The influence of crystallite size on the dimensional changes induced in carbonaceous materials by high-temperature irradiation

Carhn

1968,

Vol. 6, pp. 55-63.

Pergamon Press. Printedin GreatBritain

THE INFLUENCE OF CRYSTALLITE SIZE ON THE DIMENSIONAL CHANGES INDUCED IN CARBONACEOUS MATERIALS BY HIGH-TEMPERATURE IRRADIATION” J. C. BOKROS,

G. L. GUTHRIEt

and A. S. SCHWARTZ

Gulf General Atomic Incorporated, John Jay Hopkins Laboratory Science, San Diego, California

for Pure and Applied

(Received 11 August 1967)

Abstract-Measurement have been made of the dimensional changes induced by fast neutrons in natural graphite, annealed pyrolytic carbon, catalytically graphitised carbon, and turbostratic carbon, for irradiation temperatures below 1300°C. Plots of the rate of change of the crystallite dimensions vs. temperature show the existence of a minimum rate for all but the natural crystals. This minimum rate occurs at a temperature which increases with increasing crystallite size. For the largest crystallite sizes (natural crystals), the rate decreases monotonically with temperature up to the highest investigated ( 1300°C). For large crystallites (> 200 A) and low irradiation temperatures (- 2OO”C), the rate of dimensional change is insensitive to crystallite size. The rate becomes increasingly dependent on crystallite size as the irradiation temperature is increased. At temperatures near 12OO”C, the rate varies by over two orders of magr’ntude for the various crystallite sizes used in the present study. The functional dependencies noted from the data are qualitatively consistent with the ideas of REYNOLDS and THROWER that involve the temperature-dependent heterogeneous nucleation of widely spaced interstitial clusters.

1. INTRODUCTION WHEN

graphite

energetic

knock-on

by collisions the

graphite

atoms

is irradiated carbon

carbon

to form loops,

that are produced

or become

annihilated

tural defects such as crystallite causing

dimensional

tion temperatures, nucleation

low temperature

changes.@) the spacing

dimensional dent

by

of

the

which

average

observed clusters

in

Consequently,

produce are nearly

crystallite temperatures,

shown that the dimensional

thus

crystallite than

of heterogeneous carbons,

spacings

nucleated

irradiations

change

At high irradiation

at struc-

At low irradia-

sites, even in turbostratic

the

rates

of

indepen-

size

in

the

sample.(4)

nucleate

boundaries,

with

homogeneously

large single crystals of graphite.c3)

atoms are generated

atoms recombine,

compared

between

of neutrons with carbon atoms in carbon lattice. (1) The displaced

and the vacancies

the recoiling

large

with fast neutrons,

is

it has been depend

on

size (LE) when the L, values are larger

N 100 A. NETTLEY

compared

and MARTIN(~)

the dimensional

as-deposited in graphitised

*Work supported by U.S. Atomic Energy Commission, Contract AT(O4-3)-167, Project Agreement 12. t Present address: Battelle Northwest, P.O. Box 999, Richland, Washington 99352.

changes

changes

have

induced

in

(L, < 200 A) and pyrolytic carbon (L, = - 1000 A)

pyrolytic

carbon

after irradiations at 600” and 700°C. They found that at 6OO”C, the rate of dimensional change for the as-deposited carbon was twice as high as that 55

for the graphitised

specimens,

and

at

56

J. C. BOKROS, G. L. GUTHRIE

7OO"C, the rate for the less crystalline was

about

six

times

PRICE(~* 7) irradiated carbons

higher.

a variety

and reported

little

carbons

(L, =

temperatures,

stratic

carbons

Large

between

the rates

N 1000

A)

however,

at

for the

strain

rates

stallite

arise for materials

sizes at high

because these materials nucleation To

a unified

picture

crystallite

size

of carbonaceous

temperatures

mens of four uniformly materials

were

crystalline

included

in

capsules that were irradiated at

exposures demonstrate on

high

dimensional

changes

direction

measured

basal

tion

irradiation The

These

and

high

changes

size

irradiation

slightly carbon

material

density available. than

by annealing

in the range

3000” to

this treatment,

the

orienta-

size of N 1600 A. This in the form

parallelepipeds.

were measured

The

of small

dimensional

with a machinist

micro-

scope using 0.3 mm holes as fiducial

marks.(@)

In most of the experiments,

were cut

could

the changes be

pyrolytic

provide A

(g/ml)

(A)

