Hitoshi Ohsato1,2,3

*1Hoseo University, 2Nagoya Institute of Technology,3Nagoya Industrial Science Research Institute, 1Korea 2,3Japan* 

#### **1. Introduction**

14 Materials Science and Technology

It was found that pseudocuts containing double oxides and binder compounds (C2S, C3S, CA) have greater binder activity. The initial stage of hydration begins with leaching the surface atoms and active chemical adsorption of water molecules due to presence at active centres followed by their relation through forming OH hydroxide groups and a surfactant layer having specific surface area (to 2\*10A6 sq.m/kg) and consisting of aluminum hydroxide. At the next stage the surfactant layer of double oxides adsorbs ions Ca+2. Chemical adsorption of the cations decelerates nucleation and promotes formation of epitaxy contacts on the surface of the double oxides as well as oriented growth of hydrate formations of hydroaluminates hydrosilicates of calcium. As a result of chemical adsorption process and oriented crystallization 01 hydrates around the double oxides grains there is formed a contact zone that is significantly higher than that of pure cement stone. This

The development of new high temperature composites based on zirconium cements for the application in various consuming industries has been illustrated and is well documented in terms of performance improvements. They are meant to protect units from influence of temperature more than 2073 K. They are used for coating of high temperature headtreatment, in coating of fuel - construction, in coating of furnace for making fuel,

[2] Ilyoukha N.,Timofeeva W., 1995, UNITEGR'95, Japan, 10 November,1995, Ilyoukha

[3] Ilyoukha N.,Timofeeva W., 1997, UNITEGR'97, USA, New-Orlean, 15 November, 1997, Ilyoukha N.,Timofeeva W., *Development of zirconia hydraulic cements*. [4] Ilyoukha N. , Lebedenko E., Refractories clinker, *Chemistry and Chemical Technology of* 

[5] N. Iloukha, Z. Barsova, I. Cwhanovskaya, V. Timofeeva, Кinetic investigations of

phaseformation processes in the system BaO - Al2O3 - Fe2O3, *Chemistry and chemical* 

determines the high strength of the double oxides containing cement.

[1] Ilyoukha N., 1984, *Refractory cements,* Ukraine Publishing Company, Kiev.

carbon-reactor, H2 - Furnace, petrochemistry reactors.

N.,Timofeeva W., *Refractory cements*.

*technology of Ukraine.* V.4, № 2, 2010, Р.91-93.

*Ukraine*. V.№ 5., 2007, P. 34-39.

**4. Conclusion**

**5. References** 

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).

Fig. 1. The piezoelectric effects. (a) generated *V* by an applied force. (b) compressed crystal by an applied voltage.

Fig. 2. (a) and (b) NaCl type crystal with *i*. (c) and (d) Hexagonal unit cell without *i*.

Origin of Piezoelectricity on Langasite 17

Fig. 3. Natural quartz crystal (a) including Brazil-type twin of right and left hand crystals

RoHs directive as appeared in the Annex of the directive.

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

Table 1. Point groups and properties.

(b). *m*: mirror plane.

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 2nd to 7th columns as shown in Table 1. Here, the 1st column is Laue group with *i*, and 3rd to 6th for optical activity, 5th to 7th for pyroelectricity, and 4th and 5th for enantiomorphism. Ferroelectric materials are ones with spontaneous polarization in pyroelectricity 5th to 7th. 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 4th 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/oC, 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 31 and 32 as shown in Figure 3(b). Lithium Niobate LiNbO3 (LN) and Lithium Tantalate LiTaO3 (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 3*m* and space group *R*3*c*.

Lead-zirconate-titanate Pb(Zr,Ti)O3 (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 4*mm* (space group: *P*4*mm*) and 3*m* (*R*3*m*), respectively, belonging No.7th 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 PbZrO3 and PbTiO3 are improved more adding Pb(Mg1/3Nb2/3)O3. 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 based on directive 2001/95/EC of the European Parliament and of the Council of 27 January 2003,

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 2nd to 7th columns as shown in Table 1. Here, the 1st column is Laue group with *i*, and 3rd to 6th for optical activity, 5th to 7th for pyroelectricity, and 4th and 5th for enantiomorphism. Ferroelectric materials are ones with spontaneous polarization in pyroelectricity 5th to 7th. All ferroelectric materials show piezoelectricity, but the reverse is not true, that is, not all

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 4th 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/oC, 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 31 and 32 as shown in Figure 3(b). Lithium Niobate LiNbO3 (LN) and Lithium Tantalate LiTaO3 (LT) single crystals are used widely for SAW filter, resonator et al., which are treated poling for adjusting the polar directions because of the

Lead-zirconate-titanate Pb(Zr,Ti)O3 (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 4*mm* (space group: *P*4*mm*) and 3*m* (*R*3*m*), respectively, belonging No.7th 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 PbZrO3 and PbTiO3 are improved more adding Pb(Mg1/3Nb2/3)O3. 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

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 based on directive 2001/95/EC of the European Parliament and of the Council of 27 January 2003,

piezoelectric materials show ferroelectricity.

