**6. 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 *c*directions shrunk linearly with an increase of applied pressure. Noteworthy is that the *a*1 axis 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.

Fig. 20. Schematic cross section of diamond anvil cell.


Table 6. Crystallographic data of LGS and NGS under pressure.

brings the piezoelectricity that the centers of mass of positive charges and negative charges

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

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 *c*directions shrunk linearly with an increase of applied pressure. Noteworthy is that the *a*1 axis is preferentially shrunk direction compared to the *c*-axis. This indicates that the

step scan technique.

compression of langasite crystals occurs preferentially in the *a*1-*a*2 plane.

45<sup>o</sup>

1

Pressure (GPa) Atm.

Table 6. Crystallographic data of LGS and NGS under pressure.

2

3

7

8

11

**(1) diamond anvils**

**(7) single crystal (8) ruby**

**(13) driver screw (14) lower sliding piston (15) cylindrical sleeve (16) upper stationary disc**

Atm. 3.3 6.1 3.5 6.8 8.1674(4) 8.103(1) 8.046(3) 8.0674(5) 7.999(1) 7.926(1) 5.0964(8) 5.070(1) 5.052(1) 5.0636(9) 5.041(1) 5.011(1) 294.41(5) 288.3(1) 283.2(1) 285.40(5) 279.4(1) 272.6(1) 5.7384 5.860 5.965 6.013 6.143 6.295 228.496 233.339 237.505 258.608 264.210 270.751 3.45 4.70 6.01 3.17 5.88 4.48 3.60 5.59 7.03 3.30 6.78 5.17

LGS NGS

**(9) hemispherical plate (10) disc-shaped plate (11) inclined adjusting screw (12) lateral-position adjusting screw**

**(2) beryllium diamond support disc**

**(3) gasket (4) spacer ring (5) epoxy resin (6) adhesive**

12

**6. Crystal structure and piezoelectricity under pressure** 


are in different positions.

were refined by using the 2

2

Lattice parameter *a* (Å)

Unit cell volume (Å3) Calculated density *Dx* (g/cm<sup>3</sup>

*R wR* 4 5

9

13

10 2

15 14

Fig. 20. Schematic cross section of diamond anvil cell.

6

*c* (Å)

Linear absorption coefficient *m* (cm-1)

)

10 mm

16


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

Origin of Piezoelectricity on Langasite 35

Table 9. Atomic distances (*M*L, *N*L), center position X-*B* ion distance (*O*L), dipole moment (*M*L - *O*L) and lattice constant of *a*1 of LGS and NGS along [100] direction under the pressure.

*B A*

*O***L**

Fig. 22. Sizes of *A*-, *B*-site and open space *S*, and atomic distances of *M*L, *N*L and *O*L between

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 is not changed around 3.4 Å, and distances of *N*L (*A* ion-[open-space]- *B* ion) in LGS and NGS are shrunk from 4.75 to 4.65, and 4.70 to 4.58 Å, respectively. On the other hand, *A*-polyhedron is distorted to [ 100 ] direction. The distortion is clarified by shortage of distance *O*L between center position X on *A*-polyhedron and *B*-ion as shown in Figure 22 and 23. The *O*L lengths of LGS and NGS are shortened from 3.27 to 3.21 Å, and 3.23 to 3.17 Å, respectively. As a result, a dipole moment *P* appeared according to moving the centers of mass of positive and negative charges to produce piezoelectricity.

*N***<sup>L</sup>** *M***<sup>L</sup>**

atoms. Position X is the center of oxygen atoms on *A*-polyhedron.

