Diffusion pattern in disilicides in group IVB, VB and

Diffusion pattern in disilicides in group IVB, VB and VIB metal-silicon systems Soumitra Roy, Soma Prasad, Sergiy V. Divinski, Aloke Paul

Department of Materials Engineering Indian Institute of Science Bangalore, India 1

Objectives Back ground: Metal-Silicides are important in many applications such as electronic materials, structural materials, coatings etc. Extensive studies are conducted till date, however, mostly in thin film condition.

It is a common notion that Si is the only diffusing species especially in disilicides Objective: Bulk diffusion studies in Group IVB, VB and VIB Metal-Silicon systems to examine, if it is indeed true! Outcome: We found a particular pattern in diffusion behavior of components.

Estimated diffusion parameters Integrated diffusion coefficient

~β Dint = − Vmβ

xβ 2

~ J ∫ B dx

xβ 1

~ JB

(N =−

+ B

− N B− 2t

) (1 − Y ) Y ∫V 

x +∞

x*



* B

B

x −∞

m

* B

dx + Y

∫

x*

(1 − YB ) dx Vm

 

Ratio of the intrinsic/tracer diffusion coefficients x   + xK Y ( 1 − YB ) − B dx − N B ∫ dx   NB ∫ * V V DB J B VA DB  m  xK x −∞ m ≈ = =  xK x +∞ DA* J A VB DA  ( ) Y Y 1 − + − B B − N dx + N A ∫ dx  A ∫   V Vm xK x −∞ m   +∞

N B − N B− YB = + N B − N B−

Locating the Kirkendall marker plane

A. Paul et al. Thermodynamics, diffusion and the Kirkendall effect in solids, Springer, 2014

Locating the Kirkendall marker plane K K

1350 oC , 10 h 1300 oC , 16 h

S. Prasad and A. Paul, Intermetallics 19 (2011) 1191 P.C. Tortorici and M.A. Dayananda, Met. Mat. Traans 30A (1999) 545 M. Salamon, et al., Phil. Mage. 84 (2004) p. 737 Salamon and H. Mehrer, Z. Metallk. 96 (2005) p. 833

Systems considered IVB

VB

VIB

Ti

V

Cr

Zr

Nb

Mo

Hf

Ta

W

TiSi2 ZrSi2 , HfSi2

Around Ti atom 4 Ti and 10 Si Around Si atom 5 Ti and 9 Si

M is surrounded by 10 Si (4 Si-I and 6 Si-II) and 6 M Si-I is surrounded by 12 Si (8 Si-I and 4 Si-II) Si-II is surrounded by 10 Si (6 Si-I and 4 Si-II) and 6 M

Growth in the Ti-Si system 1200 oC for 16 hours Si

TiSi2

TiSi

Ti Ti5Si4

100

Ti5Si4

80

Ti at %

Ti 3Si 60

TiSi

40

Ti5Si3

Ti 5Si 3 Ti 5Si 4

Ti3Si

TiSi 2

20

0 -0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

Distance (µm)

S. Roy, S. Divinski, A. Paul, Phil. Mag. 94 (2014) 683.

Growth in the Ti-Si system Si

TiSi2

TiSi

Ti

Ti5Si4

DSi* =∞ DTi*

K

-14

10

-15

QTiSi 2 = 190 + - 9 kJ/mol

2

Dint , m /s

10

6.5

6.6

6.7

6.8 -4

1/T X 10 , K

6.9

7.0

7.1

-1

S. Roy, S. Divinski, A. Paul, Phil. Mag. 94 (2014) 683.

Growth in the Zr-Si and Hf-Si systems HfSi2

Si

100

Hf

80

HfSi

HfSi2

Hf at %

60

K

HfSi

40

20

0 -0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Distance (µm)

1 ZrSi2

Si

100

Zr

80

60

Zr at %

ZrSi

ZrSi2

ZrSi

40

K 20

0 0.0

0.1

0.2

0.3

0.4

0.5

Distance (µm)

S. Roy and A. Paul, Materials Chemistry and Physics 143 (2014) 1309

Growth in the Zr-Si and Hf-Si systems

QZrSi = 346 +- 34 kJ/mol

2

Dint , m /s

2

10

-13

~

10

-12

10

-13

6.6

6.7 6.8 6.9 -4 -1 1/Tx 10 , K

7.0

7.1

QHfSi = 394 +- 37 kJ/mol 2

2

Dint , m /s

6.5

~

-

10

-14

6.4

6.5

6.6

6.7 6.8 -4 -1 1/T x 10 , K

6.9

7.0

S. Roy and A. Paul, Materials Chemistry and Physics 143 (2014) 1309

Comparison of data in Group IVB Metal-Silicon system

10

-12

IVB

VB

VIB

Ti

V

Cr

Zr

Nb

Mo

Hf

Ta

W

TiSi2 - 190 kJ/mol

HfSi 2

ZrSi2 - 346 kJ/mol

10

HfSi 2

-12

HfSi2 HfSi 2

ZrSi 2 -13

10

-14

ZrSi 2 10

-13

10

-14

~

~

10

Dint (m2/s)

