Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

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Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion SUSTAINABLE HYDROGEN
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Transcript of Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Page 1: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Purpose of this talk

Ronald GriessenACTS workshopMay 24, 2007

Diffusion

SUSTAINABLEHYDROGEN

SUSTAINABLEHYDROGEN

Page 2: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Water droplet

Page 3: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Wave equation2 2

22 2

u uV

t x

Waves

Page 4: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Diffusion

Page 5: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

0c J

t x

Fick’s law Equation of continuity

x

cDJ

dx2

2

c cD

x t

JC(x,t)

Page 6: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

-10

12

34

50.0

0.2

0.4

0.60.8

1.0

0.0

0.5

1.0

1.5 D=1

conc

entr

atio

n

time

x

Dt

x

eDt

c 4

2

2

1

2

2

c cD

x t

is a solution of

Singularities decay immediately

Page 7: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

01

23

45

0.0

0.20.4

0.60.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

conc

entr

atio

n

Time

x

Dt

xerfc

21

y

p dpeyerf0

22

0 1 2 3 40.0

0.2

0.4

0.6

0.8

1.0

y

erf(y)

Diffusion in semi-infinite space

Page 8: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Diffusion into a membrane of thickness L

2 2

2

2 1

4

0

2 14 1( , ) 1 sin

2 1 2

n Dt

L

n

n xc x t e

n L

c t

c neHR

HL

n n Dt

L

n

14 1

2 1

2 1

4

0

2 2

2

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

c( Dt/L2)

Dt/L2

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

1.2

c( x/L, Dt/L2)

Dt/L2=

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

x/L

Page 9: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Hydrogen near a metal surface, for example Pd

Page 10: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

H in Nb

Diffusion coefficients of various interstitials

Page 11: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Figs.IV.11 and 12: Temperature dependence of the diffusion coefficient for hydrogen (full line),deuterium (dashed line) and tritium (dotted line) in FCC metals (blue curves) and in BCC metals (redcurves). The host metals are indicated by their symbols. Note the extreme influence of the crystalstructure in the case of the PdCu alloy.

Ni

FCCPd0.47Cu0.53

Pd

Pd0.47Cu0.53 BCC

Fe

V

Nb

Ta

V

V

NbNb

TaTa

Pd

Pd

Ni

CuDiffusion

coefficients of various

interstitials

Page 12: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Pd

Cu

YPd

Page 13: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Pd

Cu

Page 14: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Pd

Cu

Pd

Cu

Page 15: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Pd

Cu

Y

Pd

Cu

Y

Page 16: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Pd

Cu

Y

Pd

Cu

Y

Page 17: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Pd

Cu

Pd

Cu

Pd

Y

Page 18: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Pd

PdCu

Fast H diffusion in bcc Pd-Cu

Y

Page 19: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Fast H diffusion in bcc Pd-Cu

Cu atomic percent palladium

Tem

pera

ture

oC

Page 20: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Figs.IV.11 and 12: Temperature dependence of the diffusion coefficient for hydrogen (full line),deuterium (dashed line) and tritium (dotted line) in FCC metals (blue curves) and in BCC metals (redcurves). The host metals are indicated by their symbols. Note the extreme influence of the crystalstructure in the case of the PdCu alloy.

Ni

FCCPd0.47Cu0.53

Pd

Pd0.47Cu0.53 BCC

Fe

V

Nb

Ta

V

V

NbNb

TaTa

Pd

Pd

Ni

CuDiffusion

coefficients of various

interstitials

Page 21: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Fick’s law Equation of continuity

x

cDJ

0c J

t x

dx?Is this true

?Is this true

Page 22: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

P-c isotherms and phase diagram

dG SdT Vdp dN

Page 23: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Fick’s law Equation of continuity

0c J

t x

dx?

J cL

x x x t

c c

Lx c x t

x

cDJ

J Lx

Page 24: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

A real diffusion experiment

Page 25: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

0.0 0.5 1.0 1.5 2.0 2.5 3.010

-32

10-28

10-24

10-20

10-16

10-12

10-8

10-4

100

PH

2 (1

05 Pa)

x=H/Y Kooij et al. 1999

Pressure-composition isotherm of YHx at T=293 K

Page 26: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Hydrogenography in Yttrium

Den Broeder, van der Molen et al, Nature 394 (1998) 656

Y

Y2O3 Pd

H

Page 27: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

1

H/Y

0

2

3

hcp-

insulator

hcp-

metal

Page 28: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

1

H/Y

0 2 3

hcp-

insulator

hcp-

metal

1

H/Y

0 2 31

H/Y

0 2 3

hcp-

insulator

hcp-

metal

hcp-

insulator

hcp-

metal

1

H/Y

0

2

3

hcp-

insulator

hcp-

metal

Page 29: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

0.0 0.5 1.0 1.5 2.0 2.5 3.010-32

10-28

10-24

10-20

10-16

10-12

10-8

10-4

100

PH

2 (

105 P

a)