R,

Annealed massive pyrolytic carbon

2.25

1600

3.35

0.13

Natural graphite crystals

2.26

co

3.35

0

Catalytically graphitised carbon Turbostratic carbon

2.33

800

3.35

0.44

2.10

170

3.40

0.48

Supplementary

on the direct

were made to

measurements

of

changes.

uniformly

CARBONACEOUS

directly.

of density changes

a check

dimensional

specimens

in the a- and c-directions

measured

measurements

OF THE

accurate

less crystalline

After

a crystallite

included

PARAMETERS

in the

crystals were chosen as repre-

crystals were obtained

rectangular

the

from

accompanying

was irradiated

Layer spacing

Density

changes

of the

samples

and

Crystallite size L, (A)

Material

plane

calculated

of the most graphitic

material

results

of crystallite

annealed

1. STRUCTURAL

were

had a high degree of preferred

carbon, catalytically graphitised pyrolytic carbon, and a high density turbostratic carbon TABLE

using

material

selected for irradiation crystals,

microscope

carbonaceous

2. EXPERIMENTAL graphite

dimensional

plane were meas-

for 70 min.

so that

natural

The

as fiducial marks. The changes

massive pyrolytic

temperatures.

The materials

argon.

3300°C

eight

at

in

to the basal

a machinist

the natural

to various neutron

effect

with

Carbon

for

Essex

first for 4 hr at

5OO”C, speci-

temperature.

the strong

2400°C parallel

sentative

and the

materials

above

at

the c-axis

of the relation changes

(from

by heating

changes.(E)

of vacancies.

crystals

and then for an additional

determinations

offer more heterogeneous

the neutron-induced

irradiation

cry-

at

were purified and stabilised

in vacuum

twin markings

temperatures

sites for the elimination

obtain

between

with small

irradiation

irradiated

1900°C

ured

NOLDSet al.@)have suggested that high crystallite

were

graphite

New York)

changes

REY-

materials

in the range 500” to 1300°C.

prior to irradiation 4 hr

turbo-

higher.

The

natural

County,

of high density

were dramatically

1).

temperatures

100 to 200 A) and

polycrystalline graphites (L, = changed dimension at N 500°C; higher

(Table

and

of turbostratic

difference

the rate at which the crystallites turbostratic

material

BOKROS

and A. S. SCHWARTZ

crystalline

MATERIALS

Anisotropy

material

with

a

IRRADUTED

Remarks

RII 0.93 Annealed at 3000 to 3300°C for 70 min 1 Obtained from Essex County, New York 0.78 Deposited at 2100°C from 3% CH, in He; contains 2.7 atom-% Ti 0.76 Deposited at 2200°C from 12% CH, in He

THE crystallite

INFLUENCE

at 2100°C

carbon

and

in a fluidising

material

contained

particles

about

been

a titanium

furnace.

discrete

titanium

Details

and the structure

reported

This

deposition

material

was

described.(8*

in helium

lo* 11) turbostratic

carbon

furnace

and

size of 170 A. A high density

carbon

plication

was selected

to avoid

of irradiation-induced

which has been reported turbostratic

carbons

had

a

turbo-

the com-

densification,

when poorly crystalline

with a substantial

defect are irradiated Specimens

was

from 12 per cent methane

in a fluidising

crystallite stratic

density

at 2200°C

density

with fast neutrons.(ep 7* lo+r2)

of this material

were also irradiated

as strips or disks. The

degree

annealed by

of preferred

massive pyrolytic

X-ray

diffraction

nique.(13)

A modified

the

specimens

beds.04) each

using

R,

BACON tech-

of this technique

the preferred in

of preferred

was characterised

and

RI,, which

pole figure

formulated

the

deposited

degree

material

meters, (002)

The

of the

carbon was measured

version

was used to measure of

orientation

orientation the

according

fluidised

orientation

of

by two para-

are derived

from a

to the procedures

by BACON:

s” s

where the integrals

The

dimensional

pendicular

angle

4.““)

R, by RI,=

The

Table

1 -

RJ2.

structural parameters material irradiated. The

irradiations

RI,is

Table that

graphically

changes

parallel

principle

u-axis

and

per-

direction,

2, together

with

the irradiation

condi-

Specimens carbon diated again

of

the

catalytically

and the turbostratic

graphitised

carbons

were irra-

twice, first at 520” and 670°C at 840” and 900°C

and then

(see Table

2). Virgin

samples were also irradiated

at 840” and 900°C.

