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Polarized Micro-Raman Spectroscopy of Ba(Mg1/3Nb2/3)O3 Single Crystal Fibers R. L. Moreira* Departamento de Fı´sica, ICEx,UFMG, C.P. 702, 30123-970 Belo Horizonte-MG, Brazil

CRYSTAL GROWTH & DESIGN 2005 VOL. 5, NO. 4 1457-1462

M. R. B. Andreeta and A. C. Hernandes Instituto de Fı´sica de Sa˜ o Carlos, Universidade de Sa˜ o Paulo, USP, C.P. 369, 13560-970 Sa˜ o Carlos-SP, Brazil

A. Dias Departamento de Engenharia Metalu´ rgica e de Materiais, UFMG, Rua Espı´rito Santo 35, 30160-030 Belo Horizonte-MG, Brazil Received December 23, 2004;

Revised Manuscript Received May 6, 2005

ABSTRACT: Ba(Mg1/3Nb2/3)O3 (BMN) is a complex perovskite usually obtained in ceramic form and exhibiting remarkable microwave dielectric properties when sintered at high temperatures. The crystallographic and spectroscopic studies of this material indicate that it belongs to the trigonal P3 h m1 space group, with a 1:2 ordering of Mg and Nb atoms along the [111] cubic direction. Nevertheless, studies of BMN single crystals are still lacking. In this work, we report on the first preparation and study of BMN single crystal fibers obtained by the laser heated pedestal growth (LHPG) technique. The fibers were high-quality crystalline samples grown in the 〈110〉 cubic direction and presenting facets normal to the 〈112〉 cubic axes. Polarized Raman spectra in chosen directions allow us to conclude that the crystalline structure of the fibers is the same as that of well-ordered sintered ceramics, although some regions containing a different crystalline phase were also detected. It is shown that the selection rules for the symmetry and polarization of the Raman features are fully obeyed so that the modes belonging to the totally symmetric representation (A1g) and to the doubly degenerate in-plane representation (Eg) could be discerned. Introduction A(B′1/3B′′2/3)O3 ceramics (A ) Ba or Sr, B′ ) Mg, Mn, or Zn, and B′′ ) Nb or Ta) sintered at high temperatures are being extensively studied owing to their excellent microwave and millimeter-wave dielectric properties.1-4 In these materials, the polar optical phonons determine the high-frequency dielectric response, which in turn depends on the sample structure and morphology. Thus, the experimental preparation conditions play an important role in determining the final dielectric parameters (the dielectric constant and quality factors depend strongly on the sample density and long-range ordering degree).5-7 Concerning their structures, complex perovskites with the general formula A(B′1/3B′′2/3)O3 can be classified into ordered and disordered types with respect to the degree of long-range order of the divalent B′ and pentavalent B′′ cations. The disordered materials should present the simple cubic Pm3m symmetry. On the other hand, two possibilities are usually considered for the ordered compounds, depending on the B′/B′′ cation ordering: a cubic Fm3m symmetry for 1:1 order or a trigonal P3 h m1 symmetry for 1:2 order.1,6,8,9 In particular, the crystalline structure of Ba(Mg1/3Ta1/3)O3 (BMT) and Ba(Mg1/3Nb1/3)O3 (BMN) compounds could be unambiguously determined if good quality crystals were available. Guo et al. reported on the preparation of BMT single crystals by the laser heated pedestal * Correspondingauthor.Tel: +55.31.3499.5624.Fax: +55.31.3499.5600. E-mail: [email protected].

growth (LHPG) technique.5 Their structural results, together with Raman studies on these fibers,8,9 are rather conflicting, leading to the conclusion that single crystals would have a cubic structure instead of the trigonal one showed by the ceramics sintered at high temperatures. Since the Raman tensor elements of cubic and trigonal groups have different symmetry properties, which were not exploited in previous studies,2,6,8-13 we decided to revisit this problem by growing BMN single crystal fibers by the LHPG method and by performing polarized micro-Raman measurements on the oriented crystalline samples. The results obtained enabled us to confirm the P3 h m1 space group also for the BMN fibers and, moreover, to assign the trigonal A1g and Eg Raman modes. Knowledge of the number and symmetries of the lattice vibrational modes is mandatory for describing the dielectric behavior of any dielectric material at microwave frequencies, because the dielectric response in this region is determined mainly by the characteristics of the polar optical phonons. Thus, although the use of LHPG was rather limited because of relative difficulties in growing crystals, the method outlined in this work can be extended to other materials to decide among conflicting symmetries and structures of dielectric ceramics. Experimental Section Undoped Ba(Mg1/3Nb2/3)O3 (BMN) single-crystal fibers were grown from pedestal rods (source and seed) using the laser heated pedestal growth (LHPG) equipment described else-

