Modeling the Substoichiometric Behavior of 238PuO2 and 241AmO2 in the

Low Oxygen Potential Envrionments Found in Radioisotope Power Systems

C. E. Whiting, E. J. Watkinson, C. D. Barklay, D. P. Kramer, H. R. Williams, and R. M. Ambrosi

University of Dayton – Research Institute

(937) 229-2570 Chris.Whiting@udri.udayton.edu

NETS 2015 Conference Albuquerque, NM

2/24/2015

University of Dayton Research Institute Shaping the technology of tomorrow

mailto:Chris.Whiting@udri.udayton.edu

Why is PuO2 Important?

238Pu – 0.54 WT per g

Convert WT to WE using thermoelectric technology

Ceramic PuO2 used as fuel

Is PuO2 Really PuO2?

PuO2…?

Is PuO2 Really PuO2?

PuO2…?

C + O2 CO2

and

2 C + O2 2 CO

CO2 + C 2 CO

𝐊 = 𝐏𝐂𝐂𝟐

𝐏𝐂𝐂𝟐

CO can be a strong reducing agent

Is PuO2 Really PuO2?

PuO2…?

Carbon is found in several places…but where is the O2

coming from?

C + O2 CO2

and

2 C + O2 2 CO

Is PuO2 Really PuO2?

PuO2-x

Carbon is found in several places…but where is the O2

coming from?

C + O2 CO2

and

2 C + O2 2 CO

PuO2 Can Be Reduced

Relationship between “x”, , and T is very well studied

+

𝐏𝐂𝟐

PuO2-x O2 Partial Pressure

PuO2 Can Be Reduced

Relationship between “x”, , and T is very well studied

+

𝐏𝐂𝟐

PuO2-x Directly relates to oxidation potential

PuO2 Can Be Reduced

+

Since we know:

CO2 + C 2 CO

𝐊 = 𝐏𝐂𝐂𝟐

𝐏𝐂𝐂𝟐

can be found

2 CO + O2 2 CO2

𝐊 = 𝐏𝐂𝐂𝟐𝟐

𝐏𝐂𝐂𝟐 ∗ 𝐏𝐂𝟐

𝐏𝐂𝟐

Relationship Between x, T, and PO2

Once 𝐏𝐂𝟐 is known, x can be determined using the semi-empirical method described by Lindemer

RT lnPO2 = −821000 + 168.47 ∗ T − 3 RT ln1.5 ∗ x ∗ 1 − x2

13

1 − 2x43

−3x2 − 12x + 3

1 − x22

∗ (63470 − 49.36 ∗ T)

Some terms based off of the thermodynamics of the reduction of PuO2 to Pu2O3, so limited to x values between 0 and 0.5

Other terms are empirically fit to hundreds of data points in the literature

Very good empirical fit – even in miscibility gap

T.M. Besmann and T.B. Lindemer J. Nucl. Mater., 1985, 130, 489-504

The Catch

CO2

O2

CO

As the reduction occurs, PCO and 𝐏𝐂𝐂𝟐 are changing Which means 𝐏𝐂𝟐 is also changing

Iterative Process Was Developed

T (K) = 1273 Initial PO2 (atm) = 1.00E-02

mol PuO2 / Liters (n/V) = 1.E+03 1st Iteration "x" = 0.001

PCO from initial O2 (atm) = 2.00E-02 Stoichiometry = 1.999 PCO2 from initial O2 (atm) = 2.97E-06 Total P (atm) = 80.59 PO2 after rxn with C (atm) = 1.60E-22 New PO2 (atm) = 5.223E+01

Quadratic a = 1 C + CO2 --> 2 CO Quadratic b = 67

dG (J/mol) = -51904 Quadratic c = -7.04E+03 K eq = 134.81 PCO after rxn with C (atm) = 5.673E+01

PCO2 after rxn with C (atm) = 2.387E+01 2 CO + O2 --> 2 CO2 PO2 after rxn with C (atm) = 1.291E-15

dG (J/mol) = -344546 K eq = 1.3721E+14

K obtained from ∆G

∆G calculated from JANAF tables

Need to Know:

Temperature

Initial pressure of O2

n/V Ratio

With 𝐏𝐂𝟐, x can be determined

Initial O2 reacts

With new x, new 𝐏𝐂𝟐 can be determined

x converges at equilibrium value

Assumptions

Stoichiometry can be theoretically determined under any set of starting conditions, assuming:

Maximum reduction is at x = 0.5

Closed system

All O2 reacts to form CO and CO2

Excess graphite

Lindemer’s relationships can be extrapolated past the data used to create the experimental fits

- x fit between: 0 < x < 0.37 - T fit between: 680 oC < T < 1780 oC

CeO2 and AmO2 Calculations

Relationships derived using Lindemer’s method exist for CeO2 and AmO2

CeO2 - Based on over a thousand data points from 10 studies - Fit between 0 < x < 0.33 and 540 oC < T < 1550 oC - Help determine if CeO2 is a good surrogate

AmO2

- Only 1 study with ~100 data points (need more data) - Narrow fit range: 0 < x < 0.15 and 780 oC < T < 1390 oC - Evaluate behavior of AmO2 in the presence of carbon

