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Dimensional changes in graphite: The relationship between those produced by absorption of bromine and those produced by irradiation
JOURNAL
OF NUCLEAR
DIMENSIONAL
MATERIALS
9, No. 2 (1963) 197-210, NORTH-HOLLAND
CHANGES IN GRAPHITE:
BY ABSORPTION
THE RELATIONSHIP
Reactor Materials
A study
of the macroscopic
the
growth
which
occurs
absorbs bromine was made to determine
bromination-induced
BETWEEN THOSE PRODUCED
dimensional
and J. C. WEEKS*
Laboratory,
Received
graphite
CO., AMSTERDAM
OF BROMINE AND THOSE PRODUCED BY IRRADIATION
J. E. BROCKLEHURST
UKAEA,
PUBLISHING
changes
Culcheth, Warrington, Lanes.,
31 December
when
whether could
UK
1962
effect was not marked in the isotropic
material examined.
The work presents a basis for predicting,
be
tion
experiments,
the
from bromina-
irradiation-induced
dimensional
related to those which occur in graphite under fast neutron
behaviour
irradiation.
developed crystal structure. Tests can be performed cheaply
For a number
of extruded
per unit concentration
graphites
of absorbed
the initial growth
l’absorption
in the c direction
and is therefore able to close
up the oriented microporosity
which, in the initial stages of
growth, partially absorbs the crystal strain in this direction. Irradiation
growth also involves
sions of the crystallites of accommodation porosity
is important
growth behaviour. modation
graphite
sorption
of bromine
manner
which
similar
enables
from
between
the
a basis for comparing a comparison irradiation
to
work.
the bromination
made in interpreting
lites in the e and a directions levels
generation
be
in a
different made
There
with
is good
and irradiation of about 8 %
data
; above
are believed to result from an
i.e. that the thermal expansion At high
of crystal
of crystal
the irradiation
results,
coefficients
of the crystal-
are unchanged
by irradiation.
strain
there
in the anisotropic
is evidence
graphites,
macroscopique
determiner
si les changements
bromuration
pourraient
dans le graphite
of
*
Student
from
College
of Advanced
Technology,
Car-
U.K.
soumis
Pour initiale
de dimension
induits par la
& une irradiation
un nombre
de graphites
par concentration
relic au coefficient
par neutrons
directions grands
absorb6
suivant les
suivant la direction
tion du cristal suivant des cristallites
dans
absorbe partiellement cette direction.
suivant
le taux d’accomodation
la deforma-
c et le taux
suivant cette direction
macroscopique.
dans le cornOn pense que
pour un graphite don&
par la deformation
par
dans les dimen-
a une grande importance
de la croissance
de
les stades
La croissance
la direction
de la deformation,
par la ,microporositB portement
qui,
de
de cristallites
c et est done capable
orient&e
implique aussi un accroissement
d’accomodation
produit
dans les dimensions
initiaux de la croissance irradiation
est
de l’echantillon
cristalline par bromuration
la microporosite
direction
lineaire
des axes c et a. La bromuration
de graphite
sions
la croissance
de brome
initial et ceci permet d’en deduire les change-
accroissements
reduire
extrudes,
unitaire
de dilatation
ments de dimension
cristalline
est uniquesuivant
la
c.
La variation
dans le taux d’accomodation
par l’absorption
de la deforma-
orient&e est refermke
de brome fut determinee et exprimee dune
fapon qui fournit 197
de
etre relies It ceux qui se produisent
tion cristalline quand la microporosite diff,
au tours
a et& Btudiee afin de
irapides.
ment determine
but the
qui se produit
du brome par le graphite
de graphite
by
up by ab-
and expressed
up to a crystal strain in the c direction
porosity
uniquely
is closed
was determined
this level, the discrepancies assumption
macroscopic
is determined
microporosity
provides
and data
agreement
the
in the amount of accommodation
as the oriented
graphites
determining
by micro-
strain in the c direction.
The variation strain
in
and the amount
in this direction
It is believed that the amount of accom-
for a given
the crystal
an increase in the dimen-
in the c direction,
of strain
nformation.
La croissance
to be derived. Bromina-
tion causes large increases in the dimensions of the graphite crystallites
these have a well
of the original graphite
sample, and this enables the crystallite changes on bromination in the c and a axial directions
providing
on a large number of specimens and thus provide statistical
bromine is related to the
linear thermal expansion coefficient
of new graphites,
une base de comparaison
de different6
,J. E. BKO(IKLEHUKS’I’
198 graphites et permet une compsraison fournies accord pour
par les travaux entre les don&es
une deformation
atteignant
des dorm&es similaires
sur l’irradiation.
11 y a un bon
de bromuration cristalline
la direction
lichen
Stadien
teilweisc
c
environ 8 96. Au dessus de cc taux, le d&accord
Der
Betrag
des
pourrait ritsulter d’une hypothhse faite dam I’interprirtation
Richtung
clue les coefficients
Bestimmung
de dilatation thermique des cristallites suivant les directions
gleichsbetrag
c et a ne subissent
spannungen
Aux
taux
pas de variation
par l’irradiation.
6lev6s de d&formation
cristallinr.
il existe
quelque hvidence de naissance de prositt dans les graphites anisotropes, isotrope
mais l’effet n’&ait pas marquC dans le mat&au
Le travail pzrtir
presente
une base permettant
d’expkriences
dimensionnel
de
bromuration,
de prCvoir, &
le comportement
de nouveaux graphites sous l’effet de l’irradia-
Ausgleichs
durch
Die Anderung spannungen
fournir
sur un grand nombre ainsi une information
d’i?chantillons
et peuvent
Vergleich
wurden
Wachsen
L’ntersuchungen
von
Grafit
Bromabsorption len
iiber
angestellt,
verursacht
Neutronenbeschul3.
das
einmal wird
Bromination
Neutronen
und
durch
Fiir eine anzahl sorbierten
NeutronenbeschuU
pro
BeschuB
mit
unter-
schnellen
Grafiten
von Originalgrafitproben die Ableitung
Die Bromination Dimension es mcglich,
1.
ab-
zum linearen thermischen
worden.
in Richtung
ist dns
Konzentrationseinheit
Ausdehnungskoeffizienten Dies ermiiglicht
gesetzt’
der Kristallitver-
der c- und a-Achse bei Bromination.
verursacht
ein erhebliches
von Grafitkristalliten die orientierte
Wachsen
in c-Richtung.
Mikroporositlt
der
Daher ist
in den anfiing-
Introduction dimensional
changes which occur when graphite absorbs bromine was performed
to determine
if these dimensional
verandert Bei
dieser Effekt erkennbar
Bromine
enters the graphite lattice by diffusion between the 83 wt %
of
temperature,
Riidorffl) bromine
has
shown
can be taken
from
an atmosphere
bhe vapour ; X-ray
measurements
that
about
up, at room saturated
with
have indicated
t’hat the resultant material, C,Br, has a homogeneous structure of one bromine layer for every two carbon layers.
The
c-spacing’)
absorption
of bromine
of the graphite
fiir in
dieser
Grenze tratcn
auf: sie werden erklbrt durch eine Snnahme.
increases
latbice and Bloc
der Bestrahlungsergebnisse
Betrggen
ge-
auf die Vcr-
der Kristallspannungen Grafiten
konnte dagegen in isotropem
gemacht
das
bestrahlungsinduzierte Grafite
vorher
Arbeit
st,ellt
Dimensionswechselverhaltcn
abzuschltzen.
Vorausgesetzt,
Kristallstruktur
rine statistische
da0
besitzen. Solche
Versnche kiinnen ohne besonderen Kostenaufwand grol3en Zahl von Proben durchgefiihrt
an einer
werden. und ergeben
Information.
have
macroscopic
ist eine
offenkundig;
dar, urn aus Brominationsexperimenten
diese eine gut entwickelte
that it also produces
shown
dimensional
that the absorption slight contraction
thermal
nicht
Material nicht
werden. Die vorliegende
Grundlage
neuer
der
bei NeutronenbeschuB
in anisotropen
eine
Poisson’s
planes.
und den Daten
fiir Kristallspannungen
werden.
graphite layer
festgestellt;
bis etwa 8%. Oberhalb
hohen
lattice
by fast neutrons.
such den Seutronen-
mutung, da13die thermischen 3usdehnungskoeffizienten
changes could be related to those which occur when is irradiated
durch
Es wurde gute ivbereinstim-
Bromination
Kristallite in c + a-Richtungen
&?old2)
The present study of the macroscopic
die
macht wurde; diese bezieht sich insbesondere
es durch
der Versuch
von StranggepreRten
Broms in Beziehung
inderung
der
Sic ermiiglicht
Daten,
wurden.
zwischen
Porositltsbildung
Wachstum
bildet.
lhnlichen
wenn
abzuleiten.
anfhngliche
Mikroporosi-
wurde in einer Form beatimmt,
die f iir die Interpretation
nommen, eine Beziehung zwischen dem Dimensionswechsel durch
fiir die Kristall-
makroskopische
wird und einmal durch schnel-
Dabei
als glrichbleihrnd
des A4usgleichsbetrags
Grafitsorten mit
Diskrepanzen Es
dir
und erfaBt, welche die Grundlage fiir den Vergleich unterschiedlicher
c-Richtung
statistiques.
fiir
Der Aus-
Grafit fiir dir Kristall-
wird dabei
durch SchlieBen der orientierten
murlg
quement
ist wichtig
bestimmt.
beschul3 gewonnen
Cconomi-
auf.
in dieser
Wachstums.
fiir einen gegebenen
sir.
nb-
in c-Kichtung
Spannungen
die MikroporositLt
d8veloppCe.
btre entrepris
ron
in c-Richtung
indcm
Richtung
tritt ehenfalls ein An-
des makroskopischen
tion pourvu que ceux-ci aient une structure cristalline bien Des essais peuvent
in dieser
der Kristallite
t&t infolge Bromabsorption
exami&.
zu verringcrn.
Bei Hestrahlungswachst,um
wachxen der Dimensionen
des rksultat,s, d’irradiation,
B savoir
des Wachstums
die Kristallspannungcn
sorbi&.
et d’irradiation
suivant
AKill ‘I’. (‘. WEEKS
of bromine
ratio
effect
expansion
layer
of the graphite
plane
buckling
or a
similar to t’hat observed
measurements
Changes in graphite
crystallite
occur due to the displacement neutron irradiation,
may give rise to a
in the a-spacing
due t,o either
large
changes. It is also possible
in
on graphite3). dimensions
also
of atoms under fast
resulting in an increase in the
c-axis direction and a decrease in the a-axis direction (cf. Simmons
and Reynolds4) ).
Sutton and Howard5)
t’he
mal expansion
and
of the crystallites
have shown that the ther-
of bulk graphite because
part
is less than t’hat of the c-spacing
DIMENSIONAL
thermal expansion is absorbed
by porosity
CHANGES
which is
oriented parallel to the layer planes. Simmons Reynolds4)
have
irradiation
growth
shown
that
the
and
macroscopic
and bulk thermal expansion
of
graphite
are closely related and that the oriented
porosity
is closed
by crystallite
growth
perpendi-
cular to the layer planes ; this closure of oriented porosity
causes
the
the layer
planes,
distribution
geneous
complex
bromination,
C,,Br,
and addition
due to irradiation
desorption,
layer, thus forming collapse
is controlled porosity.
by
The
the
closure
absorption
of
oriented- micro-
of bromine
by graphite
also causes large changes in the crystallite
dimen-
sions in the c-axis direction.
