Control of Thermophysical Properties of Langasite-Type La3Ta0.5Ga5.5O14 Crystals for Pressure Sensors

: We present a possible method to reduce the anisotropy of the thermal stress generated on langasite-type La 3 Ta 0.5 Ga 5.5 O 14 (LTG) piezoelectric crystals arising from the mismatch of the thermal expansion coe ﬃ cients and Young’s moduli of the crystals and metals at high temperatures. To formulate this method, the thermal stresses of order-type langasite crystals, in which each cation site is occupied by one element only, were calculated and compared to each other. Our results suggest that the largest cation site a ﬀ ects the thermal stress. We attempted to replace La 3 + in LTG by a larger ion and considered Sr 2 + . Single crystals of strontium-substituted LTG (Sr-LTG) were grown using the Czochralski method. The thermal stress along the crystallographic c -axis decreased but that perpendicular to the c -axis increased by strontium substitution into the LTG crystal. The anisotropic thermal stress was reduced e ﬀ ectively. The Sr-LTG single crystal is a superior candidate material for pressure sensors usable at high temperatures.


Introduction
In recent years, the automobile industry has been faced with a number of environmental and energy problems. Consequently, improvements to fuel efficiency and reduction in exhaust gas have been required [1]. Combustion pressure sensors are attractive devices for improving the combustion efficiency of engines. Such devices are directly placed in engine cylinders and combustion efficiency is improved by feedback control of the fuel injection based on data of the combustion pressure changes in the cylinder. An engine with a combustion pressure sensor can reduce NOx emissions by approximately 30%, and the emission of CO 2 , which is a cause of global warming, by about 10% [2]. La 3 Ga 5 SiO 14 (langasite) family single crystals are attractive piezoelectric materials for use in combustion pressure sensors because they show no phase transitions up to their melting temperature and can be easily grown to large sizes using the Czochralski (Cz) technique [3][4][5][6][7][8][9]. GaPO 4 crystals [10] and rare-earth (Re) calcium oxoborate ReCa 4 O(BO 3 ) 3 crystals [11] have also been reported to be promising candidates because the former has a high phase transition temperature of 930 • C and the latter maintains the piezoelectric property to its melting temperature of approximately 1600 • C.
However, bulk growth of GaPO 4 crystals is very difficult [12], while ReCa 4 O(BO 3 ) 3 crystals have very low crystal symmetries (monoclinic m), and then show pyroelectricity [13]. Recently, gehlenite Ca 2 Al 2 SiO 7 and related crystals in the melilite group have been the subject of much study, because they exhibit piezoelectricity without any accompanying pyroelectricity [14,15]. The crystals also have very clear cleavage planes, which is a matter of concern for target applications in combustion pressure sensors.
Among the langasite family crystals, the La 3 Ta 0.5 Ga 5.5 O 14 (LTG) single crystal is the most promising candidate [16,17] because it shows weak temperature dependence of its piezoelectric properties, and high electrical resistivity at high temperatures. Fracture of the crystal element during use is a matter of concern for combustion pressure sensors [18]. The fractures can be attributed to the high impulsive force generated during abnormal combustion. During use, thermal stresses along and perpendicular to the crystallographic c-axis are anisotropically generated at a working temperature of approximately 200 • C. At high temperatures, anisotropic thermal stress is caused by the difference in the thermal expansion coefficients and Young's moduli among the LTG crystals used as the substrate and the metals used as crystal support. Reducing the anisotropic thermal stress by applying element substitution into the LTG may be an effective way to avoid this phenomenon.
In this study, first, we describe the calculation of the thermal stress using the data of the linear thermal expansion coefficients and elastic stiffness coefficients instead of the Young's moduli, of four order-type langasite family crystals and the metal at high temperatures. Then, the candidate of the substituent element Sr was selected. We have also reported the effect of Sr substitution on the LTG crystals, which demonstrated a successful reduction in the anisotropic thermal stress.

