diffusion in amorphous metals

7/28/2019 Diffusion in Amorphous Metals

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Diffusion in Amorphous Metals


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Introduction

Production Of Metallic Glasses:

techniques & Procedure

Self Diffusion in Amorphous Metals:

Dominant mechanism

Diffusion of Small Interstitial Solute Atoms:

Dominant mechanism

Evaluate Equations


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Production Of Metallic Glasses

Avoid Of Solidification By Crystallization With

Rapid Quenching below Tm

supercooled liquid

undergoes a glass transition to an amorphous glassy

Low Temp +Loss Free Vol

lose its characteristic fluidity

become relatively rigid


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Production Techinques Of Amorphous Metals

1- Sputtering and PVD or CVD techniques:

Mainly used foramorphous thin films.

2- Solid state reactions:

Diffusion couples, Mechanical alloying.

3- Electrochemical deposition:

For amorphous surface coatings.

4- Production from the melt by casting techniques:Splat quenching with RC 10

6 Ksec-1

Melt spinning with RC 104 Ksec-1

High-pressure die casting RC 102 Ksec-1

Suction mold casting with RC

102

Ksec-1


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Self Diffusion in Amorphous Metals

If a rapidly cooledmetallic glass

reheated and annealed

isothermally at Below Tg

excess free volume

will anneal out

the system attempts to relax and

equilibrate without crystallizing

Self-diffusion coefficient of59Fe in

amorphous Fe40Ni40B20 during

isothermal annealing below Tg, after

rapid quenching from liquid state

Time independent

Exhibit Arrhenius Behavior(lnDi vs 1/T appear straight line)


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Self-diffusion occurs by a direct collective mechanism

and is not aidedbypoint defects in thermal equilibrium

as in the vacancy mechanism for self-diffusion in crystalsWhy?

Cause 1

Sudden changes in temperature during diffusion

Cause instantaneous changes in the diffusivity.

if diffusion occurs by a point-defectmechanism significant time is required

Self-diffusion occurs by a direct collective mechanism

not point defects mechanism


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Cause 2

Activation Volume

for Diffusion=

Activation Volume

of Defect formation+

Activation Volume

of Defect Migration

As Mesured byExperimental

Accuracy is ZERO

Why Self-diffusion occurs by a direct collective

mechanism not point defects mechanism?

ZERO


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Why Self-diffusion occurs by a direct collective

mechanism not point defects mechanism?

Cause 3

Computer simulations of the diffusion process in relaxed

Fe-Zrglasses reveal diffusion which takes place directly

via thermally activated displacement chains


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Diffusion of Small Interstitial Solute Atoms

Small solute atoms in the interstices between the

larger host atoms in a relaxed metallic glass diffuse by

the direct interstitial mechanism.

An example is the diffusion of H solute atoms in

glassy Pd80Si20 .


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*pk = fraction of all sites that are tracer-occupied type k sites

The following quantities will be of use in describing the

interstitial self-diffusion and intrinsic chemical diffusion:

N = total number of interstitial sites

p = fraction of all interstitial sites that are occupied

*p = fraction of all sites that are tracer-interstitial occupied

Pko = fraction of all sites that are type k sites

P (k) = fraction of type k sites that are occupied

pk= fraction of all sites that are occupied type k sites


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because each site can accommodate only one interstitial,

The Occupation Probability at the various sites should

follow Fermi-Dirac statistics ,therefore:

)()(1

1)(kTGke

kp

Gk= the energy corresponding to occupation of the type k site

P (k) = fraction of type k sites that are occupied

= chemical potential of interstitial


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The Fraction of all interstitial sites that occupied:

k kTG

o

kk

o

k

ke

pNpkpkp

)()(1

)()(

The partial Concentration is:

k kkTG

o

k

o

k ppande

pkNppkp

k )()(1

)()(

Since the inert and tracer interstitials are randomlyintermixed in each local region

p

p

p

p

k

k

**

(Eq 1)

(Eq 1)

)()(

**

1kTG

o

kk

ke

p

p

pp


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Slab I Slab II

Unit area

C

X

C

X

X

X

The Jump rate of a tracer

interstitial from i site to

adjacent empty i site is:

)()(' kTGkEoGo

ki e

X0


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The net number of jumps all types crossing the x = x0plane per unit time in X direction is:

i k

xxkii

o

ikxxkii

o

ikI oo ppppppxgJ 2/'*

2/

'**

)()(

g = a purely geometrical constant

= the ratio of interstitial sites to atoms

= the average atomic volume in the glass

= the number of interstitial sites per unit volume

(pio - pi ) = the probability that a site is an empty isite


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During tracer self-diffusion, the total concentration

of inert and tracer interstitial atoms is constant

p & (pio - pi ) arIndependent of X

With perform Taylor Expansion:

i kkTG

kTGGo

ii

o

i

kTE

Ix

p

pe

epppe

xgJ

k

ok

o

*

)()(

)()()(

2* 1

1)(

)(

With using:

)/()(1

,,1)(,1kTG

o

kk

k

k

i

i

o

i

i

o

ike

pppppppp


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)()()()(

)()(

)()(

)1()(1

kTG

k

k

o

k

kTG

kkTG

kTGGo

ioo

k

ok

epppee

ep

x

pe

p

pe

xgJ kTG

kTE

I

oo

*)()(

2)(

2* )1()(


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The Simpler Form of *JI is:

x

pe

p

pDJ kTGoII

o

*)()(

2** )1(

Ficks Low

Equation

)()(2

** )1( kTGoII

o

ep

p

DD

)(2* )( kTEoIo

exgD Correspondingto


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o

II Dp

D *

ln

ln1

is Activity Coefficient A function of Concentration

and Position

diffusivity vs

concentration

prbability of

H at differenttemperatures

in Pd80Si20

*Di glassy Ni80Zr50 of

various solute atoms as

a function of their size


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DIH Concentration

Radius Metalic DI

Small Interstitial

Solute atom is

Dominant


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Discussion Time independent

Exhibit Arrhenius Behavior

1- Self Diffusion inAmorphous Metals

2-Diffusion of Small

Interstitial Solute Atoms

DIInterstitial

atom Concentration

Radius Metalic DI


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Reference

1- KINETICS OF MATERIALS Robert W. Balluffi Samuel M. Allen

W.Craig Carter

2- AMORPHOUS MATERIALS Laboratory Class Tutorial by

R.Wunderlich University of Ulm Abteilung Werkstoffe derElektro

technic Version 20 Dec 2004

3- An Explanation of Anomalous Diffusion Patterns Observed in

Electroactive Materials by Impedance Methods Juan Bisquert,* Germa

Garcia-Belmonte, and Angeles Pitarch

4-Amorphous Semiconduncer Are denser M. Popescu, F. Sava, W. HoyeraJune 2006

5- Exciting New Coatings For Amprphous Glass Pulse CoresRichard H

Wood, and Richard Lathlaen* National-Arnold Magnetics 17030 Muskrat

Ave Adelanto, CA 92301

diffusion in amorphous metals

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