10.1021/cg049565n CCC: $30.25 © 2005 American Chemical Society Published on Web 06/03/2005

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where.14 The pedestal rods were obtained from prereacted BMN powders with an organic binder. The homogeneous mixtures were molded into cylindrical pedestal shapes with 1.6 mm diameter and 50 mm length using a cold extrusion device.15 The green-rods obtained were dried in air and then used as seed and source in the growth process. The growth took place in the upward direction without seed or pedestal rod rotation and in an ambient atmosphere. The pedestal/fiber diameter ratio to produce the single crystal fiber was found to be 6.0. BMN powders used in the pedestal rods were obtained in a hydrothermal reactor from an aqueous solution of BaCl2‚ 2H2O, MgCl2‚6H2O, and NH4H2[NbO(C2O4)3]‚3H2O. NaOH was added to the solution to maintain the pH around 13.5. The synthesis occurred after 4 h at 200 °C and 20 bar.12 Chemical analyses were carried out in these powders by using atomic absorption spectrometry (Perkin-Elmer 5000) and X-ray fluorescence (Philips PW2400 sequential spectrometer, fitted with a rhodium target end window and Philips Super Q analytical software). The single crystal fibers of BMN were successfully grown by LHPG with lengths up to 2 cm and typical diameters of 500 µm. The fibers were transparent and free of microscopic inclusions and had cylindrical form, although some small facets (200 µm wide by 500 µm long, along the fiber) were discerned. The undoped fibers were a dark blue color. The sample surfaces perpendicular to fiber growth direction were polished to an optical grade before the measurements. To determine the nature of the crystalline phases present, X-ray diffraction analyses were performed in a Philips PW1830 diffractometer with Cu KR radiation (40 kV, 30 mA) and graphite monochromator. The diffractograms were taken from 10° to 100° 2θ at a speed of 0.02° 2θ/s. Laue back-reflection photographs were taken in the same system after 5 h exposition, enabling the determination of the crystallographic directions. Polarized micro-Raman scattering spectra were recorded using a Jobin-Yvon LABRAM-HR spectrometer equipped with a 1800 grooves/mm diffraction grating, a liquid-nitrogen-cooled CCD detector, and a confocal Olympus microscope (10× objective, confocal aperture of 1.0 mm). The experimental resolution was typically 1 cm-1 for 10 accumulations of 30 s. The measurements were carried out in backscattering geometry at room temperature using the 632.8 nm line of a helium-neon ion laser (power 12.5 mW) as excitation source.

Results X-ray diffraction analysis of the hydrothermal powders showed the presence of crystalline single-phase BMN (indexed by the ICDD card number 17-0173) with no impurities, as also confirmed by X-ray fluorescence and energy-dispersive spectrometry analyses. Laue back-reflection photographs of the BMN fibers were taken with the beam parallel and perpendicular to the fiber growth direction. Since the fibers present facets parallel to this axis, we chose one large facet that was placed horizontally. Therefore, Figure 1 shows the Laue images obtained with the X-ray beam (a) along the fiber axis and (b) normal to this axis and simultaneously parallel to the main facet plane. These photographs reveal clearly a C2 axis in the first case and a C3 axis in the second case. Since BMN ceramics are described as belonging to a distorted cubic superstructure (trigonal), we cannot a priori index these symmetry axes to the trigonal structure, but rather, we are restricted to indexing them to the cubic system. This point will be analyzed later with the Raman data in detail. The presence of facets normal to the C3 × C2 () t) direction indicates the anisotropy of the crystal growth rate, that

Figure 1. Laue back-reflection photographs with the X-ray beam (a) parallel and (b) perpendicular to the BMN fiber growth direction (Laue chamber radius ) 3 cm). In panel b, the beam is parallel to one of the largest facets. The beams appeared to be parallel to a C2 axis in panel a and to a C3 axis in panel b.

is, the growth rates of our BMN fibers seem to decrease from C2 to C3 and, finally, to t (although we do not have many data to make a statistical analysis). We should point out that this result is different from that of BMT fibers of ref 5 and also from micrometer BMN needles obtained by microwave-assisted hydrothermal growth.16 In the first case, the authors found the cubic direction

