Mechanism of Piezoelectricity for Langasite Based on the Framework Crystal Structure

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  • ABSTRACT

    Piezoelectric langasite crystals have superior properties such as high temperature performance and high quality Q and can be applied in combustion pressure sensors and surface acoustic wave (SAW) filters. Crystal growth,crystal structure and properties of langasite group are reviewed, and the mechanism of piezoelectricity of langasite is presented based on the crystal structure and deformation under high pressure. Finally, for the discovery of new piezoelectric materials, this paper presents the role of the framework, and recommends the search of framework crystal structure, because the characteristic of the mechanism exists on the framework of the crystal structure.

  • KEYWORD

    Mechanism of piezoelectricity , Framework structure of langasite , High temperature performance , Crystal structure under high pressure

  • 1. INTRODUCTION

    Langasite (La3Ga5SiO14 (LGS)) is piezoelectric crystal named according to its composition, that is, La, Ga and Silicate mineral is named langasite with "ite" as the ending of a mineral name. Over one hundred langasite group compounds have been found with the structural formula A3BC3D2O14 [1-3]. Here, A, B, C and D are element name in different sites. The piezoelectric properties have been compared with quartz SiO2, as the structure of langasite is trigonal, point group 32 same as quartz [4-7]. This compound is one of the lead-free piezoelectric materials which have been researched because the toxin Pb has been excluded for health reasons by the RoHs directive [8].

    The special characteristic of langasite is high temperature performance based on its lack of Curie point and lack of phase transition until melting point around 1500℃, and a lack of pyroelectricity, depending on whether or not the point group 32 is the same as quartz, which will be described later. The application for high temperature has been used for combustion (burning) pressure sensors in combusting engines as shown in Fig. 1(a) [9]. And, as the piezoelectric constant and the pass band filter characteristics are about 3 times that of quartz crystal, and because of near-zero TCf, langasite is a candidate for surface acoustic wave (SAW) filters as shown in Fig. 1 (b) [7].

    Moreover, langasite crystals have good points for single crystal growth. Single crystals are easily grown because of a low temperature melting point of about 1500℃ allowed use of Pt-crucible, none-phase transition, and congruent melting. And many kinds of methods can be used for crystal growth.

    In this review paper, crystal growth, crystal structure, the properties, the mechanism of piezoelectricity, and the crystal structure under high pressure are presented.

    2. CRYSTAL GROWTH OF LANGASITE

    Langasite group single crystals have been grown by many growing methods such as Czochralski (Cz) technique, Bridgeman method, floating zone (FZ) method, and micro-pulling down (μ-PD) technique, as these crystals grow easily [10-12].

    LGS, Pr3Ga5SiO14 (PGS) and Nd3Ga5SiO14 (NGS) single crystals shown in this chapter were grown by a conventional radiation frequency (RF)-heating Cz-method with an output power of 60kW by Sato et al. [12]. Starting melts formed from single-phase powder of langasite sintered at 1300℃ using high purity 99.99% raw materials were applied at a height of 40 mm in a platinum and iridium crucible that was 50 mm in diameter and 50 mm in height. The growth atmosphere was a mixture of Ar with 1 vol% of O2 gas in order to avoid the evaporation of gallium oxide from the melt during growth. The heating of melts was performed by Pt-crucible induction heating. The crucible was isolated by ZrO2 granules. Before seeding, the melts were clarified for at least 1 h. The pulling velocity and the crystal rotation rates were 1.0-1.5 mm/h and 10 rpm, respectively. The seeds used were small <001> oriented LGS single crystal rods. The growing crystals were kept at temperature by a passive double after-heating system made of alumina ceramics.

    Defect-free LGS, PGS and NGS single crystals with constant diameter of 22 mm and lengths up to 145 mm were grown as shown in Figs. 2(a), (b) and (c), respectively [12]. These ingot diameters were highly consistent over the whole length. The optimum pulling rates are lower than 1.5 mm/h for inclusion-free perfect single crystals, and a higher temperature gradient at the growing interface controls the growth, preventing distinct facet enlargement and asymmetrical growth leading to spiral morphology.