*M*L 3.419 3.413 3.392 3.372 3.354 3.350 *N*L 4.748 4.690 4.654 4.696 4.645 4.576 *O*L 3.271 3.249 3.215 3.229 3.203 3.172 *M*L- *O*<sup>L</sup> 0.148 0.164 0.177 0.143 0.151 0.178 *a*1 8.167 8.103 8.046 8.067 7.999 7.926

*B***L**

LGS NGS Pressure (GPa) Pressure (GPa) Atm. 3.3 6.1 Atm. 3.5 6.8

×**: Center of oxygen atom on** *A***-site**

*a***2**

**[010]**

*M*L, *N*L, *O*L, Dipole moment (*M*L-*O*L) and *a*1 (Å)

Atm.: atmosphere pressure.

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

*<sup>S</sup>***<sup>L</sup>** *<sup>A</sup>***<sup>L</sup>** Open-space

Fig. 21. Lattice parameters and volume of LGS and NGS as a function of pressure.

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*1 axis is also divided into three kinds of length. As seen in Table 8, the change in *S*L is much larger than the other length of *A*L and *B*L, indicating a larger contribution of shrinkage of an open-space. The open-space forms corner shares with *A-* and *B-*polyhedra. In contrast, *A-* and *B-*polyhedra make shared edges with each other. When the pressure induced in the [100] direction, it can be speculated that the corner-shared open-space is easily distorted compared with the edge-shared *A-* and *B*-polyhedra.


Table 8. *A*- and *B*-polyhedra size *A*L and *B*L, and open-space size *S*L along *a*-axis and *A*L*/B*<sup>L</sup> for LGS and NGS. Atm.: atmosphere pressure.

Fig. 21. Lattice parameters and volume of LGS and NGS as a function of pressure.

LGS NGS

(Å) Atm. 3.3 6.1 Atm. 3.5 6.8 *A*L 3.516 3.541 3.536 3.411 3.324 3.413 *B*L 2.956 2.949 2.848 2.982 3.024 2.869 *S*L 1.694 1.612 1.661 1.674 1.652 1.644 *A*L*/B*<sup>L</sup> 1.19 1.20 1.24 1.14 1.10 1.19

Table 8. *A*- and *B*-polyhedra size *A*L and *B*L, and open-space size *S*L along *a*-axis and *A*L*/B*<sup>L</sup>

Pressure (GPa) Pressure (GPa)

distorted compared with the edge-shared *A-* and *B*-polyhedra.

for LGS and NGS. Atm.: atmosphere pressure.

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*1 axis is also divided into three kinds of length. As seen in Table 8, the change in *S*L is much larger than the other length of *A*L and *B*L, indicating a larger contribution of shrinkage of an open-space. The open-space forms corner shares with *A-* and *B-*polyhedra. In contrast, *A-* and *B-*polyhedra make shared edges with each other. When the pressure induced in the [100] direction, it can be speculated that the corner-shared open-space is easily


Table 9. Atomic distances (*M*L, *N*L), center position X-*B* ion distance (*O*L), dipole moment (*M*L - *O*L) and lattice constant of *a*1 of LGS and NGS along [100] direction under the pressure. Atm.: atmosphere pressure.

Fig. 22. Sizes of *A*-, *B*-site and open space *S*, and atomic distances of *M*L, *N*L and *O*L between atoms. Position X is the center of oxygen atoms on *A*-polyhedron.

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 is not changed around 3.4 Å, and distances of *N*L (*A* ion-[open-space]- *B* ion) in LGS and NGS are shrunk from 4.75 to 4.65, and 4.70 to 4.58 Å, respectively. On the other hand, *A*-polyhedron is distorted to [ 100 ] direction. The distortion is clarified by shortage of distance *O*L between center position X on *A*-polyhedron and *B*-ion as shown in Figure 22 and 23. The *O*L lengths of LGS and NGS are shortened from 3.27 to 3.21 Å, and 3.23 to 3.17 Å, respectively. As a result, a dipole moment *P* appeared according to moving the centers of mass of positive and negative charges to produce piezoelectricity.

Origin of Piezoelectricity on Langasite 37

Fig. 24. The difference *M*L-*O*L (dipole moment P) for LGS and NGS as a function of pressure.