Therefore, if the stress
distribution
due to absorption
bromine
in the matrix
is similar
irradiation
growth
observation bromine
to that
and thermal
of the dimensional
absorption porosity.
it possible
occurs
expansion, graphites
should
in the influence of the
Such observations
to predict
then
how
should make
such graphites
fore, for a number of graphites, the large dimensional sorption
we have compared
changes produced
by the ab-
of bromine with their thermal expansions.
In the case of Pile Grade ‘A’ material, used as a moderator this country,
we have also compared
sional changes with those produced
in
these dimenby irradiation.
ward diffusion
Previous Work on Absorption of Bromine The limiting composition
obtained
when graphite
is exposed to bromine vapour is determined perfection
of
the
original
graphite
Bromine will not form lamellar complexes graphitised shown
by the
may
be removed
defect
sites without
On
paths blocked, an
sorption,
observed7),
initial
but it appears
with out-
bromine physically
effect
is
that the quantities
adsorption
of
adsorbed are relatively small for
well graphitised
materials and this is supported
the observations
of Riidorffi)
by
and Blackman et aLs),
who have shown that powdering
has little effect on
the limiting capacity of large well ordered specimens. X-ray
dat,al) for C,Br give a dimensional
in the c-axis direction ported
by
bromine
of 55%.
pyknometric
determinations
and microscopic
perfect crystals in the direction absorption
and desorption
measured changes
in liquid
measurements
Changes in bulk dimensions
on near
of the c-axis. of graphite
of bromine
to be greater
expansion interpreted
of artificial
volume
graphite
than the crystal
were
volume
by factors between 1.4 and 2.2. This was as being due to the generation
sity when bromine was absorbed;
accommodates
of poro-
this is the reverse
effect to that observed
the c-axis
during
have been
by Bloc and HBrold2). Apparent on specimens
change
This value is sup-
irradiation47 5), where it is postulated
have
complete
or at defects in the
with non-
materials and Maire and Mering’)
a,ny
at room tempera-
structure.
that as the degree of order in the crystal
from
structure.
observed 2.
any one layer is filled
of the layer. Desorption
graphite
currently
in nuclear power stations
on
It is
ture leaves a residual bromine content; the bromine
would
change dimensions when they are irradiated. There-
structures
of a cycle.
may be held by normal lamellar bonding
of
during
changes caused by
in different
provide valuable information oriented
which
portions
that inter-
layers are opened up, and on
bromine
is a unique function of the crystal strain in the c-axis expansion
have different
suggesteds) that on sorption, before neighbouring
direction;
this means that the thermal
further
by Maire and Mering7) and also by
compositions
of graphite
on
et ala). They have indicated
Blackman mediate
of linear
whereupon
Hysteresis effects have been observed on sorption and desorption
removal
et aL6) have
an
up to the homo-
C,Br layers start to form.
to
Martin
lattice by forming
of layers
to
proceeds.
expansion
enters the graphite
expansion
thermal
shown that the change of the coefficient thermal
bromine irregular
growth, perpendicular
bulk
increase as the crystallite
199
IN GRAPHlTE
in thermal
expansion
and
that porosity
and is closed by crystal growth
in
direction.
structure is increased, the bromine pressure required to establish a given composition limiting
uptake
increases
decreases and the
towards
the saturation
3.
Experimental Graphite
specimens,
nominally
7.6 x 0.6 cm dia,
from a calibrated
quartz spring, of
value C,Br. These studies were supported
by X-ray
were suspended
measurements
sorption,
sensitivity 200 mg/cm, in a glass vacuum apparatus_
and
showed
that
on
200
J. E. BROCKLEHURST
Bromine bulb
vapour
was admitted
containing
the liquid
and the specimen followed
surrounding
by removing the
specimen,
of air over
the
-1.2. MAIN
t’emperature,
length and weight changes were
with a cathetometer.
were obtained current
at intervals from a
at room
Desorption
curves
the bromine
vapour
either
by
specimen
passing
or by
a
partial
evacuation.
A?u’D T. (‘. \VEEKS PROCRAMME
Since the dimensional
changes
tion, the main investigation
were taken in both directions
of cut
in fig. I.
was limit,e:l t,o a study
of the lower port,ion of the growth curves. At least one sorption
and desorption
on one specimen
in each
respect, to the direction
Specimens
shown
are much greater than t’hose observed under irradia-
from
cycle was determined direction
of extrusion
all the graphites
examined.
of cut’, wibh or pressing,
The results are
from of range of artificial extruded graphites made
shown in fig. 2. Two
from
were taken for graphite A and the results were found
petroleum
Four types
coke
and coal tar pitch
of reactor
grade graphite,
A, B, C, D, with different expansion,
artificial
t,o be in close agreement.
cimen of this graphite was cycled three times and
Pressed natural com-
the results are shown in fig. 3. In general, the sorp-
graphite
‘B’
A perpendicular
cut, spe-
tion curves show an increasing growth per unit con-
graphites
represent
reactor grade materials graphitised peratures,
in each direction
of thermal
pact was also investigated. The
specimens
designated
coefficients
were investigated.
binder.
being
a range
of
at similar tem-
nearly
60’
isotropic.
Graphite ‘A’ is the Pile Grade ‘A’ material currently used in British Nuclear Power Stations. The natural compact,
which
has a high
oriented,
should
give a good
crystal
density
indication
50
of single
t
behaviour.
Thermal expansion specimens
over
the
measurements
were made on
A
range
temperature-
9
room
700” C in a silica dilatometerlO)
4.
and is well
before bromination.
“4 40 $
I
Results w
A summary
of the measurements
is given
in
2
measurements,
shown
z 2 z F Y E
development
of the
table 1 and figs. 1, 2 and 3. 4.1.
PRELIMINARY MEASUREMENTS
Preliminary
bromination
in fig. 1, were made
during
ERPENDICULAR
apparatus to determine the magnitude of the dimensional
changes.
were obtained parallel
to
In
particular,
interesting
for a natural compact
pressing.
A
linear
results
specimen
relation
cut
between
growth and uptake of bromine was obtained for this specimen, large transverse cracks eventually
opened
up and the specimen
after a
dimensional
finally
disintegrated
change of 61% at 8 at % Br/C. It was
observed
that
an increase
occurred
in the natural
geneous composition
L! BROMINE
in the linear gradient
compact
C,,Br
0
near the homo-
(6.25 at % Br/C).
Fig. 1.
CONCENTRATION
Preliminary measurements of the growth of graphite caused by absorption of bromine.
201
DIMENSIONAL CHANGES IN GRAPHITE TABLE 1 Results of main programme
Graphite
Direction of out with respect to extrusion or pressing direction
Density g/em3
j
Parallel Perpendicular
1.74
A
Initial growth per unit con- i- Mean linear thermal cent&ion of absorbed bromine e:xpansion coefficient (loo-7000 C) (% length change per at % x 1oa/v Br in C)
Number of Specimens
2
!
2
0.22 0.55
1.89 3.65
B
1.70
Parallel Perpendicular
1 1
0.51 0.60
3.54 4.24
C
1.73
Parallel Perpendicular
1 1
0.33 0.80
2.47 5.16
D
1.80
Parallel Perpendicular
1 1
0.25 0.61
1.98 3.93
Natural Compact
2.08
Parallel Perpendicular
1 1
4.9 0.44
22.0 2.24
centration absorbed
of absorbed bromine
A pronounced cases
with
bromine
as the amount
of
hysteresis effect was observed in all linear
desorption
curves,
as
of the desorption
point
reached
bromine composition. previous The
observed by Bloc and HBrold2). Fig. 3 shows that the gradient
maximum
on sorption,
curves is dependent
on
after
This effect is consistent
compositions
of the
GRAPHITE
B
residual
are approximately
C
GRAPHITE
PERPENDICULAR A
PERPENDIC”LA$
PERPENDICULAR.
/
/
RRPEN.C”LAR/{
A
3-
BROMINE
Fig. 2.
CONCENTRATION
‘(at
with
observations73 *).
desorption
GRAPHITE
GRAPHITE A (MEAN OF 2)
i
hence
there is no unique value of length change for a given
increases.
nearly
the
L
%
m/C
)
’
Growth of different graphites caused by absorption of bromine.
compounds the same for
D
all t,he ext,ruded graphites, but the natural compact
be virt,ually independent
residual
approximately
compound
has a lower bromine
than those of the extruded
graphites.
content
The residual
strains appear t,o be roughly dependent
on oriema-
t’ion.
three desorptions levels.
Fig. 3 shows that the second and third sorption by t’he previous cycle but the
residual point,, for graphite
‘A’ at least, appears t,o
from increasingly
ItI t)herefore appears
manent
curves are influenced
of previous
treatment
i\S
t,he same point, is reached cvcn after
distortion
higher
that, very
of the lattice
strain
little per-
was taking placao
in t,his case, but’ this was not true for t,hc nat,ural compact
where the length
recovery
was poor on
desorption. Nat’ural
compact
specimens
placed
in a t’ube
cont,aining bromine vapour finally disintegrated shown
GRAPHITE A (PERPENDICULAR)
in fig. 4. Extruded
specimens
graphite did not break up after prolonged to the vapour
although
as
of artificial exposure
a fine crack pat,tern was
observed.
5.
Discussion of Results
6.1. CORRELATION WITH THERMAL EXPANSION From a consideration a graphite
matrix,
of the stress distribution
Simmonsll)
in
has shown that the
linear coefficient of thermal expansion of a graphit’e specimen is given by a =Ax,+(l-AA)&,
(1)
where a, a.nd iy, are the thermal
expansion
coeffi-
cients of the crystal lattice and A is a characteristic of t’he method of preparation the specimen. pansion
Thermal
of the
and direction of cut of
expansion
crystallites
Similarly pansion
of the crystallites absorption
of the
in the a-axis direction.
of bromine
crystallites
2
J
4
CONCENTRATION
the a-axis direction
5 (at
%
Ed
Fig. 3. The effect of cycles of absorption and desorption of bromine on the bulk dimensions of graphite A.
Fig. 4.
Poisson’s bution
involves
perpendicular
layer planes and a contraction BROMINE
an exto the
below 380” C, a
layer planes and, at temperatures contraction
involves
perpendicular
an exto the
term may arise in
from layer plane buckling or a
ratio effect’. Therefore, if the stress distri-
in the graphite
matrix
strain resulting from absorption
caused
by crystal
of bromine
is the
The effect of prolonged exposure to bromine vapour on a perpendicular cut natural compact specimens.
203
DIMENSIONAL CHANGES IN GRAPHITE same
as that
resulting
from
the
obtained
during thermal expansion,
graphite
when it absorbs bromine
crystal
that is G = (dL/dB)/L
strain
the growth
of
should be given
bY
where
B = atomic rat,io Br/C.
It is then assumed that g, is very small and can be neglected ; this assumption
G=Ag,+
(1-A)g,
(2)
where g, and ga are the crystal and a-axis
directions
centration
of absorbed
scopic
strain
strains, in the c
respectively,
per unit
con-
bromine and G is the macro-
per unit
concentration
of absorbed
bromine. Sutton and Howards)
have shown that crystallite
growth in the c-axis direction closes oriented microporosity;
this results in the material being less able
to accommodate quent
further c-axis strain and a conse-
increase
produced
in the coefficient
during
bromination
large and is expected porosity
A. The growth is
comparatively
to close the oriented
and therefore
micro-
the value
of A.
Eqs. (1) and (2) must therefore be compared
in the
range of crystal
increase
growth
given
of bromine,
will be justified
of A can be determined
using the measurements
percentage
by
from
lat’er. eq. (1)
of bulk thermal expansion
in table 1 and the appropriate
and LYEgiven
Nelson
values of LYE
and Riley3).
