TECHNICAL REPORTS SERIES No. 59

Thermal Conductivity

of Uranium Dioxide

J INTERNATIONAL ATOMIC ENERGY AGENCY,VIENNA, 1966

THERMAL CONDUCTIVITY OF URANIUM DIOXIDE

The following States are Members of the International Atomic Energy Agency:

AFGHANISTAN GABON NICARAGUA ALBANIA GERMANY, FEDERAL NIGERIA ALGERIA REPUBLIC OF NORWAY ARGENTINA GHANA PAKISTAN AUSTRALIA GREECE PANAMA AUSTRIA GUATEMALA PARAGUAY BELGIUM HAITI PERU BOLIVIA HOLY SEE PHILIPPINES BRAZIL HONDURAS POLAND BULGARIA HUNGARY PORTUGAL BURMA ICELAND ROMANIA BYELORUSSIAN SOVIET INDIA SAUDI ARABIA

SOCIALIST REPUBLIC INDONESIA SENEGAL CAMBODIA IRAN SOUTH AFRICA CAMEROON IRAQ SPAIN CANADA ISRAEL SUDAN CEYLON ITALY SWEDEN CHILE IVORY COAST SWITZERLAND CHINA JAMAICA SYRIAN ARAB REPUBLIC COLOMBIA JAPAN THAILAND CONGO, DEMOCRATIC JORDAN TUNISIA

REPUBLIC OF KENYA TURKEY COSTA RICA KOREA, REPUBLIC OF UKRAINIAN SOVIET SOCIALIST CUBA KUWAIT REPUBLIC CYPRUS LEBANON UNION OF SOVIET SOCIALIST CZECHOSLOVAK SOCIALIST LIBERIA REPUBLICS

REPUBLIC LIBYA UNITED ARAB REPUBLIC DENMARK LUXEMBOURG UNITED KINGDOM OF GREAT DOMINICAN REPUBLIC MADAGASCAR BRITAIN AND NORTHERN ECUADOR MALI IRELAND EL SALVADOR MEXICO UNITED STATES OF AMERICA ETHIOPIA MONACO URUGUAY FINLAND MOROCCO VENEZUELA FRANCE NETHERLANDS VIET-NAM

NEW ZEALAND YUGOSLAVIA

The Agency's Statute was approved on 23 October 1966 by the Conference ion the Statute of the IAEA held at United Nations Headquarters, New York; i t entered into force on 29 July 1951. The Headquarters of the Agency are situated in Vienna. Its principal object ive is "to accelera te and enlarge the contribution of a tomic energy to peace , health and prosperity throughout the world".

© IAEA. 1966

Permission to reproduce or translate the information contained in this publication may be obtained by writing to the International Atomic Energy Agency, Kärntner Ring 11, A-1010 Vienna I, Austria.

Printed by the IAEA in Austria July 1966

TECHNICAL REPORTS SERIES No. 59

THERMAL CONDUCTIVITY OF URANIUM DIOXIDE

REPORT OF THE PANEL ON THERMAL CONDUCTIVITY OF URANIUM DIOXIDE

HELD IN VIENNA. 2 6 - 3 0 APRIL 1965

INTERNATIONAL ATOMIC ENERGY AGENCY VIENNA, 1966

International Atomic Energy Agency. Thermal conductivity of uranium dioxide.

Report of the Panel on Thermal Conductivity of Uranium Dioxide held in Vienna, 26-30 April 1965. Vienna, the Agency, 1966.

68 p. (IAEA, Technical reports s e r i e s no. 59)

6 6 1 . 8 7 9 . 1 2 2 536. 2:661. 879 .122 6 2 1 . 0 3 9 . 5 4 3 . 4

THERMAL CONDUCTIVITY OF URANIUM DIOXIDE . IAEA, VIENNA, 1966 "

STl/DOC/lO/59

FOREWORD

B e c a u s e of the i m p o r t a n c e of t h e r m o d y n a m i c s in n u c l e a r t echno logy , the In te rna t iona l Atomic Energy Agency has been c a r r y i n g out a p r o g r a m m e on t h e t h e r m o d y n a m i c s of n u c l e a r m a t e r i a l s . T h i s p r o g r a m m e i n c l u d e s the holding of s y m p o s i a and pane l s , and the p r e p a r a t i o n of m o n o g r a p h s . Some of the Agency pub l i ca t i ons so f a r p r o d u c e d a r e : T h e r m o d y n a m i c s of N u c l e a r M a t e r i a l s (May 1962), and T h e r m o d y n a m i c s with E m p h a s i s on N u c l e a r M a t e r i a l s and Atomic T r a n s p o r t in Sol ids (July 1965), both in the P r o c e e d i n g s Se r i e s ; The Uran ium Carbon and P lu ton ium Carbon Sys tems -A The rmochemica l Asse s smen t (Technical Repor ts Ser ies No. 14); and Tables of Thermodynamic Data (Technical Repor ts Ser ies No. 38).

In March 1964 a panel was called to a s s e s s the thermodynamic and t r a n s -p o r t p r o p e r t i e s of u r a n i u m dioxide; t he p r o c e e d i n g s w e r e pub l i shed a s Techn ica l R e p o r t s S e r i e s No. 39. U r a n i u m dioxide i s of g rea t p r a c t i c a l i n t e r e s t in nuc lea r technology, being one of the m a j o r nuc lea r fue l s . At th i s mee t ing one of the t r a n s p o r t p r o p e r t i e s , t h e r m a l conductivity, could not be deal t with in de ta i l .

The Agency t h e r e f o r e convened a f u r t h e r panel mee t ing , held in Vienna on 26 -30 A p r i l 1965, t o a s s e s s and e v a l u a t e the t h e r m a l conduc t iv i ty of t he u r a n i u m dioxide p h a s e and the e f f e c t s of t e m p e r a t u r e , s t o i c h i o m e t r y , s ta te of aggrega t ion and i r r ad i a t i on . Attention was a l so paid to m e c h a n i s m s of hea t conduct ion. The f ind ings of t h i s pane l a r e p r e s e n t e d in the p r e s e n t pub l ica t ion .

V - 2 , Radia t ion conduct ivi ty 51 V - 2 . 1 . Index of r e f r a c t i o n 51 V - 2 . 2 . Absorp t ion coeff ic ient 52

V-3 , E l e c t r o n i c heat t r a n s f e r 55

VI. RECOMMENDED FUTURE WORK 59

R e f e r e n c e s 60

L i s t of p a r t i c i p a n t s 65

R e p o r t s submi t t ed to the P a n e l 67

I. INTRODUCTION

The e a r l y i nves t i ga t ions on the t h e r m a l conduct iv i ty of u r a n i u m dioxide i n d i c a t e d t h a t it b e h a v e d a s a c l a s s i c a l m e t a l ox ide i n s u l a t o r . T h e c o n -duc t iv i t y w a s found to be d e c r e a s e d by i r r a d i a t i o n , e s p e c i a l l y n e a r r o o m t e m p e r a t u r e , but the f e w e s t i m a t e s of t he i n t e g r a t e d t h e r m a l conduc t iv i ty b e t w e e n r o o m t e m p e r a t u r e and the m e l t i n g point v a r i e d qu i te w ide ly .

In 1961, it w a s p r o p o s e d that e n e r g y t r a n s f e r by pho tons enhanced the e f fec t ive conduct ivi ty in the high t e m p e r a t u r e co lumnar g r a i n - g r o w t h reg ion in a f u e l e l e m e n t . T h i s concept led to m u c h d i s c u s s i o n and c r i t i c i s m r e -s u l t i n g in the p r o d u c t i o n of a s u b s t a n t i a l a m o u n t of new e x p e r i m e n t a l da t a in the fol lowing f o u r y e a r s . T h e r e i s now good a g r e e m e n t on the va lues f o r t he t h e r m a l conduct iv i ty of p o l y c r y s t a l l i n e s t o i c h i o m e t r i c u r a n i u m dioxide up to 1300°C o u t - o f - r e a c t o r , the cu rve tak ing the f o r m k= 1/(A + BT). How-e v e r , t h e r e i s a c o n s i d e r a b l e amount of evidence to show that unde r c e r t a i n not too w e l l - d e f i n e d condi t ions , the t h e r m a l conduct ivi ty of u r a n i u m dioxide can be h ighe r t han the n o r m a l l y accep ted va lue . The magn i tude of t h i s i m -p r o v e m e n t and the t e m p e r a t u r e r a n g e o v e r wh ich it c a n be o b t a i n e d v a r y a p p r e c i a b l y in the v a r i o u s inves t iga t ions . I n - r e a c t o r , however , t h e r e i s no d i r e c t evidence of a s ign i f ican t i n c r e a s e be ing r e a l i z e d . As a r e s u l t of both the t e c h n o l o g i c a l and s c i e n t i f i c i n t e r e s t in t h e r m a l conduct ion p r o c e s s e s in UO2 the IAEA c o n s i d e r e d the t i m e a p p r o p r i a t e t o a p p r a i s e the c u r r e n t i n -f o r m a t i o n and a pane l m e e t i n g was ca l led . Th is r e p o r t g ives a s u m m a r y of the data p r e s e n t e d at t he mee t ing and of the conclus ions r e a c h e d .

The P a n e l c o n s i d e r e d t h r e e spec i f i c a s p e c t s :

(a) A r e v i e w of a l l da ta on u n i r r a d i a t e d UO2 with s p e c i f i c a t t en t i on to the e f f e c t s of compos i t ion and g ra in s i ze , with an a t t empt to def ine the i m -po r t an t v a r i a b l e s ;

(b) A c r i t i c a l e x a m i n a t i o n of the i r r a d i a t i o n r e s u l t s c o m p a r e d , w h e r e a p -p r o p r i a t e , with the o u t - o f - r e a c t o r data , and a cons ide ra t ion of the con-di t ions unde r which it might be pos s ib l e to a t t a in i n c r e a s e d conductivi ty in an opera t ing f u e l e l ement ;

(c) A d i s c u s s i o n of t he e x p e r i m e n t a l da ta in t e r m s of t he m e c h a n i s m s by which heat i s conducted in UO2. In t h e i r d i s c u s s i o n s the p a n e l m e m b e r s e m p h a s i z e d the e x p e r i m e n t a l

a s p e c t s s ince the t h e o r y had not been advanced s igni f ican t ly dur ing the y e a r fol lowing the r e v i e w given in the r e p o r t of the P a n e l on T h e r m o d y n a m i c and T r a n s p o r t P r o p e r t i e s of Uran ium Dioxide and Re la t ed P h a s e s [1] . Alloying addi t ions , inc luding p lu ton ium, w e r e not c o n s i d e r e d .

F o r the work of the pane l it was r e c o m m e n d e d that s t o i c h i o m e t r i c u r a -n ium dioxide be def ined a s including the r ange f r o m UO2.000 to UO2.010 • Th is range of s to i ch iome t ry was chosen because : (a) it is within these O / U values that most UOz f ue l s a r e being fabr ica ted ; (b) the de terminat ion of O/U values m a y v a r y f r o m one s i t e t o a n o t h e r and m a y not a l w a y s be a c c u r a t e to t h e t h i rd d e c i m a l p lace ; (c) it can be ques t ioned if any t h e r m a l conductivi ty data have been obtained f o r exact ly s to ich iomet r i c u ran ium dioxide; and (d) values of t h e r m a l conduc t iv i ty above r o o m t e m p e r a t u r e do not v a r y s i g n i f i c a n t l y in t h i s O / U r a n g e .

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No a t t e m p t w a s m a d e t o p r o d u c e a c o m p l e t e , b a l a n c e d r e v i e w of a l l avai lable data . In those a r e a s where the data were found to be in good agree -m e n t and had a l r e a d y been r e v i e w e d fu l l y in t h e p u b l i s h e d l i t e r a t u r e , t h e e s s e n t i a l f a c t s a r e given, t o g e t h e r with r e c o m m e n d e d b e s t v a l u e s . W h e r e the da t a a r e c o n t r o v e r s i a l , o r new da ta a r e a v a i l a b l e , a m o r e c o m p r e -h e n s i v e r e v i e w i s g iven . W h e r e a p p r o p r i a t e , r e c o m m e n d a t i o n s have been m a d e f o r f u t u r e a r e a s of s tudy .

II. T H E R M A L CONDUCTIVITY O F UNIRRADIATED URANIUM DIOXIDE

T h e t h e r m a l conduct iv i ty of u n i r r a d i a t e d u r a n i u m dioxide h a s been m e a s u r e d by many w o r k e r s [2-28] . Much of the e a r l y work was p e r f o r m e d with poor ly c h a r a c t e r i z e d or u n r e p r e s e n t a t i v e m a t e r i a l s , and has s ince been s u p e r s e d e d by m o r e a c c u r a t e e x p e r i m e n t s .

B e c a u s e of the ava i l ab i l i ty of, and t echno log i ca l i n t e r e s t in, nomina l ly s t o i c h i o m e t r i c , p o l y c r y s t a l l i n e u r a n i u m dioxide, much of the m o r e p r e c i s e work has been done on th i s non- idea l m a t e r i a l . Single c r y s t a l s have recent ly b e c o m e a v a i l a b l e but i n s t e a d of c l a r i f y i n g the s u b j e c t , da t a ob ta ined f r o m s i n g l e - c r y s t a l m a t e r i a l have shown f u r t h e r unexp la ined i n c o n s i s t e n c i e s , which m u s t in p a r t be a t t r i b u t e d to the e f f e c t s of u n c h a r a c t e r i z e d (and u n -known) p a r a m e t e r s .