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 SiO4, AlO4, ZnO4. Especially, silicates including langasite make many framework structures by connection of SiO4 tetrahedra as cyclo-, ino-, phyllo-, and tecto-silicates. These framework structures are noticed recently for applications on many kinds of properties such

Here, we will present a candidate for piezoelectric materials. Nepheline (KNa3Al4Si4O16) 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 *P*63 (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

Recently, Hosono (2010) presented that Ca12Al14O32 (C12A7) clinker compound with big cages including O2- in a [Ca24Al28O64]4+ framework shows specific properties such as electride, transparent electride, transparent p-type conducting oxides, transparent semiconductor, super conductor, 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 (O2-) as shown in Figure 25(b). As this O2- is bonding weakly with the framework, this ion could be removed or exchanged with other anions easily. Transparent metal oxide (C12A7:H-) transformed to electro conductor by photon induced phase transition, C12A7 compound including much

temperature and air-condition (Matsuishi et al., 2003) are presented by Hosono group.

This C12A7 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 *I d* 43 by Cockayne & Lent (1979) and *I m* 42 by Kurashige et al. (2006). The point groups are 43*m* and 42*m* , 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

**7. New piezoelectric materials with framework structure** 

as zeolite for optical properties by absorption of special compounds.

active oxygen O- atoms (Hayashi et al., 2002), and C12A7: e-

become different, piezoelectricity will occur.

designed for SAW suitable properties.

electride stable in room

**Crystal structure (***a***1-***c* **plane)**

Fig. 23. Origin of piezoelectricity on Langasite projected from [120]. Position X is the center of oxygen atoms on *A*-polyhedron. Under pressure, *ML* does not chang and *NL* shrinks *A*ion.

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.

*<sup>A</sup> <sup>B</sup>* **[100]**

*N***L shrink**

**Pressure** *P*

*a***1**

ion.

structure.

for LGS are larger than that for NGS.

*N***L** *M***L**

**Crystal structure (***a***1-***c* **plane)**

Fig. 23. Origin of piezoelectricity on Langasite projected from [120]. Position X is the center of oxygen atoms on *A*-polyhedron. Under pressure, *ML* does not chang and *NL* shrinks *A*-

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

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

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*

series is clarified as follows: though the *A*-polyhedron is deformed to [ 100

*c* **[001]**

*M***L no change**

×**: Center of oxygen atom on** *A***-polyhedron**

**[-100]**

] with applied

Fig. 24. The difference *M*L-*O*L (dipole moment P) for LGS and NGS as a function of pressure.

#### **7. 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 SiO4, AlO4, ZnO4. Especially, silicates including langasite make many framework structures by connection of SiO4 tetrahedra as cyclo-, ino-, phyllo-, and tecto-silicates. These framework structures 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 (KNa3Al4Si4O16) 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 *P*63 (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 Ca12Al14O32 (C12A7) clinker compound with big cages including O2- in a [Ca24Al28O64]4+ framework shows specific properties such as electride, transparent electride, transparent p-type conducting oxides, transparent semiconductor, super conductor, 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 (O2-) as shown in Figure 25(b). As this O2- is bonding weakly with the framework, this ion could be removed or exchanged with other anions easily. Transparent metal oxide (C12A7:H-) transformed to electro conductor by photon induced phase transition, C12A7 compound including much active oxygen O- atoms (Hayashi et al., 2002), and C12A7: e electride stable in room temperature and air-condition (Matsuishi et al., 2003) are presented by Hosono group.

This C12A7 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 *I d* 43 by Cockayne & Lent (1979) and *I m* 42 by Kurashige et al. (2006). The point groups are 43*m* and 42*m* , 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.

