Tb3+-Doped LGS Crystals: Crystal Growth and Electro-Elastic Features

Abstract

Piezoelectric materials have garnered significant attention due to their diverse applications in technologies such as sensors, actuators, and energy-harvesting systems. This study focuses on the growth and characterization of Tb³⁺-doped La₃Ga₅SiO₁₄ (LGS) crystals. A novel 10% Tb³⁺-doped single LGS crystal was successfully grown using the Czochralski method. The crystal structure and fluorescence properties were determined, and the electro-elastic properties were evaluated by the impedance method, which assessed dielectric, piezoelectric, and elastic constants. The Tb³⁺-doped crystal was observed to crystallize in the trigonal system, with the concentration of the Tb³⁺ ion in the crystal determined to be 2.50 wt%. The piezoelectric coefficients were measured as d₁₁ = 5.41 pC/N and d₁₄ = −5.52 pC/N, and the dielectric constants were found to be 19.60 and 52.75, respectively. The temperature-dependent behavior of Tb:LGS crystals was investigated, particularly concerning their elastic constants, demonstrating favorable thermal stability. This study provides valuable insights into the relationship between the crystals’ structural characteristics and performance. Additionally, the fluorescence properties were measured; a long lifetime (τ = 1.655 ms) indicated the potential applications of Tb:LGS crystals in laser technology.

1. Introduction

Since the discovery of the piezoelectric effect by Pierre and Jacques Curie in 1900, researchers have progressively developed a variety of crystalline materials that exhibit valuable piezoelectric properties, thereby expanding their range of applications. Key areas of use for piezoelectric crystals in contemporary technology include ultrasonic devices, sensors, actuators, energy-harvesting systems, and vibration management solutions [1]. Moreover, as scientific and technological advancements continue, the demand for effective and diverse piezoelectric materials is growing.

The langasite family of crystals are multifunctional materials with the general formula A₃BC₃D₂O₁₄, where A is a dodecahedral site, B is a octahedral site, and C and D are tetrahedral sites [2]. The crystals are generally divided into two categories: structurally disordered and ordered crystals. The structurally disordered crystals, which include La₃Ga₅SiO₁₄ (LGS), La₃Ga₅.₅Nb₀.₅O₁₄ (LGN) [3], and La₃Ga₅.₅Ta₀.₅O₁₄ (LGT) [4], are distinguished by variations in ion placement at different locations within the crystal lattice. In contrast, the structurally ordered crystals comprise Ca₃TaGa₃Si₂O₁₄ (CTGS) [5], Ca₃NbGa₃Si₂O₁₄ (CNGS) [6], Sr₃TaGa₃Si₂O₁₄ (STGS) [7], and Sr₃NbGa₃Si₂O₁₄ (SNGS) [8].

Among the langasite family of crystals, LGS crystals have been extensively studied because they exhibit exceptional piezoelectric, electro-optical, and nonlinear optical characteristics [9,10,11,12,13,14,15,16,17,18]. The structure of La₃Ga₅SiO₁₄ (LGS) exhibits disorder, with the large La³⁺ cations occupying the A sites, while Ga³⁺ cations occupy the B, C, and a portion of the D sites and Si⁴⁺ occupies the remaining D sites. The LGS crystal was first investigated in 1982 [19]; then, Kaminskii et al. first reported on the laser performance of the (La_1−xNd_x)₃Ga₅SiO₁₄ (Nd:LGS) crystal, which was subsequently utilized in the optical field as a laser gain medium in 1983 [20,21]. By 1986, E.G. Bronnikova et al. had reported the fabrication of high-stability BAW monolithic filters and resonators using single LGS crystals. Due to their high piezoelectric coefficient, high electromechanical coupling factor, and relatively large usable temperature range, LGS crystals have been extensively employed in bulk acoustic wave (BAW) and surface acoustic wave (SAW) applications over the years [22,23,24].

While considerable research has focused on the piezoelectric properties of these crystals, investigations into doped crystals remain limited. Rare-earth functional crystal materials play a pivotal role in the advancement of high-tech applications. Among the various doping elements, Tb³⁺ ions have attracted significant attention from researchers due to their broad visible emission spectrum, ranging from red to green. Given the unique characteristics of the crystal structure, and considering that Tb³⁺ and La³⁺ possess the same valence state and similar ionic radii, the ion substitution method, which leverages the advantages of Tb³⁺ in conjunction with LGS, is employed to modulate the properties of these materials.

