基于团簇的多元相成分设计方法: 化学势均衡理论在非晶合金材料成分

设计中的应用

董 闯

大连理工大学三束材料改性国家重点实验室

成分敏感

多组元合金相成分设计

多组元体系

定量判据难

微观计算和模拟计算量大，且难应用于复杂体系

Phase diagram: phase vs composition

100

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10

100

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100 90 80 70 60 50 40 30 20 10

B

A C

AuBvCw

System –subsystem relationship

AxBy

相图：宏观信息 三元以上相图信息少

Al-based QCs

Bulk metallic glasses

Hydrogen storage alloys

e/a-constant

cluster line

Ra-constant

Thin film materials

Unified equi-potential rule

• Quasicrystals are intermetallic compounds

An Al-Cu-Fe icosahedral phase grain with the football shape

Icosahedral point group

Intermetallic with specific composition Al62.5Cu24.5Fe13

Ordered solid

Electronic phase e/a=1.86

• Al-Cu-Fe-Cr for

Dong, Perrot, Dubois, Belin, Mater. Sci. Forum 1994

QC-forming systems

e/a-constant line

e/a = ΣCi*(e/a)I(e/a)Al = 3, (e/a)Cu = 1, (e/a)Fe = -2

准晶成分规律Tsai, Inoue & Masumoto, Maters Trans, JIM 1989

Kp and 2KF, atomic size, e/a factor

Rabe, Kortan, Phillips & Villars Phys. Rev. B 1991

electronegativity, radius, e/a

Grushko & Velikanova J Alloys & Comp 2004

a ternary QC is a linear extension from a binary one along an e/a-constant direction

e/a --- number of valence/conduction electron per atom均原子的价电子、导带电子数

θ Cu (+1)Al (+3)

Fe（-2）

1.62.4

0.7

0.4

0.1

-0.2

-0.5

-0.8

-1.1

-1.4

-1.7-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

Al-Cu-Fe e/a diagram

2.62.8 2.0 1.8 1.4 1.22.2

IQCIQC

Al13Fe4

e/a-constant line

Dong et al. Mater. Sci. Forum 1994The e/a-constant criterion for QCs

电子化合物稳定机制的理论基础：

费米面和布里渊区相互作用（FS-BZ效应）

FS-BZ效应导致费米能级处产生伪能隙

Al Al2CuAl7Cu2Fe

QC-AlCuFe

Dong et al. Mater. Sci. Forum 1994

•准晶及其类似相是等电子浓度相•其结构及性能必然受电子浓度调控•三元准晶与二元相有联系：形成判据？

意义

Criterion 1: e/a-constant line

Dong, Scr. Met & Mat 1995

Difficulties in using this e/a-constant criterion:

•The e/a values of QCs?•The e/a values of Transition Metals?•Correlation with binary QCs?

Cluster line criterion:

θ Cu (+1)Al (+3)

Fe（-2）

1.62.4

0.7

0.4

0.1

-0.2

-0.5

-0.8

-1.1

-1.4

-1.7-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

Al-Cu-Fe e/a diagram

2.62.8 2.0 1.8 1.4 1.22.2

cluster line

IQCIQCλ-Al13Fe4

ternary QC @Icosahedron Al10.7Fe2 – Cu /

Oct. Antiprism Al8Cu3 - Fe

Ico Al10.7Fe2

Al8Cu3

第9届准晶材料国际会议邀请报告

ΔHAl-Fe = -11 kJ/mol

ΔHAl-Cu = -1 kJ/mol

ΔHCu-Fe = +13kJ/mol

Al2Cu

•-ΔH: clustering of dissimilar atoms•Atomic size difference: close packing

•Icosahedral cluster isolated from Al13Fe4

•The cluster does exist in nearby crystalline phases!a

b

c

Al10.7Fe2 (Al84.3Fe15.7)

100

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100 90 80 70 60 50 40 30 20 10