    LGS compounds with congruent melting are grown easily because of the same composition of growth crystals and liquid. In the case of solid solutions, the composition of the precipitated crystal gradually changes during crystal growth as shown in Fig. 3(a). Takeda & Tsurumi [13] presented crystal growth with homogeneous composition from quasi-congruent melt [14,15]. In the case of Al-substituted La3Ga5-xAlxSiO14 (LGASx), as the limitation of the solid solutions is located at x = 0.9 as shown in Fig. 3(b), the endmember of the solid solutions produces congruent melt. At x = 0.9 composition, good quality single crystals of LGAS0.9

    are grown as quasi-congruent melt growth.

    3. CRYSTAL STRUCTURE OF LANGASITE

    Langasite crystal structure was analyzed originally by Mill et al. [2]. The crystal structure is isostructural to Ca3Ga2Ge4O14 presented by Belokoneva et al. [1]. The crystal system is trigonal, point group 32, space group P321 (No.150), with lattice constants of approximately a = 8.1, c = 5.1 A, Z = 1, which is similar to quartz SiO2. Iwataki et al. [16] and Takeda et al. [17] determined the three langasite-groups, LGS, PGS and NGS crystals, using the initial atomic parameters presented by Mill et al. [2]. Table 1 shows the crystallographic data and experimental conditions for X-ray single crystal diffraction (XRSD) analysis.

    The crystal structure figures projected from [001] and [120] are shown in Fig. 4(a) and 4(b), respectively. The structure represented by the structural formula, A3BC3D2O14, is constructed from four sites: A-, B-, C-, and D-site projected in two ways as shown in Fig. 4. A-site is a decahedron with a coordination number (c.n.) of eight, known as twisted Thomson cube; B-site is an octahedron with a c.n. of six; and C- and D-sites are tetrahedra with a c.n. of four, as shown in Fig. 4(c). The size of D-site is slightly smaller than that of C-site. Rare earth La3+, Pr3+ and Nd3+ occupy the A-site, Ga3+ occupies the B, C and half of the D-sites, and Si4+

    half of the D-sites, respectively. This structure is constructed by a framework layer structure: B-C-D-C-D-C six-membered rings around A-site as shown in Fig. 4(a) projected from [001]. Tetrahedra C- and D-sites, and decahedra, octahedra, and open-space, form a layer structure as shown in Fig. 4(b). Large cation sites A- and B-sites, and open-spaces, makes one layer. The open-space plays an important role for piezoelectric properties as described in section 5.

    The crystal structures among LGS, PGS and NGS differ mostly in the shape of each site. In particular, the change of the A-site is remarkable. The decahedral A-site expands with the increase of ionic radius of rare earth (R) that occupies the A-site. The A-site expands greatly in [100] directions compared to the expansion in [120], which is perpendicular to [100], with the increase of the ionic radius of R.

    4. PIEZOELECTRIC PROPERITES OF LANGASITE

       4.1 Electric properties based on point group

    The point group of langasite is 32, which is the same as quartz,

    and has no inversion symmetry i. These piezoelectric materials without i are included in 20 point groups (except O = 432) of the 2nd to 7th columns shown in Table 2 [18]. Here, the 1st column is the Laue group with i, and the 3rd to 6th are for optical activity, the 5th to 7th are for pyroelectricity, and the 4th and 5th are for enantiomorphism. Ferroelectric materials are the ones with spontaneous polarization in pyroelectricity, the 5th to 7th columns. All ferroelectric materials show piezoelectricity, but the reverse is not true, that is, not all piezoelectric materials show ferroelectricity. So, the point group of piezoelectricity could be divided into two groups: one is for non-polar piezoelectricity and another is for polar piezoelectricity. It is worth pointing out that langasite in the 32 point group shows no polar piezoelectricity, that is, no pyroelectricity.

