CRYSTAL GROWTH & DESIGN
Off-Congruent LiNbO3 Crystals Prepared by Li-Poor Vapor Transport Equilibration for Integrated Optics
2008 VOL. 8, NO. 7 2125–2129
Ping-Rang Hua,† De-Long Zhang,*,† Yu-Ming Cui,† Yu-Fang Wang,‡ and Edwin Yue-Bun Pun§ Department of Opto-electronics and Information Engineering, College of Precision Instruments and Opto-electronics Engineering, Tianjin UniVersity, Tianjin 300072, P. R. China, Department of Physics, Nankai UniVersity, Tianjin 300071, P. R. China, and Department of Electronic Engineering, City UniVersity of Hong Kong, 83 Tat Chee AVenue, Kowloon, Hong Kong, P. R. China ReceiVed September 13, 2007; ReVised Manuscript ReceiVed NoVember 7, 2007
ABSTRACT: X- and Z-cut off-congruent LiNbO3 (LN) crystals for use for integrated optics were prepared by carrying out Lipoor vapor transport equilibration (VTE) treatment on 1-mm-thick congruent plates at 1100 °C for durations ranging from 65 to 170 h. The Li2O contents and crystalline phase in these Li-poor VTE-treated crystals were characterized by using Raman scattering, optical absorption, and powder X-ray diffraction spectroscopy. The studies of optical absorption in the ultraviolet region show that the Li-poor VTE treatments result in different extents of red-shifts of the optical absorption edges (OAEs), and the amount of the red-shift increases with the prolonged VTE duration. The mean Li2O contents in all VTE samples were evaluated from the measured OAEs. The results show that the VTE-induced reduction of the mean Li2O content can reach as much as ∼1 mol% for both cases of X-cut and Z-cut, and the mean Li2O content and the VTE duration follows the linear relations: cLi ) (48.62 ( 0.06) - (0.0052 ( 0.0004)t for the X-cut crystals and cLi ) (48.53 ( 0.08) - (0.0063 ( 0.0005)t for the Z-cut crystals. The out-diffusion of Li shows a slight anisotropy. The diffusivity in a Z-cut crystal is slightly larger. The results of visible absorption, Raman scattering, and powder X-ray diffraction show that all the VTE crystals still retain the LiNbO3 phase, consistent with the result predicted from the LiNbO3 phase diagram. The critical VTE duration, longer than which the VTE will induce LiNb3O8 phase in the crystal, is roughly evaluated to be about 577 and 476 h for an X-cut and a Z-cut plate, respectively.
1. Introduction Over the past 20 years, a family of Ti:Er:LiNbO3 waveguide amplifiers/lasers and relevant nonlinear optical devices has been demonstrated. 1–5 For any practical Ti:Er:LiNbO3 waveguide device, selective Er-doping is a prerequisite for the monolithic integration of active (optically pumped, Er-doped) and passive (unpumped) devices on the same substrate to avoid reabsorption in unpumped Er-doped waveguide. This is the main reason why the active ions in all Ti:Er:LiNbO3 devices demonstrated so far are incorporated by the local Er-doping method.1–5 Local Erdoping in a LiNbO3 crystal is usually realized via thermal diffusion of Er metal at a temperature close to the Curie point of the crystal (1142.3 ( 0.7 °C). The diffusion of Er into a congruent (Li2O content ≈ 48.6 mol%) LiNbO3 (CLN) crystal in an argon atmosphere (i.e., standard Er diffusion) has been studied in detail by Baumann et al.6 Their studies have shown that the solubility of Er3+ ions in a CLN is limited, ∼2.7 mol % (≈5.1 × 1020 ions/cm3) near the Curie temperature. Since the gain of a laser or an amplifier depends on the concentration of the active ions, the relatively low solubility of Er3+ ions in a CLN limits further demonstration of more efficient Ti:Er: LiNbO3 waveguide devices. In order to increase the Er3+ solubility, an off-congruent LiNbO3 crystal with more deficient Li2O contents is desired as such crystal can provide more Li vacancies to accept more Er3+ ions. Vapor transport equilibration (VTE) is a simple and practical method used for altering Li composition inside a pure or doped LN crystal. To date, most of the relevant works reported concentrated on the preparation of various near-stoichiometric * To whom correspondence should be addressed. † Tianjin University. ‡ Nankai University. § City University of Hong Kong.