Polarized Micro-Raman Spectroscopy of BMN

Figure 2. The polarized micro-Raman spectra of a BMN single crystal fiber taken in backscattering geometries on the plane of the facet of Figure 1. C2 is the fiber growth direction. The polarizer and analyzer are parallel to high-symmetry directions, as indicated on each spectrum. The inset shows a detail of the facet plane and the symmetry directions (t ) C3 × C2).

t as the fiber growth direction. The difference can be attributed to two reasons: first, those authors used micrometer grounded ceramic, while we used nanometer-sized powder (∼20 nm) as our source, and second, they also used sintered ceramic seeds (which could have preferential orientation), while we did not. Concerning the second case, where the growth direction appeared to be t or C4, the experimental conditions in the two procedures were strongly different, that is, very low temperatures (200 °C) and high pressures (20 bar) were employed in that case,16 while high temperatures (above 3000 °C) and low pressure (1 bar) were used in the present LHPG case. Since we have obtained the symmetries of the platelets of the BMN fibers, we have performed polarized Raman experiments with the incident light normal to the platelets (i.e., the incoming and outgoing light beams are parallel to the t direction). The results with a 10× objective for a stress-free region are presented in Figure 2 for polarizer and analyzer parallel to the symmetry axis (since we are dealing with a centrosymmetric structure, only these directions are relevant to the spectra). Three characteristic spectra are then presented in Figure 2: the parallel-polarized C3C3 and C2C2 and the cross-polarized C3C2. The inset shows a photograph of the facet with the definition of the directions, in accordance with the Laue images. We note that the spectra of the parallel-polarized beams are similar to each other and contain all the Raman features (typically nine bands) observed with unpolarized light for ordered BMN ceramics, which is considered as belonging to the P3 h m1 space group. Nevertheless, since we are using polarized light, if the C3 axis were that of the trigonal distortion, we would expect only totally symmetrical vibrations in this direction. Thus, it seems that either the structure would be cubic (with 1:1 B-site ordering, as proposed in refs 8 and 9) or the C3 axis in these measurements would not be the main axis of the trigonal structure. We will return to this point in detail in the next section. Concerning the cross-polarized spectrum, we observe a beautiful polarization effect with the weakening of several bands. Although the vanishing

Crystal Growth & Design, Vol. 5, No. 4, 2005 1459

Figure 3. The polarized micro-Raman spectra of a BMN fiber taken in backscattering geometries on a plane normal to the fiber growth direction. C3 is the same as in the previous figure (contained in the main facet), and C′3 is another 3-fold symmetry axis. The symbols indicate the directions of polarizer and analyzer. The inset shows a detail of the facet planes and the symmetry directions (t ) C3 × C2, t′ ) C2 × C′3).

of totally symmetrical bands could be easily demonstrated for cubic systems using the polarizability Raman tensors17 within C3C2 scattering geometry, we cannot discard, a priori, the trigonal group. So, additional data are needed to decide the correct space group of the BMN crystal. In Figure 3, we show the Raman spectra obtained in a cross section of the BMN fiber (incoming and outgoing light beams parallel to the fiber axis, that is, to C2). The inset shows the polished surface with the definition of the axes: the main platelet characterized by C3 and t as before and two new directions, C′3 contained in a second platelet normal to t′ (t′ ) C2 × C′3). We note first that we expected a second 3-fold axis in this plane, since in cubic structures one pair of the four C3 axes always has a common perpendicular C2 axis. Also, we notice that the angle between C3 and C′3 (and also that between t and t′) is 110(1)°, in perfect agreement with the 109.78° predicted for this angle in a cube. Therefore, C′3 is surely a second 3-fold symmetry axis of the cube. However, we now have a new result for the parallelpolarized C′3C′3 Raman spectrum: the weakening of several modes in the intermediate region of the spectrum. This is a very important point because this result is incompatible with a cubic structure (where all 3-fold symmetry axes are equivalent). It remains to be proven whether it could be explained by a P3 h m1 trigonal one. The t′t′ parallel-polarized spectrum presents all the features of the unpolarized spectra of BMN ceramics, being very similar to the C2C2 spectrum of Figure 2. On the other hand, the cross-polarized t′C′3 spectrum is complementary to the C′3C′3 one: it shows the relative strengthening of the bands in the intermediate region (similarly to the C3C2 spectrum of Figure 2). Before discussing the differences in the polarized micro-Raman spectra of BMN fibers, we should point out that a different phase was also detected in the fibers, as shown by the spectrum of Figure 4. This spectrum was taken in parallel-polarized light in the fiber cross section. It has no signature of a preferential direction (several angles were taken in parallel-polarized light). In this spectrum, we discern 12 well-defined bands (thinner than those usually observed in BMN). Such a

