Inorganic Scintillator and Crystal Growth Methods E-Book

Yuui Yokota

• Herausgeber: Wiley-VCH
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 313

Veröffentlichungsjahr: 2024

Beschreibung

Provides an up-to-date summary of new scintillating materials for ionization radiation detectors and recent progress in growth methods for single crystals

Scintillators, a type of material that can emit light after absorbing high-energy particles or rays, play a central role in the field of radiation detection. Scintillators are the core components of nuclear medicine imaging equipment, baggage and container security inspection, non-destructive testing of large industrial equipment, environmental monitoring, and many other applications.

Inorganic Scintillator and Crystal Growth Methods updates readers with the latest developments in the rapidly-advancing area. Opening with a brief introduction, the book covers a range of novel scintillator single crystals; gamma-ray scintillators with garnet-type oxide crystals, pyrochlore-type oxide crystals, halide crystals, neutron scintillators with fluoride crystals, halide crystals, vacuum ultraviolet (VUV) scintillators, and fluoride scintillators. Concise chapters also address self-organized scintillators with eutectic morphology and nanoparticle scintillator crystals.

• Provides a timely and reliable overview of the achievements, trends, and advances in the field
• Highlights new work on single crystals of piezoelectric and scintillator materials, as well as various growth methods of different functional single crystals
• Presented in a succinct format that allows readers to quickly ingest key information
• Includes real-world perspectives on a variety of industrial applications
• Written by an international team of experts in non-organic material science

Inorganic Scintillator and Crystal Growth Methods is a valuable resource for both academics and industry professionals, especially materials scientists, inorganic chemists, and radiation physicists.

Leseprobe

Table of Contents

Cover

Table of Contents

Title Page

Copyright

1 Introduction

1.1 History of Scintillator Developments

1.2 Introduction of Conventional Scintillators and Crystal Growth Methods

References

2 Gamma-Ray Scintillators and Crystal Growth Methods

References

2.1 Garnet-Type Scintillators and Crystal Growth Methods

2.2 Pyrosilicate-Type Scintillators and Crystal Growth Methods

2.3 Halide Scintillators and Crystal Growth Methods

3 Neutron Scintillators and Crystal Growth Methods

3.1 Development of Crystal Growth Method for Fluoride Scintillator

3.2 Lithium Scintillators

3.3 Borate Scintillators

References

4 VUV Scintillators and Crystal Growth Methods

4.1 Characteristics of VUV Scintillators

4.2 VUV Scintillators (LaF

3

, LiCaAlF

6

, LuLiF

4

, LuF

3

, CaF

2

, BaF

2

)

4.3 Elpasolite-Type VUV Scintillators

4.4 Fluorite VUV Scintillator

4.5 VUV Scintillators With Two Dopants

References

5 Perspective on Industrial Applications

5.1 Development of Mass Production Process for Scintillator Single Crystals

5.2 Development of Radiation Detectors

References

Index

End User License Agreement

List of Tables

Chapter 2.2

Table 2.2.1 Crystal structure type of RE

2

Si

2

O

7

.

Table 2.2.2 Summary of the possibility of growing single crystals from melt....

Table 2.2.3 Comparison of ionic radii of rare-earth ions.

Table 2.2.4 Comparison of Ce

3+

5d levels in Ce-doped (La,Gd)Si

2

O

7

and Ce...

Table 2.2.5 List of fitting parameters of a single barrier process.

Table 2.2.6 List of the scintillation properties of Ce-doped (La,Gd)

2

Si

2

O

7

w...

Table 2.2.7 List of fitting parameters of a single barrier process.

Chapter 2.3

Table 2.3.1 Characteristics of typical halide scintillator single crystals....

Chapter 3

Table 3.1 Representative materials of neutron scintillators containing Li.

Table 3.2 Representative borate materials of neutron scintillators containin...

Chapter 4

Table 4.1 List of typical VUV scintillators.

List of Illustrations

Chapter 1

Figure 1.1 Schematic diagram of scintillator and photo acceptance unit in ra...

Figure 1.2 History of the development of scintillator crystals with progress...

Figure 1.3 Schematic diagrams of single crystal and polycrystalline.

Figure 1.4 Single crystals grown by Cz, BS, FZ, and µ-PD methods.

Figure 1.5 Phase diagram of a binary complete solid–solution system, AO–BO....

Figure 1.6 Schematic diagrams of (a) normal freezing and (b) zone melting pr...

Figure 1.7 Schematic diagrams of super cooling and cellular growth.

Figure 1.8 Bravais lattices.

