_{12}TiO

_{20}and Bi

_{12}SiO

_{20}Single Crystals

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The full matrix of electro-elastic constants of sillenite-type crystals Bi_{12}TiO_{20} (BTO) and Bi_{12}SiO_{20} (BSO) were determined by the resonance method, with _{14} and _{14} being on the order of 40–48 pC/N and 31%–36%, respectively. In addition, double-rotated orientation dependence of _{33} was investigated, with the maximum values of 25–28 pC/N being achieved in ^{5} Ω cm at 500 °C. The temperature dependence of dielectric and piezoelectric properties were investigated. BSO exhibited a high thermal stability in the temperature range of 25–500 °C, while BTO showed a variation of ~3% in the range of 25–350 °C. The high values of _{14} and _{14}, together with the good thermal stability, make BTO and BSO crystals potential candidates for electromechanical applications in medium temperature range.

Sillenite-type Bi_{12}MO_{20} (where M = Ti, Si and Ge, known as BTO, BSO and BGO) crystals have non-centrosymmetric, body-centered cubic structure belonging to the I23 space group [_{14} ~ 40 pC/N), large electromechanical coupling factor (˃30%), large band gap energy (3.15–3.25 eV) and fast response time [

Extensive research has been carried out on the optical and room temperature piezoelectric properties of sillenite-type crystals [_{12}TiO_{20} (BTO) and Nd_{0.06}Bi_{11.94}SiO_{20} (abbreviated as Nd: BSO or BSO) crystals were determined using resonance method based on IEEE Standards on Piezoelectricity. The piezoelectric coefficient _{14} and coupling factor _{14} of BTO were calculated by two methods: length extension and face shear vibrations, respectively. The double-rotated orientation dependence of longitudinal piezoelectric response was analyzed. Furthermore, the temperature dependence of electrical resistivity, dielectric, elastic, electromechanical coupling and piezoelectric constants were investigated in the range of 25–500 °C.

^{3} was given in

(_{12}TiO_{20} (BTO) samples; (_{12}SiO_{20} (BSO) single crystal pulled along [110] direction.

The dielectric, elastic and piezoelectric constants of the BTO and BSO single crystals were measured by resonance method, as listed in _{14} of BSO larger than the reported values, which may be induced by the Nd dopant. In addition, the _{14} and _{14} of BTO crystals were measured by face shear vibration mode directly, the values were found to be on the order of 40.7 pC/N and 31.0%, respectively, being similar to those values measured by length extension mode (42.8 pC/N and 32.8%). BTO and BSO possess similar physical properties, due to the fact that the body-centered cubic sillenite-type structure can accommodate a variety of different M ions, and the oxygen tetrahedron is able to expand or contract without a major effect on the remaining atomic arrangement [

Room temperature electro-elastic constants for BTO and BSO crystals.

Electro-Elastic Constants | Symbols | BTO | BTO [ |
BSO | BSO [ |
---|---|---|---|---|---|

Relative Dielectric Permittivities | ε_{11} |
47.9 | 47.0 | 48.2 | 47.0 |

Dielectric Loss | tanδ | 0.01% | – | 0.09% | – |

Elastic Compliance Constants ^{E}^{2}/N) |
_{11} |
9.8 | 8.7 * | 10.3 | 8.5 |

_{12} |
−1.8 | −1.6 * | −2.7 | 1.5 | |

_{44} |
40.3 | 40.7 * | 40.4 | 40.0 | |

Elastic Stiffness Constants ^{E}^{1}^{0} N/m^{2}) |
_{11} |
11.2 | 12.5 | 11.9 | 12.8 |

_{12} |
2.6 | 2.8 | 4.3 | 2.8 | |

_{44} |
2.5 | 2.4 | 2.5 | 2.5 | |

Piezoelectric Strain coefficients (pC/N) | _{14} |
42.8 | 45.8 ^{#} |
47.7 | 40.0 |

Piezoelectric Stress coefficients (C/m^{2}) |
_{14} |
1.1 | 1.1 | 1.2 | 1.0 |

Coupling Factor (%) | _{14} |
32.8 | – | 36.3 | – |

* The elastic compliance constants of BTO were calculated by the formula: ^{−1}; ^{#} _{14} =

In some studies, the piezoelectric coefficient was reported to be negative value for sillenite-type crystals [_{14} can be interpreted based on the crystal structure, where the M atom was coordinated by four oxygen atoms forming perfect tetrahedron, while the Bi atom with five neighbors of oxygen atoms forming an incomplete deformed BiO_{5} octahedron, with two additional electrostatically coordinated oxygen atoms on either side of the 6s^{2} inert electron pair in Bi^{3+} [_{4} tetrahedron. In dextrorotatory Bi_{12}MO_{20}, the compressive stress applied along [111] direction deforms the tetrahedral O–M–O angles (no change in any M–O bond length), inducing a negative charge on the “M’’ side and a positive charge on the “O’’ side. So the directions of the positive piezoelectric effect correspond to the M→O directions in the MO_{4} tetrahedra, account for _{14} ˃ 0. If the Bi_{12}MO_{20} crystal is of opposite chirality, e.g., is laevorotatory, then _{14} ˂ 0, as shown in _{14} is the same for dextrorotatory and laevorotatory crystals.