B e f o r e the data f r o m d i f fe ren t w o r k e r s can be i n t e r c o m p a r e d , c o r r e c t i o n s have to be m a d e f o r d i f f e r e n c e s b e t w e e n s p e c i m e n s due t o f a c t o r s such a s p o r o s i t y , О / U r a t i o , i m p u r i t i e s and g r a i n s i z e . (See s ec t i on I I - 2 . ) C o m -p a r i s o n s can be obscu red if the c o r r e c t i o n s involved a r e l a r g e . The e a r l i e r data on t h e r m a l conductivity w e r e often obtained f r o m m a t e r i a l of low density o r u n c e r t a i n compos i t i on , homogene i ty , o r s t r u c t u r a l u n i f o r m i t y ; e x t r a p o -l a t ion of t h e s e r e s u l t s t o c o m p a r e t h e m to the m o r e m o d e r n data usua l ly i nvo lves c o n s i d e r a b l e u n c e r t a i n t y .

T h e r e f o r e , in t h i s s ec t ion we have men t ioned the e a r l i e r work b r i e f l y , and concen t r a t ed in m o r e de ta i l on data obtained f r o m h ighe r densi ty , b e t t e r c h a r a c t e r i z e d u ran ium dioxide. The m a j o r i t y of th i s m a t e r i a l was of 92-97% of f u l l t h e o r e t i c a l dens i ty (TD), with O / U r a t i o s of 2. 0 0 5 ± 0 . 005; i n t e r c o m -p a r i s o n of da ta i s , t h e r e f o r e , l i t t l e a f f ec t ed by n o r m a l i z a t i o n e r r o r s .

I I -1 . T E M P E R A T U R E S BELOW 300°K

T h e r m a l conduct ivi ty m e a s u r e m e n t s in the low t e m p e r a t u r e range f r o m 4 to 300°K have been m a d e by Bethoux et a l . [12] on s i n t e r e d po lycrys ta l l ine m a t e r i a l s and by Penninckx [ 18] and S i e v e r s and Poh l [26] on single c r y s t a l s . M e a s u r e m e n t s have a l s o been made by Godfrey et a l . [10] on po lycrys ta l l ine U 0 2 a s low a s 195°K. The d e n s i t i e s of t he s i n t e r e d p o l y c r y s t a l s u s e d by Bethoux et a l . and Godfrey et a l . w e r e 90. 9 and 93.4%, r e spec t ive ly of theo-

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L1 J 4 /

s / \

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L1 J 4 /

CURVES REFERENCES ELECTRICAL CONDUCTIVITY fotwT' cm*1)

CRYSTAL

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/ > / X

L1 J 4 / 1

2 î 4 5

M [ 2 « [«a De] [1(0

>2.001 -2.001 -2.001 2.01Î0.01

1.7 k 10"^ 1.7 д 10"® 2.5 x10"6

POLY SINGLE SINGLE SINGLE POLY /

/

w /

1 2 î 4 5

M [ 2 « [«a De] [1(0

>2.001 -2.001 -2.001 2.01Î0.01

1.7 k 10"^ 1.7 д 10"® 2.5 x10"6

POLY SINGLE SINGLE SINGLE POLY /

/

w /

6 [ г а - - SINGLE

/ /

w /

TEMPERATURE CK )

FIG. 1. Low temperatures U02 thermal conductivity

r e t i c a l dens i ty , 10 .97 g / c m 3 . The m e a s u r e d c u r v e s of к . v e r s u s Т a r e shown in F i g . 1; t h e r e s u l t s have not been c o r r e c t e d to t h e o r e t i c a l d e n s i t y .

A m i n i m u m in the t h e r m a l conductivi ty c o r r e s p o n d i n g to a p a r a m a g n e t i c a n t i - f e r r o m a g n e t i c t r a n s i t i o n h a s b e e n o b s e r v e d a t 30°K, and the e x p e r i -m e n t s have a l s o shown tha t the cu rve of к v e r s u s T p a s s e s through a m a x i - ' m u m at about 300°K.

Be tween 4 and 200°K, the data ob ta ined by P e n n i n c k x [18] and S i e v e r s and P o h l [26] u s i n g s i n g l e - c r y s t a l m a t e r i a l wi th O / U r a t i o s l a r g e r t h a n 2 . 0 0 1 a r e a p p r o x i m a t e l y s i m i l a r to t h o s e of Be thoux et a l . [12] f o r p o l y -c ry s t a l l i ne u r a n i u m dioxide. However , Penninckx [18] a l so found that s ingle c r y s t a l s (O/U r a t i o s below 2. 001) showed much higher t h e r m a l conductivi t ies b e t w e e n 4 and 30°K; t h e l o w e r the O / U r a t i o , t he h i g h e r t h e t h e r m a l c o n -ductivity. Th i s sugges t s that gra in s ize was not the f ac to r l imit ing the m e a n -f r e e pa th of the phonons in the s p e c i m e n s of high oxygen content; sma l l U4O9 p r e c i p i t a t e s h o m o g e n e o u s l y d i s t r i b u t e d in t h e UO2 m a t r i x w e r e p r o b a b l y r e s p o n s i b l e .

T h e s h a p e of t h e o b s e r v e d t h e r m a l conduc t iv i ty c u r v e s of U 0 2 s i n g l e c r y s t a l s and s i n t e r e d p o l y c r y s t a l s be tween 30 and 300°K may be adequa te ly a s c r i b e d to the f ac t that the heat capaci ty i n c r e a s e s rap id ly in t h i s t e m p e r a -t u r e r a n g e . The d i f f e r e n t v a l u e s obtkined a t 300°K f o r s i n g l e - c r y s t a l and p o l y c r y s t a l l i n e UO2 may be r e l a t e d to d i f f e r e n c e s in the O / U r a t i o and d e n -s i ty . (See sec t ion I I -2 . 1 to I I -2 . 3.)

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II—2. T E M P E R A T U R E S ABOVE 300°K

II-2. 1. Poly crystalline U02.oos±o. oos , density 92-97% of theoretical

I I - 2 . 1. 1. T e m p e r a t u r e s u p t o 1 3 0 0 ° C

T h e f i r s t d a t a on t h e v a r i a t i o n of t h e r m a l c o n d u c t i v i t y of u r a n i u m d i -ox ide o v e r a l a r g e t e m p e r a t u r e r a n g e w e r e p u b l i s h e d by K i n g e r y e t a l . [2] in 1954. They u s e d a c o m p a r a t i v e , long i tud ina l h e a t - f l o w me thod , but s i n c e t h e i r U 0 2 w a s of 73% of the t h e o r e t i c a l dens i t y , e x t r a p o l a t i o n t o h i g h e r d e n -s i t y n e c e s s i t a t e d a l a r g e p o r o s i t y c o r r e c t i o n .

Hedge and F i e l d h o u s e [4] used a r a d i a l h e a t - f l o w t echn ique , c a l i b r a t i n g t h e a p p a r a t u s a g a i n s t A r m c o i r o n . The U 0 2 d e n s i t y w a s 74.6% of t h e o r e t i c a l , and the v a l u e s o b t a i n e d w e r e abou t 20% l o w e r t h a n t h o s e of K i n g e r y et a l . ; t h e a u t h o r s m e n t i o n e d t h a t t he i r - s p e c i m e n s had shown m i c r o - c r a c k i n g .

T h e l a r g e r e l a t i v e c o r r e c t i o n f o r p o r o s i t y and the u n c e r t a i n t y in r e s p e c t of t h e c h o i c e of t h e c o r r e c t i o n f a c t o r f o r t h e s e low d e n s i t y v a l u e s m a k e it d i f f i cu l t to c o m p a r e t h e s e two s e t s of r e s u l t s wi th the r e c e n t da t a . (See s e c t i o n I I - 2 . 1. 3.)

Scot t [7] m a d e m e a s u r e m e n t s on UO2 s i n t e r e d in a r g o n at 1400°C, then r e d u c e d i n h y d r o g e n ; t h e d e n s i t y of h i s s p e c i m e n w a s 96% of t h e o r e t i c a l . The s p e c i m e n w a s h e a t e d by p a s s i n g a c u r r e n t t h rough it, and the conduct iv i -ty m e a s u r e d be tween 800 and 1150°C.

Howard and Gulvin [3] m a d e m e a s u r e m e n t s on s a m p l e s of a p p r o x i m a t e l y 95% of t h e o r e t i c a l d e n s i t y b e t w e e n 100 and 1 5 0 0 ° C . S p e c i m e n s of d e n s i t y 10. 5 g / c m 3 (96% T D ) s i n t e r e d a t 1400°С i n a r g o n and r e d u c e d t o a s t o i -c h i o m e t r i c c o m p o s i t i o n in h y d r o g e n showed a t h e r m a l conduc t iv i ty a p p r o x i -m a t e l y 15% l e s s t h a n s p e c i m e n s s i n t e r e d in c r a c k e d N H 3 at 1700°C . T h i s d i f f e r e n c e b e c a m e l e s s a t h i g h e r t e m p e r a t u r e s . It i s p o s s i b l e t h a t t h e low conduc t iv i ty of s o m e s p e c i m e n s i s due to e x c e s s oxygen ( s ee a l s o s e c t i o n I I -2 .3 ) o r m i c r o - c r a c k i n g .

T h e e f f e c t of f a b r i c a t i o n v a r i a b l e s w a s s tud i ed by L u c k s and D e e m [27] and Dan i e l et a l . [9] , who m e a s u r e d conduc t iv i t i e s f o r s i n g l e - c r y s t a l s p e c i -m e n s , s i n t e r e d and e x t r u d e d s p e c i m e n s and c o m p a c t e d c r u s h e d p a r t i c l e s . T h e y u s e d c o m p a r a t i v e l o n g i t u d i n a l h e a t - f l o w m e t h o d s ; m e a s u r e m e n t s on s i n t e r e d s p e c i m e n s v a r i e d by up t o 20% wi th a s c a t t e r of 10%. T h e s i n g l e -c r y s t a l r e s u l t s a r e d i s c u s s e d f u r t h e r in s e c t i o n I I - 2 . 3.

R e i s w i g [6] e m p l o y e d a r a d i a l h e a t - f l o w t echn ique , m e a s u r i n g t e m p e r a -t u r e s wi th an op t i ca l p y r o m e t e r , and d e t e r m i n e d t h e r m a l conduct iv i ty v a l u e s b e t w e e n 830 and 2110°С f o r s p e c i m e n s of 85% of t h e o r e t i c a l dens i ty .

Vogt et à l . [25] m a d e m e a s u r e m e n t s us ing a high t h e r m a l g rad ien t r a d i -an t h e a t - f l o w a p p a r a t u s on s p e c i m e n s of 97% of t h e o r e t i c a l d e n s i t y b e t w e e n 150 a n d 2 0 0 0 ° C , and on s p e c i m e n s of 88. 8 t o 97. 9% of t h e o r e t i c a l d e n s i t y up t o 1200°C. Up t o 1200° С t e m p e r a t u r e s w e r e m e a s u r e d by t h e r m o c o u p l e , and a b o v e t h i s by o p t i c a l p y r o m e t r y u s i n g r a d i a l s igh t h o l e s . C o r r e c t i o n s w e r e m a d e t o a l l o w f o r c h a n g e s in t h e e m i s s i v i t y of t h e UO2 s i n c e t h e m e a s u r e m e n t s w e r e not m a d e u n d e r b l a c k body c o n d i t i o n s . T h e m e a s u r e -m e n t s m a d e by t h e r m o c o u p l e s w e r e g e n e r a l l y up t o 15% h i g h e r t h a n t h o s e by p y r o m e t r y , w h e r e t h e two t e c h n i q u e s o v e r l a p p e d , so the a u t h o r s n o r -m a l i z e d t h e h igh t e m p e r a t u r e p o r t i o n of t h e c u r v e t o a g r e e wi th t h e p o r t i o n

•4

d e r i v e d f r o m t h e r m o c o u p l e m e a s u r e m e n t s . The abso lu te v a l u e s f r o m con -duc t iv i ty above 1200°C a r e , t h e r e f o r e , s u s p e c t , t hough t h e r e i s p o s s i b l y m o r e s i g n i f i c a n c e in the f a c t tha t the a u t h o r s found l i t t l e o r no i n c r e a s e in conduct iv i ty with i n c r e a s i n g t e m p e r a t u r e .

G o d f r e y et a l . [10] m a d e m e a s u r e m e n t s b e t w e e n - 5 7 and 1300°C on s p e c i m e n s of 93.4% of t h e o r e t i c a l dens i ty . A r a d i a l h e a t - f l o w method with a t e m p e r a t u r e g rad ien t of l e s s than 25°С was used; t h e i r t e m p e r a t u r e s w e r e m e a s u r e d with the rmocoup les , and the work was of high prec is ion , the quoted probable e r r o r being 0. 01 (equivalent to a s tandard deviation of ± 1 . 5%).

