Distribution Category:Light Water Reactor Technology(UC-78)

ANL-82-42

ARGONNE NATIONAL LABORATORY9700 South Cass Avenue

Argonne, Illinois 60439

LIGHT-WATER-REACTOR FISSION-PRODUCT DATA ASSESSMENT

by

P. E. Blackburn and C. E. Johnson

Chemical Technology Division

DISCLAIMER

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September 1982

Prepared for Sandia National LaboratoriesAlbuquerque, NM, under the purchase order 61-6792 A#3

AML--82-42

DE83 005940

TABLE OF CONTENTS

ABSTRACT. . . . . . . . . . . . . . . . . . . . . . . . . .

I. INTRODUCTION . . . . . . . . . . . . . .

II. FISSION PRODUCT AND ACTINIDE OXIDES...... . . .

III. FISSION PRODUCT AND ACTINIDE BROMIDES AND IODIDES

IV. FISSION PRODUCT AND STRUCTURAL MATERIAL TELLURIDES

V. FISSION PRODUCT HYDROXIDES AND HYDRIDES. . . . . .

VI. MAJOR UNCERTAINTIES IN THERMODYNAMIC PROPERTIES .

REFERENCES. . ......... . . . . . . . . . . . . . .

APPENDICES

A. Thermodynamic Data for Fission Product and ActinideCompounds . . . . . .. . . . . . . . . . . . . . .

B. Oxygen Potential Model for U02 Fuel . . . . . . . .

iii

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Page

1

1

2

7

7

11

11

15

17

31

LIST OF TABLES

No. Title Page

1. Elemental Fission Yield and Nuclide Radioactivity . . . . . . . . 3

2. Equilibrium Oxygen Potential for Fission Products andTheir Oxides . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3. Free Energy of Formation of Halide Gases from FissionProducts and Gaseous Diatomic Halogens at 1000 K . . . . . . . . . 8

4. Free Energy of Formation of fission-Product-Halide Solidsand Liquids at 1000 K . . . . . . . . . . . . . . . . . . . . . . 9

5. Free Energy of Formation of Fission Product and Structural-Element Tellurides from Fission Products, StructuralElements and Diatomic Tellurium Gas at 1500 K . . . . . . . . . . 10

6. Free Energy of Formation of Fission-Product Gaseous Hydridesand Hydroxides from Hydrogen and Fission Products in TheirStandard States at1500 K . . . . . . . . . . . . . . . . . . . . 12

7. Fission-Product Compounds with Thermodynamic Uncertaintiesof 5 kcal (21 Kj) or Greater . . . . . . . . . . . . . . . . . . . 13

A-1. Free Energy of Formation of Fission-Product and ActinideOxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

A-2. Free Energy Equ tions for Fission-Pioduct Iodides andBromides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

A-3. Free Energy of Formation of Fission-Product and Reactor-Component Tellurides . . . . . . . . . . . . . . . . . . . . . . . 25

A-4. Free Energy of Formation of Fission-Product and Reactor-Component Hydroxides and Hydrides . . . . . . . . . . . . . . . . 29

iv

LIGHT WATER REACTOR FISSIONPRODUCT DATA ASSESSMENT

by

P. E. Blackburn and C. E. Johnson

ABSTRACT

This assessment seeks (1) to determine the most probablechemical compounds formed between fission products and actinides inurania fuels under normal and accident conditions and (2) to identifygaps in our knowledge of these fission-product compounds. Theultimate goal of this effort is to develop predictive capabilityabout the behavior of fission products under normal and accidentconditions. The relevant thermochemical dcta have been organized bycompound type, the chemical stability of resultant compounds deter-mined, and data uncertainty evaluated. The assessment focused onfission-product and actinide oxides, halides, tellurides, andhydroxides. Free energy equations are given for those compounds forwhich data were available. The data base for tellurium and its com-pounds must be greatly expanded if we are to meet our goal of pre-dictive capability.

I. INTRODUCTION

The principal potential risk to the public from nuclear power plants de-rives from the highly radioactive atoms (fIssion products) generated as energyis produced in the nuclear fuel. In normal operations these fission productsreside almost entirely within the nuclear fuel where they are created. How-ever, under unusual conditions some of these fission products may be releasedfrom the fuel and find their way into the environment. If the release offission products is large, they may be dispersed in such a way as to presenta public health risk. The fractional inventory of a specific fission productreleased to the environment is known as the source-term for that species.

Critical to any accident analysis is the availability of accuratesource-term information for the fission product nuclides. In the presentsituation, greater attention must be given to the influence of core chemistryand its control over fission product release. Once the chemistry of the fis-sion products is known, their chemical behavior can be predicted during lightwater reactor (LWR) accidents. To develop predictive capability descriptiveof fission product behavior under normal and accident conditions, we areundertaking the following activities:

(1) Review of available thermophysical property data of fissionproducts relevant to expected core chemistry in LWR accidents.

(2) Use of these data to assess the stability of dominant chemicalforms of principal fission products in LWR f.asl as a function of keyfuel parameters (such as temperature, buraup, etc.).

1

2

(3) Identification of major areas of data uncertainty with regard tocharacterizing fission product behavior in fuel under mild and strongtransient conditions.

This report gives the present status of our analysis of thermodynamicdata collected for fission product oxides, iodides, bromides, tellurides andhydroxides. As many as 35 element& were considered, about 20 of which haveradioactive isotopes. The large number of fission products means that com-pounds and gases, as well as elements, must be considered. From the 35elements, thirty were chosen for study on the basis of their relative abun-dance, radioactive intensity, and potential volatility. Table 1 lists thefission products included in our assessment in order of increasing atomicnumber; also given are their ieldsl- 4 after a decay period of one year interms of atoms per atom of 23U fissioned. In addition, Table 1 lists theactivity5 of the radionuclide fission products and actinides with one or moreradioactive isotopes. Some of the fission products are low in abundance buthighly radioactive (e- -, iodine is second only to neptunium in activity, butis only 0.55% of the total fission product).

Under normal operating conditions, the rare earths Sr, Ba, Y, Zr, and Nbare assumed to exist in the fuel in their fully oxidized state. In addition,the molybdates and uranates of Cs, Rb, Sr, and Ba form to the extent allowedby temperature and oxygen potential (oxygen is released when 23 5U fissions).The oxygen taken up in the formation of these latter compounds, together withthat consumed forming the more stable oxides, is sufficient to reduce anoxygen-rich urania fuel to the stoichiometric oxygen level as burnup occurs.Although the rare earths and alkaline earths form relatively stable halides,it is their oxides that are more stable, leaving Csl, CsBr, RbI, and RbBr asthe principal fission product halides. The thermodynamic data are essentialin defining the most probable species available for release. However, suchdata are not sufficient for the release calculation, as the mechanism and therate or release must al be known.

II. FISSION PRODUCT AND ACTINIDE OXIDES

Tabulated thermodynamic data such as those in JANAF,6 Barin et al.,7 '8

Kubaschewski and Alcock,9 and oihers 10-2 4 were used to derive linear equationsfor the free energy of formation for each fission-product and actinideLipeci.s. These are listed in order of atomic number of the fission productand actinide in Table A-1 of Appendix A. The oxygen potential in the fuelmust first be calculated as it determines whether a given fission product willbe oxidized. Thermodynamic models used for the oxygen potential calculationare described in Appendix B for U02, for U-Pu-O, and for U-Pu-0-fission pro-duct. The free energy of formation wis used to calculate the oxygen potential(AG0 2 - RT In P0 2) required for oxidation of the fission products.

Table 2 lists the oxygen potentials required for formation of fission-product and actinide oxides from elements and lower oxides. The compounds aregiven in decreasing order of stability. These values were calculated from theequations for the free energy of formation found in Appendix A. The oxygenpotential is listed for each reaction at 1500 K. The third column lists thevalue of x in UO2+x, corresponding to the oxygen concentration for the urania

3

Table 1. Element of Fission Yield and Nuclide Radioactivity

Yield,bFission Atomic atoms/atom of Radioactivity, MCi inProduct Number 235U Fission Reactor Core at 3560 MWt

Se

Br

Kr

Rb

Sr

Y

Zr

Nb

Mo

Tc

Ru

Rh

Pd

Ag

Cd

In

Sb

Te

I

Xe

Cs

Ba

La

Ce

Pr

Nd

Pm

Sm

Np

Pu

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

51

52

53

54

55

56

57

5859

60

61

62

93

94

0.0042

0.001766

0.0356

0.0358

0.0926

0.05

0.3056

0.0098

0.2348

0.0608

0.1112

0.0278

0.0132

a

a

a

0.000388

0.0252

0.011

0.2342

0.1882

0.0682

0.0604

0.1586

0.0584

0.1624

0.0176

0.02660.00105c

01.00

150.6

0.028223

133.2

322

161172

151

222

53

41.6

189.2768

220

16.4

172

172392

140

65

18003.807

aThese elements are used in control rods.

bheral Fission yield af ter a decay period of one year.

cFor fuel with 32 2 3 5 U-972 2 3 8U.

4

Table 2.