Thermal Stress Calculation
A simplified structure surrounding the piezoelectric crystal substrate of the combustion pressure sensor was constructed for thermal stress calculation [19], as shown in Figure 1a. The piezoelectric X-cut of the crystal substrate and metal were in contact. The X-cut corresponds to the Miller plane (120) perpendicular to the crystallographic a-axis. The aand c-axes correspond to the xand z-axes, respectively. Langasite family crystals belong to a trigonal crystal system. Hence, the y-axis is the [120] direction. As the piezoelectric coefficient used in the combustion pressure sensor is d 11 , the x-, y-, and z-axes are as indicated in Figure 1. At the initial state, the length of the crystal is the same as that of the metal. As the crystal is strongly fixed by the metal part, the crystal attempts to extend with the metal during temperature rise. Under the conditions shown in Figure 1b, the expansions of the crystal ∆l c and the metal ∆l m caused by their own thermal expansions are expressed using the following Equations (1) and (2): where α c and α m are the linear thermal expansion coefficients (LTEC) of crystal and metal, respectively. ∆T is the change in temperature and l 0 is the length of both the crystal and metal at the initial temperature. As the metal is composed of polycrystals, α m does not depend on the direction, that is, it is isotropic. However, there are two types of α c (α 11 and α 33 ) in langasite family crystals. In this study, α 11 and α 33 are defined as α y (=α x ) and α z , respectively. It is assumed that the external force applied from the crystal to the metal is equal to that applied from the metal to the crystal, and this is defined as the thermal stress σ. The thermal stress generated between the crystal and the metal was calculated at 400 • C, which was the maximum working temperature. Stainless steel, composed of iron and carbon, is normally used for the metal, and its LTEC α m is assumed to be 11 × 10 −6 K −1 in the calculation [19]. The α y and α z values of the langasite family crystals were determined in this study. As both the crystal and metal were fixed, as shown in Figure 1c, both the crystal and metal tend to expand to the same length during heating. Therefore, the elongation λ of the crystal and metal from room temperature (23 • C) to the working temperature is expressed using the following Equations (3) and (4): where E c is the elastic stiffness of the crystal and E m is the Young's modulus of the metal. In general, the LTEC of metals is larger than that of crystals. Therefore, the metal is stressed by the crystal in the negative direction, and the crystal is stressed in the opposite direction. Finally, the thermal stress σ can be calculated as: As mentioned above, anisotropic α y and α z should be considered, and we have treated two types of thermal stresses σ independent of each other. Therefore, σ y and σ z along the y and z directions of the crystal were calculated. In this study, the Young's modulus of the metal was determined to be 152 GPa [19]. The elastic stiffness coefficients (EFC) of the crystal were determined by electroacoustic method, as described later. The aim of this study was to determine the ratio of σ y and σ z of the LTG crystal, σ y /σ z = 1 by element substitution. LTECs were obtained to investigate the thermal expansion anisotropy of order-type langasite family single crystals, as well as to calculate the thermal stress. The langasite-type crystals belong to the trigonal crystal system, point group 32, and space group P321. Thus, there are two independent expansion components, α11 and α33, along the crystallographic a-and c-axes, respectively. The LTECs were calculated using changes in the lattice constants a and c. Measurements were performed using a powder X-ray diffraction (XRD) method (Rigaku Ultim III SS), with a high-temperature furnace attachment, in the temperature range 23 to 500 °C, at intervals of 100 °C. We used Al2O3 polycrystal powder as the standard. The LTECs α11 and α33 were calculated by the following: where a0 (c0), Δa (Δc), and ΔT represent the initial lattice constant of the sample at room temperature and the displacements and temperature change, respectively. The values of α11 and α33 correspond to αy and αz in Figure 1, respectively. As mentioned later, the LTG crystals show high anisotropic thermal stress, that is, high ratio of αy and αz.
