d W

GULF GENERAL ATOMIC

G u l f - G A - A 1 2 6 1 5 ( GA - L T R - 3 )

R E V I E W OF T H E THERMAL C O N D U C T I V I T Y OF NUCLEAR G R A P H I T E UNDER HTGR C O N D I T I O N S

bY R . J . Price

d T h i s document is S e p t e m b e r 7 , 1973 i

GULF GENERAL ATOMIC COMPANY P.O. BOX 81608, SAN DIEGO, CALIFORNIA 92138

a;l~S-[pi~$lJTl~N THIS DGCUABENT 1s t irJLiMITED p * * ' ir

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

FOREWORD

This Licensing Topical Report ( L T R ) has been prepared by Gulf General Atomic t o document the technical bases of graphite thermal conductivity values used in HTGR design. comprehensive. The report represents a continuing e f f o r t a t Gulf General Atomic t o es tab l i sh the appl icabi l i ty and va l id i ty of selected important des i gn parameters.

The information presented i s detai led and

i i i

CONTENTS

FOREWORD . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i x 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . 1 2. BACKGROUND . . . . . . . . . . . . . . . . . . . . . . . . . 2 3. EXPERIMENTAL DATA . . . . . . . . . . . . . . . . . . . . . . 6

3.1. Needle-Coke Graph i te . . . . . . . . . . . . . . . . . 6 3.2. I s o t r o p i c Graphi tes . . . . . . . . . . . . . . . . . . 20

4. THEORETICAL TREATMENTS . . . . . . . . . . . . . . . . . . . 35 5. CONSOLIDATION OF DATA: DEPENDENCE ON FLUENCE, IRRADIATION

TEMPERATURE, AND MATERIAL . . . . . . . . . . . . . . . . . . 44 5.1. Approach t o S a t u r a t i o n . . . . . . . . . . . . . . . . 44 5.2. C o n d u c t i v i t y A f t e r I r r a d i a t i o n t o S a t u r a t i o n . . . . . 46 5.3. ' C o n d u c t i v i t y a t End-Of-L i fe . . . . . . . . . . . . . . 49

6. DESIGN-BASIS CURVES . . . . . . . . . . . . . . . . . . . . . 50 6.1. Methods f o r D e r i v i n g Curves . . . . . . . . . . . . . . 50 6.2. Design-Basis Curves: H-327 Graph i te . . . . . . . . . 51

6.4. Confidence L i m i t s f o r Design-Basis Curves . . . . . . . 59 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

6.3. Design-Basis Curves: H-451 Graph i te . . . . . . . . . 57

FIGURES

1. Thermal c o n d u c t i v i t y changes versus f l u e n c e f o r r e a c t o r

2. Thermal c o n d u c t i v i t y o f i r r a d i a t e d NC7 and NC8 g raph i tes

3.

4. Temperature dependence o f t h e thermal c o n d u c t i v i t y o f

5. Thermal c o n d u c t i v i t y o f i r r a d i a t e d PGA g r a p h i t e as a f u n c t i o n

g raph i tes measured a t room temperature . . . . . . . . . . . 3

versus measurement temperature . . . . . . . . . . . . . . . 4

g r a p h i t e measured a t 30°C . . . . . . . . . . . . . . . . . .

i r r a d i a t e d PGA g r a p h i t e . . . . . . . . . . . . . . . . . . . 8

of measurement temperature . . . . . . . . . . . . . . . . . 12

Summary o f da ta on t h e thermal c o n d u c t i v i t y changes o f PGA 7

V

FIGURES {continued)

6 . Reduction i n thermal conductivity a a fun t ion of i r rad ia t ion

7 . Thermal conductivity o f i r rad ia ted CSF qraphite as a function

8. Thermal conductivity of i r rad ia ted TSX graphite as a function

9. Thermal conductivity o f i r rad ia ted CHN and 780-S graphi tes

5 temperature for a fluence of 5 x 10'0 n/cm . . . . . . . . . 14 of measurement temperature . . . . . . . . . . . . . . . . . . 15

of measurement temperature . . . . . . . . . . . . . . . . . . 16

ment temperature . . . . . . . . . . . . . . . . . . . . . . . 18 measured perpendicular t o extrusion as a function of measure-

10. Fractional change i n thermal conductivity of needle-coke and

11. Room-temperature thermal conductivity of H-327 graphite para1 -

1 2 . Room temperature thermal conductivity o f H-327 graphite

13.

14. Thermal conductivity of i r r ad ia t ed H-315-A graphite measured

Gilsonite-coke graphites as a function of fluence . . . . . . 21

le1 t o extrusion as a function of f luence. . . . . . . . . . . 22

perpendicular t o extrusion as a function of fluence . . . . . 23 Thermal conductivity a t 40°C of pressed i so t ropic Gi 1 socarbon graphi te i r rad ia ted a t 600", 900°, and 1200°C . . . . . . . . 24

perpendicular t o forming axis as a function of measurement temperature . . . . . . . . . . . . . . . . . . . . . . . . . 29

15. Room temperature thermal conductivity of H-328 graphite

16. Change i n thermal conductivity measured a t 40°C paral le l t o perpendicular t o extrusion as a function of fluence . . . . . 30

the grain alignment of Gilsonite-coke graphite as a function of fluence f o r i r rad ia t ion temperatures of 450"C, 600"C,

17. Relative change i n thermal conductivity as a function o f 9OO"C, and 1200°C . . . . . . . . . . . . . . . . . . . . . . 33

measurement temperature for Gil sonite-coke and p i t c h coke graphites i r rad ia ted t o 3 x 1020 n/cm2 as a function of measurement temperature . . . . . . . . . . . . . . . . . . . 34

18. Fractional changes in thermal r e s i s t i v i t y o f pitch coke i so t ropic graphite with neutron dose . . . . . . . . . . . . . 34

19. Calculated temperature dependence of thermal conductivity of PGA graphite a f t e r i r rad ia t ion . . . . . . . . . . . . . . . . 37

20. Temperature dependence o f the thermal conductivity o f

and l a t t i c e dynamics model . . . . . . . . . . . . . . . . . . 42 i r rad ia ted CHN graphite: comparison between exnerimental data

21. Temperature dependence of the thermal conductivity of i r rad ia ted Gi 1 socarbon graphite : experimental data and l a t t i c e dynamics model , . , , , , , . , 43 comparison between

vi

FIGURES (continued)

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

1 .

2 . 3 .

Composite plot of the time constant f o r the saturat ion of the thermal conductivity change as a function of i r rad ia t ion temperature . . . . . . . . . . . . . . . . . . . . . . . . . Composite p lo t of the room-temperature thermal conductivity of needle-coke graphi t e s i r rad ia ted t o saturat ion as a function or i r rad ia t ion temperature . . . . . . . . . . . . . . . . . . Composite plot of the room temperature thermal conductivity of Gilsocarbon and pitch coke graphites i r radiated t o

Experimental measurements o f the thermal conductivity o f unirradiated H-327 graphite as a function of measurement temperature . . . . . . . . . . . . . . . . . . . . . . . . . Calculated curves of the thermal conductivity of H-327 graphite a t the i r rad ia t ion temperature as a function of fluence . . . . . . . . . . . . . . . . . . . . . . . . . . . Calculated curves of the thermal conductivity of H-327 graphite a t the i r rad ia t ion temperature as a function of i r rad ia t ion temperature . . . . . . . . . . . . . . . . . . . Calculated curves of the thermal conductivity o f H-327 graphite i r rad ia ted t o saturat ion as a function of measurement temperature . . . . . . . . . . . . . . . . . . . . . . . . . Experimental measurements o f the thermal conductivity of unirradiated H-451 graphite (perpendicular t o extrusion) as a function of measurement temperature . . . . . . . . . . . . . Calculated curves of the thermal conductivity of H-451 graphite a t the i r rad ia t ion temperature as a f u n c t i o n o f f l uence . . . . Calculated curves o f the thermal conductivity o f H-451 graphite a t the i r rad ia t ion temperature as a function of i r rad ia t ion temperature . . . . . . . . . . . . . . . . . . . . . . . . . Calculated curves o f the thermal conductivity of H-451 graphite i r rad ia ted t o saturat ion as a function of measurement temperature . . . . . . . . . . . . . . . . . . . . . . . . .

saturat ion as a function o f i r rad ia t ion temperature . . . . .

TABLES

Irradiation-induced changes i n thermal r e s i s t i v i t y o f PGA graphite specimens f rom DFR experiments 27/6 a n d 199/2 . . . . Thermal conductivity changes of i r rad ia ted graphites . . , . . Thermal conductivity o f graphites i r rad ia ted i n GGA capsules G-11 and G-12 . . . . . . . . . . . . . . . . . . . . . . . .

45

47

48

52

54

55

56

58

60

61

62

10 11

19

vi i

TABLES (continued)

4. Thermal conductivity changes f o r H-327 graphite . . . . . . . 25 5 . Thermal nductivity o f raphi te samples i r rad ia ted t o

1.8 x lo5$ n/cm2 E>0.18 YFleV) a t 1175°C . . . . . . . . . . . 27 6 . Thermal conductivity changes for H-328 graphite . , . , . . . 31 7 . Values f o r the a-axis thermal conductivity of a graphite

crystal as l imited by Umklapp processes, c r y s t a l l i t e bounda-

Means and standard deviations of experimentally determined parameters used i n formulae f o r design curves of the thermal conductivity o f i r rad ia ted H-327 and H-451 graphite . . . . . 64 on predicted thermal conductivity of i r rad ia ted H-327 and

r i e s , and p o i n t defects 39

8.

9 . Results of Flonte Carlo calculat ions f o r 90% confidence l imi t s

H-451 graphite a t i r r a d i a t i o n temperature . . . . . . . . . . 65

v i i i

SUMMARY

Experimental data on the thermal conductivity of needle-coke and i sotropi c graphi t e s i rradi ated between 500°C and 1 6OO0C are reviewed. I r radiat ion reduces the room temperature thermal conductivity; as the fluence increases, the r a t e o f reduction declines and the conductivity approaches a saturat ion level which increases as the i r rad ia t ion tem- perature increases. s t a r t s , the conductivity again decreases. approach t o saturat ion appears t o increase l inear ly w i t h i r rad ia t ion temperature, while the conductivity a f t e r saturat ion increases expo- nent ia l ly w i t h i r rad ia t ion temperature. ence o f the thermal conductivity on measurement temperature. Theoretical treatments o f thermal conduction in i r rad ia ted graphite based on the l a t t i c e dynamics o f hexagonal c r y s t a l l i t e s i n the presence of c rys ta l - l i t e boundaries and point defects a re f a i r l y well developed. Single vacancies and small i n t e r s t i t i a l c lus te rs a re believed t o control the thermal conductivity o f graphite i r rad ia ted below 30OoC; between 3OO0C and 650OC vacancies alone dominate, while above 650oC vacancy loops play an increasingly important role . The main pract ical application of the theoret ical model i s t h a t i t enables the temperature dependence o f the conductivity o f i r rad ia ted graphite t o be predicted once measurements have been made a t a s ing le temperature.