Oxidation Reaction

2'r + 3/2 02 = Y2 03

2 Pr + 3/2 02 - Pr203

2Sm + 3/2 02 = Sm203

2Ce + 3/2 02 = Ce203

2Nd + 3/2 02 = Nd 2 0 3

2La + 3/2 02 - La203

Sr + 1/2 02 = SrO

Ba + Zr + 3/2 02 BaZrO3

2Pu + 3/2 02 = Pu203U + 02 - UO2

Zr + 02 = ZrO2

Np + 02 = Np02

Ba + 1/2 02 = BaO

1/2 Pu2c 3 + 1/4 02 - Pui02

Nb + 1/2 02 - NbO

0

NbO + 1/2 02 - Nb0 2

2Cs(g) + Mo + 202 - Cs2Mo04a

2Rb(g) + Mo + 202 - Rb2MoO4a

117

107

106

128 ( 36)

(490)

(448)

(444)

100 (418)

BaO + Mo + 3/2 02 - BaMo04 98 (410)

(Cont'd)

Oxygen inF.P. Oxides/U Fissioned

Equilibrium Oxygen Potential forFission Products and Their Oxides

-AG(1500 K), Fuel -AG02,kcal/mol 02 kcal/mol(kJ/mol 02) x in UO2+x (kJ/mol)

235 (983)

223 (933)

222 (929)

222 (929)

220 (920)

218 (912)

212 (887)

210 (879)

202 (848)

197 (824)

195 (816)

185 (774)

183 (766)

136 (570)

136 (569)

5

Table 2. (Cont'd)

Oxidation Reaction

2Rb(g) + UO2 + 02 - Rb2UO4a

BaO + UG2 + 1/2 02 - BaU04

U02 + Cs(g) + 02 - CsUO4a

SrO + Mo + 3/2 02 - SrMo04

2Nb02 + 1/2 02 - Nb205

-AG(1500 K),

kcal/mol 02(kJ/mol 02)

97 (406)

95 (398)

95 (397)

93 (389)

93 (388)

x in UO2+x

Fuel -AG 0 2 ,

kcal/mol(kJ/mol)

Oxygen in

F.P. Oxides/U Fissioned

86 (360)

Mo + 02 = Mo02 78 (326)

72 (301)

SrO + U02 + 1/2 02 - SrU04 69 (288)

58 (243)

2Sb + 3/2 02 - Sb203

Tc + 02 - Tc02

Pd + 1/2 02 - PdO

1/2 Ce203 + 1/4 02 - CeO2

2Rh + 3/2 02 - Rh203

MoO2 + 1/2 02 - Mo03

Ru + 02 - RuO2

2Cs(g) + 1/2 02 - Cs20

Te + 02 - Te02

2Rb(g) + 1/2 02 - Rb20

Air (1 atm)

aCs and Rb pressure - 1 atm.

bAll 12 present as CsI and/or

5

4

3

3

2

2

1

1

1

1

2 (218)

2 (176)

5 (146)

3 (138)

6 (109)

5 (105)

4 (59)

3 (54)

2 (50)

0 (42)

5 (21)

RbI and all 1r2 present as CsBr and/or Rbdr.

10-2

10-3

6

oxygen potential in parenthesis. The urania oxygen potentials calculated withthe model are placed in order with those for the fission products and acti-nides. Note that the oxygen potentials of the fission-product and actinideoxides are for two phase equilibria (e.g., Y-Y20 3 and U-U02), whereas thosefor urania are for single-phase equilibria (e.g., U02 .0 00 0 1).

The number of fissio,.i product atoms remaining after a one year decayfor each 235U atom fissioned are listed in Table 1. From these values, thenumber of oxygen atoms reacted with the fission products were calculated andare presented in the last column of Table 2. For example, if the urania isexactly stoichiometric (i.e., 0/U is exactly 2), the oxygen potential calcula-ted from the model is -128 kcal/mol. At this level, all the rare earths, Y,Sr, Ba, Zr, and Nb are oxidized (Nb is oxidized to NbO), accounting for 1.586of the oxygen atoms released for each 235U fissioned. In the calculation,all of the cesium and rubidium (lass chat to consume all iodine as CsI and/orRbI and all bromine as CsBr and/or RbBr) is used to form the molybdates.Since the total oxygen available is exactly 2, some cesium and/or rubidiumwill be unreacted [i.e., 0.0434 (Cs + Rb)]. At x = 10-5 or U02.00 0 01 theoxygen potential is -100 kcal/mol; moreover, at this oxygen potential NbO isoxidized to Nb02 , and Cs and Rb react with Mo and 02 to form Cs2Mo04 andRb2MoO4 , respectively. These additional reactions bring the potential

number of oxygen atoms reacted with fission product to 2.0217 per 2"5Ufission.

The oxygen potential calculations are based on cesium and rubidium pres-sures of one atmosphere. However, the pressure of both cesium and rubidiummay be less than one atmosphere since they may also react with tellurium,selenium, and antimony and possibly, other fission products that are notcompletely oxidized (i.e., Mo, Tc, Ru, Rh, and Pd). If the cesium andrubidium pressures are significantly less than one atmosphere (i.e., < 0.01atm), the formation of BaMo04 and SrMo04 will consume the required oxygenat more positive oxygen potentials (-98 and -93 kcal, respectively). Theunreacted cesium and rubidium may then combine with selenium, tellurium, andpossibly antimony.

The chemistry of the fission products from urania fuel (where fissionoccurs solely in '3 5U) contrasts with that from fast breeder fuel (wherefission occurs principally in 2 39Pu) primarily because the most-stable oxideformers, i.e., rare earths, alkaline earths, tritium and zirconium, are moreabundant in the fission product spectrum of 235 U. As a result, the oxygenreleased from 2 3 5U is consumed at an oxen potential of about -100 kcal at1500 K, whereas the oxygen released by ePu is not consumed until the oxygenpotential is greater than -70 kcal. Thus during burnup, the stoichiometricmixed oxide fuel (2 38U, 2j 9Pu)02 releases oxygen; consequently, the rare earths,Y, Zr, Nb and all of the Cs, Rb (except that which forms CsI and RbI), Sr, andBa will oxidize and react to form uranates and molybdates, the remainingmolydenum oxidizes to Mo02, and the fuel oxidizes to (U,Pu)02.01. Theelements Sb Tc, Pd, Rh, and Ru remain unoxidized. Burnup of stoichiometricLWR fuel (238U, 235U)02 releases oxygen 8J that the rare earths, Y, Zr, Nb,Ba, Sr, and some of the cesium and rubidium are oxidized and react to form

uranates and molybdates, maintaining the fuel at stoichiometric U02. Some ofthe Cs, Rb and Mo remains unoxidized. None of the Sb, Tc, Pd, Rh and Ru is

7

oxidized. We show later in this report that iodine and bromine are consumedin the formation of CsI, CsBr, RbI and RbBr.

III. FISSION PRODUCT AND ACTINIDE BROMIDES AND IODIDES

Using literature data, we derived linear equations for the free energy offormation of fission-product and actinide bromides and iodides. These equa-tions are given in Appendix A.

Tables 3 and 4 present the free energy of formation of halide gases andcondensed compounds, respectively, from fission products and the diatomichalogens [i.e., Br2(g) and I2(g)]; these free energies were calculatedfrom the equations in Table A-2 of Appendix A for temperatures of 1000 K.The free energy is calculated per halogen atom and the compounds are given indecreasing order of stability. It is generally accepted that the iodine willbe tied up as CsI. Tables 3 and 4 show that RbI is nearly as stable as CsI.Because of the uncertainties in the RbI and CsI heats of formation (+2 and+2.5 kcal, respectively) and entropies (+0.2 and +2.5 e4, respectively), it isnot possible to be sure which will be the major chemical form of iodine.

Tables 3 and 4 also indicate that CsBr, RbBr, BaBr2 and SrBr2 are morestable than CsI. Since the bromine concentration is about 1/6th and the cesiumconcentration is about 15 times the iodine concentration, bromine will not bea significant competitor for the alkali metals. The Ba, Sr, Zr, La, Ce, Pu,and Nb halides are not stable enough for the halogens to replace oxygen in thevery stable oxides of these fission products. Although the fission-producthalides in Tables 3 and 4 do not include them all, the data available indicatethat the missing fission-product halides will be relatively unstable (i.e.,Tc, Ru, Pd). Thus, rubidium and cesium are the only fission products whichwill react with iodine and bromine under normal oxidizing conditions in thefuel. Reducing conditions might prevail if the Zircaloy cladding reacts withthe fuel; under such conditions the iodides will increase in stability. Theeffects of steam still have to be assessed.

IV. FISSION PRODUCT AND STRUCTURAL-MATERIAL TELLURIDES

Literature data were used to derive linear equations for the free energyof formation of the fission-product, hydrogen, oxygen, iron, and nickel tel-lurides. These equations are given in Table A-3 of Appendix A.

The free energies of formation of the tellurides calculated from theseequations are given in Table 5. Values are given in order of decreasingstability for the free energy calculated per gram-atom of tellurium at 1500 K.The lanthanide and alkaline-earth tellurides are the most stable. However,these lanthanides and alkaline earths fcrm much more stable oxides undernormal and accident conditions and, thus, are not expected to form tellurides.Some of the remaining tellurides are stable under normal conditions (i.e., Ag,In, Sn, Cd, and Pd tellurides), but only palladium is at high enough concen-tration to tie up much of the tellurium. Much more silver, cadmium and tinare available in the control rods for reaction with tellurium in the case ofsimultaneous failure of the fuel cladding and control-rod cladding.

8

Table 3. Free Energy of Formation of Halide Gases fromFission Products and Gaseous Diatomic Halogensat 1000 K

AG/g-atom-halogen

Gas kcal/mol kJ/mol

CsBr -60.89 -254.8

RbBr -57.91 -242.3

BaBr2 -57.07 -238.8

SrBr2 -55.61 -232.7

CsI -53.07 -222.1

RbI -49.94 -208.9

Ba12 -45.66 -191.0

SrI2 -43.19 -180.7

ZrBr4 -35.31 -147.7

Zr14 -22.44 -93.9

NbI5 -6.67 -27.9

MoI2 -0.31 -1.3

9

Table 4. Free Energy of Formation of Fission-Product-Halide Solids and Liquids at 1000 K

AG/g-atom-halogen

Halides kcal/mol kJ/mol

CsBr(l) -75.37 -315.3

BaBr2(c) -74.89 -313.3

RbBr(l) -73.78 -308.7

SrBr2(l) -71.81 -300.4

CsI(1) -65.74 -275.1

RbI(l) -64.03 -267.9

Ba12(l) -61.47 -257.2

Sr12(l) -58.34 -244.1

LaBr3(c) -54.61 -227.3

PuBr3(l) -52.29 -218.8

Pu13(c) -42.18 -176.5

LaI3(c) -42.07 -176.0

Ce13(c) -40.71 -170.3

ZrBr4(l) -31.82 -133.1

ZrI2(l) -23.83 -99.7

10

Table 5. Free Energy of Formation of Fission Product andStructural-Element Tellurides from Fission Pro-ducts, Structural Elements and Diatomic TelluriumGas at 1500 K

Compound

NdTe(s)

IA2Te3(s)