CeO2 and AmO2 Calculations

CeO2 Equation

RT lnPO2 = −988700 + 363.77 ∗ T + 4 RT lnN2 − 5 RT lnN1+ −70210 + 32.05 ∗ T ∗ 4N1 ∗ 1 − N2 − 5N2 ∗ 1 − N1 + −63765 + 32.05 ∗ T ∗ {4N1 ∗ −2N2 + N1 + 2N2 ∗ N2 − N1 − 5N2 ∗ 2N1 − N2 − 2N1 ∗ N1 − N2 }

Where: N1 = 2 * x and N2 = 1 – N1

AmO2 Equation

RT lnPO2 = −165371 − 332 ∗ T + 344.0 ∗ T − 4 RT ln2x

1 − 2x

− 4 ∗ 85171 − 59.3 ∗ T ∗ (1 − 4x)

Variables

Temperature - 400 to 2000 oC

Initial Quantity of O2 - Air (0.21 atm) - 1% O2 (0.01 atm) - Ultra-High Purity inert gas (1x10-5 atm) - High Vacuum pulled from air (1x10-9 atm) - High Vacuum pulled from UHP (1x10-13 atm)

n/V ratio – ratio of mol of fuel to open volume - 1x10-5 (equal to ~270 g of 238PuO2 in 100 m3) - 1x105 (equal to ~270 g of 238PuO2 in 0.05 mL)

Realistic RTG

Realistic RTG:

n/V between 0.1 to 10 - For 5 kg of 238PuO2 - 0.1 = 1.85 L open volume - 10 = 185 L open volume

Atmosphere usually UHP inert or better

Temperature varies considerably

-3.0

-2.0

-1.0

0.0

0.00001 0.001 0.1 10 1000 100000

log

x

n/V

Air1%UHPHVHV UHP

1500 oC

Effect of Initial Atmosphere on x

-3.0

-2.0

-1.0

0.0

0.00001 0.001 0.1 10 1000 100000

log

x

n/V

Air1%UHPHVHV UHP

-3.0

-2.0

-1.0

0.0

0.00001 0.001 0.1 10 1000 100000

log

x

n/V

1200 oC 900 oC

-3.0

-2.0

-1.0

0.0

0.00001 0.001 0.1 10 1000 100000

log

x

n/V

1800 oC

-3.0

-2.0

-1.0

0.0

0.00001 0.001 0.1 10 1000 100000

log

x

n/V

Air1%UHPHVHV UHP

1500 oC

Effect of Initial Atmosphere on x

Initial O2 results converge:

When n/V > 0.1

As T increases

Initial O2 < 1x10-5 atm Initial O2 appears to have minimal effect

Only UHP considered for future calculations

-3.0

-2.0

-1.0

0.0

0.00001 0.001 0.1 10 1000 100000

log

x

n/V

Air1%UHPHVHV UHP

900 oC

Effect of n/V on x for PuO2

Order of magnitude changes in volume can impact x

General Rule: 10x change in n/V ≈ 100 oC

0

0.1

0.2

0.3

0.4

0.5

0.00001 0.001 0.1 10 1000 100000

x

n/V

70080090010001100120013001400150016001700180019002000

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.00001 0.001 0.1 10 1000 100000

log

x

n/V

Effect of n/V on x for PuO2

Order of magnitude changes in volume can impact x

General Rule: 10x change in n/V ≈ 100 oC

0

0.1

0.2

0.3

0.4

0.5

0.00001 0.001 0.1 10 1000 100000

x

n/V

70080090010001100120013001400150016001700180019002000

Experimental Fit

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.00001 0.001 0.1 10 1000 100000

log

x

n/V

Effect of T on x for PuO2

x < 0.5 under all studied conditions As n/V increases ∆x decreases ∆x appears to be large for 0.05 < x < 0.40

0.0

0.1

0.2

0.3

0.4

0.5

0 500 1000 1500 2000

x

Temperature (oC)

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

10000

100000 -3.0

-2.0

-1.0

0.0

0.0003 0.0006 0.0009 0.0012

log

x

1/T (K-1)

Effect of T on x for PuO2

0.0

0.1

0.2

0.3

0.4

0.5

0 500 1000 1500 2000

x

Temperature (oC)

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

10000

100000

Experimental Fit

-3.0

-2.0

-1.0

0.0

0.0003 0.0006 0.0009 0.0012

log

x

1/T (K-1)

x < 0.5 under all studied conditions As n/V increases ∆x decreases ∆x appears to be large for 0.05 < x < 0.40

CeO2 as a Surrogate

CeO2 starts reduction at lower T

∆x for PuO2 is larger at low T and smaller at high T

0

0.1

0.2

0.3

0.4

0.5

0.00001 0.001 0.1 10 1000 100000

x

n/V

PuO2

0

0.1

0.2

0.3

0.4

0.5

0.00001 0.001 0.1 10 1000 100000

x

n/V

50060070080090010001100120013001400150016001700180019002000

CeO2

CeO2 as a Surrogate

0.0

0.1

0.2

0.3

0.4

0.5

0 500 1000 1500 2000

x

Temperature (oC)

PuO2

0

0.1

0.2

0.3

0.4

0.5

0 500 1000 1500 2000

x

Temperature (oC)

0.000010.00010.0010.010.1110100100010000100000

CeO2

CeO2 appears to be an ok as a first-order surrogate for PuO2, but very limited predictive power

AmO2 Calculations

0

0.1

0.2

0.3

0.4

0.5

0 500 1000 1500 2000

x

Temperature (oC)

1000001000010001001010.10.010.0010.00010.00001

Why does AmO2 become MORE stable at higher temps?