In this study, we demonstrate the successful growth of a 10% Tb³⁺-doped single LGS (Tb:LGS) crystal using the Czochralski (Cz) technique. We evaluated the crystal structure, the effective segregation of each element in the as-grown crystal, and the electro-elastic properties of the single Tb:LGS crystal. Additionally, we investigated the temperature stability of the electro-elastic properties over a range from room temperature to 500 °C.

2. Experimental Section

2.1. Polycrystal Powder Synthesis and Crystal Growth

The synthesis of high-purity polycrystalline materials is crucial for the successful growth of single crystals. In this study, high-temperature solid-state reactions were utilized to synthesize polycrystalline materials. The primary raw materials for crystal growth include La₂O₃, Tb₄O₇, Ga₂O₃, and SiO₂, all of which possess a purity level of 4N (sourced from Aladdin). To achieve high-purity polycrystalline materials, the raw materials were weighed according to the stoichiometric ratio. Due to the volatility of Ga₂O₃ at elevated temperatures, an excess of 1 mol% Ga₂O₃ was incorporated into the experiment. The weighed powders were mechanically blended for 15 to 24 h to achieve thorough homogeneity. Subsequently, the thoroughly mixed materials were pressed into appropriately sized pellets, transferred to a corundum crucible, and pre-sintered in a muffle furnace at 1300 °C for over 10 h to yield the polycrystalline material.

The sintered polycrystalline material was then repeatedly melted in a platinum crucible and subjected to crystal growth using the Cz method. The melting point of LGS crystals is 1470 °C, and for the doping growth of Tb³⁺ crystals, the melting point will fluctuate, but the change will not be too large. When all the polycrystalline materials in the crucible were observed to melt, the temperature was increased by 100 °C and maintained at this level for several hours. A Z-axis-oriented LGS seed crystal was slowly immersed in the melt to initiate crystal growth. A pulling speed of 0.5 to 2 mm/h and a rotation speed of 10 to 20 rpm were consistently maintained throughout the growth process. After crystal growth, the crystal was cooled to room temperature at a rate of 15 to 50 K/h. To minimize defects that could compromise the crystal quality, the grown crystal was subsequently annealed in a muffle furnace. For the growth of high-concentration doped crystals, it is essential to ensure the crystal quality. During growth process using the Cz method, a slow pulling speed, combined with a slightly faster crystal rotation rate, was employed.

2.2. Characterizations

The powder X-ray diffraction (PXRD) analysis of Tb:LGS was conducted using a Rigaku Miniflex 600 X-ray diffractometer (Rigaku Corporation, Tokyo, Japan) equipped with Cu Kα radiation. Data were collected over a test range of 10° to 80° with a scanning speed of 10 min per degree. The data were further refined using GSASΙΙ software. To gain insights into the structure of Tb:LGS, single crystal X-ray diffraction analysis was conducted. The X-ray diffraction data were collected using a Bruker D8 VENTURE diffractometer (Bruker Corporation, Berlin, Germany) equipped with a PHOTON-II CMOS detector, utilizing monochromatic Turbo X-ray Source (TXS) MoKα radiation (λ = 0.71073 Å) at 293 K. Data collection was performed in the shutterless mode, and the unit cell was determined using the Bruker APEX 4 software suite. The structure was solved by the intrinsic phasing method with the SHELXT 2018/2 program and refined using the full-matrix least squares on F² with the SHELXL 2019/3 program. The quality of the grown Tb:LGS crystal was characterized through high-resolution X-ray diffraction (HRXRD). A well-polished Z plate crystal sample was prepared for testing. The elemental composition of the as-grown Tb:LGS crystal was determined using a Panalytical Axios X-ray fluorescence spectrometer (XRF). The photoluminescence emission and excitation spectra, along with the photoluminescence decay curves, were recorded using an Edinburgh FLS-1000 fluorescence spectrophotometer (Edinburgh Instruments Ltd., Livingston, UK). A continuous xenon lamp was utilized to collect the luminescence emission and excitation spectra.