Nd2Te3 (s)

CeTe(s)

BaTe(s)

ZrTe2*

Te02(1)

Ag2Te(1)

Te02(g)

TnTe(1)

Te202(g)

ZrTe3 *

SnTe (1)

TeO(g)

SnTe (g)

FeTe2 (1)

MoTe2(1)

Sb2 Te 3 (1)

CdTe(1)

PdTe (s)

NiTe(1)

Te02(g)

H2Te(g)

FeTeO.9(1)

Estimated

AG/g-atom-tellurium

kcal/mol kJ/mol

-53.4 -223

-50.5 -211

-50.0 -209

-49.6 -208

-45 -190

-23.7 -99

-13.2 -55

-13.1 -55

-11.5 -48

-10.8 -45

-8.7 -36

-6.9 -29

-6.8 -28

-3.8 -16

-3.6 -15

-3.1 -13

-2.4 -10

-2.2 -9

-1.8 -8

-1.4 -6

0.3 1

1.7 7

1e.5 77

29.0 104i

11

Cesium is one of the fission products expected to form a stable telluride.It has been assumed that cesium will form Cs2Te. Although this compound ismentioned in the literature,2 5 X-ray data for this compound have not beendefinitely established. We have not been able to prepare this compound whencesium and tellurium are reacted in a ratio of 2:1. Instead, this mixtureproduced Cs2Te3 and cesium. Under oxidizing conditions we would expect tofind TeO(g) and TeO2(g). Tellurates are also believed to be likely compoundsformed under oxidizing conditions, but we have not found thermodynamic datafor these compounds. We plan to investigate the Cs-Te system and the tellur-ates. In these investigations we will identify the condensed and vaporspecies and establish the thermodynamic properties of these compounds.Further experimental work is also needed for volatile tellurium compounds.The only data found for gaseous tellurium species were for TeO(g), Te02(g),Te202(g), H2Te(g) and SnTe(g).

Early data2 6 ,27 indicate that fission product tellurium may react withzirconium in zircaloy cladding. We have not found any experimental thermody-namic data for zirconium tellurides. Mills1 5 has estimated thermodynamic pro-perties for ZrTe2 and ZrTe3. We have listed equations for the free energy offormation of these two tellurides in Table A-3 using Mills' estimates for heatof formation and entropy and our estimate of the heat capacity.

V. FISSION PRODUCT HYDROXIDES AND HYDRIDES

Literature data were used to derive linear equations for the free energyof formation of fission-product gaseous hydroxides and hydrides. The equationsare given in Table A-4 of Appendix A.

The free energies of formation of fission-product hydroxides and hydridesat 1500 K are given in decreasing order of stability in Table 6. The freeenergy values are calculated per gram-atom of hydrogen. Only a few hydroxidecompounds were found (alkali, alkaline earth, and molybdic acid). The avail-able data for the hydrides were also sparse, being limited to those of 0, Se,Te, Br, and I.

Further theoretical and experimental investigations are needed to be surethat none of the other fission products will form volatile hydroxides at thehigh temperatures and steam pressures expected under reactor accident con-ditions.

VI. MAJOR UNCERTAINTIES IN THERMODYNAMIC PROPERTIES

Table 7 presents the fission-product compounds given in Tables 2-6 thathave large uncertainties in the heat of formation. A detailed analysis isrequired to establish whether any of these compounds will be important in cal-culating fission-product release rates. The analysis will consist of calcula-tions with thermochemical models, to determine the concentration of thesecompounds in the condensed and vapor form under various accident conditions.If any of these compounds significantly alter the predictions for fission-product release, we will conduct experiments to obtain accurate thermodynamic

12

values for that compound. Additional unidentified compounds which need to bestudied but are not on this list (e-g., hydroxides, tellurates, tellurides,etc.) may also exist.

Table 6. Free Energy of Formation of Fission-Product GaseousHydrides and Hydroxides from Hydrogen and FissionProducts in Their Standard States at 1500 K

AGf AGf

Gas kcal/g-atom-H kJ/g-atom-H

H2Mo04 -64.2 -269

Ba(OH)2 -57.5 -241

BaOH -56.2 -235

Sr(OH)2 -54.8 -230

SrOH -54.3 -227

CsOH -48.9 -205

Cs202H2 -41.3 -173

OH -39.2 -164

H20 -19.7 -83

HPr -15.3 -64

HI -4.1 -17

H2Se 3.1 13

H2Te 9.3 39

13

Table 7. Fission-Product Compounds withThermodynamic Uncertainties of5 kcal (21 Kj) or Greater

Hf Uncertaintykcal/mol

Oxide Compounds

ZrO(g) 12

Zr02(g) 11

MoO(g) 15

CsO(g) a

Cs2(g) a

Mo03(g) 5

SeO(g) 5

TeO3(g) 6

Halide Compounds

SrBr(g) 10

ZrBr(g) 10

ZrBr2(g) 10

ZrBr3(g) a

ZrI(g) 10

SrI(g) 20

ZrI2(g) a

ZrI3(g) a

BaBr(g) 10

BaI(g) 20

LaBr3 b

CeBr3(g) b

Ce13(g) b

(Cont'd)

14

Table 7. (Cont ' d )

Hf Uncertaintykcal/mol

Halide Compounds (cont'd)

La13(g) b

SbI3(s) 7

U13 (s) 9

UI4(s) 9

Hydroxide Compounds

Sr(OH)2(g) 10

Cs202 (g) 10

BaOH(g) 10

Bal(OH)2(g) 9

U03 H2 0 6

Tellurides

BTe(s) 7

CeTe(s) b

La2Te3(s) 6.1

NdTe(s) b

Nd 2 Te3(s) b

SrTe(s) 8

Te03(s) 6

aThermodynamic values estimated.

uncertainty large, but unknown.

15

REFERENCES

1. R. Kohli, A Thermcdynamic Contribution to the Understanding of the Multi-component System: Uranium Dioxide-Fission Products-Zircaloy, AustrianStudy for Atomic Energy, Institute for Metallurgy, Seibersdorf ResearchCenter, SGAE Report No. 3014 ME-153/178, ANL-TRANS-1196 (June 1981).

2. P. Hofmann, Fission Product Yield in Fission of U-235, U-238, Pu-239, andPu-24 1 with Neutrons of Different Energies, KernfarschungrzentrumKarlsruhe KfK Ext. IMF-Report 6/70-2 (November 1970).

3. M. E. Meek and B. F. Rider, Compilation of Fission Product Yields, 1974,General Electric Company Report NEDO-12154-1, Vallecitos Nuclear Center(1974).

4. E. A. C. Crouch, Fission Product Yields from Neutron Induced Fission,Atom Data amd Nucl. Data Tables, Vol. 19, No. 5 (May 1977).

5. W. F. Pasedag, R. M. Blond, and M. W. Jandowski, Regulatory Impact ofNuclear Reactor Source Term Assumptions, Nuclear Regulatory CommissionReport NUREG-0771, (April 1981).

6. JANAF Thermochemical Tables, NSRD-NBS-37 and 1974, 1975, and 1978 supple-ments.

7. I. Barin and 0. Knacks, Thermochemical Properties of Inorganic Substances,

Springer Verlag, Berlin (1973).

8. I. Barin, 0. Knacke, and 0. Kubaschewski, Supplement Thermochemical Pro-perties of Inorganic Substances, Springer Verlag, Berlin (1977).

9. 0. Kubaschewski and C. B. Alcock, Metallurgical Thermochemistry, FifthEl., Pergammon Press, New York, NY (1979).

10. A. Glassner, The Thermodyiiamic Properties of Oxides, Fluorides, andChlorides to 2500 K, Argonne National Laboratory Report ANL-5750 (1958).

11. V. Ya Leonidov, T. N. Rezukhina, and I. A. Bereznikova, Zh Fiz.Khim 34,

1862 (1960).

12. E. H. P. Cordfunke and B. 0. Loopstra, J. Inorg. Nucl. Chem. 29, 57 (1967).

13. D. D. Wagman, Selected Values of Chemical Thermodynamic Properties,National Bureau of Standards Technical Notes 270-3, 270-4, 270-5, 270-6,and 270-7, Washington, D.C. (1968-1973).

14. D. D. Wagman, Chemical Thermodynamic Properties of Compounds of Sodium,Potassium, and Rubidium: An Interim Tabulation of Selected Values,National Bureau of Standards NBSIR76-1034, Washington, DC (1976).

15. K. C. Mills, Thermodynamic Data for Inorganic Sulfides, Selenides, andTellurides, Butterworths, London (1974).

16

16. P. A. G. O'Hare and H. R. Hoekstra, J. Chem. Thermodyn. 6, 116 and 251(1974).

17. P. A. G. O'Hare and H. R. Hoekstra, J. Chem. Thermodyn. 7, 831 (1975).

18. D. W. Osborne, P. A. Brletic, H. R. Hoekstra, and H. E. Flotow, J. Chem.Thermodyn. 8, 361 (1976).

19. D. R. Fredrickson and P. A. G. O'Hare, J. Chem. Thermodyn. 8, 353 (1976).

20. P. A. G. O'Hare, J. Boerio, and H. R. Hoekstra, J. Chem. Thermodyn. 8,845 (1976).

21. R. C. Feber, Thermodynamic Data for Selected Gas Impurities in the PrimaryCoolant of High Temperature Gas-Cooled Reactors, Los Alamos ScientificLaboratory, Report LA-NUREG-6635 (April 1977).

22. E. H. P. Cordfunke and P. A. G. O'Hare, The Chemical Thermodynamics ofActinide Elements and Compounds, Part 3 Miscellaneous Actinide Compounds,IAEA, Vienna (1978).

23. P. E. Blackburn, M. Hoch, and H. L. Johnston, J. Phys. Chem. 62, 769(1958).

24. J. Berkowitz, W. A. Chupka, and M. G. Ingram, J. Chem. Phys. 27, 85 (1957).

25. W. Klemm, H. Sodomann, and P. Langmesser, Z. Anorg. Allg. Chem. 241, 281(1939).

26. G. W. Parker, G. E. Creek, and A. L. Sutton, Jr., Influence of VariablePhysical Process Assumptions on Core-Melt Aerosol Release, InternationalMeeting on Thermal Nuclear Reactor Safety, Chicago, Illinois, August 29,1982.

