Origin of Piezoelectricity on Langasite

Piezoelectric materials produce polars in the crystal structure and charges on the surface of the crystal, when the crystals are stressed mechanically as shown in Figure 1(a). The surface charges leads to a voltage difference between the two surfaces of the crystal. On the contrary, when the crystals are applied with an electric field, they exhibit mechanical strain or distortion as shown in Figure 1(b).


Introduction
Piezoelectric materials produce polars in the crystal structure and charges on the surface of the crystal, when the crystals are stressed mechanically as shown in Figure 1(a). The surface charges leads to a voltage difference between the two surfaces of the crystal. On the contrary, when the crystals are applied with an electric field, they exhibit mechanical strain or distortion as shown in Figure 1   The crystal structure of piezoelectric materials should be no center of symmetry i that is inversion symmetry. Figure 2(a) and 2(c) shows the crystal structure with i and without i, respectively. The first one is NaCl structure with i, in which the centers of mass of positive charges and negative charges are in the same position. This case, a net dipole moment P does not appear in the crystal structure. Under mechanical stress, also the P moment does not appear, though the polarity appears under the electric field. The second one is ZnS zincblende without i, in which the centers of mass of positive and negative charges are in the same position as shown in Figure 2(c). However, under stress as shown in Figure 2(d), the centers of mass of positive charges and negative charges are in different positions. In this case, a net dipole moment P appears in the crystal structure, which is piezoelectricity.
These piezoelectric materials without i are included in point groups (except O = 432) of 2 nd to 7 th columns as shown in Table 1. Here, the 1 st column is Laue group with i, and 3 rd to 6 th for optical activity, 5 th to 7 th for pyroelectricity, and 4 th and 5 th for enantiomorphism. Ferroelectric materials are ones with spontaneous polarization in pyroelectricity 5 th to 7 th . All ferroelectric materials show piezoelectricity, but the reverse is not true, that is, not all piezoelectric materials show ferroelectricity.
Piezoelectric materials such as quartz, topaz, Rochelle salt, and tourmaline and so on were discovered in 1880 by the Curie brothers. Quartz single crystal is one of the most useful piezoelectric materials. The point group is 32 of the 4 th group in Table 1 which is none polar piezoelectric material. As the electromechanical coupling factor is small but temperature coefficient of resonant frequency (TCf) is near zero ppm/ o C, quartz has been used for bulk transducer and SAW devices. Artificial quartz single crystals fabricated by hydrothermal synthesis have been used for these devices because natural single crystals are deteriorated by Brazil-type twin weaken the piezoelectricity due to co-existence of right and left hand crystals (Figure 3(a)) in a crystal as shown. The twin brings high symmetry producing mirror symmetry by screw axes 3 1 and 3 2 as shown in Figure 3(b). Lithium Niobate LiNbO 3 (LN) and Lithium Tantalate LiTaO 3 (LT) single crystals are used widely for SAW filter, resonator et al., which are treated poling for adjusting the polar directions because of the ferroelectrocity based on the point group 3m and space group R3c.
Lead-zirconate-titanate Pb(Zr,Ti)O 3 (PZT) ceramics located on the morphtropic phase boundary (MPB) co-existing trigonal and tetragonal phases has been used for bulk piezoelectricity transducer, resonator, and SAW filter, as it shows excellent piezoelectricity that has a huge electromechanical coupling factor. Though the PZT is standing at a critical moment because of toxins for health, still it is being used for industrial applications. As PZT ceramics composed by tetragonal and trigonal crystals, point group 4mm (space group: P4mm) and 3m (R3m), respectively, belonging No.7 th group in Table 1, they are ferroelectrics having polar. So, poling treatments are useful for improving the piezoelectricity. The properties of the binary PZT compound between PbZrO 3 and PbTiO 3 are improved more adding Pb(Mg 1/3 Nb 2/3 )O 3 . The three components perovskite compounds are used IF SAW filter on 10 to more MHz region. Furthermore, the properties of these perovskite compounds are improved by applying single crystals by Hosono & Yamashita (2004) as shown in Figure 4.
