Influence of Oxygen Partial Pressure and Al Content on the Resistivity and Piezoelectric Properties of

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Influence of Oxygen Partial Pressure and Al Content on the Resistivity and Piezoelectric Properties of

Ca

3

TaGa

3-x

Al

x

Si

2

O

14

Single Crystals

July 2016

Xiuwei FU

ﾌｼｭ

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Influence of Oxygen Partial Pressure and Al Content on the Resistivity and Piezoelectric Properties of

Ca

3

TaGa

3-x

Al

x

Si

2

O

14

Single Crystals

July 2016

Waseda Univerisy

Graduate School of Advanced Science and Engineering Department of Nanoscience and Nanoengineering,

Research on Nano-structured Crystal Chemistry

Xiuwei FU

ﾌｼｭ

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PREFACE

High temperature piezoelectric sensors are highly desired in modern science and engineering due to their high sensitivity, fast response, compactness, etc. However, conventional piezoelectric materials present different drawbacks for high temperature applications, like structural transformations, pyroelectricity, instability under oxidizing or reducing atmospheres, and difficult single crystal growth. As alternative, the langasite family is attracting much attention. The compounds of this family are free of phase transitions and decomposition up to their melting point (1300-1500°C), exhibit good piezoelectric properties, are non-pyroelectric, and can be grown by the Czochralski method. Among the langasite family, the Ca3TaGa3-xAlxSi2O14 (CTGAS) single crystals are of particular interest due to their relatively high resistivity. However, the growth of these crystals has been reported to be difficult. On the other hand, the research relating to the effect of Al content and oxygen partial pressure is quite limited.

In this thesis, CTGAS single crystals are grown using the Czochralski method. The temperature dependent electrical resistivity and piezoelectric properties are systematically investigated for the first time as a function of the Al content and the oxygen partial pressure during growth. This thesis is composed of 7 chapters: Chapter 1 introduces the background, motivation and objectives of the thesis. In Chapter 2, the experimental procedures are described. Chapter 3 presents a preliminary study of reference La3Ta0.5Ga5.5-xAlxO14 single crystal. In Chapter 4, the growth of Ca3TaAl3Si2O14 single crystal was optimized. Further, the influence of oxygen partial pressure during growth is examined. Chapter 5 investigates the properties of Ca3TaGa3Si2O14 crystals as a function of growth conditions. In Chapter 6, the effect of Al content in mixed CTGAS crystals is systematically studied for the first time in terms of electrical resistivity, dielectric and piezoelectric properties. Chapter 7 summarizes the present work.

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CHAPTER 1: Introduction

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§1.1 Piezoelectricity

The piezoelectricity was first reported by the Curie brothers in α-quartz single crystal in 1880. Basically, the piezoelectric effect can be simply expressed by following equations:

P d T (1.1)

SdTE (1.2)

The Eq. (1.1) describes the direct piezoelectric effect, where the polarization P is given by the piezoelectric matrix d and the stress tensor T. Inversely, as shown in Eq. (1.2), the strain S can be given by the product of the piezoelectric matrix d^T and the electric field E, so-called reverse piezoelectric effect. d^T is the transpose of d.

Nowadays, piezoelectricity has been widely used in modern science and engineering [1-3]. Figure 1.1 shows the outline of the piezoelectricity for applications. Currently, piezoelectric substances are the second biggest applications of dielectric materials, just behand the semiconductors [4].

Fig. 1.1: Outline of the piezoelectricity for applications [4].

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§1.2 High temperature piezoelectric sensors

Piezoelectricity is very suitable for sensor applications. Piezoelectric sensors possess numerous advantages, such as high sensitivity, fast response, reliability and compactness [5].

In recent years, the field of sensing applications continues to grow, particularly in those areas involving high temperature (HT) [6]. As a relevant example of HT applications, piezoelectric combustion pressure sensors are highly desired[7]. The sensors will be installed inside the automobile engine for real-time monitoring of the combustion process in order to optimize the combustion efficiency and minimize the formation of environment-harmful gases such as CO2 and NOx.

Table 1.1 shows the features of HT piezoelectric sensor in comparison with other technologies [8]. Piezoresistive, capacitive, and fiber optic sensors are common HT sensing products in market. However, they have different drawbacks, such as inaccuracy and complex packaging. Instead, the HT piezoelectric sensor presents advantages like high resolution, wide frequency range, simple structure and ease of integration.

Table 1.1: Features of HT sensing technologies [8].

HT sensing technology

Resolution

Frequency range

Temperature range (°C)

Cost Integration

Piezoresistive 10^-6 DC-kHz <600 Low Easy

Capacitive 10^-6 DC-kHz <400 Low Easy

Fiber optic 10^-1 DC-100 kHz <1100 High Hard

Piezoelectric 10^-12 1 kHz-MHz <1000 Low Easy

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§1.3 Piezoelectric materials

The piezoelectric effect only exists in those materials with non-central symmetry. The cubic group 432 is an exception due to its high symmetry. Therefore, there are in total 20 piezoelectric point groups among the 32 crystallographic classes [4]. So far, thousands of piezoelectric materials were discovered, involving single crystals, piezoelectric ceramics, thin films and composite form [9]. The discovery of excellent piezoelectric materials leads to a rapid development of the applications of piezoelectricity.

In the case of HT applications, the piezoelectric materials should be free of phase transitions and structural decomposition. Also, the pyroelectricity is detrimental for HT applications since it will cause an undesirable electrical noise in sensing system. On the other hand, the piezoelectrics should possess good dielectric and piezoelectric properties, such as low dielectric loss (tan δ) and large piezoelectric coefficients. Further, a high resistivity at HT is needed for the purpose of reducing the electrical losses and improving the signal/noise ratio of sensors. In addition, the charge generated in the piezoelectric material when pressure is applied must be maintained a long enough time in order to be recognized by the electronic detector. This time, on the other hand, is in proportion to the time constant RC [6]. The time constant will also determine the lower limiting frequency fLL in device application. The two characteristics are inversely proportional with the following relation:

LL

1 f 2

RC

 (1.3)

where R and C are the electrical resistivity and capacitance, respectively. Therefore, the bandwidth of the sensors can be extended by a larger RC.

