• Both quasicrystals and metallic glasses are multicomponent compounds with narrow composition ranges:
• Example for stable quasicrystals
– i-Al62.5Cu24.5Fe13, i-Al69Pd22Mn9, d-Al67.5Pd14Mn18.5, i-Zr45Ti38Ni17 …
j’ i’
j
i
i' i
j'
M
R
j
k '
k
缺点：不连续
S=2.5
Composition rules based on clusters in quasicrystals and metallic glasses
Chuang DONG Dalian University of Technology, China
ζ2 Al4Cu9
e
2.6
2.4θ 2.2 2.0 1.8
1.6
Al-Cu-Fe e/a diagram
0.1
0.4 0.7
(Cu)
1.4 1.2 Cu (+1)
e/a-variant line: binary QC, ternary QC, and the 3rd element.
Fe（-2）
Criterion 2: e/a-variant line
Fe（-2）
Criterion 1:
-1.5
e/a-constant line -1.0
-0.5
-1.7 -1.4 -1.1
0.0
-0.8
0.5 b
1.0
-0.5 -0.2
1.5 Al5Fe2
2.0 Al13Fe4
2.5 α
Al (+3) 2.8
IQC
e/a-constant
e/a=1.86
Al7Cu2Fe Al10Cu9F
40 60
50 50
AxBy40
30
AuBvCw
60 70
80 20
90 10
100
100 90
80
70
60
50
40
30
20
10
A
C
• Composition rules in ternary quasicrystals
Fe（-2）
-1.5
-1.7
-1.0 -0.5 0.0
-1.4 -1.1 -0.8
Does shell composition inflates along the e/a-variant lines?
Phase diagram
Ti 100 90 80 70 60 50 40 30 20 10
10 20 30 40 50 60 70 80 90 100
100 90
80
70
60
50
• Example for “good” metallic glasses:
– Binary: Zr-Ni (Zr76Ni34), Zr-Cu… – Ternary: Zr60Al20Ni20 , Zr65Cu27.5Al7.5, – Quaternary: Zr65Al7.5Ni10Cu17.5 (Inoue alloy),
40
30
20
10
Ni
Zr
c1-Ti12Ni c2-Zr20Ti12Ni1 c3-Zr20Ti12Ni13 c4-Zr26Ti66Ni13 c6-Zr48.4Ti75.6Ni c7-Zr78.4Ti105.6Ni37 Eutec-Ni24Ti76 Eutec-Ni24Zr76 Eutec-Ni36Zr64 Eutectic Ni2Zr98 Eutectic Ni61Ti49 Eutectic Ni64Zr36 Eutectic Ni83.5Ti16.5 Eutectic Ni91.2Zr8.8 Eutectoid Ni5Ti95 Ni9Ti2Zr NiTiZr phase av QC-17-38-45
CsCl, simple cubic
CsCl 1, the basic unit: one Cs atom + one Cl 2, regard the unit Cs + Cl as a point 3, the geometry of the points = simple cubic lattice
10 20 30 40 50 60 70
D-Al80Ni20 Ni (at.%) Al4Ni3
Formation rule of ternary quasicrystals
1. e/a-constant Fermi surface and Brillouin zone interaction
3. e/a-variant ?
0.5
b
1.0
-0.5 -0.2
1.5
0.1
Al84Fe162.0
2.5
Al (+3) 2.8
IQC
Al7Cu2Fe
ζ2 Al4Cu9
2.6
θ 2.4 2.2
2.0 1.8
1.6
Al10Cu10Fe
0.4
0.7
(Cu)
1.4
1.2
Cu (+1)
• The e/a-constant line
in ternary phase e/a = 1.86 diagram:
1.35
1.30
Cluster radius 1.25
Shell radius
1.20
2
4
6
8
10
Cluster radius
atomic radius of Cluster
Shell inflation growth rule
•Atomic size: in small-middle-large cycles and ending at middle-size (~equal to average). •Three types of composition inflations: small-Ni, middle-Ti, large-Zr.
点阵与晶体结构：例子
c
g-Fe, fcc
b a
Cu3Au, simple cubic
点阵与晶体结构：例子
c
g-Fe
晶体结构例子
g-Fe
c
a-Fe
a
zx y
b
非晶结构 与晶体结
构比较
二维准晶模型：Penrose 拼图
Al-Cu-Fe单晶外形
25
Fe
Al13Fe4
Al10Fe3Ni
20 D-Al84Fe16
15 Al6Fe
10
5
Al5FeNi
Al2FeNi
D
D’
e/a =1.86 e/a variant line Al86Fe14 -Ni Al71Fe5Ni21
0 Al (at.%) 0
Al3Ni Al3Ni2
Al3Ni5
AlNi
Ni (at.%)
Ti34Cu47Zr11Ni8 – More: Zr52.5Ti5Cu17.9Ni14.6Al10,
Zr41.2Ti13.8Cu12.5Ni10Be22.5, Zr58.5Nb2.8Cu15.6Ni12.8Al10.3
B
• Basic rule:
100
alloying
90 80
10 20
30 70
b, Al75Fe22.9Ni3.1,
e/a = 1.79
,Dunlop, Phil Mag B, 1993
cc, Al71Fe5Ni24, stable, e/a = 2.03 (TOO LARGE!)
Lemmerz, Grushko, Freiburg, Jansen, Phil. Mag. Lett., 1994)
Multi-component system and its subsystems are inter-related
quantitative criteria
Explanation of the e/a-variant line
Phases in Ni-Ti-Zr system
Kelton’s group A stable Bergman-type QC Ni17Ti38Zr45 A Bergman phase W-Ni12.7Ti61.4Zr25.9
c
a-Fe, bcc
a-Fe
a
b
1, the basic unit: one Fe atom
2, regard the unit as a point
3, the geometry of the points =
Body centered cubic lattice
点阵与晶体结构：例子
Cl Cs
Steps to reach lattice 1, determine the basic unit 2, regard the unit as a point 3, the geometry of the points = lattice
物质结构
二、晶体结构
（1） 完美晶体的结构描述：晶体学 对象：原子排列方式（简化；理想；几何）
=》周期。 晶体结构＝结构单元（单胞）＋单胞周期平移
对称操作：
对称性
使图形保持不变（完全复原）的操作；
在对称操作中始终保持不变的轴、平面、或点称 为对称元素。
单胞内的原子位置由对称性操作联系。
对称操作分点对称和平移两种。