S t o r a et a l . [16] m a d e m e a s u r e m e n t s on s p e c i m e n s of 92. 2% of t h e o -r e t i c a l dens i ty be tween 300 and 2400°C. They de r ived the s h a p e of the t e m p e r a t u r e p r o f i l e s th rough the cen t r a l ly hea ted cy l indr ica l s p e c i m e n f r o m m e a s u r e m e n t s at fou r points in the spec imen . Up to 1300°С these m e a s u r e -m e n t s w e r e m a d e with t h e r m o c o u p l e s , but above t h i s t he h ighes t t e m p e r a -t u r e point w a s ob ta ined f r o m an e x p e r i m e n t a l c a l i b r a t i o n r e l a t i n g the U 0 2 t e m p e r a t u r e to that of the h e a t e r rod . The r e s u l t s a r e quoted to an accu racy of ±7%. Above 1300°C the expe r imen ta l uncer ta in ty may be h igher .

F e i t h [20] u s e d a s p e c i m e n of 97% of t h e o r e t i c a l dens i ty f o r m e a s u r e -m e n t s b e t w e e n 600 and 2000°C, e m p l o y i n g à r a d i a l h e a t - f l o w m e t h o d wi th a t e m p e r a t u r e d i f f e r e n c e a c r o s s the s p e c i m e n of l e s s t h a n 2 5 ° C . Above 1000° С t e m p e r a t u r e s w e r e m e a s u r e d by opt ical p y r o m e t r y , with sight ho les a long i s o t h e r m s .

H e t z l e r and Z e b r o s k i [23] m e a s u r e d the conduct iv i ty b e t w e e n 800 and 1850° С by p y r o m e t e r m e a s u r e m e n t s down r a d i a l sight ho les in a cy l i nd r i ca l s p e c i m e n with high t h e r m a l g r ad i en t s . This method i s subject to the s a m e e x p e r i m e n t a l u n c e r t a i n t i e s a s t h e m e t h o d of Vogt et a l . [25] and N i s h i j i m a et a l . [17], name ly those due to evapora t ion and condensat ion of UO2 vapour in the r ad ia l sight holes and to non-black body condit ions. At lower t e m p e r a -t u r e s Ni sh i j ima et a l . used t h e r m o c o u p l e s and a longitudinal hea t - f low type of a p p a r a t u s t o m e a s u r e the t h e r m a l conduc t iv i t i e s of s p e c i m e n s of 95% of t h e o r e t i c a l dens i ty .

W h e e l e r [22] m e a s u r e d the t h e r m a l d i f fu s iv i ty of f ine g r a i n , 97, 7% of t h e o r e t i c a l dens i ty , m a t e r i a l us ing a pu l s ed e l e c t r o n b e a m technique b e -tween 900 and 1800°C.

T h e m e a s u r e d v a l u e s of t he t h e r m a l conduc t iv i t y f r o m the a b o v e d e -t e r m i n a t i o n s a r e given in Tab le I, with no c o r r e c t i o n f o r d i f f e r e n c e s in po -r o s i t y . Unfor tunate ly , in many i n s t a n c e s a c r i t i c a l evaluat ion of d i f f e r e n c e s be tween data i s not pos s ib l e , b e c a u s e of the lack of e x p e r i m e n t a l de ta i l . To avoid v e r y l a r g e n o r m a l i z a t i o n c o r r e c t i o n s we have c o m p a r e d data f o r m a -t e r i a l of 92 to 97% of t h e o r e t i c a l densi ty , u s i n g t h e po ros i t y c o r r e c t i o n f a c t o r r e c o m m e n d e d in sec t ion II—2. 1. 3, and p r e s e n t t h e s e data n o r m a l i z e d to 95% of fu l l t h e o r e t i c a l dens i ty in Table II. It should be emphas i zed that t h i s c o r -r ec t ion depends on the m i c r o s t r u c t u r e of the spec imen , and i s not n e c e s s a r i -ly va l i d f o r a l l the s p e c i m e n s in the t a b l e . T h e e r r o r i n t r o d u c e d by t h i s n o r m a l i z a t i o n should be l e s s t han ±4% ( c o n s i d e r i n g t h e m a x i m u m l i m i t s of the p o r o s i t y c o r r e c t i o n ) b e c a u s e of the c l o s e s i m i l a r i t y in d e n s i t i e s .

Some of the da ta on t h e r m a l conduct ivi ty a r e s u m m a r i z e d in F i g . 2. No a t tempt has been made to n o r m a l i z e the data in th i s f igure , but even so t h e r e i s r e a s o n a b l e a g r e e m e n t up to about 1300° С wi th in the l i m i t s of p r o b a b l e e x p e r i m e n t a l e r r o r s .

5

TABLE I

M E A S U R E D VALUES O F T H E T H E R M A L C O N D U C T I V I T Y O F P O L Y C R Y S T A L L I N E URANIUM DIOXIDE k(W c m " 1 d e g C " 1 )

T e m p e r a t u r e .

CO

K i n g e r y

e t a l .

[ 2 ]

7 3 % T D

H e d g e a n d -

F i e l d h o u s e

[ 4 ]

7 4 . 6% T D

R e i s w i g

' [ 6 ]

8 5 % T D

S c o n

• [ 7 ]

96% T D

H o w a r d '

a n d G u l v i n

[ 3 ]

9 6 % T D

a

L u c k s

a n d D e e m

[ 2 7 ]

9 6 . 5% T D

b

D a n i e l e t a l .

[ 9 ]

9 6 . 5ïo T D

b

F e i t h

[ 2 0 ]

9 7 . 9 % T D

V o g t e t a l .

[ 2 5 ]

9 7 % T D

G o d f r e y e t a l .

[ 1 0 ]

9 3 . 4 % T D

S t o r a e t a l .

[ 1 6 ]

9 2 . 2 % T D

H e t z l e r a n d

Z e b r o s k i

[ 2 3 ]

N i s h i j i m a

e t a l .

' [ 1 7 ]

9 5 % T D

W h e e l e r .

[ 2 2 ]

9 7 . 7 % T D

. 2 0 0 0. 0 5 9 3 0. 0 3 9 0 0 . 0 5 5 2 - ' 0. 0 6 2 0 . 0 6 2 7 0 . 0 5 8 2 - 0 . 0 6 1 4

• 3 0 0 0 . 0 5 0 3 : 0 . 0 3 5 0 0 . 0 4 9 2 0 . 0 5 5 - 0. 0 5 3 0 . 0 5 5 2 0 . 0 5 2 4 0 . 0 5 2 0 0 . 0 5 5 5

4 0 0 0 . 0 4 3 0 0. 0 3 1 6 0 . 0 4 4 0 0 . 0 5 0 0. 047 0 . 0 4 9 0 0 . 0 4 6 5 0 . 0 4 6 3 0 . 0 4 9 6

5 0 0 0. 0 3 7 7 • 0 . 0 2 8 7 0 . 0 3 9 6 0 . 0 4 6 0. 0 4 3 0 . 0 4 3 5 0 . 0 4 1 8 0 . 0 4 1 7 0 . 0 4 4 0

6 0 0 0. 0 3 3 0 0 . 0260 . 0 . 0 3 7 2 0. 0 4 1 0. 0 3 9 5 0 . 042 0 . 0 4 0 0 0 . 0 3 8 1 0 . 0 3 7 8 0 . 0 3 8 7

7 0 0 0. 0 2 9 7 0 . 0 2 3 8 0 . 0 3 4 6 0. 0 3 7 0. 0 3 6 5 0 . 0 3 9 0. 0 3 6 7 0 . 0 3 4 8 0 , 0 3 4 6 0 . 0 3 4 4

8 0 0 0. 0 2 7 5 0 . 0 2 1 9 0 . 0 2 5 . 0 . 0 3 3 6 0. 0 3 2 2 0. 0 3 3 0 . 0 3 4 7 0. 037 0 . 0 3 4 0 0 . 0 3 2 2 0 . 0 3 1 8 0. 0 3 0 . 0 3 0 7

9 0 0 . 0. 0 2 6 3 0 . 0 2 0 2 0. 024. 0. 0 3 0 3 0. 0 3 0 4 0. 030 0 . 0 3 2 5 0 . 0 3 5 0. 0 3 2 0 0 . 0 2 9 8 0 . 0 2 9 5 0. 0 2 7 4

1 0 0 0 0 . 0 2 5 5 0. 0 1 8 7 0 , 023 - 0 . 0 2 7 7 0 . 0 2 8 6 0. 0 2 8 0 . 0 3 0 5 0 . 0 3 3 0 . 0 3 0 0 0 . 0 2 7 8 0 . 0 2 7 3 0 . 0 2 4 6 • 0. 0 3 4 8

- .1100 0. 0 1 7 5 0 . 022 0. 0 2 5 7 0 . 0 2 7 6 ' 0. 0 2 6 0. 0 2 8 5 Ö. 0 3 1 0 ; 0 2 9 2 0 . 0 2 6 3 0 . 0 2 5 6 0. 02

0 . 0 3

0 . 02 2 5 0. 0 3 3 2

1 2 0 0 0 . 0 1 6 6 0 . 0 2 1 0. 0 2 6 6 0. 0 2 7 0 . 0 3 0 5 0 . 0 2 8 5 0. 0 2 4 6 0 . 0 2 4 1 0. 0 2 0 8 0. 0 3 1 6

1 3 0 0 0 . 0 1 6 0 0 . 0 2 0 0. 0 2 6 0 0 . 0 3 0 0 . 0 2 7 6 0. 0 2 3 4 0 . 0 2 3 0 0 . 0 2 0 2 0. 0 3 0 2

1 4 0 0 0. 0 1 5 0 0 . 0 1 9 0 . 0 2 9 0 . 0 2 7 0 0 . 0 2 2 3 0. 02 0 0 0. 0 2 8 6

1 6 0 0 0 . 0 1 4 2 0 . 0 1 8 0. 0 2 9 0 . 0 2 6 5 0 . 0 2 1 6 0 . 0 2 2 0. 0 2 2 3 0. 0 2 5 6

1 8 0 0 0. 017 0. 0 2 9 5 0 . 0 2 6 2 0 . 0 2 2 2 0 . 0 2 0 0. 0 2 6 8

2 0 0 0 0. 016 0. 0 3 0 0 . 0 2 6 0 0 . 0 2 3 9 0 . 0 3 4 7

2 2 0 0 0. 0 3 2 ' 0 . 0 2 6 6

2 4 0 0 0 . 0 3 0 6

a S p e c i m e n s i n t e r e d .in N 2 .

b S p e c i m e n Ar f i r s t e x p e r i m e n t .

TABLE VI

VALUES FOR THE THERMAL CONDUCTIVITY OF SINTERED, PO L Y CR YS T A L LI NE UO2.005 , CORRECTED TO 95% OF F U L L

THEORETICAL DENSITY ( s e e s e c t i o n II-2 , 2. 1) k ( W c m - i degC"1)

T e m p e r a t u r e D a n i e l Fe i th Vogt e t a l . Stora e t a l . Godfrey N i sh i j ima (•C) e t a l . [ 9 ] [ 2 0 ] [ 2 5 ] [ 1 6 ] e t a l . [ 1 0 ] e t a l . [ 1 7 ]

wi th s ta ted error l i m i t s of:

iSPJa ±10% i7

0.08

0.07

0.06

0.05

t J 0.04 at u •о t 003 I

0.02

0.01

О 500 1000 1500 2000 2500 TEMPERATURE (°C>

FIG. 2. Thermal conductivity of unirradiated polycrystalline UOj.oo . corrected to 95% TD using 6 =2.5

II—2. 1. 2. T e m p e r a t u r e s above 1300°C

Above 1300° С the l i t e r a t u r e i s not in such good a g r e e m e n t (Table I, F ig .2) . T h i s i s p r o b a b l y due to t h e e x p e r i m e n t a l d i f f i c u l t i e s of m e a s u r i n g t h e r m a l conduct ivi ty at high t e m p e r a t u r e s , but may a l s o r e f l e c t changes in spec imen c o m p o s i t i o n s d u r i n g the d e t e r m i n a t i o n s o r r e a l d i f f e r e n c e s b e t w e e n i n d i -v idua l s p e c i m e n s . As can be seen , s o m e w o r k e r s f ind a cons tan t t h e r m a l conduc t iv i t y at t e m p e r a t u r e s above 1500° C, but t he c o n s e n s u s of op in ion s e e m s to be t h a t t h e t h e r m a l conduc t iv i ty i n c r e a s e s wi th i n c r e a s i n g t e m p e r a t u r e .

S t o r a et a l . [16] found a n . u p t u r n in the conduc t iv i ty o v e r 1600°C; t h e i n c r e a s e at 2400° С i s a p p r o x i m a t e l y 30% above the m i n i m u m va lue . F e i t h [20] a l s o found an i n c r e a s e above 1500°C, though the m a g n i t u d e i s r a t h e r l e s s (12% i n c r e a s e b e t w e e n 1500 and 2200°C) . Howeve r , F e i t h ' s s p e c i m e n may not be t r u l y r e p r e s e n t a t i v e of U02 . oos > s ince , al though it was ana lysed to be U0 2 . oi. he o b s e r v e d a d i s p e r s i o n of m e t a l l i c , u r a n i u m - r i c h p a r t i c l e s t h roughou t the s p e c i m e n , the p r e s e n c e of which i s u sua l l y t a k e n to be evidence of hypos to ich iomet ry . (See sec t ion II. 2. 2.) Although the absolute v a l u e s of Vogt e t a l . [25] a r e p o s s i b l y in e r r o r , t h e r e m a y be m o r e c o n -f idence in the r e l a t i v e va lues , in which c a s e the absence of any r i s e in con -duct iv i ty above 1500°C i s p robab ly s ign i f i can t .