Dint (m2/s)

HfSi2 - 394 kJ/mol

6.4

TiSi 2

6.5

6.6

6.7

6.8 -4

1/Tx 10 , K

-1

6.9

7.0

7.1

TiSi 2

1.176

1.180

1.184

1.188

1.192

Tm/T

Melting point (Tm) normalized integrated diffusion coefficient increases with the increase in atomic number. Overall vacancy concentration must be increasing with the increase in atomic number

Data in Group IVB Metal-Silicon systems TiSi2, oF24, C54 structure Si

TiSi Ti

TiSi2

Ti5Si4

* Si * Ti

D =∞ D

IVB

VB

VIB

Ti

V

Cr

Zr

Nb

Mo

Hf

Ta

W

K

ZrSi2

Si

Around Ti atom 4 Ti and 10 Si Around Si atom 5 Ti and 9 Si

Zr

ZrSi

DSi* =∞ * DZr

C49 (oC12)

K

Si

HfSi2

Hf HfSi

K

DSi* =∞ * DHf

M is surrounded by 10 Si (4 Si-I and 6 Si-II) and 6 M Si-I is surrounded by 12 Si (8 Si-I and 4 Si-II) Si-II is surrounded by 10 Si (6 Si-I and 4 Si-II) and 6 M

Vacancy concentration increases on Si sublattice Vacancy and antisites on sublattice for metal component must be negligible

Growth in the Group VB Metal-Silicon systems MSi2, hP9 (C40)

IVB

VB

VIB

Ti

V

Cr

Zr

Nb

Mo

Hf

Ta

W

M – 5 Si Si – 5 Si and 5 M

Growth in the V-Si system VB

VIB

Ti

V

Cr

Zr

Nb

Mo

Hf

Ta

W

1200 OC;16hrs

10

DSi* =∞ DV*

K

-13

141± 7.8 kJ/mol

10

-14

10

-15

~

Dint (m2/s)

IVB

6.2

6.4

6.6

6.8 -4

7.0

7.2

7.4

-1

1/Tx10 (K ) S. Prasad and A. Paul, J. Phase Equilibria and Diffusion 32 (2011) 212

Growth in the Nb-Si system Nb

NbSi2

Si

IVB

VB

VIB

Ti

V

Cr

Zr

Nb

Mo

Hf

Ta

W

Nb5Si3 K

DSi* = 4. 8 ± 1. 4 * DNb

30 µm Nb/Si diffusion couple, 1250 oC , 24hrs -13

193 ± 16 kJ/mol -14

10

~

Dint (m2/s)

10

-15

10

6.2

6.4

6.6

6.8

7.0

1/Tx10-4 (K -1)

S. Prasad and A. Paul, Acta Materialia 59 (2011) 1577

Growth in the Ta-Si system TaSi2

Ta

Si

Ta5Si3

IVB

VB

VIB

Ti

V

Cr

Zr

Nb

Mo

Hf

Ta

W

K

~ , m2/s D int

10

10

10

-13

Q = 550 +- 70 kJ/mol

-14

Temperature ( oC)

DSi* * DTa

in the

1200

TaSi2 phase 1.3

1225

1.2

1250

1.1

1275

1.1

-15

6.4

6.5

6.6

6.7 -4

1/T x 10 , K

-1

6.8

6.9

S. Roy and A. Paul, Philos. Mag 92 (2012) 4215

Data in Group VB Metal-Silicon systems IVB

VB

VIB

Ti

V

Cr

Zr

Nb

Mo

Hf

Ta

W

-13

10

-13

10

TaSi2

TaSi2

NbSi2

Dint (m 2/s)

VSi2 -14

10

~

Dint (m2/s)

