Chapter 6 Size-dependent lattice dynamics of BaTiO 3 nanoparticles…
6.2 Size-dependent Raman spectra of BaTiO 3 nanoparticles
The Raman spectra of BaTiO3 nanoparticles taken at RT were plotted in Figure 6.4 with particle sizes of 30 nm, 60 nm, 140 nm, and > 1 μm, respectively. First of all, there is a spectral dip around 180 cm-1 for micrometer-size sample but a spectral peak for all the nanoparticles that is assigned to A1(TO1) phonon mode. They are basically located at the same frequency of the destructive interference dip for the bulk BaTiO3. A broad band around 260 cm-1 attributed to A1(TO2) mode, a band at 305 cm-1 to B1+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)+E(LO) phonon modes. The phonon modes at 305 and 720 cm-1 specific to the tetragonal phase of BaTiO3 as described in Ref. [14] become weak and broad with decreasing
particle size. The observed broadening and weakening of tetragonal Raman bands indicate that the crystal structure becomes progressively less tetragonal due to less displacements of Ti and O(I) atoms for the smaller particle size, which is consistent with the results of XRD. The Structural model of non-polar (cubic) and polar (tetragonal) ABO3 crystal is shown in Figure 6.5. Ti atoms locate at the center of the Ti-O6 octahedron when the octahedral units are perfect in the cubic-type structure.
200 300 400 500 600 700 800
Intensity
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)
Figure 6.4: Size dependence of Raman spectra for BaTiO3 bulk (> 1m) and nanoparticles of diameter 140, 60, and 30nm, respectively.
Due to balance of the charges, the crystal is non- polar and Raman mode is inactive.
On reducing temperature, the Ti-O6 octahedron will be somewhat distorted with off-center displacement of Ti atoms toward one of the O(I) atoms while elongating the c-axis to the tetragonal structure and present spontaneous dipole. The refined atom positions in a unit cell of the tetragonal BaTiO3 nanoparticles reveal less displacement of titanium and oxygen [O(I)] atom along the c axis with decreasing particle size so that the Ti-O6 octahedron shows less distorted or less polar due to the less Ti off-center displacement resulting from the size effect.
Although we had also observed a weak peak around 810 cm-1 attributed to lattice OH group [17] and a very weak band around 930 cm-1 (not shown here) to the oxygen vacancy [18]. There are no reports on the OH groups and no direct evidence of
O(I)
O(II)
Ba
: Ti
Figure 6.5: Structural model of the cubic- and tetragonal- phase occurring with bulk BaTiO3 crystals.
oxygen vacancy that would influence the frequencies of the observed Raman modes.
The frequency shift observed in Ref. 31 should mainly results from the interface strain introduced between BaTiO3 film and substrate rather than influence of oxygen vacancy, because spectra (b) and (c) in Figure 6.4 showed therein that the A1(LO)+E(LO) modes shifted to 715 cm-1 before appearance of a very weak 930 cm-1 band due to the oxygen vacancy. Finally, we did not observe 1060 cm-1 peak attributed to BaCO3 brought out by Pithan, et al. [19] so that we had prevented the BaCO3 related peaks located in the spectral range below 200 cm-1 by acetic acid washing.
Because the three A1(TO) modes are strongly coupled and two of them are heavily damped in the tetragonal phase of ABO3, Sood, [20] and Chaves, et al. [21]
have considered three coupled A1(TO) modes to describe the complicated coupling phenomenon. The Raman intensity of the three coupled modes can be expressed by
) (
I
A [n()1]Im[T*GT], (6-1) where A is a constant, [n()1] is Bose-Einstein factor, T is a vector involving Raman scattering amplitudes, and the inverse matrix response isG-1()
Ω22I Γ. i (6-2) In Eq. (6-2), I is the unit matrix, Ω2 is the force constant matrix, and Γ is the damping matrix:Ω2 parameters; this is a reasonable approximation because they are too far from each other, having no spectral superimposition.
The asymmetric broad band around 500-600 cm-1 is attributed to superposition of E(TO) and A1(TO3) modes, so that one has to separate them before making coupled-mode analysis. These two modes are distinguishable by polarized Raman scattering in single crystals. From the results of polarized Raman study on the epitaxial BaTiO3 film by Marssi, et al. [22], the E(TO) mode is situated at the low frequency shoulder with about 1/4 intensity of the A1(TO3) mode. According to the process to refine the XRD data by using the GSAS, we can attain better fitting result in XRD analysis without considering any preferred orientation. Therefore, in our powder samples the particles should possess random orientation. We have to consider the angle dependent frequencies of these modes. It is well known that the frequency of E(TO) mode is independent of the observing angle with respect to the crystallographic axes, whereas, that of A1(TO) mode depends upon the observing
angle according to:[23] Assuming the particles are completely randomly oriented, the scattering wave vector should also randomly orient with respect to the crystallographic axis.