However, the use of piezoelectric materials for HT applications presents many challenges. On the one hand, the most common limitation is the structural instability. For

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example, the lead zirconate titanate (PZT) ceramics are well-known piezoelectric materials and exhibit large piezoelectric coefficients. However, these materials belong to ferroelectric family. Beyond their Curie temperature the piezoelectric activity will disappear owing to the ferroelectric to paraelectric transition, thus limiting their maximum usage temperature less than 350°C [6]. The α-quartz is another widely used piezoelectric material. It is non-ferroelectric and presents excellent piezoelectric properties at room temperature (RT), like high resistivity, low mechanical loss, narrow bandwidth and excellent thermally piezoelectric stability [6]. But it has a crystallographic phase transition at 570°C, and the maximum temperature in practice is even less than 450°C because of the high losses [10].

On the other hand, in recent years, several materials with relatively good piezoelectric properties have been proposed, however, these present different drawbacks for HT applications. For instance, GaPO4 exhibits a high resistivity and a good thermal stability up to 930°C, but the growth of single crystals is rather difficult, which seriously limits its potential for commercial applications. On the contrary, the rare-earth calcium oxyborate crystals (RECOB) can be easily grown with the Czochralski (Cz) technique and they can maintain high resistivity and good piezoelectric properties at HT. However, these are pyroelectric, which will be harmful for HT sensing applications. Furthermore, AlN and α-BiB3O6 are limited by a poor oxidation resistance at HT and a low melting point (726°C), respectively [11, 12].

As alternatives, the compounds of langasite family are characterized by the absence of phase transition and pyroelectricity up to 1300-1500°C, and possess a high piezoelectric coefficient d11, more than 2 times of that for α-quartz. Further, the langasite compounds can be grown using the standard Cz technique, so that the production of large-sized crystals is feasible. Therefore, the langasite family is attracting much attention for HT piezoelectric sensors [13].

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§1.4 Langasite family

In 1979, the first langasite compound, namely Ca2Ga2Ge4O14 (CGG), was reported [14].

Single crystal was grown by the Cz technique subsequently. Afterwards, several CGG-type isomorphs were discovered. These compounds crystallize in trigonal space group P321 (No.150) with the formula A3BC3D2O14 [15]. As shown in Fig. 1.2, there are four cationic sites in langasite structure, including decahedral site A, octahedral site B, and two differentiated tetrahedral sites C and D. Due to the relatively large number of cationic sites and atomic substitutions, more than 100 isomorphs have been synthesised in this family.

Table 1.2 lists the chemical formula of reported langasite phases [14, 16, 17].

Fig. 1.2: Cation coordination of langasites.

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Table 1.2: Chemical formula of reported langasite phases [14, 16, 17].

No. Chemical formula Remarks

1

Na2A²⁺Ge6O14; A = Ca/Sr

Na1.8Ca1.1Si6O14 High pressure phase

2 NaA²⁺2B³⁺Ge5O14 A = Ca/Sr/Pb; B = Al/Sc/Fe/Ga/In 3 A²⁺3B³⁺2Ge4O14 A = Ca/Sr/Ba/Pb; B = Al/Cr/Fe/Ga/In 4 Sr3A²⁺Ge5O14 A = Mg/Mn/Fe/Co/Ni/Zn

5 A²⁺3B⁵⁺C³⁺3D⁴⁺2O14

A = Ca/Sr/Ba/Pb; B = Nb/Sb/Ta;

C = Al/Fe/Ga/In; D = Si/Ge 6 Ca3Al2Ti1.5Si2.5O14 High pressure phase

7

A³⁺3Ga5B⁴⁺O14; A = La/Pr/Nd; B = Si/Ti/Ge/Zr/Sn/Hf Sm3Ga5-xAlxSiO14 3<x<5

8 Ln3M⁵⁺0.5Ga5.5O14 Ln = La/Pr/Nd; M = Nb/Ta/Sb 9 La3A⁶⁺0.33Ga5.67O14 A = Mo/W

10 A³⁺3Al3+xSi3-xO12+xN2-x A = Y/La/Ce/Nd/Sm/Gd/Dy; 0≤x≤1 11 La3SbZn3A⁴⁺2O14 A = Si/Ge

12

A²⁺B³⁺2SbGa5O14 A = Ba/Sr; B = La/Pr/Nd A²⁺La2SbAl5O14 A = Ca/Sr/Ba

13 La2SrGa4Si2O14 -

14 A⁺3TeB³⁺3C⁵⁺2O14 A = Na/K; B = Al/Fe/Ga; C = P/As/V 15 A²⁺3B⁶⁺C²⁺3D⁵⁺2O14

A = Ca/Sr/Pb; B = Te/W;

Y = Mg/Zn; Z = P/V

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In general, the langasite family is classified into two types depending on the ionic distribution. In ordered langasites each cationic site is occupied by a different element, while in disordered ones, the same element enters in more than one site. The langasite family was named by the most well-known disordered La3Ga5SiO14 (LGS), in which the large La³⁺ ions occupy the A sites, the small Si⁴⁺ ions 50% of the D sites, while the Ga³⁺ ions are occupying fully both the B and C sites, and 50% of the D sites in a ramdom way [18]. The d11 value of LGS was reported to be 6.15 pC/N, about three times of that of α-quartz (2.31 pC/N) [19, 20].

