Origin of giant piezoelectric effect in lead-free K1−xNaxTa1−yNbyO3 single crystals

A series of high-quality, large-sized (maximum size of 16 × 16 × 32 mm3) K1−xNaxTa1−yNbyO3 (x = 0.61, 0.64, and 0.70 and corresponding y = 0.58, 0.60, and 0.63) single crystals were grown using the top-seed solution growth method. The segregation of the crystals, which allowed for precise control of the individual components of the crystals during growth, was investigated. The obtained crystals exhibited excellent properties without being annealed, including a low dielectric loss (0.006), a saturated hysteresis loop, a giant piezoelectric coefficient d33 (d33 = 416 pC/N, determined by the resonance method and d33* = 480 pC/N, measured using a piezo-d33 meter), and a large electromechanical coupling factor, k33 (k33 = 83.6%), which was comparable to that of lead zirconate titanate. The reason the piezoelectric coefficient d33 of K0.39Na0.61Ta0.42Nb0.58O3 was larger than those of the other two crystals grown was elucidated through first-principles calculations. The obtained results indicated that K1−xNaxTa1−yNbyO3 crystals can be used as a high-quality, lead-free piezoelectric material.

properties of KNN is difficult. Furthermore, there have been few microscopic studies on the physical mechanism responsible for the improvement in the piezoelectric properties after doping with Ta.
In this paper, we report the successful growth of a series of high-quality, large-sized K 1−x Na x Ta 1−y Nb y O 3 (KNTN) single crystals using the TSSG method. The segregation of the crystals, which allowed for precise control over the individual components of the crystals, was investigated. The as-grown crystals exhibited excellent properties, including a saturated hysteresis loop, a giant piezoelectric coefficient, d 33 * (480 pC/N), and a large electromechanical coupling factor, k 33 (83.6%); the values of these parameters were comparable to those of PZT. Finally, the origin of the high piezoelectric effect observed in the crystals was elucidated through first-principles calculations.