Figure 4.

ferroelectrocity based on the point group 3*m* and space group *R*3*c*.


Table 1. Point groups and properties.

Fig. 3. Natural quartz crystal (a) including Brazil-type twin of right and left hand crystals (b). *m*: mirror plane.

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.

Origin of Piezoelectricity on Langasite 19

(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

(a) (b) (c)

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 oC 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*2O14 is 2.8, locating near one dimensional or ring framework with 3. -PD method is special which grows long size thin single crystal with

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 Sato et. al. (1998). Starting melts formed from single-phase powder of langasite sintered 1300 oC 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 O2 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 ZrO2 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

by few cm meters to over one meter (Figure 6(d)). A single crystal grows

*P*

*P*

Fig. 5. Mechanism of piezoelectricity of BeO. +: Be ion, -: O ion.

higher piezoelectric properties than NGS.

**2. Crystal growth of langasite** 

around 1mm

system made of alumina ceramics.

Fig. 4. Trend of piezoelectric materilas.

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, KNO3 being basically hard sintering materials was successfully formed as high density ceramics co-doping of La2O3 and Fe2O3 by Kakimoto et al. (2004), and Guo et al. (2004) found [Li0.06(Na0.5K0.5)0.94]NbO3 ceramics with excellent piezoelectric constant *d*<sup>33</sup> values reach 235 pC/N on the MPB. Saito (2004) also fabricated highly orientated (Na0.5K0.5)NbO3-LiTaO3 (NKN-LT) ceramics by template method. With the *d*33 values reach 400 pC/N. Langasite La3Ga5SiO14 (LGS) group crystals are also Pb-free piezoelectric material, which are being reviewed just in this chapter, presented by Mill et al. (1982) 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 SiO2 which is the most important piezoelectric material, the structure is also constructed by six membered SiO4 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 oC for BaTiO3.

In this chapter, LGS, Pr3Ga5SiO14 (PGS) and Nd3Ga5SiO14 (NGS) single crystals grown by Czochralski method were analysed the crystal structure by X-ray single crystal diffraction

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, KNO3 being basically hard sintering materials was successfully formed as high density ceramics co-doping of La2O3 and Fe2O3 by Kakimoto et al. (2004), and Guo et al. (2004) found [Li0.06(Na0.5K0.5)0.94]NbO3 ceramics with excellent piezoelectric constant *d*<sup>33</sup> values reach 235 pC/N on the MPB. Saito (2004) also fabricated highly orientated (Na0.5K0.5)NbO3-LiTaO3 (NKN-LT) ceramics by template method. With the *d*33 values reach 400 pC/N. Langasite La3Ga5SiO14 (LGS) group crystals are also Pb-free piezoelectric material, which are being reviewed just in this chapter, presented by Mill et al. (1982) and

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 SiO2 which is the most important piezoelectric material, the structure is also constructed by six membered SiO4 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

In this chapter, LGS, Pr3Ga5SiO14 (PGS) and Nd3Ga5SiO14 (NGS) single crystals grown by Czochralski method were analysed the crystal structure by X-ray single crystal diffraction

Fig. 4. Trend of piezoelectric materilas.

temperature about 120 oC for BaTiO3.

Kaminskii et al., (1983).

(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.

Fig. 5. Mechanism of piezoelectricity of BeO. +: Be ion, -: O ion.

#### **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, micro-pulling down (-PD) technique, as these crystals grow easily because of a low melting point around 1470 oC 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*2O14 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 Sato et. al. (1998). Starting melts formed from single-phase powder of langasite sintered 1300 oC 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 O2 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 ZrO2 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.

Origin of Piezoelectricity on Langasite 21

presented crystal growth with homogeneous composition from quasi-congruent melt (Takeda, 1998, Kumatoriya et al., 2001). In the case of Al-substituted La3Ga5-*x*Al*x*SiO14 (LGAS*x*), 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

> Composition Nd3Ga5SiO14 Pr3Ga5SiO14 LaGa5SiO14 Formula weight 1033.401 1023.415 1017.409 Crystal system Trignal Trignal Trignal Space group *P*321 *P*321 *P*321 Point group 32 32 32 Lattice parameter *a* (Å) 8.0674(5) 8.0944(5) 8.1674(4) *c* (Å) 5.0636(9) 5.0724(9) 5.0964(8)

