The dihedral angles of uranium inclusions in hypo-stoichiometric uranium carbide

JOURNAL

OF NUCLEAR

27

MATERIALS

THE DIHEDRAL

(1068)

80-87.

0 NORTH-HOLLAND

ANGLES OF URANIUM

HODKIN,

Metallurgy Division,

UKAEA,

Energy

Received

Measurements by

inclusions

hypo-stoichiometric

uranium

in the temperature

distribution wide

in the

curves

range medians

the annealing

samples

inclusion

dihedral

of the inclusion temperature

temperature

carbide

suggesting

than one characteristic The

boundaries

range of 850-1550

of the

of angles,

grain

dependence

show a marked

is exceeded;

there

from

850 “C to

10” at

by

56” at

a much

plotted

as the melting

linear followed

there

slower

de recsit,

an-

show

is an

des inclusions

a

but

against

at

lindaire

entre

contour

des inclusions

des

carbure

d’uranium

r&li&es

pour ces Bchantillons

de temp&atures distribution large plus

kchantillon.

1.

stoechiom&rique,

angulaire, dihedre

Les

mbdianes

ce qui suggere des angles

courbes

montrent

caract&istique

depuis

qu’il

to

de 56” & 850 “C

la temp&ature

jusqu’a

de 1550 “C.

die Winkel an

metrischem

den

850

Dies

Darstellung

ist ein

zeigt

de

Temperaturabhlingigkeit,

un

der

Einschliisse

erfolgt

von

niihernd aber

des

Introduction

eine

“C

ftir

der wenn

eine

mehr

Die breite

als einen

in jeder

Probe.

Winkel

gegen

deutliche

iiberschritten

Die Proben gegliiht.

zeigen

Hinweis

Mittelwerte

Gliihtemperatur

y a

Winkel

Uranein-

unterstiiichio-

werden.

1550

Fliichenwinkel

der

die von von

gebildet und

dieser

charakteristischen

6th

gemessen,

Korngrenzen

Urankarbid

zwischen

Streuung.

de

de chaque

au niveau

l’angle

plus lente mais allant en s’acc&rant

Es wurden

recuits dans le domaine

des inclusions

angle

ont

de fusion

il y a une chute approxi-

10” pour

schliissen

d’uranium

d’&hantillon

de 850 ;2 1550 “C. Les

des angles

intervalle qu’un

sous

grains

en fonction

la temp&ature

beaucoup

wurden

d’angle

au

de la temp&ature marquee

--

1100 “C fall

England

26” B 1100 “C, chute suivie d’une diminution

Verteilungskurven dispo&es

quand

in

1550 “C.

Des mesures

en fonction

of the

accelerating

Be&s.,

une variation

est d&pas&e;

mativement jusqu’lt

approximately

26”,

repartees montrent

de la temphrature,

is more

change

Harwell,

1968

inclusions,

of

“C. The

point

Establishment,

20 February

angle in each sample. angles

inclusions fall

angles

that

and D. M. POOLE

Research

have been made of the angles assumed

uranium

nealed

CARBIDE

M. NICHOLAS

Atomic

CO., AMSTERDAM

INCLUSIONS IN HYPO-STOICHIOMETRIC

URANIUM E. N.

PUBLISHING

linderung

der wird

Die die dor

Schmelzpunkt

; die Abnahme

56” bei 850 ‘C auf 26” bei

1100 “C an-

linear und auf 10” bei 1550 “C nicht so stark,

zunehmend

steiler.

hypostoichiometric uranium carbide samples annealed at temperatures ranging from 850” to 1550 “C. Apart from their use in the determination of the surface energy of uranium carbide, these results have a direct practical significance since it is important whether uranium inclusions in possibly hypostoichiometric uranium carbide reactor fuels will be distributed as discrete globules or a continuous grain boundary network. An estimate of this can be made from knowledge of the dihedral angle, 4, at the appropriate temperature.