Results and Discussion
Photographs of the as-grown KNTN crystals are shown in Fig. 1. The dimensions of the largest KNTN crystal grown were 16 × 16 × 32 mm 3 , which are much greater than those of previously reported KNTN crystals. The crystals were transparent at temperatures higher than their Curie temperature (T C ), and no cracks were observed in them. At room temperature, the crystals were milky white, because of the presence of polydomains, which scatter light. The KNTN crystals were shaped like a square with round corners, and the surfaces of the crystals were (100) C and (010) C faces.
The segregation of the crystals allowed for precise control of the individual components of the crystals during the growth process. The relationships between the composition of the KNTN crystals; the ratio of the potassium and sodium concentrations in the melt; the ratio of the tantalum and niobium concentrations in the melt; the segregation coefficient of potassium, sodium, tantalum, and niobium; and the growth temperature (T g ) are shown in Table 1. The segregation coefficient of potassium (S K ) was calculated from the equation: The similar calculations were performed for the S Na , S Ta , S Nb . The segregation of ion was determined by their properties. Moreover, it was also determined by ion concentration in melt and the condition of growth. With an increase in the tantalum content in the melt, the  Further, the segregation coefficient of potassium increased from 0.400 to 0.520, while that of sodium decreased from 2.800 to 2.560. This was in contradiction to the phase diagram of the KNbO 3 -NaNbO 3 system 25 and meant that the doping of Ta into the KNN system affected the segregation of K and Na. The XRD patterns indicated that the crystals had pure perovskite-like structures and did not contain any secondary phases (Fig. 2). The as-grown KNTN single crystals were in the orthorhombic phase at room temperature. From the XRD data, the lattice parameters of the KNTN crystals were determined using the software Jade 6.0; the results are shown in Table 2. The (202) and (020) peaks moved to the high degrees decreases in x and y, resulting in increases in the lattice parameters "a" and "b. " These changes in the lattice parameters of the KNTN crystals indicated that the volume of the lattice cell increased with the decrease in x and y. The cation radius of the tantalum r(Ta 5+ ) is slightly smaller than that of the niobium r(Nb 5+ ), while the volume of the as-grown crystals increase with decrease of Nb concentration (as Table 2 shown). Thus the main reason for the increase in the volume was the fact that the cation radius of potassium r(K + ) is larger than that of sodium r(Na + ).
The temperature dependence of the dielectric constant of the K 1−x Na x Ta 1−y Nb y O 3 crystals at 1 kHz is shown in Fig. 3. The two peaks in the curves represent the orthorhombic-tetragonal phase-transition temperature (T O-T ) and the Curie temperature (T C ), respectively; the values of these temperatures were consistent with the XRD results and suggested that the crystals were in the orthorhombic phase at room temperature. As can be seen from the data listed in Table 3, with the tantalum and sodium content varying, the value of T O-T of the KNTN crystals decreased from 84 °C to 39 °C. Concomitantly, the value of T C decreased from 228 °C to 161 °C. According to the data of pure KNN single crystals 26 , we can determine that the value of T O-T and T C of the KNN crystals slightly increased with decrease of Na concentration. However, the T C of KTN single crystals gotten by the function T C = 676x + 32 K (x is the Nb concentration in KTN crystals) 27 decreased with doping Ta. Thus, the variation of T O-T and T C mainly owed to Ta/Nb ratio 28 . In addition, the dielectric property (ε r ) of the as-grown KNTN crystals increased with the increase in the potassium and tantalum contents, and is larger than that of the pure KNN single crystals. The result is mainly reasonable because Ta could move the T O-T peak left, and room temperature is close to the T O-T peak. The quality of K 0.39 Na 0.61 Ta 0.42 Nb 0.58 O 3 was better than the other two components crystals as its tanδ was the smallest. Furthermore, it was similar or smaller than that of the crystals reported previously in the literature 26,29 . Figure 4a showed the P-E hysteresis loops of the KNTN crystals at 25 °C at a frequency of 200 Hz under a maximum electric field of 35 kV/cm. All as-grown crystals exhibit saturated curves at an electric field of 35 kV/mm, which suggests that as-grown crystals were of high quality. The values of the coercive field (E c ), remanent polarization (P r ), and spontaneous polarization (P s ) of the KNTN single crystals as well as those of the pure KNN single crystals are listed in Table 4. The E c , P r , and P s values of the KNTN crystals were smaller than those of pure KNN single crystals. The result is in good agreement with the difference between Ta 5+ and Nb 5+ in unit   Table 2. Lattice parameters of the KNTN crystals. a The lattice parameters corresponding to a symmetric orthorhombic cell were converted into the lattice parameters for a pseudo-monoclinic cell (a′ = c′ , b, and β) using the following formula a = 2d sin (β/2), c = 2a′ sin (β/2) 41 .
cell. Ta 5+ and Nb 5+ ions were randomly distributed in the B-sites. Because Nb 5+ ions moving along the 12 directions of spontaneous polarization mainly contribute to the P r , the P r decreased with doping Ta. The values of the room-temperature leakage current density (J) along the [001] C direction of the as-grown KNTN crystals are Crystal      Fig. 5. For this k 33 resonator, a resonance frequency (f r ) was 631 kHz while an antiresonance frequency (f a ) was 1.103 MHz. The values of the elastic compliance constant s 33 , electromechancical coupling factor k 33 , and piezoelectric coefficient d 33 of the samples were calculated by substituting the measured long-size l, f r and f a into the following equation: 33 33 33 . The maximum phase angle was approximately 75°; this was indicative of the existence of a polydomain state (domain engineered). The similar measurement was performed for other k 33 , k 31 , and k t resonators. The k 33 values of the samples were between 76.4% and 83.6% and larger than those reported previously for KNN-TL and PZT5A. Further, the giant piezoelectric coefficient d 33 of the K 0.39 Na 0.61 Ta 0.42 Nb 0.58 O 3 crystal was 416 pC/N, as determined by the resonance method, while d 33 * was 480 pC/N, as measured with a piezo-d 33 meter; these values are larger than those for other two as-grown single crystals and KNN-TL. As can be seen from the data, the values of most of the parameters of K 0.39 Na 0.61 Ta 0.42 Nb 0.58 O 3 which were greatly influenced by temperature were comparable to those of PZT5A.
As shown in Table 5, the piezoelectric coefficient d 33 of the K 0.39 Na 0.61 Ta 0.42 Nb 0.58 O 3 crystal was larger than those of the K 0.30 Na 0.70 Ta 0.37 Nb 0.63 O 3 and K 0.36 Na 0.64 Ta 0.40 Nb 0.60 O 3 crystals. This can be attributed to the polymorphic phase transition (PPT) which was lowered to room temperature by Ta, when the K/Na ratio was far away from 0.5/0.5 32,33 . However, the microscopic physical mechanism responsible was not involved. To elucidate the origin of the high piezoelectric effect in the microcosmic, we used first-principles calculations to calculate the free energy of the lattice cell.
Spontaneous polarization occurs in twelve directions along [011] C in the orthorhombic (mm2)-phase single crystals, while it occurs in six directions along [001] C for the tetragonal (4 mm) -phase single crystals (shown in Fig. 6). When an electric field was applied along the z-axis, the directions in which spontaneous polarization occurred in the orthorhombic phase changed to those corresponding to the tetragonal phase. In addition, according to a previous study, the reason the piezoelectric coefficient d 33 of the grown crystals was large was that the polarization directions were rotated and not stretched 34 . The internal energies of the K 1−x Na x Ta 1−y Nb y O 3 crystals corresponding to the different phases (orthorhombic phase, U o , and tetragonal phase, U t ) were calculated through first-principles calculations. For this, we calculated the internal energies of potassium tantalate (KTaO 3 , KT), potassium niobate (KNbO 3 , KN), sodium tantalate (NaTaO 3 , NT), and sodium niobate (NaNbO 3 , NN), as well as the weighted averages 35,36 of the individual coefficients. The obtained results are shown in Table 6.
It can be seen that Δ U decreased from 3.0241 eV/Å 3 to 2.5666 eV/Å 3 with an increase in the Ta fraction from 0.37 to 0.42 and an increase in the K fraction from 0.30 to 0.39. Further, the difference in the free energies of the orthorhombic and tetragonal phases of K 0.39 Na 0.61 Ta 0.42 Nb 0.58 O 3 in the absence of an electric field was the lowest. Thus, when an electric field was applied, the domain of K 0.39 Na 0.61 Ta 0.42 Nb 0.58 O 3 which was at PPT temperature, was the easiest to rotate, which can enhance piezoelectric properties 34 . The conclusion was the same as that calculated by Landau -Devonshire model in BaTiO 3 -based materials 37,38 and PZT-based materials 39 . As a result, its piezoelectric coefficient was larger than those of K 0. 30