Formula number *Z* 1 1 1

*R* 0.0320 0.0292 0.0346 *Rw* 0.0293 0.0264 0.0317 *GOF* 1.2132 1.3497 1.2169

Linear absorption coefficient (cm-1) 258.603 247.274 228.496

Table 2. Crystallographic data and reliability factors for crystal structure analysis of NGS,

Langasite crystal structure was analyzed originally by Mill et al. (1982). The crystal structure is isostructural to Ca3Ga2Ge4O14 presented by Belokoneva et al. (1980). The crystal system is trigonal, point group 32, space group *P*321 (No.150), lattice constants approximately *a* = 8.1, *c* = 5.1 Å, *Z* = 1, which is similar as quartz SiO2. We determined the three langasite-group LGS, PGS and NGS crystals using the initial atomic parameters presented by Mill et al. (1982). 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

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

 *g*(Ga) = cal. (1)

 *g*(Si) = 1/3 - *g*(Ga). (2) 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

obtained from multiplicity *g* determined by the linear constrain as follows:

) 285.40(5) 287.81(6) 294.41(5)

) 6.0127 5.9047 5.7384

radiation were corrected based on Lorentz and polarization (*Lp*)

NGS PGS LGS

quality single crystals of LGAS0.9 are grown as named quasi congruent melt growth.

Unit cell volume (Å3

Calculated density *Dx* (g/cm3

**3. Crystal structure of langasite** 

extinction corrections were performed.

PGS and LGS.

collected with MoK

Fig. 6. Single crystals of Langasite (a)-(c) and (d) grown by Cz-method, and by -PD technique, respectivery.

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 (Sato et al., 1998). 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.

Fig. 7. Crystal growth from quasi-congruent melt. (a) Crystal growth of solid solutions: composition of precipitaed should be changed gradually. (b) Formatin of quasi-congruent melt at *x* = 0.9 due to precipitated secondary phase LaAlO3.

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)

(a) (b) (c) (d)

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 (Sato et al., 1998). 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

(a) (b)

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)

Fig. 7. Crystal growth from quasi-congruent melt. (a) Crystal growth of solid solutions: composition of precipitaed should be changed gradually. (b) Formatin of quasi-congruent

*x*=0.9

Fig. 6. Single crystals of Langasite (a)-(c) and (d) grown by Cz-method, and by -PD

distinct facet enlargement and asymmetrical growth leading to spiral morphology.

Liquidus

Solidus

melt at *x* = 0.9 due to precipitated secondary phase LaAlO3.

technique, respectivery.

presented crystal growth with homogeneous composition from quasi-congruent melt (Takeda, 1998, Kumatoriya et al., 2001). In the case of Al-substituted La3Ga5-*x*Al*x*SiO14 (LGAS*x*), 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.

### **3. Crystal structure of langasite**

Langasite crystal structure was analyzed originally by Mill et al. (1982). The crystal structure is isostructural to Ca3Ga2Ge4O14 presented by Belokoneva et al. (1980). The crystal system is trigonal, point group 32, space group *P*321 (No.150), lattice constants approximately *a* = 8.1, *c* = 5.1 Å, *Z* = 1, which is similar as quartz SiO2. We determined the three langasite-group LGS, PGS and NGS crystals using the initial atomic parameters presented by Mill et al. (1982). 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:

$$
\chi(\text{Ga}) = \text{cal.}\tag{1}
$$

$$\mathbf{g(Si)} = \mathbf{1/3} \cdot \mathbf{g(Ga)}.\tag{2}$$

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.

Origin of Piezoelectricity on Langasite 23

**[010]**

*a***2**

*C* site

**[100]** *a***1**

**[001]** *c*

(c) Four kinds of cation polyhedra.

The crystal structures among LGS, PGS and NGS differ mostly in 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

Langasite shows piezoelectricity but none ferroelectricity, based on crystallographic point group 32 belonging the 4th 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

Figure 9 shows the stereographic projection of general positions on point group. Figure 9(a) shows [001] direction without polarity because of the same number positions on the

Fig. 8. Crystal structure of Langasite. (a) and (b) are viewed from [001] and [120],

octahedron

**[120]**

*A B* site site

respectively. (c) is four kinds of cation polyhedra.

**4. Piezoelectric properties of langasite** 

point group 32 for langasite is as following tensor:

**(a)** *a***1-***a***2 plane**

decahedron La3+(3*e*)

the increase of the ionic radius of *R*.

