Properties of vacancies in uranium carbide

JOURNAL

OF NUCLEAR

32 (1969)

MATERIALS

PROPERTIES

Department,

SCHULE Solid

and P.

From measurements

of changes in electrical

of uranium

due to quenching

a vacancy

formation

determined shown

energy

in uranium

and U-vacancies

occurs very

of carbon and uranium, a formation migration

energy

Furthermore temperature

range and

carbon

assumed

in

by a single t,he higher

sublattice.

to

mechanism

partir

range des

The

mesures

by

attribuees

de

sous-reseau

Aus Messungen

range

trischen

vacancy

d’uranium

et d’uranium

du carbone

et de l’uranium

r&ist,ivite

energie

dues a des traitements

plus

&levees

sent supposes

des temperatures

von

Btudiees sur la

des spezifischen Urankarbid

wurde

und eine

eine

Es

ist

Untergittern

Ab-

Bildungsenergie von

wahrscheinlich,

fur 1.46 _1:

dass

in

der C- end U-Leerstellen

vor fur

elek-

durch

Aktivierungsenergie

die Wanderung

sich geht.

fur Uranleerstellen

Weiterhin stoffatome

qui sont

Die

Bildungs-

wird zu 1.4 his 1.7 eV, die ihre

Wanderung

karm geschlossen bei

Einzelleerstellen

que

stellen

des lacunes

untersuchmn

les

stellen

a 6th Bvaluee

Temperaturen und iiber

zu

werden, unter

2.2 eV

dass Kohlen1400 “C

1400 “C uber

im Kohlenstoffteilgitter

Uranat,omen

uber

Doppelleer-

diffundieren.

Von den

wird angenommen, dass sie im gesamten Temperaturbereich uber Einzelleer-

im Uranteilgitter

diffundieren.

Introduction

In a two component metal alloy the diffusion of interstitials and vacancies often causes a geometrical rearrangement of the atoms such that A and B atoms may exchange sites. Uranium carbide crystallizes in a NaCl-structure and has a preponderant metallic behaviour, but it is not yet established whether U- and C-atoms are able to exchange sites easily or *

individuelles,

geschiitzt.

d’activa-

Pour

des lacunes

von Kohlenstoffleerstellen

Aktivierungsenergie

une energie

respectivement. de formation

de

temperature

de lacunes indiriduelles

Gluhen

bestimmt.

in ihren

la migration

que dans lo domaine

der Anderung

1.0 & 0.1 eV

0.3 eV

a lieu dans les sous-reseaus

l’energie

und

Urankarbid

11 est suggere

de

Widerstandes

die Wandertmg

in the entire

de

de migra-

de I’uranium. -____

of

von

de 1,45 & 0,3 oV, energies

lacunes d’uranium,

lower

is

variations

d’activat’ion

(< 1400 “C) les atomes de

le long

domaine

suivant’ un mecanisme

of U-atoms single

on a conclu

plus basses

diffuser sur tout l’intervalle

schrecken

on a determine

de carbone

le

in

sublattice

aux lacunes de carbone.

dans le carbure

1.

a

part, diffusent

dans

mechanism

de 1,0 & 0,l eV et une energie

tion de migration

a

diffusion

temperature

Italy

reseau du carbone. Les atomes d’uranium

and

rate

(6’a),

( > 1400 “C) par le chemin de bi-lacunes dans lo sous-

investigated. ____

et de recuit,

de formation

the

vacancy

diffusion

Blectrique du carbure d’uranium de trempe

in

diffusion

determined

in the uranium

temperature A

be

that

(< 1400 “C) the diffusion

( > 1400 “C) by a divacancy the

1.7 eV

carbone et

of 2.2 eV are estimated.

is concluded

is determined

mechanism

For U-vacancies

1.4 and

Ispra

1968

D’autre

It is

respectively.

Euratom,

temperatures

of C-

in the sublattices

energy

it

the migration

likely

between

activation

to C-vacancies.

carbide

*

t)ion a 2,2 eV.

