材料科学基础
Fundamental of Materials
Prof,Tian Min Bo
Tel,62795426, 62772851
E-mail,tmb@mail.tsinghua.edu.cn
Department of Material Science and Engineering
Tsinghua University,Beijing 100084
Lesson eight
Chapter Ⅲ
The Structures of Alloys
§ 3.1 Basic concepts of alloys
? Ⅰ.Definition
An alloy is the combination of metal(s) with
other elements through chemical bonding.
? Ⅱ.Terminology
1,Component (or constituent)
? one component system
? two component system binary system
? three component system ternary system
? four component system quarternary system
? five component system quinary system
multi-component
system
2,Composition
It can be expressed either by atomic
percentage (mol fraction) Xa or by mass
percentage Xm
?
?
?
n
j
j
i
MX
MW
X
j
i
i
1
m
m
a
)( ?
?
?
n
j
jj
ii
i
MX
MX
X
1
a
a
m
)(
3,Phase
A phase is a homogeneous part of the material in which
no abrupt change in composition,structure and properties
occurs.
An alloy may be single phase or multi-phase material.
4,Structure
Structure is a general term for the combination of atom
arrangement including the types amounts and distribution
of all types of material as well as grain size,defect etc.
? Ⅲ,Classification of Alloy Phases
1,According to structure
Solid Solution
Compound
In Solid Solution,atoms of different
component share a common lattice in variable
proportion.
2,According to position of the alloy in phase
diagram
Terminal S.S.
Intermediate S.S.
or secondary S.S.
α
BA
β
α+β
§ 3.2 Factors Affecting the
Structure of Alloy Phase
1,What is size factor
metallic radii rA+rB =d
ionic radii r++r - =d
covalent radii single bond radius
Van der Waals radii
Atomic
radii
CN radii
BCC FCC
CN of BCC:8( )+6(a) CN of FCC:12( )
rα= = rβ= =
= 0.12557nm = 0.128674nm
a23 a22
?a4
3 nm290.0
4
3 ?
?a4
2 nm36 4.0
4
2 ?
Goldschmidt atomic radii is the radii of atom in
structures with CN=12
Size factor is defined as? %100???
A
BA
d
dd?
2,What is Electrochemical factor
—— Electronegativity X
X represents the ability of an atom of an element in the
compond to attract electrons to itself.
Pauli’s empirical rule,5.0131.0
)1(
??? rnX
n,valence r(1),simple bond radius
EAA—— bonding energy between A-A atoms
EBB—— bonding energy between B-B atoms
EAB—— bonding energy between A-B atoms
? ? ABBBAA2BA )2( EEEXX ????
3,Electron concentration ( e/a )
Electron concentration ( e/a ) is the number of valence
electrons per atom on the average.
i.g,for CuZn, e/a = 3/2 =1.5
§ 3.3 Solid Solution
? Ⅰ,Classification
1,According the position of solute atoms in the
lattice of the solvent
Substitutional S.S.
Interstitial S.S.
2,According the regularity of the position occupied
by solute atoms
Ordered S.S.
Disordered S.S.
1＋ 3＋ 12× 1/4＋ 4＋ 1＝ 12
∴ Fe 12Al4＝ Fe3Al
12:Fe
4:Al
3,According to solid solubility
0~100% continuous series of S.S
S.S with restricted solubility
summary
substitutional S.S primary (terminal)
interstitial S.S secondary (intermediate)
ordered S.S continuous S.S
disordered S.S S.S with restricted solubility
Ex,Write out in full the coordinates of all
cations and anions in nucleus,
Wurtzite and CaF2 referred to a b c
axes of the anions sublattice.
? Ⅱ,Determination of types of S.S
ex p??V
Mn
M
Vn ρex p?∴
is the average atomic weigh
weighted by composition
M
Compare n with no (atoms per unit cell of
solvent)
n=no, ideal substitutional S.S.
n>no, interstitial S.S.
n<no, vacant S.S.
? Ⅲ,Hume -Rothery Rule for primary
solid solubility
1,Size factor:
Size factor＝ × 100％d0-dt
d0
If size factor ＞ 15％ solubility is very small.
NiO can be added to MgO to produce a solid solution,What
other ceramic systems are likely to exhibit 100% solid solubility
with MgO?
r(?) crystal structure
Cd+2 in CdO 0.97 47 NaCl
Ca+2 in CaO 0.99 50 NaCl
Co+2 in CoO 0.72 9 NaCl
Fe+2 in FeO 0.74 12 NaCl
Sr+2 in SrO 1.12 70 NaCl
Zn+2 in ZnO 0.74 12 NaCl
%100
2
2 ?