The data for the turbostratic

carbons

show that

at 840” and 900°C

the specimens

previously

temperature identical

(specimens

in Table

2

the behavior

irradiated

of

at a lower

a”, b”, c”, and d”) was

to that of the virgin specimens

(speci-

mens a’, b’, c’, and d’). The previous irradiation at a lower

temperature

turbostratic

carbons.

more crystalline mens

that

been

changed

no effect

the other

catalytically

had

temperature

had

On

on the

hand,

graphitised

irradiated dimension

at

a

at 840”

the

specilower and

:

2ln

related

characterise

(1+$+!)+ln(l+$?) +

In

vs. the

1 summarises

were conducted

tion capsules instrumented

the

tions.*

relation

plane normal)

parameter

to

for catalytically graphitised Al II! iI and AIJl, carbon and turbostratic carbon are listed in

from a plot of I(+) (the number of (002) poles per unit solid angle that are inclined at the angle + to the deposition

Test

3. RESULTS

oXiaI(4) sin 4 d$ can be obtained

All of the irradia-

in the Engineering

*For cases in which the changes AIJ, were derived from the changes in 111 and p, the exact

n/2I(+) sin3 4 d$

R,=

of these capsules have

previously.os)

the analysis of nickel and iron flux wires.

previously

high

57

have

either as strips or as disks of the type

The

The design and operation

CHANGES

Reactor (ETR). The integrated total fast flux for each cell of each capsule was obtained from

irradiated

deposited

DIMENSIONAL

tions were conducted

carbide

of this material

ON THE

been reported

throughout

of the

previously.@)

by

catalyst

The resulting

1 CLin dia. dispersed

microstructure.

process

SIZE

size of 800 to 900 A was obtained

co-depositing

the

OF CRYSTALLITE

to the

was used when approximate

the changes relation :

exceeded

each

in irradia-

with thermocouples.

was used when the changes

were smaller.

-

4%.

The

J. C. BOKROS, G. L. GUTHRIE

58

900°C (specimens e”, f”, g”, and h”) at a faster rate than the virgin specimens (specimens e’, f’, g’, and h’) during the irradiation at 840” and 900°C. This may be evidence for a seeding effect in the more crystalline material.(r7) The concentration of potential heterogeneous nucleaTABLE 2. DIMENSIONAL CHANGESINDUCED BY

and A. S. SCHWARTZ

tion sites in the turbostratic material was probably too high to be altered significantly by the previous irradiation at a lower temperature. The rates of crystallite dimensional changes, ln(1 + AXc/Xc> and ln(1 + AX./X.) per 1021 nvt, were used to compare the relative stability CARBON AND

INTURBOSTRATIC

IRRADIATION

AT

VARIOUS

CATALYTICALLY

Total change

Turbostratic

Catalytically graphitised carbon

carbon Neutron dose, nvt x 102r (E > 0.18 MeV)

Irradiation temperature

0.94 0.94 1.0 1.0

520 520 670 670 530 530 920 920 505 505 915 915 848 840 900 900 840 840 900 900 900 900 940 940 1225 1275

2.8 2.8 2.8 2.7 3.8 3.8 5.6 5.6 3.2 3.2 3.7 3.7 3.2 3.2 3.7 3.7 2.5 2.5 1.8 1.8 1.8 2.1

(“C)

3, x 100 111 -0.47(a) -0.48(b)

y

*

-0.55 (c) -0.52(d) 1 -1.65 -1.74 -7.40 -7.05 -4.19 -4.53 -16.7 -15.3 -10.9(a”) - 11.3(b”) - 15.5(c”) - 15.3(d”) * - 11.4 (a’) -11.2(b’) -15.3 (c’) - 15.6 (d’) -10.3 -10.5

GRAPI-IITISED CARBON

TEMPERATURES

I

x 100

+0.13 +0.20 0.00 -0.06 f1.4 +1.5 $16 +15 +7.0 +7.8 +54 +49 $26 +28 +48 +47

+28 +29 +46 +46 +21 +21

3’

x 100

F

4l

-0.11 (e) -0.12(f) -0.083 (g) -0.095(h)

-0.56 -0.63 -0.90 -0.75 -

-0.67 -0.68 -0.42 -0.47 -2.74 -2.78

t

I

x 100

+0.52 +0.70 +0.43 +0.19 +0.87 +0.97 +1.9 +1.7 +2.9 +2.2 +4.2 +4.6 +3.4 +3.3 +1.7 +1.9 +0.78 +1.1 +0.45 +0.72 +4.5 +4.9