27. I. Johnson, private communication, Argonne National Laboratory, October1982.

17

APPENDIX A

THERMODYNAMIC DATA FOR FISSION PRODUCT AND ACTINIDE COMPOUNDS

This appendix contains tables of thermodynamic data for fission-productand actinide oxides (Table A-1), halides (Table A-2), tellurides (Table A-3),and gaseous hydroxides and hydrides (Table A-4).

18

Table A-1. Free Energy of Formation of Fission-Product and Actinide Oxides

Reactants

1/2 Se2(g) + 1/2 02(g)

1/6 Se6(g) + 1/2 02(g)

1/2 Se2(g) + 02(g)

1/6 Se6(g) + 02(g)

2Rb(1) + 1/2 02(g)

2Rb(g) + 1/2 02(g)

2Rb(1) + Mo(c) + 202(g)

2Rb(g) + Mo(c) + 202(g)

Sr0(c)

Sr(c) + 1/2 02(g)

Sr(I) + 1/2 02(g)

Sr(g) + 1/2 02(g)

Sr(c) + Mo(c) + 202(g)

Se0 + Mo(c) + 3/2 02(g)

Sr(c) + U02(c) + 02(g)

Sr(1) + U02(c) + 02(g)

Sr(g) + U0 2(c) + 02(g)

SrO(c)+U02(c)+1/2 02(g)

2Y(c) + 3/2 02(g)

2Y(1) + 3/2 02(g)

Zr(c) + 1/2 02(g)

Free Energy

.__.__._

(Cont'd)

Product

= SeO(g)

- SeO(g)

= Se0 2(g)

- Se02(g)

= Rb20(c)

- Rb20(c)

- Rb2Mo04(c)

- Rb2Mo04(c)

- SrO(g)

= SrO(c)

- SrO(W)

- SrO(c)

- SrMo04(c)

- SrMo04(c)

- SrU04(c)

- SrUO4(c)

- SrU04(c)

- SrU04

- Y203(c)

' 203 (c)

- ZrO(g)

Free Energy,

cal/mol Product

AG - -2011 - 1.1T

AG - 8946 - 13.05T

AG - -42541 + 15.8T

AG - -31694 + 3.93T

AG - -78445 + 34.20T

AG - -110545 + 66.52T

AG - -353542 + 72.24T

AG - -387693 + 115.85T

AG - 135344 - 36.42T

AG - -141156 + 22.92T

AG - -142835 + 24.55T

AG - -174079 + 43.44T

AG - -371573 + 100.91T

AG - -225169 + 56.2T

AG - -217457 + 50.68T

AG - -215479 + 48.78T

AG - -180979 + 27.87T

AG - -76301 + 27.76T

AG - -453518 + 67.32T

AG - -445684 + 62.84T

AG - 12139 - 17.08T

Temperature,K

(601-2000)

(601-2000)

(313-900)

(313-900)

(312-967)

(967-MP)

(298-2938)

(298-1041)

(1041-1654)

(1654-2938)

(298-1041)

(1041-1650)

(1650-MP)

(298-1799)

(1799-2693)

19

Table A-1.(Cont'd)

Reactants

Zr02(c)

Zr02 (c)

Zr(c,1) + 02(g)

Ba + Zr + 3/2 02(g)

Nb(c) + 1/2 02(g)

Nb + 02(g)

2Nb(c) + 5/2 02

NbO(c)

Nb02(c)

Nb(c) + 1/2 02(g)

Nb(c) + 02(g)

NbO(c) + 1/2 02(g)

2Nb02(c) + 1/2 02

Mo(c) + 02(g)

Mo0 2(c)

Mo(c) + 3/2 02(g)

Mo03(1)

3Mo03(c)

3Mo03(1)

2Cs(1) + Mo(c) + 202(8)

2Cs(g) + Mo(c) + 202(g)

Mo03(c)

M002(c) + 1/2 02(g)

Product

- Zr0 2(g)

- ZrO(g) + 1

- Zr02(c)

- BaZr03(c)

- NbO(c)

- Nb02(c)

- Nb205(c)

- NbO(g)

- Nb02(g)

- NbO(g)

- Nb02(g)

- NbO 2(c)

- Nb205(c)

- M002(c)

- Mo02(5)

- Mo03(c)

- M003(g)

- M0309(g)

- M0309(g)

- Cs2Mo04(g)

- Cs2Mo04(g)

- M003(g)

- M003(c)

Free Energy,

cal/mol Product

AG - 190590 - 47.63T

/2 02 AG - '73185 - 61.15T

AG - -26-892 + 43.81T

AG - -425289 + 74.6T

AG - -99384 + 18.991

AG - -186908 + 39.64"

AG - -449096 + 98.55

AG - 145332 - 41.72T

AG - 137786 - 44.48T

AG - 45948 - 22.73T

AG - -49122 - 4.84T

AG - -87524 + 20.65T

AG - -75279 + 19.27T

G - -137854 + 39.59T

AG - 133351 - 47.6T

AG - -176700 + 58.95T

AG - 76625 - 30.4bT

AG - 80200 - 68.3T

AG - 45400 - 35.9T

- -299177 + 59.6T

AG - -325372 + 86.52T

AG - 88225 - 41.26T

AG - -36622 + 15.32T

(Cont'd)

Temperature,K

(298-1074)

(1074-2000)

(298-1074)

(1074-1500)

(298-1074)

(298-1079)

20

Table A-1.

Reactants

2Rb(1) + Mo(c) + 202(g)

2Rb(g) + Mo(c) + 202(g)

Ba(c) + Mo(c) + 202(g)

2Cs(1) + Mo(c) + 202(g)

2Cs(g) + Mo(c) + 202(g)

2Cs(g) + Mo(c) + 2 0 2(g)

Tc(z) + 02(g)

Ru(c) + 02(g)

2Rh(c) + 3/2 02(g)

Pd(c) + 1/2 02(g)

2Sb(c) + 3/2 02(g)

2Sb(1) + 3/2 02(g)

Sb(c) + 02(g)

Sb203(c) + 1/2 02(g)

Te(1) + 02

1/2 Te2(g) + 02

Te(]) + 02(g)

1/2 Te2%g) + 02(g)

1/2 I2(g) + 1/2 02(g)

Cs(g) + 1/2 02(g)

2Cs(1) + 1/2 02(g)

2Cs(g) + 1/2 02(g)

2Cs(1) + U(c) + 202(g)

. _

Temperature,

(Cont'd)

Product

- Rb2MoO4

- Rb2MoO4

- BaMo04

- Cs2Mo04(c)

- Cs2Mo04(c)

= Cs2Mo04(g)

- Tc02(c)

- RuO2(c)

- Rh203(c)

- PdO(c)

- Sb203(c)

- Sb203(1)

- SbO2(c)

- 2Sb02(c)

- Te02(c)

- TeO2(c)

- TeO2(1)

- Te02(1)

- I0(g)

- Cs0(g)

- Cs20(g)

- Cs20(g)

- Cs2U04(c)

(Cont'd)

Free Energy,cal/mol Product

AG - -353542 + 72.24T

AG - -387693 + 115.85T

AG - -369117 + 84.87T

aG - -363164 + 89.69T

AG - -389690 + 116.6T

AG - -325372 + 86.52T

AG - -101308 + 39.21T

AG - -70299 + 36.97T

AG - -88530 + 35.28T

AG - -29510 + 11.76T

AG - -170000 + 60.61T

AG - -158400 + 47.72T

AG - -108540 + 44.69T

AG - -55030 + 38.02T

AG - -75120 + 41.18T

AG - -91423 + 54.83T

AG - -68170 + 34.27T

AG - -84473 + 47.92T

AG - 34078 - 2.45T

AG - -3083 + 5.12T

AG - -24053 - 4.77T

AG - -58877 + 32.64T

AG - -462106 + 102.14T

Temperature,

K

(313-967)

(967 - MP)

(298-1895)

(301-952)

(952-MP)

(952-2892)

(298-),200)

(298-1300)

(298-1300)

(298-1123)

(298-929)

(929-1729)

(298-929)

(298-904)

(773-973)

(298-1)06)

(1006-1200)

(1006-1200)

(298-2000)

(298-2000)

(301-952)

(301-1405)

21

Table A-1 (Cont'd)

Free Energy, Temperature,Reactants Product cal/mol Product K

2Cs(1) + U0 2(c) + 02(g)

2Cs(g) + U(c) 4 202(g)

2Cs(g) + U02(c) + 02(g)

2Cs(1) + 1/2 02(g)

2Cs(g) + 1/2 02(g)

Cs2UO4(c)+U0 2(c)+1/2 02

2Cs(1) + 2U(c) + 7/202(g)

2Cs(g) + 2U(c) + 7/202(g)

3a(c) + 1/2 02(g)

Ba(1) + 1/2 02(g)

Ba(c) + 1/2 02(g)

Ba(1) + 1/2 02(g)

BaO(c)

Ba(c) + U(c) + 202(3)

U02(c) + BaO(c)+1/2 02

2La(c,1) + 3/2 02(g)

2Ce(c,1) + 3/2 02(g)

Ce203(c) + 1/2 02

2Pr(c,1) + 3/2 02(g)

2Nd(c,1) + 3/2 02(g)

2Sm(c,1) + 3/2 02(g)

U(c,1) + 02(g)

Np(c,1) + 02(g)

Pu(c,1) + 02(g)

2Pu(1) + 3/2 02(g)

= Cs2UO4(c)

= Cs2UO4(c)

= Cs2UO4(c)

= Cs 20(c)

= CB20(c)

- Cs2U207(c)

= Cs2U207(c)

Cs2U207(c)

- BaO(c)

= BaO(c)

= BaO(g)

- BaO(g)

- BaO(g)

- BaUO4(c)

- BaUO4(c)

= La203(c)

- Ce203(c)

- 2Ce02(c)

- Pr203(L)

- Nd203(c)

- Sm203(c)

- U0 2(c)

- Np0 2(c)

- Pu0 2(c)

- Pu203(c)