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Figure 4. The polarized micro-Raman spectra of a particular region of the BMN fiber, taken in backscattering geometry, on a plane normal to the fiber growth direction. This spectrum reveals the presence of an additional phase.

spectrum appears in different points of the sample, but as a rather low contribution. We remember that the scattering region of the fiber is a few square micrometers in area, so we have a very large area (500 µm diameter) to exploit in the fiber cross section. Although we do not intend to determine the nature of this additional phase, we suggest that it originates from Mgdeficient regions due to the very high fiber growth temperature (around 3000 °C). Indeed, Guo et al.5 have observed Mg-deficiency in their BMT fibers (by chemical analysis) and postulated that MgO vaporization could lead to new phases that could be Ba5Ta4O15 or BaTa2O6, although they did not have any experimental confirmation of their hypotheses. We think that micro-Raman scattering could contribute to a solution for this problem, but it deserves a specific study (because the crystalline structures and crystallographic axes are different from those of BMT or BMN). Discussion It is well-accepted that ordered BMN ceramics belong 3 to the trigonal P3 h m1 (D3d ) space with 15 atoms in the 1 primitive cell. The number and symmetries of the optical active modes of a crystalline material can be determined by group theory tools; in particular, we used the factor-group method of Rousseau et al.,18 based simply on the occupied Wyckoff sites. For the ordered BMN, two Ba ions occupy 2d sites and one Ba ion sits on a 1b site, giving ΓBa ) A1g + 2A2u + Eg + 2Eu; the Mg ion occupies a 1a site (ΓB′ ) A2u + Eu); the two Nb ions are in 2d sites (ΓB′′ ) A1g + A2u + Eg + Eu); six O ions are in 6i sites and three O ions in 3f sites (ΓO ) 2A1g + 2A1u + A2g + 4A2u + 3Eg + 6Eu). Three of these modes (2A1u + A2g) are silent, and after the acoustic modes (A2u + Eu) are subtracted, there remain nine Raman-active modes (4A1g + 5Eg) and 16 infrared-active ones (7A2u + 9Eu). The Raman and IR modes are mutually exclusive, owing to the centrosymmetric nature of the crystal group. The inelastic light scattering intensities due to the Raman effect are proportional to the square of the elements of the polarizability tensor, a second-rank tensor. Thus, the base functions of the irreducible representations (i.r.) that contain the Raman-active modes have a quadratic form, that is, they transform

Moreira et al.

like the product of the Cartesian coordinates. When dealing with crystals, we take advantage of the crystal symmetry to assign the lattice vibrations to the different i.r.17,18 In our case, we could, at least in principle, confirm the presence of the trigonal distortion in the fibers as well as separate the A1g and Eg modes by their symmetries. But, in general, we need to know all the crystalline directions, because the reference system determines both the scattering geometry and the form of the polarizability tensors. The following paragraphs develop the mathematical background to discuss the observed features in our polarized Raman spectra. In its own reference system, the polarizability tensors of the D3d point group are given by17

( )

( )

a ‚ ‚ c ‚ ‚ ‚ -c d , and A1g ) ‚ a ‚ , E(1) ) g ‚ ‚ b ‚ d ‚ ‚ -c -d ‚ E(2) g ) -c ‚ -d ‚ ‚

(

)

(1)

Thus, xy, xz, and yz are base functions of the Eg i.r., while zz relates only to the A1g i.r. The xx and yy functions are simultaneously active in both Raman i.r.’s. The intensity of the first-order Raman features are obtained by