**4.1 langasite and properites** 

*A*

*C D*

*B*

**[100]**

*a***1**

*A***L**

*B***L**

tetrahedron Ga3+(3*f*)

1/2Ga3+, 1/2Si Ga 4+(2*d*) 3+(1*a*)

*D* site

*B*

**(b)** *a***1-***c* **plane**

*A*

*C D*

tetrahedron

**Open space**

**Two layers**

(4)

Table 3(a), 3(b), and 3(c) show atomic coordinates of LGS, PGS and NGS, respectively (Iwataki, 2002, Master thesis). The equivalent isotropic temperature factors (*B*eq.) were calculated using anisotropic temperature factors by following equation:

$$B\_{v\eta} = \mathbf{1} / \mathbf{3} \,\,\Sigma\_{\hat{i}} \,\Sigma\_{\hat{l}} B\_{\hat{i}\hat{l}} \, a^\*\_{\,i} a^\*\_{\,j} a\_{\,i} \, a\_{\,\hat{l}}.\tag{3}$$

The *Beq*. values are reasonable as around 0.7 for cations and 1.5 for oxygen ions. And site occupancy ratios of Ga and Si ions in *D*-site are almost 1:1. The final reliability factors: *R* and *R*w values are fine around 0.03.

The crystal structure figures projected from [001] and [120] are shown in Figure 8(a) and 8(b), respectively. The structure represented by the structural formula, *A*3*BC*3*D*2O14, is constructed four sites: *A*-, *B*-, *C*, and *D*-site projected from two ways as shown in Figure 8. *A*-site is decahedron with eight coordination number (*c*.*n*.) named as twisted Thomson cube, *B*-site octahedron with six *c.n*., and *C*- and *D*-sites tetrahedra with four *c*.*n*. as shown in Figure 8(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 framework layer structure: *B-C-D-C-D-C* six-membered rings around *A*-site as shown in Figure 8(a) projected from [100]. Tetrahedra *C*- and *D*-site, and decahedra, octahedra and open-space form layer structure as shown in Figure 8(b). Large cation sites *A*- and *B*-sites, and open-spaces makes one layer. The openspace plays important role for piezoelectric properties as described in section 5.


Table 3. Atomic paremeters of LGS, PGS and NGS.

Table 3(a), 3(b), and 3(c) show atomic coordinates of LGS, PGS and NGS, respectively (Iwataki, 2002, Master thesis). The equivalent isotropic temperature factors (*B*eq.) were

 *Beq*. = 1/3 Σi Σj *B*ij *a*\*i *a*\*j *a*i. *a*j. (3) The *Beq*. values are reasonable as around 0.7 for cations and 1.5 for oxygen ions. And site occupancy ratios of Ga and Si ions in *D*-site are almost 1:1. The final reliability factors: *R* and

The crystal structure figures projected from [001] and [120] are shown in Figure 8(a) and 8(b), respectively. The structure represented by the structural formula, *A*3*BC*3*D*2O14, is constructed four sites: *A*-, *B*-, *C*, and *D*-site projected from two ways as shown in Figure 8. *A*-site is decahedron with eight coordination number (*c*.*n*.) named as twisted Thomson cube, *B*-site octahedron with six *c.n*., and *C*- and *D*-sites tetrahedra with four *c*.*n*. as shown in Figure 8(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 framework layer structure: *B-C-D-C-D-C* six-membered rings around *A*-site as shown in Figure 8(a) projected from [100]. Tetrahedra *C*- and *D*-site, and decahedra, octahedra and open-space form layer structure as shown in Figure 8(b). Large cation sites *A*- and *B*-sites, and open-spaces makes one layer. The open-

atom site occupancy *x y z Beq.* (Å2) La 3*e* 1 0.41865(3) 0 0 0.625(3) Ga1 1*a* 1 0 0 0 0.844(8) Ga2 3*f* 1 0.76517(6) 0 1/2 0.660(7) Ga3 2*d* 0.507(3) 1/3 2/3 0.5324(2) 0.557(8) Si 0.493 O1 2*d* 1 1/3 2/3 0.198(1) 1.16(5) O2 6*g* 1 0.4660(4) 0.3123(4) 0.3186(6) 1.41(7) O3 6*g* 1 0.2208(4) 0.0811(4) 0.7629(5) 1.56(8)

atom site occupancy *x y z Beq.* (Å2) Pr 3*e* 1 0.41787(3) 0 0 0.639(2) Ga1 1*a* 1 0 0 0 0.762(7) Ga2 3*f* 1 0.76473(5) 0 1/2 0.656(6) Ga3 2*d* 0.498(3) 1/3 2/3 0.5346(2) 0.548(7) Si 0.502 O1 2*d* 1 1/3 2/3 0.1967(9) 1.16(5) O2 6*g* 1 0.4668(4) 0.3167(4) 0.3151(5) 1.53(7) O3 6*g* 1 0.2215(4) 0.0777(4) 0.7614(4) 1.50(6)

atom site occupancy *x y z Beq.* (Å2) Nd 3*e* 1 0.41796(3) 0 0 0.660(3) Ga1 1*a* 1 0 0 0 0.782(8) Ga2 3*f* 1 0.76466(6) 0 1/2 0.669(7) Ga3 2*d* 0.498(3) 1/3 2/3 0.5351(2) 0.557(8) Si 0.502 O1 2*d* 1 1/3 2/3 0.198(1) 1.33(6) O2 6*g* 1 0.4674(4) 0.3181(4) 0.3131(7) 1.63(8) O3 6*g* 1 0.2218(4) 0.0762(4) 0.7597(5) 1.50(7)

space plays important role for piezoelectric properties as described in section 5.

calculated using anisotropic temperature factors by following equation:

*R*w values are fine around 0.03.