       4.2 Polarity direction by point group

    As langasite is a non-polar piezoelectric crystal, poling treatment is not necessary. However ceramics that are polycrystals show isotropic properties as a whole because each orientation of grains can turn to any direction. So, non-polar piezoelectric materials should be used as a single crystal. For a single crystal, the knowledge of the directions of piezoelectricity is very important. As the directions are the same as for polar, they could be derived based on the point group.

    Figure 5 shows the stereographic projection of general positions in the point group. Figure 5(a) shows the [001] direction without polarity because of the same number of ○ and × positions on the opposite sides of [001]. The [210] direction (Fig. 5(c)) is also non-polar by the same manner. Only the [100] direction shows polarity as shown in Fig. 5(b). The configurations of a typical crystal of the point group 32 are shown along the stereographic projections, with crystal surfaces plotted on the stereo projections. The crystal structures along [120] and [100] as shown in Fig. 5(d) and (e) show asymmetry and symmetry, respectively, along the left and right directions. Now, Fig. 6 shows a Y-cut of a crystal. Here, X, Y, and Z are Cartesian coordination, and hexagonal axis a and c also are shown.

       4.3 Piezoelectric properties of langasite

    Piezoelectric strain constants d11 of RGS (R = La, Pr and Nd) crystals are shown as a function of the ionic radius of R in Fig. 7(a) [12,16]. The d11 is dependent on the ionic radius of R, and LGS has the best piezoelectric properties among RGS (R = La, Pr and Nd) crystals. The d11 value of LGS is -6.16 × 10-12 C/N, which is 3 times that of quartz -2.3 × 10-12 C/N. Figure 7(b) shows the electromechanical coupling factor k12 as a function of the piezoelectric constant -d11 of the langasite group, including that of LGS, PGS, NGS and so on, compared to a quartz single crystal. In

    the A-site, cations with a larger ionic radius than La, such as Ba and Sr, are expected to have large d11. Langasite with Ba in the A-site could not be obtained as transparent crystal.

    On the other hand, Sr3Ga2Ge4O14 with Sr in the A-site has been studied by Wu et al. [19]. They produced transparent single crystal with a large d11 of -7.41 × 10-12 C/N, which is larger than that of LGS, as shown in Fig. 7 (b). The d11 and k12 of RGS (R = La, Pr and Nd) show just a linear relationship (Fig. 8(a)) with crystal structure AL/BL (Fig. 8(b)), which is the size ratio of A- and B- polyhedra along the a-axis.

    Figure 9 shows the electromechanical coupling factor k2 as a function of TCf of the piezoelectric materials for a communica-

    tion system. Langasite has been expected for use as a SAW filter to replace quartz and LiTaO3 because of its wide bandwidth and near-zero TCf. Quartz has low TCf, but narrow bandwidth. On the other hand, LiTaO3 has wide bandwidth but large TCf. AlPO4 and Li2B4O7 have good properties such as high k2 and near-zero TCf, but they have weak points for crystal growth. AlPO4 has growth problems such as twinning, and Li2B4O7 has weak points such as deliquescence and low growth rate [4].

    Figure 10(a) shows the temperature dependence of frequency and the equivalent series resistance of a filter made of Y-cut LGS single crystal [11]. The temperature dependence of frequency shows a secondary curve with good values of 1-2 ppm/℃. In the range of -20 to 70℃, the dependence of temperature shows good values of 100 to 150 ppm/℃. Figure 10(b) shows the equivalent series resistance as a function of vibration modes of resonators on the LGS and quartz single crystals [11]. The resistance of

    LGS is one order smaller than that of quartz. So, as if the surface roughness of LGS is large, high frequency oscillation is easy. Moreover, as the equivalent series resistances at the 7th and 9th modes are small, the LGS filter is useful as a high frequency wave area filter.

    Figure 11 shows pass band characteristic of a filter made of Ycut LGS single crystal [4,11]. Y-cut LGS single crystal has a very wide pass band characteristic width of 45 KHz at 3 dB attenuation,which is 3-times that of quartz with 15 KHz band width.This means the electromechanical coupling constant k12 of LGS is about 3-times larger than that of quartz.