1.0 5 0.1 eV and a

which are attributed

that

carbon

of

CCR

CO., AMSTERDAM

CARBIDE

entre 1,4 et 1,7 eV, et l’energie

and annealing,

activation energy of 1.45 + 0.3 eV were

migration

SPINDLER

3 September

resistivit,y

PUBLISHING

IN URANIUM

State Division,

Received

carbide

0 NORTH-HOLLAND

OF VACANCIES W.

Chemistry

20-29.

Now:

Metals

and Ceramics

Division,

Oak Ridge

whether they migrate only in their respective sublattices. The diffusion of carbon and uranium atoms in uranium carbide has been measured at several temperatures in poly- and monocrystalline materials. Some of the results appear to be well established even though there is no complete agreement among them. National 20

Laborat.ory,

Oak Ridge,

Tennessee,

U.S.A.

PROPERTIES A key for the identification mechanisms of

IN URANIUM

of the diffusion

is the knowledge

of the properties

Griffiths I)

succeeded

vacancies.

quenching

OF VACANCIES

has

in

uranium carbide, hut the formation

21

CARBIDE 35 mm

I

t

A

B

and migration energies of vacancies he determined appear to be not completely selfconsistent. 2. 2.1.

c

Experimental

I

Q

D

details Fig.

SPECIMENS

Two series of samples of uranium carbide produced by NUKEM, West Germany, were investigated. One series had a carbon content of 4.78 wt o/o with the impurities Hz = 6.9 ppm, 02 = 403 ppm, Nz= 309 ppm, and the second series had a carbon content of 4.83 wt o/o with

1.

Dimensions

of the samples.

the voltage drop between the “dog-ears” C and D was measured with a Diesselhorst potentiometer with an accuracy of 0.1%. The measuring current was 3 A with an accuracy of 0.05%. Slight irreproducibility of the position of the samples in the specimen holder did not result in different values of the electrical resistance.

impurities Ha= 35.6 ppm, Nz= 40 ppm, 02 = 1622 ppm. The electrical resistivity of the two materials measured at liquid nitrogen temperature was about 6.05 and 4.20$2cm, respectively. For our measurements the uranium carbide specimens were cut with an electro-erosion machine from polycrystalline cast material.* Fig. 1 shows the final shape of the samples. Before the measurements each specimen was subjected to a 5 h anneal under high vacuum (p< 10-5 Torr) at about 1970 “C and was then cooled slowly to room temperature in order to improve the resistance to cracking of the material. Only a slight decrease of the carbon

having had contact with the open air. Nevertheless, a thin black oxide surface layer could

content

not be avoided,

( < 0.1 wt o/o C) was found as a result

2.3.

QUENCHING TECHNIQUES

were annealed prior to The specimens quenching within a quartz-tube in a horizontal furnace in a purified helium atmosphere. After an annealing time of 40 min, the tube with the sample was drawn out of the furnace, quickly opened, tilted, and inserted into a metal dewar filled with liquid nitrogen. The specimen thus fell into the liquid, without

of this annealing. But no change of the carbon content during the subsequent quenching and annealing experiments (up to 1074 “C) could be ascertained.

grinding

2.2.

3.

RESISTIVITY MEASUREMENT

All resistivity measurements were carried out with the sample submerged in liquid nitrogen. A teflon frame with brass leads served as specimen holder. A constant current was sent through the specimen from A to B (fig. 1) and * We gratefully acknowledge the efforts of R. Lucas and C. Landes, Metallurgy Division, C.C.R. Euratom,

Ispra,

in preparing

the samples.

and had to be removed

to improve

the

electrical

by

contacts.

The subsequent anneals were made in a vacuum of 10-S Torr, during which no apparent oxidation occurred. Experimental

results

The experimental results obtained did not vary with the lengths of pre-anneals of the material. Most experiments were made with the material which had an electrical resistivity of 6.05 &%m at liquid nitrogen temperature. The experimental results so far obtained on the second material which had an electrical resistivity of 4.20 $2cm at liquid nitrogen temperature and which carbon content was a little

22

W.

higher

than in the other

different. the

material,

For one set of specimen

quenched

resistivity

SCHiiLE

AND

P.