2.3. Evaluation of Electro-Elastic Constants

Based on the crystal symmetry, the Tb:LGS crystal exhibited eleven independent nonzero electro-elastic constants: two independent dielectric permittivities ${\epsilon }_{11}^T$ and ${\epsilon }_{33}^T$, two independent nonzero piezoelectric coefficients (d₁₁ and d₁₄), and seven independent nonzero elastic constants ($s_{11}^E$, $s_{12}^E$, $s_{13}^E$, $s_{33}^E$, $s_{44}^E$, and $s_{66}^E$). To determine all dielectric, piezoelectric, and elastic constants using the impedance method, we fabricated eight samples with different configurations based on the IEEE standard for piezoelectricity [25], as schematically shown in Figure 1. The dimensions of the square-shaped plates were 8 × 8 × 1 mm³ [(a–c)], and the rectangular-shaped plates were 1 × 2 × 6 mm³ [(d–h)]. The samples were sputter-coated with platinum to serve as electrodes along the direction of the applied electric field. The capacitance (C), resonance frequency (f_r), and anti-resonance frequency (f_a) of the crystal samples were measured using an impedance phase–gain analyzer (HP4194A) (Hewlett- Packard, Houston, TX, USA). Table 1 summarizes the cut types, vibration modes, and vibration equations used to assess the electro-elastic properties of the Tb:LGS crystal. Additionally, the temperature stability of the electro-elastic constants was evaluated using a high-temperature furnace (KSL-1200X) (MTI Corporation, Hefei, China) for measurements.

3. Results

3.1. Crystal Structure, Quality, and Segregation Coefficient

High-quality Tb:LGS crystals with a [001] direction were successfully grown by using the Cz method, as depicted in Figure 2a. The crystal was transparent and free from cracks. As illustrated in the inset in Figure 2a, the growth direction exhibited a distinct growth ridge that reflected the symmetry of the crystal. The relationships between the crystallographic axes (a, b, and c) and physical property axes (X, Y, Z) are presented in Figure 2a. To accurately assess the crystalline quality of the obtained single crystal, the rocking curve of the (001) wafer was measured. The sample was randomly cut from a bulk crystal and carefully polished on both sides, with the results presented in Figure 2b. The Full Width at Half Maximum (FWHM) value for the Tb:LGS crystal was ascertained to be 49.78″, indicating sharp and symmetric peaks that reflected a homogeneous composition and high crystalline quality. Such high quality can offer a satisfactory basis for the measurement while meeting the requirements in practical applications.

The Tb:LGS polycrystalline sample was synthesized using the high-temperature solid-phase method. The verification of the phase purity was conducted by PXRD, and the characteristic diffraction peaks of the Tb:LGS crystals displayed good agreement with those of the standard patterns as depicted in Figure 3a. Rietveld refinement was employed for the as-grown single Tb:LGS crystals, as shown in Figure 3b. The final refinement yielded R_p and R_w values of 2.95% and 5.72%, respectively, which are within reasonable limits. This indicates that the as-grown Tb:LGS crystals were of a pure phase and that the incorporation of Tb³⁺ did not alter the crystal structure.

To further clarify its structure, crystal structure analyses (Table 2) revealed that Tb:LGS is crystallized in the trigonal system with the P321 space group. The unit cell parameters were a = b = 8.1537(4) Å and c = 5.0916(4) Å. It can be concluded that doping with Tb³⁺ results in a reduction in the unit cell volume of the Tb:LGS crystal when compared to the standard LGS crystal, which has dimensions of a = b = 8.168 Å and c = 5.095 Å. In the asymmetric unit of Tb:LGS (Figure 4), there are three distinct Ga atoms, one distinct Si atom, and three distinct O atoms. Specifically, one La atom is present, with the Tb³⁺ ion occupying part of the position of the La atom. These atoms form polyhedra with the O atoms, which are then interconnected through shared oxygen atoms, resulting in a three-dimensional framework structure. The results indicate that the structure of Tb:LGS remains unchanged when the Tb³⁺ ion is partially substituted with a La³⁺ ion.