    Table 3 shows the properties comparing some piezoelectric crystals such as LiTaO3, LGS, quartz, and La3Ga5.5Nb0.5O14 (LGN) [4]. The properties of LGS are between LiTaO3 and quartz. The electro-mechanical coupling factor k of LGS is 15 to 25%, located

    between that of LiTaO3 at 43%, and quartz at 7%. The temperature frequency variation of LGS is 100 to 150 ppm/℃, located between that of LiTaO3 at 200 to 400 ppm/℃, and quartz at 50 to 80 ppm/℃. Here, LGN single crystal substituted for Nb5+ and Ga3+ for Si4+ has superior piezoelectric properties.

       4.4 Ordered crystal structure and properties

    LGS, PGS and NGS are compositionally disordered crystals. The structural formulae are [R3]A[Ga]B[Ga3]C[GaSi]DO14 (R = La, Pr and Nd). Here, as the D-site is occupied disorderly by Ga and Si, these crystals are disordered. Ordered langasite structural formulas such as Sr3TaGa3Si2O14 (STGS), Sr3TaGa3Ge2O14 (STGG), Sr3NbGa3Si2O14 (SNGS), Ca3NbGa3Si2O14 (CNGS), and Ca3TaGa3Si2O14 (CTGS) are presented and characterized by Mill et al. [20] and Takeda et al. [21]. The structural formula is [Sr/Ca3]A[Nd/Ta]B[Ga3]C[Ge/Si]DO14; the large A-decahedron is occupied by Sr or Ca cations, the middle size B-octahedron by Nd or Ta cations, and C- and D-tetrahedra by the larger Ga and the smaller Ge or Si cations, respectively. The ordering should be called "compositional ordering," compared with ordering based on the order-disorder transition.

    Table 4 shows the characterization of disordered and ordered langasite-type piezoelectric single crystals at room temperature and 500℃ [22]. Though the ordered crystals possess lower piezoelectric coefficients than disordered ones at room temperature as shown in Fig. 12 [23], they possess much higher mechanical quality factor and electrical resistivity at an elevated temperature of 500℃. The high mechanical quality factor and the high electrical resistivity have been expected for use in a hightemperature bulk acoustic wave (BAW) and SAW resonator and ignition pressure sensor, respectively. The density and dielectric constant of ordered crystals are lower than those of disordered ones, which contribute to the high acoustic velocity in high frequency devices. LTGA and LNGA disordered crystals in Table 4 have substituted Al for Ga in La3R0.5Ga5.5-xAlxO14 (LRGAx, R = Ta or Nb), which contributes to the low raw material cost. Takeda et al. [24] presented LTG, LTGA0.3 and LTGA0.5 in which d14 values were increased to 3.68, 4.03 and 4.19 pC/N in that order, and resistivity increased to 2.2 × 107, 4.6 × 107 and 7.1 × 108 Ω · cm

    in that order, at 400℃ as shown in Fig. 13 [24]. The resistivity of LTGA0.5 increased to about 30 times that of LTG. Al-substituted LGS (La3Ga5-xAlxSiO14: LGASx) were also studied for high resistivity at elevated temperature and low cost, which was presented by Kumatoriya et al. [15] and Takeda et al. [24]. The piezoeoectric properties d11 and resistivity of LGAS0.9 were improved from 6.075 to 6.188 pC/N and 5.9 × 107 to 7.6 × 108 Ω · cm, respectively. The Al-substitution is effective for high resistivity and also reduces the raw material cost. The CTAS in Table 4 substituted Al for Ga completely and has a high resistivity of 2.7 × 109 Ω · cm. On the other hand, Fe-substituted langasite-type crystals are expected for use as multiferroic materials [25].