Further, LGS single crystal possesses high thermal stabiliy of resonance frequency [21], making it attracting for the surface acoustic wave (SAW) filter application. By partial substitution of Ga³⁺ with Ta⁵⁺ or Nb⁵⁺ and no Si⁴⁺in LGS, namely La3Ta0.5Ga5.5O14 (LTG) and La3Nb0.5Ga5.5O14 (LNG) crystals [22, 23], respectively, the piezoelectric coefficient d11

and resistivity were enhanced [24]. These crystals were studied in detail from the point view of crystal growth and electrical properties [20, 24]. It was found that, however, their applications were seriously limited by a low resistivity in HT range. For example, the electrical resistivity of LTG crystal is less than 10⁸Ω·cm at 400°C [25]. On the other hand, it was reported that, by partial substitution of Ga³⁺ with Al³⁺, their resistivity significantly increased, especially in the case of La3Ta0.5Ga5.5-xAlxO14 (LTGA) crystal. Though the piezoelectric coefficient d11 almost keeps constant, the resistivity of LTGA (x = 0.5) is more than one order higher in comparison with the un-doped one [26]. In addition, the thermal stability of piezoelectric constant was also improved by Al substitution. Therefore, LTGA crystal has been widely investigated for HT applications [27, 28], and even 4-inch single crystals were grown industrially [29].

However, one of main problems for LTGA single crystal is the structural disorder, which can cause incoherent phonon scattering and increase acoustic loss [30]. Therefore, as alternative, a family of ordered langasites, such as Ca3TaGa3Si2O14 (CTGS), Sr3TaGa3Si2O14

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(STGS), Ca3NbGa3Si2O14 (CNGS) and Sr3NbGa3Si2O14 (SNGS), has been reported, in which Ca²⁺/Sr²⁺ occupy the A-decahedral site, Ta⁵⁺/Nb⁵⁺ the B-octahedral site, and Ga³⁺ and Si⁴⁺ are in the C- and D-tetrahedral sites, respectively [31]. In comparison with the disordered crystals, the amount of high cost Ga is almost reduced by half, while the resistivity was found to increase by one or two orders of magnitude. Further, these ordered langasites possess a higher acoustic velocity and a better thermal stability of piezoelectric properties at HT [30]. Among the ordered langasites, CTGS single crystal is of particular interest recently due to its relatively high resistivity at HT [30, 32]. Its RC value has been reported to be as high as 2.36 ms at 500°C [30] (two orders of magnitude larger than LGS), what reinforces its potential for HT and low frequency sensing applications.

In general, the resistivity of oxide crystals can be affected by the oxygen partial pressure.

For example, the resistivity of LiNbO3 decreased by annealing under reduced atmosphere (90%N2+10%H2), due to the formation of oxygen vacancies in the crystal [33]. In analogous manner, high oxygen partial pressure maybe preferred in order to enhance the resistivity of langasite crystal for HT sensor applications. However, the influence of oxygen partial pressure during growth could not be investigated in the case of CTGS since so far it has been only grown using Ir crucible that critically limits the maximum concentration of oxygen to a few percent.

Besides the resistivity, a large piezoelectric coefficient is also required. CTGS presents a very stable structure [34], each cation fitting very well to its corresponding cationic site.

Therefore, by replacing a single cationic site with another cation of different ionic radius, the lattice will be distorted in a way that an increase of piezoelectric constant can be expected.

The partial or even fully substitution of Ga with Al, which has a smaller ionic radius, could be a good way. However, the growth of mixed Ca3TaGa3-xAlxSi2O14 (CTGAS) crystals has been reported to be difficult resulting to the appearance of severe cracks and inclusions,

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especially for high Al content composition [35-37]. As a result, the effect of Al content has not been systematically studied yet.

§1.5 Objectives and overview of thesis

From above viewpoints, the objectives of this thesis are defined as follows: (1) To realize high-quality growth of mixed CTGAS single crystals within the full composition range; (2) To study of the influence of the oxygen partial pressure during growth on the electrical resistivity at HT and (3) the first systematical investigation of the effect of Al content on the resistivity and the piezoelectric coefficient. All properties are analyzed as a function of the temperature in order to elucidate the potential of CTGAS crystals for HT sensor applications.

The schematic outline of this thesis is shown in Fig. 1.3. It is arranged in 7 chapters.

Chapter 1 overviews the well-known candidates for HT piezoelectric sensor applications in detail. The advantageous characteristics of the langasite family, and the state-of-the-art of these compounds are also analyzed and reviewed. Furthermore, the objectives of the present work are described.

Chapter 2 describes the experimental procedures. The equipment used for growth, sample preparation and characterization is introduced. In addition, the theoretical background about the determination of electromechanical parameters, based on the resonance method, is also presented in detail.

Chapter 3 is a preliminary study of the disordered LTGA. This crystal serves as a reference, since it is the only langasite compound which is nowadays considered for HT

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pressure sensor application. For it, a LTGA single crystal is grown using the Cz technique.

The thermal perperties, electrical resistivity and piezoelectric properties are determined.

Chapter 4 studies the growth conditions necessary for the incorporation of Al on the Ga site, namely Ca3TaAl3Si2O14 (CTAS). In addition, the influence of oxygen partial pressure during growth on the electrical resistivity and piezoelectric properties of CTAS is investigated.

Chapter 5 describes the growth and properties of CTGS crystal depending on the growth conditions, analogously to the case of CTAS.

Chapter 6 analyzes systematically for the first time the effect of Al content on the properties of mixed CTGAS crystals.

Chapter 7 concludes this thesis from viewpoints of crystal growth, the effect of oxygen partial pressure and Al content.

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Fig. 1.3: Schematic outline of this thesis.

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CHAPTER 2: Experimental

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§2.1 Polycrystalline synthesis

The polycrystalline materials were synthesized by the solid state reaction. High purity commercial oxide powders were weighed according to the composition of the desired compounds. After mixing, the powders were pressed and subsequently sintered at HT for several hours.