The determination of the surface tension of solid arc-cast. uranium carbide which is being undertaken in this laboratory requires knowledge of the ratio, ~&ss, of the uraniumcarbide uranium interfacial energy, ys~, and the uranium carbide grain-boundary energy, yss. These energies are related by the expression yss= 2~s~ cos 44 where + is the dihedral angle assumed by uranium inclusiohs in the grain boundaries of hypostoichiometric uranium carbide. The present paper describes experimental work in which measurements were made of the geometry of uranium inclusions present in

2.

Experimental Specimens

80

1

techniques cm in dia. and 0.3 cm thick

THE

were cut from uranium

DIHEDRAL

an arc-cast

carbide

ingot

ANGLES

hypostoichiometric

produced

at

AERE

OF

URANIUM

81

INCLUSIONS

angles involve three dimensions and the measurements were made on a two-dimensional

plane.

vacuum of 10-G Torr. Specimens to be annealed

Harker and Parker’s 1) analysis enables cumulative plots of inclusion angles measured on a two dimensional plane to be interpreted in

at below 1200 “C were sealed in silica capsules with sufficient argon to produce a pressure of

terms of the true dihedral angle, provided there is no preselection of the angles chosen for

Q atm at the selected

measurement

(C=4.59wt %,O=O.O3wt %andN=O.OZwt%) and were degassed at 1600 “C for 30 min in a

Immediately

mens were degassed selected

annealing

a vacuum

annealing

temperature.

prior to encapsulation

the speci-

again by heating

temperature

to the

for 30 min in

of 10-S Torr. A different

procedure

was used with specimens to be annealed at above 1100 “C. These were placed in a vacuum furnace and degassed for 30 min in a vacuum of 10-G Torr at the selected annealing temperature. The temperature was then reduced to 1100 “C before the furnace was filled with 8 atm of argon and its temperature was then raised again to that selected for the annealing treatment. The argon employed was purified by passing through a molecular sieve and zirconiumtitanium alloy swarf heated to 850 “C. The annealing treatments were continued for 84 days at 1100 “C and below, 28 days at 1150” and 1200 “C and 7 days at 1260 “C and above. These times had been found by prior experimentation to be more than sufficient for equilibrium - as defined by constancy of inclusion geometry -to be attained. After the annealing treatment, at least 0.05 cm was removed from the top surfaces of the specimens by grinding on silicon carbide paper under “Hyprez” fluid. The planes revealed were prepared for metallographic examination by grinding on pads impregnated with diamond dust down to the 0.25 micron grade, using “Hyprez” fluid as a lubricant. The samples were etched in 1 : 1 : 1 HNOs : CHaCOOH : Hz0 to reveal the uranium and photographs were taken of random areas magnified on a Vickers M 55 metallograph to 250 to 1000 times, depending on the grain and inclusion size. The angles assumed by 250 randomly selected inclusions were measured from the photographs taken of each specimen. These were not dihedral angles but “inclusion angles” since dihedral

and there is only

one dihedral

angle in the sample. Riegger and Van Vlack 2) demonstrated

that the median of 25 inclusion

angles was a good approximation angle

as

defined

by

Harker

to the dihedral and

Parker’s

analysis. As will be shown later, the range of inclusion angles observed in the hypostoichiometric carbide samples was wider than would be expected on the basis of Harker and Parker’s analysis. It was decided, therefore, to use the median of a sample of 250 rather than 25 measurements to define the inclusion angle characteristics of the samples. Some samples contained inclusions that appeared to have penetrated an appreciable distance aTong the grain boundaries to link up with other inclusions. These were considered to have zero inclusion angles if the grain boundary penetration was more than four times the width of the inclusion. 3.

Experimental

results

Metallographic examination showed the samples to contain three types of inclusion ; (a) those within the grains; (b) those at the junction of three, or occasionally more, grain boundaries; and (c) those in grain boundaries at locations remote from junctions. Examples of each type of inclusion are present in the micrograph shown in fig. 1. The inclusions in samples anneaIed at 1100 “C and below were single-phase while those in samples annealed at temperatures of 1200 “C and above were two-phase (fig. 2), Angular measurements were made for type (b) and (c) inclusions only as the objective of the programme was t’o determine the &yss ratio. The cumulative plots of these measurements, presented in fig. 3, have certain common characteristics. The distributions are approximately sigmoidal and resemble Harker and