(a) Atomic parameter of LGS

(b) Atomic parameter of PGS

(c) Atomic parameter of NGS

Table 3. Atomic paremeters of LGS, PGS and NGS.

Fig. 8. Crystal structure of Langasite. (a) and (b) are viewed from [001] and [120], respectively. (c) is four kinds of cation polyhedra.

The crystal structures among LGS, PGS and NGS differ mostly in 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 properties of langasite**

#### **4.1 langasite and properites**

Langasite shows piezoelectricity but none ferroelectricity, based on crystallographic point group 32 belonging the 4th 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:

$$
\begin{bmatrix}
\boldsymbol{d}\_{11} & \mathbf{-}\boldsymbol{d}\_{11} & \mathbf{0} & \boldsymbol{d}\_{14} & \mathbf{0} & \mathbf{0} \\
\mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{-}\boldsymbol{d}\_{14} \text{-} \mathbf{2}\boldsymbol{d}\_{11} \\
\mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{0}
\end{bmatrix}
\tag{4}
$$

Figure 9 shows the stereographic projection of general positions on point group. Figure 9(a) shows [001] direction without polarity because of the same number positions on the

Origin of Piezoelectricity on Langasite 25

LiTaO3, LGS, quartz, and La3Ga5.5Nb0.5O14 (LGN) (Fukuda et al. 1998). The properties of LGS locate between LiTaO3 and quartz. Electro-mechanical coupling factor *k* of LGS is 15 to 25 % locating between that of LiTaO3 43 % and quartz 7 %. The temperature frequency variation of LGS is 100 to 150 ppm/oC locating between that of LiTaO3 200 to 400 ppm/oC and quartz 50 to 80 ppm/oC. Here, LGN single crystal substituted Nb5+ and Ga3+ for Si4+ 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.

**Z[001]**

*c*

**Y [120]**

*a***2**

**Y-Cut**

Fig. 10. Y-cut for langasite single crystal for piezoelectric measurements.

Fig. 11. (a) Equivalent series resistance of quartz and langasite single crystals as a function of resonator vibration modes. (b) electromechanical coupling factor of langasite series as a

**X[100]**

function of piezoelectric constant.

*a***1**

opposite directions of [001] that is same number ○ and x. [210] direction (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.

Fig. 9. 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 drown for supporting the stereo projections. (d) and (e) show the crystal structure along [100] and [120] 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 7th and 9th 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*<sup>2</sup> 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/oC. In the range of -20 to 70 oC, the dependence of temperature is good value of 100 to 150 ppm/oC. Table 4 shows the properties comparing some piezoelectric crystals such as

opposite directions of [001] that is same number ○ and x. [210] direction (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

Fig. 9. 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 drown for supporting the stereo projections. (d) and (e) show the crystal structure along [100] and [120] showing asymmetry and symmetry, respectively. Dipole moment will be

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 7th and 9th 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*<sup>2</sup> 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/oC. In the range of -20 to 70 oC, the dependence of temperature is good value of 100 to 150 ppm/oC. Table 4 shows the properties comparing some piezoelectric crystals such as

shown.

appeared in (d).

LiTaO3, LGS, quartz, and La3Ga5.5Nb0.5O14 (LGN) (Fukuda et al. 1998). The properties of LGS locate between LiTaO3 and quartz. Electro-mechanical coupling factor *k* of LGS is 15 to 25 % locating between that of LiTaO3 43 % and quartz 7 %. The temperature frequency variation of LGS is 100 to 150 ppm/oC locating between that of LiTaO3 200 to 400 ppm/oC and quartz 50 to 80 ppm/oC. Here, LGN single crystal substituted Nb5+ and Ga3+ for Si4+ 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.

Fig. 10. Y-cut for langasite single crystal for piezoelectric measurements.

Fig. 11. (a) Equivalent series resistance of quartz and langasite single crystals as a function of resonator vibration modes. (b) electromechanical coupling factor of langasite series as a function of piezoelectric constant.