Therefore, the observed A1(TO3) frequency, after averaging over for Eq. ( 6-4) is
modes are separable. It is reasonable to extract the contribution of the E(TO) mode and the coupled A1(TO3) mode for these randomly oriented nanoparticles. On the other hand, A1(LO) mode is inseparable from E(LO) mode for tetragonal structure around 720 cm-1 when the scattering wave vector makes an angle with respect to crystallographic axes. It gives rise to mode mixing due to directional dispersion or called the “oblique phonon”. The observed frequency shift of angle-averaged oblique phonon in Figure 6.4 should not depend on the observing anglebut other effects, e.g., particle size. Therefore, other than Eq. (6-1) we added four Lorentzian functions representing background signal (Rayleigh scattering) which depends on the particle size, B1+E(TO+LO), E(TO), and A1(LO3)+E(LO) to fit the measured Raman spectra.
0 50 100 150 1000
Figure 6.6: The fitted parameters using the coupled-phonon model as a function of particle size.
In order to attain the best fitting to our measured data, an extra band around 640 cm-1 has to be considered especially for 60-nm and 30-nm samples. This 640 cm-1 band was assigned to the grain-boundary regions [24] or was due to the hexagonal phase [11]. However, as aforementioned there is even better fitting with smaller Rwp
for size of 30 nm in XRD analysis using single tetragonal phase, we therefore assigned the weak mode around 640 cm-1 to the grain-boundary regions for 60-nm and 30-nm samples rather than due to the hexagonal phase.
The fitting parameters of three coupled TO modes were plotted in Figure 6.6(a) that allows us to clarify the coupling behavior of phonon with decreasing particle size.
We found that the coupling strength, 12, between and 1 dramatically changes 2 from 85 cm-1 to nearly zero as the particle size decreases from few micrometers to nanometer. The weaker (or zero) coupling between and 1 in BaTiO2 3
nanoparticles leads to observing a spectral peak around 180 cm-1 for the A1(TO1) phonon mode rather than a dip at the same position. Figure 6.6(b) shows the plot of the as-read peak positions (hollow symbols and labeled as A1(TOi), i = 1, 2, 3) of three A1-symmetric TO modes from our Raman data and those obtained from the coupled-phonon model as solid symbols. It can be seen that the size-dependent decoupled (calculated) phonon frequency overlaps with the as-read one again 1 indicating weak coupling strength (12 ~ 0). With less tetragonality or small c/a due
to decreasing the particle size, we found that the approach of uncoupled 2 and 3
results in slightly increasing in 23. The larger coupling strength (23~ 300 cm-1)
repels these two modes farther such that the measured A1(TO2) [A1(TO3)] peak only slightly shifts toward the higher (lower) frequency upon decreasing the particle size.
6.3 Born effective charge and LO-TO splitting in BaTiO3 nanoparticles system
Furthermore, the dynamical matrices for the LO and TO modes, which have the same form of atomic displacements in a unit cell, 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, (q)is the optical dielectric constant, 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.
Figure 6.7 shows the peak positions of A1(LO) and A1(TO1) modes versus BaTiO3 particle size. We observed besides the expected softening of both A1(LO) and A1(TO1) modes, there is a decreasing trend of LO-TO splitting as the particle size decreases from > 1m to 30 nm. Since Ba-based ABO3 perovskites basically
0 50 100 150 1000
Figure 6.8: Normalized square difference of phonon frequencies of A1(LO3) and A1(TO1) and normalized reciprocal of unit cell volume for nanometer size samples to the micrometer size.
Figure 6.7: The LO-TO splitting of the A1(LO3) and A1(TO1) modes as function of particle size.
possesses ionic bonding [25, 26-28], the Born effective charge would not be influenced by change of structure [29, 27]. From the results of Figure 6.3(b) that the unit cell dimension of BaTiO3 particles increases with the particle decreasing from micrometer size to 30 nm; we would expect reducing LO-TO splitting. Relatively, we previously reported that the tetragonality declines with unit-cell volume diminishing as x changes from 1 to 0.7 in polycrystalline BaxSr1-xTiO3 [6]. Change of unit-cell volume was considered the dominant mechanism of increasing the LO–TO splitting in this system with negligible change of effective charge due to the substitution. In this study we directly observed the decreasing LO-TO splitting with the decline of tetragonality by decreasing the size of BaTiO3 nanoparticles which causes expansion of the unit-cell volume.