(Li2O content close to 50 mol%) LN crystals by using the Lirich VTE method. Only a few papers involved noncongruent, Li-deficient LN crystals prepared by the VTE technique.7–11 Among these papers, refs 7-10 only mentioned that the Lideficient, noncongruent LN crystals studied were prepared by the VTE technique. Reference 11 involved the preparation of the off-congruent, Li-deficient LN crystals by the VTE method. The paper studied mainly (1) how to accurately determine the crystal composition through the measurements of the Curie temperature and the noncritical phase matching temperature, (2) the location of and the peculiarities associated with the phase boundary regions, and (3) the refinement of the Li-poor VTE technique for avoidance of the problems of the ferroelectric domain multiplicity and the second phase precipitation. In this work, a number of X- and Z-cut 1-mm-thick congruent crystal plates for use for integrated optics were prepared by the Li-poor VTE method. The Li-compositions and crystalline phase in these VTE-treated crystals were characterized by Raman scattering, optical absorption, and powder X-ray diffraction spectroscopy. The empirical dependences of the mean Li2O content on the VTE duration are quantitatively established for both cases of X-cut and Z-cut. On the basis of these empirical dependences, the critical VTE duration, longer than which the VTE will induce formation of the LiNb3O8 phase in the crystal, is predicted. In addition, the issue of the anisotropy of the Li out-diffusion is also discussed.
2. Experimental Procedures For VTE experiments, a crucible was prepared at first by using Li2CO3 and Nb2O5 powder as the starting chemicals. The preparation procedure is detailed as follows. First, the two starting chemicals were homogenously mixed according to a molar ratio of 32 mol% (Li2CO3)/ 68 mol% (Nb2O5). The mixture was then pressurized and molded into a crucible model of 6 cm in inner diameter and 4 cm in height. The
10.1021/cg7008804 CCC: $40.75 2008 American Chemical Society Published on Web 05/24/2008
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Table 1. Preparation Conditions for Li-Poor VTE-Treated X-Cut and Z-Cut LN Plates sample no.
cut of plate
VTE temperature
01 02 03 04 05 06 07 08 09 10
X-cut X-cut X-cut X-cut X-cut X-cut Z-cut Z-cut Z-cut Z-cut
as-grown 1100 °C 1100 °C 1100 °C 1100 °C 1100 °C as-grown 1100 °C 1100 °C 1100 °C
VTE duration 65 h 70 h 90 h 105 h 170 h 90 h 105 h 170 h
precalcination at 1000 °C for 10 h and the further calcination at 1100 °C for 1 h allowed the preparation of a Li-poor two-phase (LiNbO3 + LiNb3O8) crucible. The solid-state chemical reaction involved can be expressed as 32 mol% Li2CO3 + 68 mol% Nb2O5 ) 32 mol% CO2v + 28 mol% LiNbO3 + 36 mol% LiNb3O8. Commercial X- and Z-cut 1.00 ( 0.02 mm thick congruent LN plates grown by the conventional Czochralski method were used as the starting crystals. Five X-cut and three Z-cut CLN plates were VTE-treated under different conditions by using the prepared Li-poor two-phase crucible. The VTE temperature was fixed at 1100 °C, while the VTE durations ranged from 65 to 170 h. A detailed VTE procedure was carried out in the following way. At first, the plates to be treated were wrapped with Pt wire and placed on a Pt foil, which was placed in the crucible prior to the plates to be treated. Then, the crucible was sealed by a lid, made also of the Li-poor two-phase powder, and heated up to 1100 °C for a scheduled duration. Because of the Li concentration gradient between the crystal and the Li-poor two-phase powder, the Li in the bulk of the crystal out-diffuses to the crystal surface at the elevated temperature and the crystal evaporates the Li2O gas, which was sunk in the twophase due to taking place the solid-state chemical reaction Li2Ov + LiNb3O8 ) 3LiNbO3. As a result, the congruent crystal became more Li-deficient due to Li evaporation. Table 1 summarizes the VTE conditions of the X- and Z-cut Lipoor plates (sample nos. 02, 03, 04, 05, 06, 08, 09, and 10) prepared. These samples are used for the Raman scattering, optical absorption and X-ray diffraction characterizations. For comparison, the spectroscopic characterizations were also performed on the corresponding asgrown crystals (i.e., sample nos. 01 and 7 listed in Table 1). Raman spectra were recorded at room temperature by using a Spex1403 double monochromator. Radiation of 532 nm with an output power of 150 mW, emitted from a semiconductor laser, was used as the j was excitation