Eventually, when i rradiation-induced expansion The time constant f o r

I r radiat ion reduces the depend-

Design-basis curves f o r the thermal conductivity o f i r rad ia ted H-327 and H-451 graphites were derived from the l a t t i c e dynamics model, assuming t h a t the important irradiation-induced defects a re vacancies or vacancy loops which a re small compared w i t h phonon wavelengths. The necessary parameters were obtained from analysis o f experimental measurements on unirradiated H-327 and H-451 graphi te , together with published data on the room-temperature conductivity o f i r rad ia ted needle-coke graphi t e s and Gilsocarbon graphites. The f ina l curves a re shown as f igures 25-32.

i x

1. INTRODUCTION

Thermal analysis of HTGR core performance requires reliable values for the thermal conductivity of the moderator block graphite as a function of fast neutron fluence, irradiation temperature, and measurement temperature. mental data and the theoretical basis for extrapolations, and recommends design-basi s curves for the thermal conductivity of needle-coke and isotropic graphites operating under HTGR conditions.

This report assesses the available experi-

1

2 . BACKGROUND

The general trends in the thermal conductivity of graphite as a function of neutron fluence have been known for many years. measurements (mostly low irradiat ion temperature data re la t ing t o the Hanford reactors) are reported by Nightingale(l1, and l a t e r measure- ments of in te res t t o AGR designers a t temperatures u p t o 65OoC were reviewed by Simmons(2). recent data extending t o i r radiat ion temperatures of 150OOC. A p l o t taken from re f . ( 3 ) i l l u s t r a t ing the change in room-temperature con- ductivity of needle-coke-based reactor graphites as a function o f fast-neutron fluence i s shown in f i g . 1 . decreases sharply with increasing fluence, b u t the change saturates a t between 1 t o 5 x 1O2I n/cm2. The saturation level increases with

Early

Engle and E a t h e r l ~ ( ~ ) summarized the more

A t f i r s t the conductivity

increasing i r rad ia t ion temperature. A t high f conductivity again decreases because breakaway graphite t o become increasingly porous.

The e f f ec t of i r radiat ion on the thermal

uences expans

onduct

the thermal on causes the

vity versus measurement temperature curve i s i l l u s t r a t ed in f i g . 2 taken from a report by Helm(4). The downwards-sloping curve character is t ic o f we1 1- graphitized polycrystall ine graphite i s lowered a n d f la t tened. The curves fo r material i r radiated below 1000°C usually have a shallow maximum above room temperature. higher temperatures as the i r radiat ion temperature i s decreased.

The position o f the maximum moves t o

Most o f the e a r l i e r measurements of the thermal conductivity of i r radiated graphites used a steady-state heat flow technique or the Kohlrausch method i n which a current i s passed th rough a long sample whose ends are connected t o heat sinks and the result ing parabolic temperature dis t r ibut ion i s measured. In recent years these methods have been largely superceded by the heat-pulse technique in which a short pulse of radiant heat i s flashed onto the front face o f a disc- shaped sample while the rear-face temperature i s monitored by a

2

n V C

I V w v, I r: V \ J

0 a W

>- I-

> I- V 3 n z 0 u J c x fY W I I-

- -

0 . 4

0.3

0.2

0.1

0

h \ 1175-1280°C

0 5 10 15 20 2 5 30

- 2 ’ (N/CM 2 ) (E>0 .050 MeV) FLUENCE X 10

F i g . 1 . Thermal conductivity changes versus fluence f o r reactor graphites measured a t room temperature (from r e f . 3 )

3

0.50

0.40 - u I 0 w cn I r: u \

0

2 0.30 u v

t I-

> t- u 3

z 0 V

J

sz rr: w I I-

- -

a 0.20

a

o. 10

0

EXPOSURE TEMP.

TYPE ( O C ) ( N / C M ~ i o 2 ' ) 0 NC 8 0 A NC 8 650 0.20

NC 8 1000 3 . 4 1 V NC 7 775 14.15 ONC 7 625 4.02

0 100 200 300 400 500

TEMPERATURE ( " C )

F i g . 2. Thermal conductivity of i r rad ia ted N C 7 a n d NC8 graphites versus measuretilent temperature (from r e f . 4)

thermocouple ( f o r temperatures u p t o a b o u t 80OoC) o r an infrared detector ( f o r higher temperatures). The time delay before the rear face temperature r i s e s t o some specified f rac t ion of i t s ultimate value i s re la ted t o the thermal d i f f u s i v i t y of the sample, which may be converted t o the thermal conductivity by multiplying by the density and the s p e c i f i c heat. working w i t h i r rad ia ted samples, notably the small sample s i z e ( typ ica l ly a d i sc 10-20 mm i n diameter by 1-2 mm th ick) and the speed w i t h which a large number of readings may be taken. of the technique i s typical ly +lo%. tes ted by the heat-pulse method and a steady temperature gradient method(5), both techniques gave the same r e s u l t s .

This technique of fe rs many advantages when

The reproducibi l i ty In t e s t s where the same sample was

Theoretical understanding of the thermal conductivity of graphite has been advanced by the work of Kelly and co-workers t o the point where thermal conductivity i s the best understood property of i r rad ia ted graphite. The theoret ical work i s summarized in r e f . ( 6 ) a n d the application of the theory t o i r rad ia ted polycrystal l ine graphite i s described i n r e f . ( 7 ) . Brief ly , thermal conduction i n graphite takes place by phonon t ransport paral le l t o the basal planes and may be t rea ted using the theory o f l a t t i c e dynamics in the graphite crystal l a t t i c e . In unirradiated material the phonon mean f r e e p a t h i s l imited by phonon-phonon collisions and crystallite boundaries. Irradiation-

induced defects cause additional sca t te r ing of phonons and reduce the conductivity. responsible f o r thermal conductivity changes a r e bel i eved t o be vacancies and small i n t e r s t i t i a1 cl us t e r s . Between 3OO0C and 650oC vacancies alone a r e responsible, whi 1 e above 650°C uncol 1 apsed vacancy 1 oops become important. I t i s not ye t possible t o ca lcu la te the thermal conductivity changes from f i r s t pr inciples . In pract ical terms, the most useful r e s u l t of the theoret ical work i s t h a t the calculated tem- perature dependence of the phonon sca t te r ing process f o r each type of defect may be used as a basis f o r estimating the thermal conductivity of i r rad ia ted graphite a t any temperature when measurements have been made a t a d i f f e r e n t temperature.

For i r rad ia t ion temperatures below 3OO0C, the defects

5

3. EXPERIMENTAL DATA

3.1 Needle-Coke Graphite

a r e of limited use because the data a r e sporadic, they r e f e r t o now- obsolete grades o f graphi te , and the exposures a re expressed i n megawatt-days per adjacent ton of fuel in the Hanford reactors and a r e not eas i ly convertible t o neutron fluences. w i 11 be ignored f o r present purposes.

The ear ly experimental measurements reported by Nightingale(’)

These measurements

A summary plot of the measurements of the fract ional change i n room temperature thermal conductivity of Br i t i sh reactor-grade graphite (PGA) i r radiated i n the Dido and Pluto reactors a t temperatures up t o 650OC, taken from r e f . 2 , i s shown i n f i g . 3. i n thermal conductivity was found t o be independent of sample or ientat ion(8-10) . These data show the i n i t i a l decrease in conductivity with fluence, b u t were n o t carr ied t o a h i g h enough fluence t o reach saturat ion. In samples i r rad ia ted a t o r bel ow 35OoC, the i rradi a t i on-i nduced con- duc t iv i ty changes s t a r t t o anneal out when the sample temperature i s raised a l i t t l e above the i r rad ia t ion temperature, and a r e completely annealed out a t 1500-1800°C f o r annealing times of a few h o ~ r s ( ~ , ~ ) .

The fract ional change

The e f f e c t o f i r rad ia t ion temperature i s c lear ly evident.

Limited data on the temperature dependence of the thermal con- duc t iv i ty o f PGA samples i r rad ia ted i n the Dido, Pluto, and DR-3 (Riso) reactors were reported by Mottershead and James( l o ) . were made by the Kohlrausch method a t temperatures between 40% and 400OC. Conductivity-versus-temperature curves for paral le l and perpen- d i c u l a r samples a r e shown i n f i g . 4 ( a a n d b ) . i r rad ia ted samples a re lower t h a n those of unirradiated material and have a posi t ive slope. The f igures a l so show curves calculated from the assumption t h a t irradiation-induced defects have a temperature- independent mean f r e e path (discussed in a l a t e r section of t h i s repor t ) . The calculated curves f a l l somewhat higher than the measurements.

The measurements

The curves f o r the

6

I I

i 2 I

OFROM LOW-FLUX IRRADIATION ( $ D - 1 0 )

o O A F R O M HIGH-FLUX IRRADIATION ( + D - 1 0 14 )

ei 25" C (44" C )

r %O ').6'&/ zoo" c ( 1 68" c ) 1 50' C ( 126" C ) ?4fp A / 2 5 O " C ( 2 1 l 0 C )

I I I 1

1 0 ~ 9 1 O2O 1021 1 022 18 10

EQUIVALENT F I S S I O N DOSE, Yo (N/CM2)

Fig. 3 . Summary o f d a t a on the thermal conductivity changes o f PGA graphite measured a t 30°C (from r e f . 2 ) . Figures in parenthesesl$re equiva- l en t i r radiat ion temperatures referred t o +,, = 8.5 x 10 .

I

7

I

- - I

I -

82 a u x \ x u I--

E < 0.010 - - 12.5 X 10'' N /CM2 (NDE) AT 250°C

0.005 I 1 I I

0.30

o A1 0 A2

I I I 1 I

100 200 300 400 500 0.20: - z u o w 0.15

a o ~a

I

u r n I - 2 .5 x i ' 0 2 ~ N / c M 2 h D E ) AT 45'0°C - ----- 3

THEORETICAL -

I I

400

A X ---- x \ K A

I-- 0.10

0.05

8 .6 X l o2 ' N/CM2 AT 350°C -

0 100 200 300

( a 1 MEASUREMENT TEMPERATURE ( " C )

0 100 200 300 400 MEASUREMENT TEMPERATURE ( " C )

( b )

F i g . 4. Temperature dependence o f t h e thermal c o n d u c t i v i t y o f i r r a d i a t e d PGA g r a p h i t e : ( a ) p a r a l l e l t o e x t r u s i o n ; A 1 and A 2 u n i r r a d i a t e d specimens; A3 and A4 i r r a d i a t e d specimens (K/Ko)40 f o r A 3 = 0.284 (K/Ko)40 f o r A4 0.145 and ( b ) pe rpend icu la r t o e x t r u s i o n B1 u n i r r a d i a t e d ; B2 i r r a d i a t e d ( K / K o ) 4 0 = 0.026 ( f r o m r e f . 10)

Later measurements of the thermal conductivity of PGA graphite i r rad ia ted in the Dounreay Fast Reactor a re given by Martin and P r i c e ( l l ) . The fract ional changes in room temperature r e s i s t i v i t y from r e f . 11 are shown in Table I . I t was concluded t h a t the thermal r e s i s t i v i t y changes a t i r rad ia t ion temperatures below 6OO0C correlated best with those obtained i n the lower flux Pluto and Dido f a c i l i t i e s i f an "equivalent temperature" was used, assuming an act ivat ion energy of 1 . 2 eV. case of i r rad ia t ions above 6OO0C no equivalent temperature correction appeared t o be necessary.