Ni

Al Fe

☼

0☼

☼☼☼☼☼

CN10 A☼CN9 Al8DQC Al7DQC Al7DQC meDQC1-1☼DQC1-2☼DQC1-3☼DQC1-4☼DQC1-5☼DQC2-1DQC2-2DQC2-3DQC2-4DQC2-5ico Al100ico Al10☼tctp-Al9NAl10Ni3

Al10Fe Al10.7Fe2

Al9Ni

DQC1

e/a=2

DQC2

Al8.7Fe

e/a=1.94

composition e/a Ra

DQC Al68Cu11Co21 1.94 1.3757

DQC1 Al72.7Ni8.5Co18.8 2 1.38086

IQC Al64Cu24Fe12 1.92 1.3748

IQC Al71.4Ni21.4Fe7.2 1.99 1.3799

DQC Al75.5Pd12.0Fe12.5 2.01 1.404

IQC Al64.5Cu21.5Ru14, 1.87 1.38515

DQC1 Al70.5Ni19.4Ru10.1 1.91 1.38599

IQC Al65Cu20Mn15 1.85 1.3745

DQC Al70.5Pd16.5Mn13, 1.86 1.39965

Ra = ΣCi*RI

DQC1

DQC2

IQC

100

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10 90

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10

100 90 80 70 60 50 40 30 20 10

Cu

Al F

☼

☼

Al10.7Fe2

Al8Cu3

IQC

e/a=1.92

100

90

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70

60

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40

30

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10100

90

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40

30

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100 90 80 70 60 50 40 30 20 10

Ni

Al Fe

☼

0☼

☼☼☼☼☼

CN10 A☼CN9 Al8DQC Al7DQC Al7DQC meDQC1-1☼DQC1-2☼DQC1-3☼DQC1-4☼DQC1-5☼DQC2-1DQC2-2DQC2-3DQC2-4DQC2-5ico Al100ico Al10☼tctp-Al9NAl10Ni3

Al10Fe Al10.7Fe2

Al9Ni

DQC1DQC1

e/a=2

DQC2

Al8.7Fe

e/a=1.94

等电子浓度

等原子尺寸

Al71.4Ni21.4Fe7.2

Al64Cu24Fe12

致密而具有高弹性变形的Ti-Zr-Ni大块准晶 (发明专利)

100

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10100

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Ni

Al Zr

12

3

45

Al2NiZr6(In2Mg)AlNiZr (Cu2Mg,Fe2P)B1-AlZr6B2-AlZr9B3-Al3Zr9B4-Al3Zr15 B5-Al6Zr15 B6-Al6Ni6Zr15 B7-Al6Ni6Zr18B8-Al6Ni6Zr24C10-Al12Ni5Zr36C1-NiZr61C2-NiZr92C3-Ni3Zr93C4-Ni3Zr154C5-Ni3Zr185C6-Al12Ni3Zr186C7-Al12Ni3Zr247C8-Al12Ni3Zr308C9-Al12Ni3Zr369

Al2NiZr6 (InMg2)

三元相成分位于Al NiZr18和Ni Al3Zr9的交线上

Ni

ZrZr

Al

ZrZr

Al3Zr9

Al:Zr=1:3Ni:Zr=1:6

NiZr6Al2NiZr6

100

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Ni

Al Zr

12

3

45

Al2NiZr6(In2Mg)AlNiZr (Cu2Mg,Fe2P)B1-AlZr6B2-AlZr9B3-Al3Zr9B4-Al3Zr15 B5-Al6Zr15 B6-Al6Ni6Zr15 B7-Al6Ni6Zr18B8-Al6Ni6Zr24C10-Al12Ni5Zr36C1-NiZr61C2-NiZr92C3-Ni3Zr93C4-Ni3Zr154C5-Ni3Zr185C6-Al12Ni3Zr186C7-Al12Ni3Zr247C8-Al12Ni3Zr308C9-Al12Ni3Zr369

Trigonal prism Ni3Zr9~ eutectic Ni24Zr76

Trigonal prism Al3Zr9~ eutectic Al29.5Zr70.5

Trigonal prism Ni3Zr7Zr60Al20Ni20

φ4*20mm BMG

Ra-constant line

e/a=1.5 line

BMG Zr60Al20Ni20: Ni3Zr9 + Al3Zr9 ; e/a~1.5; Ra ~ Ni3Zr7

Cu-Zr-based BMGs

Cu-Zr: ΔH ＝ -23 KJ/mol

1) Easy glass forming.2) Many phases (clusters abundant).3) Alloying with third elements leads to

high GFAs.

