of about 140, 60, and 30 nm, respectively.
(a) (b)
(c)
Fig. 4.1 SEM patterns of BaTiO3 samples with various mean diameters (a) 140nm (b) 60nm (c) 30nm
4.2 Analysis of Rietveld refinement
To analyze the crystal symmetry of BaTiO3 nanoparticles, high resolution diffraction patterns of various sizes of BaTiO3 nanoparticles were taken by using high-energy synchrotron radiation x-ray and refined by using the GSAS program. We choose profile function as Rietveld function, setting constraint, then refining the parameters by sequence and sequence. Table 4.1 shows the initial refinement conditions.
Crystal system：tetragonal Space group：P4mm
Lattice parameter：a = b = 3.994, c = 4.038, α=β=γ=90°
Atomic type x y z Uiso
Ba 0 0 0 0.025
Ti 0.5 0.5 0.512 0.025
O1 0.5 0.5 -0.026 0.025
O2 0 0.5 0.5 0.025
Figure 4.2 shows results and differences after Rietveld refinement for nanoparticles with sizes of 140 nm, 60 nm, and 30 nm. The observed and calculated profiles agree well. The profile around 40°in 2θ for 60 nm-sized BaTiO3 particles exhibited a shoulder splitting into (224) and (422) due to the difference in the lengths between the a and c axes of the tetragonal phase. Hence we can use a tetragonal single phase (P4mm) model to refine the crystal structure with the XRD data. Note that we also did the same analysis for particle size larger 1μm (labeled as bulk) for comparison.
Table 4.1 The structural parameter of BaTiO3
The refined structure parameters and reliability factors for nanoparticles with sizes of 140, 60, and 30 nm were listed in Table 4.2. Refined positional parameters of the tetragonal BaTiO3 suggested small displacements of oxygen atoms and Ti atom along the c axis. The lattice constants a and c, shown in Fig 4.3, simultaneously relax with decreasing the particles size. The results are consistent with the assumption proposed by Ishikawa, et al. [17] Fig. 4.4 shows that the tetragonality
Fig. 4.2 Rietveld patterns for various BaTiO3 +particle size.
Particle size are (a) 140nm (b) 60nm (c) 30nm. An enlarged profile around the (004) and (400) reflection peaks is
inserted to show the splitting.
(c/a) declines from 1.0026 to 1.0008 with expanding unit-cell volume, in both of a and c axes, as the particle size decreases from 140 nm to 30 nm. The unit-cell volume of the tetragonal BaTiO3 increases with decreasing particle size, as shown in Fig. 4.4.
Particle size ~µm
(ref. ) 140 nm 60 nm 30 nm
Rwp 11.20% 7.46% 2.78%
a (Å) 3.9940 4.01995 4.02845 4.03289
c (Å) 4.006 4.03043 4.03573 4.03615
c/a 1.003 1.00261 1.00181 1.00081
Atomic coordinate (Ti)
(0.5,0.5,0.53395) (0.5,0.5, 0.52012) (0.5,0.5, 0.51842)
Atomic coordinate (O1)
(0.5,0.5, 0.02987) (0.5, 0.5, 0.01595) (0.5,0.5, 0.00611)
Atomic coordinate (O2)
(0, 0.5, 0.50923) (0, 0.5, 0.50959) (0, 0.5, 0.50737)
Table 4.2 Refined structure parameters and reliability factors for BaTiO3 nanoparticles at RT.