    5. CRYSTAL STRUCTURE UNDER PRESSURE AND MECHANISM OF PIEZOELECTRICITY OF LANGASITE

       5.1 Crystal structure under pressure

    In this section, the mechanism of the piezoelectricity has been presented based on the crystal structure and deformation under applied pressure. Pressures applied to the single crystals using a diamond anvil cell (DAC) as shown in Fig. 14 were calibrated by the ruby fluorescence technique. The DAC was set on the four-circle diffractometer. The unit cell parameters were refined by using the 2Θ-ω step scan technique. Table 5 shows crystallographic data of LGS and NGS including the lattice parameters measured at various pressures.

    The pressure dependence of lattice parameters (a1 and c) and unit cell volume are plotted in Fig. 15. Both lattice parameters along a1- and c-directions shrunk linearly with an increase of applied pressure. Noteworthy is that the a1-axis is preferentially shrunk compared to the c-axis. This indicates that the compression of langasite crystals occurs preferentially in the a1-a2 plane. Table 6 compares the variation polyhedra sizes along the [100]

    direction of AL, BL and SL, which are presented in Fig. 16, based on the crystal structures obtained at an atmospheric pressure of around 3 and 6 GPa [26]. Lattice parameter a1 equals the sum of AL+BL+SL. Therefore, we can consider that the preferential shrinkage observed along the a1-axis is also divided into three kinds of lengths. As seen in Table 6, the change in SL is much larger than the other lengths of AL and BL, indicating a larger contribution to shrinkage of an open-space. The open-space is surrounded by the A-, B- and C-polyhedra shared corners. In contrast, A- and B-polyhedra make shared edges with each other. When the pressure is induced in the [100] direction, it can be speculated that the corner-shared open-space is easily distorted compared with the edge-shared A- and B-polyhedra.

       5.2 Mechanism of piezoelectricity of langasite

    Iwataki et al. [16] presented the mechanism of piezoelectricity

    of langasite based on the deformation of the A-site. Piezoelectricity originates from polarization caused by the destruction of charge balance depending on the displacement of ions when pressure is induced. The piezoelectricity of langasite is known to be generated in the [100] direction. From the rule of symmetrical operation, langasite should have polarization in A- and C-polyhedra in contrast with no polarization in B- and D-polyhedra. And also, the reason for La-langasite having larger piezoelectricity than Nd-langasite is clarified.

    Figure 17. Mechanism of piezoelectricity on langasite projected from [120]. Position X is the center of oxygen atoms on A-polyhedron. Under pressure, ML does not change and NL shrinks because of the role of open-space as a damper.

    With an induced pressure, the distance ML between A and B

    cations as shown in Fig. 16 and Table 7 is not changed around 3.4 A, and the distances of NL (A ion-[open-space]- B ion) in LGS and NGS are shrunk from 4.75 to 4.65, and 4.70 to 4.58 A, respectively. On the other hand, A-polyhedron is distorted to the [-100] direction. The distortion is clarified by the shortening of the distance OL between the center position X on A-polyhedron and B-ion as shown in Figs. 16 and 17. The OL lengths of LGS and NGS are shortened from 3.27 to 3.21 A, and 3.23 to 3.17A, respectively. As a result, a dipole moment P appeared from moving the centers of mass of positive and negative charges to produce piezoelectricity. Here, the differences (ML-OL) between center positions X and A-ion positions on the LGS and NGS calculated based on crystal structure are equivalent to polarization as shown in Table 7 and Fig. 18. The values of LGS and NGS as a function of pressure are increased from 0.147 to 0.177 A (at 6.1 GPa) and 0.143 to 0.178 A (at 6.8 GPa), respectively. The value increases with pressure. So, the mechanism of piezoelectricity on the langasite structure series is presented as follows: though the A-polyhedron is deformed to [-100] with applied force, A-ion stays in the same position by repulsion force from B-ion under the existence of open-space, which has no atoms in the center and is working as a damper. The difference between A-cation and center position X should make a net dipole moment P along the a-axis. Dipole moment should be enhanced if the distance between the charge centers of cations and anions becomes large. Therefore, the enhancement of piezoelectric properties is related with the shrinkage of open-space in langasite crystal structure, and it is clear that the increase of polarization is caused by the induced pressure in the [100] direction of langasite structure.