Then
the
value of A L/L, for 2 % crystal strain is
given by 2A from eq. (2). Thus G,, t’he value of G at’ low crystal strain, is obtained the data in fig. 5 to determine this value of A L/L,,
by extrapolating the value of G at
i.e. corresponding
to a crystal
strain of 2 % . G0 was determined in two directions corresponding
in this way for each graphite
of cut and plotted
against
values of a, the coefficient
t,hermal expansion
the
of linear
measured over the range 100 to
I.Or
strains where the strains due to
thermal expansion are comparable by absorption
The value
PERPENDICULAR
with those caused
and this means that the
per unit concentration
of bromine
where
AL/L,, --f 0 should be used. The coefficient A should then have a value which may be determined eq. (1) using thermal
expansion
and g, at low bromine calculated using eq. (2). Unfortunately, accurately
concentrations to
be
determine
G
g
0.8/
3
--f 0; also when the bromine
is small a substantial
bromine may be physically
fraction
PARALLEL
of the
during thermal expansion
strains up to 2%
to 2% caused by absorption and it is assumed
D
for
and it seems reasonable
PRESSED NATURAL COMPACT PERPENDICULAR
therefore to assume the same for crystal strains up of G has been determined
GRAPHITE
Martin and
Entwisle12) habe shown that the coefficient A is not crystal
C
this bromine would not
to crystal strains. However,
changed significantly
GRAPHITE
adsorbed on the surfaces
of the pores in the graphite; contribute
can
/-PERPENDICULAR
it is difficult
when AL/L,
concentration
from
data, and then ge
of bromine. The value
at a crysta,l strain of 2%
that this value
applies
at all
strains less than 2 % . Fig. 5 shows the variation of G, the growth of the different graphites per unit concentration as a function
of AL/L,,.
of bromine STRAIN (%
G is expressed as the per-
centage strain per unit atomic ratio Br/C x 100.
Fig. 5.
Al /Lo)
Variation of G with macroscopic strain.
J. E. BROCKLEHCRST
204
700” C. The results are shown in fig. 6. The mean values of ac and cyaover this temperature range are 28
x
1O-s and zero respectively+). Thus from eq. (l),
zero. The difference is not completely understood.
and eq. (2) can be written in the form 28
xa 1o-6
(Se-gal +
It is seen from the insert in fig. 6 that the natural compact data do not agree with the data obtained for the extruded graphites. In particular, the value of gc for natural compact is 6.4, and ga is nearer
A = (u/(28 x 10-6)
Go =
Ah’D T. C. WEEKS
However, the extruded graphites are all manufactured from similar materials and are graphitised
Sa
Therefore if the analysisis correct, the plot of G,, gc - Sa 28 x 10-s and intercept equal to ga when a is zero. Fig. 6 shows that G,, for the extruded graphites is a linear function of a, and a negative intercept on the G, axis is observed indicating a very small contraction in the a-axis direction. Therefore, the previous assumption involving the neglect of ga to determine the bulk strain for a crystal strain of 2 % is justified. Values of g, and ga have been deduced from the best straight line drawn through the points in fig. 6. These are: against a should be linear with gradient
gc = 4.8 + 0.2 % per at % Br/C and ga = - 0.10 -& 0.02 % per at % Br/C
at similar temperatures, thus the crystallite sizes in the extruded graphites will be very similar. On the other hand, the crystallite size in the natural compact is much larger than that in the extruded graphites. Therefore, if gc and ga are functions of crystallite size the difference in behaviour could be explained. Blackman et aLs) have suggested that any one layer in the graphite lattice is filled before neighbouring layers are opened up. If this is the case and gc is defined as 1 dX, SC= x, dB where Xc is the crystallite dimension in the c-axis direction, then dX,/dB should be a constant independent of the amount of bromine absorbed. Taking
O.B-
Y
r &
LD
0.7.
& 4
EXTRUDED
A
GRAPHITE5
8
a x
C
a
D
A
PRESSED
4’
cp
IO o( “IO‘
15
20
5 ,,:N
Fig. 6.
Correlation
LINEAR
of thermal
EXPANSION
expansion
and growth
o((100
caused
-7:OV)
X IO6
by absorption
of bromine.
25
6
DIMENSIONAL CHANGES IN GRAPHITE
205
the initial value of gc as 4.8% per at % Br/C, the crystal strain for a composition of C,Br is 60%)
tures. Martin et al.‘) have used these data to show that at irradiation temperatures between 150” C
which compares reasonably well with Riidorff’sl) X-ray measurement of 55%. The relation between
and 250” C, A, is a unique function of E,, the crystal strain in the c-axis direction. The same
growth and amount of absorbed bromine observed in fig. 1 for the natural compact supports the hypo-
,relation may apply at higher irradiation tempera-
thesis that dX,/dB is constant at least up to a composition of C,,Br. On the other hand, if the
mental data. Martin et aL6) point out that the crystal strain in the a-axis direction becomes a
initial value of gc = 6.4 appropriate to the natural compact is used then the crystal strain at CsBr
irradiation temperature is raised; this may cause
is 80% ; this is much higher than Riidorff’s value and makes no allowance for the observation made in fig. 1 that in the natural compact dX,/dB appears to increase when the composition has reached C,,Br. If such an increase does take place, this will further increase the discrepancies between the interpretation of the bulk measurements and the X-ray measurements on the C,Br compound. Further work is required to resolve these anomalies, but it is thought that the large growth of the natural compact is due to generation of additional porosity. 5.2. CORRELATION WITH IRRADIATION-INDUCED DIMENSIONAL CHANGES Simmons and Reynolds*) have related the bulk linear thermal expansion coefficients and irradiation induced growth rates of different graphites to the thermal expansion coefficients and irradiationinduced growth rates of graphite crystals perpendicular and parallel to the layer planes in the following equation 1 dX, 1 dl, -- =&X,m+ 1, dD
(1 -A”)$d$
a
(3)
1 dl, where i d-D = growth per unit irradiation dose of z the graphite aggregate in direction 5, 1 dX, = growth per unit irradiation dose of X, dD each crystal in the c-axis direction,
1 dX,
= growth per unit irradiation X, dD of each crystal in the a-axis direction,
dose
and A,, the value of A in direction x, is determined from eq. (1). They have used this equation to determine the crystal strains, AX,/X, and 0X,/X,, at different irradiation doses and different tempera-
tures but as yet this is not justified by experi-
larger fraction of that in the c-axis direction as the the relation obtained by Martin et aL6) to break down when X, AX,/X, AX, ceases to be small. However, at low irradiation temperatures the data show that A, is a unique function of E, and is unaffected by crystal strain in the a-axis direction. A, changes under irradiation because the crystal growth in the c-axis direction fills up the oriented porosity observed by Sutton and Howards) and this reduces the amount of accommodation that can be provided for any further crystal growth which takes place. It can be postulated therefore that the change in A, due to absorption of bromine should give the same relation between change in A, and crystal strain as that observed due to irradiation, provided that the stress distribution developed in the graphite matrix is similar in both cases. Since it has already been shown that both irradiation and bromination growth are closely related to thermal expansion ,for small crystal strains, the stress distribution must be similar in all three cases at least when the crystal strains are small. Also, since the crystal shrinkage in the a-axis direction during irradiation does not appear to influence the variation of A, with E,, the much smaller a-axis shrinkage observed during bromination should also have little effect on A,. The variation of A with the amount of bromine absorbed is shown in fig. 7 for the two directions of cut for each of the extruded graphites. The coefficient A was determined by using eq. (2) with the experimental data in fig. 2 and the values of ge and ga obtained at low strain for the extruded graphites, assuming that dX,/dB and dX,ldB are constant and are independent of the amount of bromine which has been absorbed. Fig. 7 shows that in the anisotropic graphites A, C and D, the variations of A with bromine concentration are
206
J. E. I~RO(‘KLEHUKS’I’
similar
except
that
A increases
more
graphite A, up to a bromine concentration
AND ‘I’. (‘. \vEEI+
steeply
in
of 3 at, ?b
Br/C, t,han it does in graphites C and D. Graphites A, C and D were made from t,he same raw materials but graphites
C und D were twice
with pitch before graphitisation, was a singly impregnated in behaviour
between
and D suggests altered
rial, graphite compared
material.
graphite
The difference
A and graphit’es C
that t,he extra impregnation
the spectrum
accommodates
impregnated
whereas graphite A
of oriented
porosity
has which
c-axis expansion. The isotropic mateB, exhibits
very different
to that of the anisotropic
behaviour
graphites;
2 4 =I
---
7
-
is assumed
to be constant,
8
13
12
14
lb
I8
BROMINATION
DATA
IRRADIATION
DATA OF MARTIN
THEORETKAL VALVES No KC’J’WDATION )
!3
et
::
in
22
1 24
olb)
FOR
? 2 ”
0.2
P
the
2
-
-.-‘-
ha,, . xp-a)
0.1. o-
2
4
CRYSTAL
it is
possible to convert the amount of absorbed bromine
-
B
less severe. Since dX,/dB
6
~
a
A in graphit’e B is much
change of the coefficient
4
Fig. 8.
’ IO
I2
IN THE
t’axa
6
STRAIN
14
16
I8
20
DIRECTION
(%
cc)
Comparison of the changes in A values obtained
from into
G
the bromination
crystal
strain
and irradiation
in the c-axis
data. cC. This
direction,
has been done in fig. 7. It will be seen that the GRAPHITE
A
A does not increase until a crystal strain
coefficient
of about 2% or more is reached;
0’
2
I
3
4
3
we had previously
assumed that A was independent
(at % m/c)
of crystal strain
up to 2% and fig. 5 clearly shows that at this value strain A should
of crystal
increase
in all cases.
In fig. 7 the crystal strain has been calculated GRAPHITE
0’
4 (at
4
3
2
I
%
8
the amount of bromine absorbed
has been made for surface adsorption
WC)
which would not contribute
from
and no allowance of bromine
to dimensional
changes
OS-
in the crystal. This effect would lead to a shift in the
0.4.
crystal strain scales in fig. 7 and an increase in the A
0.3-
GRAPHITE
w
C
0.2w
coefficient observed
at a crystal for graphite
strain in excess of 2 A. The crystal
for graphite A has been moved
O.lk 0
I
2
4
3
i (at
in fig. 8 so that the coefficient
YQ eric)
by a small amount
when
0.4.
movement
of the scale corresponds
adsorption
of about
O.JGRAPHITE
D
o.z-
0
2 BROHINE
I 0
2
4
CRYSTAL
Fig. 7.
6
8
STRAIN
Variation
Y)
I2
IN THE
_$ (at
%
m/c)
Ib
‘C’-AXIS
ia
h
k
;4(%Ec)
DIRECTION
of the coefficient
0.2 at % Br/C;
amount
of
to a physical the work
of
was physically
adsorbed
by
a very
similar type of graphite.
8, ,
Also shown in fig, 8 are the changes in A coeffi-
~NCENTR~TION. 14
The required
Maire and Mering7) also suggested that this amount of bromine
0.1
as
A starts to increase
0.5.
P
the strain is 2%.
% ,
strain scale
A with the amount of
absorbed bromine.
cient, for both directions
of cut as a function
of
observed in graphite A when it is irradiated6). There is excellent behaviour
agreement
between
and the irradiation
the bromination
behaviour
up t,o a
DIMENSIONAL
crystal
strain of 8%
there are marked
but at higher crystal
discrepancies.