In the crystal structure of the langasite family, there are four types of cation sites, and the chemical formula can be represented as A3BC3D2O14. The corresponding crystal structure is schematically shown in Figure 2. A and B represent the decahedral and octahedral sites, respectively; C and D represent tetrahedral sites, with the D site being smaller than the C site. In the LTG crystal, La 3+ occupies the A sites, Ta 5+ occupies half of the B sites, and Ga 3+ occupies another half of the B sites and both the C and D sites. The langasite family crystals are classified into two types depending on their site occupation patterns [20]. One is known as a disorder-type structure (such as LGS and LTG), LTECs were obtained to investigate the thermal expansion anisotropy of order-type langasite family single crystals, as well as to calculate the thermal stress. The langasite-type crystals belong to the trigonal crystal system, point group 32, and space group P321. Thus, there are two independent expansion components, α 11 and α 33 , along the crystallographic aand c-axes, respectively. The LTECs were calculated using changes in the lattice constants a and c. Measurements were performed using a powder X-ray diffraction (XRD) method (Rigaku Ultim III SS), with a high-temperature furnace attachment, in the temperature range 23 to 500 • C, at intervals of 100 • C. We used Al 2 O 3 polycrystal powder as the standard. The LTECs α 11 and α 33 were calculated by the following: where a 0 (c 0 ), ∆a (∆c), and ∆T represent the initial lattice constant of the sample at room temperature and the displacements and temperature change, respectively. The values of α 11 and α 33 correspond to α y and α z in Figure 1, respectively. As mentioned later, the LTG crystals show high anisotropic thermal stress, that is, high ratio of α y and α z .
In the crystal structure of the langasite family, there are four types of cation sites, and the chemical formula can be represented as A 3 BC 3 D 2 O 14 . The corresponding crystal structure is schematically shown in Figure 2. A and B represent the decahedral and octahedral sites, respectively; C and D represent tetrahedral sites, with the D site being smaller than the C site. In the LTG crystal, La 3+ occupies the A sites, Ta 5+ occupies half of the B sites, and Ga 3+ occupies another half of the B sites and both the C and D sites. The langasite family crystals are classified into two types depending on their site occupation patterns [20]. One is known as a disorder-type structure (such as LGS and LTG), in which at least one of the four cation sites is occupied by two or more different elements (Ta and Ga in LTG). The other is known as an order-type structure (such as Sr 3 TaGa 3 Si 2 O 14 ), in which all cation sites are occupied by a single element [21]. In this study, we measured the LTEC using Ca 3 TaGa 3 Si 2 O 14 (CTGS) [22], Ba 3 TaGa 3 Si 2 O 14 (BTGS) [23], Ca 3 NbGa 3 Si 2 O 14 (CNGS) [24], and Ca 3 TaAl 3 Si 2 O 14 (CTAS) [25] crystals. By comparing the thermal stress ratio α y /α z of each crystal, it was found that the four sites were effective in reducing the anisotropic thermal stress of the LTG crystal. The CTGS, BTGS, CNGS, and CTAS crystal ingots have been reported in other studies [22][23][24][25]. These crystals were pulverized and used for powder XRD. As mentioned later, we found that the largest cation A site affects the thermal stress. Then, we formulated an idea to replace La 3+ in LTG by larger ions, such as Sr 2+ . On the basis of this idea, we attempted to grow strontium-substituted LTG (Sr-LTG) single crystals.
Crystals 2020, 10, x FOR PEER REVIEW 4 of 9 in which at least one of the four cation sites is occupied by two or more different elements (Ta and Ga in LTG). The other is known as an order-type structure (such as Sr3TaGa3Si2O14), in which all cation sites are occupied by a single element [21]. In this study, we measured the LTEC using Ca3TaGa3Si2O14 (CTGS) [22], Ba3TaGa3Si2O14 (BTGS) [23], Ca3NbGa3Si2O14 (CNGS) [24], and Ca3TaAl3Si2O14 (CTAS) [25] crystals. By comparing the thermal stress ratio αy/αz of each crystal, it was found that the four sites were effective in reducing the anisotropic thermal stress of the LTG crystal. The CTGS, BTGS, CNGS, and CTAS crystal ingots have been reported in other studies [22][23][24][25]. These crystals were pulverized and used for powder XRD. As mentioned later, we found that the largest cation A site affects the thermal stress. Then, we formulated an idea to replace La 3+ in LTG by larger ions, such as Sr 2+ . On the basis of this idea, we attempted to grow strontium-substituted LTG (Sr-LTG) single crystals.