82

Fig. 1. Micrograph showing various t>yes of inelusions present in a hype-stoichiomotric uranium

Fig. 2. Micrograph showing the two-phase structure within a uranium inclusion in a hypo-stoichiometric

carbide

uranium

sample

annealed

for

X4 days

at

1050

“C!.

carbide

sample

x 400

amlealed

1200 “C.

for

28 days

at

x 400

Parker distributions at high but not at low cumulative percentages. Many of the experi-

ture was increased. The range of inclusion angles lying between the 25 and 75 cumulative

mental

percentiles

distributions

centages

of zero

percentage

contained angle

increasing

appreciable

inclusions

per-

(fig. 4), the

as the annealing

tempera-

Parker’s

84 DAYS

.i

analysis.

to the

of Harker

These differences

suggest

_*.’

04 DAYS 95oOc

tip

50” as opposed

on the basis

P

84 DAYS 9ooOc

850°C

50-

30” to

.u-

.a-” 75 -

was

5” to 20” expected

.f /

.I ,d ,f

..

/

25-

.’

04 DAYS 1000°C

./

f

.r’ d

.-e

*.*- _-,

___a--,.e--

,*----

e-rl

.d f

f f .f ,d

84 DAYS

28 DAYS

I 100°C

l150°C

,d

r’

25

__--

.*

r’

S102

rr /

CAPSULE

28 DAYS I I5OOC

4

/

VACUUM

FURNACE

I

75r 50 i 25 s i

f _______e-*. /o--

75 -

,r

28 DAYS 1200° c

bf

7 DAYS 126O’C 8’

/

1

I

20

40

I

I

I

60

00 INCLUSION

#

7 DAYS 136O’C

f’

20

ANGLE,

60

7 DAYS 146O’C

I

I

I

I

80

20

40

I

1

40

,’

I

60

DEGREES

7 DAYS r5so”c

50- / ,

Fig. 3.

The inclusior L atngle distributions

of samples

annealed

at various

temperatures.

I

80

and that

THE DIHEDRAL

ANGLES

ANNEALING

Fig. 4.

TEMPERATURE,

INCLUSIONS

83

*C

Percentage of mxnium inclusions with zero angles plotted as a function of the sample annealing temperature.

the specimens contained more than one dihedral angle. Stickels and Hucke 3) examined the effect of small variations in yss and ys~ on the distribution of inclusion angles but their analysis did not include the effect of the presence of zero dihedral angles. Because of the lack of a theoretical analysis, it was assumed arbitrarily that the ‘
OF URANIUM

Discussion

The first and most important point requiring discussion is whether the experimental results are meaningful. While there can be little doubt that the median values of the inclusion angles characterise the metallography of the samples it is uncertain whether they are valid as measurements of the dihedral angle. It was suggested in the previous section that the differences between Harker and Parker’s theoretical distribution and the experimental distributions of inclusion angles were due to the

presence of more than one dihedral angle in the samples ; this cannot be proven but the experimental results provide support for the suggestion. Thus the percentage ofzero inclusion angles observed in samples annealed at 1050 “C and above (fig. 4), is too great to be accounted for by the fortuitous intersection of the observational plane and the grain edges and too small to be due to a unique 0’ dihedral angle. An idea of the effect of a range of dihedral angles on the distribution of inclusion angles can be gained by summing the Harker and Parker distributions for the individual angles assumed to be present. Such calculations have been made for samples containing dihedral angles ranging from 0’ to 75” 4) and the results are summarised in table 1. The presence of more than one dihedral markedly increases the range of inclusion angles as was also found by Stiokels and Hucke, but, providing the dihedral angle mixture is fairly homogeneous and does not contain more than 40% zero angles, the mean of the dihedral angle mixture is close to the median inclusion angle. If the mixtures contained no zero angles the mean dihedral

54

E.

N.

HODKIN

ET

AL.

L

900

I100

1300

ANNEALING

Fig.

5.

The

medians

of the

angles

TEMPERATURE,

assumed

by

uranium

annealing

I500

1700

‘C

inclusions

plotted

as a function

of the sample

temperature.

TABLE

1

Mean

Median

dihedral

inclusion

angle

angle

(deg)

(deg)

30

29.1

.