CHANGES IN GRAPHITE
strains
We shall now try
to analyse why these discrepancies and dX,ldB
to be independent
and dX,/dB
of bromine
possible to determine
crystal per unit concentration at any bromine concentration. to determine
bromine
volume
of absorbed concentration
it is of the
bromine
Similarly it is possible expansion
on the
change
bromine
per unit con-
varies
with
for the extruded
the
graphites
and also for the graphite crystal. Initially
the bulk is much
porosity
per unit bromine that
of
absorbs
the
concentration
crystal
because
oriented
part of the crystal expansion.
crystal expansion
proceeds,
the bulk expansion approaches
this porosity
per unit bromine
closer to the crystal
As
closes and
concentration
value and finally
exceeds that of the crystal. This means that at large bromine the
concentrations
crystals
porosity.
in the
the anisotropic
bulk
Such an effect
material
growth
of
is generating
has previously
been ob-
OS -20
5
0
between the isotropic
and the anisotropic
graphite B
graphites. The oriented porosity
graphite
fills up much less readily
than that in the anisotropic
materials, so that even
Fig. 10.
at large pansion
---lOr
ESTIMATED
-APPARENT
CRYSTAL VOLUME
WLUME
GROWTH
GROWTH
crystal
/IkING
strains,
per unit
the
bromine
that of the bulk isotropic
crystal
IRRADIATION ‘A’ VALUES
I”
volume
from irradiation
A which have been
data are used in eq. (2)
with the bromination
expansion
growth
per unit bromine
sets of data into agreement. the percentage
volume
concentration
This is also shown in data are correct,
growth
unit bromine concentration
difficult to believe, particularly compact
0
5 BRhlNE
Fig. 9.
C:NCENTRAflON
(at
$0 Brk)
Volume growth on bromination.
data indicate
per
and is always much
larger than that of the bulk material.
(
then
of the crystal
must increase markedly
at high bromine concentrations
St,,
data
how the
of the crystal must vary in order to bring the two fig. 9 and if the irradiation
/
ex-
exceeds
material.
If values of the coefficient in conjunction
volume
concentration
for graphite A, it is possible to determine
RATES
I’ 8-
RATES
I5
Predicted change in crystallite dimensions with irradiation dose.
determined g h
IO
t Y ID”
DOSE #(Ni)
served by Bloc and HBrold2). Fig. 9 also shows a marked difference in t’he isotropic
“’
con-
expansion less than
BULK VALUES PRESENTED IN REF.4 WITH BROMINATION ,,I’ ‘A’ VALUES I’
the data in fig. 2. Fig. 9 shows
how the percentage centration
expansion
of absorbed
the bulk volume
same basis from
REF 4
-USING
are assumed
concentration,
the volume
----
exist.
Since g, and g, are known at low bromine centrations,
60
207
This is very
because t’he natural
that dX,/dB
is constant
at
least up to 6 at % Br/C. The
crystal
Reynolds4)
strains
obtained
at three irradiation
shown in fig. 10 as a function
by
Simmons
and
temperatures
are
of neutron
dose as
208
J. E. BROCKLEHURST
measured
by
nickel
activation.
Also
plotted
in
fig. 10 are t,he crystal strains which are calculated to
occur
on irradiation
determined
when
the
values
from the bromine experiments
in eq. (3). At large doses the bromination much
smaller crystal
tion
experiments,
physical
of the crystal
A
are used ob-
and lead to a
picture from a considera-
and bulk density
changes
on
irradiation. been calculated
with measurements coefficient
from irradiation
using eq. (1) in conjunction
of the linear thermal expansion
of irradiated
specimens,
that 0~~and a, are unchanged bromination
and
compatible
data
by irradiation.
irradiation
if IY, decreases
and assuming
data
can
be made
and iya increases
crystal strain in the c-axis direction
The
crystal
strain cause the pore volume
Sutton
If the following
and Howards)
that the volume
notation
observed
of cleavage
which accommodates
increases
in
to increase
of t,he crystalline
cracks
graphitising closed
solid and that this volume
formed
They during
temperatures
by a lattice
bromination
work
A
c-axis strain, was 4-6 % of that
measurements. were
in graphite
crack microporosity,
similar to the closed porosity
obtained
was
by helium
deduced cooling
that
these
down
from
and that they should be
expansion suggests,
of about by
fig. 11, that while a considerable
6%.
The
consideration amount
of
of closed
porosity is removed by a crystal strain of 6%, some cracks are not closed until the crystal strain exceeds at least 16 % . It is unlikely that these latter cracks
of ‘Y, and LYE were formed during cooling from the graphitisation present
BY
further
again.
temperature
OF PORES
16%,
with
tion: the reason for such a dependence
CLOSURE
has been closed at a
strain of about
during irradia-
is not understood. 5.3.
porosity
crystal
density
The values of A determined have
a net value of 5%
data give
strains than the values
tained from irradiation more acceptable
of
AND T. C. WEEKS
CRYSTAL
OROWTH
is used:
and it is more likely that t#hey were
in the original
coke particles.
The work
therefore indicates that there is a spectrum of crack widths
and
VA = bulk volume of the graphite specimen VC = crystal volume in the graphite specimen
formed
during the cooling
Vp = pore volume in the graphite specimen B = concentration of bromine in the gra-
temperature
Sutton
only
some
of these
and Howards)
cracks
may
be
process. have shown
range 100-700”
that in the
C.
phite specimen then AVA = AVc
AVc
AVA
Therefore
+ AVp
__
AVp
= !?&’ x ~
VAo
Vco +
VAo
~
where LY,,and (Ye are the bulk linear thermal
VA0
where VA,, and VQ, are the values of VA and Vc when the graphite
contains
no bromine.
Now the
density of graphite A was 1.74 g/cm3 and the density
ex-
pansion coefficients in the parallel and perpendicular directions
respectively,
determined
K,
and K,
are constants
by the degree of preferred
orientation
of crystals in this type of graphite is 2.263 g/cm3 “).
AVp ~~~
Therefore
=
v~~
AVIA
~
VA0
_
1.74
AVc _ 2.263 Vco
_____ -~
where AVp is the change in pore volume caused by a concentration be evaluated
of bromine B. Hence A VP/ VAN can from the bulk data in fig. 2 and the
derived crystal data. A VP/ V_Q,has been plotted for graphite
A as a function
of crystal
strain in the
c-axis direction in fig. 11, allowing a small correction for
the
mentioned
shift
in
crystal
strain
for graphite A. Initially
scale
previously
the pore volume
decreases as the crystal strain increases
and when
2 ff
Fig. 11.
-61
0
I2
8 CRYS:AL
Change
STRAIN
IN
THE'C' A%IS
lb DIRECTION
in pore volume of graphite crystallite strain.
24
20 (%
EC)
A with
DIMENSIONAL
CHANGES IN GRAPHITE
of the crystals
in the two directions
accommodation
coefficient
and y is an
c-axis direction.
Thus K, and K, can be determined
for crystal strain in the
and they are equal to the corresponding the coefficient
A when there is no accommodation, 1 dVo
values
linear
thermal
values
of
d A equal
is obtained.
to Kl (I--y)
when a crystal
bromine
of absorbed
because
up oriented porosity modated
of A are K, y and K, y respectively
no accommodation
and
strain of about
Strains in excess of 17%
cause
the crystal
which had previously
isotropic
graphite;
at crystal
17 % , the anisotropic porosity.
The
strains higher than
graphites generate additional
change
in accommodation
of manufacture
Brocklehurst13)
in this range.
has measured
the thermal
pansion of residual bromine compounds
ex-
of graphites
graphite
contained
bromine, the compound higher
volume
similar
amounts
expansion
than the com-
pound from graphite B. It was postulated was due different
to
the two
compounds
higher volume
types because
present paper indicates
graphite
suffers
forming B had
a
than graphite
A
The work described
in the
that the difference
may be
due to the fact that the compound far less accommodation
than the compound
that this
of graphite
thermal expansion
prior to bromination.
of
from graphite A had a much
thermal
from graphite A of crystal
of the graphite
strain
of graphite B when the crystal
as crystal
growth
proceeds
irradiation-induced
Future Work
can influence
of crystal
strain
is the same both
for
c-axis strains and bromination
induced strains, up to a crystal strain of about 8 % . At higher strains the bromination data
are inconsistent.
discrepancies
are
caused
irradiation-induced calculated
by
by
strains
assuming
changed by irradiation; crystal
and irradiation
It is considered the
have
that
fact been
that
the
that
the
previously
ac and a,
are un-
if they are changed at high
strains, then this could bring the two sets
of data into agreement. Further work is required to prove that the present is correct. Even so, the agreement in
the data is reasonably 6.
and it has been
this change in accommodation.
interpretation
strains are large.
as the
by the method
shown that an additional impregnation The change in accommodation
A and B. It was shown that when the compounds
accom-
graphites tend to fill up this porosity faster than the
the values of A to rise still further, thus indicating of porosity
strain fills
part of the crystal strain. The anisotropic
generation
each
bromine in
The macroscopic
crystal strain increases is influenced
of
expansion
This has made
the growth of the crystal-
lites per unit concentration
absorbed
V’p dB .
K, (1 -y) are plotted in fig. 8; it is seen that there is 17%
the
both the c and a-axis directions.
1 dVr
V’c dB
VA dB the
by
of the original graphite.
growth per at % Br/C increases with the amount of 1 dVA
and
coefficient
it possible to determine
values of
i.e. when
Initial
is determined
209
15%
good up to crystal strains of
and large irradiation
doses
present
reactor
obtain
such
tion and bromination
graphite can now be regarded as a cheap and simple
macroscopic
changes
for
are being investigated.
hoped to prove conclusively and bromination
in dimensions
growth
that irradiation
a
It is growth
can be correlated
com-
method graphites
pancies which are observed at present are caused by
structures.
that
a,
and a,
are unchanged
during
irradiation. 7.
The absorb
growth bromine
change which
suggesting
of different
graphites
has been investigated.
growth per unit concentration
when
they
The initial
of absorbed
bromine
the
behaviour
have
well
in order
to
bromination
of
irradiation-induced of
new improved
developed
graphite
Acknowledgements The authors
Conclusions
Therefore
determining
dimensional
pletely at large crystal strains and that the discreassuming
of
strains,
conditions
at
range of different graphites caused by both irradia-
The
operating
are required
This
that
paper
Managing
wish to thank Mr. B. T. Kelly this work
is published
Director,
dom Atomic
Energy
Reactor
should by
permission
Group,
Authority.
for
be performed. United
of
the
King-
310
.J. E. BRO(:KLEHII
LtS’I’ ,\?;l) ‘I’. (‘. WEEKS
References
‘) a)
W. Kiidorff, F. Bloc
and
Z. anorg. allgem. Chem. A. H&old,
245 (1941)
C. R. Acad. Sci. Paris
383 251
‘)
-1.Maire and J. Mering, Proc. 3rd (‘onf. on (‘arbon,
*)
I,. C. F. Blackman,
Buffalo
i. B. Nelson and D. P. Riley,
Proc.
Phys. Sot. (Lon-
“)
J. H. W. Simmons
and W. N. Reynolds,
Metals Monograph
No. 27 (Uranium
Institute
and
of
A. L.
Sutton
and
V. C. Howard,
J. Nucl. Mat. 7
(1962) 58
a) W. H. Martin,
B. T. Kelly
Eng. 7 (1962) 484
”
lo)
Graphite)
(1962) 75
7
(1957) 337
J. P. Mathews
and
L. C. F. Blackman,
and P. T. Nettley,
Nucl.
A. lb. I’bbr-
G. Saunders and A. R,. 1’bhelohdr.
Proc. Roy. Sot. [A] 264 (1961)
don) 57 (1945) 477
“)
Press. London)
lohdc, Proc. Roy. Sot. r-41 256 (1960) 15
(1960) 2038
3,
(Pergamon
R and DB (C) Report, 11)
19
8. H. Makin, J. Standring and P. $1. Hunter, UKAEA, TN-45
(1952)
J. H. W. Simmons,
Proc.