Crystal Growth and Characterization
Sr-LTG crystals were grown using a conventional RF-heating Czochralski (Cz) technique. Stoichiometric amounts of oxides and carbonates with 99.99% purity, corresponding to La2.9Sr0.1Ta0.55Ga5.45O14 (Sr-LTG) were prepared and calcined at 1300 °C, for 5 h, in air. The chemical composition of the Sr-LTG was selected based on a previous study [26]. An iridium crucible was used with a diameter and height of 50 mm. The calcined powder was charged into a crucible. The growth atmosphere was achieved by flowing argon gas at 10 −3 m 3 /min and oxygen gas at 10 −5 m 3 /min. A pure LTG single crystal bar was used as the seed. The pulling rate and rotation rates were 0.5 mm/h and 15 rpm, respectively. Phase identification of the as-grown crystals was performed by powder XRD. The crystal density was calculated using the lattice parameter, and the chemical composition was determined using an electron probe microanalyzer (EPMA).
In the Sr-LTG crystals, the independent material constants consisted of two dielectric, two piezoelectric, and six elastic compliance constants (εij, dij, and sij, respectively). These material constants were determined using an impedance/gain phase analyzer (HP 4194A, Agilent) as reported previously [27,28]. The electromechanical coupling factor kij and the piezoelectric modulus were evaluated by measuring the mechanical series resonance frequency fs and parallel resonance frequency fp of the equivalent resonators. The equivalent resonators were fabricated in the form of plates according to the length-extensional vibration mode. The dielectric constants, εij, were determined by measuring the capacitances of the resonators by considering the parasitic capacitance. Figure 3 shows the temperature dependence of the lattice constants along the crystallographic a-and c-axes of the Ba3TaGa3Si2O14 (BTGS) crystal. These lattice constants changed linearly across the entire temperature range. The calculated LTEC of the a-axis was almost the same as that of the c-axis, as shown in Table 1. The LTECs at 400 °C were all positive, indicating that the LTEC of the BTGS crystal is anisotropic. To calculate the thermal stress for the langasite family crystals, the LTECs of

Crystal Growth and Characterization
Sr-LTG crystals were grown using a conventional RF-heating Czochralski (Cz) technique. Stoichiometric amounts of oxides and carbonates with 99.99% purity, corresponding to La 2.9 Sr 0.1 Ta 0.55 Ga 5.45 O 14 (Sr-LTG) were prepared and calcined at 1300 • C, for 5 h, in air. The chemical composition of the Sr-LTG was selected based on a previous study [26]. An iridium crucible was used with a diameter and height of 50 mm. The calcined powder was charged into a crucible. The growth atmosphere was achieved by flowing argon gas at 10 −3 m 3 /min and oxygen gas at 10 −5 m 3 /min. A pure LTG single crystal bar was used as the seed. The pulling rate and rotation rates were 0.5 mm/h and 15 rpm, respectively. Phase identification of the as-grown crystals was performed by powder XRD. The crystal density was calculated using the lattice parameter, and the chemical composition was determined using an electron probe microanalyzer (EPMA).
In the Sr-LTG crystals, the independent material constants consisted of two dielectric, two piezoelectric, and six elastic compliance constants (ε ij , d ij , and s ij , respectively). These material constants were determined using an impedance/gain phase analyzer (HP 4194A, Agilent) as reported previously [27,28]. The electromechanical coupling factor k ij and the piezoelectric modulus were evaluated by measuring the mechanical series resonance frequency f s and parallel resonance frequency f p of the equivalent resonators. The equivalent resonators were fabricated in the form of plates according to the length-extensional vibration mode. The dielectric constants, ε ij , were determined by measuring the capacitances of the resonators by considering the parasitic capacitance. Figure 3 shows the temperature dependence of the lattice constants along the crystallographic aand c-axes of the Ba 3 TaGa 3 Si 2 O 14 (BTGS) crystal. These lattice constants changed linearly across the entire temperature range. The calculated LTEC of the a-axis was almost the same as that of the c-axis, as shown in Table 1. The LTECs at 400 • C were all positive, indicating that the LTEC of the BTGS crystal is anisotropic. To calculate the thermal stress for the langasite family crystals, the LTECs of Ca 3 TaGa 3 Si 2 O 14 , Ca 3 NbGa 3 Si 2 O 14 , Ca 3 TaAl 3 Si 2 O 14 , and La 3 Ta 0.5 Ga 5.5 O 14 crystals were also measured using the same process used for the BTGS crystal. All the LTECs and the elastic stiffness data are provided in Table 1 for the calculation of the thermal stresses.

