ellingham diagram - national energy technology laboratory library/research/coal/energy...

Ellingham Diagram

Growth rates of selected oxidesCoO>NiO>Cr2O3>Al2O3

Thermodynamic stabilities of selected oxides Al2O3>Cr2O3>CoO>NiO

Effect of Electrical Current on Oxidation Rate

x

Cations

Electrons

Anions

Cation Vacancies

Metal GasOxideMO

MOO2eM 2212 =++ −+

−− =+ 222

1 O2eOor

−− +=+ 2eMOOM 2

−+ += 2eMM 2

or

1Ma 2Op

M O2

o

MO2 2MO;O2M G∆=+Overall reaction:

p'O2

( )M/MO

= exp 2 G∆ MOO

RT a"M

exp ∆GMOO

RT= p"O2

( )1

½

Oxidation Under Open Circuit Conditions

vBN x

Z Fxi

i

A

ii= − +( )

∂µ∂

∂φ∂

1

)(x

FZxN

BCvCj i

i

A

iiiii ∂

∂φ∂∂µ

+−==

2)( FZCRTN

DkTBii

iAii

κ==

Replace Bi in ji

⎟⎠⎞

⎜⎝⎛ +−=

xFZ

xFZj i

i

i

ii ∂

∂φ∂∂µκ

22

Consider a scale growing by cations moving outward.

jZ F x

Z Fxc

c

c

cc= − +⎛

⎝⎜⎞⎠⎟

κ ∂µ∂

∂φ∂2 2

(B.)

jZ F x

Z Fxe

e

e

ee= − +⎛

⎝⎜⎞⎠⎟

κ ∂µ∂

∂φ∂2 2

Electrical Neutrality (C.)Z j Z jc c e e+ = 0

(A.)

(B.)

( )∂φ∂ κ κ

κ ∂µ∂

κ ∂µ∂x F Z x Z xc e

c

c

c e

e

e= −+

+⎡

⎣⎢

⎤

⎦⎥

1

The cation flux now becomes:

( )j

Z F xZZ xc

c e

c c e

c c

e

e= −+

−⎡

⎣⎢

⎤

⎦⎥

κ κκ κ

∂µ∂

∂µ∂2 2

Considering ionic equilibrium and integrating across the oxide

jZ F x

dcc

c e

c eM

M

M= −

+′

″

∫1

2 2

κ κκ κ

µµ

µ

The relation between jC and scale growth rate is

j C dxdtc M=

CM mol cm-3

Comparison with the parabolic rate equation

dxdt

kx

=′

where k’ is the parabolic rate constant in cm2s-1.

′ =+″

′

∫kZ F C

dc M

c e

c eM

M

M12 2

κ κκ κ

µµ

µ

( )∂φ∂ κ κ

κ ∂µ∂

κ ∂µ∂x F Z x Z xc e

c

c

c e

e

e= −+

+⎡

⎣⎢

⎤

⎦⎥

1

The cation flux now becomes:

( )j

Z F xZZ xc

c e

c c e

c c

e

e= −+

−⎡

⎣⎢

⎤

⎦⎥

κ κκ κ

∂µ∂

∂µ∂2 2

Considering ionic equilibrium and integrating across the oxide

jZ F x

dcc

c e

c eM

M

M= −

+′

″

∫1

2 2

κ κκ κ

µµ

µ

The relation between jC and scale growth rate is

j C dxdtc M=

CM mol cm-3

Comparison with the parabolic rate equation

dxdt

kx

=′

where k’ is the parabolic rate constant in cm2s-1.