3rd
Buffalo
Press,
London)
(Pergamon
Conf.
on
(1957)
Carbon, p. 559
12)
W. H. Martin and F. Entwisle, J. Nucl. Mat. IO (1963) 1
13)
J. E. Brocklehurst,
Nature
194 (1962) 247
OF NUCLEAR
DIMENSIONAL
MATERIALS
9, No. 2 (1963) 197-210, NORTH-HOLLAND
CHANGES IN GRAPHITE:
BY ABSORPTION
THE RELATIONSHIP
Reactor Materials
A study
of the macroscopic
the
growth
which
occurs
absorbs bromine was made to determine
bromination-induced
BETWEEN THOSE PRODUCED
dimensional
and J. C. WEEKS*
Laboratory,
Received
graphite
CO., AMSTERDAM
OF BROMINE AND THOSE PRODUCED BY IRRADIATION
J. E. BROCKLEHURST
UKAEA,
PUBLISHING
changes
Culcheth, Warrington, Lanes.,
31 December
when
whether could
UK
1962
effect was not marked in the isotropic
material examined.
The work presents a basis for predicting,
be
tion
experiments,
the
from bromina-
irradiation-induced
dimensional
related to those which occur in graphite under fast neutron
behaviour
irradiation.
developed crystal structure. Tests can be performed cheaply
For a number
of extruded
per unit concentration
graphites
of absorbed
the initial growth
l’absorption
in the c direction
and is therefore able to close
up the oriented microporosity
which, in the initial stages of
growth, partially absorbs the crystal strain in this direction. Irradiation
growth also involves
sions of the crystallites of accommodation porosity
is important
growth behaviour. modation
graphite
sorption
of bromine
manner
which
similar
enables
from
between
the
a basis for comparing a comparison irradiation
to
work.
the bromination
made in interpreting
lites in the e and a directions levels
generation
be
in a
different made
There
with
is good
and irradiation of about 8 %
data
; above
are believed to result from an
i.e. that the thermal expansion At high
of crystal
of crystal
the irradiation
results,
coefficients
of the crystal-
are unchanged
by irradiation.
strain
there
in the anisotropic
is evidence
graphites,
macroscopique
determiner
si les changements
bromuration
pourraient
dans le graphite
of
*
Student
from
College
of Advanced
Technology,
Car-
U.K.
soumis
Pour initiale
de dimension
induits par la
& une irradiation
un nombre
de graphites
par concentration
relic au coefficient
par neutrons
directions grands
absorb6
suivant les
suivant la direction
tion du cristal suivant des cristallites
dans
absorbe partiellement cette direction.
suivant
le taux d’accomodation
la deforma-
c et le taux
suivant cette direction
macroscopique.
dans le cornOn pense que
pour un graphite don&
par la deformation
par
dans les dimen-
a une grande importance
de la croissance
de
les stades
La croissance
la direction
de la deformation,
par la ,microporositB portement
qui,
de
de cristallites
c et est done capable
orient&e
implique aussi un accroissement
d’accomodation
produit
dans les dimensions
initiaux de la croissance irradiation
est
de l’echantillon
cristalline par bromuration
la microporosite
direction
lineaire
des axes c et a. La bromuration
de graphite
sions
la croissance
de brome
initial et ceci permet d’en deduire les change-
accroissements
reduire
extrudes,
unitaire
de dilatation
ments de dimension
cristalline
est uniquesuivant
la
c.
La variation
dans le taux d’accomodation
par l’absorption
de la deforma-
orient&e est refermke
de brome fut determinee et exprimee dune
fapon qui fournit 197
de
etre relies It ceux qui se produisent
tion cristalline quand la microporosite diff,
au tours
a et& Btudiee afin de
irapides.
ment determine
but the
qui se produit
du brome par le graphite
de graphite
by
up by ab-
and expressed
up to a crystal strain in the c direction
porosity
uniquely
is closed
was determined
this level, the discrepancies assumption
macroscopic
is determined
microporosity
provides
and data
agreement
the
in the amount of accommodation
as the oriented
graphites
determining
by micro-
strain in the c direction.
The variation strain
in
and the amount
in this direction
It is believed that the amount of accom-
for a given
the crystal
an increase in the dimen-
in the c direction,
of strain
nformation.
La croissance
to be derived. Bromina-
tion causes large increases in the dimensions of the graphite crystallites
these have a well
of the original graphite
sample, and this enables the crystallite changes on bromination in the c and a axial directions
providing
on a large number of specimens and thus provide statistical
bromine is related to the
linear thermal expansion coefficient
of new graphites,
une base de comparaison
de different6
,J. E. BKO(IKLEHUKS’I’
198 graphites et permet une compsraison fournies accord pour
par les travaux entre les don&es
une deformation
atteignant
des dorm&es similaires
sur l’irradiation.
11 y a un bon
de bromuration cristalline
la direction
lichen
Stadien
teilweisc
c
environ 8 96. Au dessus de cc taux, le d&accord
Der
Betrag
des
pourrait ritsulter d’une hypothhse faite dam I’interprirtation
Richtung
clue les coefficients
Bestimmung
de dilatation thermique des cristallites suivant les directions
gleichsbetrag
c et a ne subissent
spannungen
Aux
taux
pas de variation
par l’irradiation.
6lev6s de d&formation
cristallinr.
il existe
quelque hvidence de naissance de prositt dans les graphites anisotropes, isotrope
mais l’effet n’&ait pas marquC dans le mat&au
Le travail pzrtir
presente
une base permettant
d’expkriences
dimensionnel
de
bromuration,
de prCvoir, &
le comportement
de nouveaux graphites sous l’effet de l’irradia-
Ausgleichs
durch
Die Anderung spannungen
fournir
sur un grand nombre ainsi une information
d’i?chantillons
et peuvent
Vergleich
wurden
Wachsen
L’ntersuchungen
von
Grafit
Bromabsorption len
iiber
angestellt,
verursacht
Neutronenbeschul3.
das
einmal wird
Bromination
Neutronen
und
durch
Fiir eine anzahl sorbierten
NeutronenbeschuU
pro
BeschuB
mit
unter-
schnellen
Grafiten
von Originalgrafitproben die Ableitung
Die Bromination Dimension es mcglich,
1.
ab-
zum linearen thermischen
worden.
in Richtung
ist dns
Konzentrationseinheit
Ausdehnungskoeffizienten Dies ermiiglicht
gesetzt’
der Kristallitver-
der c- und a-Achse bei Bromination.
verursacht
ein erhebliches
von Grafitkristalliten die orientierte
Wachsen
in c-Richtung.
Mikroporositlt
der
Daher ist
in den anfiing-
Introduction dimensional
changes which occur when graphite absorbs bromine was performed
to determine
if these dimensional
verandert Bei
dieser Effekt erkennbar
Bromine
enters the graphite lattice by diffusion between the 83 wt %
of
temperature,
Riidorffl) bromine
has
shown
can be taken
from
an atmosphere
bhe vapour ; X-ray
measurements
that
about
up, at room saturated
with
have indicated
t’hat the resultant material, C,Br, has a homogeneous structure of one bromine layer for every two carbon layers.
The
c-spacing’)
absorption
of bromine
of the graphite
fiir in
dieser
Grenze tratcn
auf: sie werden erklbrt durch eine Snnahme.
increases
latbice and Bloc
der Bestrahlungsergebnisse
Betrggen
ge-
auf die Vcr-
der Kristallspannungen Grafiten
konnte dagegen in isotropem
gemacht
das
bestrahlungsinduzierte Grafite
vorher
Arbeit
st,ellt
Dimensionswechselverhaltcn
abzuschltzen.
Vorausgesetzt,
Kristallstruktur
rine statistische
da0
besitzen. Solche
Versnche kiinnen ohne besonderen Kostenaufwand grol3en Zahl von Proben durchgefiihrt
an einer
werden. und ergeben
Information.
have
macroscopic
ist eine
offenkundig;
dar, urn aus Brominationsexperimenten
diese eine gut entwickelte
that it also produces
shown
dimensional
that the absorption slight contraction
thermal
nicht
Material nicht
werden. Die vorliegende
Grundlage
neuer
der
bei NeutronenbeschuB
in anisotropen
eine
Poisson’s
planes.
und den Daten
fiir Kristallspannungen
werden.
graphite layer
festgestellt;
bis etwa 8%. Oberhalb
hohen
lattice
by fast neutrons.
such den Seutronen-
mutung, da13die thermischen 3usdehnungskoeffizienten
changes could be related to those which occur when is irradiated
durch
Es wurde gute ivbereinstim-
Bromination
Kristallite in c + a-Richtungen
&?old2)
The present study of the macroscopic
die
macht wurde; diese bezieht sich insbesondere
es durch
der Versuch
von StranggepreRten
Broms in Beziehung
inderung
der
Sic ermiiglicht
Daten,
wurden.
zwischen
Porositltsbildung
Wachstum
bildet.
lhnlichen
wenn
abzuleiten.
anfhngliche
Mikroporosi-
wurde in einer Form beatimmt,
die f iir die Interpretation
nommen, eine Beziehung zwischen dem Dimensionswechsel durch
fiir die Kristall-
makroskopische
wird und einmal durch schnel-
Dabei
als glrichbleihrnd
des A4usgleichsbetrags
Grafitsorten mit
Diskrepanzen Es
dir
und erfaBt, welche die Grundlage fiir den Vergleich unterschiedlicher
c-Richtung
statistiques.
fiir
Der Aus-
Grafit fiir dir Kristall-
wird dabei
durch SchlieBen der orientierten
murlg
quement
ist wichtig
bestimmt.
beschul3 gewonnen
Cconomi-
auf.
in dieser
Wachstums.
fiir einen gegebenen
sir.
nb-
in c-Kichtung
Spannungen
die MikroporositLt
d8veloppCe.
btre entrepris
ron
in c-Richtung
indcm
Richtung
tritt ehenfalls ein An-
des makroskopischen
tion pourvu que ceux-ci aient une structure cristalline bien Des essais peuvent
in dieser
der Kristallite
t&t infolge Bromabsorption
exami&.
zu verringcrn.
Bei Hestrahlungswachst,um
wachxen der Dimensionen
des rksultat,s, d’irradiation,
B savoir
des Wachstums
die Kristallspannungcn
sorbi&.
et d’irradiation
suivant
AKill ‘I’. (‘. WEEKS
of bromine
ratio
effect
expansion
layer
of the graphite
plane
buckling
or a
similar to t’hat observed
measurements
Changes in graphite
crystallite
occur due to the displacement neutron irradiation,
may give rise to a
in the a-spacing
due t,o either
large
changes. It is also possible
in
on graphite3). dimensions
also
of atoms under fast
resulting in an increase in the
c-axis direction and a decrease in the a-axis direction (cf. Simmons
and Reynolds4) ).
Sutton and Howard5)
t’he
mal expansion
and
of the crystallites
have shown that the ther-
of bulk graphite because
part
is less than t’hat of the c-spacing
DIMENSIONAL
thermal expansion is absorbed
by porosity
CHANGES
which is
oriented parallel to the layer planes. Simmons Reynolds4)
have
irradiation
growth
shown
that
the
and
macroscopic
and bulk thermal expansion
of
graphite
are closely related and that the oriented
porosity
is closed
by crystallite
growth
perpendi-
cular to the layer planes ; this closure of oriented porosity
causes
the
the layer
planes,
distribution
geneous
complex
bromination,
C,,Br,
and addition
due to irradiation
desorption,
layer, thus forming collapse
is controlled porosity.
by
The
the
closure
absorption
of
oriented- micro-
of bromine
by graphite
also causes large changes in the crystallite
dimen-
sions in the c-axis direction.