    The reason for La-langasite having larger piezoelectricity than Nd-langasite is clarified by the difference of the ML-OL (dipole moments P). As shown in Fig. 18, the dipole moments P for LGS are larger than that for NGS.

    6. NEW PIEZOELECTRIC MATERIALS WITH FRAMEWORK CRYSTAL STRUCTURE

    Langasite is a kind of materials formed a framework structure without inversion symmetry i. Quartz and BeO also have framework structures formed mainly by a covalent bond such as SiO4, AlO4, ZnO4. Especially, silicates including langasite make many framework structures by connection of SiO4 tetrahedra as cyclo-, ino-, phyllo-, and tecto-silicates. These framework structures have been noticed recently for many kinds of properties, such as zeolite for optical properties by absorption of special compounds.

    Recently, Hosono [27] presented that Ca12Al14O32 (C12A7) clinker compound with big cages including O2- in a [Ca24Al28O64]4+ framework shows specific properties such as electride, transparent electride, transparent p-type conducting oxides, transparent semiconductor, super conductor, and other properties. The crystal structure has 12 cages of 4.4 A in diameter in a unit cell of a 12 A cube, and 2 cages of those 12 include oxygen ion (O2-) as shown in Fig. 19(a). As this O2- is bonding weakly with the framework, this ion could be removed or exchanged with other anions easily. Transparent metal oxide (C12A7:H-) transformed to electro conductor by photon-induced phase transition, C12A7 compound including much active oxygen O- atoms [28,29], and C12A7: e-electride stable in room temperature and air-condition [30] are presented by Hosono group. C12A7 crystal grown by Cockayne & Lent [31] is expected for use in SAW, because of the high SAW velocity and reasonable bulk electromechanical coupling by Whatmore (to be published). Two space groups are reported such as I43d by Cockayne & Lent [31] and I42m by Kurashige et al. [32]. The point groups are 43m and 42m, respectively. Both point groups without i show piezoelectricity, and the latter shows additional rotatory power. Moreover, additional atoms grouped in the cages of the frame structure are expected to be designed for SAW-suitable properties.

    Here, we will present a candidate for piezoelectric materials. Nepheline (KNa3Al4Si4O16) is one of the alumino-silicates with framework as shown in Fig. 19(b). The crystal structure has a hexagonal ring framework without i based on the space group P63 (No. 173), the point group 6. When stress is added to the ring, the ring will deform and cations located in tetrahedra and near the center of the ring will shift. If the center of cations and anions will become different, piezoelectricity will occur.

    7. CONCLUSIONS

    This review paper is presented about the crystal structure and mechanism of piezoelectricity of langasite. The mechanism of piezoelectricity was derived based on the crystal structure and deformation of crystal structure under high pressure. Openspace in the langasite framework structure plays a key role in the mechanism of piezoelectricity. So, the framework structure should be noticed from the point of view of the piezoelectricity. And general knowledge for properties is presented based on the point groups which are applied for derivation of the piezoelectricity direction. Moreover, there are two important aspects for applications of langasite: one is the easy crystal growth based on a low melting point of 1,470℃ resulting in no phase transition and congruent melting; another is the high performance piezoelectricity properties such as high temperature performance based on the lack of phase transition and better piezoelectric properties compared to quartz. This reviewed paper is written based on "Origin of Piezoelectricity on Langasite" [33].