Zr Cu

ΔE

Tx/Tm

Activation energies for crystallization (ΔE) reach peak values at cluster compositions.

Buschow K H L. J Phys. F: Met. Phys., 1984; 14: 593

Cu9Zr4Cu5Zr8 Cu8Zr5Cu6Zr5Cu5Zr6

Cu60Zr40

Cu64Zr36

Cu50Zr50

Cu46Zr54

Cu64.5Zr35.5

special BMG compositions

Xu et al, Acta Mater. 2004

Wang et al, Appl. Phys. Lett. 2004

Inoue et al, JIM 2004

Tang et al, Chin. Phys. Lett. 2004φ2 mm (max)

glass forming range

Cu Zr

φ3mm BMG-forming zone in Zr-Al-Cu

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0 0.0

0.2

0.4

0.6

0.8

1.0

Al

Cu

Zr

Eutectic

eutectics

GFA (Tg/Tm and ΔE) increases with increasing e/a

Cu5Zr8

Cu5Zr6

Cu6Zr5

Cu8Zr5

Cu9Zr4

Cu58.1Zr35.9Al6

0mm

15mm

φ4mmCu55Zr40Al5 Reference

cluster

Inoue et al, Mater. Sci. Eng. 1994Schumacher et al, J. Appl.Phys. 1994Inoue et al, JIM, 2002Xu et al, Phys. Rev. Lett. 2004Wang et al, Acta Mater. 2005

φ3mm BMG-forming zone in Zr-Al-Cu

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0 0.0

0.2

0.4

0.6

0.8

1.0

Al

Cu

ZrEutectics

Cu5Zr6

Cu6Zr5

Cu8Zr5

Cu39.7Zr47.1Al13.2

Cu58.1Zr35.9Al6

Cluster

Ra ~ Cu8Zr5e/a = 1.48

Ra-constant line

Ra:average atomic radius

Ra ~ Cu5Zr6e/a = 1.5

ico-Cu8Zr5 from Cu8Zr3 phase

deep eutectic point

Cu8Zr3 phase

Δ = (R0/1-R*)/R*= 0.4%

topologically dense packing

Cu8Zr5

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.00.0

0.2

0.4

0.6

0.8

1.0

M

Cu

Zr

ECu61.8Zr38.2

Cu8Zr5

Cu-Zr-M 体系

M=Nb, Sn, Mo, Si, V, Ag, Al, Ti

Cu8Zr5-M

Cu64Zr36=(Cu8Zr5)1Cu1

Cu64Zr36-M

Xia et al. Appl. Phys. Lett., 2006, 88:1.

Cluster + glue atom(Cluster + glue atom) + minor alloying element

Cluster + glue atom

Proof for Cu8Zr5

Our new BMGs:

Zr-(Al, Ti)-(Ni, Co)Cu-Zr-M (Nb, Sn, Ag, Al, Ti)(Ce, Sm,Y)-Al-(Ni,Co)(Fe,Co)-based

Appl. Phys. Lett. 2006Mater Sci & Eng. R 2004 Acta Mater. 2003

1. 量化的成分设计。

2.联系微观团簇结构和宏观相图特征。

3. 连接亚组元体系和多组元体系。

成分判据特征

Some physics…

由Sanderson电负性均衡原理：

Electronegativity Equalization Principle (EEM)Upon molecule formation, the electronegativities of all the constituent atoms of a molecule become equal

R.T. Sanderson, Science, 121, 207 (1955)Quantum mechanical proof

A B AB

χA0

χB0

χBχA

+

R.G. Parr et al, J.Chem.Phys., 68, 3801 (1978)