0 50 100 150 1000 3.99
4.00 4.01 4.02 4.03 4.04
Particle size (nm)
Lattice constants (Angstrom)
a-axis c-axis (a)
0 50 100 150 1000
1.0010 1.0015 1.0020 1.0025 1.0030
Particle size (nm)
64.0 64.5 65.0 65.5
c/a ratio cell volume (Angstrom 3)
(b)
Fig. 4.4 Lattice constant ration c/a and cell volume of BaTiO3 nanoparticles after Rietvelt refinementprocedure Fig. 4.3 Lattice constant a and c of BaTiO3 nanoparticles after Rietvelt refinement procedure
The trend of phase transition for our synthesized BaTiO3 nanoparticles with decreasing particle size agrees with other previous reports. [3,8-12] Nevertheless, our results of XRD refinement reveal the critical size of BaTiO3 nanoparticles, which is the size of the phase transition from tetragonal to cubic at RT, may be smaller than 30 nm, that differs from the argument reported by Yashima, et al., [12] in which the size-induced phase transition occurs between 40 nm and 30 nm. According to Table I, the refined atom positions in a unit cell of the tetragonal BaTiO3 nanoparticles suggest less displacement of titanium and oxygen (O1) atoms along the c axis with decreasing particle size.
4.3 Analysis of the Raman spectra
The Raman spectra of BaTiO3 nanoparticles taken at RT were plotted in Fig. 4.5 with particle sizes of 30 nm, 60 nm, 140 nm, and > 1 µm (bulk from Ref. 7), respectively.
Around 180 cm-1 which is assigned to A1(TO1) phonon mode has a spectral dip for the bulk sample but that for nanoparticles becomes a spectral peak. A broad band around 260 cm-1 attributed to A1(TO2) mode, a band at 305 cm-1 to B1 and E(TO+LO) modes, the asymmetric band around 520 cm-1 to E(TO) and A1(TO3) modes, and the highest frequency band around 720 cm-1 to A1(LO) and E(LO) phonon modes, respectively. The observed Raman spectral peak positions of BaTiO3
nanoparticles agree well with those reported by Yashima, et al. [11,12] However, even with size of 30 nm we did not observe Raman modes resulting from the hexagonal phase as observed in Ref. [12] That phenomenon is consistent with our results of GSAS refinement.
200 300 400 500 600 700 800 Fre q uency (c m
-1)
A1(TO)
A1(TO)
B1,E(TO+LO)
A1(LO),E(LO) E(TO),A
1(TO)
bulk
30nm 60nm 140nm
Raman shift (cm
-1)
Fig. 4.5 Size dependence of Raman spectra for various size BaTiO3. Bulk (> 1μm) and nanoparticles of diameter 140, 60, and 30nm, respectively.
As the size decreases from bulk to nanoparticles, we found spectral peaks at 180 cm-1 in all the nanoparticles are basically located at the same frequency of the destructive interference dip for the bulk BaTiO3. The results indicate that the anharmonic phonon coupling maybe dependent on the grain size. The phonon modes at 305 and 720 cm-1 specific to the tetragonal phase of BaTiO3 as described in Ref. [18] become weak and broad with decreasing particle size. In comparison with the results of XRD, the observed broadening of Raman peaks indicates that the crystal structure becomes progressively less tetragonal factor due to less displacements of Ti and O1 atoms.
As forementioned, the three A1(TO) modes are strongly coupled together and two of them are heavily damped in the tetragonal phase of ABO3. In order to ascertain the influence of the coupling phenomenon, Sood [19] and Chaves et al. [20] have considered three individual phonon coupled A1(TO) modes to distinguish them from the Raman spectra. The Raman intensity of the three coupled modes can be expressed as
) (ω
I = A[n(ω)+1]Im [T*GT], (1) where the inverse matrix response is
G-1(ω) = Ω2−ω2I−iωΓ, (2) A is a constant, [n(ω)+1] is Bose-Einstein factor, T is a vector involving Raman scattering amplitudes, I is the unit matrix, Ω2 is the force constant matrix, and Γ the damping matrix:
Here ω and i ω ( ,ij i j=1, 2,3) are the frequencies of uncoupled modes and the coupling strength between modes i and j . The coupling between the lowest
)
(ω1 and the highest (ω modes was set to zero (3) ω13 =0) to allow less fitting parameters. This is a reasonable approximation because they are too far from each other. Hence they have no spectral superimposition.