§2.2 Crystal growth

As the objective compounds in this thesis are melt-congruent, the RF-heating Cz mehod is applied for the crystal growth. This method is widely used for the preparation of bulk crystals in modern science and industry. For example, well-known crystals, such as silicon, Nd:Y3Al5O12 and LiNbO3, are grown mainly using this method [38]. Figure 2.1 illustrates the schematic of Cz method. The growth processes are as follows:

(1) Melting: Reacted polycrystalline materials are loaded into the crucible. A power setting is applied in order to melt the raw materials. In general, the flowing of atmosphere gases is necessary through the entire growth period in order to, e.g.

protect the crucibles or suppress the evaporation.

(2) Seeding and necking: The materials are molten and kept at HT (around the melting point) for several hours before seeding in order to homogenize the melt. Then the seed position is adjusted to touch the melting surface. The crystallization starts from the seed. The size of the seed crystal could decrease by adjusting the melting temperature slightly higher than the melting point of the compound at seeding position, so-called necking. This process can be beneficial to avoid the extension of defects from the

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seed and, thus, improve the crystal quality.

(3) Shouldering: The seed is pulled up with proper rotation rate and pulling speed. The crystal can expand under suitable conditions.

(4) Body part: In this stage, the crystal diameter will be controlled in a desired size.

(5) Separation and cooling: After reaching the desired length, a relatively fast pulling speed is used to separate the crystal from the melt. Then a power program will be set to cool down the crystal.

Fig. 2.1: Schematic diagram of Cz method.

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In general, we should consider following aspects for Cz growth: (1) Well alignment of the coil, hot zone, crucible and seed. (2) Crucible: Pt and Ir are preferred since they are very stable at HT. Pt crucible has a high resistance to O2. But its maximum usage temperature is less than 1500°C. Instead, Ir crucible can be used up to 2000°C. (3) Growth atmosphere: For example, the inert gas atmosphere is necessary in the case of Ir crucible to prevent its oxidation, while oxygen-containing atmosphere is beneficial to suppress the evaporation of i.e. Ga2O3 and oxygen vacancies. (4) Seed: Crystal growth will be affected by the composition and orientation of the seed. (5) Rotation rate and pulling speed. (6) Temperature gradient: This is determined by the hot zone, which is very important for the crystal growth.

For example, it is necessary to create an extremely low gradient for the growth of CTAS crystal.

§2.3 Characterization techniqures 2.3.1 Chemical composition

The chemical composition was determined by the induced coupled plasma optical emission spectroscopy (ICP-OES) method, using a SPS3520UV-DD model from SII nano technology Inc.

2.3.2 X-ray analysis

The X-ray rocking curve (XRC) was measured with a PANalytical X'Pert MRD diffractometer, which was equipped with a hybrid two-bounce Ge (220) monochromator and a Cu K1 target ( = 1.54059 Å).

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RT powder X-ray diffraction (XRD) measurements were carried out using a Rigaku XRD/RINT Ultima III diffractometer equipped with a Cu Kα radiation, while the temperature dependence of XRD was measured using a Rigaku SmartLab 9 kW diffractometer equipped with a one-dimensional semiconductor X-ray detector and a Cu Kα1 radiation.

Single crystal XRD analysis was carried out using a Rigaku VariMax Saturn diﬀractometer equipped with a Mo Kα radiation (λ = 0.71073 Å) and CCD detector. A millimeter-size crystal was fixed on a glass fiber and cooled to around 110 K with cold N2

gas. The collected data was refined and reduced with a Rigaku software suite CrystalClear (d*trek program package). A dual-space algorithm SHELXT method was applied for structural solution [39]. The final refinement was performed on a WinGX program package [40] using SHELXL-2014/7 [41] by full-matrix least squares on F².

2.3.3 Transmittance

The transmission curves were recorded with a Jasco V570 spectrometer (190-2500 nm, with a resolution of 1 nm) and a PerkinElmer Spectrum GX FT-IR system (2500-8500 nm, with a resolution of 4 cm^-1).

2.3.4 Thermal properties

The thermal expansion was determined by a Bruker TD 5000S dilatometer. The specific heat was measured with a NETZSCH STA 449 F3 Jupiter. The thermal diffusivity measurements were carried out by a Netzsch apparatus Nanoflash LFA 457.

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2.3.5 Electrical resistivity

The electrical resistivity was measured with a HIOKI SM8220 Super Megohmmeter. Pt electrodes of a 5 mm square area were pasted in the middle of 10 mm square Y-cut plates of 1 mm in thickness. The measurements were carried out under air.

2.3.6 Electromechanical properties

The dielectric and piezoelectric parameters were determined by the resonance method based on the IEEE Standard on Piezoelectricity [42]. The matrices of dielectric permittivity

ijT, piezoelectric coefficient dij and elastic compliance constant sijE for langasite family are shown as follows:

11

ij 11

33

0 0

T



 



 

 

  

 

 

(2.1)

11 11 14

ij 14 11

0 0 0

0 0 0 0 2

0 0 0 0 0 0

d d d

  

 

   

 

 

(2.2)

11 12 13 14

12 11 13 14

13 13 33

ij

14 14 44

44 14

14 11 12

0 0

0 0 0

0 0 0 0 2

0 0 0 0 2 2( )

E

s s s s

s s s

s s s s

s s

s s s

 

  

 

  

  

 

  

 

(2.3)

As can be seen, there are in total 10 independent parameters for langasite crystals: 11T

and 33T are the two dielectric permittivities, d11 and d14 are the two piezoelectric coefficients, and s11E, s12E, s13E, s14E, s33E and s44E are the six elastic compliances. The piezoelectric

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equations can be obtained according to the matrices 2.1-2.3:

1 11 1 12 2 13 3 14 4 11

E E E E

S s T s T s T s T d Ex (2.4)

2 12 1 11 2 13 3 14 4 11

E E E E

S s T s T s T s T d Ex (2.5)

3 13 1 13 2 33 3

E E E

S s T s T s T (2.6)

4 14 1 14 2 44 4 14

E E E

S s T s T s T d Ex (2.7)

5 44 5^E 2 14 6^E 14 _y

S s T  s T d E (2.8)