I n the

PGA graphite w i t h a double pitch impregnation (Dragon grade 5 9 / 2 ) was i r rad ia ted i n the H i g h Flux Reactor, Petten (HFR) a t 6 O O 0 C , 900°C, and 1200°C(12). The r e s u l t s a r e included i n Table 11. only temperature where comparison i s possible) the r e s u l t s agree reason- ably well w i t h those obtained on PGA i r rad ia ted in Dido and Pluto.

A t 600OC ( t h e

Three measurements of the room-temperature thermal conductivity o f PGA graphite i r rad ia ted a t 1200°C _+ 100°C in the Dido reactor were reported by Reynolds e t . a 1 . ( l 3 ) . the thermal conductivity of two paral le l -cut samples had been reduced 32% a n d 33%, while t h a t of a perpendicular-cut sample was reduced 41%.

A t a fluence of 0.73 x 1O2I n/cm2

French work on Pechiney (coke L ) nuclear graphite and Bri t ish PGA

Conductivities were measured graphite i s reported in r e f s . 14 and 15. by the Kohlrausch method. Plots of the thermal conductivity versus temperature curves f o r PGA a re shown in f i g . 5. of the room-temperature conductivity are i n f a i r l y good agreement w i t h the Br i t i sh work(2,8,10) a t s imi la r temperatures, b u t the sharp change in conductivity between 20°C and 5 0 O C has n o t been observed by other workers. Since there i s no theoret ical reason t o expect a discont inui ty in the curve, the e f f e c t i s probably an a r t e f a c t associated with s t a r t i n g the measurements u p from room temperature. The dependence of the room temperature conductivity change on the i r rad ia t ion temperature

The absolute values

9

I

Capsule

1

2

3

4

5

6

7

a

9

10

11

Table I

Irradiation-Induced Changes in Thermal Resistivity of PGA Graphite Specimens

From DFR Experiments 27/6 and 199/2 (Taken from Ref. 11)

Direction Re1 a t i ve to Extrusion

Di rec t ion

Paral le1 Perpendi cul a r Paral 1 e l Perpendicular Paral le1 Perpendicular Parallel Perpendicular Paral 1 e l Perpendicular Paral 1 e l Perpendicular Paral 1 e l Pe rpend i cu 1 ar Paral 1 e l Perpendicular Parallel Perpendicular Paral 1 el Perpendicular Pa ra 1 1 e l Perpendicular

Fast Fluence ( N D E ) x 10-21

(n/cm2)

3.2

3.6

4.3

4.5

4.8

5.0

5.0

4.9

4.4

3.9

3.2

~-

Experiment 27/6

Temperature

(OC)

340

34 0

360

380

400

430

470

500

530

550

570

+ KO i s the thermal conductivity before i r rad ia t ion .

Y, i s the thermal conductivity a f t e r i r rad ia t ion .

32.5 26.4 37.7 32.4 20.6 17.9 20.4 17.1 16.5 15.5 16.2 15.0 13.7 11.4 13.1 11.1 12.6 9.9

10.7 8.9

10.0 8.7

Experiment 199/2

Fast F1 uence ( N D E ) x

(n/cm2)

3.0

3.7

4.1

4.7

5.1

5.2

5.3

5.2

5.0

4.3

3.7

Temperature

(OC)

430

450

480

51 0

600

570

550

540

540

540

540

t

[>- 1 1 7.6

6.0 5.8 5.6 5.8 5.9 5.8

7.8

--- --- 5.0 4.8 5.0 5.1 5.0 5.0 4.9 5.0 5.8 5.7 4.8 5.2

7 /

L Q,

Table I1

Thermal Conduct ivi ty Changes of I r r a d i a t e d Graphi tes (Taken From Ref. 12 )

Graphi te

1 : Pre-product ion pressed Gilsocarbon

axi a1

d i r e c t i o n

59/2: PGA wi th double p i t c h impregnation

d i r e c t i o n [ '1::: ]

Neutron Dose

n c r 2 ) ( N i Dido)

0

0.5

1 .o

2.0

3.0

0

0 .5

1 .o 2.0

Thermal Londuct ivi t y a t 40OC a f t e r I r r a d i a t i o n a t 600, 900 and 1200OC

6OO0C

0.255

0.15

0.09

0.07

0.50

0.14

0.10

0.09

( c a l /cm-sec-oC)

9oooc

0.255

0.17

0.11

0.075

0.075

0.50

0.17

0.14

0.12

1200oc

0.255

0 .18

0.13

0.103

0.095

0.50

0.26

0.25

0.21

0.280

0.230

0.180

0.130

0.080

0.030

I RRAD. D I RECT I ON

170°C 0 0 2 w 0 c a

0 50 100 150 200 250 300 350 400

MEASUREMENT TEMPERATURE ("C)

Thermal conductivity of i r rad ia ted PGA graphite as a function of measurement temperature (from r e f . 1 4 )

1 2

-. . . . . . . . . - . . . . . . . . . . . . . . . . . . . . - - . . . . . . -

f o r a fluence of 5 x lo2" n/cm2 i s plotted in f i g . 6 , and i s agreement with the r e s u l t s of workers i n the U.S.A. and U . K .

Thermal conductivity data obtained a t Battell e Northwest from heat-pulse measurements on samples i r radiated i n the ETR

n f a i r

Laboratories were

summarized by Helm('+) and a few r e s u l t s were reported by Baker(16). Helm's curves summarizing the r e s u l t s on NC-7 and NC-8 ( E G C R moderator graphi te) a re given in f i g . 2 , and the r e s u l t s on two other needle coke graphites, CSF and TSX, a re shown i n f i g s . 7 and 8. The r e s u l t s show t h a t the increase in conductivity with increasing i r r a d i a t i o n temperature f o r a given fluence observed during lower-temperature i r rad ia t ions on PGA graphite continues u p t o 1000°C. Later resu l t s obtained by Baker(17) on transverse samples of EGCR graphite i r radiated a t 750-800°C showed t h a t a t h i g h f luences, when the sample has entered the expansion region, the thermal conductivity again decreases. One sample i r radiated t o 2 x a t room temperature and 0.044 cal/cm-sec-°C a t 5OO0C, and a second sample i r rad ia ted t o 2 . 4 x 0.01 2 cal /cm-sec-°C a t room temperature and 0.01 8 cal /cm-sec-OC a t 50OOC.

n/cm2 (3% expansion) had a conductivity o f 0.027 cal/cm-sec-OC

n/cm2 (20% expansion) showed a conductivity of

Data obtained a t Gulf General Atomic on i r rad ia ted needle coke graphites were reported in r e f s . 5 and 18-20. All measurements between 2 2 O C and 8OO0C were made by t h e h e a t - p u l s e method on d i s c - s h a p e d

samples i r rad ia ted i n GGA capsules G-10, G-11 and 6-12 and/or the BNWL s e r i e s of GEH-13 capsules ( i r rad ia ted i n the E T R ) . The measurements between 800 and 2 2 O O O C ( r e f . 5 ) described by Longmire(21), u s i n g e l e c t r i c a l l y heated rectangular s labs measuring 20 mm x 6 mm x 1 mm. Wherever possible the i r rad ia t ion temperatures reported here have been revised t o take account of recent measurements of neutron-induced thermocouple decali b r a t i o n ( 2 2 ) . have not been a l te red from those or ig ina l ly reported; a l l of the data from i r rad ia t ions in the ETR were based on the Fe5'+ ( n , p ) Mn5'+ reaction and were expressed in terms of integrated neutron fluence w i t h energies above 0.18 MeV, using an e f fec t ive act ivat ion cross section of 57.1 mb.

were made by a s teady-state flow method

Fluences

13

20

15

10

5

0

0 SIMMONS [2] A NIGHTINGALE [ l ]

C.E.A.

100 150 200 250 300 350 400

I RRAD I AT I ON TEMPERATURE ( " C )

F i g . 6. Reduction in thermal conductivity as a function of i r rad ia t ion temperature for a fluence of 5 x 1020 n / c d (from ref . 14)

14

0.30 - V 0 I V w U - J I x V \ -I 0.20 a u W

> I-

> I- u 3

z 0 V

-I Q E cc w I I-

- - n 0.10

O

y---+v-v

I I I I I

I

TAT I ON - ( o c ) ( N / C M ~ 1 oL I ) A I1 475 0.92 01. 0

0 1. 700 1.17 v -I- 775 1.27

0 100 200 300 400 500

TEMPERATURE ("C)

F i g . 7 . Thermal conductivity of i r r ad ia t ed CSF graphite as a function of measurement temperature (from re f . 4 )

i 15

0.50

n 0.40 V

I V w v) I x u \

u

> I-

> I- V => z 0 u -I

z a2 W I I-

0

2 0.30 v

- - n 0.20

a

o. 10

C

-% a,

I I I I I

OR i EN- TAT I ON

EXPOSURE TEMP. ( O C ) ( N / C M ~ x i o 2 ' )

0.00 0.00 1.20 1.17 0.87 1.20 7.00 1.21 1.16 7.00

0 100 200 300 400 500 600

TEMPERATURE ( " C )

Fig. 8. Thermal conductivity o f i r rad ia ted TSX graphite as a function of measurement temperature (from r e f . 4 )

1 6

F i g . 9 shows the thermal conductivity as a function of measurement temperature for CHN graphite i r radiated in capsule G - 1 0 ( r e f . 5 ) . i n i t i a l portions of the curves a re similar t o those obtained a t lower i r radiat ion temperatures ( f i g s . 7 and 8 ) , and in addition they show tha t the irradiation-induced change i n conductivity becomes progressively smaller as the i r radiat ion temperature increases u p t o 1 5 O O O C . higher temperature parts of the curves show the e f f e c t of thermal annealing during the t e s t ; when the t e s t temperature exceeds the i r radiat ion temperature the curves approach the curve f o r unirradiated material. i r radiated a t 123OoC showed tha t the irradiation-induced conductivity change was essent ia l ly recovered a f t e r annealing a t 15OOOC.

The

The

A se r i e s of stepwise anneals on a sample of CHN graphite

Further measurements on the thermal conductivity of needle coke graphites i r radiated in GGA capsules G - 1 1 and 6-12 are shown i n r e f . 17 as a function of i r radiat ion and measurement temperature. a r e re-tabulated i n Table 111 of the present report t o r e f l e c t the re-calculated temperatures. a t 550-800°C are i n reasonable agreement w i t h those reported previously. However, f o r i r radiat ions i n capsule G-12 a t 950° and 1 2 2 5 O C , the room- temperature conductivities a re considerably lower than previous values and the conductivity-versus-temperature curve i s f l a t o r slowly rising u p t o 400°C, compared w i t h a decreas ing curve o b t a i n e d i n o t h e r measure-

ments on samples i r radiated a t s imilar temperatures ( fo r example, f i g . 9 ) . A f l a t o r r i s ing K-versus-T curve i s charac te r i s t ic of a h i g h concentration of point defects and seems inconsistent w i t h the 6-12 i r radiat ion temper- a tures . mental inaccuracies may have contributed t o the anomalous curves. A second poss ib i l i ty i s t h a t the samples experienced a s ign i f icant neutron exposure a t low temperatures during cool-down. Unfortunately a l l b u t one of the thermocouples i n the h i g h temperature c e l l s f a i l ed before the end of the i r radiat ion and the temperature records f o r cool-down are inadequate t o check t h i s poss ib i l i t y . d a t a were excluded from consideration when the design-basis curves were constructed.