R e i s w i g [6] d e t e c t e d no u p t u r n in conduc t iv i ty up t o about 2100°C; h i s s p e c i m e n was of low dens i ty so t h i s behav iou r i s not n e c e s s a r i l y typ ica l of m a t e r i a l of 95% of t h e o r e t i c a l densi ty . Nish i j ima et al. [17] r epo r t ed a ve ry m a r k e d i n c r e a s e in conductivity above 1400°C, whe reas Hetz le r a n d Z e b r o s k i [23] and Whee le r [22] found no i n c r e a s e up to 1800°C.

V \

X DANIEL ETAL. [9]

STORA ETAL.[ l6j

VOGT ET Al. [25]

GOOFREY ET AL. [ id ]

FEITH [20]

NISHIJIMA ETAL. [ l7]

w • A

DANIEL ETAL. [9]

STORA ETAL.[ l6j

VOGT ET Al. [25]

GOOFREY ET AL. [ id ]

FEITH [20]

NISHIJIMA ETAL. [ l7]

DANIEL ETAL. [9]

STORA ETAL.[ l6j

VOGT ET Al. [25]

GOOFREY ET AL. [ id ]

FEITH [20]

NISHIJIMA ETAL. [ l7]

• WHEELER [22]

8

T h e m o s t r e l i a b l e m e a s u r e m e n t s , t h o s e due t o S t o r a et a l . [16] and F e i t h [20] , i n d i c a t e an u p t u r n in conduc t iv i ty at h igh t e m p e r a t u r e s , whi le o ther , m o r e ques t ionable m e a s u r e m e n t s show no i n c r e a s e with t e m p e r a t u r e . In the absence of quant i ta t ive a g r e e m e n t between two de t e rmina t i ons we c a n -not de f ine a unique conduc t iv i ty c u r v e above 1300° C; a l l we can s a y i s t h a t the mos t p robab le f o r m a p p e a r s to be that due to Stora et a l . , but some s p e c i m e n s m a y show l o w e r v a l u e s , down t o a p o s s i b l e m i n i m u m of about 0. 022 W cm" 1 degC-i independent of t e m p e r a t u r e (above 1600°C). If an en -h a n c e m e n t in conduct iv i ty i s due to hea t t r a n s f e r by pho tons ( s ec t i on V - 2 ) , f a c t o r s such a s gra in s ize , s ize dis t r ibut ion of poros i ty and smal l d i f fe rences in O / U r a t i o may a f fec t t h i s high t e m p e r a t u r e reg ion ve ry marked ly , so the obse rved d i f f e r e n c e s between s p e c i m e n s may be r e a l and not a consequence of d i f f e ren t e x p e r i m e n t a l t echn iques .

I I -2 . 1. 3. E f fec t of dens i ty

It i s conven ien t ( though t h e o r e t i c a l l y not f u l l y j u s t i f i e d ) t o r e p r e s e n t the e f f ec t of changes in dens i ty on the t h e r m a l conduct iv i ty in t e r m s of t he equat ion

w h e r e кд i s the t h e r m a l conductivity at densi ty pA and kB i s the t h e r m a l con-duc t iv i ty at dens i ty pB , and ß i s a p a r a m e t e r tha t d e p e n d s on the m a t e r i a l .

Most of the pub l i shed work on t h e r m a l conduct ivi ty of U 0 2 h a s used a ß value of unity f o r n o r m a l i z i n g the data to t h e o r e t i c a l densi ty ( ze ro poros i ty ) . However , a l l the inves t iga t ions of t he dependence of the conductivi ty on den -s i t y f o r UO2 have i n d i c a t e d a ß va lue h i g h e r t h a n 1. 0. T h u s R o s s [29] showed that ß was a p p r o x i m a t e l y 2 f o r m a t e r i a l wi th d e n s i t i e s be tween 8. 4 and 10.7 g / c m 3 at 60°C. Vogt et a l . [25] m e a s u r e d the t h e r m a l conductivity of m a t e r i a l wi th d e n s i t i e s b e t w e e n 9. 7 and 10. 7 g / c m 3 at t e m p e r a t u r e s up to 1200°C; t h e i r da t a i nd i ca t e a ß va lue of 3 . 2 + 1 , but s i n c e the f r a c t i o n a l d i f f e r e n c e be tween the high and low dens i ty s p e c i m e n s i s g r e a t e r at 1200°C than a t 100° С the f o r m a l i s m of the equat ion above i s obviously o v e r s i m p l i -f i ed . Notley [30] ana lysed an i r r a d i a t i o n e x p e r i m e n t to deduce a ß value of 2 .6±.0,8, f o r d e n s i t i e s b e t w e e n 10.4 and 10.75 g / c m 3 , s u b j e c t to a s s u m p t i o n s conce rn ing the use of g ra in growth a s a t e m p e r a t u r e m a r k e r . (See sect ion III-3.)

R o s s [29] p roposed that the i r r e g u l a r shape of the poros i ty was r e s -p o n s i b l e f o r d e v i a t i o n s f r o m a ß v a l u e of 1 . 0 ( i . e . t he i m p e d a n c e to h e a t f low of a p l a t e - l i k e p o r e i s g r e a t e r t h a n t h a t of a s p h e r i c a l p o r e of e q u a l volume) . He a l so sugges ted that the t h e r m a l r e s i s t a n c e of g ra in bounda r i e s might be s igni f icant in s a m p l e s of v e r y s m a l l g ra in s i ze . It fo l lows that the value of ß might v a r y with the spec imen f a b r i c a t i o n route , and t h i s i s a p a r a -m e t e r that should be e s t i m a t e d f o r the p a r t i c u l a r m a t e r i a l under t e s t in any f u t u r e t h e r m a l conduct iv i ty m e a s u r e m e n t s . It m a y be p o s s i b l e even tua l l y to e s t i m a t e ß f r o m m i c r o s t r u c t u r a l examinat ion , with i n t e r c o m p a r i s o n with su i tab le s t a n d a r d s .

It a p p e a r s t h e r e f o r e , t ha t f o r p o l y c r y s t a l l i n e UOz ß can v a r y b e t w e e n 1 and 4, depend ing on the m o r p h o l o g y of t he m a t e r i a l . T h e a v e r a g e va lue

9

f o r the m a t e r i a l s tudied in R e f s . [25, 29, 30] was approx ima te ly 2. 5; t h e r e -f o r e th i s value has been used in the r e m a i n d e r of t h i s document f o r n o r m a -l izat ion of d i f f e r e n c e s in densi ty . Whereve r poss ib le , we have p r e f e r r e d to n o r m a l i z e t o 95 r a t h e r t han to 100% of t h e o r e t i c a l dens i ty , to r e d u c e the magn i tude of the c o r r e c t i o n .

If the ß value of typica l product ion UO2 fuel i s as high a s 2. 5 t h e r e s e e m s to be some incentive towards use of higher density, since a 4% change in density would r e su l t in a 10% change in t h e r m a l conductivity. When evalu-ating fuel e lement i r r ad ia t ions , the possible effect of density changes during the expe r imen t should be t aken into account . Th i s i s p a r t i c u l a r l y t r u e f o r powder f u e l e l emen t s , w h e r e s in te r ing , dens i f i ca t ion and changes in shape of the poros i ty may i n c r e a s e the t h e r m a l conductivi ty ve ry m a r k e d l y . (See sec t ion III. 4.)

It is r ecommended that uncor rec ted values be quoted, or , if co r rec t ions a r e given, the de ta i l s of the method used be desc r ibed .

I I - 2 . 1 . 4 . Effec t of gra in boundar ies

The effect of gra in boundar ies i s to some extent obscured by d i f fe rences in composi t ion between- spec imens . Some, but not all , s i ng l e - c rys t a l spec i -m e n s a r e hypos to ich iomet r i c in the a s - g r o w n s ta te . Many w o r k e r s , t h e r e -f o r e , give t h e m a high t e m p e r a t u r e anneal in wet hydrogen to oxidize t hem to a s t o i c h i o m e t r i c compos i t ion . However , t h e s e s p e c i m e n s may s t i l l be of a lower oxygen content than, the po lyc rys t a l l i ne s i n t e r ed s p e c i m e n s p r e -p a r e d by convent ional f a b r i c a t i o n t echn iques .

The f i r s t expe r imen ta l evidence of an i nc rea sed t h e r m a l conductivity in l a r g e g ra in U0 2 was r e p o r t e d by Daniel et a l . [9] (Fig . 3). S i n g l e - c r y s t a l UO2.001 d i sp layed an i n c r e a s i n g h e a t - t r a n s f e r r a t e at t e m p e r a t u r e s above 700°C. The t h e r m a l conductivity was 1. 6 t i m e s that of po lycrys ta l l ine UO2 at 800°C and,2. 6 t i m e s at 1200°C.

May et al . [15] found no effect of gra in boundar ies using a s imple com-pa ra t ive type of appa ra tus , but l a t e r Notley et al. [31] re f ined the i r e x p e r i -m e n t a l t echn ique and c o n f i r m e d tha t s i ng l e - c rys t a l -UO 2 . 005 had a s l igh t ly g r e a t e r t h e r m a l conduct iv i ty than p o l y c r y s t a l l i n e UO2.005 > though t h i s d i f f e r e n c e was s m a l l compared to that caused by hypos to ich iomet ry . (See sec t ion I I -2 . 2.)

B a t e s et a l . [24] r e p o r t e d a m a x i m u m in the t h e r m a l d i f fus iv i ty of s i n g l e - c r y s t a l m a t e r i a l at about 1000°C. In a comparat ive r ad ia l heat - f low a p p a r a t u s C h r i s t e n s e n [33] obse rved a m a x i m u m at a s i m i l a r t e m p e r a t u r e . However , be tween about 1200 and 1400°С the conductivity appea red to drop r a p i d l y . T h e s e o b s e r v a t i o n s a r e be l i eved t o ind ica te r e l a t i v e c h a n g e s in conductivity, but the au thors s ta te that the i r quanti tat ive e s t i m a t e s a r e l e s s s igni f icant .

W h e e l e r and H e d g e r [32] p e r f o r m e d t h e r m a l d i f fus iv i ty e x p e r i m e n t s , u s ing s i n g l e - c r y s t a l m a t e r i a l . The f o r m u l a

Cp = 1 8 . 4 5 t 2 . 4 3 1 X 1 0 - 3 T - 2. 272X10-5T-2 c a l / m o l e degK

was 'used to convert the data to t h e r m a l conductivity (Fig. 3). An unannealed single c r y s t a l (density > 10. 9 g / c m 3 ) with an init ial O /U ra t io of 2. 09, gave

10

FIG. 3. Thermal conductivity of single-crystal U02 compared to polycrystalline U02 . 005 , corrected to 100% TD

a conductivity of approximate ly 0. 024 W c m - i degC"1 between 800 and 1730°C. When cooled down to 800°C, the conduct iv i ty r o s e to 0 . 0 3 1 W c m - i degC" 1 -On f u r t h e r t h e r m a l cyc l ing the s p e c i m e n r e a c h e d a s t e a d y condi t ion in which the conduct iv i ty v a r i e d l i n e a r l y with t e m p e r a t u r e f r o m a va lue of 0. 034 W c m - i degC- i at 800°C to 0. 028 W c m " 1 degC" 1 a t 1700°C. T h i s change in conduct iv i ty w a s p r e s u m e d to be due to l o s s of oxygen. S i m i l a r c r y s t a l s w e r e t h e n h e a t - t r e a t e d in p u r i f i e d a r g o n f o r 2 h o u r s , and h e a t -t r e a t e d , i n hydrogen with a t a n t a l u m g e t t e r f o r 2 h o u r s . F u r t h e r i n c r e a s e s in t h e r m a l conduc t iv i ty w e r e noted , the heat t r e a t m e n t in a r g o n g iv ing v a l u e s which v a r i e d l i n e a r l y b e t w e e n 0 .037 W c m " 1 degC."1 at 800°C and 0. 030 W cm" 1 degC"1 at 1700°C, and the heat t r e a t m e n t in hydrogen resu l t ing in v a l u e s of 0,. 038 W cm".i degC" 1 a t 800° С and 0. 034 W c m * 1 d e g C " 1 a t 1700° C. À po lyc rys t a l l i ne s p e c i m e n of U02.002 under the s a m e expe r imen ta l t echn iques gave a c u r v e which a g r e e d , v e r y c lose ly with o the r w o r k on s i m i -l a r m a t e r i a l . (See sec t ion I I -2 . 1, and F ig . 3).

T h e s e r e s u l t s a r e apparen t ly incompat ib le with those of Danie l et a l . [9.],, B a t e s et a l . [24] and C h r i s t e n s e n [33] m e n t i o n e d a b o v e , in t h a t a l t h o u g h t h e y show a s l i g h t l y h i g h e r t h e r m a l conduc t iv i ty f o r s i n g l e - c r y s t a l t h a n p o l y c r y s t a l l i n e m a t e r i a l , t h e magn i tude of the e n h a n c e m e n t o r t he shape of the c u r v e of conduct ivi ty v e r s u s t e m p e r a t u r e a r e not s i m i l a r to the f ind ings of t h e o t h e r w o r k e r s . Without a d e q u a t e c h a r a c t e r i z a t i o n of s a m p l e s and i n t e r c o m p a r i s o n of e x p e r i m e n t a l t e c h n i q u e s t h e s e i n c o n s i s t e n c i e s c anno t be r e s o l v e d .