*Specimens a”, b”, C” and d” were previously irradiated at 520” and 670°C (specimens a, b, c and d); the neutron doses and length changes listed for the specimens irradiated at 840” and 900°C are those accumulated at 840” and 9OO’C and are in addition to those due to the irradiation at 520” and 670°C. Specimens a’, b’, c’ and d’ are virgin specimens irradiated at 840” and 900°C. tSpecimens e”, f”, g” and h” were previously irradiated at 520” and 670°C (specimens e, f, g and h); the neutron doses and length changes listed for the specimens irradiated at 840” and 900°C are those accumulated at 840’ and 900°C and are in addition to those due to the irradiation at 520’ and 670°C. Specimens e’, f’, g’ and h’ are virgin specimens irradiated at 840” and 900°C.

THE of the

INFLUENCE

materials

graphite

irradiated.

crystals,

For

these quantities

by direct measurement; it was necessary

OF CRYSTALLITE the

SIZE ON THE DIMENSIONAL

natural

were obtained

for the other materials,

to derive the crystallite

changes

carbon

are

function

plotted

in Figs.

of the irradiation

59

CHANGES la

and

1 b as a

temperature.

Similar

plots with a reduced abscissa for the catalytically graphitised

and

turbostratic

carbons

are

pre-

from the bulk changes by plotting ln( 1 + Al II/I1,) and ln(1 + Al,/ll) as a function of the corre-

sented in Figs. 2a and 2b. To facilitate

sponding parameters, Iill and R,, and extrapolating to R = 0 and R = 1. This procedure

Fig.

of the curves from Fig. 2a are plotted on Fig. la.

is based on the BACON formulation:

Near

son, the curves from Fig. 2 without

the data

of one another,

1 are also drawn points,

6OO”C, the rates

for the four materials

comparion

and a portion

of dimensional

change

are within a factor of four

but at 12OO”C, the strain rates

of the most and the least crystalline materials differ by over two orders of magnitude.

.

I

which

has been shown to be appropriate for materials.‘B* ‘9 12) The quantities pyrolytic

and In( 1 + A&/X,) are the ln(l + AX/-K) crystallite changes and are given by the ordinate intercepts

R =

at

the

were normalised (E >

abscissa

1, respectively. 0.18

graphite

values

R = 0 and

comparison,

all data

linearly to a unit dose of 1OZ1nvt

MeV). crystals

For The

and

data the

for

annealed

the

natural pyrolytic

FIG. 1b. Average crystallite growth rates, ln( 1 + AX,l Xc) per lOa nvt (E > 0.18 MeV), for natural graphite crystals and annealed pyrolytic carbon. 4. DISCUSSION The data in Figs. I and 2 provide picture

of the influence

on irradiation-induced carbonaceous

dimensional

materials.

These

perfection changes

data

in

together

with those reported

earlier(g= 7, 12f show that the

crystallite

growth

rates,

10Z1 nvt,

for dense

sizes less than FIG. la, Average crystallite shrinkage rates, ln(l + AX,Ix,) per lOa nvt (E > 0.18 MeV), for natural graphite crystals and annealed pyrolytic carbon.

a unif$ng

of crystalline

temperatures

ln( 1 +

materials

A-X,/X$.) per

with

crystallite

N 200 A saturate for irradiation above 1000°C at a value of N 0.4

Using the damage function calculated by THOMPSON and WRIGHT”*) and the fact that for large

interstitial

clusters,

the fractional

c-axis

J. C. BOKROS,

60

G. L. GUTHRIE

and A. S. SCHWARTZ

is smaller, heterogeneous the damage rate.oo-24) The dimensional line

behavior

carbonaceous

poorly

nucleation

phases

pret.oo-*a* 24) This dense crystallites,

difficulty

submicroscopic due

arises,

not

density

to

phases

defect

by irradiation,(8* the

densification

only

in small that

(present

inter- and intra-crystalline

sity) are densified strains

contain to inter-

nucleation

but also because

a substantial

that

is difficult

because of the heterogeneous contain

of the polycrystal-

conglomerates

crystalline

increases

as

poro-

‘* 10. 12) and provide

an

I .o

FIG. ?a. Average crystallite shrinkage rates, ln(l + A&/X,) per 10’1 nvt (E > 0.18 MeV), for catalytically graphitised carbon and turbostratic carbon. approximately