χA= χB= χAB

由密度泛函理论，有：

∫+=++= drrVrrFrVrVrTrE HKeene )()()]([)]([)]([)]([)]([ ρρρρρρ

)()(

rVr

F�F HK +=δρδμ化学势

W. Kohn, L.J. Sham, Phys. Rev. A, 140, 1133 (1965)

),( VNEE =

基于密度泛函理论 Parr给出化学势与电负性的关系：

χρ

μ −=∂

∂=

∂∂

= VV rE

NE )

)(()(

R. G. Parr et al., J. Chem. Phys. 68, 3801(1978)

Heats of Formation of Transition-Metal Alloys

This Letter proposes a scheme for obtaining the d-electron energy-band parameters to be used in a simple analytic model of the alloy heat of formation, ΔH. The scheme employs, as an intermediate step, the equalization of the local chemical potentials of the two sites. Calculations for 3d, 4d, and 5d metal alloys yield ΔH in accord with experimental trends, but, unlike earlier estimates, with d charge transfer in the direction indicated by experiment.

R. E. Watson Phys. Rev. Lett. 43, 1130–1134 (1979)

Formation of an electric dipole at metal-semiconductor interfaces

A recent theory showed that the polarization of the chemical bonds at metal semiconductor interfaces could quantitatively account for the experimentally observed strength of Fermi level pinning on different semiconductors, without regard to the actual distribution of gap states. The method used in this theory, the electrochemical potential equalization method hitherto employed only in molecular physics, and its limitations are here discussed in detail, especially in the context of application to solid interfaces. Similarities and differences between this theory and the metal induced gap state theory are also discussed.

Raymond T. Tung Phys. Rev. B 64, 205310 (2001)

服从费米-狄拉克分布规律的理想电子气体的化学势为：

2

[1 ( ) ]12

BF

F

k TEE

πμ = − +L22

2 3( 0) (3 )2F

NT Em V

μ π= ≡ =h

T=0K时的化学势也称为费米能EF

化学势

),(2

)3( 2

322

32

2aa

a

aF RND

RN

mcE βπμ ==≈

h

iia NCN ∑= iia RCR ∑=)/( ae

2

32

),(a

aaa R

NRND = 单位：nm-2

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.00.0

0.2

0.4

0.6

0.8

1.0

M

Cu

Zr

ECu61.8Zr38.2

Cu8Zr5

Cu-Zr-M 体系

M=Nb, Sn, Mo, Si, V, Ag, Al, Ti

Cu8Zr5-M

Cu64Zr36=(Cu8Zr5)1Cu1

Cu64Zr36-M

Xia et al. Appl. Phys. Lett., 2006, 88:1.

Cluster + glue atom(Cluster + glue atom) + minor alloying element

Cluster + glue atom

统一判据

化学势均衡判据在双基元非晶结构中的应用

其结构可以描述为 团簇+连接原子G

两个局部结构的化学势相同！

cluster G Gxμ μ=

G cluster Gx D D=

(Cu8Zr5)1Gx BMGsCu8Zr5团簇+G

RCu8Zr5 = CCu*RCu+ CZr*RZr = 0.1403 nm,Na = CCu*NCu+ CZr*NZr = 1.385

DCu8Zr5 = = 63.1103 /nm-2== 2

32

2

32

1403.01.385

a

a

RN

cluster G Gxμ μ=

G cluster Gx D D=

(Cu8Zr5)(Cu)x BMGThe equi-potential then occurs between (Cu8Zr5) - (Cu) x

RCu8Zr5 = CCu*RCu+ CZr*RZr = = 0.1403 nm, Na = CCu*NCu+ CZr*NZr = 1.385

DCu8Zr5 = 63.1103 /nm-2

DCu = 61.035 /nm-2

x= DCu8Zr5/DCu =1.034

(Cu8Zr5)Cu1.034 ≈ Cu64.4Zr35.6Experimental Cu64Zr36 [Xu et al. Acta Mater 2004]

举例

bulk metallic glass composition chart in the Cu-Zr-G(Al,Ti,Ag) system

0.0 0.2 0.4 0.6 0.8 1.0

0.2

0.4

0.6

0.8

1.0

0.0

0.0

0.2

0.4

0.6

0.8

1.0G

Cu

Zr

cluster lines

Cu58.7Zr36.7Al4.6

Cu57.8Zr36.1Ti6.1

Cu55.8Zr34.9Ag9.3

Cu64.4Zr35.6

Cu58.7Zr36.7Al4.6

Cu57.7Zr36.1Ti6.2

Cu55.9Zr34.9Ag9.2

Calculated comp. Experimental comp.