Origin of Piezoelectricity on Langasite 39

Belokoneva, E. L., Simonov, M. A., Butashin, A. V., Mill, B. V., & Belov, N. V., (1980). "Crystal

analog Ba3Fe2Ge4O14 = Ba3Fe[(FeGe2)Ge2O14]" *Sov. Phys. Dokl*., 25, pp. 954-957. Bussen, W., & Eitel, A., (1936). "Die Struktur des Pentacalciumtrialuminats" *Z. Kryst*., 95, pp.

Cockayne, B., & Leat, B., (1979). "SINGLE CRYSTAL GROWTH OF 12 CaO 7 A12O3" *J. Crystal* 

European Commission - Environment - Waste – WEEE. Date of access: 2nd, November, 2011, [web1]http://ec.europa.eu/environment/waste/weee/index\_en.htm

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Guo, Y., Kakimoto, K., & Ohsato, H., (2004). "Phase transitional behaviour and piezoelectric properties of (Na0.5K0.5)NbO3-LiNbO3 ceramics" *App. Phys. Lett.*, 18, pp. 4121-4123. Hayashi, K., Hirano, M., Matsuishi, S., & Hosono, H., (2002). "Microporous Crystal 12CaO•7Al2O3 Encaging Abundant O-Radicals" *J. Am. Chem. Soc*., 124, pp. 738-739. Hosono, H., (2010). Chap.10, in Handbook of Transparent Conductors, Edited by Ginley, D.,

Hosono, H., Hayashi, K., Kamiya, T., Atou, T., & Susaki:, T., (2011). "New functionalities in

Hosono, Y., & Yamashita, Y., (2004). "High-Efficiency Piezoelectric Single Crystal", *Toshiba* 

Iwataki, T., (2002). "Study for the relationship between crystal structure and piezoelectric

Iwataki, T., Ohsato, H., Tanaka, K., Morikoshi, H., Sato, J., & Kawasaki, K., (2001). "Mechanism

Kakimoto, K., Masuda I., & Ohsato, H., (2004). "Ferroelectricity and Solid-Solution Structure of KNbO3 Ceramics Doped with La and Fe" *Key Eng. Mater.*, 269, pp. 7-10. Kaminskii, A. A., Mill, B. V., Khodzhabagyan, G. G., Konstantinova, A. F., Okorochkov, A. I.,

Growth and optical Properties" *Physica Status Solidi (a)*, 80(1), pp. 387–398. Katsuro, H., Matsuishi, S., Kamiya, T., Hirano, M., & Hosono, H., (2002). "Light-induced

Kazuhisa, K., Toda, Y., Matstuishi, S., Hayashi, K., Hirano, M., & Hosono, H., (2006).

Kumatoriya, M., Sato, H., Nakanishi, J., Fujii, T., Kadota M., & Sakabe, Y., (2001). "Crystal

abundant element oxides: ubiquitous element strategy" *Sci. Technol. Adv. Mater*., 12,

properties of langasite-type piezoelectric crystals" *Master-thesis of Nagoya Institute of* 

of the piezoelectricity of langasite based on the crystal structures" *J. Eur. Ceram. Soc*.,

& Silvestrova, M., (1983). "Investigation of trigonal (La1−xNdx)3Ga5SiO14 crystals. I.

conversion of an insulating refractory oxide into a persistent electronic conductor"

"Czochralski Growth of 12CaO•7Al2O3 Crystals" *Cryst. Growth Design*, 6, pp. 1602-1605.

growth and electromechanical properties of Al substituted langasite (La3Ga5-

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Sato, M., (1998). "Growth of New Langasite Single Crystals for Piezoelectric Applications" *Proceedings of the Eleventh IEEE International Symposium*, ISBN:0-7803-

175-188. (Germany).

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4959-8, Montreux, Switzerland, August 1998.

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PP. 034303 (22pp).

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*Technology*. (Japanese)

*Nature*, 419, pp. 462-465.

xAlxSiO14)" *J. Cryst. Growth*, 229, pp. 289-293.