Based on Eq. (6-5), we normalized the square difference of phonon frequencies of A1(LO3) and A1(TO1) for nanometer size samples to the one of micrometer-size and plotted in Figure 6.8 to compare with the normalized reciprocal of unit cell volume also to the micrometer-size one’s. It shows that the normalized square difference of phonon frequencies of A1(LO3) and A1(TO1) almost coincides with the normalized reciprocal unit cell volume with less than 2% deviation. This result indicates that the
value of
is a constant, namely, the Born effective charges should not be
influenced by change of structure or size, and the change of unit-cell volume is the dominant mechanism for the tendency of the LO–TO splitting in BaTiO3 system without complication of ion replacement.
6.4 Summary
The size effect on structure for BaTiO3 nanoparticles synthesized by the glycothermal method has been investigated using FESEM, synchrotron XRD, and Raman spectroscopy. We further applied a single tetragonal-phase model to refine the crystal structure and the coupled-phonon model to analyze the coupled A1(TO) modes upon particle size decreasing from 140 nm to 30 nm. We explained that the weak strength of 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 and found that the approach of uncoupled2 and 3 with less tetragonality due to decreasing the particle size results in slightly increasing in 23. The larger coupling strength repels these two modes farther so that the less reducing in spectral separation. According to the results of decomposition, we also observed the decreasing LO-TO splitting with the decline of tetragonality and expansion of the unit-cell volume. And the change of unit-cell volume is the dominant mechanism for the tendency of the LO-TO splitting in BaTiO3 system without complication of ion replacement.
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Chapter 7 Correlating phonon frequency shift with
magnetoelectric effect in the PbTiO
3-CoFe
2O
4multiferroic system due to interfacial stress
We discussed the substitution effect on perovskite structure in Chapters 4 and 5 and size effect in the last chapter. In this chapter, we continue to discuss the influence of strain effect resulting from the lattice misfit between the different media on ferroics.
The ME coupling results from the elastic bonding at the interface and is transmitted through the stress/strain exerted by magnetized magnetostrictive phase on piezoelectric phase or vice versa along their boundary and hence it induces a net polarization or magnetization [1, 2, 3]. Moreover, it is well known that the behavior of interfacial phonon is sensitive to the giant residual stress/strain resulting from the lattice misfit between the different media [4]. It is interesting and important to investigate the relationship between the ME effect and the behavior of interfacial phonon. Recently, some studies about the behavior of phonon on multiferroics were reported [5-7] with lack of concrete conclusion.
In this chapter, we report on the stress dependence of the behavior of interfacial phonon and the magnetic properties in three multiferroics consisting of the different
geometric shapes (see Figure 7.1 ) of ferromagnetic CoFe2O4 (CFO) embedded in ferroelectrics PbTiO3 (PTO) by using the micro-Raman spectroscopy and superconducting quantum interference device (SQUID). Their energy of interfacial phonon and ferromagnetic properties depend on stress due to not only the lattice misfit but also the degree of chemical bonding at the interface between CFO and PTO matrices. The disk-3 type structure, the self-assembled CFO disks embedded in PTO matrix, illustrates the strong elastic interactions between the two phases. The larger nonsymmetrical coercivity Hc and the absence of saturation magnetization Ms of CFO matches with the larger Raman shift of A1(TO2) and A1(TO3) modes of PTO found in the disk-3 type than the other types of the CFO and PTO multilayered structure and the CFO particles embedded in PTO matrix.
7.1 Microstructure and morphology
The top view images of the disk-3 type shown in Figure 7.2 by using OM and FESEM were found consisting of sub-10 m CFO discs embedded in PTO matrix rather than nanometer sized CFO rods in PTO matrix [2]. It reveals the similar morphology as illustrated in Figure 7.1(c). Forming the CFO discs instead of CFO rods may be due to the cohesion of CFO gel is stronger than the adhesive force between CFO and PTO gels. According to the mechanism of synthesis, we may infer that the CFO and PTO multilayered structure (2-2 type) and the CFO particles
embedded in PTO matrix (0-3 type) as illustrated in Figure 7.1(a) and Figure 7.1(b), respectively.
Figure 7.2: Top view of FESEM and OM images of the disk-3 type showing the CoFe2O4 disks in the PbTiO3 matrix.
Figure 7.1: Schematic illustration of three thin films with different connectivity schemes: the 0-3 type with CFO particles embedded in PTO matrix, the 2-2 type with CFO and PTO nanolayers, and the disk-3 type with CFO disc aligned in PTO matrix.
20 25 30 35 45 50 55 60
The XRD patterns of the pure CFO and pure PTO powders, and three multiferroic films on Pt/Si substrates taken at RT as shown in Figure 7.3 reveal the correct phases with various planes without obvious secondary phases, and “*” and “O” represent Si and Pt signals from the substrates, respectively. By using the refinement analysis of XRD data, the refined structure parameters were listed in Table 7-1 and Table 7-2.