source. The backward scattering configuration X(ZY)X j for the Z-cut samples. Under adopted for the X-cut samples and Z(YY)Z the former configuration the recorded spectrum is the clear E(TO) mode; under the latter one, the recorded spectrum results from the overlap of the A1(LO) and E(TO) modes. Nevertheless, the 153 cm-1 Raman peak which we are interested in corresponds to the pure E(TO) phonon. The widths and heights of both the entrance and the exit slits were set at 200 µm and 5 mm, respectively. Under such silt size, the resolution is better than 2 cm-1. All Raman spectra were recorded in the wavenumber range of 50-1000 cm-1. The scanning step and integration time are 1 cm-1 and 0.5 s, respectively. The visible absorption spectra were recorded at room temperature using a Shimadzu UV-3600 spectrophotometer. For the X-cut samples, the σ-polarized absorption spectra were measured. For the Z-cut crystals, R-polarized spectra were recorded. The scanning wavelength range is 200-600 nm. The scanning step and speed were fixed at 0.2 and 120 nm/min, respectively. The powder X-ray diffraction experiment was accomplished by using a Rigaku D/MAX-2500 diffractometer equipped with a Cu target. The target voltage and current operated at 40 kV and 100 mA, respectively. The scanning range of the 2θ angle was 10-90°. The scanning speed and step were 8°/min and 0.04°, respectively.
3. Results and Discussion Li2O Content. The Li-composition in a LN crystal can be determined by many methods.12 Here, the characteristics of the line width of the 153 cm-1 E(TO) phonon and the optical
Figure 1. The measured 153 cm-1 E(TO) phonons of (a) X- and (b) Z-cut as-grown and Li-poor VTE-treated (105 h) LN crystals. For convenience of comparison, the two peaks of the as-grown and the VTE crystals have been normalized to the same height.
absorption edge at the absorption coefficient of 20 cm-1 are used to determine the Li2O contents in our VTE samples qualitatively and quantitatively, respectively. As an example, in Figure 1 we show the measured 153 cm-1 E(TO) phonons of the X- and Z-cut crystals that were VTEtreated for 105 h. For comparison purposes, the Raman spectra of the corresponding as-grown (congruent) crystals are also shown. For convenience, the two peaks of the as-grown and the VTE crystals have been normalized to the same height. One can see that the phonon line width of the VTE-treated crystal becomes considerably broadening as compared with that of the corresponding as-grown crystal for both cases of X-cut and Z-cut. A similar spectral feature was also observed for the other VTE samples. It was found that the longer the VTE duration is, the more obvious the broadening is. Schlarb et al.13 reported that the phonon line width broadens continuously with the reduction of the Li2O content in a LN crystal. We may qualitatively conclude from the observed 153 cm-1 phonon line width feature that the Li-poor VTE procedure has given rise to the reduction of Li2O contents inside our VTE samples, and the reduction increases with the prolonged VTE duration. This conclusion is confirmed by the further OAE measurement results. Figure 2 shows the absorption spectra with corrected reflection in the ultraviolet region of all as-grown and Li-poor VTE-treated samples listed in Table 1. It can be clearly seen that the Li-poor VTE treatment results in considerable shift of the OAE toward the long wavelength region for both cases of X-cut and Z-cut. The longer the VTE duration is and the larger the amount of the redshift is. Table 2 collects the OAEs (at the absorption coefficient of 20 cm-1) of all as-grown and VTEtreated samples studied. One can see that, as usually,12,14,15 the OAEs of the two as-grown samples are located around 320 nm. After the 170 h VTE treatment, the redshift can reach 5-6 nm (Note that the wavelength resolution of the spectrophotometer used for the optical absorption measurement is better than 0.3 nm in the ultraviolet region). The red-shift of the OAE is the indication of the reduction of the Li2O content inside the
LiNbO3 Crystals Prepared by Li-Poor VTE
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Figure 2. Absorption spectra of (a) X-cut and (b) Z-cut as-grown and Li-poor VTE-treated LN crystals in the ultraviolet region. The reflection arising from the crystal’s two surfaces has been removed for each spectrum. Table 2. Measured OAEs (at the Absorption Coefficient of 20 cm-1) of X- and Z-Cut As-Grown and Li-Poor VTE-Treated LN Crystalsa sample no.