Figure 1.9 (a) Schottky, (b) Frenkel, and (c) anti-site defects.

Figure 1.10 (a) Doping of ion with different valence and (b) oxygen nonstoic...

Figure 1.11 (a) Schematic diagram of XRC measurement and the X-ray diffracto...

Figure 1.12 Pole figures of single crystals.

Figure 1.13 (a) Schematic diagrams of Laue camera, (b) Laue camera device us...

Figure 1.14 (a) Schematic diagram and (b) actual furnace (high-frequency ind...

Figure 1.15 (a) Ir crucible and seed holder for Cz method. (b) Pt-Rh crucibl...

Figure 1.16 Relationship between the solid–liquid interface shape and the ro...

Figure 1.17 Bulk single crystals grown by the Cz method.

Figure 1.18 Change of concentration during crystal growth in Cz method. (a) ...

Figure 1.19 (a) Schematic diagram and (b) actual furnace of VB with the resi...

Figure 1.20 Schematic diagram of the VGF method.

Figure 1.21 Crucibles for the VB method.

Figure 1.22 Bulk single crystals grown by the BS method.

Figure 1.23 The schematic diagram and actual furnace of infrared heating–typ...

Figure 1.24 Change of concentration during crystal growth in FZ method.

Figure 1.25 Concentration distribution in single crystal grown by FZ method....

Figure 1.26 Schematic diagram of traveling solvent FZ (TSFZ) method.

Figure 1.27 Schematic diagram and actual furnace of µ-PD method for oxide si...

Figure 1.28 Crucibles for µ-PD method, and schematic diagram and actual imag...

Figure 1.29 Schematic diagrams of crystal growth with small and large thickn...

Figure 1.30 Effect of number of capillaries on Ce segregation in YAG:Ce sing...

Figure 1.32 (a) Schematic diagram of crystal growth for tube-shaped fluoride...

Figure 1.31 (a) Schematic diagram of shape-controlled crystal growth by the ...

Figure 1.33 (a) Schematic diagram of A-µ-PD method and developed A-µ-PD furn...

Figure 1.34 Flow chart of crystal growth using µ-PD method.

Figure 1.35 Schematic diagram of EFG method.

Figure 1.36 Schematic diagram of Verneuil method.

Figure 1.37 Schematic diagram of LHPG method.

Figure 1.38 Schematic diagram of skull melting method.

Figure 1.39 Schematic diagram of TSSG method.

Figure 1.40 Schematic diagram and actual furnace of arc melting method.

Figure 1.41 Schematic diagram of heat-exchange method.

Figure 1.42 Schematic diagram of crystal growth method integrating µ-PD meth...

Chapter 2.1

Figure 2.1.1 The energy-level diagram pertains to the material design discus...

Figure 2.1.2 A GGAG:Ce crystal with a diameter of (a) 2 in., (b) 3 in., and ...

Figure 2.1.3 The schematic description of “the distributed weight cooling te...

Figure 2.1.4 The energy resolution of the Gd

3

(Ga, Al)

5

O

12

:Ce sample, with an...

Figure 2.1.5 Diagram illustrating the involvement of stable Ce

4+

in the ...

Figure 2.1.6 Time-resolved decay curves of Gd

3

(Ga, Al)

5

O

12

:Ce, Mg samples up...

Figure 2.1.7 (a) Energy resolution measurements obtained for the samples acr...

Figure 2.1.8 Optical absorption spectra of GGAG:Ce,Li samples. Figure shows ...

Figure 2.1.9 Temperature dependence of PL decay time for varying Ce/Li conce...

Figure 2.1.10 Energy diagram of bidirectional energy transfer in garnet-type...

Figure 2.1.11 An example of shape-controlled single-crystal fibers grown by ...

Figure 2.1.12 The experimental setup employed by Kamada et al. [78] for sapp...

Figure 2.1.13 Die geometry of Mo crucible used by Yoshino et al. [85] for gr...

Figure 2.1.14 Schematic image of the CH method.

Figure 2.1.15 Schematic image of the SAM method.

Figure 2.1.16 Schematic image of the OCCC method.

Chapter 2.2

Figure 2.2.1 Relationship between rare-earth ions and crystal structure of R...

Figure 2.2.2 PL emission and excitation spectra of LPS:Ce at 77 and 300 K....

Figure 2.2.3 Temperature dependence of PL decay time for LPS:Ce.

Figure 2.2.4 PL excitation spectrum of Ce-doped Sc

2

Si

2

O

7

.

Figure 2.2.5 PL emission spectrum of Ce-doped Sc

2

Si

2

O

7

.