The asymmetric broad band around 500-600 cm-1 is attributed to superposition of E(TO) and A1(TO3) modes. We find the results of polarized Raman study on the epitaxial BaTiO3 film by Marssi, et al., [21] the E(TO) mode is situated at the low frequency shoulder with about 1/4 intensity of the A1(TO3) mode. Hence, it is reasonable to extract the contribution of the E(TO) mode about 1/4 compare to the intensity of A1(TO3) mode for these randomly oriented nanoparticles. Besides, the fitting results will not show the difference from that if the contribution of E(TO) is ignored. The fitted parameters are plotted in Fig. 4.6 that allows us to clarify the coupling behavior of phonon with decreasing particle size.
We found that the coupling strength, ω12, betweenω1 and ω2 dramatically changes from 85 cm-1 to nearly zero as the particle size decreases from few micrometers to nanometers. The weaker (or zero) coupling betweenω1 and ω2 in BaTiO3 nanoparticles leads to observe a spectral peak around 180 cm-1 A1(TO1) phonon mode for the nanoparticles rather than a dip for bulk at the same position.
Figure 4.7 shows the as-read peak positions of three A1-symmetric TO modes from our Raman data (labeled as A1(TOi), i = 1,2,3). These data obtained from the uncoupled-phonon model sign as hollow symbols and that obtained from the coupled-phonon model sign as solid symbols. From Fig. 4.7 we can see that the size-dependent decoupled (calculated) phonon frequency ω overlaps with the
0 50 100 150 1000 0
100 200 300 400 500
Particle size (nm) Frequenc y (c m
-1)
Γ 2
Γ3 Γ 1
ω12 ω3
ω2 ω23 ω1 (a)
as-read A1(TO1) so it again reveal weak coupling strength (ω12 ~ 0). Due to decreasing the particle size with less tetragonality or small c/a, we found that the approach of uncoupled ω2 and ω3 results in slightly increasing in ω23. The stronger coupling strength (ω ~ 300 cm23 -1) makes these two modes approach. Therefore the measured A1(TO2) peak slightly shifts toward the higher frequency and the measured A1(TO3) peak slightly shifts toward the lower frequency upon decreasing the particle size.
Fig. 4.6 The fitted parameters using the coupled-phonon
0 50 100 150 1000 100
200 300 400 500 600
Particle size (nm) Fre q ue nc y ( c m
-1)
A
1(TO
1) A
1(TO
2) A
1(TO
3)
ω3
ω2
ω1
(b)
Fig. 4.7 The as-read peak positions from the data and the decoupled frequencies plotted as a function of particle size.
According to the calculation of Born effective charges of ABO3 perovskites by Zhong et al., [14] we comprehend that the calculated mode effective charge for the softest TO mode is the largest as listed in Table Ⅲ of Ref. 14. It means that the softest TO mode will couple most strongly with the electric field. Due to strong mode mixing via Coulomb interaction, the softest TO mode [A1(TO1)] is the most closely associated with the hardest LO mode A1(LO3) that gives rise to giant LO–TO splitting in ABO3 structure, especially for the ferroelectric phonon modes. The general representation of the dynamical matrices for LO and TO modes at q = 0 are related by
where D represents the dynamical matrix that is proportional to the square of the vibration frequency, V is the volume of the unit cell, ε∞(0) is the optical dielectric constant at q = 0, and Z* is the Born effective charge of the corresponding vibration.
The Coulomb interaction would play an important role in the behavior of LO-TO splitting.
According to the polarized Raman results [21], the asymmetric broad band near 750 cm-1 in Fig. 4.5 can be resolved as A1(LO) mode and a lower intensity E(LO) mode at the higher frequency side. From the decomposed result reported in Ref.
(21), the intensity of E(LO) mode locates at the higher frequency is about 1/3 intensity of the A1(LO) mode for BaTiO3 bulk. With decreasing the particle size, the spectra still keep the same trend of the higher intensity for the A1(LO) mode than for the E(LO) mode.