OAE@ 20 cm-1 (nm)
Li2O content (mol %)
X-cut 01 02 03 04 05 06
320.0 ( 0.3 321.6 ( 0.3 321.7 ( 0.3 322.5 ( 0.3 324.4 ( 0.3 325.6 ( 0.3
48.57 ( 0.13 48.35 ( 0.13 48.33 ( 0.13 48.22 ( 0.13 47.93 ( 0.13 47.74 ( 0.13
Z-cut 07 08 09 10
319.3 ( 0.3 322.1 ( 0.3 324.0 ( 0.3 325.2 ( 0.3
48.54 ( 0.13 48.07 ( 0.13 47.73 ( 0.13 47.50 ( 0.13
a The data listed in the right column are the mean Li2O content evaluated from the measured OAEs.
crystal.15 On the basis of the measured OAE data, there are two empirical formula that can be used to quantitatively evaluate the Li2O content in a LN crystal. One is the second-order polynomial fit reported by Wo¨hlecke et al.12 The other is the photon-energy fit reported by Kova´cs et al.15 The polynomial fit is suitable for the Li2O content ranging from 48.83 to 50 mol%. The photon-energy fit validates a wider Li2O content range from 47.5 to 50 mol%. It appears that the photon-energy fit is valid for the Li-poor crystals studied here. According to Kova´cs et al.,15 the photon energy E (in the unit of eV) corresponding to a given OAE has the following empirical relationship to the corresponding Li2O content cLi (in the unit of mol%) in the crystal.
E ) k √50 - cLi + E0
(1)
where k and E0 are the fitting parameters that can be found in ref 15. By using the preceding equation, the Li2O contents in the Li-poor VTE crystals were calculated from the measured
Figure 3. VTE duration dependence of the mean Li2O content (full squares) in (a) X-cut and (b) Z-cut Li-poor VTE-treated LN crystals. The solid-lines represent the linear fit to the scattered data. The fitted expressions are indicated.
OAEs. The results are shown in Table 2. In the calculations, the k and E0 parameters suitable for the ordinary ray are utilized. The total error of the Li2O content is estimated to be ( 0.13 mol%. Two contributions are included. One comes from the accuracy of the OAE method, 0.1 mol%,15 contributed mainly from the uncertainty of the OAE measurement (∼0.3 nm) and the error of the fitting parameters k and E0. The other contribution results from the error of the sample thickness, ( 0.02 mm, which results in a (0.4 cm-1 error of the absorption coefficient around 20 cm-1. The absorption error, equivalent to an OAE uncertainty of 0.2 nm, yields a Li2O content error of (0.03 mol%. For the X-cut samples, the Li2O content decreases from 48.35 mol% to 47.74 mol% as the VTE duration is increased from 65 to 170 h. For the Z-cut samples, the Li2O content decreases from 48.07 mol% to 47.50 mol% as the VTE duration is increased from 90 to 170 h. The decrease relative to the congruent point (48.6 mol%) reaches as much as ∼1 mol% for both cases of X-cut and Z-cut. To show the VTE duration dependence of the Li2O content more straightforwardly, the composition data shown in Table 2 are illustrated in Figure 3 (see the full squares). One can see that the Li2O content decreases in a nearly linear relation to the VTE duration t in both cases of X-cut and Z-cut. The solid lines in Figure 3a,b represent the results of the linear fitting to the experimental data. The fitted expressions are cLi ) (48.62 ( 0.06) - (0.0052 ( 0.0004)t and cLi ) (48.53 ( 0.08) - (0.0063 ( 0.0005)t for the X-cut and the Z-cut crystals, respectively. It is noted from the two expressions that the reduction rate of the Li2O content in the Z-cut crystal is slightly faster than that in the X-cut crystal. This means that the out-diffusion of Li has a slight anisotropy and the diffusivity in a Z-cut crystal is slightly larger than that in an X-cut crystal. This feature is consistent with the case of Li-rich VTE treatment.16
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Figure 4. Phase diagram of the Li2O-Nb2O5 system. S. S.: solid solution.