Figure 2.2.6 X-ray diffraction patterns of undoped and Ce-doped Yb

2

Si

2

O

7

....

Figure 2.2.7 Transmission spectra of undoped and Ce-doped Yb

2

Si

2

O

7

.

Figure 2.2.8 Temperature dependence of photoluminescence emission spectra fo...

Figure 2.2.9 Radioluminescence emission spectra of undoped and Ce-doped Yb

2

S...

Figure 2.2.10 PL excitation spectrum of Ce-doped Y

2

Si

2

O

7

.

Figure 2.2.11 PL emission and X-ray excited luminescence spectra of Ce-doped...

Figure 2.2.12 PL emission and excitation spectra of GPS:Ce with orthorhombic...

Figure 2.2.13 PL emission and excitation spectra of GPS:Ce with triclinic ph...

Figure 2.2.14 PL emission and excitation spectra of GPS:Ce with monoclinic p...

Figure 2.2.15 X-ray radioluminescence spectra of GPS:Ce with orthorhombic an...

Figure 2.2.16 PL emission spectrum of Ce-doped Pr

2

Si

2

O

7

.

Figure 2.2.17 X-ray diffraction pattern of Ce

2

Si

2

O

7

.

Figure 2.2.18 Photoluminescence excitation (dashed line) and emission (solid...

Figure 2.2.19 Photoluminescence excitation (dashed line) and emission (solid...

Figure 2.2.20 Temperature dependence of quantum yield for Ce

2

Si

2

O

7

.

Figure 2.2.21 Pulse height spectra of Ce

2

Si

2

O

7

.

Figure 2.2.22 Scintillation decay curve of Ce

2

Si

2

O

7

.

Figure 2.2.23 PL emission spectrum of Ce-doped La

2

Si

2

O

7

.

Figure 2.2.24 Comparison of photoluminescence emission spectra of Ce-doped (...

Figure 2.2.25 Pulse height spectra of La 23.5 at.% substituted Ce:La-GPS (le...

Figure 2.2.26 Temperature dependence of light yield for Ce-doped (La,Gd)

2

Si

2

Figure 2.2.27 X-ray diffraction pattern of (Ce

0.015

La

0.600

Y

0.385

)

2

Si

2

O

7

.

Figure 2.2.28 PL emission and excitation spectra of (Ce

0.015

La

0.600

Y

0.385

)

2

S...

Figure 2.2.29 Temperature dependence of PL emission spectrum for (Ce

0.015

La

0

...

Figure 2.2.30 PL decay curves of (Ce

0.015

La

0.600

Y

0.385

)

2

Si

2

O

7

.

Figure 2.2.31 Temperature dependence of PL decay time for (Ce

0.015

La

0.600

Y

0.

...

Figure 2.2.32 Pulse height spectra of (Ce

0.015

La

0.600

Y

0.385

)

2

Si

2

O

7

.

Figure 2.2.33 Scintillation decay curve of (Ce

0.015

La

0.600

Y

0.385

)

2

Si

2

O

7

.

Chapter 2.3

Figure 2.3.1 Band-gap dependence of the light yield for oxide, fluoride, and...

Figure 2.3.2 Light yield dependence of the energy resolution for oxide, fluo...

Figure 2.3.3 Schematic diagram of the VB method using sealed quartz ampoule ...

Figure 2.3.4 Schematic diagram of H-µ-PD method and actual furnace.

Figure 2.3.5 Procedure of crystal growth by the H-VB method.

Figure 2.3.6 Schematic diagrams of (a) modified EFG method and (b) Cz method...

Figure 2.3.7 Measurement equipment for halide scintillator single crystals. ...

Figure 2.3.8 Equipment for processing halide single crystals.

Figure 2.3.9 Crystal structures of NaI and CsI

3

.

Figure 2.3.10 Crystal structures of CeBr

3

and LaBr

3

.

Figure 2.3.12 Pulse-height spectrum and decay curve under γ-ray irradiation ...

Figure 2.3.11 Photoluminescence spectra and decay curve of LaBr

3

:Ce single c...

Figure 2.3.13 (a) Dimensions of four types of carbon after-heaters and (b) C...

Figure 2.3.14 (a) Emission spectra and (b) pulse-height spectra of the CeBr

3

Figure 2.3.15 Crystal structure of SrI

2

.

Figure 2.3.16 SrI

2

:Eu single crystals grown by the H-µ-PD method.

Figure 2.3.17 (a) Pulse-height spectra and (b) decay curves of SrI

2

:Eu singl...