Therefore, if the stress
distribution
due to absorption
bromine
in the matrix
is similar
irradiation
growth
observation bromine
to that
and thermal
of the dimensional
absorption porosity.
it possible
occurs
expansion, graphites
should
in the influence of the
Such observations
to predict
then
how
should make
such graphites
fore, for a number of graphites, the large dimensional sorption
we have compared
changes produced
by the ab-
of bromine with their thermal expansions.
In the case of Pile Grade ‘A’ material, used as a moderator this country,
we have also compared
sional changes with those produced
in
these dimenby irradiation.
ward diffusion
Previous Work on Absorption of Bromine The limiting composition
obtained
when graphite
is exposed to bromine vapour is determined perfection
of
the
original
graphite
Bromine will not form lamellar complexes graphitised shown
by the
may
be removed
defect
sites without
On
paths blocked, an
sorption,
observed7),
initial
but it appears
with out-
bromine physically
effect
is
that the quantities
adsorption
of
adsorbed are relatively small for
well graphitised
materials and this is supported
the observations
of Riidorffi)
by
and Blackman et aLs),
who have shown that powdering
has little effect on
the limiting capacity of large well ordered specimens. X-ray
dat,al) for C,Br give a dimensional
in the c-axis direction ported
by
bromine
of 55%.
pyknometric
determinations
and microscopic
perfect crystals in the direction absorption
and desorption
measured changes
in liquid
measurements
Changes in bulk dimensions
on near
of the c-axis. of graphite
of bromine
to be greater
expansion interpreted
of artificial
volume
graphite
than the crystal
were
volume
by factors between 1.4 and 2.2. This was as being due to the generation
sity when bromine was absorbed;
accommodates
of poro-
this is the reverse
effect to that observed
the c-axis
during
have been
by Bloc and HBrold2). Apparent on specimens
change
This value is sup-
irradiation47 5), where it is postulated
have
complete
or at defects in the
with non-
materials and Maire and Mering’)
a,ny
at room tempera-
structure.
that as the degree of order in the crystal
from
structure.
observed 2.
any one layer is filled
of the layer. Desorption
graphite
currently
in nuclear power stations
on
It is
ture leaves a residual bromine content; the bromine
would
change dimensions when they are irradiated. There-
structures
of a cycle.
may be held by normal lamellar bonding
of
during
changes caused by
in different
provide valuable information oriented
which
portions
that inter-
layers are opened up, and on
bromine
is a unique function of the crystal strain in the c-axis expansion
have different
suggesteds) that on sorption, before neighbouring
direction;
this means that the thermal
further
by Maire and Mering7) and also by
compositions
of graphite
on
et ala). They have indicated
Blackman mediate
of linear
whereupon
Hysteresis effects have been observed on sorption and desorption
removal
et aL6) have
an
up to the homo-
C,Br layers start to form.
to
Martin
lattice by forming
of layers
to
proceeds.
expansion
enters the graphite
expansion
thermal
shown that the change of the coefficient thermal
bromine irregular
growth, perpendicular
bulk
increase as the crystallite
199
IN GRAPHlTE
in thermal
expansion
and
that porosity
and is closed by crystal growth
in
direction.
structure is increased, the bromine pressure required to establish a given composition limiting
uptake
increases
decreases and the
towards
the saturation
3.
Experimental Graphite
specimens,
nominally
7.6 x 0.6 cm dia,
from a calibrated
quartz spring, of
value C,Br. These studies were supported
by X-ray
were suspended
measurements
sorption,
sensitivity 200 mg/cm, in a glass vacuum apparatus_
and
showed
that
on
200
J. E. BROCKLEHURST
Bromine bulb
vapour
was admitted
containing
the liquid
and the specimen followed
surrounding
by removing the
specimen,
of air over
the
-1.2. MAIN
t’emperature,
length and weight changes were
with a cathetometer.
were obtained current
at intervals from a
at room
Desorption
curves
the bromine
vapour
either
by
specimen
passing
or by
a
partial
evacuation.
A?u’D T. (‘. \VEEKS PROCRAMME
Since the dimensional
changes
tion, the main investigation
were taken in both directions
of cut
in fig. I.
was limit,e:l t,o a study
of the lower port,ion of the growth curves. At least one sorption
and desorption
on one specimen
in each
respect, to the direction
Specimens
shown
are much greater than t’hose observed under irradia-
from
cycle was determined direction
of extrusion
all the graphites
examined.
of cut’, wibh or pressing,
The results are
from of range of artificial extruded graphites made
shown in fig. 2. Two
from
were taken for graphite A and the results were found
petroleum
Four types
coke
and coal tar pitch
of reactor
grade graphite,
A, B, C, D, with different expansion,
artificial
t,o be in close agreement.
cimen of this graphite was cycled three times and
Pressed natural com-
the results are shown in fig. 3. In general, the sorp-
graphite
‘B’
A perpendicular
cut, spe-
tion curves show an increasing growth per unit con-
graphites
represent
reactor grade materials graphitised peratures,
in each direction
of thermal
pact was also investigated. The
specimens
designated
coefficients
were investigated.
binder.
being
a range
of
at similar tem-
nearly
60’
isotropic.
Graphite ‘A’ is the Pile Grade ‘A’ material currently used in British Nuclear Power Stations. The natural compact,
which
has a high
oriented,
should
give a good
crystal
density
indication
50
of single
t
behaviour.
Thermal expansion specimens
over
the
measurements
were made on
A
range
temperature-
9
room
700” C in a silica dilatometerlO)
4.
and is well
before bromination.
“4 40 $
I
Results w
A summary
of the measurements
is given
in
2
measurements,
shown
z 2 z F Y E
development
of the
table 1 and figs. 1, 2 and 3. 4.1.
PRELIMINARY MEASUREMENTS
Preliminary
bromination
in fig. 1, were made
during
ERPENDICULAR
apparatus to determine the magnitude of the dimensional
changes.
were obtained parallel
to
In
particular,
interesting
for a natural compact
pressing.
A
linear
results
specimen
relation
cut
between
growth and uptake of bromine was obtained for this specimen, large transverse cracks eventually
opened
up and the specimen
after a
dimensional
finally
disintegrated
change of 61% at 8 at % Br/C. It was
observed
that
an increase
occurred
in the natural
geneous composition
L! BROMINE
in the linear gradient
compact
C,,Br
0
near the homo-
(6.25 at % Br/C).
Fig. 1.
CONCENTRATION
Preliminary measurements of the growth of graphite caused by absorption of bromine.
201
DIMENSIONAL CHANGES IN GRAPHITE TABLE 1 Results of main programme
Graphite
Direction of out with respect to extrusion or pressing direction
Density g/em3
j
Parallel Perpendicular
1.74
A
Initial growth per unit con- i- Mean linear thermal cent&ion of absorbed bromine e:xpansion coefficient (loo-7000 C) (% length change per at % x 1oa/v Br in C)
Number of Specimens
2
!
2
0.22 0.55
1.89 3.65
B
1.70
Parallel Perpendicular
1 1
0.51 0.60
3.54 4.24
C
1.73
Parallel Perpendicular
1 1
0.33 0.80
2.47 5.16
D
1.80
Parallel Perpendicular
1 1
0.25 0.61
1.98 3.93
Natural Compact
2.08
Parallel Perpendicular
1 1
4.9 0.44
22.0 2.24
centration absorbed
of absorbed bromine
A pronounced cases
with
bromine
as the amount
of
hysteresis effect was observed in all linear
desorption
curves,
as
of the desorption
point
reached
bromine composition. previous The
observed by Bloc and HBrold2). Fig. 3 shows that the gradient
maximum
on sorption,
curves is dependent
on
after
This effect is consistent
compositions
of the
GRAPHITE
B
residual
are approximately
C
GRAPHITE
PERPENDICULAR A
PERPENDIC”LA$
PERPENDICULAR.
/
/
RRPEN.C”LAR/{
A
3-
BROMINE
Fig. 2.
CONCENTRATION
‘(at
with
observations73 *).
desorption
GRAPHITE
GRAPHITE A (MEAN OF 2)
i
hence
there is no unique value of length change for a given
increases.
nearly
the
L
%
m/C
)
’
Growth of different graphites caused by absorption of bromine.
compounds the same for
D
all t,he ext,ruded graphites, but the natural compact
be virt,ually independent
residual
approximately
compound
has a lower bromine
than those of the extruded
graphites.
content
The residual
strains appear t,o be roughly dependent
on oriema-
t’ion.
three desorptions levels.
Fig. 3 shows that the second and third sorption by t’he previous cycle but the
residual point,, for graphite
‘A’ at least, appears t,o
from increasingly
ItI t)herefore appears
manent
curves are influenced
of previous
treatment
i\S
t,he same point, is reached cvcn after
distortion
higher
that, very
of the lattice
strain
little per-
was taking placao
in t,his case, but’ this was not true for t,hc nat,ural compact
where the length
recovery
was poor on
desorption. Nat’ural
compact
specimens
placed
in a t’ube
cont,aining bromine vapour finally disintegrated shown
GRAPHITE A (PERPENDICULAR)
in fig. 4. Extruded
specimens
graphite did not break up after prolonged to the vapour
although
as
of artificial exposure
a fine crack pat,tern was
observed.
5.
Discussion of Results
6.1. CORRELATION WITH THERMAL EXPANSION From a consideration a graphite
matrix,
of the stress distribution
Simmonsll)
in
has shown that the
linear coefficient of thermal expansion of a graphit’e specimen is given by a =Ax,+(l-AA)&,
(1)
where a, a.nd iy, are the thermal
expansion
coeffi-
cients of the crystal lattice and A is a characteristic of t’he method of preparation the specimen. pansion
Thermal
of the
and direction of cut of
expansion
crystallites
Similarly pansion
of the crystallites absorption
of the
in the a-axis direction.
of bromine
crystallites
2
J
4
CONCENTRATION
the a-axis direction
5 (at
%
Ed
Fig. 3. The effect of cycles of absorption and desorption of bromine on the bulk dimensions of graphite A.
Fig. 4.
Poisson’s bution
involves
perpendicular
layer planes and a contraction BROMINE
an exto the
below 380” C, a
layer planes and, at temperatures contraction
involves
perpendicular
an exto the
term may arise in
from layer plane buckling or a
ratio effect’. Therefore, if the stress distri-
in the graphite
matrix
strain resulting from absorption
caused
by crystal
of bromine
is the
The effect of prolonged exposure to bromine vapour on a perpendicular cut natural compact specimens.
203
DIMENSIONAL CHANGES IN GRAPHITE same
as that
resulting
from
the
obtained
during thermal expansion,
graphite
when it absorbs bromine
crystal
that is G = (dL/dB)/L
strain
the growth
of
should be given
bY
where
B = atomic rat,io Br/C.
It is then assumed that g, is very small and can be neglected ; this assumption
G=Ag,+
(1-A)g,
(2)
where g, and ga are the crystal and a-axis
directions
centration
of absorbed
scopic
strain
strains, in the c
respectively,
per unit
con-
bromine and G is the macro-
per unit
concentration
of absorbed
bromine. Sutton and Howards)
have shown that crystallite
growth in the c-axis direction closes oriented microporosity;
this results in the material being less able
to accommodate quent
further c-axis strain and a conse-
increase
produced
in the coefficient
during
bromination
large and is expected porosity
A. The growth is
comparatively
to close the oriented
and therefore
micro-
the value
of A.
Eqs. (1) and (2) must therefore be compared
in the
range of crystal
increase
growth
given
of bromine,
will be justified
of A can be determined
using the measurements
percentage
by
from
lat’er. eq. (1)
of bulk thermal expansion
in table 1 and the appropriate
and LYEgiven
Nelson
values of LYE
and Riley3).