30

27.5

19

. . . . . . . . . . . . . . . .

30

27.5

26

30

26

28

30

22

30.5

45

43.9

12.2

7. Three dihedral angles, 30, 45 and 60” occurring with frequencies of 1 : 2 : 1 . . . . . . . . . . . . .

45

43

22.5

8. Three dihedral angles, 15, 45 and 75” occurring with frequencies of 1 : 2 : 1 . . . . . . . . . . . .

45

42.8

41

9. Three dihedral angles with equal frequency

Sample

1.

One dihedral

2.

Three dihedral frequencies

3. Three

angle,

of 1

dihedral

:2 :1

angles,

equal frequency 4. Three

dihedral

frequencies 5. Two

frequency 6.

angles,

of 2

dihedral

One dihedral

30”

angles,

:

1 :2

. . . . . . . . . . . .

15, 30 and 45” occurring .

.

.

.

.

.

.

.

.

.

15, 30 and 45’ occurring 15, 30 and 45” occurring

.

.

the

25 and 75 percentiles of the cumulative 8.6

with with

with equal

. . . . . . _ . . . . . . . . . . . angle of 45” . . . . . . . . . . .

of 30, 45 and

of inclusion

with

. . . . . . . . . . . . .

angles 15 and 45” occurring

Range

angles between

60” occurring

. . . . . . . . . . . . .

45

42.2

27.5

angles of 15, 30, 45, 60 and 75” 10. Five dihedral occurring with frequencies of 1 : 1 : 4 : 1 : 1 . . .

45

43.5

29

11. Five dihedral angles of 15, 30, 45, 60 and 75” occurring with equal frequency . . . . . . . . .

45

41.8

41

plot

THE

DIHEDRAL

ANGLES

TABLE

OF

85

INCLUSIONS

I (Cont’d)

Sample

12. Four dihedral angles of 15, 30, 60 and 75” occurring with equal frequency ............. 13. Two dihedral angles, 0 and 15” occurring with frequencies of (a) 1:l ................... (b)l:l+. .................. (c) 1:2 ................... (d)l:4 ................... (e) 1:8 ................... (f) 0:l ................... 14. Two dihedral angles, 0 and 30” occurring with frequencies of (a) 1:l ................... (b)l:l+. .................. (c) 1:2 ................... (d)l:4 ................... (e) 1:s ................... (f) 0:l ................... 15. Two dihedral angles, 0 and 45’ occurring with frequencies of (a)l:l ................... (b)l:li ................... (c) 1:2 ................... (d)l:4 ................... (e) 1:8 ................... (f) 0:l ................... 16. Two dihedral angles, 0 and 60” occurring with frequencies of (a) 1:l ................... (b)l:lg. .................. (c)1:2 ................... (d)l:4 ................... (e) 1:s ................... (f) 0:l ................... 17. Six dihedral angles, 0, 15, 30, 45, 60, 75” occurring with equal frequency .............

angle is about 10% more than the median inclusion angle, but if the mixture does contain an appreciable proportion, lo- 40%, of zero angles, then the mean dihedral angle is about 10% less than the median inclusion angle. Thus in order to obtain a better characterisation of the dihedral angles of samples annealed at 1050 “C and below, the effective dihedral angles should be increased by about 10% and those

URANIUM

Mean dihedral angle (de&

Median inclusion angle (de&

Range of inclusion angles between the 25 and 75 percentiles of the cumulative plot

45

35

46

7.5 9 10 12 13.3 15

0 9.7 11.2 12.5 13.5 14.1

14.2 15.4 15.9 10.7 8.2 4.8

15 18 20 24 26.7 30

0 19.8 23.1 26.5 28 29.1

28.5 29.8 30.5 21 12.8 8.6

22.5 27 30 36 40 45

0 30.5 36 40.5 42 43.9

43.8 45.1 46.2 28.5 18.7 12.2

30 36 40 48 53.5 60

0 42 48.7 55 58.6 59

59 60.8 61.5 36.1 22.3 17.1

37.4

31.5

45.5

of samples annealed at higher temperatures reduced by a similar amount. The reason for measuring dihedral angles in the present work was to gain knowledge of the y&ss ratio of the uranium carbide-uranium system. The ratios derived from the median inclusion angles of samples annealed at different temperatures are plotted in fig. 6. It has been argued that the samples contained more than

86

E.