These data

The measurements on samples i r radiated

The small sample s i z e made the measurements d i f f i c u l t and experi-

Because of the anomalies, these

1 7

n

0 0.3 I 0 w m

I z o \ J

5 0.2 v

> I-

> I- o 3

- -

0.1 0 0

J

E aL W I I-

a

c

Fig. 9.

I I I I

\ U N I R R A D I A T E D , 780-S AND CHN

1 x i o 2 1 N / c M 2 - 021 N / C M ~

021 N/CM*

\\ .. ... CHN, 3000c, 1.5 x N / C M ~

I I I 1

2000 1 500 1000 1500

MEASUREMENT TEMPERATURE ( O C )

Thermal conducti vi t y of i r r ad ia t ed CHN and 780-S graphi t e s measured perpendicular t o extrusion as a function of measurement temperature (from r e f . 5 )

Table I 1 1

Thermal Conductivity o f Graphites I r r a d i a t e d i n GGA Capsules G-11 and 6-12

22%

0.040 0.045 0.077 0.074 0.060 0.094 0.062 0.967 0.047

0.055 0.065 0.033 0.053 0.048 0.075 0.034 0.063 0.075 0.060 0.038 0.065

Capsule lO0OC

0.050 0.050 0.082 0.077 0.062 0.099 0.077 0.072 0.050

0.062 0.070 0.038 0.064 0.057 0.085 0.035 0.070 0.060 0.070 0.045 0.071

G - 1 1 G-11 G-11 G-11 G-11 G-11 G-11 G-11 G - 1 1

G - 1 2 G-12 G-12 G-12 G-12 G-12 6-12 G-12 G-12 G-12 G-12 G-12

-I

W

7OO0C

0.044

0.065

0.054 0.082

3.040

0.074

----- 0.070 0.055

0.065 0.070 0.038

0.065 0.084 0.038 0.060 0.058 0.070 0.054

0.065

-----

Graphite Grade

H-327 .H-327 TS-688 TS-688 TS- 688 TS-688 9567 9567

'H-328

H-327 H-327 H-327 H-327 H-327 H-327 H-327 H-327 TS-688 TS-688 TS-688 TS-688

800OC

0.042

0.064

0.053 0.079

----- -----

----- ----- 0.050

0.072 0.085 0.037

0.084 0.075 0.037 0.070 0.049 0.064 0.054

-----

-----

Sample Or ien ta t ion

Perp. Perp. Perp. Perp. Perp. Perp. Perp. Perp. Perp.

Perp. Perp. Perp. Perp. Perp. Perp. Perp. Perp. Perp. Perp. Perp. Pew.

Sample Number

79 80 49 64 77 97 82 83

103

184 195 167 170 196 197 171 174 287 290 273 275

Fas t Neutron Fluence x 10-21

(n/cm2, E> 0.18 MeV)

1.75 1.75 1.70 1.75 1.75 1.70 1.75 1.75 1.70

2.30 2.30 4.5 4.5 5.1 5.1 5.7 5.7 5.1 5.1 5.7 5 .7

Mean I r r a d i a t i o n Temperature

(OC)

550 550 525 54 5 550 790 550 550 790

625 625 950 950 950 950

1225 1225

950 950

1225 1225

Thermal Conductivity a t Various Measurement Temperatures ( ca l /cm- sec-oC ) -

200%

0.050 0.055 0.082 0.082 0.065 0.104 0.078 0.077 0.062

0.072 0.076 0.040 0.075 0.066 0.095 0.038 0.066 0.060 0.080 0.050 0.074

- - 3OO0C

0.050 0.055 0.082 0.082 0.065 0.102 0.078 0.089 0.062

0.071 0.080 0.044 0.078 0.075 0.099 0.040 0.068 0.060 0.084 0.052 0.074

- 3.050 3.054 3.078 3.079 0.064 3.100 3.077 3.079 3.062

3.070 0.082 3.045 0.080 0.078 0.103 0.040 0.069 0.064 0.085 0.055 0.075

- 500OC

0.048 0.050 0.074 0.079 0.062 0.096 0.065 0.075 0.059

0.071 0.079 0.044 0.078 0.080 0.102 0.040 0.070 0.065 0.085 0.055 0.075

- 600OC

0.046 0.044 0.067 0.076 0.059 0.085 0.075 0.072 0.052

0.070 0.078 0.042 0.074 0.078 0.095 0.038 0.072 0.064 0.080 0.054 -----

Run Number

F-0401 F-0400 F-0431 F-0432 F-0433 F-0434 F-0399 F-0398 F-0430

6-0116 G-0117 G-0114 G-0115 G-0106 G-0107 6-0110 6-01 11 G-0108 G-0109 G-0112 G-0113

Thermal conductivity measurements on the disc-shaped samples i r rad ia ted in the GEH-13 s e r i e s of capsules i n cooperation with Bat te l le Northwest Laboratories were made a t room temperature only. a r e reported in r e f s . 18 and 19. The room-temperature conductivity changes i n CHN graphite a re shown in f i g . 10 (from r e f . 18), and those i n H-327 a r e given in f i g s . 11 and 1 2 ( r e f . 1 9 ) . The individual measurements corre- sponding t o f i g s . 11 and 12 are l i s t e d i n Table IV. All temperatures and fluences i n f i g s . 10-12 and Table IV have been updated t o r e f l e c t recent recalculat ions. The curves i n f i g s . 11 and 12 show t h a t as the i r rad ia t ion temperature increases toward 160OOC the reduction i n thermal conductivity becomes progressively l e s s severe. The data confirm t h a t the r e s u l t s obtained from samples i r rad ia ted a t 950-1225OC i n the 6-12 capsule were anomalously low. Figure 10 includes a point f o r a sample of CHN graphite i r r a d i a t e d t o 1.8 x increments in the s e r i e s o f GEH-13 capsules. fluence data f o r s imi la r samples i s shown i n Table V . In s p i t e of measurement problems associated w i t h the d is tor t ion and porosity induced by the very h i g h f luence, the data confirm e a r l i e r ind ica t ions( l6) t h a t the thermal conductivity i s f u r t h e r reduced a f t e r very h i g h fluence i r r a d i a t i o n .

The r e s u l t s

n/cm2 a f t e r repeated i r rad ia t ion The remainder o f the high

3 . 2 Isotropic Graphites Irradiation-induced changes i n the thermal conductivity o f Gilsocarbon-

based graphi t e s have been measured by Dragon project workers ( 1 2 2 3 )

I r radiat ions were car r ied out i n the HFR (Pet ten) a t temperatures of 600 _+ 300C, 900 5 3OoC, and 1100-1250°C t o fluences of 3.5 x 1021 n/cm2 (Nickel Dido Equivalent). The material used was a preproduction molded G i 1 socarbon graphite (Gragon reference no . 1 ) . a t 40OC as a function of neutron fluence i s shown i n f i g . 13 (from ref . 2 3 ) , and the numerical data (from r e f . 1 2 ) a r e included in Table 11. The absolute values of conductivity a re considerably lower than those o f para1 1 el -cut impregnated PGA graphite (Dragon reference no. 59/2) i r rad ia ted under the same conditions, b u t the f ract ional reduction i n

The thermal conductivity

20

ll

I- C z 0

m

m

*X

0

-...I

I N

d

n

z

\ 0

x h,

v

n

m

0

00

x (D <

V d

v

FRAC

TIO

NAL

CHA

NGE

IN T

HERM

AL

CON

DUCT

I V I T

Y ,

1 -K

K

(%)

0

h,

w

ev

l

o\

vo

ou

)

0 0 0 0 0 0

0 0

d

0 0 0

- I

I W

d -

- --I

m

- 0 0 - --I m

0 I

z

z

m

W r

m 0

0

7

m

G,

W I

--I

m

m F -

0

I

\%

d

d

u) 0

0 0

h,

\

0 . 6

0 . 5

0.4

0 0.3

w 0.2

= 0.1 0

- 0.6

T = 875-900"C n 0

I 0

u, I

0 \ -I 6 0

0

O hl 0.5 T = 1475-1550"C hl

I- 0.4

t 0 . 3

5 0.2

" 0.1 n

0

a

I- -

I-

3

z 0 u -J 0.6 1 1 1

T = 1550-1600"C 6 -

0 . 3 8 - 0.2 - 0.1 - m

2 4 6 8 0 0 (NICM', E > 0.18 M E V ) -2 1 FAST NEUTRON FLUENCE X 10

Fig. 1 1 . Room-temperature thermal conductivity of H-327 graphite para1 le1 t o extrusion as a function o f fluence ( rep lo t ted from r e f . 20)

22

T = 875-900°C - 0.3 0.2 -

0.1 - 0 I 1

8 0 2 4 6 0 2 4 6

::: ;j 0.2

T = 1550-1 6 0 0 ~ ~ 0.1 c

0 0 2 4 6 8

( N / -2 1 FAST NEUTRON F L U E N C E X 10 2 ,M , E > 0. 8 M E V )

F ig . 12. Room temperature thermal c o n d u c t i v i t y o f H-327 g r a p h i t e perpen- d i c u l a r t o e x t r u s i o n as a f u n c t i o n o f f l u e n c e ( r e p l o t t e d f rom r e f . 20)

23

n 0 0

I 0 w m I x u \ -I

u a v

t I-

> I- u 3 a z 0 0

-I

x a L w I I-

- -

a

O. 30

0.20

0.10

0.00

Fig. 13.

1 I I I

0

1 200” c

I I I I

1 2 3 4 NEUTRON FLUENCE X 10 -” (N/CM?

Thermal conductivity a t 40°C of pressed i so t ropic Gilsocarbon graphi te (Dragon r e f . no. 1 ) i r r ad ia t ed a t 600°, 900°, and 1200°C (from re f . 23)

24

Table IV

(Retabulated from Kef. 20) Thermal Conductivity Changes for H-327 Graphite

Orientati'

. I1

1

It

1

It

1

Jnirradiated W (callan-sec-Y

0.525 0.563

0.364 0.365

_ _ _ _

0.369 0.351

0.541 0.549 0.525

0.371 0.372 0.363 0.365

Fluence 1

(E >0.18 MeV: x 10-21 ("lcm:

0.5

0.5

1.2

1.2

3.7

3.7

Temperature ('0 625

625

875

875

1225

1225

K fcal/cm-sec-'C

0.198 0.177 0.200 0.216 0.218 0.200 0.169

0.106 0.096 0.129 0.096

::;;$I 0.103(b) 0.120 0.109 0.125 0.122 0.115 0.142 0.124

0.157

0.089 0.104

_ _ _ _ 0.185 0.176 0.205 0.182 0.201 0.182 0.176 0.209 0.177 0.207 0.212 0.159 0.174 0.199 0 162(b) o:202(b)

_ _ -_

Flusnca 2 10-21 (n/cm2 (E >O.l8 MeV)

0.3

0.3

0.3

0.8

0.8

0.8

0.8

2.6

2.6

2.6

2.6

remperature ('0 625

625

625

900

900

900

900

1300

1300

1300

1300

Total Fluenca

: 10-21 (nlcm2

0.7

0.3

0.7

2.0

0.8

2.0

0.8

6.3

2.6

6.3

2.6

625

625

625

173-900

900

25-900

900

25-1301

1300

25-13N

1300

K (callcm-sec-'C)

0.100 0.175 0.207 0.148

0.110 0.080 0.105 0.080 _- _ _ _ _

0.088 0.093 0.106 0.134 0.140 0.102 0.097 0,110 0.106 0.123

0.123 0.145 0.151 0.126 0.150 _ _ 0.219(a)

0.119 0.093 0.102 0.088 0,100 0.109 -_ _ _

0.093(')

_ _ 0.303 0.287 _ _ 0.296 (') 0.291(8)

0.198 0.234 0.202 0.271 0.220 0.212 0.197 0.200 0.204 _ _ __ 0.215") 0.203(')

{:;Added for 2nd irradiation. Removed after 1st irradiation.