6 2 14 5^E 66 6^E 2 11 _y

S  s T s T  d E (2.9)

1 11 1 11 2 14 4 11

T

D d T d T d T  Ex (2.10)

2 14 5 2 11 6 22^T _y

D  d T  d T  E (2.11)

3 33

T

D  Ez (2.12)

where S and T denote the strain and stress tensors, respectively, E and D represent the electric field and displacement, respectively. Then, the necessary sample cuts determined by the piezoelectric equations are shown in Fig. 2.2. The notation of crystal palte is defined in IEEE standard on Piezoelectricity [42]. The first and/or second letters (X, Y, or Z) represent the initial axes of the plate in thickness t and length l directions, respectively. The angles Φ, Θ and Ψ are the first, second and third rotation along l, w and t directions, respectively. w denotes the width of the sample. An example of full rotational types could be (XYlwt) Φ/Θ/Ψ. Therefore, as examples in the Fig. 2.2, YX plate indicates the directions of t and l are along Y and X axes, respectively. (XYt) Ψ suggests that the initial directions of t and l are along X and Y axes, respectively. The rotation along the t direction is equal to Ψ.

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Fig. 2.2: Sample cuts used for the determination of the dielectric, piezoelectric and elastic parameters.

Table 2.1 lists the equations used for for the calculation of the corresponding dielectric, piezoelectric and elastic parameters. In the Eqs. 2.13-2.23, 0 and ρ are the vacuum permittivity and the density, respectively. C, fr and fa are the capacitance, resonance frequency and anti-resonance frequency, respectively, which can be measured by the impedance analyzer. k12 and k26 are the electromechanical coupling factors, which relate to the conversion efficiency between electrical and mechanical energy. c66D is one of elastic stiffness constants. d₁₂ and s₂₂^E represent the parameters of the samples after the rotation angle of α.

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Table 2.1: Samples and equations used for the corresponding dielectric, piezoelectric and elastic parameters.

Specimens Parameters Related equations

Z-cut plate



₃₃^T 33 0

T Ct

 lw

 _(2.13)

XY plate

11

sE

d

11

2 12

1 2 tan 2

a a r

r r

f f f

k

k f f

 ^  ^

  

   (2.14)

11 22 2 2

1 4

E E

r

s s

l f

  _(2.15)

2 2 2

11 12 12 22 11

E T

d d k s



(2.16)

YX plate s₄₄^E 44 55 2 2

1 4

E E

r

s s

l f

  _(2.17)

XYtα(+30°)

d

₁₄

13

sE

14

sE

33

sE

 

12 11 14

1 1 cos 2 sin 2

d  2d   d  (2.18)

XYtα(+15°) XYtα(-15°)

 

4 4 3

22 11 33 14

2 2

13 44

cos sin 2 cos sin

2 sin cos

E E E E

E E

s s s s

s s

   

 

   

  (2.19)

XYtα(-30°)

Y-cut plate

11



T

12

sE

11 0

T Ct

 lw

 _(2.20)

2

26 tan

2 2

a a r

r r

f f f

k f f

 ^  ^

  

  (2.21)

2 2

66^D 4 _a

c 



t f (2.22)



14 14 11 44



² 14²

12 2 11

44 11 66 44

2 1 2

2

E E E

E E

E T D E

d s d s s

s s

s  c s

  

 

    

 

 

(2.23)

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§2.4 Conclusions

This chapter describes the experimental procedures, including polycrystalline synthesis, crystal growth and characterizations. The schematic of experimental section is shown in Fig.

2.3.

Fig. 2.3: The schematic of experimental procedures.

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CHAPTER 3: Reference La

3

Ta

0.5

Ga

5.1

Al

0.4

O

14

(LTGA)

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§3.1 Introduction

Among the langasite family, one of considered materials for HT sensor applications is LTGA single crystal [26], which has been studied in detail from the point view of crystal growth, electrical, piezoelectric, acoustic and scintillation properties [27, 28, 43-46]. Its thermal expansion has been measured from RT to 600°C [28]. However, to date, there are no reports about the dependence of other thermal properties on temperature, such as thermal conductivity and specific heat. In the case of HT applications, thermal expansion will affect the piezoelectric properties and device fabrication. At this point, it should be noticed that the piezoelectric coefficients depend on the elastic constants, and the later depend in turn on the dimensions and density (lattice parameters) of the material (related equations are given in Chapter 2). Therefore, in order to further understand the LTGA crystal and evaluate its feasibility for practical applications, it is essential to investigate its thermal behavior at HT range.

In this chapter, LTGA has been studied as a reference of CTGAS single crystals. For it, a LTGA crystal was grown using the Cz technique. Its crystalline quality was assessed by the XRC measurements. The transmittance was studied as a function of annealing conditions.

The temperature dependent thermal properties of grown crystal were investigated. The resistivity and piezoelectric properties were also determined.

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§3.2 Experimental

3.2.1 Polycrystalline synthesis

Commercial powders, La2O3, Ta2O5, Ga2O3 and Al2O3 of 4N purity, were weighed stoichiometrically according to La3Ta0.5Ga5.1Al0.4O14, except Ga2O3, which was 1 at.%

enriched for the compensation of its evaporation during the growth. After mixing, the powders were pressed at 300 MPa and subsequently sintered at 1350°C for 30 h.

3.2.2 Crystal growth

Reacted polycrystalline LTGA was loaded into an Ir-crucible. A single crystal was pulled with a c-oriented LTGA seed by the Cz method. The growth atmosphere was N2 with 1% O2, in order to suppress Ga2O3 evaporation while preventing the oxidation of crucible. The rotation rate was 15 rpm. The pulling speed was 0.8 mm/h.

3.2.3 Characterizations

The crystallinity of reference LTGA crystal was investigated through XRC measurements. High-resolution spectra were measured on a fine polished a-cut plate with a scan step of 0.0001° and 0.5 s integration. Temperature dependent powder XRD was also measured. 2θ/θ scans were recorded at RT, then every 100°C up to 1000°C, and finally every 50°C up to 1300°C. The transmittance was measured with the as-grown and annealed Y-cut samples of 1 mm in thickness from ultraviolet-visible (UV-vis) to near infrared (IR) range.