It should be stressed that the Li2O content along the thickness direction of the crystal plate may be inhomogeneous. At the crystal surface the Li concentration is minimum. As the depth is increased, the Li concentration increases gradually. At the midway of the crystal’s thickness, the Li2O content is maximum. This implies that the optical absorption measurements yield actually the averaged OAE over the crystal thickness (all are 1 mm in the present study). Therefore, each Li2O content given in Table 2 (excluding the data of the as-grown crystals) represents the averaged result over the crystal thickness. Detailed Li-profile and Li-diffusivity need additional experiments such as secondary ion mass spectrometry (SIMS) analysis, etc. That is our future work. Crystalline Phase. It is obvious that the Li-poor VTE-treated crystals should still retain the LN phase. Otherwise, if the VTE procedure has induced the formation of other non-LN phase, then the crystals prepared by the Li-poor VTE method may be useless for integrated optics. (Here, the wording “may be useless” takes into account the possibility that the subsequent rare-earth doping procedure may recover the original LN phase due to the incorporation of rare-earth ions.) The argument that the Li-poor VTE treatment may induce formation of other nonLN phase originates from the LN phase diagram. Figure 4 shows the phase diagram of the Li2O-Nb2O5 system, taken from ref 11. One can see that two phases, LiNb3O8 and solid-solution LiNbO3, can be in equilibrium in the Li-poor regime. The appearance or not of the LiNb3O8 phase in the crystal depends on the growth, annealing, or VTE temperature adopted. Under the temperature 1100 °C, which was adopted in our VTE experiment, the possibility that the solid-solution LiNbO3 phase is in equilibrium with the LiNb3O8 phase does not exist for the Li2O content below ∼45.6 mol%.11 This implies that all of the VTE crystals studied in this work should not contain the LiNb3O8 phase as the mean Li2O contents in all crystals are higher than 47.5 mol%. However, this prediction needs to be verified experimentally because, as mentioned above, the depth profile of the Li2O content is unknown at present and the Li2O contents near the crystal surface are unambiguously lower than the mean value. It is reasonable to exemplify the two VTE-170 h plates to carry out crystalline phase analysis because the two samples have undergone the longest VTE duration. At first, the absorption spectra in the visible region show that the background absorption in the two samples is only slightly larger than that in the as-grown crystals (The difference of the absorption coefficient is smaller than 0.2
Figure 5. (a) A1(LO) + E(TO) Raman spectra of Z-cut as-grown and Li-poor VTE-treated LN crystal with the duration of 170 h; (b) pure E(TO) Raman spectra of X-cut as-grown and Li-poor VTE treated LN crystal with the duration of 170 h.
cm-1.). This observation implies that after the 170 h VTE treatment the transparency of the crystal is still retained and the possibility that VTE treatment induces the formation of other non-LN phase is small. Further Raman scattering and powder X-ray diffraction studies reach the same conclusion. Figure 5 shows the comparisons of the Raman spectra of as-grown crystals (solid-line curves) and the two plates with the VTE duration of 170 h (full square marked curves). For the Z-cut crystals, the mixed A1(LO) + E(TO) spectra are shown, and for the X-cut plates, the clear E(TO) spectra are shown. The assignment of the Raman spectra of the LN crystal has been reported in refs 17- 19. In Figure 5 the spectrum of the VTE crystal has been shifted upward along the vertical axis for clarity. It is clear that the spectrum of the VTE-treated plate is essentially identical to that of the corresponding as-grown LN crystal. No additional peak appears and no peak disappears. Even the peaking position is the same as each other within the resolution of 2 cm-1. It is well-known that Raman scattering is only as a complementary tool of the X-ray spectroscopy to determine the crystalline phase of a matter. Thus, the above Raman scattering results cannot provide yet the sufficient evidence for the argument that the Li-poor VTE treatment did not induce the formation of the LiNb3O8 phase. To clarify this argument, X-ray diffraction results are necessary. As an example, in Figure 6 we show X-ray diffraction pattern of the sample powdered from the Z-cut VTE170 h crystal. For comparison, the pattern of the sample powered from the as-grown crystal is also shown. According to the X-ray powder diffraction file (PDF) no. 36-307, provided by Joint Committee on Powder Diffraction Standards (JCPDS), the LiNb3O8 phase is characterized mainly by two strongest reflexes around the 2θ angles of 30.22° (relative intensity: 98) and 30.26° (relative intensity: 100), corresponding to the d-value of 0.2955 and 0.2951 nm, respectively. The insets in Figure 6 show expanded views in the 2θ angle range of 20-40°. When the pattern was checked around the 2θ angle of 30.22°, no reflex could be resolved. In the
LiNbO3 Crystals Prepared by Li-Poor VTE
Figure 6. Powder X-ray diffraction patterns of the Z-cut as-grown and VTE-170 h LN crystals. The insets show expanded views around the 2θ angle of 30°.