2 5

Table IV (continued)

orientatior nirradiated K cal/cm-sec-*C)

0.531 0.502 0.525 0.505

0.374 0.361 0,360 0.374

4.3

4.3

4.5

4.5

("Added for 2nd irradiation. (b)Removed after 1st irradiation.

1550

1550

1600

1600

0.266 0.292 0.326 0.336 0.333 0.296 0.359 0.337(b)

_ _

0.248 0.212

0.310 0.290 0.383 0.364 (b) 0.339 (b)

0.252 0.288 0.270 LI. 252 (b) 0.244(b)

3.0

3.0

3.0

3 .0

3.2

3.2

3.2

3 .2

1475

1475

1475

1475

1550

1550

1550

1550

3.0

7.30

3.0

7.7

3.2

7.7

3.2

- Temp. Range ("C)

175-1550

1475

075-1550

1475

1550-160

1550

1550-160

1550

0.285 0.251 0.260 0.243 0.219 0 . 2 2 1 0.224

0.252(a)

0.252 0.227 0.242

0.215(') 0. 253(a)

0.371 0.408 0.431 _ _

_ _

0.406(')

0.359 0.272 0.274 _- _ _ 0. 243(a)

26

Table V

Graphite Grade

CHN

CHN

71 1 -TS

71 1 -TS

71 1 -TS

71 1 -TS

H-283

H-319

H-319

H-315A

H-315A

Thermal Conductivity o f Graphite Samples Irradiated to

1 .8 x n/cm2 (E>0.18 MeV) at 1175OC (Ref. 22)

Sample Orientation

Paral le1

Perpendicular

Paral 1 el

Paral 1 el

Perpendicular

Perpendicular

Perpendicular

Paral le1

Perpendicular

Parallel

Perpendicular

Sample Number

41 B

30 B

31 -1

31-2

32-1

32-2

26-8

43-B

34-B

53-B

28-0

Samp 1 e Dens i ty (g/cm3)

1.048

1.096

1.382

0.62

1.323

1.391

0.774

1.182

1.146

1.346

1.518

Run Number

50263

50258

50262

50265

50267

50268

50260

50261

50259

5 02 64

50266

Thermal Conductivity at 22oC (cal/cm-sec-OC)

0.042

0.029

0.064

0.030

0.048

0.035

0.017

0.047

0.040

0.076

0.037

27

conductivity resulting from irradiation i s generally somewhat less in the Gilsocarbon-based material than in the more crystalline material.

Measurements on two molded Gi lsocarbon-based graphites (H-328 and H-315A) have been made at GGA. The thermal conductivity o f H-315A samples irradiated in the G-10 capsule is shown as a function of measurement temperature in fig. 14 (from ref. 5). Post-irradiation step-annealing on a sample irradiated at 123OOC indicated that annealing o f the con- ductivity changes was more difficult in the Gilsocarbon-based material than in needle-coke-based CHN graphite; about 15% o f the irradiation- induced room-temperature conductivity change in H-315A remained unannealed after annealing to ZOOOOC. re-irradiated to higher exposures are included in fig. 10, and some high- fluence d a t a a r e included in Table V .

Some additional measurements on H-315A graphite

The room-temperature thermal conductivity of H-328 graphite samples irradiated in the GEH-13 series of capsules were reported in ref; 20. Measurements were made by the heat-pulse method on disc-shaped samples. The conductivity changes are shown in fig. 15 as a function o f fluence and the data are tabulated in Table VI. When the conductivities of the irradiated Gilsocarbon graphite grades are compared with those of needle- coke graphites irradiated in the same capsules, it can be seen that the fractional change in conductivity is usually somewhat less for Gilsocarbon graphite than for needle-coke graphite. Thus the Gilsocarbon graphite, whose pre-irradiation thermal conductivity is lower than that o f needle- coke graphite, reaches an irradiated thermal conductivity comparable to perpendicular-cut needle-coke graphite (see figs. 1 1 , 12 and 15).

The measurements for a mean irradiation temperature of 625OC agree well with the Dragon measurements on Gilsocarbon graphite irradiated at 6OO0C (Table I I ) , but the conductivities for the 1225-13OOOC irradiation are considerably higher than the Dragon measurements for an irradiation temperature of 1200OC. The higher mean i rradi ati on temperature and the

28

n 0 0

I 0

v, I E 0 \ -1

0

w 0.3

a

> 0.2 W

I-

> I- o 3

z

- -

n

p . 1 1 a x lY W I I-

0

F i g . 14.

UN I RRAD; ATED

1230°C, 2 .9 X 1021 N/CM2

\ I I I

G-10

32OoC, 1.7 X 10" N/CM2

I I I I 500 1000 1500 2000

MEASUREMENT TEMPERATURE ( " C )

Thermal conductivity of i r rad ia ted H-315-A graphite measured perpendicular t o forming axis as a function of measurement temperature (from r e f . 5 )

29

0.3 ,

0.2 n o 0

I

0.1 Ln I z 0

0 0

T = 625°C

I I

1 2 3

T = 1225-1 3000 c 1 1 0 2 4 6 - 0 . 3

0

CV c\I

0

I- 0.2 a > I-

> I- o 3 D

- - 0 . 1

- L

I I I 2 4 6 8

O 0 1 0

0

2 0 . 3 . x & w I I-

0.2 -

I T = 1550- 1600" c I 0 . 1 1 I 1 I I

0 2 4 6 8

FAST NEUTRON FLUENCE X 10 -" ( N / c M ~ , E > 0.18 M W )

F i g . 15. Room temperature thermal c o n d u c t i v i t y o f H-328 g r a p h i t e perpen- d i c u l a r t o e x t r u s i o n as a f u n c t i o n o f f l u e n c e ( r e p l o t t e d f r o m r e f . 20)

30

Unirradiated K (calIcm-sec-'C:

0.285 0.280

0.283 0.276 0.293 0.277

0.285

0.281

0.280 0.283

0.273

0.5

3.7

4.3

4.5

Table VI Thermal Conductivity Chanaes for H-328 GraDhite ~-

(Perpendicular Specimens) (Retabulated from ref. 20)

emperature ("C)

625

1225

1550

1600

K :cal/cm-sec-'C)

0.138 0.141 0.139 0.141 O-. 142 0.136 0.136 0.132(a) 0.126(a)

0.184 0.239 0.187

0.188 0.189 0.160 0.190

0.188

0.175 0.177 0.199 0.186 0.176 0.192 0.196 0. 186(a) 0 .182(a )

0.206 0.194 0.203 0.2u2 0.223(b)

Fluence 2

(E >0.18 MeV) R 10-21 (nIcm2

0.3

0.3

2.6

2.6

3.0

3.0

3 . 2

3.2

Temperature 2 ("C)

625

625

1300

1300

1475

1475

1550

1550

(E ,0.18 MeV)

0.9

0.3

6.3

2.6

7.3

3.0

7.7

3.2

625

625

1225-1300

1300

1475-1550

1475

1550-1600

1550

K callcm-sec-"C)

0.097 0.133 0.121 0.128 0.114 0.134 0.134

0.257 0.190 0.181 0.182 0.183 0.200 0.179 0.182

0,226 0.193 0.213 0.207 0.194 0.211 0.207

0 .192(h)

0.273 0.263 0.256 0.257 _ _

0.239 (a)

(a)Removed after 1st irradiation. (b)Added for 2nd irradiation.

31

wide temperature spread f o r b o t h s e t s of data ( 5 about 100°C) probably account f o r the difference. versus-fluence curve f o r the highest i r rad ia t ion temperature ( f i g . 15 ) i s unlikely t o be a real e f f e c t and probably r e s u l t s from a higher f i n a l temperature d u r i n g the second i r rad ia t ion period. (The thermocouples i n the highest temperature c e l l s f a i l e d before the f ina l cycle and temper- a ture records did not extend t o the end of i r r a d i a t i o n . )

The apparent u p t u r n i n the conductivity-

Thermal conductivity measurements on a Gilsocarbon graphite i r rad ia ted i n the HFR (Pet ten) and the Dounreay Fast Reactor were reported by D e l l e ( 2 4 ) . The measurements were made by a steady-state heat flow method a t 40%. The data a r e shown i n f i g . 16. The r e s u l t s a r e s imi la r t o the Dragon r e s u l t s ( f i g . 1 3 ) , except t h a t the highest fluence points a t 9 and 1 2 x 1O2I n/cm2 (NDE) show a pronounced down- turn. the breakaway expansion region. f i g . 16 i s t h a t the conductivity does not show a c l e a r saturat ion zone where i t does not change w i t h f luence. saturat ion zone may be masked by s c a t t e r i n the data . of the thermal conductivity as a function of measurement temperature were made on Gilsocarbon graphite and pitch coke graphite i r rad ia ted t o 3 x 1020 n/cm2 ( N D E ) . f ract ional change i n thermal conductivity versus measurement temperature, a re reproduced i n f i g . 17. The plots show c lear ly how the i r rad ia t ion- induced change becomes smaller as e i t h e r the measurement temperature o r the i r rad ia t ion temperature i s increased.