Figure 2.3.18 (a) 1.5 in. SrI

2

:Eu single crystal and polished specimen cut o...

Figure 2.3.19 Crystal structure of Cs

2

HfCl

6

.

Figure 2.3.20 Crystal structure of KCaI

3

.

Figure 2.3.21 Crystal structure of CsPbBr

3

(cubic structure).

Chapter 3

Figure 3.1 Schematic diagram and actual furnace of µ-PD method for fluoride ...

Figure 3.2 Carbon crucible and insulator for crystal growth of fluoride scin...

Figure 3.3 Solid–liquid interface during crystal growth of fluoride single c...

Figure 3.4 Schematic diagram and actual furnace of Cz method for fluoride si...

Figure 3.5 A 1 in. LiYF

4

:Ce bulk single crystal grown by the Cz method using...

Figure 3.6 Undoped and Ce-doped LiYF

4

crystals with various Ce concentration...

Figure 3.7 Schematic diagram of crystal growth by µ-PD method using quenchin...

Figure 3.8 Growth of single crystal of phase below

T

p

using self-flux.

Figure 3.9 The schematic diagram of emission mechanism by neutron irradiatio...

Figure 3.10 Crystal structure of LiCaAlF

6

.

Figure 3.11 (a) Mechanism of Na co-doping for the LiCAF:Ce single crystal. (...

Figure 3.12 (a) Mechanism of using Al metal as starting material for LiCAF:E...

Figure 3.13 (a) LiCSAF:Eu single crystals with various Ca/Sr ratios grown by...

Figure 3.14 Crystal structure of LiYF

4

.

Figure 3.15 Phase diagram of LiF-YF

3

, LiF-LuF

3

, LiF-GdF

3

, and LiF-CeF

3

.

Figure 3.16 (a) LYF:Ce single crystals grown by µ-PD and Cz methods. (b) Ce ...

Figure 3.17 (a) In-, Pb-, and Sn-doped LiCaAlF

6

single crystals grown by µ-P...

Figure 3.18 (a) Phase diagram of LiF-LuF

3

. (b) Grown LiYF

4

/LiF and LiLuF

4

/Li...

Figure 3.19 Crystal structures of (a)

AE

3

RE

Cl

6

and (b) LiAlO

2

.

Figure 3.20 Crystal structures of (a) Sr

3

Y(BO

3

)

3

and (b) Ca

3

(BO

3

)

2

.

Chapter 4

Figure 4.1 CaF

2

:Nd single crystal grown by Cz method and the X-ray radiolumi...

Figure 4.2 (a) VUV fluoride single crystals grown by µ-PD method. (b) Emissi...

Chapter 5

Figure 5.1 Schematic diagram of Cz method using double crucibles.

Figure 5.2 Schematic diagram of Cz method with automatic diameter control (A...

Figure 5.3 Continuous crystal growth process of Cz method using residual mel...

Figure 5.4 Schematic diagrams of multiple shaped single crystals growth by E...

Figure 5.5 (a) Square-shaped YAG:Ce single crystals grown by the µ-PD method...

Figure 5.6 Schematic diagram of µ-PD methods using crucible with a tube die ...

Figure 5.7 Schematic diagrams of µ-PD methods using crucible with multiple d...

Figure 5.8 Schematic diagrams of µ-PD methods with continuous charging syste...

Figure 5.9 Schematic diagram of multiple crystal growth of VB method.

Figure 5.10 Schematic diagram of scintillator array and actual GGAG scintill...

Figure 5.11 Packaged halide bulk scintillator single crystal.

Guide

Cover

Table of Contents

Title Page

Copyright

Begin Reading

Index

End User License Agreement

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Inorganic Scintillator and Crystal Growth Methods

Yuui Yokota

Masao Yoshino

Takahiko Horiai

Authors

Prof. Yuui YokotaTohoku University2-1-1, KatahiraAoba-ku, SendaiMiyagi 980-8577Japan

Prof. Masao YoshinoTohoku University2-1-1, KatahiraAoba-ku, SendaiMiyagi 980-8577Japan

Prof. Takahiko HoriaiTohoku University2-1-1, KatahiraAoba-ku, SendaiMiyagi 980-8577Japan

Cover Image: © Ekaterina Demidova/Getty Images

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1Introduction

1.1 History of Scintillator Developments

A scintillator can convert radiation (alpha-ray, beta-ray, gamma-ray, X-ray, and neutron) into light (photon), and radiation detectors using scintillators and photo acceptance units have been used for various applications in medical, security, environmental, high-energy fields, etc. (Figure 1.1). Photo acceptance units such as photomultiplier tubes (PMT), photodiodes, and multi-pixel photon counters (MPPC) can convert light into electrical signals, which enables detection and measurement (count) of radiation using multi-channel analyzers.