AG

AG

AG

AG

AG

AG

AG

AG

AG

AG

AG

AG

AG

AG

AG

AG

AG

AG

AG

AG

AG

AG

AG

AG

AG

= -203212

= -492046

+

+

61.28T

132.48T

(301-952)

_ -233152 + 91.62T

- -77103 + 38.3T

- -105193 + 66.79T

_ -33506 + 15.78T

_ -752876 + 157.2T

= -785573 + 190.12T

- -117713 + 16.7

= -119622 + 18.61T

_ -31367 - 12.95T

_ -38373 - 6.76T

- 98138 - 33.21 T

- -473010 + 87.3T

_ -81517 + 22.32T

- -427666 + 67.41T

- -433255 + 66.29T

- -87155 + 34.94T

- -434043 + 66.16T

- -431200 + 67.89T

- -438155 + 70.0T

- -258894 + 42.1T

- -245818 + 40.82T

- -251207 + 43.OT

- -399600 + 63.8T

(301-763)

(298-763)

(298-983)

(983-2122)

(298-983)

(983-2268)

(298-1403)

(298-2593)

(298-1960)

(298-2545)

(1600-2150)

22

Table A-2. Free Energy Equations for Fission-Product Iodides and Bromides

Reactants

1/2 B=2(g)

1/2 Br2(g) + 1/2 I2(g)

1/2 Br2(g) + Rb(g)

1/2 Br2(g) + Rb(1)

1/2 Br2(g) + Rb(g)

Br(g) + Rb(g)

Rb(g) + 1/2 i2(g)

Rb(1) + 1/2 I2(g)

Rb(g) + 1/2 I2(g)

Rb(g) + I(g)

Cs(g) + 1/2 Br2(g)

Cs(1) + 1/2 Br2(g)

Cs(g) + 1/2 Br2(g)

Cs(g) + Br(g)

Sr(c) + Br2(g)

Sr(1) + Br2(g)

Sr(c) + Br2(g)

Sr(1) + Br2(g)

Sr(c) + I2(g)

Sr(1) + I2(g)

Sr(c) + 12(g)

Sr(1) + I2(g)

(Cont'd)

Product

= Br(g)

= BrI(g)

= RbBr(g)

= RbBr(g)

= RbBr(1)

= RbBr(g)

= RbI(g)

- RbI(g)

= RbI(1)

= RbI(g)

= CsBr(g)

- CsBr(g)

= CsBr(1)

- CsBr(g)

- SrBr2(c)

- SrBr2(1)

- SrBr2(g)

- SrBr2(g)

- SrI2(c)

- SrI2(1)

- Sr12(g)

- SrI2(g)

Free Energy,

cal/mol Product

AG = 23484 - 13.29T

AG - -1372 + 1.42T

AG = -68349 + 9.68T

AG = -87156 + 29.25T

AG = -108132 + 34.35T

AG = -91829 + 22.97T

AG = -60044 + 9.97T

AG - -50163 + 8.0T

AG = -98020 + 34.5T

AG = -78466 + 22.60T

AG - -64867 + 4.66T

AG = -47863 - 13.03T

AG - -105765 + 30.9T

AG = -88346 + 17.95T

AG - -177267 + 33.05T

AG - -170495 + 26.27T

AG - -105286 - 4.85T

AG - -108578 - 1.55T

AG - -147600 + 33.56T

AG - -140905 + 25.49T

AG - -81431 - 4.95T

AG - -85005 - 1.44T

Temperature,K

(298-2000)

(313-961)

(961-1b25)

(313-961)

(913-1577)

(302-955)

(908-1573)

(331-930)

(930-1648)

(331-930)

(1041-1654)

(458-811)

(811-1648)

(458-1043)

(1043-1648)

23

Table A-2.

Reactants

Sr(c,1) + 1/2 I2(g)

Zr(c) + Br2(g)

Zr(c) + Br2(g)

Zr(c) + Br2(g)

Zr(c) + 3/2 Br2(g)

Zr(c) + 3/2 Br2(g)

Zr(c) + 2Br2(g)

Zr(c) + 2Br2(g)

Zr(c) + 1/2 I2(g)

Zr(c) + I2(g)

Zr(c) + I2(g)

Zr(c) + I2(g)

Zr(c) + 3/2 I2(g)

Zr(c) + 3/2 I2(g)

Zr(c) + 2I2(g)

Zr(c) + 212(g)

Nb(c) + 5/2 I2(g)

Mo(c) + 21(g)

1/2 I2(g)

Cs(1) + 1/2 I2(g)

Cs(g) + 1/2 I2(g)

Cs(g) + 1/2 12(g)

Temperature,

(Cont 'd)

Product

= SrI(g)

= ZrBr2(c)

= ZrBr2(1)

= ZrBr2(g)

= ZrBr3(c)

= ZrBr3(g)

= ZrBr4(c)

= ZrBr4(g)

= ZrI2(g)

= ZrI(c)

= ZrI2 (1)

= ZrI2(g)

- ZrI3(c)

- Zr1 3 (g)

- ZrI4(c)

- Zr14(g)

= NbIg5(g)

- MoI2(g)

- I(g)

- CsI(g)

- CsT(g)

- CsI(1)

(Cont'd)

Free Energy,cal/mol Product

AG = -17232 - 16.85T

AG = -101794 + 35.O1T

AG = -84644 + 16.19T

AG = -50309 - 5.81T

AG = -161261 + 51.98T

AG = -115164 + 10.14T

AG = -193655 + 66.7T

AG = -168438 + 27.2T

AG = 131506 - 21.44T

AG = -75409 + 31.79T

AG = -63362 + 17.49T

AG = -32971 - 7.?5T

AG = -115372 + 49.19T

AG = -76204 + 9.35T

AG - -143811 + 65.2T

AG - -116730 + 26.96T

AG - -70737 + 37.4T

AG - -25000 - 9.5T

AG - 18406 - 12.;2T

AG - -37620 - 14.58T

AG = -54633 + 3.11T

AG - -97145 + 30.07T

Temperature ,

K

(458-1648)

(313-900)

(900-1555)

(313-735)

(298-700)

(700-1300)

(458-2100)

(298-970)

(970-2100)

(458-705)

(458-2100)

(1050-1500)

(302-955)

(894-1553)

24

Table A-2. (Cont'd)

Reactants

Cs(g) + I(g) -

Ba(c ) + 1/2 Br2 (g ) -

Ba(c,1) + Br2(g) -

Ba(c,1) + Br2(g) =

Ba(c,1) + 1/2 I2(g) -

Ba(c) + I2(g) -

Ba(1) + I2(g) =

Ba12(c) -

Ba12 (1) =

La + 3/2 Br2(g) -

La + 3/2 Br2(g) -

La + 3/2 I2(g) -

La + 3/2 I2(g) -

Ce + 3/2 I2(g) -

Ce + 3/2I2(g) -

Pu(c) + 3/2 Br2(g)

Pu 1) + 3/2 Br2(g) -

Pu(c) + 3/2 I2(g) -

Pu(1) + 3/2 I2(g) -

Product

CsI(g)

BaBr(g)

BaBr2(c,1)

BaBr2(g)

'taI(g)

BaI2(g)

Ba12(g)

Ba12(g)

Ba12(g)

LaBr3(c)

LaBr3(1)

LaI3(c)

La13 (1)

CeI3(c)

CeI3(1)

PuBr3(c)

PuBr3(1)

Pul3(c)

PuI3(1)

AG

AG

AG

AG

AG

A(

AC

AG

A(

A(

A(

A(

A(

A(

A4

Free Energy,cal/mol Product

= -73041+ 15.81T

= -34674 - 12.63T

= -184439 + 31.95T

= -113164 - 0.97T

- -22164 - 12.78T

= -89003 - 2.32T

= -95851 + 3.74T

J

G

G

G

G

G

G

G

G

G

= 69927 -

= 51917 -

= -216855

- -202953

- -177362

- -162588

- -176104

_ -170960

- -228616

- -192303

- -176438

- -162804

38.39T

22.61T

+ 53.OT

+ 39.11T

+ 51.17T

+ 36.39T

+ 53.98T

+ 48.8T

+ 71.73T

+ 35.42T

+ 49.89T

+ 36.25T

Temperature,K

(983-1895)

(298-983)

(983-1895)

(298-985)

(985-2800)

(313-1061)

(1061-1859)

(298-1051)

(1051-1745)

(458-1033)

(1033-MP)

(298-954)

(954-1748)

(298-1050)

(1050-MP)

25

Table A-3.

Reactants

Te(s)

Te(1)

2Te(s)

2Te(1)

Te(s) + H2(g)

Te(1) + H2(g)

1/2 Te2(g) + H2(g)

Te(s) + 1/2 02(g)

Te(i) + 1/2 02(g)

1/2 Te(g) + 1/2 02(g)

Te(s) + 02(g)

Te(1) + 02(g)

1/2 Te2(g) + 02(g)

1/? Te2(g) + 02(g)

Te(s) + 02(g)

Te(1) + 02(g)

1/2 Te2(g) + 02(g)

2Te(s) + 02(g)

2Te(1) + 02(g)

Te2(g) + 02(g)

2Te(s) + Fe(s)

2Te(1) + Fe(s)

Te2(g) + Fe(s)

Free Energy of Formation of Fission-Productand Reactor-Component Tellurides

Free Energy, Temperature,

Product

= Te(g)

= Te(g)

= Te2(g)

= Te2(g)

- H2Te(g)

= H2Te(g)

- H2Te(g)

= TeO(g)

- TeO(g)

= TeO(g)

- TeO2(s)

= TeO2(s)

- TeO2(s)

- TeO2(1)

- Te02(g)

- Te0 2(g)

- TeO2 (g)

- Te202(g)

- Te202(g)

- Te202(g)

- FeTe2(s)

- FeTe2(s)

- FeTe2(s)

(Cont'd)

