電子セラミックスと固体化学
Electroceramics
and Solid State Cheminstry
格子欠陥の利用
Application of Lattice Defects
工学部 応用化学科
片山 恵一
Today's subjects
電子セラミックスとは？ 固体化学とは？
What is
What is
Solid State Chemistry?
Electroceramics?
これらの関係は？
What is the relationship between these two subjects
?
この関係は何に利用されている？
What has this relationship been utilized for?
The interdisciplinary study of these two subjects has
developed technology, and has been producing lots of
sophisticated products underpinned modern society.
講義の流れ
Flow of today's talk
• 電子セラミックスとは？
• What is Electroceramics?
• 固体化学
• Solid State Chemistry
• 実用例
• Application
電子セラミックスとは？
What is Electroceramics?
セラミックスとは？
What is a ceramic?
加熱して作製される非金属無機固体化合物
A ceramic is an inorganic, non-metallic solid
prepared by heating.
例：陶磁器 pottery
半導体材料として広範に利用されている。
In the 20th century, new ceramic materials
were developed for use in advanced ceramic
engineering; for example, in semiconductors.
Definition of Ceramics
セラミックスの定義
The term ‘ceramics’ is restricted to polycrystalline,
inorganic, non-metallic materials that can acquire
their mechanical strength through a firing or
sintering process. Glass and single crystals are
sometimes included as a matter of convenience.
厳密には多結晶を対象とするが、単結晶･ガラスを含む
場合もある
電子セラミックス
Classification of Electroceramics
•
•
•
•
•
•
•
Insulators (絶縁体 ) 基板、点火プラグ
Magnetics (磁性体 ) 磁石、記録装置
Dielectrics (誘電体 ) ｺﾝﾃﾞﾝｻ、メモリー
Conductors (導電体 ) 抵抗、ｻｰﾐｽﾀ、発熱体、ｶﾞｽｾﾝｻ
Piezoelectrics (圧電体 ) ｽﾋﾟｰｶ、ﾌｨﾙﾀ、超音波診断装置
Pyroelectrics (焦電体 ) 赤外線ｾﾝｻ
Optics (光学材料 ) 光ﾌｧｲﾊﾞｰ、透明電極
・
・
・
固体化学の基礎
Fundamental
Solid State Chemistry
固体化学って何？
What is Solid State Chemistry?
•
•
•
•
•
•
•
Preparative methods
Crystal chemistry
Phase diagrams
Phase transition
Electrical properties
Magnetic properties
Optical properties
•
•
•
Electroceramics
Crystal defects
Non-stoichiometry
Solid solution
Crystal defects
Point Defects




Schottky defect
Frenkel defect
intrinsic and extrinsic defects
Interchanged Atoms
Perfect and Imperfect Crystals
• Perfect Crystals
in which all atoms are at rest on their correct
lattice positions.
At all real temperatures, crystals are imperfect.
• Imperfect Crystals
which contain random defects, resulting in the
deficiency of one element.
Stoichiometry and Non-stoichiometry
• Stoichiometric compounds
（化学量論組成化合物）
• Non-stoichiometric compounds
（非化学量論組成化合物）
Example of
Non-stoichiometric compounds
Ferrous oxide: FeO（酸化鉄( )）
Ideal formula : FeO
Actual formula : Fe1-XO (X≈0.05)
In the latter formula, Fe3+ ions are present
and O2− vacancies are formed.
Why non-stoichiometry exists?
Since the solid needs to be overall
electrically neutral, the missing atom's
charge needs to be compensated by a
change in the charge for another atom in
the solid, by changing the oxidation state,
or by replacing it with an atom of a
different element with a different charge.
Types of Defect
• Schottky defect（ショットキー欠陥）:
A pair of vacant sites, a cation defect and an anion
defect （一対の陽イオンと陰イオンが抜ける）
• Frenkel defect（フレンケル欠陥） :
An atom displaced off its lattice site into an
interstitial site （片方のイオンが格子間位置に移動）
These defects are described
using the Kroger-Vink notation.
Types of Defect
• Schottky defect
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
Cl
Na
At room temperature, only one in 1015 of both
ion sites in NaCl is vacant.
Types of Defect
• Frenkel defect
Ag
Cl
Ag
Cl
Ag
Cl
Ag
Cl
Ag
Cl
Ag
Cl
Ag
Cl
Ag
Ag
Cl
Cl
Ag
Ag
Cl
Cl
C
Ag
Cl
Ag
Cl
Ag
Cl
Ag
Cl
Ag
Cl
Ag
Cl
Ag
Kroger-Vink notation
クレーガー･ビンク記号
• The symbol for the atom involved, or “V” if
the site is vacant （空孔はVで表す）
• A superscript indicating the net charge: “” for
charge 1, “” for zero net charge, “ ” for
charge 1
（元に比べて“＋”の場合“”
、”－“の場合は“ ” 、変化なしの場合は“” ）
• A subscript to indicated the nature of the site in
an ideal crystal, with ” i” for an interstitial site
and “s” for a surface site （格子間位置は” i” )
Kroger-Vink notation
NaNa , ClCl  : Na+ and Cl ions on regular lattice
sites, zero net charge
VNa : a Na+ ion vacancy, net charge 1
: a Cl ion vacancy, net charge 1
Cl
V
Na
Mgi  : a substitutional Mg2+ ion on a Na site,
i charge +1
Ag  : an interstitial Ag+ ion in AgCl, charge 1
F  : an interstitial F ion in CaF2, charge 1
Examples of Kroger-Vink notation
• NaCl
null → VNa’+VCl•
無
空のNa+格子点
空のCl–格子点
(NaxNa+ClxCl→ VNa’+VCl• +Naxs +Clxs )
• AgCl
AgAgx → Ag•i + VAg’
本来の格子点にあるAg+
空のAg+格子点
格子間位置にあるAg+
(AgxAg+ClxCl→ Agi•+V’Ag+ClxCl)
Other examples of Defects
• Intrinsic defects: defects which are thermally
created
Example: ZnO(Zn1+xO), NiO(Ni1-xO)
• Extrinsic defects: defects which are
associated with dopants or impurities
Example 1: Al2O3 including Cr2O3
Example 2: ZnO including Al2O3
Solid Solutions（固溶体）
• A crystalline phase
that can have variable composition
(規則性なく組成が変化する結晶相）
水とエタノールの混合と同じ！
Examples
• Fe0.95O : Mixtures of FeO and Fe2O3
Problem 1: Calculate the molar fraction of each
compounds in Fe0.95O.
Answer to the problem
The formation of Fe0.95O is;
x FeO + y Fe2O3 →Fe0.95O
(x: mols of FeO in SS, y: mols of Fe2O3 in SS)
x+2y=0.95 ·····(1)
x+3y=1.00 ·····(2)
(2) – (1); y=0.05, x=0.85
Answer: FeO = 0.85 / 0.90 = 94.4 mol%
Fe2O3= 100 – 94.4 = 5.6 mol%
Types of Solid Solutions
• Substitutional solid solutions (置換型)