In these applications, there are some required properties of scintillators, and the required performance that is considered important varies greatly depending on the type of application. Typical parameters considered important in scintillator crystals include light yield, energy resolution, decay time, density, effective atomic number, emission wavelength, and afterglow. Furthermore, mass productivity, chemical stability, crystal workability, radiation resistance, etc. are also important for commercial use. For example, high light yield, large density and effective atomic number, and short decay time are required in applications under gamma-ray irradiation with the short measurement time.

One of the most important characteristics of scintillators is the light yield, which is directly related to radiation detection sensitivity. For the emitted light in the scintillator under radiation to efficiently enter the photo acceptance unit, the scintillator must be transparent at the emission wavelength. Especially in the case of high-energy radiation such as gamma-ray, the scintillator becomes large enough to stop the radiation inside, so efficient extraction of the emitted light inside greatly affects the performance of the scintillator. Therefore, many scintillators have been utilized as single crystals with high transparency.

Figure 1.1 Schematic diagram of scintillator and photo acceptance unit in radiation detector.

1.2 Introduction of Conventional Scintillators and Crystal Growth Methods

1.2.1 Conventional Scintillator Single Crystals

Figure 1.2 shows the history of the development of scintillator crystals with the progress of crystal growth method. The development of scintillator single crystals has progressed along with that of crystal growth technology. In order to indicate excellent luminescence and scintillation performance (high light yield, great energy resolution, high transparency etc.), scintillator single crystals are required to be of high quality, and, as a result, progress in crystal growth technology is also highly recommended.

Figure 1.2 History of the development of scintillator crystals with progress of growth method.

First, CsI:Tl and NaI:Tl single crystals were developed as the most familiar and inexpensive scintillator single crystals [1, 2]. They are widely used in application devices because these large bulk single crystals can easily be grown by the conventional melt-growth method and they have relatively low hygroscopicity.

After that, various oxide scintillator single crystals have been developed along with the establishment of crystal growth methods using precious metal crucibles such as iridium (Ir) and platinum (Pt) for oxide single crystals with a high melting point near 2000 °C. Among them, typical oxide scintillator single crystals are the garnet-type Y3Al5O12:Ce and Lu3Al5O12:Pr, perovskite-type YAlO3:Ce and LuAlO3:Ce, and silicate-type Lu2SiO5:Ce, (Lu,Y)2SiO5:Ce, and Gd2SiO5:Ce [3–9]. In addition, as a high-density and effective atomic number scintillator, Bi4Ge3O12, CdWO4 and PbWO4 have been developed for detection of high-energy radiation [10–12].

Around the year 2000, global attention was focused on the high scintillation properties (high light yield and great energy resolution) of halide single crystals. However, many of the halide materials have strong hygroscopicity, and it was difficult to grow high-quality single crystals. Therefore, various techniques for growing single crystals of halide materials with strong hygroscopicity have been developed since then, and the development of halide scintillator single crystals has largely progressed. As a result, halides scintillator single crystals were first developed, centering on binary compounds such as LaBr3:Ce, CeBr3, and SrI2:Eu with high light yield and great energy resolution [13–15]. After that, the material research expanded to complex compounds of halide materials such as Cs2HfCl6 and Cs2LiLaBr6:Ce [16, 17]. In recent years, high-performance chloride scintillator single crystals with relatively low hygroscopicity compared to bromide and iodide scintillator single crystals have been refocused, and they have been actively studied [18, 19].

1.2.2 Feature of Single Crystal

1.2.2.1 Characteristics of Single Crystal

Single crystals consist of a single grain, and they have a lot of special characteristics derived from the structure. Schematic diagrams of single crystal and polycrystalline are shown in Figure 1.3. There is no grain boundary in the single crystal and no grain boundary enables high transparency even in crystal systems with refractive index anisotropy. This high transmittance enables its use in optical applications. In the materials with cubic structure without the refractive index anisotropy, various transparent ceramics with high transparency have been developed by eliminating voids in grains and grain boundaries. However, the transmittance of the transparent ceramics decreases as the thickness increases, while the transmittance of single crystals without voids and cracks doesn’t change even if the thickness is changed. Furthermore, the transmittance of transparent ceramics decreases even if voids are eliminated in a material system with refractive index anisotropy. Therefore, some single crystals have been applied for optical devices such as laser, lens, wavelength conversion element, and nonlinear materials and scintillators.