VSi2

~

NbSi2

-14

10

NbSi2 - 193 kJ/mol VSi2 - 141 kJ/mol TaSi2 - 550 kJ/mol

-15

-15

10

10

6.3

6.4

6.5

6.6

6.7

6.8 1/Tx10 (K ) -4

-1

6.9

7.0

7.1

1.2

1.3

1.4

1.5

1.6

1.7

Tm/T

Again melting point normalized integrated diffusion coefficient increases with the increase in atomic number. Overall concentration of defects assisting the diffusion must be increasing with the increasing atomic number S. Roy, S. Prasad, S.V. Divinski and A. Paul, Philos. Mag. 94 (2014) 1508

Data in Group IVB Metal-Silicon systems MSi2, hP9 (C40) DSi* =∞ DV*

K

NbSi 2

Nb Nb 5 Si 3

VIB

Ti

V

Cr

Zr

Nb

Mo

Hf

Ta

W

DSi* = 4.8 ± 1.4 * DNb

30 µm TaSi2

VB

Si

K

Ta

IVB

M – 5 Si Si – 5 Si and 5 M

Si

Ta5Si3

K

DSi* = 1.1 − 1.3 * DTa Concentration of metal antisites must be increasing with the increasing atomic number

Growth in the Group VB Metal-Silicon systems

CrSi2 MSi2, hP9 (C40)

M – 5 Si Si – 5 Si and 5 M

IVB

VB

VIB

Ti

V

Cr

Zr

Nb

Mo

Hf

Ta

W

MoSi2 ,WSi2 tI6, C11b

M – 10 Si Si – 5 Si and 5 M

Growth in the Cr-Si system IVB

VB

VIB

Ti

V

Cr

Zr

Nb

Mo

Hf

Ta

W Cr

Cr5Si3

CrSi2

CrSi

K

1250 oC 16 hrs DSi* =∞ * DCr

Si

Growth in the Mo-Si system IVB

VB

VIB

Ti

V

Cr

Zr

Nb

Mo

Hf

Ta

W

K

1300 oC , 16hrs DSi* =∞ * DMo -13

10

K

-14

10

~

Dint (m2/s)

153 kJ/mol

-15

10

6.3

1350 oC , 10 hrs

6.4

6.5

6.6

6.7 -4

6.8

6.9

7.0

7.1

-1

1/Tx10 (K )

S. Prasad and A. Paul, Intermetallics 19 (2011) 1191-1200 P.C. Tortorici and M.A. Dayananda, Met. Mat. Traans 30A (1999) 545

Growth in the W-Si system VIB

Ti

V

Cr

Zr

Nb

Mo

Hf

Ta

W

W

WSi2

Si

DSi* = 13.7 DW*

K

10

-13

8x10

-14

6x10

-14

4x10

-14

2x10

-14

Q = 152 +- 7 kJ/mol

~ 2 Dint , m /s

VB

~

IVB

6.4

6.5

6.6

6.7

6.8 -4

1225 oC; 9 hrs

1/T x 10 ,K

6.9

7.0

7.1

-1

S. Roy and A. Paul, Intermetallics 37 (2013) 83

Data in Group IVB Metal-Silicon systems

-13

VB

VIB

Ti

V

Cr

Zr

Nb

Mo

Hf

Ta

W

-13

10

10

WSi2

Dint (m2/s)

WSi2

MoSi2

-14

10

MoSi2

-14

10

~

~

Dint (m2/s)

IVB

MoSi2

MoSi2 - 153 kJ/mol

WSi2

WSi2 - 152 kJ/mol

-15

-15

10

6.3

10 6.4

6.5

6.6

6.7

6.8 1/Tx10-4 (K -1)

6.9

7.0

7.1

1.4

1.5

1.6

1.7

Tm/T

Again integrated diffusion coefficient increases with the increase in atomic number. Overall concentration of defects must be increasing with the increase in atomic number.

1.8

Data in Group IVB Metal-Silicon systems

Cr

CrSi2

Cr5Si3

CrSi

Si

DSi* =∞ * DCr

K

K

W

WSi2

DSi* =∞ * DMo

IVB

VB

VIB

Ti

V

Cr

Zr

Nb

Mo

Hf

Ta

W

M – 5 Si Si – 5 Si and 5 M

CrSi2, hP9 (C40)

Si

M – 10 Si Si – 5 Si and 5 W

DSi* = 13.7 DW*

K MSi2, tI6, C11b

W antisites must be present

Conclusions VB M - Si

IVB M - Si -13

10

TaSi2

HfSi 2

-12

Dint (m2/s)

ZrSi 2 10

-13

TiSi 2

1.176

1.180

1.184

1.188

1.192 -15

10

Tm/T

1.2

1.3

1.4

Tm/T

VIB M - Si -13

10

WSi2

MoSi2

-14

10

~

Dint (m 2/s)