Results and Discussion
Crystals 2020, 10, x FOR PEER REVIEW 5 of 9 Ca3TaGa3Si2O14, Ca3NbGa3Si2O14, Ca3TaAl3Si2O14, and La3Ta0.5Ga5.5O14 crystals were also measured using the same process used for the BTGS crystal. All the LTECs and the elastic stiffness data are provided in Table 1 for the calculation of the thermal stresses.
(a) a-axis (b) c-axis  Using the ESCs and LTECs in Table 1, the thermal stresses were calculated using Equation (5) and are presented in Figure 4. The thermal stress of the LTG crystal, the most promising candidate for the combustion pressure sensor, was also calculated. The data of the LTG crystal were calculated using the values reported in previous studies [29,30]. As σy was twice the σz value in the LTG crystal, the anisotropy of thermal stress was high. There are two possible methods to reduce the anisotropy of thermal stress in LTG crystals. One method is to increase σy, and the other method is to decrease σz. By comparing the σy of CTGS, BTGS, CNGS, and CTAS crystals, it was demonstrated that the A site ion with a higher ionic radius effectively increased the value of σy. However, as the σz values were the same in all the crystals used in this study, it was inferred that not all substituent elements led to a decrease in the σz of the LTG. Therefore, by substituting atoms with larger ionic radii for the A site, such as CTGS and BTGS, it was expected that the anisotropy of the thermal stress could be reduced by increasing σy. Bi 3+ (1.17 Å), Na + (1.18 Å), Sr 2+ (1.26 Å), Pb 2+ (1.29 Å), and Ba 2+ (1.42 Å) were possible candidates for ions with an ionic radius larger than that of La 3+ (1.16 Å) [31]. The ionic radii of Bi 3+ and Na + are almost the same as that of La, and the change in the anisotropy of the thermal stress should be small. Moreover, Pb 2+ was excluded because of its toxicity, and Ba 2+ was not considered because it is difficult to introduce Ba 2+ into the LTG crystal lattice [26]. Therefore, in the present study, the growth of Sr-LTG single crystals was attempted based on a previous study [26].  Using the ESCs and LTECs in Table 1, the thermal stresses were calculated using Equation (5) and are presented in Figure 4. The thermal stress of the LTG crystal, the most promising candidate for the combustion pressure sensor, was also calculated. The data of the LTG crystal were calculated using the values reported in previous studies [29,30]. As σ y was twice the σ z value in the LTG crystal, the anisotropy of thermal stress was high. There are two possible methods to reduce the anisotropy of thermal stress in LTG crystals. One method is to increase σ y , and the other method is to decrease σ z . By comparing the σ y of CTGS, BTGS, CNGS, and CTAS crystals, it was demonstrated that the A site ion with a higher ionic radius effectively increased the value of σ y . However, as the σ z values were the same in all the crystals used in this study, it was inferred that not all substituent elements led to a decrease in the σ z of the LTG. Therefore, by substituting atoms with larger ionic radii for the A site, such as CTGS and BTGS, it was expected that the anisotropy of the thermal stress could be reduced by increasing σ y . Bi 3+ (1.17 Å), Na + (1.18 Å), Sr 2+ (1.26 Å), Pb 2+ (1.29 Å), and Ba 2+ (1.42 Å) were possible candidates for ions with an ionic radius larger than that of La 3+ (1.16 Å) [31]. The ionic radii of Bi 3+ and Na + are almost the same as that of La, and the change in the anisotropy of the thermal stress should be small. Moreover, Pb 2+ was excluded because of its toxicity, and Ba 2+ was not considered because it is difficult to introduce Ba 2+ into the LTG crystal lattice [26]. Therefore, in the present study, the growth of Sr-LTG single crystals was attempted based on a previous study [26].  Table 1. CTGS, BTGS, CNGS, CTAS, and LTG are the abbreviations for Ca3TaGa3Si2O14, Ba3TaGa3Si2O14, Ca3NbGa3Si2O14, Ca3TaAl3Si2O14, La3Ta0.5Ga5.5O14, respectively.