Recently, Pb-free piezoelectric materials have been researched because of the toxin of Pb for health. It was applied as restriction of hazardous substances (RoHs) from 1 July 2006   that new electrical and electronic equipment put on the market does not contain lead, mercury, cadmium, hexavalent chromium, polybrominated biphenyls (PBB) or polybrominated diphenyl ethers (PBDE) as appeared in Article 4 of the directive [web site 1]. Lead in electronic ceramic parts (e.g. piezoelectric devices) has been excluded from the RoHs directive as appeared in the Annex of the directive. There are candidate materials for the Pb-free piezoelectric materials such as niobate based ceramics group, tungsten-bronze group, and perovskite relative materials. In the author's laboratory, KNO 3 being basically hard sintering materials was successfully formed as high density ceramics co-doping of La 2 O 3 and Fe 2 O 3 by Kakimoto et al. (2004), and Guo et al. (2004) found [Li 0.06 (Na 0.5 K 0.5 ) 0.94 ]NbO 3 ceramics with excellent piezoelectric constant d 33 values reach 235 pC/N on the MPB. Saito (2004) also fabricated highly orientated (Na 0.5 K 0.5 )NbO 3 -LiTaO 3 (NKN-LT) ceramics by template method. With the d 33 values reach 400 pC/N. Langasite La 3 Ga 5 SiO 14 (LGS) group crystals are also Pb-free piezoelectric material, which are being reviewed just in this chapter, presented by  and Kaminskii et al., (1983).
The target of in this chapter is to state mechanism of piezoelectricity on Langasite. So, some mechanisms of piezoelectricity should be presented here. Figure 5 shows mechanism of piezoelectricity in the case of BeO. Figure 5(a) is crystal structure of BeO in the absence of an applied force, here, +: Be, -:O. Under an applied force, the center of mass for positive and negative ions are different positions producing a net dipole moment P which generate negative and negative charges on the surfaces as shown in Figure 5(b). In the case of quartz SiO 2 which is the most important piezoelectric material, the structure is also constructed by six membered SiO 4 rings. The mechanism of piezoelectricity is similar with BeO, which is produced by the deformation of the six membered ring. Perovskite structures which are very important crystal structure for electro materials show very great piezoelectricity. The structure has some polymorphs such as cubic, tetragonal, orthorhombic and hexagonal. Cubic structure has center of symmetry i, and transform to tetragonal without i at curie temperature about 120 o C for BaTiO 3 .
In this chapter, LGS, Pr 3 Ga 5 SiO 14 (PGS) and Nd 3 Ga 5 SiO 14 (NGS) single crystals grown by Czochralski method were analysed the crystal structure by X-ray single crystal diffraction (XRSD) and clarified the differences of crystal structure. The mechanism of the piezoelectricity was clarified based on the crystal structure, which was confirmed by the deformation of the crystal structure under high pressure. Also relationships between the crystal structure and the properties are discussed, and it was also clarified that LGS has higher piezoelectric properties than NGS.

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, micro-pulling down (-PD) technique, as these crystals grow easily because of a low melting point around 1470 o C being able to use stably Pt-crucible, no phase transition and congruent melting. The most useful method is Cz-method which is pulling up a single crystal using the seed crystal from melts in a crucible heated (Figure 6(a)-(c)). Bridgeman method is easy, which is grown in a crucible with gradient temperature spontaneously nucleating in the bottom of the crucible. FZ-method has a melting and crystallizing zone between seed crystal and sintered ceramic rod with same composition as grown crystal, which is grown without contamination because of no crucible. The viscosity of langasite crystals is considered suitable for FZ-method, because the ratio between oxygen ions and cations in tetrahedra C and D-site in the crystal structure A 3 BC 3 D 2 O 14 is 2.8, locating near one dimensional or ring framework with 3. -PD method is special which grows long size thin single crystal with around 1mm  by few cm meters to over one meter (Figure 6(d)). A single crystal grows during pulling down from the bottom small hole of a container made by a heater such as Pt.