The atoms or ions that is being introduced
directly replaces an atom or ion in the parent
structure
• Interstitial solid solutions （格子間型）

The introduced species occupies a site that is
normally empty and no ions or atoms are left out
Substitutional solid solutions
• Al2-xCrxO3 (0≤x ≤ 2) (derived from Al2O3)



Al3+ and Cr3+ ions are distributed at random
the probability that it is one or the other is related to the
composition x.
(each site is occupied by an ‘average cation’)
Average cation whose properties, atomic number,
size, etc., are intermediate between those of Al3+
and Cr3+ ions (固溶体の物性値は、それぞれの値の
平均！)
Example Ionic radius of a cation in Al1.6Cr0.4O3 is
calculated to be 69.1 nm from ionic radii of
Al3+: 67.5 nm and Cr3+: 75.5 nm.
Interstitial solid solutions
• If the solute atoms are small, they may
dissolve interstitially in the host crystal.
 YF3 in CaF2
• Y3+ is interstitially located in the lattice,
and V•Ca is created.

PdHx(0 ≤ x ≤ 0.7)
• Pd metal occludes(吸蔵する) H2 gas, and
H atoms occupy interstitial sites.
応用例1：BaTiO3系サーミスタ
PTC thernistor
Temperature-sensitive Resistors
(Thermal Resistors :Thermistors)
6
5
NTC Thermistor
4
log(ρ/Ω m)
• Negative
temperature
coefficient of
resistance
(NTC)
• Positive
temperature
coefficient of
resistance
(PTC)
3
2
PTC Thermistor
1
Pt wire
0
0
40
80
T/ºC
120
160
Transformation of BaTiO3
相変態
単斜晶
立方晶
菱面体晶
正方晶
6
5
NTC Thermistor
log(ρ/Ω m)
4
3
2
PTC Thermistor
1
Pt wire
0
0
40
80
T/ºC
120
160
PTC Thermistors
• Lanthanum-doped BaTiO3(Ba1-XLaXTiO3)
or
• Niobium-doped BaTiO3 (BaTi1-XNbXO3)
Defect chemistry of BaTiO3
• In case of addition of La2O3 and forming nonstoichiometric BaTiO3
 BaO is formed or vacancies of Ti are formed.
La2O3 → 2La•Ba + 2BaO +2e’ + 1/2O2
La2O3 → 2La•Ba + 2V••••Ti + 10e’ + 1/2O2
• In case of addition of La2O3 and forming stoichiometric
BaTiO3
 La2O3(+2TiO2)
La2O3 → 2La•Ba + 2OXO +2e’ + 1/2O2
• La•Ba is compensated by an electron ( 2TiO2 + 2BaO →
2BaXBa + 2TiXTi + 6OXO ).
Defect chemistry of BaTiO3
• In case of another stoichiometric BaTiO3

Nb2O5(+2BaO)
Nb2O5 → 2Nb•Ti + 4OXO +2e’ + 1/2O2
• In case of stoichiometric BaTiO3
–Al2O3(+2TiO2)
Al2O3 → 2Al’Ti + 3OXO +V••O
or Al2O3 + 1/2O2 +2e- → 2Al’Ti + 4OXO
Electroceramics
電子セラミックス
Solid state chemistry
固体化学
Electroceramics
and Solid State Cheminstry
電子セラミックスと固体化学
Application of Lattice Defects
格子欠陥の利用
工学部 応用化学科
片山 恵一
The End
Assignment
Explain the relationship
between electroceramics and crystal defects
within 200 words or less.
（日本語の場合は500字以内）
Submission deadline: Feb. 27
E-mail to:
Katayama Keiichi<katakei@keyaki.cc.u-tokai.ac.jp>