Origin of Piezoelectricity on Langasite 27

LGS, PGS and NGS having been described here are compositionally disordered crystals. The structural formulae are [*R*3]*A*[Ga]*B*[Ga3]*C*[GaSi]*D*O14 (*R* = La, Pr and Nd). Here, as *D*-site is occupied disorderly by Ga and Si, these crystals are disordered. An ordered langasite structural formula such as Sr3TaGa3Si2O14 (STGS), Sr3TaGa3Ge2O14 (STGG), Sr3NbGa3Si2O14 (SNGS), Ca3NbGa3Si2O14 (CNGS), and Ca3TaGa3Si2O14 (CTGS) are presented and characterized by Mill et al., (1998) and Takeda et al., (2000). The structural formula is [Sr/Ca3]*A*[Nd/Ta]*B*[Ga3]*C*[Ge/Si]*D*O14 : 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

Table 5 shows characterization of disordered and ordered langasite-type piezoelectric single crystals at room temperature and 500 oC (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 oC. 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 La3*R*0.5Ga5.5-*x*Al*x*O14 (L*R*GA*x*, *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 107, 4.6 x 107 and 7.1 x 108 •cm in the order at 400 oC 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 (La3Ga5-*x*Al*x*SiO14: LGAS*x*) 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 107 to 7.6 x 108 •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 2.7x109•cm. On the other hand, Fe-

ordering" compared with ordering based on the order-disorder transition.

Table 4. Comparison of properties of each crystal.

**4.2 Ordered crystal structure and properties** 

Fig. 12. (a) Electromechanical coupling factor vs. temperature coefficent of frequency of piezeelectric materials. (b) Frequency variation/equivalent series resistance as a function of temperature on the La3Ga5SiO14 filter.

Fig. 13. Filter properties of La3Ga5SiO14 single crystal.

(a) (b)

Fig. 12. (a) Electromechanical coupling factor vs. temperature coefficent of frequency of piezeelectric materials. (b) Frequency variation/equivalent series resistance as a function of

Temperature (oC) Temperature coefficent of

frequency (ppm/oC)

temperature on the La3Ga5SiO14 filter.

Fig. 13. Filter properties of La3Ga5SiO14 single crystal.


Table 4. Comparison of properties of each crystal.

#### **4.2 Ordered crystal structure and properties**

LGS, PGS and NGS having been described here are compositionally disordered crystals. The structural formulae are [*R*3]*A*[Ga]*B*[Ga3]*C*[GaSi]*D*O14 (*R* = La, Pr and Nd). Here, as *D*-site is occupied disorderly by Ga and Si, these crystals are disordered. An ordered langasite structural formula such as Sr3TaGa3Si2O14 (STGS), Sr3TaGa3Ge2O14 (STGG), Sr3NbGa3Si2O14 (SNGS), Ca3NbGa3Si2O14 (CNGS), and Ca3TaGa3Si2O14 (CTGS) are presented and characterized by Mill et al., (1998) and Takeda et al., (2000). The structural formula is [Sr/Ca3]*A*[Nd/Ta]*B*[Ga3]*C*[Ge/Si]*D*O14 : 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 oC (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 oC. 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 La3*R*0.5Ga5.5-*x*Al*x*O14 (L*R*GA*x*, *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 107, 4.6 x 107 and 7.1 x 108 •cm in the order at 400 oC 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 (La3Ga5-*x*Al*x*SiO14: LGAS*x*) 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 107 to 7.6 x 108 •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 2.7x109•cm. On the other hand, Fe-

Origin of Piezoelectricity on Langasite 29

**5. 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(b). Here, *A*<sup>L</sup> and *B*L are lengths of *A*-site and *B*-site along [100], respectively. Three components

compounds: LGS, PGS and NGS show just linear relationship with *d*11 and *k*12.

Fig. 15. (a) Piezoelectric constant *d*11 as a function of lattice constant for Langasite series

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(b), the ratio *A*L1/*A*L2 increases

crystals. (b) *d*11 of LGS, RGS and NGS as a function of ionic radius.


substituted langasite-type crystals are expected for multiferroic materials (C. Lee, et al., 2010).

Table 5. Characterization of disordered and ordered langasite-type piezoelectric single crystals at room temperature and 500 oC. 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. 14. Resistivity of LTG, LTGA0.3 and 0.5 at elevated temperature. Al-substituted LTG 0.5 was improved about 30 times at 400 oC. More high resistivity is expected.

substituted langasite-type crystals are expected for multiferroic materials (C. Lee, et al.,