C o m p a r i s o n of the data f o r s ingle c r y s t a l s with those f o r po lyc rys t a l l i ne u r a n i u m dioxide i s given in F i g . 3. M e a s u r e d v a l u e s have been n o r m a l i z e d t o t h a t f o r the t h e o r e t i c a l dens i t y by u s ing aßvalue of 2 .5 . (See s ec t i on 11^2. 1.) The d i f f e r e n c e in t h e r m a l conduct iv i ty shown by the data f o r s i n g l e - c r y s t a l and p o l y c r y s t a l l i n e m a t e r i a l h a s b e e n sugges t ed by B a t e s [34], de H a l a s [35] ,

11

and Viskanta [36] t o b e due to heat t r a n s f e r by photons. P h o t o n t r a n s m i s s i o n will v a r y with t e m p e r a t u r e , O / U r a t i o , and s m a l l d e f e c t s ( p r ec ip i t a t e s , po ros i t y , e t c . ), so the extent of such a cont r ibut ion may wel l be a f f ec t ed v e r y g rea t ly by changes in s p e c i m e n p a r a m e t e r s that have been undetec ted by the c h a r a c -t e r i z a t i o n t echn iques employed to date (see sec t ion V-2) .

11-2. 2. Effect of O/U ratios below 2.000 on the thermal conductivity of unirradiated specimens

In many i n s t a n c e s w h e r e the t h e r m a l conductivi ty of hypos to ich iomet r i c UO z i s m e a s u r e d , no O / U r a t i o i s quoted , e v i d e n c e of h y p o s t o i c h i o m e t r y b e i n g t a k e n a s the m e t a l l o g r a p h i c i den t i f i c a t i on of f r e e u r a n i u m in the s a m p l e . Even if u r a n i u m p r e c i p i t a t e s a r e obse rved o r the spec imen i s a n a -lysed to be oxygen def ic ient , it has been suggested that the m a t r i x i tself could s t i l l be s t o i c h i o m e t r i c . On t h e o t h e r h a n d , i t i s a l s o p o s s i b l e t h a t h y p o -s t o i c h i o m e t r i c U02 can be f o r m e d in the a b s e n c e of o b s e r v a b l e u r a n i u m p r e c i p i t a t e s .

The pub l i shed da ta a r e p r e s e n t e d in F i g . 4, w h e r e t h e y a r e c o m p a r e d with the ' r e c o m m e n d e d ' va lues f o r U02 . 005 of 95% of t h e o r e t i c a l densi ty that a r e given in sec t ion I I -2 . 1.

May et a l . [15] or ig inal ly demons t ra t ed that hypos to ich iomet r ic u ran ium d iox ide showed a h i g h e r t h e r m a l conduc t iv i ty in t h e l a b o r a t o r y t h a n s t o i -c h i o m e t r i c m a t e r i a l ; May and Stoute [37] extended the work, us ing a s imple t h e r m a l c o m p a r i s o n method, and compared the t h e r m a l conductivity of hypo-s t o i c h i o m e t r i c and n o m i n a l l y s t o i c h i o m e t r i c s p e c i m e n s a t m e a n t e m p e r a -t u r e s up to 1200°C. A s ignif icant i n c r e a s e was found in the t h e r m a l conduc-t iv i ty of both po lyc rys t a l l i ne and s i n g l e - c r y s t a l hypos to i ch iomet r i c spec imens ; a l though the magni tude of t h i s i n c r e a s e h a s not been e s t i m a t e d , it a p p e a r e d to be g r e a t e r than the d i f f e r e n c e be tween s i n g l e - c r y s t a l and po lyc rys t a l l i ne spec imens of the s a m e compos i t ions . Kollie et al. [38] r epor t ed a m e a s u r e -m e n t u s i n g a P o w e l l - t y p e t h e r m a l c o m p a r a t o r , and showed no d i f f e r e n c e be tween the conduct iv i t ies of s i n t e r e d s t o i c h i o m e t r i c and hypos to ich iomet r i c u r a n i u m dioxide at 75°C, but a 17% g r e a t e r conductivity f o r the hypostoichio-m e t r i c m a t e r i a l at 300° C. Fe i th [21] m e a s u r e d the t h e r m a l conductivity of a s p e c i m e n tha t was hypos to i ch iome t r i c at the end of the expe r imen t ; be tween 1000 and 2500°C, h i s v a l u e s a r e f r o m 30 to 100% g r e a t e r t han v a l u e s m e a s u r e d on s t o i c h i o m e t r i c U 0 2 by o ther w o r k e r s . C h r i s t e n s e n et a l . [14] found an e n h a n c e m e n t in conduc t iv i ty (about 20%) a t 1900°С and l i t t l e i n -c r e a s e at 1100°C, f o r a s p e c i m e n that changed in compos i t i on f r o m U02 .01 t o UO 1,99 du r ing t hé e x p e r i m e n t .

H e t z l e r and Z e b r o s k i [23] found an approx ima te ly 50% i n c r e a s e in con-duc t iv i ty a t 900°C in h y p o s t o i c h i o m è t r i c p o l y c r y s t a l l i n e u r a n i u m d iox ide , but the d i f f e r e n c e be tween hypos to i ch iome t r i c and s t o i c h i o m e t r i c m a t e r i a l van i shed at 1400°C.

Vogt et a l . [25] r e p o r t that a spec imen containing 0. 5 - 1 wt. % f r e e u r a -nium showed no h igher t h e r m a l conductivity than that expected f r o m a mecha-n i c a l m i x t u r e of U and U 0 2 , up to 1200°C. De ta i l s of the c h a r a c t e r i z a t i o n a r e not g iven; it i s p o s s i b l e tha t t he m a t r i x of t he s p e c i m e n w a s not h y p o -s t o i c h i o m e t r i c .

12

0.0t

0.07

о 0.06

î J 0.05

> 0.04 н и э 0 z 8 0.03

1 I 0.02

0.01

О 200 400 GOO 800 1000 1200 1400 1600 1800 2000 2200 2400

TEMPERATURE C O

FIG.4. Thermal conductivity of hypostoichiometric U02 compared to that of UOj^ds of 9b°lo TD

T h e above e v i d e n c e i n d i c a t e s tha t h y p o s t o i c h i o m e t r i c p o l y c r y s t a l l i n e u r a n i u m dioxide can o f t en show a h ighe r t h e r m a l conduct ivi ty than s to i ch io -m e t r i c m a t e r i a l in t he t e m p e r a t u r e r a n g e 3 0 0 - 1 4 0 0 ° C . The v a r i a t i o n s in the magn i tude of the e f f ec t a r e u n d e r s t a n d a b l e in the l ight of t he inadequate c h a r a c t e r i z a t i o n of t h e s a m p l e s . H o w e v e r , i t i s un l ike ly t h a t a l l t h e r e -por ted obse rva t ions of enhanced t h e r m a l conductivity a r e due solely to hypo-s t o i c h i o m e t r y . T h u s t h e s i n g l e - c r y s t a l r e s u l t s of Dan ie l et a l . [9], which a r e t h e h ighes t r e p o r t e d v a l u e s f o r the t h e r m a l conduct iv i ty below 1200°C, w e r e obta ined on a s p e c i m e n which a n a l y s e d a s U O 2 . 0 0 5 ± 0 .005 and which showed no t r a c e s of f r e e u r a n i u m .

T h e enhanced t h e r m a l conduct iv i ty i s unl ike ly to be due to photon h e a t t r a n s f e r , s i n c e many of the s p e c i m e n s showing the e f f ec t w e r e p o r o u s and po lycrys ta l l ine ; s i m i l a r l y , heat t r a n s f e r by e l e c t r i c a l charge c a r r i e r s i s not s i g n i f i c a n t be low 1000° C. (See s e c t i o n V-3 . ) It h a s b e e n s u g g e s t e d t h a t s m a l l c h a n g e s in O / U r a t i o n e a r s t o i c h i o m e t r y could a f f e c t t he l a t t i c e pe r iod ic i ty (anharmonic i ty of v ibra t ion of the oxygen a toms) which may affect the phonon conductivi ty o r the in te rac t ion of the va r ious m e a n s of heat t r a n s -p o r t . A s ye t , t h e o r y a p p e a r s i n a d e q u a t e t o d e v e l o p t h e s e i d e a s f u r t h e r .

II-2. 3. E f f e c t of O/U ratios above 2. 010

The data obtained by R o s s [29] and Howard and Gulvin [3] f o r the e f fec t of e x c e s s oxygen on the t h e r m a l conduc t iv i ty of u r a n i u m dioxide at 60 and 920°C, r e s p e c t i v e l y , i s shown in F i g . 5(a). W h e e l e r and H e d g e r [32] have r e c e n t l y m e a s u r e d an i n c r e a s e in conduct iv i ty on a s ing le c r y s t a l at 800°C, when the m a t e r i a l was r educed f r o m UO 2 09 to U 0 2 0 . (See a l s o sec t ion I I -2 .1 .4

13

RELATIVE TO UO2 .01

FIG. 5. Effect of U/O ratios greater than 2.00 on the thermal conductivity of U02

f o r de t a i l s . ) All the above data a r e in r e a s o n a b l e a g r e e m e n t cons ide r ing the p robab le l i m i t s of e x p e r i m e n t a l e r r o r (Fig . 5(b)).

It should be noted that the change in conduct iv i ty p lo t ted in F i g . 5(a) i s r e f e r r e d to a s p e c i m e n of compos i t ion UO2. 01; it i s not n e c e s s a r i l y val id to e x t r a p o l a t e t h e s e data back to U02 . 000 < s ince t h e r e i s a poss ib i l i ty tha t the in t e rac t ions of the a tomic la t t ice may be marked ly affected by sma l l amounts of e x c e s s oxygen [1] .

Godfrey ef al , [10] ana lyse the t h e r m a l r e s i s t i v i t y in t roduced by exces s oxygen in t e r m s of t he equation

г = A + B T к

w h e r e A c o r r e s p o n d s to the i m p u r i t y r e s i s t a n c e R i , and ВТ r e p r e s e n t s the la t t i ce r e s i s t a n c e R L . F o r . t h e i r spec imen , where t h e r e were approximate ly 15 i m p u r i t y a t o m s ( including e x c e s s oxygen) p e r 1000 m o l e c u l e s of U 0 2 , a change of compos i t i on f r o m U02.012 to UO2. 006 w a s found to change A f r o m 5.67 to 4.42 c m degK W" 1 . T h e change in Ri w a s deduced to be a p p r o x i m a t e l y

ARi = Ä = 5X ( - j ^ ) = - 2 c m degK W"i

w h e r e N i s the" n u m b e r of impur i ty a t o m s p e r thousand. • The rough ca l cu l a -t ion adequate ly d e s c r i b e d the d i rec t ion and o r d e r of magnitude of the change. T h i s ana ly s i s ind ica tes that the magnitude of any change in t h e r m a l conduct-iv i ty c a u s e d by a change in oxygen content would be a f u n c t i o n of t he t o t a l i m p u r i t y content of t he s p e c i m e n , and a l s o e n a b l e s u s to e s t i m a t e the p r o b a b l e e f f e c t of any change in i m p u r i t y l e v e l .

14

хЮ"3 M>

70

60

\ 50 •i •D

' б 40 Ï

30

20

t o

0 2 4 6 8 10 12 14 16 18 20 22 24 26 2»

TEMPERATURE (°C)

FIG. 6. Thermal conductivity 'of powder UO2

II-2. 4. Powder thermal conductivity

S e v e r a l l a b o r a t o r i e s have d e r i v e d v a l u e s f o r t he t h e r m a l conduc t iv i ty of p o w d e r UO2 f r o m m e a s u r e m e n t s of i n t e g r a t e d conduc t iv i t y [9, 3 9 - 4 6 ] . Mos t of t h é ë x p e r i m e n t a l da t a a r e p lo t t ed on F i g s . 6 and 7.