LGS, PGS and NGS single crystals as shown used in this chapter were grown by a conventional radiation frequency (RF)-heating Cz-method with output power 60kW by . Starting melts formed from single-phase powder of langasite sintered 1300 o C using high purity 99.99 % low materials were applied a height of 40 mm in platinum and iridium crucible with 50 mm in diameter and 50 mm in height. The growth atmosphere was a mixture of Ar and 1 vol % of O 2 gases in order to avoid the evaporation of gallium oxide from the melt during growth. The heating of melts was performed by Pt-crucible itself by induction heating. The crucible was isolated by ZrO 2 granules. Before seeding, the melts was clarified during 1 h at least. The pulling velocity and the crystal rotation rates were 1.0-1.5 mm/h and 10 rpm, respectively. The seeds were used a small <001> oriented LGS single crystal rods. Growing crystal was kept the 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 Figure 6(a), (b) and (c), respectively . These ingot diameters were high constancy over the whole length. The optimum pulling rates are not exceeding 1.5 mm/h for inclusion-free perfect single crystals, and a higher temperature gradient at the growing interface controls the growth preventing a distinct facet enlargement and asymmetrical growth leading to spiral morphology. LGS compounds with congruent melting are grown easily because of same composition of growth crystals and liquid. In the case of solid solutions, composition of precipitated crystal gradually changes during crystal growth as shown in Figure 7(a). Takeda & Tsurumi (2011) presented crystal growth with homogeneous composition from quasi-congruent melt (Takeda, 1998, Kumatoriya et al., 2001. In the case of Al-substituted La 3 Ga 5-x Al x SiO 14 (LGASx), as the limitation of the solid solutions is located at x = 0.9 as shown in Figure 7(b), endmember of the solid solutions makes congruent melt. At x = 0.9 composition, good quality single crystals of LGAS0.9 are grown as named quasi congruent melt growth.  Table 2. Crystallographic data and reliability factors for crystal structure analysis of NGS, PGS and LGS.

Crystal structure of langasite
Langasite crystal structure was analyzed originally by . The crystal structure is isostructural to Ca 3 Ga 2 Ge 4 O 14 presented by Belokoneva et al. (1980). The crystal system is trigonal, point group 32, space group P321 (No.150), lattice constants approximately a = 8.1, c = 5.1 Å, Z = 1, which is similar as quartz SiO 2 . We determined the three langasite-group LGS, PGS and NGS crystals using the initial atomic parameters presented by . Table 2 shows the crystallographic data and experimental conditions for X-ray single crystal diffraction (XRSD) analysis. Sphere single crystals around 0.04 mm diameter grounded a cut single crystal were used for the single-crystal structure analysis performed by a four-circle diffractometer with graphite monochrometer. After X-ray intensity data collected with MoK radiation were corrected based on Lorentz and polarization (Lp) correction and absorption, the refinements of the crystal structure were performed by fullmatrix least-squares program RADY (Sasaki, 1982). The site occupancy of D-site Ga:Si was obtained from multiplicity g determined by the linear constrain as follows: On the procedure of crystal structure analyzing, a scale factor, coordinates of each atoms, and anisotropic temperature factors were refined, and at final step of refinement, anisotropic extinction corrections were performed.  (Iwataki, 2002, Master thesis). The equivalent isotropic temperature factors (Beq.) were calculated using anisotropic temperature factors by following equation: The B eq. values are reasonable as around 0.7 for cations and 1.5 for oxygen ions.