21, pp. 1409-1412.

structure of calcium gallogermanate Ca3Ga2Ge4O14 = Ca3Ge[(Ga2Ge)Ge2O14] and its

Fig. 25. (a) Nepheline structure as an example of alumino-silicates with framework. (b) Crystal structure of aluminate calcium C12A7. New-type superior properties such as superconductor were designed from this structure.

#### **8. 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 C12A7 compounds with framework also for piezoelectricity.

#### **9. 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.

#### **10. References**


Fig. 25. (a) Nepheline structure as an example of alumino-silicates with framework. (b) Crystal structure of aluminate calcium C12A7. New-type superior properties such as super-

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 C12A7

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

Araki, N., (2004). "Crystallographic Study for the piezoelectric mechanism of langasite under

Araki, N., Ohsato, H., Kakimoto, K., Kuribayashi, T., Kudoh, Y., & Morikoshi, H., (2007).

high pressure, electric field & high & low temperature." *Master-thesis of Nagoya* 

"Origin of Piezoelectricity for Langasite A3Ga5SiO12 (A = La & Nd) under high

conditions. Moreover, my wife Keiko Ohsato for supporting my health conditions.

Pressure" *J. Eur. Ceram. Soc.*, 27, pp. 4099-4102.

conductor were designed from this structure.

compounds with framework also for piezoelectricity.

**8. Conclusion** 

**9. Acknowledgment** 

**10. References** 

*Institute of Technology*.


**1. Introduction**

of merit of a material

Quantum theory predicts a number of phenomena for materials scaled down to a size where confinement effects occur in one or more dimensions. Numerous devices that are based on these effects have been developed, as for example tunnel diodes, quantum well lasers, etc. An essential component in many of these device concepts are interfaces between conductive materials. To make the devices as efficient as possible in a reproducible way, the interfaces need to be controllable and tunable in their shape, morphology, and transport properties. For multilayer growth, investigations have already shown that a proper control of the quality of the interfaces between the stacked layers is of major importance for the device performance (Fasol et al., 1988; Hillmer et al., 1990). For in-plane interfaces, however, a proper characterization is still missing. To date and to our knowledge, only investigations of grain boundaries have been reported, in which the interfaces were arranged randomly (Schwartz,

**Photolithography and Self-Aligned Subtractive** 

Gert Homm, Steve Petznick, Torsten Henning and Peter J. Klar

**and Additive Patterning of Conductive Materials** 

A typical example are thermoelectric materials. Theory predicts that the thermoelectric figure

where *S* is the Seebeck coefficient, *σ* the electrical conductivity and *κ* the thermal conductivity, could be significantly improved by reducing the dimensions of this material, namely by artificial structuring (Dresselhaus et al., 2007; Hicks & Dresselhaus, 1993a;b). As can be seen from equation (1), an improvement can be achieved by either increasing *S*2*σ* (the so called power factor) or by decreasing *κ*, without affecting the other parameters in an unwanted way. Assuming a constant Seebeck coefficient, the equation (1) implies that materials with a high electrical conductivity and a low thermal conductivity are desired, a design goal which, for metals, is somewhat contradicted by the Wiedemann-Franz law (Franz & Wiedemann, 1853; Lorenz, 1872). This directly leads to semiconductors as the materials class of choice for thermoelectrics. Here, numerous advantages over the metals can be used: The free carrier concentration can be adjusted by doping such that the electric conductivity is still fairly high, but the thermal conductivity is dominated by phonon transport. Simultaneously, the thermal conductivity can be reduced further by phonon blocking almost without affecting the free carrier transport, an approach for which various methods have been developed.

*T*, (1)

**3**

*Justus Liebig University,* 

*Germany* 

*Institute of Experimental Physics I, Gießen* 

*ZT* <sup>=</sup> *<sup>S</sup>*2*<sup>σ</sup> κ*

1998; Watanabe, 1985; 1993; Watanabe & Tsurekawa, 1999).