?
?
?
?
?
?
?
? ?
?
?
Mg
Mgio n
r
rr
FeO-MgO system will probably display unlimited solid solubility.
CoO and ZnO systems also have appropriate radius ratios and crystal structures.
Example
d0
1.15d0
0.85d0
d
ZZ1 Z2
2,Crystal structure
The materials must have the same crystal
structure; otherwise there is some point at which
a transition occurs from one phase to a second
phase with a different structure.
3,Electrochemical factor
If the difference in X is great,the solubility is
also very restricted,
Formation of stable compound will
restrict the solid solubility.
Parameter,Electronegativity (x)
Semiemperies formulas
Where,r1—— single bond radius
n —— valency
5.0131.0
1
???
?
?
???
? ???
r
nX
x0
x0+0.4
x0－ 0.4
x
RR00.85R0 1.15R0
Dorken-Gurry graphic
4,Electron concentration factor,e/a
e,the number of valence electrons
a,the number of atoms
e/a = average number of valence
electrons per atom.
Experimental findings:
① Zn,Ga,Ge,As in Cu (solute-solvent)
If composition is
expressed in terms of
e/a rather than at%,the
solid solubility of all
elements in Cu will be
roughly the same,
② Structure vs,e/a
for CuZn alloy system
α(CuZn) —— e/a = 3/2 = 21/14
β(Cu5Zn8)—— e/a = 21/13
γ(CuZn3) —— e/a = 7/4 = 21/12
? Ⅳ,Properties of S.S
1,lattice constants properties
Vagard’s law
ass = ao + (a - ao)x
for alloy S.S
Δa = K(ZA-ZB)2
ZA,ZB are valences of
solute and solvent.
a
Cu
Au
Ni
x
1.00
正偏差
负偏差
2,Mechanical properties
σ0.2 is great,ductility is lower —— solid solution
strengthening.
3,Electrical properties
In general ρS.S > ρele
ρ A
ρBL
L+S
S
Cu-Ni
Examples and Discussions
Exercise
Thank you !
8
Fundamental of Materials
Prof,Tian Min Bo
Tel,62795426, 62772851
E-mail,tmb@mail.tsinghua.edu.cn
Department of Material Science and Engineering
Tsinghua University,Beijing 100084
Lesson eight
Chapter Ⅲ
The Structures of Alloys
§ 3.1 Basic concepts of alloys
? Ⅰ.Definition
An alloy is the combination of metal(s) with
other elements through chemical bonding.
? Ⅱ.Terminology
1,Component (or constituent)
? one component system
? two component system binary system
? three component system ternary system
? four component system quarternary system
? five component system quinary system
multi-component
system
2,Composition
It can be expressed either by atomic
percentage (mol fraction) Xa or by mass
percentage Xm
?
?
?
n
j
j
i
MX
MW
X
j
i
i
1
m
m
a
)( ?
?
?
n
j
jj
ii
i
MX
MX
X
1
a
a
m
)(
3,Phase
A phase is a homogeneous part of the material in which
no abrupt change in composition,structure and properties
occurs.
An alloy may be single phase or multi-phase material.
4,Structure
Structure is a general term for the combination of atom
arrangement including the types amounts and distribution
of all types of material as well as grain size,defect etc.
? Ⅲ,Classification of Alloy Phases
1,According to structure
Solid Solution
Compound
In Solid Solution,atoms of different
component share a common lattice in variable
proportion.
2,According to position of the alloy in phase
diagram
Terminal S.S.
Intermediate S.S.
or secondary S.S.
α
BA
β
α+β
§ 3.2 Factors Affecting the
Structure of Alloy Phase
1,What is size factor
metallic radii rA+rB =d
ionic radii r++r - =d
covalent radii single bond radius
Van der Waals radii
Atomic
radii
CN radii
BCC FCC
CN of BCC:8( )+6(a) CN of FCC:12( )
rα= = rβ= =
= 0.12557nm = 0.128674nm
a23 a22
?a4
3 nm290.0
4
3 ?
?a4
2 nm36 4.0
4
2 ?
Goldschmidt atomic radii is the radii of atom in
structures with CN=12
Size factor is defined as? %100???
A
BA
d
dd?