The concentrations of Tb³⁺, La³⁺, Ga³⁺, Si⁴⁺, and O²⁻ ions in the as-grown Tb:LGS crystal was ascertained using XRF. The effective segregation coefficient of each element in the Tb:LGS crystal can be obtained as follows:

$k_{eff}={\displaystyle \frac{C_S}{C_L}}$

in which C_S represents the concentration in the as-grown Tb:LGS crystal and C_L denotes the concentration of the melt. Based on the XRF results, the effective segregation coefficient k_eff could be obtained and is presented in Table 3. The concentration of the Tb³⁺ ion in the crystal was determined to be 2.50 wt%. The effective segregation coefficients for La³⁺, Ga³⁺, Si⁴⁺, and O²⁻ were approximately equal to 1, indicating that the composition of the solid phase and the melt remains consistent at the solid–liquid interface during crystal growth. The effective segregation coefficient for the Tb³⁺ ion was calculated to be 0.541, suggesting that the incorporation of the Tb³⁺ ion into the crystal is challenging.

3.2. Fluorescence Properties

Figure 5a presents the emission spectra obtained under 375 nm excitation at room temperature. The four primary emission bands observed at approximately 491 nm, 544 nm, 585 nm, and 624 nm correspond to the transitions from the excited state ⁵D₄ to the ⁷F₆, ⁷F₅, ⁷F₄, and ⁷F₃ states, respectively. Notably, the emission band at 544 nm exhibited the highest intensity. Figure 5b illustrates the decay curve of transient photoluminescence at room temperature, which can be accurately fitted using a biexponential function.

$I=A_1{e}^{-t/{\tau }_1}+A_2{e}^{-t/{\tau }_2}$

and the fluorescence lifetime (τ) is calculated to be 1.655 ms using the following formula:

$\tau ={\displaystyle \frac{A_1{\tau }_1^2+A_2{\tau }_2^2}{A_1{\tau }_1+A_2{\tau }_2}}$

An extended lifetime significantly reduces the pump threshold necessary for achieving population inversion during laser generation. This characteristic is advantageous for energy storage during the lasing process, indicating potential applications in laser technology.

3.3. Electro-Elastic Properties and Temperature Stability

The complete sets of the electro-elastic constants for the Tb:LGS crystals were determined using the impedance at room temperature, and the results are summarized in Table 4. The electro-elastic constants of the LGS crystals [11] are also listed for comparison. The dielectric permittivities of the Tb:LGS crystal were 19.60 and 52.75, which are slightly higher than those of the LGS crystal. In comparison with LGS crystals, the piezoelectric coefficients of Tb:LGS crystals were slightly lower, at 5.41 and −3.26 pC/N, respectively. The reason may be that when La³⁺ is replaced by Tb³⁺ with a small ionic radius, the cell parameters and volume are reduced, which reduces the degree of polyhedral distortion and leads to a decrease in the piezoelectric constant. These observations provide a strong basis for the further exploration of the relationship between the properties and structures of these crystals.

The temperature-dependent behavior of the electro-elastic constants for the Tb:LGS crystal was studied over a temperature range from 25 °C to 500 °C. Figure 6 depicts the variations in the relative dielectric permittivity ${\epsilon }_{ii}^T/{\epsilon }_0$ (i = 1 and 3) as a function of the temperature. The results reveal that the relative dielectric permittivities ${\epsilon }_{11}^T/{\epsilon }_0$ and ${\epsilon }_{33}^T/{\epsilon }_0$ exhibited an increasing trend with rising temperatures, with changes recorded at 23.4% and 32.1%, respectively. In a manner similar to that of the dielectric permittivity, the dielectric loss also gradually increased with the temperature. Notably, for tanδ₁₁, a significant mutation was observed at 300 °C and 350 °C, which may be attributed to the formation of space charges within the crystal structure.

Figure 7 illustrates the variation in the elastic compliance constants of the Tb:LGS crystal with the temperature. The results indicate that the elastic compliance constants exhibited commendable temperature stability. The changes in $s_{11}^E$, $s_{12}^E$, $s_{13}^E$, $s_{33}^E$, $s_{44}^E$, and $s_{66}^E$ were recorded as 1.35%, −3.79%, 2.82%, 5.69%, 0.23%, and −0.51%, respectively. As the temperature increased from room temperature to 500 °C, the maximum value of the elastic compliance constant ($s_{11}^E$) decreased slightly from 26.88 pm²/N to 26.74 pm²/N, demonstrating favorable thermal stability.