growth

atoms present

equals

found that a large fraction that

are

interstitial

the

in the interstitial

displaced

(-

sites. The

fraction

must

natural

of

clusters,(r@) it is

of the carbon

0.4)

c

atoms

end

graphite

up

at

crystals,

on the other hand, retain little damage at 1200°C and the crystallite

c-axis growth

orders of magnitude measured the

rates

are two

less. The values of AX,/X,

for these crystals are compatible

size

and

distribution

of interstitial

with loops

observed by REYNOLDS and THROWER in natural crystals

after irradiation

For irradiation the

high

produce may

be

vacancies

temperatures

survival c-axis due

at 1200”C.(8)

growth in

part

by diffusion

at lower temperatures for turbostratic

above N lOOO”C,

of interstitials

carbons

in sites

in turbostratic to

the

that

carbons

elimination

to crystal

defects,@)

the higher

growth

of but rates

with L, = 40 A (data

point

on Fig. 2 of ref. 6 and also the result of NETTLEY and MARTIN(~)) must be attributed to the heterogeneous

nucleation

of interstitials

FIG. 2b. Average crystallite growth rates, In( 1 + A&/ Xc) per lO*r nvt (E > 0.18 MeV), for catalytically graphitixd carbon and turbostratic carbon.

at

pre-existing crystal defects. At still lower temperatures near 2OO”C, the crystal growth rates appear to be controlled by homogeneous nucleation for materials with crystallite sizes greater than N 200 A; (4) however, when the crystallite

additional

unannealable

superimposed crystallite that the poorly

upon

shrinkage which is irradiation-induced

the

shape change.o*) irradiation-induced

crystalline

It should be noted densification of

phases is quite different

from

the densification of bulk carbonaceous conglomerates that occurs by the closure of large intra-crystalline cracks by irradiation-induced c-axis growth. (u) Because of these complexities, the purported that

verifications

use some selected

or rejections

ofmodels

set of “standard

single

crystal data” and are supposed to represent the behavior of some carbonaceous conglomerate

THE under

INFLUENCE

irradiation

are

and controversy When

not

always

SIZE

dimensional

ON THE

at about

convincing,

benefit

in this area abounds.

crystallite

calculated crystalline

OF CRYSTALLITE

changes

are

from dimensional changes of polyconglomerates after irradiation at

The

DIMENSIONAL

650°C

that more crystalline

temperatures.

quacies of the available portion

of phases

appears

present

effort

characterise

merates

if their

irradiation

to increase

carbonaceous

treatment

the raw materials in poorly case

in refs. 28 through

size by

may offer

the stability

of some

especially

when

histories

crystalline

conglomerates

of certain

isotropic

used such

graphites.

carbon,

graphite

above

sensitively

for natural

stability

under

hanced

when

carbon

irradiation the

during

at 2 lOO”C, the

is substantially

irradiation

during

cial graphite containing that

the

graphitisation

can be realised

additives most

en-

temperature

above about 700°C. PARKER et a1.(27) have reported densification

the

is

that increased of commermetal-

are used. They conjectured stable

graphites

rates become

would be those which densified

lite

increased

To test their supposition, treated

irradiated

with various

heat

additives

(together

bodies

prepared

with controls)

size

materials

with

temperature,

than

increasingly the

with

the

rate occurs

size increases.

These

results show that the change

dimension

to crystallite

is near 200°C

until

to The were

size when

and the crystallite

200 A. However, dependent

irradiation

these

on crystal-

temperature

at temperatures

near

is

12OO”C,

the rates vary by over two orders of magnitude with crystallite size. The dependence of the rate at which

the crystallites

for high density carbonaceous *For nuclear applications where the conservation of neutrons is important, it may be desirable to use a metal catalyst of low cross section, e.g. zirconium, or to remove the catalyst by purification after the graphitisation process.

1300°C. that

insensitive

as

size. The dimension

at first and then increase

with earlier

sizes are greater

irradiation

continuously

of about

as the crystallite

the irradiation

processing

a higher final density.

decreases

at which the minimum

are relatively

the most during they

change

rate at which the crystallites

under irradiation

and as a result had

5OO”C, the changes

irradiation

data together

if certain

dimensionally

increasing

and

about

for all of the other

temperature

at

on the crystallite

crystals

increasing

carbon,

that

temperatures

studied decrease

titanium*

pyrolytic

show

rate at which the crystallites irradiation

changes

annealed

graphitised

carbon

temperatures depend

dimensional

crystals,

catalytically

turbostratic

rates

of pyrolytic

are found

33.