Fig. 4.8(a) shows the square difference of A1(LO) and A1(TO1) modes phonon frequencies versus BaTiO3 particle size. We observe the decreasing trend of LO-TO
splitting as the particle size decreases from > 1µm to 30 nm, and that phenomenon agree with the inference of Ref. [14]. Since Ba-based ABO3 perovskites basically possesses ionic bonding [22-25], the Born effective charge would not be influenced by changing the structure. From our results of Fig. 4.4, the unit cell dimension increases when the particle size decreasing from micrometer size to 30 nm.
According to the general representation of the dynamical matrices for LO and TO modes at q = 0, we can expect reducing LO-TO splitting when unit cell dimension increase.
Fig. 4.8(b) shows the normalized square difference of A1(LO) and A1(TO1) modes phonon frequencies and normalized unit cell volume versus BaTiO3 particle
size. We observe the
* *
4 2
(0)
m n
e Z Z
π ε∞ can be regarded as a constant, because the
difference between the normalized square difference of A1(LO) and A1(TO1) modes phonon frequencies and normalized unit cell volume is very small. We can expect unit cell dimension is the dominated factor for LO-TO splitting.
Previously, we reported that the tetragonality declines with unit-cell volume decreasing as x changes from 1 to 0.7 in polycrystalline BaxSr1-xTiO3. [7]
Neglecting the change of effective charge due to the substitution, the variation of the unit-cell volume was considered be the dominant mechanism of increasing the LO–TO splitting in BaxSr1-xTiO3 system. In compare to that study, we directly observe the decreasing LO-TO splitting when declining the tetragonality as decreasing the size of BaTiO3 nanoparticles. That causes expansion of the unit-cell volume. We conclude that the change of unit-cell volume is also the dominant mechanism for the tendency of the LO–TO splitting in BaTiO3 system without
0 50 100 150 1000
Fig. 4.8 Size dependent LO-TO spolitting. (a) The difference between square of A1(LO3) and A1(TO1) phonon frequencies. (b) Normalized difference between square of A1(LO3) and A1(TO1) phonon frequencies and normalized cell volume.
Chapter 5 Conclusion
5.1 Conclusion
In summary, we have investigated the size effect on crystal structure of BaTiO3
nanoparticles synthesized by the glycothermal method by using FESEM, high-resolution synchrotron XRD, and Raman spectroscopy. The crystal structure was made use of a single tetragonal-phase model to refine XRD data by Rietveld analysis of GSAS program. A enlarging unit-cell volume was confirmed with decreasing particle size. The large cell volume could be ascribed to (1) some lattice defects, (2) the surface effect of the fine particles, and (3) the metastable state in the chemical reaction from the intermediate amorphous phase to the tetragonal BaTiO3
with a large c/a ratio.
We explained that the experimental evidence of weaker strength coupling between A1(TO1) and A1(TO2) leads to a change from a spectral dip at 180 cm-1 for A1(TO1) phonon to a peak at the same position. We also found that the approach of uncoupled ω2 and ω3 with less tetragonality due to decreasing the particle size results in slightly increasing in ω23. According to the results of decomposition, the spectra still keep the same trend of the higher intensity for the A1(LO) mode than the E(LO).
We also observed the decreasing LO-TO splitting with the decline of tetragonality when expansion of the unit-cell volume. Therefore, the change of unit-cell volume is the dominant mechanism for the tendency of the LO–TO splitting in BaTiO3 system without complicated ion replacement.
5.2 Future work
Enormous interest in nanostructured materials for photonic applications has emerged in recent years. One class of such materials is represented by rare-earth doped nanocrystals that have been investigated for use as phosphors in amplifiers, lasers, and imaging for biological systems. The promising optical properties of rare-earth doped nanocrystals for photonic applications such as Led are investigated of frequency upconversion. Presently it is recognized that the upconversion efficiency depends on the nanoparticle shape, the site symmetry, and the statistical distribution of active ions. Also, the process of miniaturizing materials to the nanometer scale revealed that the radiative electronic relaxation probabilities of rare-earth ions doped in dielectric nanoparticles may be significantly different from their bulk counterparts.