In addition, a single crystal has only “one” crystal orientation because it is composed of a single grain. As a result, it is possible to develop devices using crystal anisotropy of materials, and it enables the use of crystal orientation that indicates the best properties of functional materials. Therefore, single crystals are used in various fields using crystal anisotropy such as semiconductors, substrates, piezoelectric elements, and magnetic and electronic materials. For example, in the piezoelectric and semiconductor crystals, the crystal orientation that maximizes their piezoelectric and electrical properties is used, respectively. In the substrate crystal, the crystal orientation with the lattice constant that best matches that of the deposition material is chosen.

Figure 1.3 Schematic diagrams of single crystal and polycrystalline.

1.2.2.2 Growth Methods of Single Crystal

Single crystals of materials with the congruent composition can be grown from the melts by the unidirectional solidification under a temperature gradient, and it is the “melt-growth method.” Various melt-growth methods such as Czochralski (Cz), Bridgman–Stockbarger (BS), and Floating Zone (FZ) have been developed for researches and commercial uses, and of course they have been also used for development of scintillator single crystals. Especially, Cz and BS methods can grow a large bulk single crystal, and they have achieved mass production of the functional single crystals. On the other hand, micro-pulling-down (µ-PD) and laser heating pedestal growth (LHPG) methods have been recently used for material research of functional single crystals because of the faster growth rate than conventional melt-growth methods such as Cz and BS methods. As a result, various novel single crystals have been developed by the µ-PD and LHPG methods. Figure 1.4 displays single crystals of sapphire, scintillator, piezoelectric material, laser material, and magnetic and electrical materials grown by Cz, BS, FZ, and µ-PD methods.

Figure 1.4 Single crystals grown by Cz, BS, FZ, and µ-PD methods.

Many scintillator single crystals represented by NaI:Tl, CsI:Tl, and Lu2SiO5:Ce have been developed by the melt-growth methods, and the developments and applications of radiation detectors equipped with the scintillator single crystals have progressed. On the other hand, novel melt-growth methods have been developed to perform material research in areas that have not been explored so far for various reasons recently. As a result, the development of various novel scintillator single crystals is proceeding with newly developed and modified melt-growth methods.

1.2.2.3 Segregation

Some scintillator single crystals include dopant element as an emission center such as NaI:Tl, CsI:Tl, and Lu2SiO5:Ce, and the solid solution is used for improvements of scintillation properties by controls of the band structure and the crystal field around the emission center such as (Lu,Y)2SiO5:Ce and Gd3(Ga,Al)5O12:Ce. In addition, starting materials contain small amounts of impurities even if they are of high purity, and the amount and distribution of impurities in the scintillator single crystals may affect the scintillation properties. In the crystal growth from the melt of the solid–solution system, chemical composition of the single crystal becomes non-uniform or impurity phases precipitate. That is, “segregation.”

Figure 1.5 shows the phase diagram of a binary complete solid–solution system, AO–BO. According to the phase diagram, 50 mol%AO liquid phase (Cl) and 20 mol%BO solid phase coexist in equilibrium at a temperature T. “Distribution coefficient, k” is used as a factor indicating the degree of difference between the compositions at solid and liquid phases. “Equilibrium distribution coefficient, keq” is the composition ratio of the liquid and solid phases that can be read from the phase diagram, and it is represented by the following equation.

Figure 1.5 Phase diagram of a binary complete solid–solution system, AO–BO.

In the case of keq < 1, the solute concentration in the solid phase becomes lower than that in the liquid phase. On the other hand, in the case of keq > 1, the solute concentration in the solid phase becomes higher than that in the liquid phase. And at keq = 1, the solute concentration in the solid and liquid phases is matched. In the AO–BO system with keq < 1, when the starting material of 50 mol%BO (Cl) is melted and the liquid phase is cooled, the crystal of 20 mol%BO (Cs) is precipitated at the temperature T, and the concentration of BO in the liquid phase increases above 50 mol%BO. As it cools further, the composition of the liquid and crystal phases changes to the BO excess side. As a result, the concentration of BO in the precipitated crystal increases continuously from 20 mol%BO.