-14

-14

10

~

10

NbSi2

VSi2

~

Dint (m2/s)

10

MoSi2 WSi2 -15

10

1.4

1.5

1.6

Tm/T

1.7

1.8

1.5

1.6

1.7

IVB

VB

VIB

Ti

V

Cr

Zr

Nb

Mo

Hf

Ta

W

Conclusions VB M-Si

IVB M-Si Si

VIB M-Si

TiSi Ti

TiSi2

Cr

Cr5Si3

CrSi2

Ti5Si4

Si

K K

DSi* =∞ DTi*

ZrSi2

Si

Zr

CrSi

DSi* =∞ DV* NbSi 2

Nb Nb 5 Si 3

Si

K

DSi* =∞ * DCr

K

ZrSi K

* Si * Zr

D =∞ D

K

DSi* = 4.8 ± 1.4 * DNb TaSi2

Ta Si

HfSi2

Hf Ta5Si3

30 µm Si

DSi* =∞ * DMo W

WSi2

HfSi

K

K

DSi* =∞ * DHf

DSi* = 1.1 − 1.3 * DTa

DSi* = 13.7 DW*

K

Si

Conclusions We have shown a particular pattern of diffusing components in disilicides Similar pattern is found in 5:3 silicides also (not shown here) Not necessarily Si is the only diffusing component In all the disilicides, Si can easily diffuse via its own sublattice. Metals can diffuse only if anitsites are present. In Group VIB M/Si systems, vacancies on the Si sublattice must be increasing since diffusion rate increases with the increase in atomic number. However, metal antisites must be missing since it does not diffuse. In Group VB M/Si systems, metal antisites must be present (since metal components diffuse) along with the increase in vacancy concentration to have higher diffusion rate. Same is true even for VIB M/Si systems.

Further read/references 1. Aloke Paul, Tomi Laurila, Vesa Vuorinen, Sergiy Divinski, A text book on Thermodynamics, Diffusion and the Kirkendall effect in Solids, Springer, Heidelberg, Germany, 2014 2. Aloke Paul, The Kirkendall effect in solid state diffusion, PhD Thesis, Technische Universiteit Eindhoven, Eindhoven, The Netherlands, 2004 3. A. Paul, M.J.H. van Dal, A.A. Kodentsov and F.J.J. van Loo, The Kirkendall Effect in Multiphase Diffusion, Acta Materialia 52 (2004) 623-630 4. S. Prasad and A. Paul, Growth mechanism of phases by interdiffusion and diffusion of species in the Nb-Si system, Acta Materialia 59 (2011) 1577-1585 5. S. Prasad and A. Paul, An overview of diffusion studies in the V-Si system, Defects and Diffusion Forum vol. 312-315, p. 731-736, year 2011. 6. S. Prasad and A. Paul, Reactive diffusion between Vanadium and Silicon, Journal of Phase Equilibria and Diffusion 32 (2011) 212-218 7. S. Prasad and A. Paul, Growth mechanism of phases by interdiffusion and atomic mechanism of diffusion in the molybdenum-silicon system, Intermetallics 19 (2011) 1191-1200 8. S. Prasad and A. Paul, Diffusion mechanism in XSi2 and X5Si3 (X = Nb, Mo, V) phases, Defects and Diffusion Forum vol. 323-325 p. 459-464, year 2012 (http://www.scientific.net/DDF.323-325.459) 9. S. Prasad and A. Paul, Growth mechanism of the Nb(X)Si2 and [Nb(X)]5Si3 phases by reactive diffusion in Nb (X = Ti, Mo, or Zr)-Si systems, Intermetallics 22 (2012) 210-217 10. S. Roy and A. Paul, Growth mechanism of tantalum silicides by interdiffusion, Philosophical Magazine, 92 (2012) 4215-4229 11. S. Roy and A. Paul, Diffusion in tungsten silicides, Intermetallics 37 (2013) 83-87 12. S. Roy, S. Divinski and A. Paul, Reactive diffusion in the Ti-Si system and the significance of the parabolic growth constant, Philosophical Magazine 94 (2014) 683-699 13. S. Roy and A. Paul, Growth of hafnium and zirconium silicides by reactive diffusion, Materials Chemistry and Physics, 143 (2014) 1309-1314 14. S. Roy, S. Prasad, S. Divinski and A. Paul, Philosophical Magazine, 94 (2014) 1508-1528 15. S. Roy, S. Prasad and A. Paul, An overview of the interdiffusion studies in Mo-Si and W-Si systems, Defects and Diffusion Forum, vol. 354, p. 79-84, year 2014