As the temperature increased, the electromechanical coupling coefficients k₁₂ and k₂₆ exhibited an upward trend, as shown in Figure 8. At room temperature, k₁₂ and k₂₆ were measured at 14.01% and 10.18%, respectively. When the temperature rose to 500 °C, these values increased to 15.14% and 13.26%, respectively. The variation in k₁₂ and k₂₆ was 8.06% and 30.25%, respectively. Notably, k₁₂ demonstrated better temperature stability. Figure 9 presents the temperature stability of the piezoelectric coefficients, which was derived from the dielectric permittivity, elastic constant, and electromechanical coupling coefficient. It was observed that the piezoelectric coefficient d₁₁ increased from 5.41 pC/N at room temperature to 6.77 pC/N at 500 °C, reflecting a variation of 25.0%. Similarly, the piezoelectric coefficient d₁₄ changed from −5.52 pC/N at room temperature to −6.99 pC/N at 500 °C, resulting in a variation of 26.6%.

4. Conclusions

Single Tb:LGS crystals with 2.50 wt% Tb³⁺ were successfully grown by the Czochralski method, and the crystal structure was investigated. The crystal structure of the Tb:LGS crystal was determined to be a trigonal system with unit cell parameters of a = b = 8.1537(4) Å and c = 5.0916(4) Å. The electro-elastic properties of single Tb:LGS crystals were investigated. The complete matrix of the dielectric, elastic, and piezoelectric constants was determined using the resonance method. The piezoelectric coefficients d₁₁ and d₁₄ were measured to be 5.41 and −5.52 pC/N, respectively. Tb:LGS crystals were found to exhibit relatively high piezoelectric properties and excellent temperature stability. Compared to LGS crystals, Tb:LGS is a promising piezoelectric crystal. Meanwhile, the Tb:LGS crystal offers valuable insights into the relationship between the properties and structures of these crystals.

Author Contributions

N.Z.: writing—original draft preparation; J.W.: data curation; H.Z.: conceptualization; F.C.: revised manuscript; F.Y.: methodology; L.S.: investigation; X.Z.: supervision. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data are contained within the article.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

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Figures and Tables

Figure 1. Crystal cut configurations of Tb:LGS crystal for evaluation of electro-elastic constants: (a) X plate; (b) Y plate; (c) Z plate; (d–h) YXt/θ (θ = 0°, 30°, 45°, 85°, and −45°.

Figure 2. (a) As-grown single Tb:LGS crystal; theoretical morphology for the Tb: LGS crystal (inset). (b) Rocking curve of the (001) wafer of the Tb:LGS crystal.

Figure 3. (a) Experimental and calculated PXRD patterns of Tb:LGS polycrystalline samples; (b) Rietveld refinement plots of as-grown single Tb:LGS crystals.

Figure 4. The structure of the Tb:LGS crystal.

Figure 5. Fluorescence properties of the Tb:LGS crystal: (a) excitation spectra; (b) decay curve of transient photoluminescence. Red dots are the experimental data, and the blue curve is the one fitted by a double exponential function.

Figure 6. Relative dielectric constants of the Tb:LGS crystal as a function of the temperature.

Figure 7. Elastic compliance of the Tb:LGS crystal as a function of the temperature.

Figure 8. Electromechanical coupling factors of the Tb:LGS crystal as a function of the temperature.

Figure 9. Piezoelectric coefficients of the Tb:LGS crystal as a function of the temperature.

Table 1

The cut types, vibration modes, and equations for assessing the electro-elastic properties of the Tb:LGS crystal.