langasite and properites
Langasite shows piezoelectricity but none ferroelectricity, based on crystallographic point group 32 belonging the 4 th group in Table 1. This point group is the same with that of quartz showing excellent piezoelectricity. As langasite is none polar piezoelectric crystal, poling treatment is not necessary. However ceramics that is polycrystals show isotropic properties as a whole because each orientation of grains turns to every 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 one of polar, they could be derived based on the point group. The Piezoelectric constants of the point group 32 for langasite is as following tensor: (4) Figure 9 shows the stereographic projection of general positions on point group. Figure 9( (Figure 9(c)) also is non-polarity by the same manner. Only [100] direction shows polarity as shown in Figure  9(b). The configurations of a typical crystal with a point group 32 are shown along the stereographic projections, which crystal surfaces are plotted on the stereo projections. The crystal structures along [120] and [100] as shown in Figure 9(d) and (e) show asymmetry, and symmetry, respectively, along left and right directions. Now, Figure 10 shows Y-cut of crystal. Here, X, Y, and Z are Cartesian coordination, and hexagonal axis a and c also are shown. showing asymmetry and symmetry, respectively. Dipole moment will be appeared in (d).
Figure 11(a) shows equivalent series resistance as a function of vibration modes of resonators on the LGS and quartz single crystals (Shimamura, 1996). 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 high vibration mode as 7 th and 9 th are small, LGS filter is useful for high frequency wave area filter. Figure 11(b) shows electromechanical coupling factor k 12 as a function of piezoelectric constant -d 11 on the langasite group such as LGS. PGS, NGS and so on, comparing quartz single crystal. Figure 12(a) shows electromechanical coupling factor k 2 as a function of TCf on the piezoelectric materials. The value of langasite is near zero. Figure 12(b) shows temperature dependence of frequency and equivalent series resistance of filter made of Y-cut LGS single crystal (Shimamura, 1996). The temperature dependence of frequency shows a secondary curve with good values of 1-2 ppm/ o C. In the range of -20 to 70 o C, the dependence of temperature is good value of 100 to 150 ppm/ o C. Table 4 shows the properties comparing some piezoelectric crystals such as LiTaO 3 , LGS, quartz, and La 3 Ga 5.5 Nb 0.5 O 14 (LGN) ). The properties of LGS locate between LiTaO 3 and quartz. Electro-mechanical coupling factor k of LGS is 15 to 25 % locating between that of LiTaO 3 43 % and quartz 7 %. The temperature frequency variation of LGS is 100 to 150 ppm/ o C locating between that of LiTaO 3 200 to 400 ppm/ o C and quartz 50 to 80 ppm/ o C. Here, LGN single crystal substituted Nb 5+ and Ga 3+ for Si 4+ has superior properties for piezoelectric properties. Figure 13 shows Pass band characteristic of filter made of Y-cut LGS single crystal (Fukuda, 1995). 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 K 12 of LGS is about 3-times larger than that of quartz.