′ =+″

′

∫kZ F C

dc M

c e

c eM

M

M12 2

κ κκ κ

µµ

µ

( )∂φ∂ κ κ

κ ∂µ∂

κ ∂µ∂x F Z x Z xc e

c

c

c e

e

e= −+

+⎡

⎣⎢

⎤

⎦⎥

1

The cation flux now becomes:

( )j

Z F xZZ xc

c e

c c e

c c

e

e= −+

−⎡

⎣⎢

⎤

⎦⎥

κ κκ κ

∂µ∂

∂µ∂2 2

Considering ionic equilibrium and integrating across the oxide

jZ F x

dcc

c e

c eM

M

M= −

+′

″

∫1

2 2

κ κκ κ

µµ

µ

The relation between jC and scale growth rate is

j C dxdtc M=

CM mol cm-3

Comparison with the parabolic rate equation

dxdt

kx

=′

where k’ is the parabolic rate constant in cm2s-1.

′ =+″

′

∫kZ F C

dc M

c e

c eM

M

M12 2

κ κκ κ

µµ

µ

( )∂φ∂ κ κ

κ ∂µ∂

κ ∂µ∂x F Z x Z xc e

c

c

c e

e

e= −+

+⎡

⎣⎢

⎤

⎦⎥

1

The cation flux now becomes:

( )j

Z F xZZ xc

c e

c c e

c c

e

e= −+

−⎡

⎣⎢

⎤

⎦⎥

κ κκ κ

∂µ∂

∂µ∂2 2

Considering ionic equilibrium and integrating across the oxide

jZ F x

dcc

c e

c eM

M

M= −

+′

″

∫1

2 2

κ κκ κ

µµ

µ

The relation between jC and scale growth rate is

j C dxdtc M=

dxdt

kx

=′

where k’ is the parabolic rate constant in cm2s-1.

′ =+″

′

∫kZ F C

dc M

c e

c eM

M

M12 2

κ κκ κ

µµ

µ

Oxidation in the Presence of an Impressed CurrentEquations (A) and (B) are unchanged. Equation (C) is written:

iFjZFjZ eecc =+

( ) ( )ec

e

e

ec

c

c

ec

ixZxZFx κκ∂

∂µκ∂∂µκ

κκ∂∂φ

+−⎥

⎦

⎤⎢⎣

⎡++

+−=

1

κκ

∂∂µ

∂∂µ

κκκ

FZi

xZZ

xFZj

c

ce

e

cc

c

ecc +⎥

⎦

⎤⎢⎣

⎡−−= 22

xFZi M

c

eStop

µκ ∆=

Note: If the external oxygen pressure is 1 atm, oMOM G∆=∆µ

⎥⎥⎦

⎤

⎢⎢⎣

⎡−′=′

StopOC i

ikk 1

For chromia at 900oC: κe = 10-2 (ohm cm)-1 Park & Natesan, 1990∆Go = -820,000 J/mole

For a 1 µm thick oxide: iStop = -140 A/cm2

For a typical Fuel Cell current density of 1 A/cm2,OCkk ′=′

(Note: if Park & Natesan’s 2-probe data are correct there could be asubstantial effect of current on chromia growth.)

Parabolic Rate Constants 900C dry air

y = 1.23E-11x

y = 2.61E-11x

0

2 E -0 6

4 E -0 6

6 E -0 6

8 E -0 6

1 E -0 5

1 E -0 5

0 5 0 0 0 0 1 0 0 0 0 0 1 5 0 0 0 0 2 0 0 0 0 0 2 5 0 0 0 0 3 0 0 0 0 0 3 5 0 0 0 0 4 0 0 0 0 0 4 5 0 0 0 0 5 0 0 0 0 0seconds

g2/cm4

Nickel

Sr-doped Nickel

Parabolic Rate ConstantNickel 2.61x10-11 g2/cm4sSr-doped Nickel 2.23x10-11 g2/cm4s

Surface Micrographs

Nickel 900C Sr-doped Nickel 900C

Planar SOFC Configuration

Repeat Components

⎟⎟⎠

⎞⎜⎜⎝

⎛−= C

O

AO

pp

FRTV

2

2ln40

voltsV 7.0≈

2/1 cmAmpi ≈Electrolyte – YSZ Cathode – La/Sr-Manganite (LSM) Anode – Ni/YSZ Interconnect – Metallic