A t ' t e m p e r a t u r e s be tween 0 and 1000° С the l a r g e s t va r i a t i ons in the UO2 powder t h e r m a l conductivity data r e su l t f r o m the influence of powder density, s i ze , shape and the f i l l i ng gas and i t s p r e s s u r e . Danie l et a l . [9] obtained the s a m e r e s u l t s f o r UO2 powder of 86. 8% TD, i r r e s p e c t i v e of whe the r the f i l l ing g a s w a s hel ium or argon, with a t h e r m a l conductivity (0.02 W cm"1 degC"1), independent of t e m p e r a t u r e up to 1000°C (Fig . 6, cu rve 3). On the o ther hand, the da t a g iven by L e b l a n c [45] show the t h e r m a l conduc t iv i ty of p o w d e r t o be g r e a t l y a f f e c t e d in the low t e m p e r a t u r e r a n g e by the type of ga s and the gas p r e s s u r e (Fig . 7). T h e s e r e s u l t s a r e s i m i l a r t o those obse rved by E ian and D e i s s l e r [39] who m e a s u r e d the t h e r m a l conductivity of u r a n i u m dioxide p o w d e r s with the f i l l i ng g a s e s he l ium, a rgon , and a i r . The gas p h a s e w a s m o r e impor tan t than the sol id in de t e rmin ing the t h e r m a l conductivity of low dens i t y p o w d e r s (53 - 64% TD), and the conduc t iv i ty w a s a f u n c t i o n of g a s p r e s s u r e depending upon the type of gas, the t e m p e r a t u r e and the c h a r a c t e r -i s t i c s of the void v o l u m e . F o r a l l t h e p o w d e r s , t he conduct iv i ty in h e l i u m was much g r e a t e r than in o ther g a s e s . The e f f ec t s of d i f fe ren t f i l l ing g a s e s and g a s p r e s s u r e s on the e f f ec t ive t h e r m a l conduct iv i ty of a p o w d e r g a s m i x t u r e can be s a t i s f a c t o r i l y explained by the kinet ic t heo ry of g a s e s . Using the r a t i o of t he m e a n - f r e e pa th of t h e gas m o l e c u l e s to a c h a r a c t e r i s t i c d i -m e n s i o n of t he voids be tween p a r t i c l e s , one can e s t i m a t e the e f f e c t of ga s p r e s s u r e on the e f fec t ive t h e r m a l conduct iv i ty . Heat t r a n s f e r by f r e e con -vec t i on of t h e f iHing gas t h r o u g h i n t e r - c o n n e c t e d vo ids cannot b e r e j e c t e d a p r i o r i , p a r t i c u l a r l y when t h e r m a l g r a d i e n t s a r e v e r y h igh.

15

TEMPERATURE (°C)

FIG. 7. Integral conductivity values for powder UO2 elements

The e s t a b l i s h m e n t of an a p p r o p r i a t e t h e r m a l conduct iv i ty c u r v e f o r p o w d e r UO2 at h igh t e m p e r a t u r e s i s an even m o r e d i f f i cu l t u n d e r t a k i n g if s i n t e r i n g , d e n s i f i c a t i o n and g r a i n growth o c c u r . Using a r a d i a l h e a t - f l o w a p p a r a t u s , A n d r i e s s e n and L e b l a n c [43] and L e b l a n c [44] m e a s u r e d U 0 2 powder t h e r m a l conductivi ty unde r he l ium p r e s s u r e s up to 400 mmHg. They p r o p o s e d an i n t e g r a t e d t h e r m a l conduct iv i ty f r o m 0°C to m e l t i n g of 53 and 60 W cm" 1 f o r U0 2 powder between 85 and 88% TD, respec t ive ly . The curve of JkdT v e r s u s T i n c r e a s e d slowly f r o m 1500 to 1700°C.

T h e p o r o s i t y c o r r e c t i o n used f o r s i n t e r e d UO2 cannot be appl ied to the t h e r m a l conduc t iv i ty of U0 2 p o w d e r b e c a u s e of t h e d i m e n s i o n s and i n t e r -connec t ion of p o r e s .

The p r e s e n t l y ava i l ab le data on the t h e r m a l conductivi ty of U0 2 powder e l e m e n t s show a v e r y wide v a r i a t i o n in v a l u e s . F u r t h e r w o r k i s r e q u i r e d to e x a m i n e s y s t e m a t i c a l l y t h e e f f e c t s of t he v a r i o u s p a r a m e t e r s in o r d e r to ob ta in a b e t t e r u n d e r s t a n d i n g of the m e c h a n i s m s invo lved .

IJ-2. 5. Conclusions

(a) Up to 1300° С the t h e r m a l conductivi ty of p o l y c r y s t a l l i n e U O 2 . 0 0 5 to. oos of 95% of fu l l t h e o r e t i c a l dens i ty i s given by

k = 11. 75+ 0. 02351 w h e r e t i s in

within about ±3% (to 95% probab i l i t y ) . Above 1300°C the v a r i a t i o n of t h e r m a l conduc t iv i ty with t e m p e r a t u r e

i s l e s s we l l -de f ined , but on the b a s i s of the ava i lab le e x p e r i m e n t a l evidence

16

i s thought to i n c r e a s e g r adua l l y with i n c r e a s i n g t e m p e r a t u r e in the m a n n e r found by S to ra et a l . [16] ( s e e Tab le I). H o w e v e r , s o m e w o r k e r s i n d i c a t e a cons t an t conduc t iv i ty with i n c r e a s i n g t e m p e r a t u r e wi th a p r o b a b l e va lue of 0. 022 W cm" 1 degC" 1 above 1500°C. Some of the a p p a r e n t d i s a g r e e m e n t may be due to r e a l d i f f e r e n c e s be tween s p e c i m e n s .

(b) P o r o s i t y h a s b e e n shown to d e c r e a s e t h e t h e r m a l c o n d u c t i v i t y of u r a n i u m d iox ide , by a n a m o u n t g iven by t h e e m p i r i c a l e q u a t i o n

kp = к [ 1 - (2. 5 ± 1. 5)p]

w h e r e p i s the f r a c t i o n a l p o r o s i t y and k p i s t he t h e r m a l conduc t iv i ty of t he p o r o u s m a t e r i a l . The coef f ic ien t of p in t h i s expansion probab ly depends on the shape of the p o r o s i t y , so can be expected to v a r y with d i f f e r en t f a b r i c a -t ion r o u t e s e t c . At h igh t e m p e r a t u r e s , r a d i a t i o n hea t t r a n s f e r a c r o s s p o r o s i t y may a f fec t the magni tude of the dependence of the t h e r m a l con-duct ivi ty on p o r o s i t y .

(c) The e f fec t of oxygen in e x c e s s of the s t o i c h i o m e t r i c compos i t i on i s to r e d u c e the t h e r m a l conduc t iv i ty . At low t e m p e r a t u r e s t h e i n t r o d u c t i o n of i m p u r i t y s c a t t e r i n g c e n t r e s i n c r e a s e s t h e phonon r e s i s t i v i t y , w h i l e a t high t e m p e r a t u r e s exces s oxygen a l so d e c r e a s e s any heat t r a n s f e r by photons. (See a l so sect ion V-2.)

(d) The t h e r m a l conduct ivi ty of s i n g l e - c r y s t a l u r a n i u m dioxide be tween 20 and 1500°С a p p e a r s to be h igher than that of polycrys ta l l ine m a t e r i a l (nor -m a l i z e d to the s a m e dens i ty ) . The magn i tude of the e f fec t a p p e a r s to v a r y f r o m s p e c i m e n to s p e c i m e n . W h e t h e r t h i s r e f l e c t s d i f f e r e n c e s in e x p e r i -men ta l technique o r r e a l d i f f e r e n c e s between spec imens i s not resolved; how-e v e r , s i n c e the e n h a n c e m e n t in conduc t iv i ty i s p r o b a b l y due to photon hea t t r a n s f e r , s m a l l d i f f e r e n c e s in p a r a m e t e r s such a s impur i ty content, porosity, o r s u b g r a i n b o u n d a r y concen t ra t ion may be r e s p o n s i b l e . (See a l s o sec t ion V-2. )

(e) Many w o r k e r s have shown that h y p o s t o i c h i o m e t r i c u r a n i u m dioxide can h a v e a s i g n i f i c a n t l y h i g h e r t h e r m a l conduc t iv i ty t h a n U 0 2 . oos- Not a l l h y p o s t o i c h i o m e t r i c s p e c i m e n s show t h i s b e h a v i o u r , but aga in t h i s m a y r e f l e c t m i n o r , unde tec ted , d i f f e r e n c e s be tween s p e c i m e n s . The r e a s o n f o r the enhanced conduct ivi ty i s not known, but ava i lab le evidence ind ica tes that it i s un l ike ly t o be due to photon conduc t ion ( s i nce m a n y s p e c i m e n s w e r e p o r o u s ) o r e l e c t r o n i c conduc t ion .

III. T H E R M A L CONDUCTIVITY O F I R R A D I A T E D URANIUM DIOXIDE

T h r e e qui te d i s t inc t a p p r o a c h e s have been appl ied to the inves t iga t ions into the e f f e c t s of i r r a d i a t i o n on the t h e r m a l conduct iv i ty of U 0 2 . (a) C o m p a r i s o n of the t h e r m a l c o n d u c t i v i t y of U O s m e a s u r e d b e f o r e and

a f t e r i r r a d i a t i o n . T h e s e p r e - p o s t m e a s u r e m e n t s a r e r e s t r i c t e d to f a i r l y s m a l l s a m p l e s and low i r r a d i a t i o n e x p o s u r e s and a r e e s p e c i a l l y s u i t a b l e f o r t he i n v e s t i g a t i o n of l o w - d o s e e f f e c t s and t h e r e c o v e r y of t h e s e e f f e c t s wi th a n n e a l i n g .

17

(b) D i r e c t i n - r e a c t o r m e a s u r e m e n t s during i r r a d i a t i o n using thermocouples embedded in the UO2. Th i s technique r e q u i r e s cons ide rab l e e m p h a s i s on the a c c u r a t e m e a s u r e m e n t of hea t g e n e r a t i o n f r o m the s a m p l e . Unt i l r ecen t ly , m e a s u r e m e n t s were l imi t ed to a m a x i m u m t e m p e r a t u r e of ~ 1600°C due to t h e r m o c o u p l e l i fe , but the s u c c e s s f u l app l ica t ion of a h igh t e m p e r a t u r e g a s bulb t h e r m o m e t e r c a p a b l e of m e a s u r i n g up to the mel t ing point of U 0 2 i n - r e a c t o r has now usefu l ly extended the r ange .

(c) I n d i r e c t m e a s u r e m e n t s u s i n g m e t a l l o g r a p h i c o b s e r v a t i o n s of g r a i n growth and c e n t r e mel t ing o r au toradiographic obse rva t ions as t e m p e r a -t u r e i n d i c a t o r s . This technique has been applied to both shor t and long-t e r m i r r a d i a t i o n s and has unt i l r ecen t ly been the only method ava i l ab le f o r t he high t e m p e r a t u r e r e g i o n . A c c u r a t e c a l o r i m e t r y i s a g a i n an e s s e n t i a l f a c t o r . Combined i n t e g r a l c u r v e s have been c o n s t r u c t e d us ing i n f o r m a t i o n de-

r ived f r o m the t h r e e m e t h o d s . In the fol lowing r e v i e w of the e x p e r i m e n t a l da ta i t has been found m o r e

c o n v e n i e n t t o c o n s i d e r t h e i n f o r m a t i o n u n d e r t h r e e t e m p e r a t u r e z o n e s : (i) low t e m p e r a t u r e s (< 500°C), the da ta be ing f r o m both p r e - p o s t and

d i r e c t i n - r e a c t o r m e a s u r e m e n t s ; (ii) d i r e c t i n - r e a c t o r m e a s u r e m e n t s above 500°C; (ii i) m e a s u r e m e n t s to the m e l t i n g point u s i n g i n d i r e c t m e t h o d s .

I I I - l . E F F E C T S O F IRRADIATION AT T E M P E R A T U R E S B E L O W 500°C

Both Chalk R ive r [29] and Hanford w o r k e r s jointly with Bat tel le [9] have shown tha t i r r a d i a t i o n of s i n t e r e d s t o i c h i o m e t r i c po lyc rys t a l l i ne UO2 at low t e m p e r a t u r e s can c a u s e a m a r k e d d e c r e a s e in t h e r m a l conduct ivi ty .

R o s s [29] r e p o r t e d that a f t e r an exposu re of 2 X 1 0 1 7 n c m - 2 (~ 2X1016 f i s s i o n s / c m 3 ) at an i r r a d i a t i o n t e m p e r a t u r e below 450°C, the t h e r m a l con-duc t iv i t y m e a s u r e d a f t e r i r r a d i a t i o n at 60°C w a s 26% l o w e r t h a n t h e u n -i r r a d i a t e d va lue ; i r r a d i a t i o n to 6.8 X 1019 n c m ' 2 ( ~ 7 X 101 8 f i s s i o n s / c m 3 ) c a u s e d no f u r t h e r d e c r e a s e (F ig . 8). Heating at t e m p e r a t u r e s up to 1000°C r e s u l t e d in some anneal ing of the damage, the amount of r e c o v e r y at a given annea l ing t e m p e r a t u r e d e c r e a s i n g with i n c r e a s i n g e x p o s u r e . At the h i g h e r d o s e s s o m e damage s t i l l r e m a i n e d a f t e r anneal ing at 1000°C. Th is damage ( p e r c e n t a g e d e c r e a s e in t h e r m a l conduc t iv i ty ) w a s e x p r e s s e d in t e r m s of s i m p l e , i n t e r m e d i a t e and c o m p l e x c o m p o n e n t s with the c o m p l e x type p r e -d o m i n a t i n g at h i g h e r e x p o s u r e l e v e l s .

Work by Danie l et a l . [9] l a r g e l y conf i rmed R o s s ' s f indings; i r r a d i a t i o n a t < 100°C c a u s e d a d e c r e a s e of up to 50% of the u n i r r a d i a t e d v a l u e , t he l a r g e r changes be ing probab ly due to a lower i r r a d i a t i o n t e m p e r a t u r e . Ex -p o s u r e s r anged f r o m 1.4 X 1018 to 1.1 X 1019 f i s s i o n s / c m 3 with no s a t u r a t i o n a t t h e l a t t e r b u r n - u p l e v e l ( F i g . 8). P r o n o u n c e d s t a g e s of r e c o v e r y w e r e appa ren t at ~ 150°C and 300°C,with a l e s s def ined s t a g e at 800°C. T h e s e annea l ing s t e p s co inc ide f a i r l y wel l with c r y s t a l l a t t i c e p a r a m e t e r changes o c c u r r i n g at low d o s e l e v e l s , i nd i ca t ed by X - r a y d i f f r a c t i o n w o r k on UO2 [48, 49 ] . Above 1000°C, > 90% recove ry on anneal ing o c c u r r e d . The extent of r e c o v e r y was aga in dependen t on the d o s e a s w e l l a s t he a n n e a l i n g t e m p e r a t u r e .