Conclusions
In this study, a series of large-sized (size of largest crystal = 16 × 16 × 32 mm 3 ) orthorhombic K 1−x Na x Ta 1− y Nb y O 3 (x = 0.61, 0.64, and 0.70 and corresponding y = 0.58, 0.60, and 0.63) single crystals were grown using the TSSG method. The crystals exhibited excellent dielectric, piezoelectric, and ferroelectric properties, including  6%). The leakage currents of the K 1−x Na x Ta 1−y Nb y O 3 crystals were very low and of the order of 10 −5 A/cm 2 . The piezoelectric properties of the K 1−x Na x Ta 1−y Nb y O 3 crystals improved with an increase in the potassium and tantalum contents when the phase of the K 1−x Na x Ta 1−y Nb y O 3 crystals was orthorhombic. Finally, the difference in the free energies of the orthorhombic and tetragonal phases of K 0.39 Na 0.61 Ta 0.42 Nb 0.58 O 3 in the absence of an electric field was 2.5666 eV/Å 3 ; this was determined by first-principles calculations. This crystal was the smallest of the grown single crystals. Further, its domain was the easiest to rotate. Therefore, it exhibited the best piezoelectric properties.

Piezoelectric materials
Elastic compliance constants s E , s D (10 −12 m 2 /N)     The polycrystal was melted in a medium-frequency induction furnace at 1250 °C ~ 1375 °C, which is ~100 °C higher than the temperature for crystal growth, in order to eliminate the residual carbon dioxide and mix the compounds at the atomic level. Then, the temperature was decreased to the growth temperature, and a single crystal began to grow on a [001] C seed that was cut from a high-quality potassium tantalate niobate crystal. During crystal growth, the rotational and pulling rates were 15 r/min and 0.25 mm/h, respectively. After the completion of the growth process, the as-grown crystal was cooled to the room temperature at 35 °C/h. The compositions of the as-grown crystals were determined by electron microprobe analysis (EPMA-1720, Shimadzu, Kyoto, Japan). The structures of the crystals were confirmed by X-ray diffraction (XRD) analyses (XRD-6000, Shimadzu, Kyoto, Japan). The crystals were oriented using a Laue X-ray machine. The (001) C in pseudo cubic structure structure surfaces of the samples were covered with silver electrodes, and the dielectric properties of the samples were measured as functions of the temperature using an inductance -capacitance − resistance (LCR) meter (E4980A, Agilent Technologies, Santa Rosa, CA). The polarization vs. electric field (P-E) hysteresis loops of the crystals were measured at 200 Hz using the ferroelectric test system (Precision Premier II, Radiant Technology, Inc., Albuquerque, NM, USA); the leakage current densities of the crystals were recorded using the same instrument. Cuts of the crystals with dimensions similar to those mentioned in IEEE standards were poled in silicon oil at a temperature of T O-T − 10 °C under an electric field of 30 kV/cm. The resonance and antiresonance frequencies were measured using an HP 4294 A impedance phase analyzer. The piezoelectric coefficients and electromechanical coupling factors were determined at the resonance and antiresonance frequencies, according to the IEEE standards. The piezoelectric constant d 33 * was measured using a piezo-d 33 meter (Zj-3A, Institute of Acoustics, Academic Sinica, Beijing, China).