Cu64Zr36

Cu58.1Zr35.9Al6

Cu57.2Zr35.3Ti7.5

Cu56.9Zr35.1Ag8

～

(Cu8Zr5)(CuMy)x BMGsThe equi-potential then occurs both between Cu - My

and between (Cu8Zr5) - (CuMy).

Example: (Cu8Zr5)(CuNby)x

DCu=y⋅DNb, DCu8Zr5 =x⋅DCuNby x = 0.66

(Cu8Zr5)(CuNb0.451)0.660 = Cu8.66Zr5Nb0.30 = Cu62.0Zr35.8Nb2.2

Experimental Cu62.7Zr35.3Nb2 [Xia et al. APL 2006]

举例

0.0 0.2 0.4 0.6 0.8 1.0

0.2

0.4

0.6

0.8

1.0

0.0

0.0

0.2

0.4

0.6

0.8

1.0M

Cu

Zr

cluster lines

Cu62.1Zr35.8Nb2.1

Cu62.1Zr35.8Ta2.1

Cu61.7Zr35.3Sn3

Cu64Zr36

Fig. 5 The bulk metallic glass composition chart in the Cu-Zr-G(CuM) system

Calculated comp. Experimental comp.

～Cu62.1Zr35.8Nb2.1

Cu62.1Zr35.8Ta2.1

Cu61.7Zr35.3Sn3

Cu61.9Zr36.6Nb1.5

Cu61.9Zr36.6Ta1.5

Cu61.6Zr36.6Sn1.8

New Applications in more useful alloys

1. H-storage alloy systems

a. 稀土系ΑΒ5型：Η< 1.4 wt.%b. Ti系AB型 : Η 1.2−1.8 wt.% c. Mg系A2B型 : Η 3.6−7.6 wt.% d. Zr、Ti系Laves phase AB2型 : Η 1.5−2.0 wt.%e. V系固溶体型: Η 1.5−2.4 wt.%

与Laves phase相关的一类合金体系

Ti-Cr-V alloy system

Ico-Cr7Ti6 Cluster linee/a-constant lineRa-constant line

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.51E-3

0.01

0.1

1

10

H2 P

ress

ure

(MP

a)

H / M

313K

Cr7Ti6-V线上Cr32.3Ti27.7V40合金313 K时的PCT曲线

Η/Μ: 3.22 wt. %

QuasicrystalsBulk metallic glassesLaves phase alloys

Icosahedron-based

“Icosahedron cluster alloys”

H-storage behavior

More common characteristics?

0.00 0.25 0.50 0.75 1.000.00

0.25

0.50

0.75

1.000.00

0.25

0.50

0.75

1.00

B4N

e/a=4.57 line

β-C3N4

BN4

B2CN2

BC4N BC3N

C

B

N

BC2N

BN

e/a=4 line

2. 薄膜材料：非金属体系硬质涂层材料 B-C-N system：

e/a=4.57 (Ra=0.73)

e/a=4 (Ra=0.78)

e/a-constant lineRa-constant line

国家自然科学基金一项

Thank you

王清

韩光

陈伟荣

羌建兵 王英敏

吴江李艳辉李艳辉

姜楠 陈凤

Nigel 夏俊海 高鹏

Cu-Zr晶体相中共存在23种可能的团簇结构

团簇选取准则1. 拓扑密堆准则：原子尺寸因素

R0/1＝r0 / r1r0为团簇中心原子半径

r1为团簇第一壳层上原子的平均原子半径

Δ=(R0/1-R*) / R* R*为团簇配位数一定时的原子密排堆垛时的临界半径比

Δ绝对值越小说明团簇结构越满足拓扑密堆排列的要求

Miracle D B, Sanders W S. Philos. Mag., 2003.