I ) |eo†‚R‚ei|2

(2)

where R are the polarizability tensors given in eq 1 and ei and eo are the incoming and outgoing light polarization directions. As shown in the previous section, our BMN fibers grew according to the simple cubic directions. In this reference system, the totally symmetric Raman tensor is a diagonal one ()a1), irrespective of any particular point group. Moreover, the parallel-polarized scattered light along any cube diagonal should be equal (because of the equivalency of all 3-fold axes in the cubic systems). This indicates that the relatively different spectra obtained in the C3C3 and C′3C′3 geometries (Figures 2 and 3) show that our BMN single crystal fibers do not belong to any cubic symmetry. However, now we face the following problem: if the crystalline P3 h m1 structure holds for our BMN fibers, we should either turn the Raman tensors for the fiber axes or turn the polarization axes to the reference system of the Raman tensors in eq 1. These two alternatives are completely equivalent, because if R is the unitary matrix that rotates cubic to trigonal axes, then the Raman intensities can be obtained by

I ) |eo†R†‚R‚Rei|2

(3)

Equation 3 shows the equality of turning R or e. To keep the meaning of the axes, we prefer to rotate the matrices of the trigonal base. In both cases, we need first to obtain R and then to transform the polarizability tensors of eq 1. As stated before, R is the matrix that rotates cubic to trigonal reference axes. Choosing the trigonal z-axis as the [111] cube diagonal, this matrix is obtained by taking

Polarized Micro-Raman Spectroscopy of BMN

at )

1 (-ac + cc) x2

bt )

1 (-ac + bc) x2

Crystal Growth & Design, Vol. 5, No. 4, 2005 1461 Table 1. Raman Intensities Calculated for Special Scattering Geometries Specified by the Directions of Incoming and Outgoing Light Beam Polarization Directionsa

1 ct ) (ac + bc + cc) x3

(4)

In these equations, the subscripts c and t mean cubic (laboratory) and trigonal systems, respectively. Now, replacing at by the cross product between bt and ct, we have the R matrix

(

1 1 -2 1 -x3 x3 0 R) x6 x2 x2 x2

)

(5)

R†R

Then, we proceed to the transformations tR ) Rc, obtaining the matrices (eq 1) in the cubic reference system, which leads to

A1g )

E(1) g

(

E(2) g )

(

(

2a + b b - a b - a 1 b - a 2a + b b - a 3 b - a b - a 2a + b

)

-2c - 2x6d 4c -2c - x6d 1 ) 4c x6d -2c + x6d -2c + 2 6 -2c - x6d -2c + x6d 4c

)

C3C3 C2C2 C2C3 C′3C′3 C′3t′ t′t′

A1g

E(1) g

E(2) g

(2) E(1) g + Eg

((8a + b)/9)2 a2 0 b2 0 a2

(8c/9)2 c2 d2/9 0 0 c2

(4 d/9)2 0 8c2/9 0 d2 0

(64c2 + 32d2)/81 c2 (8c2 + d2)/9 0 d2 c2

a The directions are C′ ) [111], C ) [1 h 10], t′) [112 h ], and C3 ) 3 2 [1 h1 h 1].

Table 2. Raman Fitting Parameters and Assignments for the BMN Single Crystal Fibers Obtained from Averaging Only over the Polarized Spectraa position (cm-1)

fwhm (cm-1)

intensity (arb. units)

109 670 730 780 125 170 309 380 445

8 25 35 30 12 22 20 27 22

32 31 19 100 93 17 62 100 51

assignment A1g

Eg

a The intensities were calculated independently for each irreducible representation.

)

2x3c - 2x2d -2x2d -2x3c + x2d 1 x -2x3c - 2x2d 2x3c + x2d 6 -2 2d 4x2d -2x3c + x2d 2x3c + x2d (6) With these matrices, the Raman intensities can now be easily calculated using eq 2 (instead of eq 3), where the directions of light beam polarizations are simply taken from the laboratory. We note that by writing the R matrix we have already chosen three special cubic directions, the main trigonal direction as [111], a 2-fold axis perpendicular to this direction, that is, [1h 10], and a third direction simultaneously perpendicular to both directions, say [112h ]. Since we have observed a special behavior in our Raman spectra of Figure 3, we will identify these directions as our C′3, C2, and t′ axes. This choice is not unique, but the results do not change if we identify the growing direction with another C2 axis (because this implies also changing t′, C3, and t, and we note that all other three C3 directions are equivalent). For this particular choice of axes, we also have C3 ) [1 h1 h 1] and t ) [112]. The calculated Raman intensities for the six scattering geometries used in this work (Figures 2 and 3) are summarized in Table 1. We note that, besides the correct number of observed modes (nine bands), our model correctly describes the selection rules for the symmetry of the modes: all modes predicted and observed in C3C3, C2C2, and t′t′ scattering geometries; only A1g modes seen in the C′3C′3 configuration; only the Eg modes seen in C2C3 and t′C′3 configurations.