 Density *s*E11 *d*11 *� RC*  Material Structure (g/cm3) *�*<sup>11</sup> Loss *K*<sup>12</sup> (pm2/N) (pC/N) *Q* (� cm) (ms) LGS Disordered 5.85 18.0 >0.001 0.16 8.86 6.20 **···** 9.0x106 0.02 LTG Disordered 6.12 19.6 >0.001 0.17 9.07 7.10 **···** 1.5x107 0.03 LNG Disordered 5.95 20.7 >0.001 0.18 9.27 7.40 **···** 5.0 x107 0.10 LTGA Disordered 6.07 21.0 >0.001 0.16 9.15 6.60 1000 2.2 x107 0.05 LNGA Disordered 5.90 19.5 >0.001 0.16 9.90 6.90 1000 1.1 x108 0.22 SNGS Ordered 4.65 12.4 <0.001 0.17 8.80 5.40 7500 6.3 x107 0.08 STGS Ordered 5.12 11.8 <0.001 0.16 8.69 4.90 11000 3.7 x108 0.42 CNGS Ordered 4.15 17.5 <0.001 0.11 8.75 4.00 8000 6.9 x107 0.11 CTGS Ordered 4.63 16.5 <0.001 0.11 8.95 4.00 19000 1.7 x109 2.36 CTAS Ordered 4.04 13.0 <0.001 0.14 8.51 4.30 20000 2.7 x109 3.25

500 oC

Table 5. Characterization of disordered and ordered langasite-type piezoelectric single crystals at room temperature and 500 oC. LTG:La3Ta0.5Ga5.5O14; LNG:La3Nb5GaO14; LTGA:

**30 x**

**Target**

Temperature (oC)

Fig. 14. Resistivity of LTG, LTGA0.3 and 0.5 at elevated temperature. Al-substituted LTG 0.5

was improved about 30 times at 400 oC. More high resistivity is expected.

La3Ta0.5Ga5.3Al0.2O14; LNGA: La3Nb0.5Ga5.3Al0.2O14;SNGS: Sr3NbGa3Si2O14; STGS: Sr3TaGa3Si2O14; CNGS: Ca3NbGa3Si2O14; CTGS: Ca3TaGa3Si2O14;CTAS: Ca3TaAl3Si2O14.

2010).

#### **5. 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(b). Here, *A*<sup>L</sup> and *B*L are lengths of *A*-site and *B*-site along [100], respectively. Three components compounds: LGS, PGS and NGS show just linear relationship with *d*11 and *k*12.

Fig. 15. (a) Piezoelectric constant *d*11 as a function of lattice constant for Langasite series crystals. (b) *d*11 of LGS, RGS and NGS as a function of ionic radius.

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(b), the ratio *A*L1/*A*L2 increases

Origin of Piezoelectricity on Langasite 31

Fig. 18. (a) Size *A*L1 and *A*L2 of *A*-polyhedron along [100] and [120], respectively. (b) The ratio

origin of unit cell, and *A*-ion locates in the decahedron contacted with *B*1-octahedron and

*A*L1/*A*L2 and piezoelectric modulus |*d*11| as a function of ionic radius of *R*.

shrink no change

*P*

*A*

repulsion

*B*

(a) (b)

Fig. 19. Mechanism of piezoelectricity presented imaginary based on role of open-space in

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

Then polarization occurs due to the destruction of charge balance.

Whereas the *A*-polyhedron is deformed.

Piezoelectricity appeared

The bond length between *A-* and *B-*ions does not change because of the repulsion of cations

When forces are applied along *a*-axis,

and the bond length between *A-* and *B'-*ions shrink because of the presence of open-space*.*

force *B' <sup>A</sup> <sup>B</sup>*

*B*- *A*- *B*-polyherdon

**Open-space**

open-space.

[100] *a*1

force

*<sup>A</sup> <sup>B</sup>*

the crystal structure.

Role of open-space

[001] *c*

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.

Fig. 16. Deformation of *A*-decahedron. I:O3, II and III:O2. When *A*-site was occupied by large ion such as La, the *A*-site will be deformed to arrow direction of oxygen ions anisotropically.

Fig. 17. (b) Piezoelectric constant *d*11/electromechanical coupling factor *k*12 of LGS, PGS and NGS as a function of *A*L/*B*L which is shown in (a).

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: *A*decahedron 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 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

**I**

**III**

Fig. 16. Deformation of *A*-decahedron. I:O3, II and III:O2. When *A*-site was occupied by large ion such as La, the *A*-site will be deformed to arrow direction of oxygen ions

Fig. 17. (b) Piezoelectric constant *d*11/electromechanical coupling factor *k*12 of LGS, PGS and

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: *A*decahedron 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

NGS as a function of *A*L/*B*L which is shown in (a).

anisotropically.

**II**

brings larger *d*11 more than PGS and NGS with Pr and Nd, respectively.

Fig. 18. (a) Size *A*L1 and *A*L2 of *A*-polyhedron along [100] and [120], respectively. (b) The ratio *A*L1/*A*L2 and piezoelectric modulus |*d*11| as a function of ionic radius of *R*.

origin of unit cell, and *A*-ion locates in the decahedron contacted with *B*1-octahedron and open-space.