Growth of Sr-LTG crystals has been reported [26], and therefore the starting composition of Sr-LTG was set as La2.9Sr0.1Ta0.55Ga5.45O14. The Sr-LTG single crystal without any inclusions was successfully grown by the Cz method, as shown in Figure 5. The Sr-LTG crystals grown, in this study, were transparent, orange in color, and 23 mm in diameter and 70 mm in length. The upper part of the boule contained six developed flat surfaces, which consisted of planes parallel to the <001> growth direction. Backscattering Laue X-ray analysis showed that the flat surfaces correspond to {100} planes. Small cracks and bubbles were observed in the lower part of the boule. All peaks of the crystal powder XRD patterns agreed with those of the LTG structure. We carefully eliminated these macro defects via proper sample preparation, including cutting and polishing, for material constant measurement. The solidification fraction, g = Wcrystal/Winitial, where Wcrystal and Winitial are the weights of the grown crystal and the starting melt, respectively, was 0.36. The Sr content of the LTG crystal was smaller than that of the starting raw materials, taking into account the accuracy of EPMA analysis conducted in this study. This result agrees well with that reported in [26]. The grown crystal was pulverized, and its powder was also used for measurement of LTEC. The ESC and LTEC of the Sr-LTG crystal were measured, and the thermal stresses σy and σz were calculated and are listed in Table 2, along with those of the LTG crystal [29]. The ESCs, cy and cz, were higher and lower, respectively, for Sr-LTG than for LTG, indicating that the LTG crystal lattice was hardened along the direction perpendicular to the c-axis and softened along the c-axis, due to Sr substitution, respectively. The reasons for this should be clarified from the viewpoint of changes to crystal structure by Sr substitution. Detailed structural analysis is currently under investigation. The thermal stresses, αy and αz, of the Sr-LTG crystal were higher and lower than those of the LTG crystal, respectively. Thus, the thermal stress ratio αy/αz of the Sr-LTG crystal was closer to unity than that of  Table 1 Growth of Sr-LTG crystals has been reported [26], and therefore the starting composition of Sr-LTG was set as La 2.9 Sr 0.1 Ta 0.55 Ga 5.45 O 14. The Sr-LTG single crystal without any inclusions was successfully grown by the Cz method, as shown in Figure 5. The Sr-LTG crystals grown, in this study, were transparent, orange in color, and 23 mm in diameter and 70 mm in length. The upper part of the boule contained six developed flat surfaces, which consisted of planes parallel to the <001> growth direction. Backscattering Laue X-ray analysis showed that the flat surfaces correspond to {100} planes. Small cracks and bubbles were observed in the lower part of the boule. All peaks of the crystal powder XRD patterns agreed with those of the LTG structure. We carefully eliminated these macro defects via proper sample preparation, including cutting and polishing, for material constant measurement. The solidification fraction, g = W crystal /W initial , where W crystal and W initial are the weights of the grown crystal and the starting melt, respectively, was 0.36. The Sr content of the LTG crystal was smaller than that of the starting raw materials, taking into account the accuracy of EPMA analysis conducted in this study. This result agrees well with that reported in [26]. The grown crystal was pulverized, and its powder was also used for measurement of LTEC.