From the point of view of symmetry of the modes, the only difference compared to cubic structures is that concerning the C′3C′3 scattering configuration, but the agreement between the predicted and observed number of modes for the different scattering geometries is clear enough to convince us of the trigonal structure of our system. Once having identified the spectra corresponding to the two different i.r., we then propose a new assignment of the four A1g and five Eg Raman modes, presented in Table 2. Our results are to be compared with those obtained in mixed BMN-BMT ceramic samples13,19 and in large grain ceramic samples.16 Naturally, we hope our method could give new insight into the determination of the Raman modes symmetry of BMN, but we should remember that some discrepancies could be found because each material system has its own peculiarities and limitations. Therefore, we will not focus on the differences between our results and those of refs 13, 16, and 19, because we believe that the main contributions of our present work are the direct observation of symmetries in Raman modes and the confirmation of the trigonal structure of BMN single crystal. Conclusions BMN single crystal fibers were obtained for the first time by the LHPG technique and investigated by polarized Raman spectroscopy. The fibers grew in the 〈110〉 cubic direction and presented facets denoting anisotropic growth rates. The sample facets formed were normal to the 〈112〉 direction. The behavior of the Raman features with the scattering geometries was explained by rotating the Raman tensor elements of the trigonal D3d group to the reference system of the laboratory. Thus, we were able to identify, experimentally, the modes of A1g and Eg symmetry. This method

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can be extended to other A(B′1/3B′′2/3)O3 material with cubic or trigonal symmetry. Acknowledgment. The authors acknowledge the financial support from the Brazilian agencies CNPq, MCT (The Millennium Institute: Water, a mineral approach), FAPEMIG, and FAPESP. We also thank Alexandre M. Moreira for his help in X-ray diffraction experiments. References (1) Galasso, F. S. Structure, Properties and Preparation of Perovskite-Type Compounds; Pergamon Press: Oxford, U.K., 1969; pp 13-15, 55. (2) Tamura, H.; Sagala, D. A.; Wakino, K. Jpn. J. Appl. Phys. 1986, 25, 787. (3) Sagala, D. A.; Koyasu, S. J. Am. Ceram. Soc. 1993, 76, 2433. (4) Lu, C. H.; Tsai, C. C. J. Mater. Res. 1996, 11, 1219. (5) Guo, R.; Bhalla, A. S.; Cross, L. E. J. Appl. Phys. 1994, 75, 4704. (6) Moreira, R. L.; Matinaga, F. M.; Dias, A. Appl. Phys. Lett. 2001, 78, 428. (7) Dias, A.; Ciminelli, V. S. T. Chem. Mater. 2003, 15, 1344.

Moreira et al. (8) Siny, I. G.; Katiyar, R. S.; Bhalla, A. S. J. Raman Spectrosc. 1998, 29, 385. (9) Siny, I. G.; Tao, R.; Katiyar, R. S.; Guo, R.; Bhalla, A. S. J. Phys. Chem. Solids 1998, 59, 181. (10) Furuya, M. J. Korean Phys. Soc. 1998, 32, S353. (11) Sagala, D. A.; Nambu, S. J. Phys. Soc. Jpn. 1992, 61, 1791. (12) Dias, A.; Ciminelli, V. S. T.; Matinaga, F. M.; Moreira, R. L. J. Eur. Ceram. Soc. 2001, 21, 2739. (13) Chia, C. T.; Chen, Y. C.; Cheng, H. F.; Lin, I. N. J. Appl. Phys. 2003, 94, 3364. (14) Hernandes, A. C. Recent Research Developments in Crystal Growth Research; Transworld Research Network: Trivandrum, India, 1999; p 123. (15) Andreeta, E. R. M.; Andreeta, M. R. B.; Hernandes, A. C. J. Cryst. Growth 2002, 234, 782. (16) Moreira, R. L.; Dias, A. J. Eur. Ceram. Soc., 2005, 25, 2843. (17) Hayes, W.; Loudon, R. Scattering of Light by Crystals; Wiley: New York, 1978. (18) Rousseau, D. L.; Bauman, R. P.; Porto, S. P. S. J. Raman Spectrosc. 1981, 10, 253. (19) Lin, I. N.; Chia, C. T.; Liu, H. L.; Cheng, H. F.; Chi, C. C. Jpn. J. Appl. Phys. 2002, 41, 6950.

CG049565N