Ordered crystal structure and properties
LGS, PGS and NGS having been described here are compositionally disordered crystals.  Mill et al., (1998) and Takeda et al., (2000). The structural formula is large A-decahedron is occupied by Sr or Ca cations, 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 as "compositional ordering" compared with ordering based on the order-disorder transition. Table 5 shows characterization of disordered and ordered langasite-type piezoelectric single crystals at room temperature and 500 o C (Zhang, 2009). Though the ordered crystals posess lower piezoelectric coefficients than disordered ones at room temperature, they posess much higher mechanical quality factor and electrical resistivity at elevated temperature of 500 o C. The high mechanical quality factor and the high electrical resistivity has been expected for a high-temperature bulk acoustic wave (BAW) and SAW resonator and ignition pressure sensor, respectively. Density and dielectric constant of ordered cyrstals are lower than those of disordered ones, which contribute to the high acoustic velocity on the high frequency devices. LTGA and LNGA disordered crystals in the Table 5 are substituted Al for Ga on the La 3 R 0.5 Ga 5.5-x Al x O 14 (LRGAx, R=Ta or Nb), which are contributed to the low raw material cost. Takeda et al. (2005) presented LTG, LTGA0.3 and 0.5 in which d 14 values are increased 3.68, 4.03 and 4.19 pC/N in the order, and those resistivity increased 2.2 x 10 7 , 4.6 x 10 7 and 7.1 x 10 8 •cm in the order at 400 o C as shown in Figure 14 (Takeda et al., 2005). The resistivity of LTGA0.5 increased about 30 times of that of LTG. Also Alsubstituted LGS (La 3 Ga 5-x Al x SiO 14 : LGASx) are studied for high resistivity at elevated temperature and low cost, which are presented by Kumatoriya et al. (2001), Takeda et al. (2002). The piezoeoectric properties d 11 and resistivity of LGAS0.9 was improved from 6.075 to 6.188 pC/N and 5.9 x 10 7 to 7.6 x 10 8 •cm, respectively. The Al-substitution is effective for high resistivity and also reduce the raw material cost. CTAS in the Table 5 is substituted Al for Ga compleatly which has high resistivity of 2.7x10 9 •cm. On the other hand, Fe-substituted langasite-type crystals are expected for multiferroic materials (C. Lee, et al., 2010).

Mechanism of piezoelectricity of langasite based on the crystal structure
In this section, mechanism of piezoelectricity of langasite will be presented based on the crystal structure. Fukuda et al. (1995) and Sato et al. (1998) presented an excellent relationship between the piezoelectric properties of LGS, PGS and NGS, and the lattice parameters and the ionic radius of R-ion in A-decahedron as shown in Figure 15(a) and (b), respectively. Now, we will consider the reason why LGS has the best piezoelectric properties among LGS, PGS and NGS. The volumes of A-site increase depending on the ionic size, and the lattice parameter of a-axis elongates by 0.100 Å larger than that 0.023 Å of c-axis based on the crystal structure as described section 3. Deformation of A-site along [100] direction might bring the piezoelectricity. The direction is just direction generating the piezoelectricity as shown in Figure 9 described in the Section 4. So, we will consider the deformation of A-site based on the crystal structure obtained. Figure 16 shows the deformation of A-decahedron. This decahedron is a twisted Thomson cube with 8 coordination numbers composed of three kinds of oxygen ions: O1, O2 and O3 as shown in Table 3 in Section 3. Here, important oxygen ions for the deformation are named by I, II and III as shown in Figure 16. The I anion is O3, and the II and III anions are equivalent of O2 by 3-fold axis. Here, O1 on the top oxygen of D-tetrahedron just located on the 3-fold axis. These I, II and III anions are shifted toward arrow direction in Nd, Pr and La order based on the crystal structure obtained. For the III anion, coordinate x increased, and y also increased. On the contrary, for the II anion, coordinate x decreased and y also decreased. As a result, the A-site deforms anisotropically as expanding to [100] and shrinking to [120] direction. Though other sites also deform a little, the explanations will be elsewhere because it is not so important for piezoelectric properties in this crystal structure. This A-site deformation compared with B-site: A L /B L as shown in Figure 17(a) has relationships with piezoelectric constant d 11 and electromechanical coupling factor k 12 as shown in Figure 17 Iwataki et al. (2001) also shows relationship between A L1 /A L2 and piezoelectric modulus |d 11 | as shown in Figure 18. Here, A L1 is same length with A L as shown in Fig.17, and A L2 is length along [120] of A-polyhedron. As seen from Figure 18( with the ionic radius of R and the piezoelectric modulus also increases. The ratio shows distortion of A-polyhedron, and large distortion brings high d 11 .