Fig. 19. Mechanism of piezoelectricity presented imaginary based on role of open-space in the crystal structure.

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

Origin of Piezoelectricity on Langasite 33

La 3*e* 1 0.41862(3) 0 0 0.632(3)

La 3*e* 1 0.4212(3) 0 0 1.00(4)

La 3*e* 1 0.4216(4) 0 0 0.94(6)

Nd 3*e* 1 0.41796(3) 0 0 0.658(3)

Nd 3*e* 1 0.4193(4) 0 0 1.02(6)

Nd 3*e* 1 0.4227(3) 0 0 0.79(5)

0.849(8) 0.665(7)

*B*eq. (Å2)

0.553(7)

1.14(5) 1.43(7) 1.57(8)

1.4(1) 1.08(7)

*B*eq. (Å2)

1.4(5) 2.2(4) 1.6(3)

1.4(2) 0.96(10)

*B*eq. (Å2)

1.0(7) 2.2(5) 2.2(6)

0.776(7) 0.667(6)

*B*eq. (Å2)

0.559(7)

1.31(6) 1.60(7) 1.46(7)

1.1(2) 1.12(10)

*B*eq. (Å2)

0.8(2)

2.2(10) 2.1(6) 2.5(6)

1.2(1) 0.90(8)

*B*eq. (Å2)

2.3(9) 2.6(5) 3.1(6)

1.0(1)

0.8(2)

1.1(1)

0.3165(7) 0.7639(6)

> 0.306(5) 0.765(4)

> 0.312(6) 0.757(5)

0.3104(7) 0.7607(5)

> 0.316(5) 0.770(5)

> 0.312(5) 0.768(5)

> 0.534(1)

0.535(2)

0.5352(2)

0.531(2)

0.531(2)

0.5324(2)

atom site occupancy *xyz*

(a) Atomic parameter of LGS at atmospheric pressure

Ga1 1*a* 1000 Ga2 3*f* 1 0.76514(6) 0 1/2

2*d* 1/3 2/3

atom site occupancy *xyz*

Ga1 1*a* 1000 Ga2 3*f* 1 0.7671(5) 0 1/2

2*d* 1/3 2/3

atom site occupancy *xyz*

Ga1 1*a* 1000 Ga2 3*f* 1 0.7675(8) 0 1/2

2*d* 1/3 2/3

atom site occupancy *xyz*

(d) Atomic parameter of NGS at atmospheric pressure

Ga1 1*a* 1000 Ga2 3*f* 1 0.76460(6) 0 1/2

2*d* 1/3 2/3

atom site occupancy *xyz*

Ga1 1*a* 1000 Ga2 3*f* 1 0.7667(9) 0 1/2

2*d* 1/3 2/3

atom site occupancy *xyz*

Ga1 1*a* 1000 Ga2 3*f* 1 0.7688(7) 0 1/2

2*d* 1/3 2/3

O1 2*d* 1 1/3 2/3 0.181(8)

Table 7. Atomic parameter of LGS (a) to (c) and NGS (d) to (f) under the pressure.

O1 2*d* 1 1/3 2/3 0.189(9)

O1 2*d* 1 1/3 2/3 0.196(1)

O2 6*g* 1 0.4673(5) 0.3174(5) O3 6*g* 1 0.2234(5) 0.0771(5)

(e) Atomic parameter of NGS at 3.5 GPa

(f) Atomic parameter of NGS at 6.8 GPa

O2 6*g* 1 0.469(5) 0.322(5) O3 6*g* 1 0.227(5) 0.076(5)

O2 6*g* 1 0.467(6) 0.319(4) O3 6*g* 1 0.224(5) 0.075(4)

O1 2*d* 1 1/3 2/3 0.205(8)

O1 2*d* 1 1/3 2/3 0.199(7)

O1 2*d* 1 1/3 2/3 0.196(1)

O2 6*g* 1 0.4655(5) 0.3114(5) O3 6*g* 1 0.2218(5) 0.0816(5)

(b) Atomic parameter of LGS at 3.3 GPa

(c) Atomic parameter of LGS at 6.1 GPa

O2 6*g* 1 0.456(4) 0.306(3) O3 6*g* 1 0.224(3) 0.084(3)

O2 6*g* 1 0.459(5) 0.308(4) O3 6*g* 1 0.217(5) 0.080(5)

Ga3 0.5 S i 0.5

Ga3 0.5 S i 0.5

Ga3 0.5 S i 0.5

Ga3 0.5 S i 0.5

Ga3 0.5 S i 0.5

Ga3 0.5 S i 0.5

brings the piezoelectricity that the centers of mass of positive charges and negative charges are in different positions.