Crystal Cuts	Vibration Modes	Material Constants	Related Equations
X plate (a)	/	${\epsilon }_{11}^T/{\epsilon }_0$	${\displaystyle \frac{{\epsilon }_{ii}^T}{{\epsilon }_0}}={\displaystyle \frac{C\cdot t}{A\cdot {\epsilon }_0}}$
Z plate (c)	/	${\epsilon }_{33}^T/{\epsilon }_0$
XY plate (d)	Length extension	$d_{12}(=d_{11}) s_{22}^E\left(=s_{11}^E\right)$	$s_{ii}^E={\displaystyle \frac{1}{4\rho {\left(l{f}_r\right)}^2}}$ ${\displaystyle \frac{k_{12}^2}{k_{12}^2-1}}={\displaystyle \frac{\pi }{2}}\cdot {\displaystyle \frac{f_a}{f_r}}\cdot \cot \left({\displaystyle \frac{\pi }{2}}\cdot {\displaystyle \frac{f_a}{f_r}}\right)$ $d_{12}=k_{12}{\left({\epsilon }_{11}^T{s}_{22}^E\right)}^{{\displaystyle \frac{1}{2}}}$
XYt/45° plate (f)	Length extension	d 14 $2s_{13}^E+s_{44}^E$	$d_{12}^{\prime }\left({45}^o\right)=-{\displaystyle \frac{1}{2}}{d}_{11}+{\displaystyle \frac{1}{2}}{d}_{14}$ $\begin{array}{l}{s}_{22}^{E\prime }\left(\theta \right)=s_{11}^E{\cos }^4\theta +\left(2s_{13}^E+s_{44}^E\right){\cos }^2\theta {\sin }^2\theta \\ -2s_{14}^E{\cos }^3\theta \sin \theta +s_{33}^E{\sin }^4\theta \end{array}$
XYt/−45° plate (h)	Length extension	$s_{14}^E$ together with XYt/45°
XYt/−30° plate (e)	Length extension	$2s_{13}^E+s_{44}^E$ $, s_{33}^E$
XYt/85° plate (g)	Length extension	$s_{33}^E$
Y plate (b)	Face shear	$s_{55}^E$	$\begin{array}{l}{\displaystyle \frac{s_{55}^E}{F^2}}={\displaystyle \frac{1}{4\rho {\left(l{f}_r\right)}^2}}\\ F=1.2916-0.0458\sqrt{{\displaystyle \frac{s_{11}^E+s_{33}^E}{s_{55}^E}}}\end{array}$
	Thickness shear	$s_{66}^E,s_{12}^E$	$\begin{array}{l}{k}_{26}^2={\displaystyle \frac{\pi }{2}}\cdot {\displaystyle \frac{f_r}{f_a}}\cdot \cot \left({\displaystyle \frac{\pi }{2}}\cdot {\displaystyle \frac{f_r}{f_a}}\right)\\ c_{66}^E=4\rho {\left(t{f}_a\right)}^2\left(1-k_{26}^2\right)\\ s_{66}^E={\displaystyle \frac{1}{c_{66}^E}}+{\displaystyle \frac{4s_{14}^{E^2}}{s_{44}^E}}\\ s_{66}^E=2\left(s_{11}^E-s_{12}^E\right)\end{array}$

Table 2

Crystal information and structure refinement of Tb:LGS.

Empirical Formula	La2.7Tb0.3Ga5SiO14
Formula weight (g·mol−1)	1023.42
Temperature (K)	293.00
Crystal system	trigonal
Space group	P321
a (Å)	8.1537(4)
b (Å)	8.1537(4)
c (Å)	5.0916(4)
Volume (Å3)	293.15(4)
Z	1
F (000)	454.0
Goodness of fit on F2	1.162
Final R indexes [I >= 2σ (I)]	R1 = 0.0145, wR2 = 0.0349
Final R indexes [all data]	R1 = 0.0146, wR2 = 0.0350

Table 3

XRF analysis of single Tb:LGS crystal.

	La	Ga	O	Si	Tb
Standard (wt%)	36.65	34.06	21.89	2.74	4.66
Sample (wt%)	39.73	32.87	22.21	2.66	2.52
keff	1.084	0.965	1.015	0.970	0.541

Table 4

Summary of the electro-elastic constants of the single Tb:LGS crystal compared to those of LGS crystals [11].

Relative dielectric permittivities, ${\epsilon }_{ij}^T$/${\epsilon }_0$
	${\epsilon }_{11}^T/{\epsilon }_0$	${\epsilon }_{33}^T/{\epsilon }_0$
Tb:LGS	19.60	52.75
LGS	19.2	50.7
Piezoelectric charge coefficients, dij (pC/N)
	d11	d14
Tb:LGS	5.41	−5.52
LGS	6.15	−6.01
Elastic compliance constants, $s_{ij}^E$ (pm2/N)
	$s_{11}^E$	$s_{12}^E$	$s_{13}^E$	$s_{14}^E$	$s_{33}^E$	$s_{44}^E$	$s_{66}^E$
Tb:LGS	8.60	−4.84	−3.96	−4.83	9.93	19.35	26.88
LGS	8.86	−4.24	−1.79	−3.48	5.19	20.32	26.19
Electromechanical coupling coefficients, kij (%)
	k12	k26
Tb:LGS	14.01	10.18
LGS	16	13.4

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