Ico-Cu8Zr5

R0/1 = 0.906

Δ = 0.4%

R*= 0.902Cu

Zr

2. 化学短程序准则：优化的异类原子配位

RD=RD0*(1-RD

1)

RD0=(CN-x) / CN

RD1= y / E

RD值越大 团簇内部强有序+弱团簇连接 无序密堆

负混合焓 异类原子配位 团簇化

团簇之间的弱结合 同类原子连接团簇

两者的综合

RD0 = 5/12 = 0.417

RD1 = 15/30 = 0.5

RD = 0.209

Cu

Zr

Ico-Cu8Zr5

从动力学的角度来看，

靠近深共晶点的团簇结构更利于非晶形成

靠近晶体相成分的团簇：Cu14Zr4，Cu6Zr6，Cu13Zr5，Cu12Zr5

与非晶形成相关的团簇结构

将满足以上两个准则的团簇分为三类

靠近共晶点成分的团簇：Cu16Zr，Cu18Zr2，Cu8Zr5，Cu6Zr5，Cu5Zr6

介于两者之间的团簇：Cu9Zr4，Cu5Zr8

•1.5 •1.6 •1.7 •1.8 •1.9 •2.0 •2.1•0.00

•0.05

•0.10

•0.15

•0.20

•0.25

•0.30

•0.35

•e/a

•μW

C

•0.06

•0.08

•0.10

•0.12

•0.14

•0.16

•0.18

•e/a = 1.86

•diamond

•indentor

•WC indenter

•0.35%

•0.38%

•μ

β1

β4

β3

oF

β+IQC

IQC1

ω

D

电子浓度对摩擦系数的影响

Criterion 1:e/a-constant line

Cu (+1)

β

Al13Fe4

(Cu)Al4Cu9Al7Cu2FeAl10Cu9Fe

IQCIQC e/a-constante/a=1.86α

θ

ζ2

Al (+3)

Fe（-2）

1.62.4

0.7

0.4

0.1

-0.2

-0.5

-0.8

-1.1

-1.4

-1.7-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

Al-Cu-Fe e/a diagram

2.62.8 2.0 1.8 1.4 1.22.2

d-Al6Fe

Dong, Scr. Met & Mat 1995

Criterion 2:‘e/a-variant’ line

θ Cu (+1)Al (+3)

Fe（-2）

1.62.4

0.7

0.4

0.1

-0.2

-0.5

-0.8

-1.1

-1.4

-1.7-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

Al-Cu-Fe e/a diagram

2.62.8 2.0 1.8 1.4 1.22.2

e/a-variant line: binary QC, ternary QC, and the 3rd element.

‘e/a-variant’ line

IQCIQCd-Al6Fe

Al13Fe4

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.00.0

0.2

0.4

0.6

0.8

1.0Y

B

Fe

Fe72B22Y6

Fe12Y

Fe8B3Fe8B2Fe83B17

Fe9B

1

234

1：Fe68.6B25.7Y5.72： Fe74.9B18.8Y6.33： Fe77.6B15.9Y6.5

4： Fe83.7B9.3Y7

Δ=7.1%

Δ=8.7%

Δ=1.2%Δ=11.4%

(intersection)96Nb2Zr2

Minor adjusting

Amor.

Connection of icosahedron Al10.7Fe2 and CN10 Al8Cu3 by sharing a common rhombus, giving the basic configuration of the Mackay-type QCs.

Al

Fe

Al

Cu

Al10.7Fe2

Al8Cu3

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0 0.0

0.2

0.4

0.6

0.8

1.0

Co12Si

Co9B3

Co9B

Co8B3

Si

B

Co

Co7B3

Δ=16%

Δ=2.6%

Δ=10.4%

Δ=-7.7%

Δ= 17.1 %

123

4

Co12Si-B与CoB-Si的交点：1： Co66.2B28.3Si5.52： Co68.6B25.7Si5.7 3： Co70.6B23.5Si5.9

4：Co83.7B9.3Si7

(intersection)96Nb4

Minor adjusting

Amor.