The high-fluence downturn i s probably due t o the samples entering A second unusual feature of the data i n

However, the presence o f a Some measurements

The r e s u l t s , p lot ted as the irradiation-induced

Other measurements on near-isotropic coke include work reported by Nettley and Mart in(25) on a coal t a r pitch coke w i t h a room temperature

thermal conductivity of 0.25 cal/cm-sec-OC (reference code P R ) i r rad ia ted in the Dounreay Fast Reactor t o a maximum exposure of a t temperatures u p t o 75OoC. shown in f i g . 18. on Gilsocarbon graphites i r rad ia ted a t .~600OC ( f i g s . 13, 15, 16) .

n/cm2 ( N D E ) The fract ional changes i n conductivity a re

The changes a t 580-750°C f a l l ra ther lower than data

32

I-

0.20

0.15

0.10

0.05 b

0 0 2 4 6 8 1 0 1 2

FLUENCE ( 1 02' N / C M ~ , N I CKEL D I DO EQUIVALENT)

Fig. 16. Change i n thermal c o n d u c t i v i t y measured a t 40°C p a r a l l e l t o the g r a i n a l ignment o f G i l son i te -coke g r a p h i t e as a f u n c t i o n o f f l uence f o r i r r a d i a t i o n temperatures o f 450°C, 600°C, 900°C, and 1200°C ( f rom r e f . 24)

33

O r I

-50 CAL/CM-"C-SEC

0 . 1 2 t o . 0 1 \\,02,"c 1000"c 950°C C A L ~ C M - O C - S E C

I I I -100 I I I I I n~ I

-50 C AL/ CM- " C- S E C " t CAL/CM-"C-SEC

I I I I I I I I I I - 1 00

0 200 400 600 800 1000

MEASUREMENT TEMPERATURE ( " C )

Relative change in thermal conductivity as a function of measure- ment temperature fo r ilson 3 te-coke and pitch-coke graphites i r radiated t o 3 x n/cm as a function of measurement temperature (from re f . 24)

Fig. 18. Fractional changes in thermal r e s i s t i v i t of pitch coke isotropic graphite with neutron dose (from re f . 257

34

0

4. THEORETICAL TREATMENTS

A simp1 i f i e d t rea tment f o r t h e thermal c o n d u c t i v i t y o f i r r a d i a t e d g r a p h i t e proposed by N e t t l e y e t . a l . ( 2 6 ) has been a p p l i e d w i t h cons ider -

a b l e success. I n an a n i s o t r o p i c m a t e r i a l such as g r a p h i t e where heat conduct ion takes p l a c e by l a t t i c e waves i n t h e l a y e r p lan, t h e thermal

c o n d u c t i v i t y a t temperature T i n t h e a - d i r e c t i o n o f a c r y s t a l l i t e i s approximated by:

Ka ( T ) = 1/2 C (T) A(T) v ( 1 ) P

where C (T) i s t h e s p e c i f i c heat a t temperature T, x ( T ) i s t h e phonon mean f r e e p a t h a t temperature T, and v i s t h e phonon mean group v e l o c i t y (assumed t o be independent o f temperature) . A(T) i s c o n t r o l l e d by t h e c r y s t a l l i t e boundary spacing and phonon-

phonon c o l l i s i o n s . independent s c a t t e r i n g mechanism which reduces t h e phonon mean f r e e p a t h

t o x ' ( T ) :

P

I n u n i r r a d i a t e d m a t e r i a l ,

I r r a d i a t i o n i s assumed t o add a temperature-

7 = x m + - 1 1 1 AD A T

where X~ i s t h e mean f r e e p a t h l i m i t e d by i r r a d i a t i o n - i n d u c e d d e f e c t s . S ince i s assumed independent of temperature, and t h e thermal conduc-

t i v i t y o f a p o l y c r y s t a l l i n e sample i s p r o p o r t i o n a l t o t h a t o f t h e

c r y s t a l l i t e s , t h e thermal c o n d u c t i v i t y a f t e r i r r a d i a t i o n , K ' , i s g i v e n by:

L> KO =Po 5 (k - 6) CPT \K'o -

where KT and C

temperature T, and KO, K ' i r r a d i a t e d c o n d u c t i v i t y , and s p e c i f i c heat a t another temperature

a r e t h e u n i r r a d i a t e d c o n d u c t i v i t y and s p e c i f i c heat a t PT

and C 0, PO

a r e t h e u n i r r a d i a t e d c o n d u c t i v i t y ,

35

(usually room temperature). f a c t t h a t the thermal conductivity versus temperature curve f o r i r r a d i - ated graphite can be predicted from t h a t of unirradiated graphite once the thermal conductivity of an i r rad ia ted sample has been measured a t a s ing le temperature. i s limited t o measurements a t o r around room temperature, th i s is a useful r e s u l t .

The usefulness of equation 2 l i e s i n the

Since much of the data reported i n the l i t e r a t u r e

Families of curves f o r the conductivity of i r rad ia ted PGA graphite, based on eq. 2 , are shown i n f i g . 19. Extrapolations based on eq. 1 form the basis of the Dragon project curves f o r the expected thermal conductivity of i r rad ia ted Gilsocarbon graphite(12 3 2 3 ) . Mottershead e t . a1 . ( l o ) compared the thermal conductivity versus temperature curves of PGA graphite i r rad ia ted a t 250-450°C w i t h eq. 2 and found t h a t the equation overestimated the conductivity by 10-15% a t higher measurement temperatures (see f i g . 4 ) .

A much more rigorous treatment o f thermal conduction i n graphite c r y s t a l s was carr ied out by Kelly, u s i n g the theory of the l a t t i c e dynamics of an anisotropic hexagonal c rys ta l and taking i n t o account phonon-phonon sca t te r ing , isotope sca t te r ing , and crys ta l boundary sca t te r ing . conduction in polycrystal l ine graphite i s assumed t o take place by phonon t ransport para l le l t o the basal planes of the c r y s t a l l i t e s , and the e f f e c t s of c r y s t a l l i t e junctions and c-axis conductivity a r e ignored, Kel ly 's treatment gives r i s e t o the following expression f o r K ( T ) :

The r e s u l t s of th i s work a re reviewed in r e f . 6. I f heat

where cx i s a porosi ty- tor tuosi ty f a c t o r representing the r a t i o of the crystal 1 i t e a-di rection conductivity t o the conductivity of the

36

0.4

0 . 3

0.2

0.1

0

1 I I I 1 1 I

0 K

0 100 200 300 400 500 600 700 800 TEMPERATURE ( " C )

Fig. 19. Cal cul ated temperature dependence o f thermal conducti vi t y of PGA graphi te a f t e r i r r ad ia t ion (perpendicular d i r ec t ion ) (from ref. 26 1

37

p o l y c r y s t a l 1 i n e sample (a i s assumed t o be independent o f temperature), and Ku(T), KB(T) and KD(T) a r e t h e c r y s t a l l i t e c o n d u c t i v i t i e s a t temperature T w i t h Umklapp processes, boundary s c a t t e r i n g , o r p o i n t

d e f e c t s c a t t e r i n g processes dominant r e s p e c t i v e l y . Values o f Ku(T) a r e taken from T a y l o r ' s exper imenta l measurements o f t h e a-d i r e c t i o n

c o n d u c t i v i t y o f h i g h l y o r i e n t e d , wel l -annealed p y r o l y t i c c a r b o n ( 2 7 )

Absolute values o f KB(T) and KD(T) depend on t h e c r y s t a l l i t e boundary

spacing, La, t h e p o i n t d e f e c t concent ra t ion , cd' and t h e mass d i f f e r e n c e

f o r p o i n t d e f e c t s c a t t e r i n g , D. s D KD(T) cd (-J are a v a i l a b l e from K e l l y ' s l a t t i c e dynamics c a l c u l a t i o n s and a r e l i s t e d i n Table V I I . o f a p o l y c r y s t a l l i n e sample then becomes:

KB(T) T h e o r e t i c a l values f o r - and 6D 2 La

The express ion f o r t h e thermal c o n d u c t i v i t y

where t h e a p p r o p r i a t e values o f Ku(T) and t h e terms i n square brackets can be ob ta ined f rom Table V I I .

c o n t r i b u t i o n i s l i m i t e d t o t h e e f f e c t s o f 1.1% I3C i s o t o p e present i n carbon, and t h i s te rm may be neg lec ted i n comparison w i t h t h e Umklapp

and boundary s c a t t e r i n g terms. The thermal c o n d u c t i v i t y versus temperature curve may t h e r e f o r e be descr ibed by eq. 3, s e t t i n g CD = 0 and u s i n g

a p p r o p r i a t e values f o r a and La.

parameters, eq. 3 p rov ides a very good fit t o t h e observed thermal con-

d u c t i v i t y curves f o r many p o l y c r y s t a l l i n e g r a p h i t e ~ ( ~ ' 9 3 1 ) *

F o r u n i r r a d i a t e d g r a p h i t e t h e p o i n t d e f e c t

By t r e a t i n g ~1 and La as a d j u s t a b l e

The a p p l i c a t i o n o f a l a t t i c e dynamics t rea tment t o i r r a d i a t e d g r a p h i t e

i s descr ibed i n r e f s . 6 and 7. I r r a d i a t i o n - c r e a t e d vacancies and smal l i n t e r s t i t i a l c l u s t e r s can be t r e a t e d as p o i n t d e f e c t s . The r e s u l t i n g equat ions resemble eq. (3) except t h a t i n the mass d i f f e r e n c e s c a t t e r i n g

term (%)2 i s rep laced by a s c a t t e r i n g parameter Sv ( f o r vacancies) o r

Si ( f o r i n t e r s t i t i a l c l u s t e r s ) . Exper imental measurements o f t h e room- temperature c o n d u c t i v i t y o f PGA g r a p h i t e i r r a d i a t e d a t 200-450OC, t o g e t h e r

2

2

38

Table V I 1 Values f o r t h e a-ax is Thermal C o n d u c t i v i t y o f a Graph i te

C r y s t a l as L i m i t e d by Umklapp Processes, C r y s t a l 1 i t e Boundaries,

and P o i n t Defects ( f r o m Refs. 6 and 28-30)

Tempera t u re (OC)

E x t r a p o l a t e d Values

-1 73 -123 - 73 - 23

27 77

127 227 327 427 527 627 727

' 827 927

1027 1127 1227 1327 1427 1527

Thermal Conduc t iv i ty Components, cal/cm-sec-OK

KU

* Kg - x 10-4 La

* K ~ C ~ (%I x 103

93.5 48.8 12 .8 6.38 4.79 3.56 2.90 2.22 1.91 1.64 1.48 1.34 1.23

1.10 1.01 0.94 0.88 0.84 0.80 0.765 0.74

2.88 5.95 9.60

13.25 16.65

22.5 27.0 30.3 32.7 34.7 35.5 36.0

36.0 36.0 36.0 36.0 36.0 36.0 36.0 36.0

---

4.46

3.21

3.02

3.24 3.51 3.66 3 .78 3.88 3.91 3.94

3.94 3.94 3.94 3.94 3.94 3.94 3.94 3.94

----

---- -___

* La = c r y s t a l l i t e boundary spac ing i n cm.

Cd = p o i n t d e f e c t c o n c e n t r a t i o n .

- _ aD - p o i n t d e f e c t mass d i f f e r e n c e = S$ o r S f ( s c a t t e r i n g D paramete r s ) f o r vacancies o r in ters t i t i a l s .

39

w i t h estimates of the vacancy and i n t e r s t i t i a l concentrations based on l a t t i c e parameter changes, were used in estimating Sv t o be 0.72 and Si t o be 3.2. The irradiation-induced change i n thermal r e s i s t i v i t y f o r annealed, oriented pyrolytic carbon i r rad ia ted a t 30-450°C was determined a t temperatures between 1 OO°K and 700°K. The temperature dependence was f o u n d t o agree well w i t h t h a t calculated for point defects (Table V I I ) above 300°K, b u t the r e s i s t i v i t y was higher than the calcu- la ted value a t lower temperatures. uncollapsed vacancy loops led t o the conclusion t h a t f o r loops whose radius i s large compared w i t h the phonon wavelength, the phonon mean path will be independent of frequency and equal t o 4, where ro is the loop radius and CvlooD i s the concentration of vacancies i n uncollapsed loops. o f such loops should be similar to that o f crystallite boundaries (see Table V I I). between 650% and 135OoC was analyzed on the assumption t h a t vacancy looljs make a major contribution t o the thermal res i s tance , and the corresponding 1 oop radi i were cal cul a ted. The cal cul ated radi i were between 5 1 and 20 A, which i s ra ther small f o r the assumption of a frequency-independent sca t te r ing cross section t o be j u s t i f i e d . tunately no experimental data on the temperature dependence of the vacancy 1 oop thermal res is tance were avai 1 ab1 e t o t e s t the hypothesis of frequency-independent sca t te r ing . The overall conclusions of this work were t h a t the irradiation-induced thermal res is tance of graphite i r rad ia ted a t o r below 300OC could be understood on the basis of s ing le vacancies and small (2-4 atoms) i n t e r s t i t i a1 c l u s t e r s . Between 300OC and 6 5 0 O C vacancies alone a re important, while a t i r rad ia t ion temperatures between 650OC and 135OOC uncol 1 apsed vacancy 1 oops pl ay an increasingly important ro le . t i a l loops have a negl igible e f f e c t on thermal res is tance.