We will synthesize Er-doped BaTiO3 nanoparticles to investigate the luminescence properties of size dependent effects. In particular our interest is concerned with the structural changes occurring in nanoparticles Er-doped BaTiO3
with different sizes and the investigation of their luminescence properties by evaluation of Ω parameters form the Judd-Ofelt theory.[26-27]
References
1. L. E. Cross, Am. Ceram. Soc. Bull., 63, 586-90 (1984).
2. D. H. Yoon and B. I. Lee, J. Eur.Ceram. Soc. 24, 753 (2004) 3. R. Pirc and R. Blinc, Phys. Rev. B 70, 134107 (2004)
4. J. I´n˜ iguez and D. Vanderbilit, Phys. Rev. Lett. 89, 115503 (2002) 5. D. Damjanovic, F. Brem, and N. Setter, Appl. Phys. Lett. 80, 652
(2002)
6. U. D. Venkateswaran, V. M. Naik, and R. Naik, Phys. Rev. B 58, 14256 (1998)
7. S. Y. Kuo, W. Y. Liao, and W. F. Hsieh, 64, 224103 (2001) 8. M. H. Frey and D. A. Payne, Phys. Rev. B 54, 3158 (1996) 9. S. Tsunekawa, S. Ito, T. Mori, K. Ishikawa, Z.Q. Li, and Y.
Kawazoe1, Phys. Rev B 62, 3065 (2000)
10. Z. Zhao, V. Buscaglia, M. Viviani, M. T. Buscaglia, L. Mitoseriu, A.
Testino, M.Nygren, M. Johnsson, and P. Nanni, Phys. Rev. B 70, 024107 (2004)
11. T. Hoshina, H. Kakemoto, T. Tsurumi, S. Wada, and M. Yashima, J.
Appl. Phys. 99, 054311 (2006)
12. M. Yashima, T. Hoshina, D. Ishimura, S. Kobayashi, W. Nakamura, T.
Tsurumi and S. Wada J. Appl. Phys. 98, 014313 (2005)
13. C. N. R. Rao and K. J. Rao: Phase Transitions in Soild (Megrqw-Hill International Book Company, 1978).
14. W. Zhong, R. D. King-Smith and D. Vanderbilt, Phys. Rev. Lett. 72,
3618 (1994).
15. The Rietveld Method, R.A. Young, Oxford university press (1993) 16. Manual of GSAS software, A.C. Larson and R.V. Dreele, Los Alamos
National laboratory (2000)
17. K. Ishikawa and T. Uemori, Phys. Rev. B 60, 11841 (1999)
18. R. Naik, J. J. Nazarko, C. S. Flattery, U. D. Venkateswaran, V. M.
Naik, M. S. Mohammed, G. W. Auner, J. V. Mantese, N. W.
Schubring, A. L. Micheli, and A. B. Catalan, Phys. Rev. B 61, 11367 (2000).
19. A. K. Sood, N. Chandrabhas, D. V. S. Muthu, and A. Jayaraman, Phys. Rev. B 51, 8892 (1995).
20. A. Chaves, R. S. Katiyar, and S. P. S. Porto, Phys. Rev. B 10, 3522 (1974)
21. M. El Marssi, F. Le Marrec, I. A. Lukyanchuk, and M. G. Karkut, J.
Appl. Phys. 94, 3307 (2003).
22. R. E. Cohen, Nature (London) 358, 136 (1992)
23. Y. Kuroiwa, S. Aoyagi, and A. Sawada, Phys. Rev. Lett. 87, 217601 (2001).
24. Shou-Yi Kuo, Chung-Ting Li, and Wen-Feng Hsieh, Appl. Phys.
Letts. 81(16) , 3019 (2002).
25. J. C. Jan, H. M. Tsai, C. W. Pao, J. W. Chiou, K. Asokan, K. P.
Krishna Kumar, W. F. Pong, Y. H. Tang, M.-H. Tsai, S. Y. Kuo, and W. F. Hsieh, Appl. Phys. Letts. 87, 012103 (2005).
26. B. R. Judd, Phys. Rev. 127, 750 (1962) 27. G. S. Ofelt, J. Chem. Phys. 37, 511 (1962)
28.