The distribution of solute concentration in the crystal varies depending on the growth method. Cz and BS methods crystallize a starting material from one side after melting the entire it, and their growth methods are called “normal freezing method.” On the other hand, the FZ method crystallizes a starting material by melting part of a starting material and moving the melt relatively while supplying a staring material, and it is called “zone melting method.” Verneuil method performs starting material supply and crystallization at the same time, and it can be regarded as a kind of zone melting method. In the normal freezing and zone melting methods, the solute concentration in the crystal when crystallized by moving the sample or the heater is expressed by the following equations [20]:

where C is the solute concentration in the crystal, C0 the solute concentration in the starting material, k the distribution coefficient, g the segregation for all starting materials, x the distance from initial crystallization, and l the length of melting zone. As shown in Figure 1.6a, in the normal freezing process, the relative concentration C/C0 changes continuously as the crystal growth progresses when k is not 1. On the other hand, in the zone melting process (Figure 1.6b), the solution concentration in the crystal approaches the concentration of starting materials as the crystal growth progresses.

When segregation occurs during the melt growth, supercooling may occur due to the concentration gradient of the melt around the solid–liquid interface. Figure 1.7 shows the schematic diagram of super cooling and cellular growth. At equilibrium state, the diffusion of atoms and ions in solid and liquid phases is extremely fast. Therefore, the solute concentration in the solid phase, Cs, is represented by

according to the phase diagram under the assumption of phase equilibrium. However, the diffusion of atoms and ions in the liquid phase is slow in actual crystal growth. Under this condition, the solid phase with a lower solute concentration than the liquid phase precipitates, and the concentration gradient due to diffusion occurs without sufficient agitation. The area is called “diffusion layer.” The solute concentration near the solid–liquid interface Cs′, becomes Cs′ = keqCl′, and it is greater than the solute concentration in equilibrium state Cs. At this time, the apparent distribution coefficient (effective distribution coefficient), keff, becomes keff = Cs′/Cl. The relationship between the effective distribution coefficient keff and equilibrium distribution coefficient keq can be expressed by the following formula [21].

Figure 1.6 Schematic diagrams of (a) normal freezing and (b) zone melting processes.

Figure 1.7 Schematic diagrams of super cooling and cellular growth.

According to the formula, the effective distribution coefficient keff depends on the growth speed v, thickness of diffusion layer δ, and diffusion coefficient D. The faster the growth speed, the closer keff is to 1.

In the diffusion layer, the solute concentration in the liquid phase decreases with increasing distance from the solid–liquid interface, resulting in an increase of the liquidus temperature. If the actual temperature gradient at the solid–liquid interface is greater than the gradient of the liquidus temperature, the region of the diffusion layer is in the liquid state. On the other hand, if the actual temperature gradient at the solid–liquid interface is less than the gradient of the liquidus temperature, supercooling occurs because the actual temperature is lower than the liquidus temperature. Such a supercooling is called “compositional supercooling,” and the growth interface becomes unstable, making it easier for cellular growth to occur. Cellular growth is often confirmed in the growth of actual scintillator single crystals. For example, in a scintillator containing a dopant with a small keff, cellular growth occurs due to the compositional supercooling when the dopant concentration is relatively high.

1.2.2.4 Crystal Structure

Simple lattices are classified into 14 types of Bravais lattices as shown in Figure 1.8. Cubic structure has the same lattice constant on all axes, a, b, and c, and all axes are orthogonal. As a result, many transparent ceramics with the cubic structure have been developed because the refractive index is the same in all directions [22–24]. Even during the crystal growth of single crystal with the cubic structure, cracks in the grown single crystal are less likely to occur because there is no anisotropy of lattice changes (extension and contraction) during the cooling process. Many garnet-type and perovskite-type scintillator single crystals with the cubic structure are being mass produced [25, 26].

Figure 1.8 Bravais lattices.

Tetragonal is a cubic structure extended (contracted) in one direction, and it also has relatively high symmetry. Materials with the tetragonal structure may have plate-like crystal shape and consist of plate-shaped grains, and orientation may be exhibited by the plate-shaped grains. Orthorhombic is a tetragonal structure extended (contracted) in another direction, and all lattice constants are different. In the case of the orthorhombic material with large anisotropy, cracks are likely to occur during the crystal growth and cooling process due to the differences in linear expansion coefficient for each direction. Since the growth rate varies with orientation in the materials with the orthorhombic structure, the choice of growth direction can be an important factor in the case of crystal growth by unidirectional solidification. Although all angles between axes of rhombohedral (trigonal) and hexagonal are not 90°, the symmetry is relatively high, and their structures are suitable for growing single crystals. On the other hand, monoclinic and triclinic have low symmetry compared to other structures, and cracks are generally more likely to occur. Therefore, for materials with the structures with low symmetry such as orthorhombic, monoclinic, and triclinic, the selection of the growth direction is one of the most important factors to improve the crystal quality and decrease cracks during the crystal growth. In addition, it is necessary to select a slower growth rate for materials with the low symmetric structures.