2

2

A calculat ion of the e f f e c t s of

*r0 cvl oop

The temperature dependence o f the thermal res is tance

The room-temperature conductivity of PGA graphite i r r a d i a t e d

0

Unfor-

Collapsed vacancy l i n e s and large interplanar i n t e r s t i -

Since the published analyses discussed above do n o t define the temperature dependence of irradiation-induced thermal res is tance i n

40

g r a p h i t e i r r a d i a t e d a t HTGR temperatures, f u r t h e r a n a l y s i s was undertaken. Kel l y ' s t h e o r e t i c a l r e s u l t s were compared w i th t h e measurements o f thermal c o n d u c t i v i t y i n needle-coke and Gi lsocarbon g raph i tes i r r a d i a t e d between

3OO0C and 134OoC r e p o r t e d i n re fe rences 5 and 24.

t a k i n g t h e room-temperature thermal c o n d u c t i v i t y o f u n i r r a d i a t e d and i r r a d i a t e d samples and c a l c u l a t i n g t h e mean f r e e pa th due t o i r r a d i a t i o n -

induced de fec ts . The thermal c o n d u c t i v i t y as a f u n c t i o n o f temperature was then c a l c u l a t e d from eq. 3 and Table V I I , assuming t h a t t h e de fec ts c rea ted by i r r a d i a t i o n were e i t h e r ( a ) p o i n t de fec ts , o r ( b ) extended

de fec ts such as vacancy loops l a r g e compared w i t h phonon wavelengths

which can be t r e a t e d l i k e c r y s t a l l i t e boundaries. which i m p l i e s a frequency-independent mean f r e e path, y i e l d s r e s u l t s

s i m i l a r t o N e t t l e y ' s e q u a t i o n ( 2 6 ) . ) The r e s u l t s o f t h e c a l c u l a t i o n s

a r e shown i n f i g s . 20 and 21.

dependence, p o i n t d e f e c t s g i v e a s l i g h t l y lower thermal c o n d u c t i v i t y

than extended de fec ts a t e leva ted temperatures. It may be seen from

f i g s . 20 and 21 t h a t t h e exper imental da ta p o i n t s g e n e r a l l y f a l l between

the two t h e o r e t i c a l curves b u t agreement i s more s a t i s f a c t o r y w i t h t h e

p o i n t - d e f e c t model. The d e v i a t i o n o f t h e da ta p o i n t s f rom t h e p o i n t -

d e f e c t l i n e was always l e s s than 10% and i n most cases b e t t e r than 5%. Since these d e v i a t i o n s a r e on t h e same o rde r as t h e exper imental e r r o r ,

agreement w i t h t h e p o i n t - d e f e c t model can be regarded as adequate f o r e x t r a p o l a t i o n purposes.

equa t ion (based on t h e assumption o f a frequency-independent mean f r e e p a t h ) overes t imates t h e high-temperature c o n d u c t i v i t y by up t o 20%.

This was done by

(Assumption ( b ) ,

Because o f t h e d i f f e r e n t temperature

On t h e o t h e r hand, i t may be noted t h a t N e t t l e y ' s

41

ION (REPLOTTED F R ~ M ENGLE AND

=EXPERIMENTAL DATA

THEORETICAL, ASSUMING

A THEORETICAL, ASSUMING

EXTENDED DEFECTS

PO I NT DEFECTS

UNIRRADIATED

V v

>- I-

> - - I- u 1 3 x 1 O Z 1 N/CM2 AT 300°C 3 t 3 z 0 u -I

z CY w I I-

a

O

I I I I I I

MEASUREMENT TEMPERATURE ("C)

Fig. 20. Temperature dependence o f t h e thermal c o n d u c t i v i t y o f i r r a d i a t e d CHN g r a p h i t e : dynami cs mode 1

comparison between exper imenta l data and l a t t i c e

4 2

0.3

0 .2

n 0

O1 0.1 0 W m I x u \ J

0 0 a W

>- I-

> I- u

- -

2 0.3 z 0 u -I a 5 E 0.2 w

0.1

0

I I I I I

GILSOCARBON GRAPHITE (REPLOTTED FROM DELLE, REF. 2 4 )

UN I RRAD IATED

IRRADIATED TO 3 X l O 2 ' N/CM2 AT 950°C \

I I I I I

0 EXPERIMENTAL DATA

0 THEORETICAL, ASSUMING EXTENDED DEFECTS

A THEORETICAL, ASSUMING POINT DEFECTS

UNIRRADIATED

'\ IRRADIATED TO 3 X l O Z 0 N/CM2 AT 1340°C

I I I I I

0 2 0 0 400 600 800 1000 1 2 0 0

MEASUREMENT TEMPERATURE ( " C )

F ig . 21. Temperature dependence of t h e thermal c o n d u c t i v i t y of i r r a d i a t e d Gi lsocarbon g r a p h i t e : comparison between exper imenta l data and 1 a t t i ce dynami cs model

43

5. CONSOLIDATION OF DATA: DEPENDENCE ON

FLUENCE, IRRADIATION TEMPERATURE, AND MATERIAL

5.1 Approach t o S a t u r a t i o n

The exper imenta l da ta discussed e a r l i e r i n t h i s r e p o r t show t h a t i r r a d i a t i o n reduces t h e thermal c o n d u c t i v i t y o f a g i ven grade o f g r a p h i t e ,

w i t h t h e r a t e o f d e c l i n e f a l l i n g o f f and approaching s a t u r a t i o n as t h e

f l u e n c e increases . Th is behav io r p a t t e r n ho lds up t o t h e onset o f breakaway expansion and may be represented by an express ion o f t h e type:

= Ksa t + (KO - K s a t ) e x p ( - 5)

where K i s t h e c o n d u c t i v i t y a f t e r a f l u e n c e ( + t ) , KO i s t h e u n i r r a d i a t e d

thermal c o n d u c t i v i t y , Ksat t h e c o n d u c t i v i t y a f t e r i r r a d i a t i o n t o sa tu ra - t i o n , and T i s t h e " t ime cons tan t " ( a c t u a l l y a f l u e n c e ) f o r s a t u r a t i o n .

The number o f measurements w i t h s u f f i c i e n t l ow- f l uence da ta p o i n t s t o

e s t i m a t e T i s l i m i t e d , b u t t i m e cons tan ts es t imated from seve ra l s e t s

o f da ta a r e p l o t t e d i n f i g . 22 as a f u n c t i o n o f i r r a d i a t i o n temperature.

Fluences a r e expressed i n terms of neut rons w i t h energ ies g r e a t e r t han

0.18 MeV. i s v i s i b l e .

f i g . 22 g i ves the f o l l o w i n g e m p i r i c a l equa t ion f o r t h e t i m e cons tan t , T, as a f u n c t i o n o f i r r a d i a t i o n temperature, T(OC):

No sys temat i c d i f f e r e n c e between d i f f e r e n t types o f g r a p h i t e A l eas t - squares l i n e a r r e g r e s s i o n a n a l y s i s f o r t h e da ta i n

T = [(1.589 k0.677) x T-(0.641 k 0.581) x 1021 n/cm2 (E>0.18 MeV) 1 where t h e e r r o r l i m i t s r e p r e s e n t 90% conf idence l i m i t s on t h e parameters.

44

1 I I I I 1 1 GRADE REF. E

0 0

A V 0

A v

H - 3 2 7 ( 1 1 ) 20 H - 3 2 7 (1) 20 H - 3 2 8 (1) 20 NC-7 AND NC-8 4 PETROLEUM COKE 2 4 GILSOCARBON 24 G I LSOCARBON 23 PGA 10

90% CONFIDENCE L I M I T S 0

/ LEAST-SQUARES L I N E

/

A = 0

. ’ / I I = /

I

V I ’/

/ LEAST-.SQUARES L I N E , A N / 93’ 7 = 1.589 X 10-3T-0.641

/ I I I I I I I d 600 700 800 900 1000 1 1 0 0 1200

I RRAD I AT I ON TEMPERATURE ( ” C )

F ig . 22. Composite p l o t o f t h e t i m e c o n s t a n t f o r t h e s a t u r a t i o n o f t h e thermal c o n d u c t i v i t y change as a f u n c t i o n o f i r r a d i a t i o n tempera t u r e

4 5

5.2 Conductivity a f t e r I r rad ia t ion t o Saturation After i r r a d i a t i o n t o a fluence high enough f o r saturat ion t o occur

b u t too low f o r breakaway expansion t o s t a r t , the thermal conductivity i s dependent only on the i r r a d i a t i o n temperature and the grade and or ientat ion o f the graphi te . determined empirically by lumping together a l l avai lable data on a given type of graphite i r rad ia ted t o a fluence high enough f o r satur- a t ion t o have occurred. f i g s . 23 and 24, where room-temperature conduct ivi t ies taken from the l i t e r a t u r e a r e plot ted against i r r a d i a t i o n temperature f o r needle-coke graphi t e s (para1 le1 and perpendicular) and i so t ropic ( G i 1 socarbon-based) graphi tes . Some lower-fluence data were a l so included by extrapolating the measurements t o s a t u r a t i o n , u s i n g eq. 4 . High-fluence measurements a f fec ted by sample expansion, and the da ta of doubtful r e l i a b i l i t y from capsule 6-12, were excluded from the p lo t . rated conductivity r i s e s exponentially with increasing i r r a d i a t i o n tem-

The temperature dependence can best be

This procedure was followed i n constructing

I t may be seen t h a t the satu-

perature over the temperature range 4OO0C t o 160OOC. regression analysis o f the data in f i g s . 23 and 24 y i e l d s the follow empirical expressions f o r the conductivity a f t e r i r r a d i a t i o n t o satu- r a t i o n , K s a t , i n terms of the i r r a d i a t i o n temperature, T ( O C ) :

Needle coke graphi te , para l le l t o extrusion: Ksat = exp [(1.1820.17

Least-squares

1 x 10'3T - (2 .99k0.18) cal /cm-sec-OC

Needle coke graphi te , perpendicular t o extrusion: Ksat = exp [ ( I . Q ~ ~ . I Z ) x 10-3T - ( 3 . 6 4 i O . I Z ) I cal /cm-sec-oC

Gilsocarbon graphi te , any d i rec t ion : K s a t - ( 3

The ? f igures a r e 90% confidence l imi t s ca s t a t i s t i c s .