H/Y

1

H/Y

0 2 3

hcp-

insulator

hcp-

metal

1

H/Y

0 2 31

H/Y

0 2 3

hcp-

insulator

hcp-

metal

hcp-

insulator

hcp-

metal

Page 30: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

This picture demonstrates that

instead of j Lx

c

j Dx

Page 31: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Y2O3 PdY

SiO2

H

V

Switchable mirrors as indicators

Page 32: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

SiO2

V V

Sample architecture

Page 33: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Pd 10 nm

Y 50 nm

SiO2

V V

Sample architecture

Page 34: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

HPd

Y

SiO2

V V

x

x=0

Hydrogen loading

Page 35: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

dV

25 nm

50 nm

75 nm

100 nm

125 nm

10 m

m

Pd

YH2 front

x=0

x

H-loading: 473K, 1mbar, 3h

Page 36: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Diffusion in a multilayer

The chemical potential MUST be continuous

The concentration MAY have discontinuities

Page 37: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

x

cDJ

Usual diffusion Real diffusion

J Lx

c

Lc x

?

Page 38: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

0

En

erg

y

1

1

kTe

n

n

nkT

1ln

oc

ckT

1ln

)1( cc

kT

c

Particles in a lattice gas

X

Page 39: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

x

cDJ

Usual diffusion Real diffusion

J Lx

c

Lc x

o

cJ D

x

(1 )

kT

c c c

1

kT cL

c c x

(1 )

o

c cL D

kT

However, the chemical potential MUST be continuous

Page 40: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Ni

Ti

Ni

Ti

Mg

Mg

Ti-H Mg-H Ni-HΔH < ΔH < ΔH

Page 41: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Ni

Ti

Ni

Ti

Mg

Mg

c = c(x,t) cH = f(t)

Ti-H Mg-H Ni-HΔH < ΔH < ΔH

Page 42: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Ni

Ti

Ni

Ti

c = c(x,t) cH = f(t)

Mg

Mg

Fast loading, Very slow unloading

Relatively slow loading, Very fast unloading

Page 43: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Diffusion and Snell’s law

Page 44: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.
Page 45: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

2

2 a

U UD v U

t x

Random walk of a photon

With v the velocity of lighta the absorption coefficient

Page 46: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

So

The aquarium experiment

Page 47: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

O’Leary et al., Phys. Rev. Lett. 69 (1992) 2658

Page 48: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

SiO2

Pd 10 nmV 50 nm

V 250 nm

Y 50 nm

Sample architecture

Page 49: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

YH2

YH3

Pd

32 min1 bar373 K

V 50 nm

V 250 nm

Hydrogen loading

Page 50: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

YH2

YH3

Pd

110 min1 bar373 K

Page 51: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

YH2

YH3Pd

216 min1 bar373 K

Page 52: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

YH2

YH3

Pd

442 min1 bar373 K

Page 53: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

2’ 32’ 55’ 110’216’332’442’ 90’

1

2

1

2

sin

sin

Time evolution of contours

Page 54: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

1

2

1

2

1

2

sin

sin

D

D

Ray tracing alongthe phase – gradientat small angles

A. Remhof, R. J. Wijngaarden, and B. R. Griessen, Refraction and reflection of

diffusion fronts, C. Phys. Rev. Lett., 90 (2003) 145502

Snell’s law for diffusion !

Page 55: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Electromigration

Page 56: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

L eZx

j E

In presence of an electric field

Page 57: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

x

cDJ

Usual diffusion Real electro-diffusion

J L eZEx

c

L eZEc x

(1 )o

c c cJ D eZE

x kT

(1 )

kT

c c c

(1 )o

c cL D

kT

Page 58: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Electromigration

0.0 0.2 0.4 0.6 0.8 1.00.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

2.50

c( x/L, Dt/L2)

Dt/L2=

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

x/L

0.0 0.2 0.4 0.6 0.8 1.00.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

2.50

c( x/L, Dt/L2)

Dt/L2= 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

x/L

Electric field ON Electric field OFF

Page 59: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Electromigration of H in V

Electric field ON Electric field OFF

Page 60: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

ElectromigrationDen Broeder, van der Molen et al. Nature 394 (1998) 656

Pd

Y

Y2O3H H

Page 61: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

Electro-diffusion of hydrogen in

yttriumDen Broeder, van der Molen et al. Nature 394 (1998) 656

Pd

Y

Y2O3

j=0

j=20 mA

j=40 mA

+_

H behaves like a negative ion

H H

Page 62: Purpose of this talk Ronald Griessen ACTS workshop May 24, 2007 Diffusion.

SUSTAINABLEHYDROGEN

SUSTAINABLEHYDROGEN