2,What is Electrochemical factor
—— Electronegativity X
X represents the ability of an atom of an element in the
compond to attract electrons to itself.
Pauli’s empirical rule,5.0131.0
)1(
??? rnX
n,valence r(1),simple bond radius
EAA—— bonding energy between A-A atoms
EBB—— bonding energy between B-B atoms
EAB—— bonding energy between A-B atoms
? ? ABBBAA2BA )2( EEEXX ????
3,Electron concentration ( e/a )
Electron concentration ( e/a ) is the number of valence
electrons per atom on the average.
i.g,for CuZn, e/a = 3/2 =1.5
§ 3.3 Solid Solution
? Ⅰ,Classification
1,According the position of solute atoms in the
lattice of the solvent
Substitutional S.S.
Interstitial S.S.
2,According the regularity of the position occupied
by solute atoms
Ordered S.S.
Disordered S.S.
1＋ 3＋ 12× 1/4＋ 4＋ 1＝ 12
∴ Fe 12Al4＝ Fe3Al
12:Fe
4:Al
3,According to solid solubility
0~100% continuous series of S.S
S.S with restricted solubility
summary
substitutional S.S primary (terminal)
interstitial S.S secondary (intermediate)
ordered S.S continuous S.S
disordered S.S S.S with restricted solubility
Ex,Write out in full the coordinates of all
cations and anions in nucleus,
Wurtzite and CaF2 referred to a b c
axes of the anions sublattice.
? Ⅱ,Determination of types of S.S
ex p??V
Mn
M
Vn ρex p?∴
is the average atomic weigh
weighted by composition
M
Compare n with no (atoms per unit cell of
solvent)
n=no, ideal substitutional S.S.
n>no, interstitial S.S.
n<no, vacant S.S.
? Ⅲ,Hume -Rothery Rule for primary
solid solubility
1,Size factor:
Size factor＝ × 100％d0-dt
d0
If size factor ＞ 15％ solubility is very small.
NiO can be added to MgO to produce a solid solution,What
other ceramic systems are likely to exhibit 100% solid solubility
with MgO?
r(?) crystal structure
Cd+2 in CdO 0.97 47 NaCl
Ca+2 in CaO 0.99 50 NaCl
Co+2 in CoO 0.72 9 NaCl
Fe+2 in FeO 0.74 12 NaCl
Sr+2 in SrO 1.12 70 NaCl
Zn+2 in ZnO 0.74 12 NaCl
%100
2
2 ?
?
?
?
?
?
?
?
? ?
?
?
Mg
Mgio n
r
rr
FeO-MgO system will probably display unlimited solid solubility.
CoO and ZnO systems also have appropriate radius ratios and crystal structures.
Example
d0
1.15d0
0.85d0
d
ZZ1 Z2
2,Crystal structure
The materials must have the same crystal
structure; otherwise there is some point at which
a transition occurs from one phase to a second
phase with a different structure.
3,Electrochemical factor
If the difference in X is great,the solubility is
also very restricted,
Formation of stable compound will
restrict the solid solubility.
Parameter,Electronegativity (x)
Semiemperies formulas
Where,r1—— single bond radius
n —— valency
5.0131.0
1
???
?
?
???
? ???
r
nX
x0
x0+0.4
x0－ 0.4
x
RR00.85R0 1.15R0
Dorken-Gurry graphic
4,Electron concentration factor,e/a
e,the number of valence electrons
a,the number of atoms
e/a = average number of valence
electrons per atom.
Experimental findings:
① Zn,Ga,Ge,As in Cu (solute-solvent)
If composition is
expressed in terms of
e/a rather than at%,the
solid solubility of all
elements in Cu will be
roughly the same,
② Structure vs,e/a
for CuZn alloy system
α(CuZn) —— e/a = 3/2 = 21/14
β(Cu5Zn8)—— e/a = 21/13
γ(CuZn3) —— e/a = 7/4 = 21/12
? Ⅳ,Properties of S.S
1,lattice constants properties
Vagard’s law
ass = ao + (a - ao)x
for alloy S.S
Δa = K(ZA-ZB)2
ZA,ZB are valences of
solute and solvent.
a
Cu
Au
Ni
x
1.00
正偏差
负偏差
2,Mechanical properties
σ0.2 is great,ductility is lower —— solid solution
strengthening.
3,Electrical properties
In general ρS.S > ρele
ρ A
ρBL
L+S
S
Cu-Ni
Examples and Discussions
Exercise
Thank you !
8