other 2θ region, no additional reflexes could be resolved too. With the exception of the change of the relative intensities, the pattern of the VTE crystal corresponds well to that of the as-grown crystal. It is therefore concluded from the above optical absorption, Raman scattering and X-ray diffraction results that the argued LiNb3O8 crystalline phase cannot be induced in an X-cut or Z-cut LN crystal for the VTE duration up to 170 h. With the known Li-poor phase boundary Li2O content (45.6 mol%),11 the critical VTE duration, longer than which the phase equilibrium between the LiNb3O8 and LN begins to take place, can be evaluated by using the above-given empirical relationships of the mean Li2O content to the VTE duration. For the case of X-cut, it is evaluated to be about 577 h. For the case of Z-cut, a relatively short duration about 476 h is predicted. It should be pointed out that such estimations are made with ignored Li2O content depth profile. The results given are hereafter very rough and are only as the reference. The actual critical VTE durations with the consideration on the depth profile of the Li2O content should be shorter than these rough values. Finally, let us simply discuss the mechanism of the Li-poor VTE process. The total solid-state chemical reaction of the Lipoor VTE may be expressed as Li2Ov (released from crystal) + LiNb3O8 (two phase powder) + LiNbO3 (two phase powder) ) 3LiNbO3 (two phase powder) + LiNbO3 (crystal). The equilibrium between the LN phases in the powder and in the crystal guarantees that the crystalline phase of the crystal retains still the pure LN phase. The loss of the Li+ ions further increases the Li vacancies inside the crystal (the congruent LN has already about 4% Li vacancies).
4. Conclusion A number of X- and Z-cut off-congruent LN plates, which have the potential for use of the integrated optics substrates, have been prepared by carrying out Li-poor VTE treatment on 1-mm-thick congruent materials at 1100 °C for the durations ranging from 65 to 170 h. The optical absorption studies show that the Li-poor VTE treatments result in different extents of red-shifts of the OAEs, depending on the VTE duration. The longer the VTE duration is and the larger the amount of the red-shift is. For the VTE duration of 170 h, the shift can reach as much as 5-6 nm for both cases of X-cut and Z-cut. Evaluation of Li-compositions from the measured OAEs shows that the mean Li2O content in the X-cut plate decreases from 48.35 mol% to 47.74 mol% as the VTE duration is increased
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from 65 to 170 h. For the case of Z-cut, the mean Li2O content decreases from 48.07 mol% to 47.50 mol% as the VTE duration is increased from 90 to 170 h. The decrease relative to the congruent point (48.6 mol%) reaches as much as ∼1 mol% for both cases of X-cut and Z-cut. Further linear fit shows that the mean Li2O content and the VTE duration follows the linear relations: cLi ) (48.62 ( 0.06) - (0.0052 ( 0.0004)t for the X-cut crystals and cLi ) (48.53 ( 0.08) - (0.0063 ( 0.0005)t for the Z-cut crystals. It appears that the out-diffusion of Li has a slight anisotropy. The diffusivity in a Z-cut crystal is slightly larger than that in an X-cut crystal, being consistent with the case of Li-rich VTE treatment. Overall investigations of visible absorption, Raman scattering and powder X-ray diffraction show that the LN phase is retained still in these Li-deficient crystals and no other non-LN crystalline phase was induced by the VTE treatments. This experimental result is consistent with that predicted qualitatively from the LN phase diagram on the basis of the evaluated Li2O contents in the VTE crystals. On the basis of the established relationships of the mean Li2O content to the VTE duration and the Li-poor phase boundary Li2O content (45.6 mol%) reported previously, the critical VTE duration, longer than which the phase equilibrium between the LiNb3O8 and LN begins to take place, is roughly predicted to be about 577 and 476 h for a 1-mm-thick X-cut and Z-cut plate, respectively. Acknowledgment. This work was supported by National Natural Science Foundation of China under Project No. 60577012, and the Research Grants Council of the Hong Kong Special Administrative Region, China, under Project No. CityU1194/07.
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