N.

HODKIN

ET

AL.

0.58 -

\e

o’56y \ l

l

Jul. s”,I

0.54

l l

0.52\

I

I

900’

z-e

I

1100 ANNEALING

Fig. 6.

_

a

0

I

I

I

1300 TEMPERATURE,

I

I

I500

I 1700

‘C

The ratio ~SL/~SS plotted as a function of the sample annealing temperature.

one dihedral angle and, therefore, the ratios are merely averages. Furthermore, since the median inclusion angles probably differ from the mean dihedral angle by about lo%, the true average ratios will differ somewhat from the values plotted in the figure. This difference does not have a proportional effect on the ratio, however, since this is equal to the inverse of 2 cos &$ where q5is the average dihedral angle. With 4 equal to 60”, the difference is about, 4%, but with $ equal to 30” or less the difference is smaller than 1%. The ratios plotted in fig. 6, therefore, can be regarded as good approximations to the true ratios. There are two notable features about the shape of the plot of ysdyss against the annealing temperature, shown in fig. 6. First, the plot shows a marked change in slope at about 1100 “C, the temperature dependance of the ratio below 1100 “C being much larger than that above. This change is presumably due to the melting of the metallic inclusions, since a change in the phase structure of the inclusions at temperatures above 1100 “C was noted (compare figs. 1 and 2). While the melting point of pure uranium is 1130 “C, an eutectic at

0.06 wt y. carbon and 1117 “C has been reportde by Guinet, Vaugoyeau and Blum 5) and a peritectic at 0.078 wt y. carbon and 1137 “C by Althaus, Cook and Bicker 6). In view of the uncertainty in the literature, speculation as to the exact temperature at which the slope changes is unwarranted. The second notable feature about fig. 6 is the absence of a discontinuity in the y ratio at the temperature at which the slope changes. A discontinuity was expected because it was thought that a change in YSL would occur as the annealing temperature was raised above the inclusion melting temperature, the change being of a similar magnitude to the change in the surface tension of uranium. Reliable values for the surface tension of uranium are not yet, available, but it is probable that a decrease of 10 - 20% will occur on melting. The reason for the discrepancy is unknown and no explanation can be offered at present. Extrapolation of the data in fig. 6 indicates that the ys~/yss ratio will be 0.50 at 16501700 “C. At any temperature above 1700 “C? therefore, the uranium carbide grains will be completely surrounded by a liquid network and

THE

the mechanical

DIHEDRAL

properties

ANGLES

OF

of the material will

be poor. While intergranular

cohesion

cease because

force is required

an appreciable

will not

to separate two solids joined by a liquid film, it would be unwise to use hypostoichiometric uranium carbide as structural temperature

reactors

account

the

information

inclusion

angle characteristics.

elements in high

without now

taking available

into on

Acknowledgements The authors would like to express their thanks to Professor M. B. Waldron of the University of Surrey and former Physical Metallurgy Group Leader at AERE for his interest in this work and to Dr. W. J. M. Salter of the United

URANIUM

Steel

INCLUSIONS

Companies

Laboratories,

87

Research

and

Rotherham,

Yorks,

Development for

helpful

discussions.

References l) D. Harker and E. Parker, Trans. ASM 34 (1945) 156 ‘) 0. K. Riegger and L. H. van Vlack, Trans. Met. Sot. AIME

218 (1960)

934

3, C. A. Stickels and E. E. Hucke, Trans. Met. Sot. AIME

230 (1964)

4, E. N. Hodkin, AERE

Rept.

795

M.

Nicholas

R-5582

5, P. Guinet, H. Vaugoyeau Acad.

Sci. 261 (1965)

6) W. A. Althaus, National NLCO-968

Lead (1966)

H.

and

D.

M.

Poole,

(1967) and P. L. Blum,

C.R.

1312

M. Cook and R.

Company,

Ohio,

J. Bicker,

U.S.A.

Rept.