Then
the
value of A L/L, for 2 % crystal strain is
given by 2A from eq. (2). Thus G,, t’he value of G at’ low crystal strain, is obtained the data in fig. 5 to determine this value of A L/L,,
by extrapolating the value of G at
i.e. corresponding
to a crystal
strain of 2 % . G0 was determined in two directions corresponding
in this way for each graphite
of cut and plotted
against
values of a, the coefficient
t,hermal expansion
the
of linear
measured over the range 100 to
I.Or
strains where the strains due to
thermal expansion are comparable by absorption
The value
PERPENDICULAR
with those caused
and this means that the
per unit concentration
of bromine
where
AL/L,, --f 0 should be used. The coefficient A should then have a value which may be determined eq. (1) using thermal
expansion
and g, at low bromine calculated using eq. (2). Unfortunately, accurately
concentrations to
be
determine
G
g
0.8/
3
--f 0; also when the bromine
is small a substantial
bromine may be physically
fraction
PARALLEL
of the
during thermal expansion
strains up to 2%
to 2% caused by absorption and it is assumed
D
for
and it seems reasonable
PRESSED NATURAL COMPACT PERPENDICULAR
therefore to assume the same for crystal strains up of G has been determined
GRAPHITE
Martin and
Entwisle12) habe shown that the coefficient A is not crystal
C
this bromine would not
to crystal strains. However,
changed significantly
GRAPHITE
adsorbed on the surfaces
of the pores in the graphite; contribute
can
/-PERPENDICULAR
it is difficult
when AL/L,
concentration
from
data, and then ge
of bromine. The value
at a crysta,l strain of 2%
that this value
applies
at all
strains less than 2 % . Fig. 5 shows the variation of G, the growth of the different graphites per unit concentration as a function
of AL/L,,.
of bromine STRAIN (%
G is expressed as the per-
centage strain per unit atomic ratio Br/C x 100.
Fig. 5.
Al /Lo)
Variation of G with macroscopic strain.
J. E. BROCKLEHCRST
204
700” C. The results are shown in fig. 6. The mean values of ac and cyaover this temperature range are 28
x
1O-s and zero respectively+). Thus from eq. (l),
zero. The difference is not completely understood.
and eq. (2) can be written in the form 28
xa 1o-6
(Se-gal +
It is seen from the insert in fig. 6 that the natural compact data do not agree with the data obtained for the extruded graphites. In particular, the value of gc for natural compact is 6.4, and ga is nearer
A = (u/(28 x 10-6)
Go =
Ah’D T. C. WEEKS
However, the extruded graphites are all manufactured from similar materials and are graphitised
Sa
Therefore if the analysisis correct, the plot of G,, gc - Sa 28 x 10-s and intercept equal to ga when a is zero. Fig. 6 shows that G,, for the extruded graphites is a linear function of a, and a negative intercept on the G, axis is observed indicating a very small contraction in the a-axis direction. Therefore, the previous assumption involving the neglect of ga to determine the bulk strain for a crystal strain of 2 % is justified. Values of g, and ga have been deduced from the best straight line drawn through the points in fig. 6. These are: against a should be linear with gradient
gc = 4.8 + 0.2 % per at % Br/C and ga = - 0.10 -& 0.02 % per at % Br/C
at similar temperatures, thus the crystallite sizes in the extruded graphites will be very similar. On the other hand, the crystallite size in the natural compact is much larger than that in the extruded graphites. Therefore, if gc and ga are functions of crystallite size the difference in behaviour could be explained. Blackman et aLs) have suggested that any one layer in the graphite lattice is filled before neighbouring layers are opened up. If this is the case and gc is defined as 1 dX, SC= x, dB where Xc is the crystallite dimension in the c-axis direction, then dX,/dB should be a constant independent of the amount of bromine absorbed. Taking
O.B-
Y
r &
LD
0.7.
& 4
EXTRUDED
A
GRAPHITE5
8
a x
C
a
D
A
PRESSED
4’
cp
IO o( “IO‘
15
20
5 ,,:N
Fig. 6.
Correlation
LINEAR
of thermal
EXPANSION
expansion
and growth
o((100
caused
-7:OV)
X IO6
by absorption
of bromine.
25
6
DIMENSIONAL CHANGES IN GRAPHITE
205
the initial value of gc as 4.8% per at % Br/C, the crystal strain for a composition of C,Br is 60%)
tures. Martin et al.‘) have used these data to show that at irradiation temperatures between 150” C
which compares reasonably well with Riidorff’sl) X-ray measurement of 55%. The relation between
and 250” C, A, is a unique function of E,, the crystal strain in the c-axis direction. The same
growth and amount of absorbed bromine observed in fig. 1 for the natural compact supports the hypo-
,relation may apply at higher irradiation tempera-
thesis that dX,/dB is constant at least up to a composition of C,,Br. On the other hand, if the
mental data. Martin et aL6) point out that the crystal strain in the a-axis direction becomes a
initial value of gc = 6.4 appropriate to the natural compact is used then the crystal strain at CsBr
irradiation temperature is raised; this may cause
is 80% ; this is much higher than Riidorff’s value and makes no allowance for the observation made in fig. 1 that in the natural compact dX,/dB appears to increase when the composition has reached C,,Br. If such an increase does take place, this will further increase the discrepancies between the interpretation of the bulk measurements and the X-ray measurements on the C,Br compound. Further work is required to resolve these anomalies, but it is thought that the large growth of the natural compact is due to generation of additional porosity. 5.2. CORRELATION WITH IRRADIATION-INDUCED DIMENSIONAL CHANGES Simmons and Reynolds*) have related the bulk linear thermal expansion coefficients and irradiation induced growth rates of different graphites to the thermal expansion coefficients and irradiationinduced growth rates of graphite crystals perpendicular and parallel to the layer planes in the following equation 1 dX, 1 dl, -- =&X,m+ 1, dD
(1 -A”)$d$
a
(3)
1 dl, where i d-D = growth per unit irradiation dose of z the graphite aggregate in direction 5, 1 dX, = growth per unit irradiation dose of X, dD each crystal in the c-axis direction,
1 dX,
= growth per unit irradiation X, dD of each crystal in the a-axis direction,
dose
and A,, the value of A in direction x, is determined from eq. (1). They have used this equation to determine the crystal strains, AX,/X, and 0X,/X,, at different irradiation doses and different tempera-
tures but as yet this is not justified by experi-
larger fraction of that in the c-axis direction as the the relation obtained by Martin et aL6) to break down when X, AX,/X, AX, ceases to be small. However, at low irradiation temperatures the data show that A, is a unique function of E, and is unaffected by crystal strain in the a-axis direction. A, changes under irradiation because the crystal growth in the c-axis direction fills up the oriented porosity observed by Sutton and Howards) and this reduces the amount of accommodation that can be provided for any further crystal growth which takes place. It can be postulated therefore that the change in A, due to absorption of bromine should give the same relation between change in A, and crystal strain as that observed due to irradiation, provided that the stress distribution developed in the graphite matrix is similar in both cases. Since it has already been shown that both irradiation and bromination growth are closely related to thermal expansion ,for small crystal strains, the stress distribution must be similar in all three cases at least when the crystal strains are small. Also, since the crystal shrinkage in the a-axis direction during irradiation does not appear to influence the variation of A, with E,, the much smaller a-axis shrinkage observed during bromination should also have little effect on A,. The variation of A with the amount of bromine absorbed is shown in fig. 7 for the two directions of cut for each of the extruded graphites. The coefficient A was determined by using eq. (2) with the experimental data in fig. 2 and the values of ge and ga obtained at low strain for the extruded graphites, assuming that dX,/dB and dX,ldB are constant and are independent of the amount of bromine which has been absorbed. Fig. 7 shows that in the anisotropic graphites A, C and D, the variations of A with bromine concentration are
206
J. E. I~RO(‘KLEHUKS’I’
similar
except
that
A increases
more
graphite A, up to a bromine concentration
AND ‘I’. (‘. \vEEI+
steeply
in
of 3 at, ?b
Br/C, t,han it does in graphites C and D. Graphites A, C and D were made from t,he same raw materials but graphites
C und D were twice
with pitch before graphitisation, was a singly impregnated in behaviour
between
and D suggests altered
rial, graphite compared
material.
graphite
The difference
A and graphit’es C
that t,he extra impregnation
the spectrum
accommodates
impregnated
whereas graphite A
of oriented
porosity
has which
c-axis expansion. The isotropic mateB, exhibits
very different
to that of the anisotropic
behaviour
graphites;
2 4 =I
---
7
-
is assumed
to be constant,
8
13
12
14
lb
I8
BROMINATION
DATA
IRRADIATION
DATA OF MARTIN
THEORETKAL VALVES No KC’J’WDATION )
!3
et
::
in
22
1 24
olb)
FOR
? 2 ”
0.2
P
the
2
-
-.-‘-
ha,, . xp-a)
0.1. o-
2
4
CRYSTAL
it is
possible to convert the amount of absorbed bromine
-
B
less severe. Since dX,/dB
6
~
a
A in graphit’e B is much
change of the coefficient
4
Fig. 8.
’ IO
I2
IN THE
t’axa
6
STRAIN
14
16
I8
20
DIRECTION
(%
cc)
Comparison of the changes in A values obtained
from into
G
the bromination
crystal
strain
and irradiation
in the c-axis
data. cC. This
direction,
has been done in fig. 7. It will be seen that the GRAPHITE
A
A does not increase until a crystal strain
coefficient
of about 2% or more is reached;
0’
2
I
3
4
3
we had previously
assumed that A was independent
(at % m/c)
of crystal strain
up to 2% and fig. 5 clearly shows that at this value strain A should
of crystal
increase
in all cases.
In fig. 7 the crystal strain has been calculated GRAPHITE
0’
4 (at
4
3
2
I
%
8
the amount of bromine absorbed
has been made for surface adsorption
WC)
which would not contribute
from
and no allowance of bromine
to dimensional
changes
OS-
in the crystal. This effect would lead to a shift in the
0.4.
crystal strain scales in fig. 7 and an increase in the A
0.3-
GRAPHITE
w
C
0.2w
coefficient observed
at a crystal for graphite
strain in excess of 2 A. The crystal
for graphite A has been moved
O.lk 0
I
2
4
3
i (at
in fig. 8 so that the coefficient
YQ eric)
by a small amount
when
0.4.
movement
of the scale corresponds
adsorption
of about
O.JGRAPHITE
D
o.z-
0
2 BROHINE
I 0
2
4
CRYSTAL
Fig. 7.
6
8
STRAIN
Variation
Y)
I2
IN THE
_$ (at
%
m/c)
Ib
‘C’-AXIS
ia
h
k
;4(%Ec)
DIRECTION
of the coefficient
0.2 at % Br/C;
amount
of
to a physical the work
of
was physically
adsorbed
by
a very
similar type of graphite.
8, ,
Also shown in fig, 8 are the changes in A coeffi-
~NCENTR~TION. 14
The required
Maire and Mering7) also suggested that this amount of bromine
0.1
as
A starts to increase
0.5.
P
the strain is 2%.
% ,
strain scale
A with the amount of
absorbed bromine.
cient, for both directions
of cut as a function
of
observed in graphite A when it is irradiated6). There is excellent behaviour
agreement
between
and the irradiation
the bromination
behaviour
up t,o a
DIMENSIONAL
crystal
strain of 8%
there are marked
but at higher crystal
discrepancies.