18

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0 . 0 7 -

Ь 0.06-

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I oo« . h— cj э о

о 0 . 0 3 -и i з

£ 0.02 х I-

0 01 -

TYPICAL CURVE FOR UNIRRADIATED UO2

• ROSS (CHALK RIVER j fcä] IRRADIATED BETWEEN 20°C AND 450°C SITUATION AT A DOSE OF Ю " FISSIONS/an1

I UNIRRADIATED VALUE г. IRRADIATED AND ANNEALED AT 1000' 3 ANNEALED AT 700° 4 AMIEALED AT 600° 5 IRRADIATED VALUE

LUE I • С I 1° С Г PC

200 «00 600 800 1000 TEMPERATURE < ° C )

1200

FIG. 8. Post-irradiation annealing of irradiated U02

Hawkings and R o b e r t s o n [50] and Hawkings and Ba in [51] no ted p r o -g r e s s i v e de t e r i o r a t i on dur ing i r r a d i a t i o n on the absolute t h e r m a l conductivity of f u e l e l e m e n t s with s u r f a c e t e m p e r a t u r e s be low about 500°C, wi th the g r e a t e s t r a t e of i n c r e a s e of d a m a g e o c c u r r i n g in t h o s e wi th low s u r f a c e t e m p e r a t u r e s ( ~ 1 0 0 ° C ) . The r a t e of d e c r e a s e was r a p i d be tween 1015-101G

f i s s i o n s / c m 3 , but b e c a m e slow above 101 8 f i s s i o n s / c m 3 . In a t e s t run at Sac l ay [52] a d e c r e a s e in t h e r m a l conduc t iv i ty f r o m

0.061 W c m " 1 degC" 1 to 0.048 W c m - 1 degC" 1 a f t e r 7X10 1 8 f i s s i o n s / c m 3 at t e m p e r a t u r e s be low 500°C was r e p o r t e d . T h i s was a d i r e c t m e a s u r e m e n t u s i n g t h e r m o c o u p l e s s i t u a t e d on the c e n t r e - l i n e and one on the p e r i p h e r y . Since the fue l c en t r e t e m p e r a t u r e va r ied during the i r r ad i a t i on f rom an ini t ial va lue of 460°C to a f ina l va lue of 580°C, which in i t se l f would r e su l t in about a 10% d e c r e a s e in conduct iv i ty , it i s not p o s s i b l e quan t i t a t ive ly to s e p a r a t e the i n f l u e n c e of i r r a d i a t i o n , though it i s a p p a r e n t tha t s o m e d e c r e a s e i n c o n d u c t i v i t y due to i r r a d i a t i o n o c c u r r e d .

The WAPD-22 s e r i e s of expe r imen t s [53], r epor t ed in 1960, gave f igures f o r the ' e f fec t ive 1 t h e r m a l conductivi ty of UO2 up to 700°C. The ef fec t of the in i t i a l f u e l / c l a d g a s gap was s tud ied by se l ec t ing a r a n g e of c l e a r a n c e s and d i f f e r en t ga s m i x t u r e s . A c e n t r a l t he rmocoup le was used f o r the UO2 t e m p e r a -t u r e m e a s u r e m e n t and the heat output e s t i m a t e d f r o m the t e m p e r a t u r e d r o p a c r o s s a t h i ck s t e e l s h e a t h . T h e da t a f r o m t h i s r e p o r t h a v e s u b s e q u e n t l y been r e - c a l c u l a t e d , u s ing b e t t e r da ta f o r the g a m m a hea t ing in the c a p s u l e

19

IRRADIATION TIME ( d )

FIG. 9. Dose dependence of thermal conductivity of U0 2 below 500°C [19]

[54] . The only r e s u l t s f r o m which d i r e c t i n d i c a t i o n s of t he e f f e c t s in t h e UO2 c a n b e ob t a ined a r e on s p e c i m e n s hav ing a n o m i n a l z e r o f u e l / c l a d c l e a r a n c e . On i n i t i a l s t a r t - u p , t he ' e f f e c t i v e ' c o n d u c t i v i t y r a n g e d f r o m 0.050 W cm" 1 degC"1 at 100°C to 0.042 W cm" 1 degC"1 at 500°C. The va lues ob t a ined d u r i n g s u c c e s s i v e r e a c t o r c y c l e s (up to a t o t a l d o s e of 3.5 X10 1 9

f i s s i o n s / c m 3 ) be low 600°C w e r e l o w e r , d e c r e a s i n g with t e m p e r a t u r e f r o m 0.040 W c m " 1 degC" 1 a t 500°C down to a v a l u e of 0 .030 W c m " 1 d e g C " 1 a t 100°C. Even with t h e s e i r r a d i a t i o n condi t ions i t i s not p o s s i b l e to s e p a r a t e i r r a d i a t i o n e f f e c t s f r o m those changes due to d e c r e a s e in con tac t p r e s s u r e b e t w e e n f u e l and c lad a t low t e m p e r a t u r e ; the a u t h o r s c o n s i d e r e d tha t t he r e d u c t i o n r e s u l t e d p r i m a r i l y f r o m the l a t t e r .

Clough and S a y e r s [19] in an e x p e r i m e n t involving d i r e c t m e a s u r e m e n t i n - r e a c t o r s h o w e d tha t t h e t h e r m a l conduc t iv i ty of s t o i c h i o m e t r i c UO2 i s p r o g r e s s i v e l y r educed at i r r a d i a t i o n t e m p e r a t u r e s below 500°C. I r r a d i a t i o n of two c a p s u l e s at m e a n UO2 t e m p e r a t u r e s of 180 and 320°C, r e s p e c t i v e l y , p roduced a g r a d u a l reduc t ion in t h e r m a l conductivi ty with dose (Fig . 9). The c u r v e s show tha t t he m a j o r i t y of t he change o c c u r r e d b e l o w an i n t e g r a t e d dose of 5 X 1017 f i s s i o n s / c m 3 and the e f fec t s w e r e tending to s a t u r a t e above 5 X 101 8 f i s s i o n s / c m 3 . C o m p a r a t i v e v a l u e s a f t e r 1.5 X 10 1 9 f i s s i o n s / c m 3

showed a d e c r e a s e in conduc t iv i t y of 20% at a m e a n t e m p e r a t u r e of 320°C

20

FIG. 10. Effect of annealing on the low-temperature thermal conductivity [ 19]

[ДТ ( a c r o s s the U0 2 ) = 50 degC], compared with 25%, at a mean t e m p e r a t u r e of 180°C (AT = 40 degC) . It I s a s s u m e d tha t no s i g n i f i c a n t change had o c -c u r r e d p r i o r to t h e f i r s t r e a d i n g s wh ich w e r e t a k e n a f t e r d o s e s b e t w e e n 1.5 X 101 5 and 4 . 5 X 10 l s f i s s i o n s / c m 3 . No m e a s u r a b l e c h a n g e in t h e r m a l conduct iv i ty was de tec t ed in the s p e c i m e n i r r a d i a t e d at a m e a n t e m p e r a t u r e of 520°C (ДТ = 110 degC).

I n - r e a c t o r anneal ing at cons tant power in the spec imen , us ing e l e c t r i c a l h e a t i n g , s h o w e d tha t a t d o s e l e v e l s in the r a n g e 101 8- 101 9 f i s s i o n s / c m 3 a s ign i f ican t p r o p o r t i o n of the to ta l damage i n s e r t e d at 180 and 320°C could be annealed out, e . g . the 180°C capsu le annealed at 450°C f o r twen ty - four hours a f t e r a c c u m u l a t i n g a d o s e of 2 X 10 1 8 f i s s i o n s / c m 3 s h o w e d 70% r e c o v e r y , w h i l s t a l m o s t c o m p l e t e r e c o v e r y w a s a t t a i n e d in t h e 320°C c a p s u l e a f t e r 4 X 101 8 f i s s i o n s / c m 3 when a n n e a l e d at 750°C f o r t he s a m e t i m e ( F i g . 10). When the o r i g i n a l t e m p e r a t u r e was rega ined , the t h e r m a l conduct ivi ty r e t u r n e d to the s a m e va lue as that a t ta ined p r i o r to anneal ing within a few hour s (= 1017 f i s s i o n s / c m 3 ) tha t i s , somewhat m o r e rap id ly than on in i t i a l s t a r t - u p . As i r r a d i a t i o n p r o c e e d e d , t he f r a c t i o n a l r e c o v e r y on a n n e a l i n g d e c r e a s e d ; v i z . a f t e r 3 c y c l e s (5 X 1018 f i s s i o n s / c m 3 ) , only 10% r e c o v e r y cou ld be e f -f ec t ed by annea l ing the 180°C s p e c i m e n at 450°C f o r t w e n t y - f o u r h o u r s . At h i g h e r d o s e s (> 101 9 f i s s i o n s / c m 3 ) l i t t l e o r no r e c o v e r y w a s ev iden t a f t e r the s a m e a n n e a l i n g t r e a t m e n t s .

It s e e m s c e r t a i n , t h e r e f o r e , t ha t the t h e r m a l c o n d u c t i v i t y of UO2 de -c r e a s e s when i r r a d i a t e d at t e m p e r a t u r e s u n d e r 500°C. The m a g n i t u d e of the d e c r e a s e i s dependent on both the i r r a d i a t i o n t e m p e r a t u r e and the b u r n -u p . Bo th the p r e - p o s t and i n - r e a c t o r e x p e r i m e n t s h a v e s h o w n t h a t i t b e -c o m e s p r o g r e s s i v e l y m o r e d i f f icul t to annea l the d a m a g e as i r r a d i a t i o n p r o -ceeds , although sa tu ra t i on o c c u r r e d e a r l i e r in the p r e - p o s t s tudies , probably due to a continuous s e l f -annea l ing p r o c e s s o c c u r r i n g i n - r e a c t o r .

2 1

008-

• Г 0 0 7 0 о» « "О

006

Ï

È 0.05 >

и э 1 0 0 4 0 и

1 0 0 3 ш s

002

0 200 400 600 800 Ю00 1200 1400 1600 VOO

TEMPERATURE («С)

FIG. 11. Summary curve SD 551/1 and SD 551/2 results [ 19]

It a p p e a r s tha t o v e r t he t e m p e r a t u r e r a n g e 150 - 500°C the s a t u r a t i o n va lue obta ined u n d e r i r r a d i a t i o n at a cons tan t t e m p e r a t u r e a p p r o a c h e s the c o n d u c t i v i t y v a l u e a t 500°C ( F i g . 11). F o r s p e c i m e n s s u b j e c t e d to v a r i e d t h e r m a l and i r r a d i a t i o n h i s t o r y t h e r e can be no unique va lue , e . g . a l though t h e r e w a s l i t t l e o r no c h a n g e in c o n d u c t i v i t y m e a s u r e d in a s p e c i m e n i r -r a d i a t e d a t 520°C, it h a s b e e n shown tha t a f t e r d o s e s of 1019 f i s s i o n s / c m 3

o r g r e a t e r , not a l l t he d a m a g e i n s e r t e d at 320°C cou ld be a n n e a l e d out at 750°C. D i r e c t c o m p a r i s o n of i n - r e a c t o r t h e r m a l c o n d u c t i v i t y v a l u e s c a n t h e r e f o r e be c o n f u s e d by low t e m p e r a t u r e o p e r a t i o n , and th i s ha s r e s u l t e d in t h e r e c o m m e n d a t i o n t h a t / k d T v a l u e s be c o m p a r e d wi th r e f e r e n c e to a l o w e r t e m p e r a t u r e l i m i t of 500°C r a t h e r t h a n 0°C.

Th i s type of i r r a d i a t i o n b e h a v i o u r s u g g e s t s tha t m o r e than one d a m a g e m e c h a n i s m i s o p e r a t i n g . T h e i n t e r p r e t a t i o n i s t h a t i n i t i a l l y i r r a d i a t i o n p r o d u c e s i s o l a t e d poin t d e f e c t s and s m a l l c l u s t e r s of d i s p l a c e d a t o m s and f i s s ion p roduc t s caus ing a reduc t ion in e f fec t ive phonon m e a n - f r e e path, and th i s i s followed by the nuc lea t ion and growth of l a r g e c l u s t e r s and mig ra t i on to s u b - g r a i n b o u n d a r i e s . A q u a s i - s t e a d y s t a t e develops at h igher doses with only a r e l a t i v e l y s m a l l d e f e c t c o n c e n t r a t i o n , showing the s t a b i l i t y of t he f l u o r i t e s t r u c t u r e i n r e s i s t i n g d e f e c t d a m a g e .