Free Energy,

cal/mol Product

AG = 50327 - 30.99T

AG = 44226 - 22.71T

AG - 37325 - 36.49T

AG - 24793 - 19.45T

AG - 23095 - 9.51T

AG - 14759 - 1.35T

AG - 3899 + 9.74T

AG - 17432 - 20.05T

AG - 11085 - 11.43T

AG - -1331 - 1.65T

AG - -76963 + 42.1T

AG - -80390 + 46.751

AG - -95115 + 59.161

AG - -78711 + 43.691

AG - -14611 - 3.58T

aG - -20689 + 4.68T

AG - -33165 + 14.451

AG - -26393 - 4.34T

AG - -37363 + 10.521

AG - -126114 + 56T

AG - -17517 + 6.88T

AG - -27436 + 20.56'

AG - -54544 + 42.08'

T

T

r

T

T

T

T

Temperature,

K

(298-723)

(723-1282)

(298-723)

(723-1282)

(298-723)

(723-2000)

(298-2000)

(298-723)

(723-2000)

(298-2000)

(298-723)

(723-1006)

(298-1006)

(1006-1200)

(298-723)

(723-1282)

(298-2000)

(298-723)

(723-1223)

(298-2000)

(298-723)

(723-933)

(298-933)

26

Reactants

Te2(g) - Fe(s)

Ni(s) + Te(s)

Ni(s) + 1/2 Te2(g)

*Zr(s) + 2Te(s)

*Zr(s) + 2Te(1)

*Zr(s) + Te2(g)

*Zr(s) + 3Te(s)

*Zr(s) + 3Te(1)

*Zr(s) + 3/2 Te2(g)

Pd(s) + Te(s)

Pd(s) + Te(1)

Pd(s) + 1/2 Te2(g)

1/2 Te2(g) + 2Ag(s)

1/2 Te2(g) + 2Ag(1)

Te(s) + 2Ag(s)

Cd(s) + Te(s)

Cd(1) + Te(1)

Cd(g) + 1/2 Te2(g)

In(s) + Te(s)

In(1) + Te(1)

In(1) + Te(1)

In(1) + 1/2 Te2(g)

In(g) + 1/2 Te2(g)

_

Temperature,

Product

- FeTe2(J

- NiTe(s

- NiTe(s

= ZrTe2(!

- ZrTe2 (f

- ZrTe2(f

- ZrTe3(f

= ZrTe3 (!

- ZrTe3(i

= PdTe(s

- PdTe(s

= PdTe(s;

- Ag2Te(i

- Ag2 Te(i

= Ag2Te(I

- CdTe(s

- CdTe(s

- CdTe(1

InTe(1

- InTe(s

- InTe(1

- InTe(1

- InTe(1

Table A-3. (Cont'd)

Free Energy,t cal/mol Product

L) AG - -48982 + 36.72T

AG = -8619 + 0.12T

AG - -27282 + 18.37T

s) AG - -71700 + 6.34T

s) AG = -83600 + 21.88T

s) AG - -107500 + 40.13T

s) AG - -69600 + 18.07T

s) AG = -86800 + 40.597T

s) AG = -123100 + 68.19T

) AG - -9075 - C.33T

) AG - -13909 + 6.32T

) AG - -27540 + 17.46T

s) AG - -24394 + 7.53T

s) AG - -158992 + 67.03T

s) AG - -11595 - 2.60T

) AG - -24347 + 2.07T

) AG - -29907 + 10.15T

) AG - -55002 + 35.45T

) AG - -17226 + 0.48T

) AG - -23211 + 9.8T

) AG - -14956 + 1.37T

) AG = -27073 + 10.88T

) AG - -83844 + 35.34T

(Cont'd)

Temperature,

K

(933-1812)

(298-723)

(298-800)

(298-723)

(723-MP)

(298-MP)

(298-723)

(723-MP)

(298-MP)

(298-723)

(723-993)

(298-993)

(421-1232)

(421-1232)

(723-1232)

(298-594)

(723-1364)

(1364-2000)

(298-430)

(723-968)

(968 -1282)

(968-1282)

(968-1282)

27

Reactants

Sn(s) + Te(s)

Sn(1) + Te(s)

Sn(1) + Te(l)

Sn(1) + 1/2 Te2(g)

Sn(1) + 1/2 Te2(g)

Sn(1) + 1/2 Te2(g)

2Sb(1) + 3/2 Te2(g)

Te(s) + Ba(s)

Te(1) + Ba(s)

1/2 Te2(g) + Ba(s)

1/2 Te2(g) + Ba(1)

3Te(s) + 2La(s)

3Te(1) + 2La(s)

3/2 Te2(g) + 2La(1)

2La(1) + 3/2 Te2(g)

Te(s) + Ce(s)

Te(1) + Ce(s)

Te(1) + Ce(1)

1/2 Te2(g) + Ce(s)

1/2 Te2(g) + Ce(1)

Nd(s) + Te(s)

Nd(s) + Te(1)

Nd(s) + 1/2 Te2(g)

Temperature

Produc

= SnTe(s

- SnTe(s

= SnTe(s

= SnTe(s

= SnTe(J

- SnTe(g

= Sb2Tei

= BaTe(s

= BaTe(E

- BaTe(s

- BaTe(E

= La2Te:

- La2Te'

= La2Te'

- La2Te:

= CeTe(E

- CeTe(u

- CeTe(u

- CeTe(g

- CeTe(i

- NdTe(g

- NdTe(g

- NdTe(i

Table A-3. (Cont'd)

Free Energycal/mol Product

s ) AG = -14542 + 0.6T

AG - -16590 + 4.62T

s) AG = -21267 + 11.02T

s) AG = -34323 + 21.47T

1) AG - -21601 + 9.88T

) AG - -13132 - 11.14T

3(1) AG - -52141 + 30.19T

s) AG = -64986 + 4.69T

B) AG - -72068 + 14.56T

3) AG - -83960 + 23.66T

B) AG = -89817 + 29.59T

3(s) AG - -187728 + 7.98T

3(s) AG - -203622 + 29.64T

3(s) AG - -244036 + 61.72T

3(1) AG - -225655 + 51.3T

s) AG - -72550 + 6.76T

B) AG - -79829 + 17.15T

B) AG - -87579 + 24.1T

B) AG - -91714 + 71' 5r

B) AG - -98141 + 32.34T

s) AG - -72225 + 6.19T

s) AG - -78901 + 15.14T

e) AG - -90953 + 24.55T

(Cont'd)

Temperature

K

(298-505)

(505-723)

(723-1079)

(505-1079)

(1079-2000)

(1079-2000)

(904-2000)

(298-723)

(723-1002)

(298-1002)

(1002-1500)

(298-723)

(723-1193)

(1193-1760)

(1760-2000)

(298-723)

(723-1071)

(1071-2000)

(298-1071)

(1071-2000)

(298-723)

(723-1289)

(298-1289)

28

Table A-3. (Cont'd)

Reactants

Nd(1) + Te(1)

Nd(1) + 1/2 Te2(g)

2Nd(s) + 3Te(s)

2Nd(s) + 3Te(1)

2Nd(s) + 3/2 Te2(g)

2Nd(1) + 3Te(1)

2Nd(1) + 3/2 Te2(g)

1/2 Te2(g) + 1/2 Se2(g)

Te2 (g) + Mo(s)

Te2(g) + Mo(s)

Product

= NdTe(s)

- NdTe(s)

= Nd2Te3 (s)

= Nd2Te3(s)

- Nd2Te3 (s)

- Nd2Te3 (s)

= Nd 2 Te3(s)

- TeSe(g)

- MoTe2 (s)

- MoTe2(1)

Free Energy,

cal/mol Product

AG - -85115 + 19.91T

AG - -95245 + 27.9T

AG = -190280 + 9.71T

AG - -208058 + 33.63T

AG = -245749 + 63.3T

AG - -220978 + 43.54T

AG - -251367 + 67.52T

AG - 1925 - 1.78T

AG - -92600 + 74.3T

AG = -64500 + 39.8T

Temperature,

K

(1289-2000)

(1289-2000)

(298-723)

(723-1289)

(298-1289)

(1289-1650)

(1289-1650)

(298-2000)

(298-810)

(810-1000)

heat capacityHeat of formation and entropy at 298 K estimated by Mills1 5 ,estimated by authors.

29

Table A-4. Free Energy of Formation of Fission-Productand Reactor-Component Hydroxides and Hydrides

Reactants

1/2 H2(g) + 1/2 02(g)

H2(g) + 1/2 02(g)

H2(g) + 1/2 Se2(g)

1/2 H2(g) + 1/2 Br2(g)

Sr(s) + 1/2 02 + 1/2 H2(g)

Sr(1) + 1/202(g) + 1/2H2(g)

Sr(1) + 02(g) + H2(g)

Sr(g) + 02(g) + H2(g)

Moss) + H2(g) + 202(g)

H2(g) + Te2(s)

H2(g) + Te(1)

H2(g) + 1/2 Te2(g)

1/2 H2(g) + 1/2 12(g)

1/2 H2(g) + 1/2 12(s)

1/2 H2(g) + 1/2 12(1)

Cs(1) + 1/202(g) + 1/2H2(g)

Cs(g) + 1/202(g) + 1/2H2(g)

2Cs(1) + 02(g) + H2(g)

2Cs(g) + 02(g) + H2(g)

Ba(s) + 1/202(g) + 1/2H2(g)

Ba(1) + 1/202(g) + 1/2H2(g)

Ba(g) + 1/202(g) + 1/2H2(g)

Ba(s) + 02(g) + H2(g)

Free Energya Temperature,

(Cont'd)

Product

= OH(g)

= H20(g)

- H2Se(g)

- HBr(g)

- SrOH(g)

- SrOH(g)

- Sr(0H)2(g)

- Sr(OH)2(g)

- H2Mo04(g)

- H2Te(g)

- H2Te(g)

- H2Te(g)

- HI(g)

- HI(g)

- HI(g)

- CsO!.(g)

- Cs2H(g)

- Cs202H2(g)

- Cs202H2(g)

- BaOH(g)

- BaOH(g)

- BaOH(g)

- Ba(OH)2(g)