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  • [Fig. 1.] (a) Combustion pressure sensor installed in cylinder for control of combustion. (b) SAW filter using langasite with low dielectric losses.
    (a) Combustion pressure sensor installed in cylinder for control of combustion. (b) SAW filter using langasite with low dielectric losses.
  • [Fig. 2.] Single crystals of langasite (a)-(c) and (d) grown by Cz-method, and by μ-PD technique, respectively.
    Single crystals of langasite (a)-(c) and (d) grown by Cz-method, and by μ-PD technique, respectively.
  • [Fig. 3.] Crystal growth from quasi-congruent melt. (a) crystal growth of solid solutions: composition of precipitated should be changed gradually. (b) formation of quasi-congruent melt at x = 0.9 due to precipitated secondary phase LaAlO3.
    Crystal growth from quasi-congruent melt. (a) crystal growth of solid solutions: composition of precipitated should be changed gradually. (b) formation of quasi-congruent melt at x = 0.9 due to precipitated secondary phase LaAlO3.
  • [Table 1.] Crystallographic data of NGS, PGS and LGS.
    Crystallographic data of NGS, PGS and LGS.
  • [Fig. 4.] Crystal structure of Langasite. (a) a1-a2 plane and (b) a1-c plane are viewed from [001] and [120], respectively. (c) four kinds of cation of cation polyhedra. is four kinds of cation polyhedra.
    Crystal structure of Langasite. (a) a1-a2 plane and (b) a1-c plane are viewed from [001] and [120], respectively. (c) four kinds of cation of cation polyhedra. is four kinds of cation polyhedra.
  • [Table 2.] Point group and properties.
    Point group and properties.
  • [Fig. 5.] Determination of piezoelectricity direction based on point group 32. Stereo graphs (a), (b) and (c) with equivalent points are projected from [001], [100], and [210], respectively. x:upper points, o: opposite points. Configurations of a crystal with point group 32 also are drawn for supporting the stereo projections. (d) and (e) show the crystal structure along [100] and [120] showing asymmetry and symmetry, respectively. Dipole moment will appear in (d).
    Determination of piezoelectricity direction based on point group 32. Stereo graphs (a), (b) and (c) with equivalent points are projected from [001], [100], and [210], respectively. x:upper points, o: opposite points. Configurations of a crystal with point group 32 also are drawn for supporting the stereo projections. (d) and (e) show the crystal structure along [100] and [120] showing asymmetry and symmetry, respectively. Dipole moment will appear in (d).
  • [Fig. 6.] Y-cut for langasite single crystal for piezoelectric measurements.
    Y-cut for langasite single crystal for piezoelectric measurements.
  • [Fig. 7.] (a) Piezoelectric constant d11 of LGS, RGS and NGS as a function of ionic radius. (b) electromechanical coupling factor k12 of langasite series as a function of d11.
    (a) Piezoelectric constant d11 of LGS, RGS and NGS as a function of ionic radius. (b) electromechanical coupling factor k12 of langasite series as a function of d11.
  • [Fig. 8.] (a) Piezoelectric constant d11/electromechanical coupling factor k12 of LGS, PGS and NGS as a function of AL/BL which is shown in (b).
    (a) Piezoelectric constant d11/electromechanical coupling factor k12 of LGS, PGS and NGS as a function of AL/BL which is shown in (b).
  • [Fig. 9.] Electromechanical coupling factor vs. temperature coefficient of frequency of piezeelectric materials.
    Electromechanical coupling factor vs. temperature coefficient of frequency of piezeelectric materials.
  • [Fig. 10.] (a) Frequency variation/equivalent series resistance as a function of temperature on the La3Ga5SiO14 filter. (b) equivalent series resistance of quartz and langasite single crystals as a function of resonator vibration modes.
    (a) Frequency variation/equivalent series resistance as a function of temperature on the La3Ga5SiO14 filter. (b) equivalent series resistance of quartz and langasite single crystals as a function of resonator vibration modes.