LGS with large La ion brings larger d 11 more than PGS and NGS with Pr and Nd, respectively.  We will consider a mechanism for piezoelectricity based on the information obtained before. The direction for piezoelectricity is [100] direction based on point group 32 as shown in Figure 9 described in Section 4. Along the [100] direction, there are two cation polyhedra: Adecahedron and B-octahedron, and open-space located among the polyhedra, which play an important role for piezoelectricity as sown in Figure 19. B-ions in octahedron locate on the With an induced pressure, though all polyhedra are compressed, distances between cations show different movements. The distance between A and B shows no change, and that between A and B' shows shrinkage. This phenomenon could be explained by the existence of open-space, that is, no change in the distance between A and B should be generated by the repulsion between the cation charges and by the role of shock absorption of the openspace. The shrinkage between A and B' is generated by the shock absorption of the openspace. As a result, the position of A-cation is shifted from the center of the decahedron, so, it brings the piezoelectricity that the centers of mass of positive charges and negative charges are in different positions.

Crystal structure and piezoelectricity under pressure
In this section, the mechanism of the piezoelectricity presented imaginary in section 5 will be confirmed under applied pressure. Pressures applied to the single crystals using a diamond anvil cell (DAC) as shown in Figure 20 were calibrated by the ruby fluorescence technique. The DAC was putted on the four-circle diffractmeter. The unit cell parameters were refined by using the 2- step scan technique. Table 6 shows crystallographic data of LGS and NGS including the lattice parameters measured at various pressures. The pressure dependence of lattice parameters (a 1 and c) and unit cell volume are plotted in Figure 21. Both of lattice parameters along a 1 -and cdirections shrunk linearly with an increase of applied pressure. Noteworthy is that the a 1axis is preferentially shrunk direction compared to the c-axis. This indicates that the compression of langasite crystals occurs preferentially in the a 1 -a 2 plane.  LGS NGS Atm.  (7) 1.14(5) 1.43 (7) 1.57 (8) 0.553 (7) Ga1 1a (7) 0.667 (6) 1.31 (6) 1.60 (7) 1.46 (7) 0.559 (7) Ga1 1a 1000 Ga2 3f 1 0.76460(6) 0 1/2 Ga3 0.5 Si 0.5 O1 2d 11 / 3 2 / 3 0 . 1 9 6 ( 1 ) 0.3104 (7) Table 7 shows atomic parameters of LGS and NGS under pressure. The site occupancies of Ga and Si ions on the D-site are fixed to 0.5 according to the data as shown in Table 3. The temperature coefficients are calculated from anisotropic temperature coefficients obtained. Bond lengths and volumes of this structure are calculated from these data. Table  8 compares the variation of A L , B L and S L , presented in Figure 22, along [100] direction between atmospheric pressure, around 3 and 6 GPa. Lattice parameter a 1 equals the sum of A L +B L +S L . Therefore, we can consider that preferential shrinkage observed along a 1axis is also divided into three kinds of length. As seen in Table 8 LGS    Piezoelectricity is originated 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. We have already stated the mechanism of piezoelectricity imaginary on Langasite as shown in Figure 19 in section 5. In this section, evidence of the mechanism is clarified based on crystal structure analysis under the pressure. And also, the reason of La-langasite having larger piezoelectricity than Nd-langasite is clarified. With an induced pressure, distance M L between A and B cations as shown in Figure 22 and Table 9  Here, differences (M L -O L ) 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  9, and Figure 24. The values of LGS and NGS as a function of pressure are increased from 0.147 to 0.177 Å (at 6.1 GPa) and 0.143 to 0.178 Å (at 6.8 GPa), respectively. The value increases with pressure. So, the mechanism of piezoelectricity on the langasite structure series is clarified as follows: though the A-polyhedron is deformed to [ 100  ] with applied force, A-ion stay on 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 damper. The difference between A-cation and center position X should make a net dipole moment P along 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 [1 0 0] direction of langasite structure.
The reason of La-langasite having larger piezoelectricity than Nd-langasite is clarified by the difference of the M L -O L (dipole moments P). As shown in Figure 24, the dipole moments P for LGS are larger than that for NGS.