The thermal expansion was measured from RT to 900°C using a heating rate of 5°C/minute.

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Two samples of 3×3×10 mm³ (a- and c-axis) were polished on the faces perpendicular to the length direction. The specific heat was obtained from 50 to 1000°C, at a heating speed of 20°C/minute. A 1 mm thick single crystal disc of 5 mm in diameter was used. The measurement was carried out under Ar with sapphire as the reference material. The thermal diffusivity was measured from RT up to 700°C. Square a- and c-cut samples of 4×4×1 mm³ were coated with graphite in order to fully absorb the laser radiation. The electrical resistivity was measured with a Y-cut LTGA sample. The measurements were performed under air between 200 and 900°C, with 30 minutes holding time at each temperature. The applied voltage was 50 V. The dielectric, piezoelectric and elastic constants were determined using the measured C, fr and fa according to IEEE standards [42].

§3.3 Results and discussion 3.3.1 Crystal growth

A 100 mm long and 27 mm in diameter LTGA single crystal was successfully grown using the Cz technique. The photograph of the as grown crystal is shown in Fig. 3.1. It is free of cracking and inclusions, presenting an orange coloration. The up-left image shows the presence of 6 ridges in the upper cone, while six facets are observed in the main body part.

This crystal habit correlates very well with the one predicted by the DFDH method [47, 48]

using the software Materials Studio [49]. As seen in the right schematic, the crystal facets correspond to the (100) and equivalent planes.

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Fig. 3.1: Photograph of the as-grown LTGA crystal and expected habit of LTG crystal based on the BFDH method.

3.3.2 XRC measurements

Figure 3.2 shows XRCs of the (110) diffraction peak around the <100> and <001>

rocking axes in order to analyze the tilting and twisting, respectively. The curves are very symmetric. In both cases, the full width at half maximum (FWHM) was found to be as small as 26 arcsec, indicating the high crystalline quality of the LTGA crystal.

3.3.3 HT powder XRD and thermal expansion

The HT Powder XRD measurements were carried out over the temperature range of RT-1300°C. As an example, Figure 3.3 shows the good agreement between the XRD pattern at 1300°C and the calculated one using the software Mercury. All patterns were similar, i.e.

the single phase observed is stable up to 1300°C, thus proving the absence of a crystallographic phase transition.

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Fig. 3.2: LTGA (110) XRCs around the rocking axes <100> and <001>.

Fig. 3.3: XRD patterns of simulated LTG and as-grown LTGA crystal at 1300°C.

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In the case of the langasite family, the two components of the thermal expansion coefficient α correspond to the expansion of a (αa) and c (αc) lattice constants. Using the temperature dependent XRD data, the lattice parameters were calculated with the software FullProf [50]. At RT, the lattice constants are a = 8.223 Å and c = 5.116 Å. With the increase of temperature, both values are increasing. The estimated thermal expansion ratios along the axes a and c are shown in Fig. 3.4, which were fitted by the following equations:

9 2 6 4

/ 0 1.06 10 7.03 10 2.62 10

a a ^ T ^ T ^

       (3.1)

9 2 6 4

/ 0 1.29 10 4.56 10 1.63 10

c c ^ T ^ T ^

       (3.2)

where Δa and Δc are the variation of lattice parameters, a0 and c0 are the lattice parameters at RT, and T is the temperature in Celsius. The fits almost coincide with those obtained with the dilatometer (also shown in Fig. 3.4), indicating the accuracy of the two independent measurements. The average thermal expansion coefficients obtained by linear fits are α^a= 8.48×10^-6 K^-1 and α^c= 6.32×10^-6 K^-1, larger compared to the reported values, α^a= 6.56×10^-6 K^-1 and αc = 4.38×10^-6 K^-1, respectively [28]. As the measured values for lattice expansion are quite close along both axes, the LTGA crystal exhibits a weak anisotropy, what is beneficial to prevent cracking, especially for HT applications.

The volume of the unit cell (v) was also calculated from the calculated lattice parameters.

The volume at RT was 299.548 Å³, and it increased quite linearly to 308.420 Å³ at 1300°C.

The corresponding coefficient of volume expansion is 2.35×10^-5 K^-1.

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Fig. 3.4: Thermal expansion ratio of LTGA crystal versus temperature.

3.3.4 Density

The density of as-grown LTGA crystal at RT, measured by the Archimedes method, was found to be 6.09±0.03 g/cm³. On the other hand, the density was also estimated using following equation:

cal

0 a

MZ

 N

 _(3.3)

where M is the molar weight, Z is the number of formula for one unit cell (Z = 1), v0 is the volume of the unit cell at RT, and Na is the Avogadro constant. The density was calculated to be 6.08 g/cm³, in good agreement with the measured value.

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The temperature dependent density can be determined by the equation:

0 0 T

T

  

  _(3.4)

where ρ⁰ and v0 are the density and volume of unit cell at RT, respectively, while the ρ^T and vT

are the corresponding values at temperature T. The density decreases linearly from 6.09 g/cm³ at RT to 5.91 g/cm³ at 1300°C.

3.3.5 Transmittance

The coloration of grown crystal was studied by the transmittance spectra. Figure 3.5 shows the transmittance of as-grown and annealed LTGA together with the corresponding crystal photographs. As indicated in transmittance spetra, the orange coloration is caused by an absorption band around 480 nm. This absorption band can be efficiently eliminated by annealing under N2 at 1200°C, so that the crystal becomes colorless (as illustrated in the inset of Fig. 3.5). Instead, the UV absorption band at 355 nm doesn’t change significantly. On the other hand, both 355 and 480 nm absorption bands increase when annealing under air, suggesting the connection of oxygen atoms with the defect structure of this disordered compound. In addition, an IR band at around 1870 nm is observed.