One unit cell of Bi_{12}MO_{20} showing the M–O tetrahedron and the polarization direction resulting from compression along [111]: (

For cubic 23 symmetry, only face shear _{14} = _{25} = _{36} exist. However, longitudinal coefficient _{11} = _{22} = _{33} appears in the rotated coordinate. The orientation dependence of the longitudinal piezoelectric coefficient _{14} sinα cosα sin^{2}β cosβ

The orientation dependence of piezoelectric coefficient

The highest

The coordinate rotation for

The electrical resistivity as a function of temperature for BTO and BSO crystals are plotted in _{a}^{5} Ω·cm at 500 °C.

Resistivity as a function of temperature for BTO and BSO crystals.

Dielectric behaviors as a function of temperature for BTO and BSO crystals.

_{11}, _{12} and _{44} was found to increase linearly from 40.3 to 44.1 pm^{2}/N with increasing temperature, with the variation of ˂9%. As shown in _{11} and _{12} shows an opposite trend. In addition, elastic constants _{44} was found to increase linearly from 40.4 to 45.1 pm^{2}/N over 25–500 °C, with the variation being on the order of 12%.

_{14} of BTO was found to increase from 42.8 to 44.1 pC/N with temperature increasing to 350 °C, with the variation of 3%, while _{14} and

Elastic compliance as a function of temperature for BTO and BSO crystals.

Piezoelectric coefficients as a function of temperature for BTO and BSO crystals.

The coupling factors as a function of temperature are given in _{14} and

Coupling factor as a function of temperature for BTO and BSO crystals.

Raw materials of Bi_{2}O_{3}, TiO_{2}, SiO_{2} and Nd_{2}O_{3} were used to grow Bi_{12}TiO_{20} and Nd_{0.06}Bi_{11.94}SiO_{20} single crystals by the Czochralski technique. The crystals can be grown from congruent melt above their melting points of 880–900 °C. It is important to point out that BTO is non-congruent melting, an excess of Bi_{2}O_{3} was add to the starting materials as self-cosolvent. The detailed crystal growth process was given in reference [

For sillenite-type crystals with cubic symmetry, there are 5 nonzero independent material constants, as shown in Equations (5)–(7). A schematic of the samples used for electrical measurements with different orientations is shown in ^{3} for ^{3} for long stripes, two to three samples were prepared for every crystal cuts. All the samples were vacuum sputtered with 200 nm platinum thin films on the large faces as electrodes. The resonance and anti-resonance frequencies were measured for determination of the material constants based on IEEE standards [

Orientation of samples: (1)

The capacitance _{p} was measured on

The length extension vibration can be excited in the long strips of _{14} by the following equations:

_{r}^{3} for BTO and BSO, respectively.

_{0} is a root of the equation: tan ƙ_{0} + ƙ_{0} =0, with the first root equals to 2.0288 and α = 1 − 0.05015 ×

After obtaining the elastic constant _{14} can be calculated by Equation of (14).

On the other hand, the _{14} and _{14} can be directly determined by measuring the face shear square plate [_{a}

The full matrix of electro-elastic constants of BTO and BSO crystals were determined, with _{14} and _{14} of 40–48 pC/N and 31%–36%, respectively, based on which, the highest double rotated ^{5} Ω·cm at 500 °C, two orders higher than that of BTO. Of particular importance is that both BTO and BSO crystals shown high thermal stability of piezoelectric properties over the temperature range of 25–350 and 25–500 °C, respectively, with the variations of ˂6%, demonstrating that the sillenite-type crystals are potential piezoelectric materials for electromechanical applications in a medium temperature range.

The authors would like to thank Thomas R. Shrout for the helpful discussion. The author Chuanying Shen acknowledged the financial support from the China Scholarship Council.

The experiments were designed by Chuanying Shen, Huaijin Zhang and Shujun Zhang; Chuanying Shen performed the experiments; Chuanying Shen, Huaijin Zhang and Shujun Zhang prepared the manuscript. All authors discussed the results and contributed to the refinement of the paper.

The authors declare no conflict of interest.

_{12}GeO

_{20}

_{14}coefficient in laevorotatory Bi

_{12}SiO

_{20}

_{12}TiO

_{20}

_{12}SiO

_{20}sillenite from experiment and theory

_{12}SiO

_{20}

_{12}SiO

_{20}and Bi

_{12}GeO

_{20}

_{12}TiO

_{20}crystals

_{12}SiO

_{20}(BSO) and Bi

_{12}TiO

_{20}(BTO) obtained by mechanical alloying

_{12}SiO

_{20})

_{12}GeO

_{20}(BGO), Bi

_{12}TiO

_{20}(BTO) crystals

_{12}TiO

_{20}crystals with an external electric AC field

_{12}SiO

_{20}single crystal

_{12}SiO

_{20}

_{12}GeO

_{20}and Bi

_{12}SiO

_{20}Crystals

_{12}MO

_{20}single crystals with sillenite structure (M = Si, Si

_{0.995}Mn

_{0.005}, Bi

_{0.53}Mn

_{0.47})

_{12}TiO

_{20}

_{3}single crystals