1.2.2.5 Crystallinity and Defects

Crystallinity is one of the important factors for evaluating the crystal quality of single crystals. All single crystals are not perfect single crystals and have various kinds of defects. Crystallinity is an indicator of how far from perfect the single crystal is, and improvement of the crystallinity results in higher quality of single crystals. Single crystals include various kinds of defects in the lattice structure, and the most common defects are Schottky and Frenkel defects. They are illustrated in Figure 1.9. The defects are generated from the entropy effect of heat and are called “intrinsic defect.” In the case of the Schottky defect, both defects of cation and anion are generated simultaneously to maintain electrical neutrality in the crystal as illustrated in Figure 1.9a. When an ion is displaced from the regular position to the interstitial position, a defect pair of the defect at the regular position and the interstitial ion is formed, which is called “Frenkel defect” (Figure 1.9b). To generate the interstitial ion in the lattice, the ionic radius is important factor, and it generally occurs in the case of cations with a relatively small ionic radius.

When cations with the same valence and similar ionic radii are included in chemical compositions such as the garnet-type structure, the anti-site defect occurs owing to the two cations exchanging positions (Figure 1.9c) [27]. The anti-site defect becomes a factor in deteriorating the luminescence properties of scintillator single crystals by creating new energy levels in the band structure [28], and there are some reports regarding the mechanism and countermeasures of the anti-site defects.

Figure 1.9 (a) Schottky, (b) Frenkel, and (c) anti-site defects.

On the other hand, there are “extrinsic defects” generated from the external factors such as doping of ion with different valence and control of atmosphere during the crystal growth. In the material with dopant ion (cation) with difference valence, anion defects were generated to achieve the electrical neutrality condition around the dopant ion as illustrated in Figure 1.10a. Then, the material including a transition element may become a nonstoichiometric composition depending on the growth and annealing conditions. For example, TiO2 is composed of Ti4+ ion (cation) and O2− ion (anion), and Ti is a transition-metal element. Therefore, when TiO2 single crystal is grown under reduction atmosphere, part of Ti4+ ion becomes Ti3+ ion and defects of oxygen site are generated (Figure 1.10b). As a result, the TiO2−δ single crystal grown under reduction atmosphere shows black color originating from the oxygen defect [29].

Figure 1.10 (a) Doping of ion with different valence and (b) oxygen nonstoichiometry of TiO2−δ.

Figure 1.11 (a) Schematic diagram of XRC measurement and the X-ray diffractometer with 4 axes. (b) XRC of LiCaAlF6:Ce,Na single crystals [30].

Figure 1.12 Pole figures of single crystals.

Crystallinity can be evaluated by the X-ray diffraction measurements. X-ray rocking curve (XRC) is the ω scan on each diffraction peak using the X-ray diffractometer with four axes (2θ, χ, φ, and ω) (Figure 1.11a). The broadening and splitting of the XRC peak indicate the degree of the crystallinity for the single crystal. The sharper the XRC peak, the higher the crystallinity. In addition, peak splitting and appearance of satellite peaks suggest the presence of polycrystallization and mosaic structure, respectively. A shoulder at the peak may appear as crystallinity decreases as shown in Figure 1.11b. Full width at half maximum (FWHM) on the XRC is used for evaluations of crystallinity for the single crystal. In general, it is said that a single crystal can be produced as a commercially available single crystal when the value of FWHM is lower than 100 arcsec. However, the required degree of crystallinity varies depending on the applications.

The pole figure measurement can evaluate the crystal orientation of a single crystal and an oriented sample using the same X-ray diffractometer used in the XRC measurement. It is possible to investigate which direction a specific plane of a small single crystal is facing. In general, before the evaluation of crystallinity by the XRC measurement, the pole figure measurement is performed to detect the specific diffraction peak you want to measure by the XRC (Figure 1.12). In addition, degree of the orientation can be estimated in the oriented sample.

On the other hand, the Laue camera is used to evaluate the crystal orientation of a bulk single crystal by the Laue image (Figure 1.13). By the use of continuous spectrum from the X-ray source, lines with wavelengths that satisfy Bragg’s law are diffracted from a fixed single crystal. Therefore, white X-ray without the monochromatic is used in the measurement of the Laue image. The crystal orientation can be estimated from the pattern of the obtained Laue image because the Laue pattern depends on the symmetry axes and lattice constants. The Laue image cannot be obtained for polycrystals composed of grains with random crystal orientations, so it is also used to determine whether the grown crystal is single crystal. Electron back-scattered diffraction (EBSD