CHANGES IN GRAPHITE
strains
We shall now try
to analyse why these discrepancies and dX,ldB
to be independent
and dX,/dB
of bromine
possible to determine
crystal per unit concentration at any bromine concentration. to determine
bromine
volume
of absorbed concentration
it is of the
bromine
Similarly it is possible expansion
on the
change
bromine
per unit con-
varies
with
for the extruded
the
graphites
and also for the graphite crystal. Initially
the bulk is much
porosity
per unit bromine that
of
absorbs
the
concentration
crystal
because
oriented
part of the crystal expansion.
crystal expansion
proceeds,
the bulk expansion approaches
this porosity
per unit bromine
closer to the crystal
As
closes and
concentration
value and finally
exceeds that of the crystal. This means that at large bromine the
concentrations
crystals
porosity.
in the
the anisotropic
bulk
Such an effect
material
growth
of
is generating
has previously
been ob-
OS -20
5
0
between the isotropic
and the anisotropic
graphite B
graphites. The oriented porosity
graphite
fills up much less readily
than that in the anisotropic
materials, so that even
Fig. 10.
at large pansion
---lOr
ESTIMATED
-APPARENT
CRYSTAL VOLUME
WLUME
GROWTH
GROWTH
crystal
/IkING
strains,
per unit
the
bromine
that of the bulk isotropic
crystal
IRRADIATION ‘A’ VALUES
I”
volume
from irradiation
A which have been
data are used in eq. (2)
with the bromination
expansion
growth
per unit bromine
sets of data into agreement. the percentage
volume
concentration
This is also shown in data are correct,
growth
unit bromine concentration
difficult to believe, particularly compact
0
5 BRhlNE
Fig. 9.
C:NCENTRAflON
(at
$0 Brk)
Volume growth on bromination.
data indicate
per
and is always much
larger than that of the bulk material.
(
then
of the crystal
must increase markedly
at high bromine concentrations
St,,
data
how the
of the crystal must vary in order to bring the two fig. 9 and if the irradiation
/
ex-
exceeds
material.
If values of the coefficient in conjunction
volume
concentration
for graphite A, it is possible to determine
RATES
I’ 8-
RATES
I5
Predicted change in crystallite dimensions with irradiation dose.
determined g h
IO
t Y ID”
DOSE #(Ni)
served by Bloc and HBrold2). Fig. 9 also shows a marked difference in t’he isotropic
“’
con-
expansion less than
BULK VALUES PRESENTED IN REF.4 WITH BROMINATION ,,I’ ‘A’ VALUES I’
the data in fig. 2. Fig. 9 shows
how the percentage centration
expansion
of absorbed
the bulk volume
same basis from
REF 4
-USING
are assumed
concentration,
the volume
----
exist.
Since g, and g, are known at low bromine centrations,
60
207
This is very
because t’he natural
that dX,/dB
is constant
at
least up to 6 at % Br/C. The
crystal
Reynolds4)
strains
obtained
at three irradiation
shown in fig. 10 as a function
by
Simmons
and
temperatures
are
of neutron
dose as
208
J. E. BROCKLEHURST
measured
by
nickel
activation.
Also
plotted
in
fig. 10 are t,he crystal strains which are calculated to
occur
on irradiation
determined
when
the
values
from the bromine experiments
in eq. (3). At large doses the bromination much
smaller crystal
tion
experiments,
physical
of the crystal
A
are used ob-
and lead to a
picture from a considera-
and bulk density
changes
on
irradiation. been calculated
with measurements coefficient
from irradiation
using eq. (1) in conjunction
of the linear thermal expansion
of irradiated
specimens,
that 0~~and a, are unchanged bromination
and
compatible
data
by irradiation.
irradiation
if IY, decreases
and assuming
data
can
be made
and iya increases
crystal strain in the c-axis direction
The
crystal
strain cause the pore volume
Sutton
If the following
and Howards)
that the volume
notation
observed
of cleavage
which accommodates
increases
in
to increase
of t,he crystalline
cracks
graphitising closed
solid and that this volume
formed
They during
temperatures
by a lattice
bromination
work
A
c-axis strain, was 4-6 % of that
measurements. were
in graphite
crack microporosity,
similar to the closed porosity
obtained
was
by helium
deduced cooling
that
these
down
from
and that they should be
expansion suggests,
of about by
fig. 11, that while a considerable
6%.
The
consideration amount
of
of closed
porosity is removed by a crystal strain of 6%, some cracks are not closed until the crystal strain exceeds at least 16 % . It is unlikely that these latter cracks
of ‘Y, and LYE were formed during cooling from the graphitisation present
BY
further
again.
temperature
OF PORES
16%,
with
tion: the reason for such a dependence
CLOSURE
has been closed at a
strain of about
during irradia-
is not understood. 5.3.
porosity
crystal
density
The values of A determined have
a net value of 5%
data give
strains than the values
tained from irradiation more acceptable
of
AND T. C. WEEKS
CRYSTAL
OROWTH
is used:
and it is more likely that t#hey were
in the original
coke particles.
The work
therefore indicates that there is a spectrum of crack widths
and
VA = bulk volume of the graphite specimen VC = crystal volume in the graphite specimen
formed
during the cooling
Vp = pore volume in the graphite specimen B = concentration of bromine in the gra-
temperature
Sutton
only
some
of these
and Howards)
cracks
may
be
process. have shown
range 100-700”
that in the
C.
phite specimen then AVA = AVc
AVc
AVA
Therefore
+ AVp
__
AVp
= !?&’ x ~
VAo
Vco +
VAo
~
where LY,,and (Ye are the bulk linear thermal
VA0
where VA,, and VQ, are the values of VA and Vc when the graphite
contains
no bromine.
Now the
density of graphite A was 1.74 g/cm3 and the density
ex-
pansion coefficients in the parallel and perpendicular directions
respectively,
determined
K,
and K,
are constants
by the degree of preferred
orientation
of crystals in this type of graphite is 2.263 g/cm3 “).
AVp ~~~
Therefore
=
v~~
AVIA
~
VA0
_
1.74
AVc _ 2.263 Vco
_____ -~
where AVp is the change in pore volume caused by a concentration be evaluated
of bromine B. Hence A VP/ VAN can from the bulk data in fig. 2 and the
derived crystal data. A VP/ V_Q,has been plotted for graphite
A as a function
of crystal
strain in the
c-axis direction in fig. 11, allowing a small correction for
the
mentioned
shift
in
crystal
strain
for graphite A. Initially
scale
previously
the pore volume
decreases as the crystal strain increases
and when
2 ff
Fig. 11.
-61
0
I2
8 CRYS:AL
Change
STRAIN
IN
THE'C' A%IS
lb DIRECTION
in pore volume of graphite crystallite strain.
24
20 (%
EC)
A with
DIMENSIONAL
CHANGES IN GRAPHITE
of the crystals
in the two directions
accommodation
coefficient
and y is an
c-axis direction.
Thus K, and K, can be determined
for crystal strain in the
and they are equal to the corresponding the coefficient
A when there is no accommodation, 1 dVo
values
linear
thermal
values
of
d A equal
is obtained.
to Kl (I--y)
when a crystal
bromine
of absorbed
because
up oriented porosity modated
of A are K, y and K, y respectively
no accommodation
and
strain of about
Strains in excess of 17%
cause
the crystal
which had previously
isotropic
graphite;
at crystal
17 % , the anisotropic porosity.
The
strains higher than
graphites generate additional
change
in accommodation
of manufacture
Brocklehurst13)
in this range.
has measured
the thermal
pansion of residual bromine compounds
ex-
of graphites
graphite
contained
bromine, the compound higher
volume
similar
amounts
expansion
than the com-
pound from graphite B. It was postulated was due different
to
the two
compounds
higher volume
types because
present paper indicates
graphite
suffers
forming B had
a
than graphite
A
The work described
in the
that the difference
may be
due to the fact that the compound far less accommodation
than the compound
that this
of graphite
thermal expansion
prior to bromination.
of
from graphite A had a much
thermal
from graphite A of crystal
of the graphite
strain
of graphite B when the crystal
as crystal
growth
proceeds
irradiation-induced
Future Work
can influence
of crystal
strain
is the same both
for
c-axis strains and bromination
induced strains, up to a crystal strain of about 8 % . At higher strains the bromination data
are inconsistent.
discrepancies
are
caused
irradiation-induced calculated
by
by
strains
assuming
changed by irradiation; crystal
and irradiation
It is considered the
have
that
fact been
that
the
that
the
previously
ac and a,
are un-
if they are changed at high
strains, then this could bring the two sets
of data into agreement. Further work is required to prove that the present is correct. Even so, the agreement in
the data is reasonably 6.
and it has been
this change in accommodation.
interpretation
strains are large.
as the
by the method
shown that an additional impregnation The change in accommodation
A and B. It was shown that when the compounds
accom-
graphites tend to fill up this porosity faster than the
the values of A to rise still further, thus indicating of porosity
strain fills
part of the crystal strain. The anisotropic
generation
each
bromine in
The macroscopic
crystal strain increases is influenced
of
expansion
This has made
the growth of the crystal-
lites per unit concentration
absorbed
V’p dB .
K, (1 -y) are plotted in fig. 8; it is seen that there is 17%
the
both the c and a-axis directions.
1 dVr
V’c dB
VA dB the
by
of the original graphite.
growth per at % Br/C increases with the amount of 1 dVA
and
coefficient
it possible to determine
values of
i.e. when
Initial
is determined
209
15%
good up to crystal strains of
and large irradiation
doses
present
reactor
obtain
such
tion and bromination
graphite can now be regarded as a cheap and simple
macroscopic
changes
for
are being investigated.
hoped to prove conclusively and bromination
in dimensions
growth
that irradiation
a
It is growth
can be correlated
com-
method graphites
pancies which are observed at present are caused by
structures.
that
a,
and a,
are unchanged
during
irradiation. 7.
The absorb
growth bromine
change which
suggesting
of different
graphites
has been investigated.
growth per unit concentration
when
they
The initial
of absorbed
bromine
the
behaviour
have
well
in order
to
bromination
of
irradiation-induced of
new improved
developed
graphite
Acknowledgements The authors
Conclusions
Therefore
determining
dimensional
pletely at large crystal strains and that the discreassuming
of
strains,
conditions
at
range of different graphites caused by both irradia-
The
operating
are required
This
that
paper
Managing
wish to thank Mr. B. T. Kelly this work
is published
Director,
dom Atomic
Energy
Reactor
should by
permission
Group,
Authority.
for
be performed. United
of
the
King-
310
.J. E. BRO(:KLEHII
LtS’I’ ,\?;l) ‘I’. (‘. WEEKS
References
‘) a)
W. Kiidorff, F. Bloc
and
Z. anorg. allgem. Chem. A. H&old,
245 (1941)
C. R. Acad. Sci. Paris
383 251
‘)
-1.Maire and J. Mering, Proc. 3rd (‘onf. on (‘arbon,
*)
I,. C. F. Blackman,
Buffalo
i. B. Nelson and D. P. Riley,
Proc.
Phys. Sot. (Lon-
“)
J. H. W. Simmons
and W. N. Reynolds,
Metals Monograph
No. 27 (Uranium
Institute
and
of
A. L.
Sutton
and
V. C. Howard,
J. Nucl. Mat. 7
(1962) 58
a) W. H. Martin,
B. T. Kelly
Eng. 7 (1962) 484
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lo)
Graphite)
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and
L. C. F. Blackman,
and P. T. Nettley,
Nucl.
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G. Saunders and A. R,. 1’bhelohdr.
Proc. Roy. Sot. [A] 264 (1961)
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“)
Press. London)
lohdc, Proc. Roy. Sot. r-41 256 (1960) 15
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8. H. Makin, J. Standring and P. $1. Hunter, UKAEA, TN-45
(1952)
J. H. W. Simmons,
Proc.
3rd
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Press,
London)
(Pergamon
Conf.
on
(1957)
Carbon, p. 559
12)
W. H. Martin and F. Entwisle, J. Nucl. Mat. IO (1963) 1
13)
J. E. Brocklehurst,
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194 (1962) 247