I l l - 2 . E F F E C T S O F IRRADIATION ON S I N T E R E D P O L Y C R Y S T A L L I N E U0 2 AT TEMPERATURES ABOVE 500°C (DIRECT MEASUREMENTS)

III-2. 1. Temperature range 500- 1800°C

' Of the e x p e r i m e n t s designed to m e a s u r e d i rec t ly the t h e r m a l conductivity of U 0 2 i n - r e a c t o r i t was c o n s i d e r e d tha t f o r t he t e m p e r a t u r e r a n g e up to 1800°C only the Cha lk R i v e r , G r e n o b l e , and H a r w e l l e x p e r i m e n t s h a v e a t -

22

t e m p t e d to m e a s u r e the conduc t iv i ty of the UO2 r a t h e r t han the i n t e g r a t e d conduc t iv i ty of a UO2 f u e l e l e m e n t .

The Chalk R ive r w o r k e r s c a r r i e d out two d i r ec t m e a s u r e m e n t s i n - r e a c t o r in 1958 and 1959 on p o l y c r y s t a l l i n e s t o i c h i o m e t r i c UO2 (pe l le t r o d s III and IV) up to c e n t r e t e m p e r a t u r e s of 1200°C [50]. Th i s was a n ' e f f e c t i v e ' t h e r m a l conduc t iv i ty m e a s u r e m e n t f r o m which a b s o l u t e v a l u e s w e r e o b t a i n e d , t h e U 0 2 s u r f a c e t e m p e r a t u r e b e i n g d e r i v e d f r o m a knowledge of t he coo l an t t e m p e r a t u r e and l a b o r a t o r y - d e t e r m i n e d da t a f o r t he f u e l / c l a d conduc t ance [55] . A l a t e r e x p e r i m e n t [56] (X-201) of a s i m i l a r type p r o d u c e d a s ing le m e a s u r e m e n t a t a c e n t r e t e m p e r a t u r e of 1800°C f o r a s h o r t p e r i o d . In a l l c a s e s the c a l o r i m e t r i c m e a s u r e m e n t s of hea t output w e r e checked by p o s t -i r r a d i a t i o n b u r n - u p a n a l y s i s .

A s no ted p r e v i o u s l y in s e c t i o n I I I -1 , a p r o g r e s s i v e d e t e r i o r a t i o n in o v e r a l l t h e r m a l c o n d u c t i v i t y w a s o b s e r v e d , wh ich w a s b e l i e v e d to be due to that por t ion of the fue l opera t ing at low t e m p e r a t u r e s ( < 500°C). Although the JkdT value f o r the t e m p e r a t u r e r a n g e 500 - 1600°C obtained f r o m t h e s e e x p e r i m e n t s a g r e e d c l o s e l y with that f o r u n i r r a d i a t e d m a t e r i a l , the de r ived c u r v e s of к v e r s u s T ( i r r a d i a t e d ) given in t h e s e r e f e r e n c e s a r e s ign i f ican t ly d i f f e r e n t f r o m t h o s e f o r u n i r r a d i a t e d m a t e r i a l . T h i s d i f f e r e n c e i s m o r e apparen t than r e a l . The e r r o r l i m i t s on the s lope of an JkdT v e r s u s T cu rve d rawn t h r o u g h a l i m i t e d n u m b e r of po in ts a r e s u f f i c i e n t l y high, so i t i s r e -commended that conventional t h e r m a l conductivity de te rmina t ions (k v e r s u s T ) be c o n v e r t e d to JkdT v e r s u s T f o r c o m p a r i s o n with i n t e g r a l t h e r m a l c o n -duc t iv i ty da ta , r a t h e r t h a n v i c e v e r s a .

Two r ecen t i n - r e a c t o r e x p e r i m e n t s p e r f o r m e d by the Grenob le w o r k e r s [16] c o n f i r m e d the v a l u e s o b t a i n e d on an e a r l i e r e x p e r i m e n t [52] . T h e method used gave abso lu te v a l u e s of conduct iv i ty with t h e r m o c o u p l e s p laced on the c e n t r e - l i n e and on the p e r i p h e r y of the s a m p l e . A continuous m e a s u r e of the hea t output i s ob ta ined by m e a s u r i n g the t e m p e r a t u r e d r o p a c r o s s a th ick s t a i n l e s s - s t e e l o r Z i r c a l o y - 2 c a n . The cho ice of a v e r y s m a l l i n i t i a l gap (0.035 ± 0.015 mm) a s s u r e s that no apprec iab le eccen t r i c i ty of the pe l le t s can o c c u r du r ing m e a s u r e m e n t s . The i n t e g r a t e d va lues de r ived i n - r e a c t o r were plot ted d i r ec t l y aga ins t those obtained in the l a b o r a t o r y using a c e n t r a l h e a t e r r a d i a l f low t e c h n i q u e . O v e r the t e m p e r a t u r e r a n g e 500 - 1300°C no s ign i f ican t dévia t ions f r o m the o u t - o f - r e a c t o r m e a s u r e m e n t s w e r e o b s e r v e d up to a dose of 7 X 1017 f i s s i o n s / c m 3 . The e x p e r i m e n t a l data given b y t h e s e independent e x p e r i m e n t s a r e in a g r e e m e n t [57] .

A c l o s e l y c o n t r o l l e d e x p e r i m e n t was c a r r i e d out at H a r w e l l [19] u s ing e s s e n t i a l l y the s a m e t e c h n i q u e d e s c r i b e d p r e v i o u s l y in s e c t i o n I I I - l , i . e . t h e r m o c o u p l e s w e r e loca ted both on the c e n t r e - l i n e and in two c i r c u m f e r e n -t i a l pos i t ions in the f u e l to e l im ina t e c o r r e c t i o n s f o r the t h e r m a l r e s i s t a n c e of the f u e l - c l a d d i n g i n t e r f a c e . Continuous m e a s u r e m e n t of heat g e n e r a t i o n w a s ob t a ined by m e a s u r i n g the t e m p e r a t u r e d r o p a c r o s s a c a l i b r a t e d g a s gap and independen t c h e c k s on the b u r n - u p w e r e m a d e on p o s t - i r r a d i a t i o n examina t i on . In the e x p e r i m e n t , which involved t h r e e c a p s u l e s , no s ign i f i can t change in the t h e r m a l conduc t iv i t y of t he UO2 (95% TD) was ev iden t in t h e t e m p e r a t u r e range 5 0 0 - 1600°C up to a m a x i m u m dose of 4X10 1 9 f i s s i o n s / c m 3 . F o r the m a j o r i t y of the i r r a d i a t i o n p e r i o d the f u e l o p e r a t e d in the t e m p e r a -t u r e r a n g e 700 - 1200°C; m e a s u r e m e n t s be low 700°C w e r e ob ta ined d u r i n g

23

CURVE 1. SACLAY [16] 2. CHALK RIVER [56] 3. AERE [19] 4. AERE UNIRRADIATED [32] 5. GE SAN JOSÉ [58]

(BASED ON FIT TO ORNL CURVE FOR UNIRRADIATED U0 2 AT IOWER TEMPERATURES [59]

0.01

200 400 600 BOO 1000 1200 1400' 1600 1600

TEMPERATURE ( ° C )

FIG. 12. Thermal conductivity of irradiated stoichiometric polycrystalline UO,

the p e r i o d s at r e d u c e d p o w e r d u r i n g s u c c e s s i v e r e a c t o r s t a r t - u p s . Above 1200°C c o m p a r a t i v e v a l u e s w e r e obta ined in a s h o r t p e r i o d of o p e r a t i o n in a h i g h e r n e u t r o n f lux, the dose a c c u m u l a t e d in t h i s pos i t i on be ing only 5 X 1016 f i s s i o n s / c m 3 . L a b o r a t o r y m e a s u r e m e n t s us ing a t h e r m a l d i f fus iv i ty technique p e r f o r m e d on un i r r ad i a t ed samples f r o m the s ame batch of m a t e r i a l o v e r t h e t e m p e r a t u r e r a n g e 900 - 1800°C g a v e a l m o s t i d e n t i c a l v a l u e s t o t h o s e o b t a i n e d i n - r e a c t o r ( F i g . 12).

The r e s u l t s f r o m t h e s e t h r e e s e t s of da ta a r e p lo t ted aga in s t the c u r v e f o r u n i r r a d i a t e d u r a n i u m d iox ide in F i g s . 12 and 13. T h e v a l u e s f o r t h e i n t e g r a l o v e r the t e m p e r a t u r e r a n g e 500- 1500°C f r o m the f o u r l a b o r a t o r i e s can be e x p r e s s e d a s 31.5 ± 1 W c m " 1 .

Ш-2. 2. Temperature range up to 2800"C

The range of d i r ec t i n - r e a c t o r m e a s u r e m e n t s has recent ly been extended in two s e p a r a t e s e t s of e x p e r i m e n t s . In the f i r s t , a r h e n i u m g a s - b u l b t h e r m o m e t e r i s u s e d a s the s e n s o r i n s t e a d of a t h e r m o c o u p l e f o r the h igh t e m p e r a t u r e m e a s u r e m e n t s . In t h i s d e v i c e the p r e s s u r e of a r g o n in t h e bulb i s m e a s u r e d u s ing a m u l t i - b a l a n c e p r e s s u r e t r a n s d u c e r away f r o m the high t e m p e r a t u r e zone . The body of the t h e r m o m e t e r is 3 in. long and o v e r 95% of t h e v o l u m e i s in the s e n s i t i v e p o r t i o n of t he g a s bu lb . C a l i b r a t i o n of the bu lb i s c a r r i e d out p r i o r to i t s u s e in an i r r a d i a t i o n c a p s u l e [61] .

Two e x p e r i m e n t s have been c a r r i e d out on s i n t e r e d s to ich iomet r i c UO2 u s i n g t h i s d e v i c e [47] . T h e s e w e r e e f f e c t i v e c o n d u c t i v i t y m e a s u r e m e n t s

24

FIG. 13. Comparison of integral thermal conductivity values (500 - 1500 °C)

on Z i r c a l o y c l a d f u e l . The f i r s t e x p e r i m e n t c a r r i e d out on n o r m a l g r a i n s i z e UO2 o p e r a t e d up to a c e n t r e t e m p e r a t u r e of 2750°C f o r two h o u r s , and the second on l a r g e g r a i n e d f u e l (60 ц т ) o p e r a t e d to a m a x i m u m of 2400°C f o r s ix h o u r s . The r e s u l t s f r o m both t h e s e t e s t s a r e s u p e r i m p o s e d on the g r a p h of J k d T wi th t e m p e r a t u r e s tha t had b e e n d e r i v e d f r o m g r a i n g r o w t h and c e n t r e - m e l t i n g o b s e r v a t i o n s by the s a m e w o r k e r s ( sec t ion III-3), us ing the s a m e m e t h o d s of c a l c u l a t i o n to ob ta in t h e s u r f a c e t e m p e r a t u r e of t he UO2 (F ig . 14). T h e s e r e s u l t s a r e in excel lent a g r e e m e n t with the p rev ious ly der ived cu rve and showed no de tec table effect due to var ia t ion in ini t ia l g ra in s i z e .

C h r i s t e n s e n and Al l io [62] f r o m the W e s t i n g h o u s e l a b o r a t o r y have r e c e n t l y c a r r i e d out a d i r e c t in^ r e a c t o r m e a s u r e m e n t to 2150°C on s i n t e r e d po lyc rys ta l l i r i e m a t e r i a l ( U O 2 0 0 5 ) u s ing h i g h - t e m p e r a t u r e t h e r m o c o u p l e s to m e a s u r e the change in t e m p e r a t u r e g r a d i e n t a c r o s s the c o l u m n a r reg ion a s t h e s e g r a i n s f o r m e d dur ing i r r a d i a t i o n . Dur ing a pe r iod of e igh teen h o u r s at cons tant power the t e m p e r a t u r e g rad ien t a c r o s s the c o l u m n a r g ra in region d e c r e a s e d by an amount equivalent to a 2 - 6% i n c r e a s e in mean UO2 t h e r m a l conduc t iv i ty . T h i s i n c r e a s e p r o b a b l y r e f l e c t s a change in f u e l d e n s i t y in this r eg ion . The au tho r s i n f e r f r o m t h e s e r e s u l t s that rad ian t t r a n s f e r does not cont r ibu te s igni f icant ly to the t h e r m a l conductivity in the co lumnar region, and the c o l u m n a r r eg ion p e r s e has no s ign i f i can t e f fec t on the t e m p e r a t u r e d i s t r ibu t ion in the UO2 f ue l c o r e .

T h e s e data suppor t those prev ious ly r epo r t ed by Notley [63] which showed tha t t h e r e w a s no s i g n i f i c a n t a l t e r a t i o n in the t h e r m a l c o n d u c t i v i t y of t h e h i g h - t e m p e r a t u r e region in U 0 2 due to the growth of c o l u m n a r g r a i n . These data , which w e r e obtained f r o m me ta l l og raph ic o b s e r v a t i o n s , and hence a r e subjec t to a s sumpt ions concern ing the i n t e rp re t a t i on of the extent of melt ing, do not exclude the poss ib i l i ty that enhanced conduct ivi ty can occu r in U 0 2 in the r e a c t o r , but do indica te that it i s not n e c e s s a r i l y a p r o p e r t y of s ing le -c r y s t a l m a t e r i a l .

25

9 0

eo

70

'e во и г - 5 0 •о j*

4 0

3 0

20

10

1200 1600 2000

CENTRAL TEMPERATURE {»С)

FIG. 14. Directly measured pellet thermal conductivity data

III-2. 3. Effects of departu