  • [Fig. 11.] Filter properties of La3Ga5SiO14 single crystal.
    Filter properties of La3Ga5SiO14 single crystal.
  • [Table 3.] Comparison of properties of each crystal.
    Comparison of properties of each crystal.
  • [Table 4.] Characterization of disordered and ordered langasitetype piezoelectric single crystals at room temperature and 500℃. LTG:La3Ta0.5Ga5.5O14; LNG:La3Nb5GaO14; LTGA: La3Ta0.5Ga5.3Al0.2O14; LNGA: La3Nb0.5Ga5.3Al0.2O14; SNGS: Sr3NbGa3Si2O14; STGS: Sr3TaGa3Si2O14; CNGS: Ca3NbGa3Si2O14; CTGS: Ca3TaGa3Si2O14; CTAS: Ca3TaAl3Si2O14.
    Characterization of disordered and ordered langasitetype piezoelectric single crystals at room temperature and 500℃. LTG:La3Ta0.5Ga5.5O14; LNG:La3Nb5GaO14;  LTGA: La3Ta0.5Ga5.3Al0.2O14; LNGA: La3Nb0.5Ga5.3Al0.2O14; SNGS: Sr3NbGa3Si2O14; STGS: Sr3TaGa3Si2O14; CNGS: Ca3NbGa3Si2O14; CTGS: Ca3TaGa3Si2O14; CTAS: Ca3TaAl3Si2O14.
  • [Fig. 12.] (a) Piezoelectric constant d11 as a function of lattice constant for langasite series crystals.
    (a) Piezoelectric constant d11 as a function of lattice constant for langasite series crystals.
  • [Fig. 13.] Resistivity of LTG LTGA0.3 and LTGA0.5 at elevated temperature. Al-substituted LTGA0.5 was improved by about 30 times at 400℃. Higher resistivity is expected.
    Resistivity of LTG LTGA0.3 and LTGA0.5 at elevated temperature. Al-substituted LTGA0.5 was improved by about 30 times at 400℃. Higher resistivity is expected.
  • [Fig. 14.] Schematic cross section of diamond anvil cell.
    Schematic cross section of diamond anvil cell.
  • [Table 5.] Crystallographic data of LGS and NGS under pressure.
    Crystallographic data of LGS and NGS under pressure.
  • [Fig. 15.] Lattice parameters of LGS and NGS as a function of pressure.
    Lattice parameters of LGS and NGS as a function of pressure.
  • [Table 6.] A- and B-polyhedra size AL and BL, and open-space size SL along a-axis and AL/BL for LGS and NGS. Atm.: atmosphere pressure.
    A- and B-polyhedra size AL and BL, and open-space size SL along a-axis and AL/BL for LGS and NGS. Atm.: atmosphere pressure.
  • [Fig. 16.] Sizes of A-, B-site and open space S, and atomic distances of ML, NL and OL between atoms. Position X is the center of oxygen atoms on A-polyhedron.
    Sizes of A-, B-site and open space S, and atomic distances of ML, NL and OL between atoms. Position X is the center of oxygen atoms on A-polyhedron.
  • [Table 7.] Atomic distances (ML NL) center position X-B ion distance (OL) dipole moment (ML - OL) and lattice constant of a1 of LGS and NGS along [100] direction under the pressure. Atm.: atmosphere pressure.
    Atomic distances (ML NL) center position X-B ion distance (OL) dipole moment (ML - OL) and lattice constant of a1 of LGS and NGS along [100] direction under the pressure. Atm.: atmosphere pressure.
  • [Fig. 17.] Mechanism of piezoelectricity on langasite projected from [120]. Position X is the center of oxygen atoms on A-polyhedron. Under pressure, ML does not change and NL shrinks because of the role of open-space as a damper.
    Mechanism of piezoelectricity on langasite projected from [120]. Position X is the center of oxygen atoms on A-polyhedron. Under pressure, ML does not change and NL shrinks because of the role of open-space as a damper.
  • [Fig. 18.] The difference ML-OL (dipole moment P) for LGS and NGS as a function of pressure.
    The difference ML-OL (dipole moment P) for LGS and NGS as a function of pressure.
  • [Fig. 19.] (a) Crystal structure of aluminate calcium C12A7 with framework crystal structure. New-type superior properties such as superconductor were designed from this structure. (b) nepheline structure as an example of alumino-silicates with framework.
    (a) Crystal structure of aluminate calcium C12A7 with framework crystal structure. New-type superior properties such as superconductor were designed from this structure. (b) nepheline structure as an example of alumino-silicates with framework.