Oxidized Ni-50 Cr AlloyCr-Rich Second Phase has Dissolved in the Cr-Depleted Zone

Cr O32

Cr-depleted zone

Alloy

H2-3%H2OAir

Air

AirAir

H2-3%H2O

Thermocouple

Exhaust

Materials:

• 10 mil thick Ag tube

Experimental Arrangement

Materials:

• 10 mil thick Ag tube

Variables:

• Temperatures, 700, 600, 500oC;

• Simultaneous exposures to H2+3%H2O and air;

Variables:

• Temperatures, 700, 600, 500oC;

• Simultaneous exposures to H2+3%H2O and air;Courtesy of Dr. Prabhakar

Singh, PNNL

Diagram of Apparatus

Dry Air Exposures – 700oCTime vs. Mass Change / Area (700oC, dry air)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0 200 400 600 800 1000 1200 1400 1600 1800 2000Exposure (Cycles)

Mas

s C

hang

e / A

rea

(mg/

cm2 )

Crofer - 1

Crofer - 2

E-brite - 1

E-brite - 2

AL453 - 1

AL453 - 2

ZMG232 - 1

ZMG232 - 2

Simulated Anode Gas (Ar-4%H2, H2O) Exposures – 700oC

Time vs. Mass Change / Area for Crofer, E-brite, AL453, & Ni (700oC, Ar/H2/H20)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Exposure (cycles)

Mas

s C

hang

e / A

rea

(mg/

cm2 )

Crofer - 1Crofer - 2E-brite - 1E-brite - 2E-brite - 3AL453 - 1AL453 - 2Ni

Microstructural and Phase IdentificationCrofer 700oC

Cr2O3MnCr2O4

Dry Air2000 cycles

Internal Al2O3Wet Air1017 cycles

Internal Al2O3

SAG2000 cycles

Internal Al2O3

Cr2O3

Cr2O3

MnCr2O4

Si rich oxide Si rich oxide

MnCr2O4

Si rich oxide

Degradation Mechanism

H2(g) = 2[H]Ag

[H]Ag

O2(g)= 2[O]Ag [O]Ag

[O]Ag+[H]A==H2O(g)

H2(g)Air

Reaction Steps1. (H2)g = 2(H)Ag Ag/Fuel interface

2. (O2) g = 2(O)Ag Ag/ Air Interface

3. 2(H) Ag + (O)Ag = (H2O) g Bulk Ag

Bulk Degradation Related to :1.Dissociation and dissolution of H and O in the bulk metal2. Interaction between dissolved H & O to form High pressure H2O gas3. Nucleation and growth of steam bubbles/voids at GB/defects

Courtesy of Dr. Prabhakar Singh, PNNL

Pressure of CrO3

-18

-16

-14

-12

-10

-8

-6

0.7 0.75 0.8 0.85 0.9 0.95 1 1.051/T*103 (K-1)

log

p CrO

3 (at

m)

log p(Cr) log p(Mn)(A) log p(La) log p(Mn)(B)

Cr2O3

LaCrO3

MnCr2O4

Partial pressures of CrO3 in Equilibrium with

Cr2O3, MnO-saturated MnCr2O4, and LaCrO3

Note: similar reductions would be achieved in the pressure of CrO2(OH)2

Crofer oxidized in contact with LaSrMnO4(cathode) for 88hrs at 900oC in air + 0.1atm H2O

Crofer (side in contact with cathode)

MnCr2O4with ~1.5% Sr and ~2.6% La

Cr2O3 with ~2% Sr, ~4% La, and ~4.7% Mn

~74.9% Fe ~20% Cr ~2.2% La ~2% Mn ~0.9% Sr

Crofer (side opposite cathode)

MnCr2O4

Cr2O3

After exposure, the cathode contained ~0.9% Cr and ~1.8% Al