Flaws in the empirical fit

Experimental Fit

AmO2 Calculations

0

0.1

0.2

0.3

0.4

0.5

0 500 1000 1500 2000

x

Temperature (oC)

1000001000010001001010.10.010.0010.00010.00001

𝐏𝐂𝟐 values predicted converge! when x ~ 0.371

This result is completely irrational

Equation doesn’t fit as well at larger x

AmO2 Calculations

Even though numerical results from the AmO2 equations are not reliable, they still tell an important story

0

0.1

0.2

0.3

0.4

0.5

0 500 1000 1500 2000

x

Temperature (oC)

1000001000010001001010.10.010.0010.00010.00001

AmO2 is very easy to reduce

CO/CO2 from graphite generates huge reduction

potential

Massive reduction expected

Perhaps complete reduction to Am2O3?

AmO2 Calculations

All three models fit the empirical data well in this range

0

0.1

0.2

0.3

0.4

0.5

0 500 1000 1500 2000

x

Temperature (oC)

1000001000010001001010.10.010.0010.00010.00001

@ 900 oC and x = 0.10

PuO2 has 𝐏𝐂𝟐 = 7.0x10-27

CeO2 has 𝐏𝐂𝟐 = 1.4x10-18

AmO2 has 𝐏𝐂𝟐 = 1.0x10-6

PuO2 < CeO2

AmO2 Calculations

0

0.1

0.2

0.3

0.4

0.5

0 500 1000 1500 2000

x

Temperature (oC)

1000001000010001001010.10.010.0010.00010.00001

@ 900 oC and x = 0.10

PuO2 has 𝐏𝐂𝟐 = -587 kJ/mol

CeO2 has 𝐏𝐂𝟐 = -401 kJ/mol

AmO2 has 𝐏𝐂𝟐 = -135 kJ/mol

PuO2 < CeO2

Conclusions

Graphite creates a significant reduction potential that can affect the stoichiometry of PuO2, CeO2, and AmO2 - Contact with graphite is not required - In order of reduction severity: PuO2 < CeO2

Conclusions

Initial O2 pressures to not impact reaction much - Reduction is driven by the O2 released from the fuel - In a realistic RTG initial O2 pressure is irrelevant

Small changes in volume will not impact reduction - Factor of 10 change in n/V ~ 100 o change in temperature

Need more data on the AmO2-x, 𝐏𝐂𝟐, and T relationship - Current models do not behave well at large x values

Graphite will be consumed in this reduction reaction

Acknowledgements

DOE Contract #: DE-NE0000422

Prof. Howie Knachel

Students Bethany Cremeans (Barklay) and Emily Kaufman

CeO2 as a Surrogate for PuO2

Same crystallographic space grouping - 𝑭𝑭𝟑�𝑭; #𝟐𝟐𝟐

Similar solid state chemistry

Similar oxygen behavior

PuO2 Can Be Reduced

Pu(IV) is the preferred state

Reducing conditions create Pu(III) and O2

O2 reacts with C to form CO/CO2

+

Known Limitations

Use of Lindemer’s relationships is limited under certain circumstances:

When x falls in the miscibility gap iterative method fails and a trial-and-error method was required

At very small x values (i.e. < 0.05), Lindemer notes that his fits can have a high degree of error

Solid Condensate

Modeling the Substoichiometric Behavior of 238PuO2 and 241AmO2 in the Low Oxygen Potential Envrionments Found in Radioisotope Power SystemsWhy is PuO2 Important?Is PuO2 Really PuO2?Is PuO2 Really PuO2?Is PuO2 Really PuO2?Is PuO2 Really PuO2?PuO2 Can Be ReducedPuO2 Can Be ReducedPuO2 Can Be ReducedRelationship Between x, T, and PO2The CatchIterative Process Was DevelopedAssumptionsCeO2 and AmO2 CalculationsCeO2 and AmO2 CalculationsVariablesRealistic RTGEffect of Initial Atmosphere on xEffect of Initial Atmosphere on xEffect of n/V on x for PuO2Effect of n/V on x for PuO2Effect of T on x for PuO2Effect of T on x for PuO2CeO2 as a SurrogateCeO2 as a SurrogateAmO2 CalculationsAmO2 CalculationsAmO2 CalculationsAmO2 CalculationsAmO2 CalculationsConclusionsConclusionsAcknowledgementsCeO2 as a Surrogate for PuO2PuO2 Can Be ReducedKnown LimitationsSolid Condensate