The irradiation-induced

of

deposition

data on the

5. SUMMARY

under

the crystallite

with catalysts

cent

Further

a

for each

conglo-

is to be fully

and processing

atom-per

is needed

of catalysts on graphitisation

The data in Fig. 2 show that with the addition 2.7

is formed when a

in ref. 9 show that

condition.

aggregate.

It

data

of catalyst

influence

behavior

conglomerates,

The

amount

in natural

of improving

as in the

heat

graphite

must be made

temperature

means of graphitisation a method

critical

that

results from the fact

is used and further show that a real is realised only at higher irradiation

in the crystal-

carbonaceous

dimensional

at high

understood. The ability

result

in the

that a concerted

better

in Fig.

models, but a substantial

must be due to variations

linity to

material

may arise from inade-

little

the use of the additives.

with catalysts

the

graphitized

from

data in Fig. 2 show that the stability

is obtained catalyst benefit

catalytically

and found that relatively

accrued

temperatures above about 6OO”C, the data scatter in the areas on either side of the curve for 2.(26) Part of this scatter

61

CHANGES

change

dimension

materials

on their

crystallite size and the irradiation temperature is illustrated in Fig. 3. These dependences are qualitatively

consistent

with ideas due to REY-

NOLDS and THROWER which,

at a given irradia-

tion

the

temperature,

involve

heterogeneous

62

J. C. BOKROS, G. L. GUTHRIE

and A. S. SCHWARTZ

3. REYNOLDS W. N. and THROWERP. A., Phil. Mag. 12, 573 (1965). 4. KELLY B. T., MARTIN W. H. and NETTLEY P. T., Phil. Trans. Roy. Sot. London, Ser. A260,37 (1966).

5. NETTLEY P. T. and MARTIN W. H., Paper presented at the AIME Nuclear Metallurgy Symposium on High-Temperature Nuclear Fuels, Delevan, Wisconsin, October 1966. To be published. J. C. and PRICER. J., Carbon 4,441 (1966). 6. BOKROS J. C. and PRICER. J., Carbon 5,301 (1967). 7. BOKROS 8. REYNOLDSW. N., THROWERP. A. and SIMMONS J. H. W., Second Conference on Industrial Carbon and Graphite, p. 493. Society of Chemical Industry, London ( 1966). 9. SCHWARTZA. S. and BOKROSJ. C., Carbon 5,

CRYsrALLlTE DIMENSIONAL CHANQE

325 (1967).

10. BOKROSJ. C. and SCHWARTZA. S., Trans. AIME 239, 7 (1967). IRRADIATION

TEMPERATURE

FIG. 3. Schematic diagram showing the dependence on irradiation temperatu?e of the neutron-induced crystallite dimensional change rates for carbons with various crystallite sizes. nucleation spacing

of

interstitial

of heterogeneous

clusters nucleating

when

the

centers is

11. BOKROSJ. C., Carbon 3, 17 (1965). 12. BOKROSJ. C. and SCHWARTZA. S., General Atomic Report GA-7700, March 1967 (to be published). 13. BACONG. E., J. Ap~l. Chem. 6,477 (1956). 14. BOKROS.J. C., Carbon 3, 167 (1965). 15. PRICE R. J. and BOKR~SJ. C., J.‘Appl. Phys. 36, 1897 (1965’). 16. CARPENTERF. D. et al., In International Symposium on Developments in Irradiation Capsule Technology, Pleasanton, California, May 1966 p, 421 (D. R. HOFFMAN, ed.), USAEC Report CONF-6605 11

above a critical value.o* 3, s* a4) authors thank F. C. CARPENTER, B. B. SPILLANEand R. J. GRENDAfor incorporating the carbon specimens in the irradiation capsule; W. H. ELLIS and F. J. GAGNONfor performing a large portion of the experimental measurements; and G. W. HINMANfor the natural graphite crystals. The irradiations were conducted under USAEC Contracts AT(O4-3)-633 and AT(04-3)-167 (Project Agreement No. 12). The preparation of some of the carbon specimens was supported by the High Temperature Reactor Development Associates (HTRDA) Fuel and Fuel Cycle Development Program. The HTRDA group consists of 23 investor-owned electric utility companies located in the United States. Acknowledgments-The

REFERENCES

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THE

INFLUENCE

OF CRYSTALLITE

SIZE ON THE DIMENSIONAL

CHANGES

63

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