46

= exp [(1.20 20.22) x 1 0 - 3 ~ 31 i 0.26) 3 cal/cm-sec-0C culated from the curve- f i t t ing

1 .oo 0.80

0.60 0.50

0.30

0.20

0.40

0.10 0.08 0.06 0.05 I I I I I I I

I 1 I I I I

- NEEDLE COKE GRAPHITE, PARALLEL - TO EXTRUSION - 90% CONFIDENCE LIMITS-

0.40

Oa30

0.20 -

NEEDLE COKE GRAPHITE, PERPENDICULAR - TO EXTRUS ION

0.10 - 0.08 - 90% CONFIDENCE L I M I T S

ON LEAST-SQUARES L I N E 0.06 - - -

LEAST-SQUARES L I N E ,

K = EXP 0.03 - - 0.02 I I 1 I I I

(1.52T - 3.64)

400 600 800 1000 1200 1400 1600 I RRAD I A T I ON TEMPERATURE ( O C )

REF. - RADE 0 PGA 2 0 5912 12 TSX 4

18 e CHN 5 0 PGA 8 H - 3 2 7 a PGA 10 9. H - 3 2 7 20 + TS-688 18 V PGA 1 1 A NC-8 4 x 9567 18 0 PGA 13 . CSF 4

Fig. 23. Composite p l o t o f the room-temperature thermal conductivity of needle-coke graphites i r radiated t o saturation as a function o f i r rad ia t ion temperature

47

0 . 5 s 1 I 1 I 0.4 - ISOTROPIC GRAPHITE (GILSOCARBON OR P I T C H COKE)-

0. 3c- 90% CONFIDENCE L I M I T S ON LEAST-SQUARES L I N E -

0 . 2 -

1 I

e d

-.

LEAST-SQUARES L I N E , .I - 0 K = EXP ( 1 . 2 0 T - 3 . 3 1 )

0.05 0 . 0 4 -

0 . 0 3 - * 0 . 0 2 -

- - -

I I I I I 1

F i g . 24. Composite p l o t of the room temperature thermal conductivity of Gi 1 socarbon and p i tch coke graphi t e s i r r ad ia t ed t o sa tu ra t ion as a function of i r r a d i a t i o n temperature

4 8

5.3 C o n d u c t i v i t y a t End-o f -L i fe

The measurements r e p o r t e d by B a k e r ( ’ 6 ) and Engle and Koyama(22)

(Table V ) l e a v e no doubt t h a t t h e thermal c o n d u c t i v i t y o f samples i r r a d i a t e d w e l l i n t o t h e volume expansion regime ($2 x n/cm2 a t 800-15OOoC) i s f u r t h e r reduced by a t l e a s t 50% o f t h e s a t u r a t i o n va lue. Determinat ion o f t h e p o i n t where t h i s second decrease s t a r t s i s less s t r a i g h t f o r w a r d . Some r e l e v a n t observa t ions are: ( a ) The samples o f

H-327 and H-328 g r a p h i t e i r r a d i a ted i n capsules GEH-13-421 and

GEH-13-422 whose c o n d u c t i v i t y changes a r e shown i n f i g s . 11, 12, and 15 show no s i g n o f a h i g h - f l u e n c e degradat ion i n room-temperature

c o n d u c t i v i t y . Examinat ion o f t h e dimensional changes o f samples o f

t h e same m a t e r i a l s f rom t h e same c a p s u l e s ( 3 2 ) i n d i c a t e s t h a t a t t h e

f i n a l f l u e n c e p o i n t t h e samples would j u s t about have reached t h e

p o i n t o f minimum volume. ( b ) Among t h e Gi lsocarbon-based samples r e p o r t e d by D e l l e ( f i g . 16) , o n l y those i r r a d i a t e d t o 12 x l o z 1 n/cm2 (NDE) a t 1200°C and t o 9 x 1021 n/cm2 (NDE) a t 900°C show a c l e a r decrease below t h e s a t u r a t i o n l e v e l . The volume o f these samples would have been i n c r e a s i n g w i t h f luence, a l though t h a t o f t h e 9OOOC samples would s t i l l have been l o w e r than t h e p r e - i r r a d i a t i o n

The samples represented by t h e prev ious d a t a p o i n t s on t h e curves would

s t i l l have been c o n t r a c t i n g .

Based on t h i s evidence, t o g e t h e r w i t h a few o t h e r da ta p o i n t s where t h e sample volume change r a t e i s l e s s w e l l d e f i r ~ e d ( ~ , ’ ~ ) , i t

may reasonably be assumed t h a t t h e onset o f t h e second c o n d u c t i v i t y decrease c o i n c i d e s w i t h t h e p o i n t o f volume turnaround on a dimen-

s i o n a l change-versus-f luence curve.

4 9

hb 6. DESIGN-BASIS CURVES

6.1 Methods f o r Deriving Curves

unirradiated samples, u s i n g the r e s u l t s of Kelly 's l a t t i c e dynamics treatment and assuming t h a t a t HTGR temperatures the important irradiation-induced defects will be vacancies o r vacancy loops which a re small compared with phonon wavelengths. conditions, the conductivity a t tem.perature T , K ( T ) , i s given by:

Design-basis curves were derived from experimental data on

Restating eq. 3 f o r these

1 qT) =

a and La ( t h e poros

i L a 1 q-V+q KB(T)- ( 5 ) ty - tor tuos i ty f a c t o r and mean c r y s t a l l i t e boundary

spacing) were determined by f i t t i n g eq. 5 t o experimental data on unirradiated samples, and the terms i n square brackets a re tabulated functions (Table VII ) . cds t (vacancy concentration mu1 t i p l i e d by s c a t t e r i n g parameter) f o r a p a r t i c u l a r fluence and i r r a d i a t i o n temper- a t u r e was obtained from data on the room-temperature conductivity, K I R T Y of s imi la r i r r a d i a t e d graphi tes :

KORT i s the room-temperature conductivity o f unirradiated graphite and

type of graphite ( see eq. 4 and f i g s . 22-24) . was determined from the analysis of avai lable data on the appropriate K ' ~ ~

These expressions were assumed t o hold up t o the point where the neutron-induced volume contraction r a t e becomes zero. For needle-coke graphite t h i s i s a b o u t 8 x 1021 n/cm2 a t 1000°C, 7 x 1021 a t llOOOC,

50

2

r

and 6 x 1021 Icm2 a t 12OOOC. For i o t r o p i c g r a p h i t e s , t h e volume t u r n - around p o i n t was taken t o occur a t a f l u e n c e l o z 1 n/cm2 h i g h e r than f o r needle-coke g r a p h i t e i r r a d i a t e d a t t h e same temperature.

6.2 Design-Basis Curves: H-327 G r a p h i t e

Measurements o f t h e thermal c o n d u c t i v i t y o f u n i r r a d i a t e d H-327 were made by t h e heat -pu lse method between room temperature and 800oC. The samples were taken f rom a mid- rad ius p o s i t i o n near t h e end o f a

p roduc t ion-grade l o g (GGA reference number 5651 -57; r e c e i v e d 12/12/72). S i x samples each were used t o measure t h e c o n d u c t i v i t y p a r a l l e l and

p e r p e n d i c u l a r t o t h e e x t r u s i o n a x i s . The r e s u l t s a r e shown i n f i g . 25, t o g e t h e r w i t h curves o b t a i n e d f rom eq. 5 by s e t t i n g cd equal t o zero

and o b t a i n i n g b e s t - f i t values f o r ~1 and La. O r i g i n a l exper imenta l

r e s u l t s a r e recorded under Thermophysical P r o p e r t i e s Labora tory f i l e numbers L-0094 th rough L-0105.

Design-basis curves were ob ta ined by u s i n g t h e a p p r o p r i a t e cons tan ts i n eqs. 5 and 6. f o r t h e thermal c o n d u c t i v i t y a t temperature T f o r m a t e r i a l i r r a d i a t e d

t o ( $ t ) n/cm2 (E>0.18 MeV)* a t a temperature Ti ( O C ) :

The f o l l o w i n g express ions were o b t a i n e d

H-327 Graph i te , P a r a l l e l t o E x t r u s i o n :

1

+ e x p ( l . 1 8 x 10-3Ti-2.99) -$t x 10- [0*45 exp (1 3 9 x i o - j ~ ~ k 4 1 )

11 -2.222 *

Fluence i n t h e L-8 o r 1-12 p o s i t i o n o f t h e ETR, based on FeS4 (n,p) rvln5'+ dos imet ry with an assuriied c ross s e c t i o n o f 57.1 mb.

51

( 7 )

0.5

0.4

- 0.3 : 0.2

Qo 0.1

0

I 0

0

I x 0 \ -I

W

>- I- - > 0 - 0 3

z 0.4 0 0

I I I I I 1 I

H - 3 2 7 G R A P H I T E , P A R A L L E L TO E X T R U S I O N (HEAT P U L S E METHOD, MEAN AND RANGE OF 6 SAMPLES)

H - 3 2 7 G R A P H I T E , P E R P E N D I C U L A R TO E X T R U S I O N - ( H E A T P U L S E METHOD, MEAN AND

RANGE OF 6 SAMPLES)

I I I I I I I 1

F I T T E D CURVE: Q = 6.66 L a = 2696 A

I 1 I 1 I I I

Fig. 25. Experimental measurements of the thermal conductivity of unirradiated H-327 graphi te as a function o f measurement temperature

52

H-327 Graphi te , Perpendi c u l a r t o Ex t rus ion :

1 1 3.709 x 104 4.535 x 10-4 -K,(t) rKB(T) /La J [KD(T)CdSG]

- 1

The non-numerical terms i n eqs. 7 and 8 a re t a b u l a t e d i n Table VII. The equat ions would be expected t o h o l d up t o t h e p o i n t where r a t e o f

volume change becomes zero. Curves based on eqs. 7 and 8 a re shown i n f i g s . 26-28. F ig . 26 shows t h e thermal c o n d u c t i v i t y a t t he i r r a d i a t i o n temperature as a f u n c t i o n o f f l uence f o r a s e r i e s o f i r r a d i a t i o n tem-

pera tures ; f i g . 27 shows t h e thermal c o n d u c t i v i t y a t t h e i r r a d i a t i o n

temperature as a f u n c t i o n o f t he i r r a d i a t i o n temperature f o r a s e r i e s o f f luences; and f i g . 28 shows t h e thermal c o n d u c t i v i t y as a f u n c t i o n o f

measurement temperature (below t h e i r r a d i a t i o n temperature) f o r m a t e r i a l i r r a d i a t e d t o the s a t u r a t i o n f luence. F i g s . 26 and 27 may b e used t o determine t h e thermal c o n d u c t i v i t y o f r e a c t o r g r a p h i t e under steady

o p e r a t i n g c o n d i t i o n s , and f i g . 28 should be used f o r t he c o n d u c t i v i t y d u r i n g s t a r t - u p and cool-down. Dur ing t r a n s i e n t c o n d i t i o n s when t h e

temperature r i s e s above t h e s teady i r r a d i a t i o n temperature, annea l ing

e f f e c t s w i l l tend t o inc rease t h e g r a p h i t e c o n d u c t i v i t y above t h e l e v e l s shown i n f i g s . 26-28 toward t h e u n i r r a d i a t e d c o n d u c t i v i t y ( f i g . 2 5 ) .

5 3

1

0.2

0.1

I I I I I I I 1

H - 3 2 7 G R A P H I T E , P A R A L L E L TO E X T R U S I O N

IRRAD. TEMP ("C)

1400

8oo / / 600

I I I I I I 1 I I

0.2 I I I I 1 I 1 1 H - 3