Free Energy,a

cal/mol Product

AG = 9236 - 3.48T

AG - -59180 + 13.32T

AG - -10738 4 11.32T

AG - -12511 - 0.30T

AG - -49808 - 4.35T

AG - -54342 + 0.05T

AG - -146444 + 24.59T

AG - -181224 + 45.79T

AG - -201973 + 48.94T

AG - 23095 - 9.51T

AG - 14759 + 1.35T

AG - 3899 + 9.74T

AG - -1574 - 1.75T

AG - 6178 - 19.46T

AG - 4060 - 13.98T

AG - - 63202 + 3.01T

AG - -79848 + 20.61T

AG - -167017 + 42.89T

AG - -200637 + 78.7ST

AG - -55076 - 2.69T

AG - -60541 + 3.02T

AG - -96486 + 20.08T

AG - -150430 + 21.83T

Temperature,

K

(298-2000)

(298-2000)

(298-2000)

(298-2000)

(298-783)

(783-2000)

(1041-1654)

(298-2000)

(298-2000)

(298-723)

(723-2000)

(298-2000)

(298-2500)

(298-387)

(387-458)

(302-952)

(952-2500)

(302-952)

(952-2500)

(298-983)

(983-1895)

(298-2000)

(681-983)

30

Table A-4. (Cont'd)

Free Energy,a Temperature,Reactants Product cal/mol Product K

Ba(l) + 02(g) + H2(g) - Ba(OH)2(g) AG = -154987 } 26.6T (983-1895)

Ba(g) + 02(g) + H?(g) = Ba(OH)2(g) AG = -191651 + 44.14T (298-2000)

aAG (J) - 4.184 AG (cal)

31

APPENDIX B

OXYGEN POTENTIAL MODEL FOR U02 FUEL

Oxygen dominates the fuel chemistry, constituting 2/3 of the total. Theoxygen, uranium, and fission product concentration, as well as the temperature,set the oxygen potential in the system. The oxygen potential and fissior-pro-duct oxide thermodynamics determine which fission products will be oxidized.

The process used to calculate the oxygen potential in uranium oxide isdescribed below. This model is described in some detail to demonstrate themechanism used in all three models for U02, (U,Pu)02 and (U,Pu,FP)02. Thethermodynamic model for oxygen potentials in UO2.+ consists of four equations:two equations define the relation of oxygen pressure to the charge distributionin the uranium lattice; a third equation defines the conservation of uranium;and the fourth equation defines the conditions for electrical neutrality. Thefirst two e uations are based on the law of mass action for equilibria amongU2+, U4+, O'-, and 02 gas in hypostoichiometric UO2-x, and among U4+, U6+, 02-,and 02 gas in hyperstoichiometric UO2.. -In these two equations, oxygenpressure equations are derived, and the Duhem-Marqules equation is applied todetermine uranium and urania (U02) activity. These two equations, alongwith phase boundary data and thermodynamic data, are then used to evaluatetemperature-dependent equilibrium constants. The model 2-4 requires oxygenpressure data only to decide which cations are in UO2-x and UO2+y (i.e., U4+and U3+ or U2+ for UO2..x; U4+ and U5+ or U6+ for UO2+y). The oxygen pressuredata fit the uranium cations U2+, U4+, and U+. The derivation of theequilibrium equations are given below.

UO2 -, Equations

In UO2-x, the ionic lattice-gas phase equilibrium is given by

2U4+ + 02- - 2U2+ + 02(g) (1)

For this equilibrium one may write

NU4+1nP0 2 - 2 In + 2 In N0 2- + In K1 (2)

2 NU2+

where Nj is the number of moles of j ions.

Except near the stoichiometric composition, the number of ions canbe approximated by NU4+ - 1-x, NU 2 + - x and N 2- - 2-x. (Near thestoichiometric composition there are also a finite number of U+ ions.)Equation (2) may be rewritten in terms of the oxygen deficiency x as

1np0 2 - 2 ln(1-x) - 2 ln(x) + 2 ln(2-x) + lnKI (3)

To evaluate K1 , it is necessary to derive an equation for uraniumactivity and an equation relating oxygen pressure and uranium activityto the free energy of formation of U02 .

32

The uranium activity is obtained by application of the Gibbs-Duhemequation. That is,

N0 2din aU - - - dln P0 2 (4)NU

If equation (3) is differentiated and substituted into equation (4) along withNO2/NU - (2 - x)/2, integration yields

lnaU - -ln(1-x) + 2 ln(x) + x + C1 (5)

At temperatures below the eutectic temperature (2700 K), the uraniumactivity at the metal-rich boundary of UO2-x is greater than 0.9, whichcan be approximated as aU - 1. When equation (5) is evaluated at theboundary to solve for the integration constant C1, the uranium activityis given by

lnaU--In lX +2 In x- +x - xs (6)1-xs xs

where xs is the phase boundary of the UO2-x phase. Below 2700 K, xsis given by

xs - exp(-12913/T + 3.767) (7)

Now K1 in equations (2) and (3) may be evaluated by noting that at x - 0,

+ ln AGf(U02 )U7, P0 2 x-o + in aU x-o - RT-(8)

Thus, on substituting equations (3) and (6) into equation (8), we find

AGf(U02 )lnKi - RT - 2 In 2 - ln(1-xs)

+ 2 ln(xs) + xs (9)

Thermodynamic and phase-boundary data may be used to evaluate KI as

lnKi - - 156600 + 27.2 (10)

Substituting equation (10) into equation (2), dividing by 2, and rearrangingyield the first of the four equations for the urania oxygen potential,

NU4+ PO1/2- 2 exp(78300/T - 13.6) (11)

NU2+ N02-

33

UO2+y Equation

A similar treatment for the reaction,

2U6+ + 202- - 2U4+ + 02 (12)

leads to the UO2+y equation,

1/2

= exp(16500/T - 5.1) (13)NU4+ No2-

The remaining equations are the conservation equation,

NU2+ + NU4+ + NU6+ = 1 (14)

and the electrical neutrality equation,

N02 - - NU2+ + 2NU4+ + 3NU6+ (15)

Equations (11) and (13-15) may be solved simultaneously to obtain (1) theoxygen concentration for a given oxygen pressure or oxygen potential (AG02 -RT In P0 2,) or (2) the oxygen pressure or oxygen potential for a given oxygenconcentration.

Oxygen Pressure over Urania

The temperature dependent constants in equations (11) and (13) are given

by

A - exp(783J0/T - 13.6) (16)

B = exp(16500/T - 5.1) (17)

The square root of the oxygen pressure can be calculated from a variationof the quadratic equation solution for * < 2.05,

1/2 - (0-2) + [(0-2)2 + 4B(3-)(-1)/A]1/2(18)02 2B(3-4)/#

where * - O/U ratio and A and B are defined in equations (16) and (17).

Oxygen Concentration in Urania

To calculate oxygen concentration in urania, equations (11) and (13-15)are used to produce four equations which may be solved for O/U ratio by iter-ation. In these equations, the notation is simplified by setting U2 - N 2+,U4 - NU4+, U6 - NU6+, G2 - PoP/2 , * - 0/U and A and B are given by eqatons(16) and (17). Hence,

34

U2 - 1/[1 + G2*A/O + G22*A*B/$2] (19)

U4 - U2*G2*A/o (20)

U6 - U4-G2*B/m (21)

* - U2 + U4 + U6 (22)

The value of 0 may be obtained by starting with 0 = 2 and solving equations(19-22) through several iterations.

Model for U-Pu-0

Since the capture of a neutron by 2 3 8U lea 3 to production of severalplutonium isotopes at about the same rate as 235U is fissioned there willbe a significant amount of plutonium in the fuel as burnup of3U proceeds.An oxygen potential model has been devised for U-Pu-0 based on the sameprinciples used in the U0 2 model. The urania model is based on thermo-dynamic and phase data. The mixed oxide (U-Pu-0) model had to be fitted toexperimental oxygen-pressure measurements because of insufficient phase andthermodynamic data for the Pu-0 system. The U-Pu-0 model contains twotemperature-dependent constants in addition to those in equations (16) and(17). These constants are

C - exp (47000/T - 11.25) (23)

D - exp(25100/T - 4.9) (24)

In addition to the notation used for urania alone (see above ,4 the

following are used: Pu2 - NPu2+, Pu3 - NPu3+, Pu4 - Npu4+, G = yP2 (totalplutonium concentration) - Pu2 + Pu3 +Pu4, and 1-y (total uraniumconcentration) - U2 + U4 + U6. Seven equations are required todefine the system:

U2 - (1-y)/[1 + G2-A/. + G2 2 *AeB/42] (25)

U4 - U2.G2.A/# (26)

U6 - U4-G2-B/, (27)

Pu2 - y/[1 + G-C/ * + G2.C.D/.] (28)

Pu3 - Pu2eG*C/ * (29)

Pu4 - Pu3'GeD/ * (30)

* - U2 + 2U4 + 3U6 + Pu2 + 1.5Pu3 + 2Pu4 (31)

For a given temperature, the constants A, B, C and D may be calculated fromequations (16)i, 17), (23), fgg (24), respectively. For a given oxygen

pressure G - P02 and G2 - P0 2 . A trial value for * (e.g., * - 2)

and the plutonium concentration y are required. A few iterations of the

35

seven equations will provide the concentration for 4 between the metal-rich orsolidus boundary (4<2) and '2.1, for temperatures up to the melting point ofthe oxide. Oxygen pressures can be obtained for given * by solving severaliterations of equations (25-30), where the oxygen pressure (G2 and G) is varieduntil 4 calculated with equation (31) agrees with the desired 4.

Model for U-Pu-O-FP

A model for uranium-plutonium-oxide-fission product (FP) has been writtenbased on the same principles used for urania and urania-plutonia.However, thereare no reliable thermodynamic or oxygen pressure data for the U-Pu-0-FP system.Furthermore, phase data on the individual oxides are limited. The present U-Pu-O-FP model like the U-Pu-0 model is based on the assumption that all theoxides form an ideal solution. This assumption may be tenuous as some of thefission product oxides such as Rb2MoO4, Rb2UO4, Cs2UO4, and Cs2MoO4 may existas separate phases. Thus, the present model as described below needs somerevision, particularly with respect to the manner in which it handles thepotential dissolution of uranates and molybdates in the U-Pu oxide lattice andto the manner in which one estimates activity data for the halides (I and Br)and chalcogens (Te and Se) rather than assuming their concentration. Inaddition, the intermetallics and metal alloys must be included. The pressuresof volatile species are also required for the program to be complete.