We also define strain as variation in lattice constant in this study.
Figure 7.3: X-ray diffraction patterns of the 2-2, 0-3, and disk-3 multiferroics together with those of, pure CFO powder, pure PTO powder, and PTO on Pt/Si film for comparison.
Table 7-1 The refined lattice parameters of PTO for the pure PTO powder and the disk-3/Pt/Si 2.9032 3.8871 0.6604 3.9814 -0.9331 1.0269 0-3/Pt/Si 3.1619 3.8872 0.6629 3.9470 -1.7890 1.0120 2-2/Pt/Si 3.6929 3.9078 1.1964 3.9422 -1.9085 1.0088
Table 7-2 The refined lattice parameters of CFO for the films with different types CFO
According to Table 7-1, the result of pure PTO powder agrees with the JCPDS-International Center for Diffraction Data No. 78-0298; and its intensity ratio of diffraction peaks (100) and (001) is close to 2, indicating the random orientation.
On the other hand, prefer-oriented vertical a-axis growth with the c-axis lying on the substrate surface is obvious in the 2-2 type and the 0-3 type films but is less in the disk-3 type film and pure PTO/Pt/Si film. We also found that the a-axis of PTO matrix is lengthening with the compression of c-axis for all type films and PTO/Pt/Si film. The compression of c-axis is the most obvious in 2-2 type and is the least in PTO/Pt/Si film. The lattice constant of Pt is about 3.9240 Å and that of CFO is
about 8.3873 Å. For PTO/Pt/Si film, the tensile stress of lattice a and the compressed one of lattice c in PTO matrix arise from mismatch of the Pt lattice, whose lattice constant lies in between them. The stain/stress of PTO matrix is due to the interface of PTO and Pt substrate only. However, for three multiferroic samples, the stress in PTO matrix arises from both the interface of PTO and Pt substrate and that of PTO and CFO matrices.
There are more than twice as many lattice constant of CFO (8.3873 Å) to those of PTO (a: 3.8616 Å, c: 4.0189 Å). Having the larger mismatch along a of PTO with CFO than along c, CFO exerts the larger tensile stress on the a-lattice of PTO.
Therefore, the PTO matrices in all the CFO-embedded PTO samples are strongly elongated in a-axis that leads to compress in the c-axis for preserving the unit cell volume. Consequently, the decreasing trend of c/a for PTO matrix is not difficult to comprehend as a result of the tensile stress induces a-lattice elongation with the compressive c-axis.
From the information of lattice parameters of PTO matrices in Table 7-1, it is difficult to differentiate the stress/strain due to the interface of PTO and CFO matrices from that of PTO and Pt layer. We therefore predict the lattice parameters of the CFO matrices for all types of samples in Table 7-2 and find that the lattices of CFO matrices are compressed for all types. Because in three multiferroic films the CFO
matrices only bond to the PTO ones, the stresses exerted in CFO matrices should be only on the interfaces of PTO and CFO matrices. As mentioned previously, more than twice as many lattice constant of CFO to the PTO ones, PTO exerts compressive stress on the lattice of CFO. From Table 7-2, we found the most obvious compression is in the disk-3 type and the least compression in the 0-3 type for these three types of samples. Therefore, the train/stress caused by the lattice mismatch between the CFO and PTO matrices is the most pronounced in the disk-3 type and is the least in the 0-3 type that will be further confirmed by micro-Raman spectroscopy later on..
The ME coupling effect resulting from the elastic bonding at the interface [1, 2, 3]
should also be transmitted through the stress/strain between the interface of CFO and PTO matrices. The magnetic properties in our CFO/PTO multiferrics should be influenced by the stress/strain, thus it is more important to directly observe the interfacial stress/strain using another appropriate probe of local behavior besides the peak shifts of XRD diffractions of CFO which covers mm2 area and sub-m depth.
In the following study, we used SQUID to investigate the ferromagnetic properties in our multiferroics and the micro-Raman measurement system to probe the stress dependence of behavior of interfacial phonon, which is sensitive to the interfacial stress/strain.
7.2 Magnetic properties
We measured the RT magnetizations by applying the magnetic fields perpendicular and parallel to the surface of the films. Figure 7.4 shows the measured magnetic hysteresis loops for pure cobalt ferrite and different geometrical CFO contained multiferroics. The out-of-plane (Figure 7.4(a)) and the in-plane (Figure
We measured the RT magnetizations by applying the magnetic fields perpendicular and parallel to the surface of the films. Figure 7.4 shows the measured magnetic hysteresis loops for pure cobalt ferrite and different geometrical CFO contained multiferroics. The out-of-plane (Figure 7.4(a)) and the in-plane (Figure