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Unformatted text preview: 材材材材材材
Fundamental of Materials
Prof: Tian Min Bo
Tel: 62795426 材 62772851
Department of Material Science and Engineering
Tsinghua University. Beijing 100084 Lesson eight Chapter Ⅲ
The Structures of Alloys §3.1 Basic concepts of alloys
An alloy is the combination of metal(s) with
other elements through chemical bonding. chemical Ⅱ.Terminology 1. Component (or constituent)
one component system two component system three component system four component system five component system binary system
system 2. Composition
It can be expressed either by atomic
percentage (mol fraction) Xa or by mass
percentage Xm X ai = Wmi M i
j =1 j M j) X mi = X ai M i
n ∑ ( X aj M j )
j =1 3. Phase
A phase is a homogeneous part of the material in which
no abrupt change in composition, structure and properties
An alloy may be single phase or multi-phase material.
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
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.
α β Intermediate S.S.
or secondary S.S. α+β
A B §3.2 Factors Affecting the Structure of
1. What is size factor
radii metallic radii rA+rB =d
ionic radii r++r - =d
covalent radii single bond radius
Van der Waals radii CN
4 BCC 3
CN of BCC:8(
= 0.12557nm radii ∆
r FCC 2
CN of FCC:12(
= 4 × 0.364nm
= 0.128674nm Goldschmidt atomic radii is the radii of atom in
structures with CN=12
Size factor δ is defined as δ = d A − dB
dA ×100% 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:
n: valence n +1
X = 0.31
r(1) r(1): simple bond radius ( XA − XB) 2 EAA − EBB
) − EAB
2 EAA—— bonding energy between A-A atoms
EBB—— bonding energy between B-B atoms
EAB—— bonding energy between A-B atoms
A-B atoms 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
e/a §3.3 Solid Solution
§3.3 Ⅰ. Classification 1. According the position of solute atoms in the
lattice of the solvent
Interstitial 2. According the regularity of the position occupied
by solute atoms
Disordered Al : 4
Fe : 12
1 材 3 材 12×1/4 材 4 材 1 材 12
∴ Fe12Al4 材 Fe3Al 3. According to solid solubility
0~100% continuous series of S.S
S.S with restricted solubility
S.S 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.
axes Ⅱ. Determination of types of S.S
= ρ exp
M ∴ n= Vρexp
M is the average atomic weigh weighted by composition Compare n with no (atoms per unit cell of
n=no : ideal substitutional S.S.
n>no : interstitial S.S.
n<no : vacant S.S. Ⅲ. Hume-Rothery Rule for primary
solid 1. Size factor:
Size factor 材
d0 ×100 材
×100 If size factor ＞ 15 ＞ solubility is very small.
15 solubility Example
NiO can be added to MgO to produce a solid solution. What
other ceramic systems are likely to exhibit 100% solid solubility
r(Å) rion − rMg + 2 ×100% rMg + 2 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 FeO-MgO system will probably display unlimited solid solubility.
CoO and ZnO systems also have appropriate radius ratios and crystal structures. d
0.85d0 Z1 Z2 Z 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
3. 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 n′ + 1 X = 0.31 r + 0.5 1 Where: r1——single bond radius
n ——valency x
x0 ＞ 0.4 0.85R0 R0 1.15R0 R 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:
a. 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. b.
b. 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
1. 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 Au Cu
0 1.0 x 2. Mechanical properties σ0.2 is great, ductility is lower —— solid solution
strengthening. 3. Electrical properties IIn general ρS.S > ρele
L+S ρA S Cu-Ni Examples and Discussions
Exercise Thank you !
Thank you !
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- Spring '11