A N2-annealed sample was partially exposed under 254 nm UV exicitation. The transmittance as well as crystal photograph are shown in Fig. 3.6. As can be seen, after UV excitation, the coloration of the sample changed to be orange (as shown in the inset of Fig.

3.6). Accordingly, the 480 nm band is observed on the transmittance of corresponding crystal part. Therefore, the color-related defects of LTGA can be affected by both annealing and UV excitation.

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Fig. 3.5: transmittance of as-grown and annealed LTGA together with the corresponding crystal photographs.

Fig. 3.6: Transmittance of LTGA by N2 annealing and UV excitation as well as corresponding crystal photograph.

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3.3.6 Specific heat

The temperature dependent molar specific heat Cp of grown LTGA is illustrated in Fig.

3.7. It shows a monotonous increase from 484 J/(mol∙K) at 50°C to 646 J/(mol∙K) at 1000°C, which is larger than that of LGS crystal (from 458 to 580 J/(mol∙K) from RT to 1000°C) [51].

From this measurement, the specific heat at constant volume Cv is calculated by the thermodynamic equation [52]:

2

v p

C C  VT

   (3.5)

where α and V represent the thermal expansion coefficient and the specific volume, respectively, T denotes the absolute temperature, and β is the coefficient of compressibility, which can be obtained using the following equation [53]:



11 12



3 s 2s

   (3.6)

whereas s11 and s12 are two elastic compliance constants. These values have been reported by Karaki et al. from RT to 1000°C [28]. The calculated Cv is shown together with the Cp in Fig.

3.7, showing a continuous increase, 447-620 J/(mol∙K), from 100 to 1000°C. On the other hand, the Cv at HT can be estimated by the law of Kopp [54] as:

3 3 574 / ( )

v A

C       k N n R n J mol K 

(3.7) where k and R are Boltzmann’s and gas constants, respectively, and n is the number of atoms in the chemical formula (23 in the case of LTGA), obtaining a value of 574 J/(mol∙K) (horizontal line in Fig. 3.7). This value is only about 8% lower than the experimental one, indicating the good approximation given by the simple Kopp’s equation.

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Fig. 3.7: Calculated Cp, Cv and Kopp values as a function of temperature.

3.3.7 Thermal diffusivity and conductivity

Figure 3.8 shows the temperature dependence of thermal diffusivity . From RT to about 450°C, the value along the c-axis decreases continuously from 0.79 to 0.63 mm²/s, and then it increases to 0.71 mm²/s. On the contrary, the value along the a-axis increases monotonically along the whole temperature range, varying from 0.47 to 0.64 mm²/s. Therefore, at RT, the thermal diffusivity along the c-axis is almost double that along the a-axis and they exhibit opposite trends with the temperature. However, at HT they become close and show a similar temperature dependence. We presume that this behavior is closely due to the large variation of resistivity with the temperature, as shown below. At RT, because the crystal resistivity is

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very high (estimated in the order of 10¹⁶Ω cm from Fig. 3.10), the heat is transferred through lattice vibrations, i.e. by means of phonons. On the other side, as the temperature is increased, the resistivity reduces by orders of magnitude and the heat transfer through carriers starts to play a more dominant role. Therefore, the thermal diffusivity exhibits an increasing trend and a less anisotropic dependence. In the case of LGS, the thermal diffusivity shows in the same temperature range a continuous decrease along both axes, 0.49-0.37 mm²/s and 0.72-0.48 mm²/s for a- and c-axis, respectively [51]. Therefore, although LTGA and LGS have comparable values at RT, they exhibit different trends and values with increasing temperature.

Fig. 3.8: Temperature dependence of thermal diffusivity of LTGA crystal.

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The Thermal conductivity can be derived from the previously measured parameters using the following equation [55]:

Cp

  

   (3.8)

Figure 3.9 shows the calculated for the a- and c-axes, as a function of temperature.

Along the a-axis the value increases almost linearly from 1.2 W/mK at 50°C to 2.2 W/mK at 700°C. Along the c-axis, after a slight decrease to the minimum at about 200°C (1.9 W/mK), gradually increases, reaching a value of 2.4 W/mK at 700°C. The of grown LTGA are comparable to those reported for LGS at RT, a = 1.3 W/mK and c = 1.9 W/mK, and higher than those of LGS at elevated temperature [51], a = 1.1 W/mK and c = 1.4 W/mK at 700°C, which favors a more efficient heat release.

Fig. 3.9: Calculated thermal conductivity of LTGA crystal as a function of temperature.

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3.3.8 Electrical resistvity

The resistivity ρ of grown LTGA crystal up to 900°C is shown in Fig. 3.10 together with reported one [27]. As can be observed, the resistivity decreases continuously from 4×10¹⁰ Ω cm at 200°C to 2×10⁵ Ω cm at 900°C, in good agreement with the reported one [27] and according to the Arrhenius law [11]:

0exp ^a

B

E

  ^k T^

  (3.9)

where ρ⁰ is the resistivity for T = ∞, kB is the Boltzmann’s constant, and Ea is the activation energy, which reflects the slope of the Arrhenius line. From the least square fit, the Ea is estimated to be 0.82 eV, which is comparable to the reported value, 0.77 eV.

3.3.9 Electromechanical properties

Table 3.1 lists the dielectric, piezoelectric and elastic constants of LTGA and LGS crystals. In comparison with LGS [20], the LTGA crystal has a larger d11 and a smaller d14. Furthermore, the measured values (d11 = 6.94 pC/N, k12 = 17%, and Q = 12000) are larger than the reported ones for LTGA (d11 = 6.6 pC/N, k12 = 16%, and Q = 4500, respectively [27]).

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Fig. 3.10: Temperature dependence of resistivity of LTGA crystal.

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Table 3.1: Relative dielectric constants ijT, piezoelectric coefficients dij (10^-12 C/N), and elastic compliances sijE (10^-12 m²/N).