New piezoelectric materials with framework structure
Langasite is a kind of materials with framework structure without inversion symmetry i. quartz and BeO are also framework structure which is formed mainly by a covalent bond such as SiO 4 , AlO 4 , ZnO 4 . Especially, silicates including langasite make many framework structures by connection of SiO 4 tetrahedra as cyclo-, ino-, phyllo-, and tecto-silicates. These framework structures are noticed recently for applications on many kinds of properties such as zeolite for optical properties by absorption of special compounds.
Here, we will present a candidate for piezoelectric materials. Nepheline (KNa 3 Al 4 Si 4 O 16 ) is one of the alumino-silicates with framework as shown in Figure 25(a). The crystal structure has hexagonal ring framework without i based on the space group P6 3 (No. 173), the point group 6. When stress will be added to the ring, the ring will deform and cations located in tetrahedra and near the center of ring will shift. If the center of cations and anions will become different, piezoelectricity will occur.
Recently, Hosono (2010) presented that Ca 12 Al 14 O 32 (C 12 A 7 ) clinker compound with big cages including O 2-in a [Ca 24 Al 28 O 64 ] 4+ framework shows specific properties such as electride, transparent electride, transparent p-type conducting oxides, transparent semiconductor, super conductor, etc. The crystal structure has 12 cages of 4.4 Å in diameter in a unit cell of 12 Å cube, and 2 cages of 12 cages include oxygen ion (O 2-) as shown in Figure 25(b). As this O 2-is bonding weakly with the framework, this ion could be removed or exchanged with other anions easily. Transparent metal oxide (C 12 A 7 :H -) transformed to electro conductor by photon induced phase transition, C 12 A 7 compound including much active oxygen Oatoms (Hayashi et al., 2002), and C 12 A 7 : eelectride stable in room temperature and air-condition (Matsuishi et al., 2003) are presented by Hosono group.
This C 12 A 7 crystal grown by Cockayne & Lent (1979) is expected for SAW, because of the high SAW velocity and reasonable bulk electromechanical coupling by Whatmore (to be published). Two space groups are reported such as 43 Id by Cockayne & Lent (1979) and 42 Im by Kurashige et al. (2006). 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 group in the cages of the frame structure are expected to be designed for SAW suitable properties. Crystal structure of aluminate calcium C 12 A 7 . New-type superior properties such as superconductor were designed from this structure.

Conclusion
Origin of piezoelectricity on Langasite has been explained based on the crystal structure, and clarified by crystal structure analysis under high pressure. In the introduction, the principle of piezoelectricity and present condition required such as Pb-free piezoelectricity are stated. Next, crystal growth of langasite, crystal structure analysis and piezoelectric properties of langasite are stated, and mechanism of piezoelectricity are presented based on the crystal structure and properties. And the mechanism is confirmed by crystal structure analysis under high pressure. Finally, a search of new piezoelectric materials are proposed on the direction of framework compound such as nepheline, and introduced the C 12 A 7 compounds with framework also for piezoelectricity.

Acknowledgment
The author would like to thank Dr. Katsumi Kawasaki, Jun Sato and Hiroki Morikoshi of TDK Co. for the presenting of single crystal LGS, PGS and NGS. Professor Hiroaki Takeda of Tokyo Institute of Technology and Dr. Hiroki Morikoshi for supporting writing this chapter. Also, M. Eng. Tsuyoshi Iwataki and Nobukazu Araki of NIT for studying crystal structure analysis and experiments under high pressure. And Professors Yasuhiro Kudo and Takahiro Kuribayashi of Tohoku University for supporting crystal structure analysis under high pressure, Professors Cheon Chae-Il and Kim Jeong-Seog of Hoseo University Korea for discussion of the contents, Professors Ken-ichi Kakimoto and Isao Kagomiya of NIT for supporting experimental conditions. Moreover, my wife Keiko Ohsato for supporting my health conditions.