Crystals 2020, 10, x FOR PEER REVIEW 6 of 9  Growth of Sr-LTG crystals has been reported [26], and therefore the starting composition of Sr-LTG was set as La2.9Sr0.1Ta0.55Ga5.45O14. The Sr-LTG single crystal without any inclusions was successfully grown by the Cz method, as shown in Figure 5. The Sr-LTG crystals grown, in this study, were transparent, orange in color, and 23 mm in diameter and 70 mm in length. The upper part of the boule contained six developed flat surfaces, which consisted of planes parallel to the <001> growth direction. Backscattering Laue X-ray analysis showed that the flat surfaces correspond to {100} planes. Small cracks and bubbles were observed in the lower part of the boule. All peaks of the crystal powder XRD patterns agreed with those of the LTG structure. We carefully eliminated these macro defects via proper sample preparation, including cutting and polishing, for material constant measurement. The solidification fraction, g = Wcrystal/Winitial, where Wcrystal and Winitial are the weights of the grown crystal and the starting melt, respectively, was 0.36. The Sr content of the LTG crystal was smaller than that of the starting raw materials, taking into account the accuracy of EPMA analysis conducted in this study. This result agrees well with that reported in [26]. The grown crystal was pulverized, and its powder was also used for measurement of LTEC. The ESC and LTEC of the Sr-LTG crystal were measured, and the thermal stresses σy and σz were calculated and are listed in Table 2, along with those of the LTG crystal [29]. The ESCs, cy and cz, were higher and lower, respectively, for Sr-LTG than for LTG, indicating that the LTG crystal lattice was hardened along the direction perpendicular to the c-axis and softened along the c-axis, due to Sr substitution, respectively. The reasons for this should be clarified from the viewpoint of changes to crystal structure by Sr substitution. Detailed structural analysis is currently under investigation. The thermal stresses, αy and αz, of the Sr-LTG crystal were higher and lower than those of the LTG crystal, respectively. Thus, the thermal stress ratio αy/αz of the Sr-LTG crystal was closer to unity than that of The ESC and LTEC of the Sr-LTG crystal were measured, and the thermal stresses σ y and σ z were calculated and are listed in Table 2, along with those of the LTG crystal [29]. The ESCs, c y and c z , were higher and lower, respectively, for Sr-LTG than for LTG, indicating that the LTG crystal lattice was hardened along the direction perpendicular to the c-axis and softened along the c-axis, due to Sr substitution, respectively. The reasons for this should be clarified from the viewpoint of changes to crystal structure by Sr substitution. Detailed structural analysis is currently under investigation.
The thermal stresses, α y and α z , of the Sr-LTG crystal were higher and lower than those of the LTG crystal, respectively. Thus, the thermal stress ratio α y /α z of the Sr-LTG crystal was closer to unity than that of the LTG crystal. Consequently, the anisotropy of the thermal stress was effectively reduced by the Sr substitution into the LTG lattice. Electromechanical properties were characterized using the (XYt)θ • (θ = 0, 30, 60, and −30) substrates of the Sr-LTG crystals. The d 11 values determined were 5.81 pC/N for the Sr-LTG. The magnitude of the piezoelectric d 11 coefficient for Sr-LTG was lower than that for LTG (7.06 pC/N [32]). The reduction by Sr substitution has been previously reported [26]. The reason for this remains under consideration and will be clarified by combining the detailed crystal structural analysis and characterization of all the electromechanical coefficients. The d 11 coefficient was still higher than the d 11 values of quartz (2.30 pC/N [33]), and hence suggested that the Sr-LTG crystal is a superior candidate material for combustion pressure sensors.

Conclusions
In this study, we formulated a method to reduce the anisotropy of the thermal stress generated on LTG crystals when the LTG crystal was used as a combustion pressure sensor. This was achieved by comparing the anisotropy of the thermal stress of order-type langasite family crystals. The solution included the A site (La 3+ ) in the LTG crystal being substituted with the larger Sr 2+ ions. Therefore, the crystal growth of Sr-LTG was undertaken using the Cz method. The Sr-LTG single crystal without any inclusions was successfully grown. By Sr substitution, the thermal stress ratio α y /α z of the LTG crystal was effectively reduced, while maintaining the piezoelectric property. We conclude that the Sr-LTG single crystal is a superior candidate material for pressure sensors usable at high temperatures.