Parameters LGS [20] LTGA

11T/ 0 19.2 21.2

33T/ 0 50.7 70.0

d11 6.15 6.94

d14 -6.01 -4.67

s11E 8.86 9.02

s12E -4.24 -4.18

s13E -1.79 -2.23

s14E -3.48 -3.60

s33E 5.19 8.10

s44E 20.32 20.89

§3.4 Conclusions

This chapter is a preliminary study of the LTGA which serves as a reference, since it is the langasite compound which is nowadays considered for HT pressure sensors. A LTGA single crystal has been grown using the Cz method with N2+1% O2. The 26 arcsec FWHM of XRC confirmed the high crystallinity of the LTGA crystal. High temperature XRD measurements indicate the absence of phase transitions up to 1300°C. The transmittance suggests that the color-related defects can be affected by both annealing and UV excitation.

The thermal properties of the crystal are analyzed in a wide temperature range. The average

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thermal expansion coefficients are αa = 8.48×10^-6 K^-1 and αc = 6.32×10^-6 K^-1. Thethermal conductivities along the a and c axes at 50°C are 1.2 and 2.0 W/mK, respectively. The resistivity of grown crystal at 400°C is 6.7×10⁷Ω cm. The measured piezoelectric coefficient d11, electromechanical coupling factor k12 and corresponding mechanical quality factor Q at RT are 6.94 pC/N, 17% and 12000, respectively.

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CHAPTER 4: Ca

3

TaAl

3

Si

2

O

14

(CTAS) single crystal

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§4.1 Introduction

In chapter 1, it is mentioned that the incorporation of Al for CTGS on the Ga site may increase the lattice distortion, thus enhancing the piezoelectric coefficient. However, so far the reported CTAS single crystals present severe cracking and inclusions [35]. On the other hand, the effect of oxygen partial pressure during growth could not be studied due to the use of Ir crucible, since it will be oxided under high O2 concentrations. This chapter aims at the growth of CTAS single crystals under several conditions in order to optimize the growth and to improve the electrical and piezoelectric properties. To this end, the growth conditions necessary for high quality CTAS single crystals were investigated. Further, Pt crucible has been proposed for the first time to investigate the effect of oxygen partial pressure during growth. The influence is systematically examined in terms of transmittance, resistivity and piezoelectric properties.

§4.2 Experimental

4.2.1 Polycrystalline synthesis

The polycrystalline CTAS was synthesized by the solid state reaction method. Powder materials of 4N purity, CaCO3, Ta2O5, Al2O3 and SiO2, were weighed stoichiometrically.

After mixing, the powders were compressed at 30 MPa and subsequently sintered at HT for 25 h in order to release the CO2.

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4.2.2 Crystal growth

CTAS single crystals were grown using the Cz method with a 30 kW RF generator. The first CTAS single crystal was pulled up with an a-oriented CTGS seed. From this crystal CTAS seeds were prepared and used for the subsequent growths. The fixed rotation rate of 12 rpm and pulling speed of 0.5 mm/h were used from the seeding till the final separation. The growth conditions in terms of crucible type and growth atmosphere are shown in Table 4.1.

Table 4.1: Growth conditions of CTAS single crystals.

Run No. Crucible Growth atmosphere

1

Pt

N2

2 N2+1%O2

3 N2+10%O2

4 Air

5

Ir

N2

6 N2+1%O2

4.2.3 Characterizations

The 2θ scans of powder XRD were carried out at various temperatures between RT and 1200°C. Chemical analysis was done by the ICP-OES method. Transmittance spectra were measured with 1 mm thick a- and c-cut plates. The electrical resistivity of 1 mm thick Y-cut samples was measured from 400 to 1000°C. The applied voltage was 50 V from 400 to 700°C,

Influence of Oxygen Partial Pressure and Al Content on the Resistivity and Piezoelectric Properties of

Influence of Oxygen Partial Pressure and Al Content on the Resistivity and Piezoelectric Properties of

Ca

TaGa

Al

Si

O

Single Crystals

July 2016

Xiuwei FU

ﾌ ｼｭ

Influence of Oxygen Partial Pressure and Al Content on the Resistivity and Piezoelectric Properties of

Ca

TaGa

Al

Si

O

Single Crystals

July 2016

Waseda Univerisy

Graduate School of Advanced Science and Engineering Department of Nanoscience and Nanoengineering,

Research on Nano-structured Crystal Chemistry

Xiuwei FU

ﾌ ｼｭ

PREFACE

TABLE OF CONTENTS

CHAPTER 1: Introduction

§1.1 Piezoelectricity

§1.2 High temperature piezoelectric sensors

§1.3 Piezoelectric materials

§1.4 Langasite family

§1.5 Objectives and overview of thesis

CHAPTER 2: Experimental

§2.1 Polycrystalline synthesis

§2.2 Crystal growth

§2.3 Characterization techniqures 2.3.1 Chemical composition

2.3.2 X-ray analysis

2.3.3 Transmittance

2.3.4 Thermal properties

2.3.5 Electrical resistivity

2.3.6 Electromechanical properties



d



d

 









§2.4 Conclusions

CHAPTER 3: Reference La

Ta

Ga

Al

O

(LTGA)

§3.1 Introduction

§3.2 Experimental

3.2.1 Polycrystalline synthesis

3.2.2 Crystal growth

3.2.3 Characterizations

§3.3 Results and discussion 3.3.1 Crystal growth

3.3.2 XRC measurements

3.3.3 HT powder XRD and thermal expansion

3.3.4 Density

3.3.5 Transmittance

3.3.6 Specific heat





3 3 574 / ( )

C       k N n R n J mol K 

3.3.7 Thermal diffusivity and conductivity

  

3.3.8 Electrical resistvity

3.3.9 Electromechanical properties

§3.4 Conclusions

CHAPTER 4: Ca

TaAl

Si

ﾌｼｭ

ﾌｼｭ