The present U-Pu-0-FP model is described here to indicate what has beendone and what needs to be done to provide a complete model.

For fission products the temperature-dependent equilibrium constants arebased either on literature data for oxygen pressures over binary fission-product oxides or on integral thermodynamic data for fission-product oxidesystems adjusted for phase boundary effects observed in the U-0 and U-Pu-0systems.

The effects on oxygen potentials of the alkali and alkaline-earth uranatesand binary oxides, as well as the alkali molybdates, are included in the com-p'iter program. For computational purposes, barium and strontium were treatedas if the increased oxygen in the uranates were balanced by an increase in thevalence of barium or strontium cations from two to four. This expedient wasused because the concentration of BaU04 or SrU04 depends on the oxygenpressure and the barium or strontium concentration, rather than on the uraniumconcentration, even though the actual increase in the valance of uranium isfrom four to six.

A similar device was usec' to compute the amount of cesium and rubidium,which form either alkali uranates and/or molybdates. In this case, the cesiumand rubidium are considered to be either zero-valent or divalent, whereas, infact, they are monovalent, combined with hexavalent uranium and molybdenum, inthe uranates and molybdates, Although the uranates and molybdates are mostlikely to appear as separate phases, the present model treats these phases auif they were dissolved in. the fuel.

To simplify calculation, the fission products were grouped according tosimilarities in chemical properties. Thus, barium and strontium are combinedand labeled BS, cesium and rubidium are labeled CR, and yttrium and all the

36

rare earths, except cerium, are labeled RE. The rare earths, RE, are given afixed valence of three for all temperatures and compositions, whereas ceriummay be either trivalent or tetravalent, depending on the oxygen potential.

All the Se, Te, I, and Br are assumed to react with cesium and rubidium(CR) to form CR2Se, CR2Te,* CRI, and CRBr as separate phases that condense atthe cladding or at the cooler end of the fuel pin. The rubidium and cesiumconcentrations in the fuel are, therefore, reduced to account for the formationof halides, tellurides, and selenides.

Of the remaining fission products, only those forming relatively stableoxides are taken into account in the computation. Zirconium is trivalent andtetravalent. Niobium is zero-, di-, tetra-, or pentavalent. Molybdenum iszero- or tetravalent; thus, instead of being hexavalent as in the molybdates,the additional charge is ascribed to the alkali metal for computational con-venience (see above). Technetium and cadmium are zero- or divalent. Indiumand antimony are zero- and trivalent. Tin is zero-, di-, and tetravalent.

The computer subroutine Is outlined below. The chemical symbols (e.g.,U = uranium concentration) are used for concentrations of each element exceptwhere combinations are used as described above (e.g., CR - Cs + Rb). Thesesame symbols followed by digits are used for concentrations of cations of thegiven valence (e.g., Pu4 = concentration of Pi 4+). Single, double, or tripleletters followed by chemical symbols are used to identify the particularequilibrium constant. For example, QNb, QQNb, and QQQNb are equilibrium con-stants for calculating the di-, tetra-, and pentavalent niobium concentrations(Nb2, Nb4, and Nb5), respectively, as shown in equations (80-82). To calculatethe zero-valent niobium concentration, one requires all the equilibium con-stants, as seen in equation (79).

The subroutine requires temperature in kelvins (T); concentrations ofuranium (U), plutonium (Pu), oxygen (Ox), and all fission products describedabove; and trial values for the O/M ratio (OM equals oxyge , ivided by all themetal ions in the oxide phase), the oxygen pressure (G = P0 2 ), and thecesium pressure (PCS).

The cesium pressure may be controlled (1) by liquid 'esium at T1, thetemperature of the cladding inner surface, or (2) by dissociation of Cs2UO4 atT, the fuel surface temperature. The first case is given by

PCS - exp(-8655/Ti + 9.1) (32)

and the second is given by

PCS - exp(-58600/T + 23.6)/P02 (33)

where P0 2 is the oxygen pressure computed from the program. The lowerof these two cesium pressures is that used in the program. Becauseof the cesium-oxygen pressure relation, the PCS values are obtained byconvergence during iteration of the program.

*The existence of CR2Te is not definitely established. (See above.)

37

The equilibrium constants used in equations (59-91) are given by

AU xp(78300/T - 13.6)

AAU = exp(16500/T - 5.16)

BPu = exp(47000/T - 11.25)

BBPu = exp(25100/T - 4.9)

CBS = exp(47000/T - 12.6)

DCd = exp(38000/T - 14.7)

ECR = exp(70400/T - 29.5)

EECR = exp(99600/T - 31.7)

FCe = exp(20300/T - 4.9)

HIn = exp(73000/T -- 27.9)

PMo = exp(83600/T - 25.6)

QNb = exp(48800/T - 10.3)

QQNb = exp(59600/T - 14.4)

QQQNb = exp(22100/T - 4.8)

RSb = exp('48500/T - 19)

SSn = exp(43000/T - 14.5)

SSSn = exp(43600/T - 16.7)

VTe = exp(32000/T - 12.9)

WZr - exp(36300/T - 6.5)

The following relations are used for convenience:

G -=

G2 -

G3 =

G4 -

OM2 -

PO 1/4

G2

G3

G4

(o/M)2

(34)

(35)

(36)

(37)

(38)

(39)

(40)

(41)

(42)

(43)

(44)

(45)

(46)

(47)

(48)

(49)

(50)

(51)

(52)

(53)

(54)

(55)

(56)

(57)

38

02M = SQRT(0/M) (58)

While adjusting the value of the oxygen pressure (G = P0 ), the pro-gram iterates the equations given below until the oxygen pressure calculatedfrom the cation concentration in the fuel, Oy (equation 93), converges to thatin the fuel, Ox. The cesium pressure convergence also is involved in thisiteration.

Pu2 - Pu/(1 + GeBPu/02M + G2'BPueBBPu/OM)

Pu3 = G*BPu*Pu2/02M

Pu4 = G*BBPu'Pu3/02M

BS2 - BS/(1 + G2*CBS/OM)

BS4 = BS2*G2*CBS/OM

CdO - Cd/(1 + G2*DCd/OM)

Cd2 - CdO*G2*DCd/OM

CR0 = CR/(1 + G2'ECR*PCS + G4*EECR*PCS/0M2)

CRMo2a - CRO*G4*EECR*PCS/0M2

CRU2b - CRO'G2*ECR PCS/OM

U2 - (U - CRU2/2 - BS4)/(1 + G2eAU/OM + G4eAU-AAU/0M2)

U6 - U2 G4*AU*AAU/0M2

U4 - U - U2 - U6

CR2 - CRU2 + CRMo2

Ce3 - Ce/(1 + G*FCe/02M)

Ce4 - Ce3*G"FCe/02M

InO - In/(1 + G3eHIn/0M 3 / 2 )

In3 - In0G3*HIn/0M3/2

Moo - (Mo - CRMo2/2)/(1 + G4-PMo/0M2)

Mo4 - MoO*G4*PMo/0M2 + CrMo2/2

aCRMo2 - cesium + rubidium in Cs2MoO4 or Rb2Mo04.

bCRU2 - cesium + rubidium in Cs2UO4 or Rb2UO4.

(59)

(60)

(61)

(62)

(63)

(64)

(65)

(66)

(67)

(68)

(69)

(70)

(71)

(72)

(73)

(74)

(75)

(76)

(77)

(78)

39

NbO = Nb/(l + G2 eQNb/OM + G4*QNb*QQNb/0M2

+ G4*G*QNb*"QQNb"QQQNb/0M 5 / 2 ) (79)

Nb2 = NbO G2*QNb/OM (80)

Nb4 = Nb2*G2*QQNb/OM (81)

Nb5 = Nb4*G*QQQNb/02M (82)

SbO = Sb/(1 + G3*RSb/0M 3 / 2 ) (83)

Sb3 = SbO"G3*RSb/0M 3 / 2 (84)

SnO = Sn/(1 + G2*SSn/OM + G4*SSn*SSSn/0M2) (85)

Sn2 = SnO'G2'SSn/OM (86)

Sn4 = Sn2*G2*SSSn/OM (87)

TcO = Tc/(1 + G2*VTc/OM) (88)

Tc2 = Tc0*G2*VTc/OM (89)

Zr3 = Zr/(1 + G'WZr/02M) (90)

Zr4 = Zr3*G*WZr/02M (91)

OM = sum of all oxidized metals (92)

Oy = U2 + Pu2 + BS2 + Cd2 + CR2 + Nb2 + Sn2 + Te2+ 1.5(Pu3 + RE + Ce3 + In3 + Sb3 + Zr3)+ 2(U4 + Pu4 + BS4 + Ce4 + Mo4 + Nb4 + Sn4 + Zr4)+ 2.5Nb5 + 3U6 (93)

One method found useful for adjusting the oxygen pressure (G) is tochoose an initial oxygen potential (e.g., -100 kcal) and then add orsubtract from the chosen value an incremental potential (initially 50 kcal).After each iteration, the increment is diminished by 1/3. If Oy is greater(or less) than Ox, the increment is subtracted (or added). To calculatethe cation valence distribution, iteration is continued with each new valueof G until (Ox-Oy)/Ox is equal to the desired precision.

40

References

1. P. E. Blackburn, Oxygen Pressures Over Fast Breeder Reactor Fuel (I)A Model for UO2+x, J. Nucl. Mater. 46, 244-252 (1973).

2. P. E. Blackburn, in Chemical Engineering Division Fuels and MaterialsChemistry Semi-Annual Report, July-December 1972, Argonne NationalLaboratory Report ANL-7977, p. 2 (1973).

3. P. E. Blackburn, in Chemical Engineering Division Fuels and MaterialsChemistry Annual Report, July 1974-June 1975, Argonne NationalLaboratory Report ANL-75-48, p. 5 (1976).

4. P. E. Blackburn, in ChemicallEngineering Division Fuels and MaterialsChemistry Annual Report, July 1975-June 1976, Argonne NationalLaboratory Report ANL-76-103, p. 10 (1977).