SPINDLER

were not

(6.05 $&rn)

was determined

be-

tween 600 “C and 1074 “C. For every quenching temperature three resistivity measurements were performed. The specimen was annealed at 1000 “C and slowly cooled to room temperature. After this treatment the resistivity was measured at liquid nitrogen temperature and gave the value ea. For the second measurement the specimen was quenched from the quenching temperature Tq. The resistivity value obtained at liquid nitrogen temperature was called es. The quenched specimen was isochronally annealed up to 1000 “C and measured at the standard liquid nitrogen temperature. The value after this treatment was denominated et. In all experiments ea was equal to et and the “quenched-in resistivity” could be determined from (es -es) and (es -et). fig. 2 the logarithm of the percent resis-

ANNEALING

TEMPERATURE

IN “C

Fig. 3. Recovery of electrical resistivity after quenching from 1040 “C (~0=6.05

,uQ cm; 30 min anneal at

each temperature).

tivity change is plotted versus the reciprocal quenching temperature (“K-1). Between 600 and 800 “C the points fit a straight line. From this straight line a formation energy of 1.0 & 0.1 eV was determined. At higher quenching temperatures the data do not fit the extrapolation of the straight line observed between 600 and 800

“C.

Fig.

I OJl 7

I

8 RECIPROCAL

Fig.

2.

Logarithm

I

9

I

I

10

11

TEMPERATURE

12

IN 10Llo_K

of quenched-in

reciprocal quenching temperature

1

resistivity versus

measured at liquid

nitrogen temperature (Q= 6.0 @km). Open circles represent the quenched-in resistivity, fnll circles give the amount of the recovered resistivity after annealing at 1000 “C.

one

of three

experimental determinations of the electrical resistance of a UC specimen from 1040 “C due to annealing at temperatures (isochronal annealing).

3 shows

the results

of

change of quenched increasing The speci-

men was kept for 30 min at each annealing temperature. From the diagram it is seen that the extra resistivity begins to decrease rapidly at about 200 “C. Between 300 and 400 “C the biggest resistance change is observed and at about 600 “C the total amount of resistance obtained by quenching is recovered. It has to be mentioned that in many isochronal and isothermal annealing curves, before recovery starts; a slight increase of the electrical resistivity was observed, amounting to about 0.5% of the total resistivity increase. This is not shown in the figure. In fig. 4 the change of the electrical resistivity

PROPERTIES

OF VACANCIES

IN

URANIUM

third temperature annealing

23

CARBIDE

increase to Tr,= 371 “C the

times were 35, 60 and 80 min.

The activation

energy

the electrical resistivity

for the recovery

can be determined from

the slopes of the curves in the points the temperature I

of the isothermal

changed (slope-change-method).

I

I

where

annealing is

From the data

of fig. 4 two values for the activation were obtained,

of

energy

the average being 1.45 eV, with

an accuracy of about rt 0.3 eV. The quenching rate can be evaluated

from

fig. 5. Between 800 and 500 “C it is approximately 250 deg/sec. The quenched specimen was cooled to room temperature in about 9.5 sec. 4. 4.1.

Discussion FORMATION

ENERGY OF VACANCIES

The plot of the logarithm of the quenched-m versus the reciprocal absolute resistivity quenching temperature (fig. 2) is typical for metals so that fig. 2 may be compared, for with the results of Bauerle and example,

40

60

I

I

120

160

Annealing

Fig. 4.

I

200

time

240

280

PO

360

(min)

Isothermal change of electrical resistivity (~0=4.20 &km).

is plotted against annealing time for a specimen quenched from 808 “C. After the evaluation of the quenched-in resistivity the specimen was first annealed

at the temperature

TI= 301 “C

for 20, 50, 90 and 120 min. The annealing temperature was raised to Tz= 345 “C and the specimen was annealed in further steps of 20, 40, 60, 80, 100, 140 and 160 min. After the

Koehler 2) on gold.* We assume from the straight line (fig. 2) obtained at the lower quenching temperatures (800 to 600 “C) that for this range all vacancies which are in thermodynamic equilibrium at the quenching temperature are frozen in by the quenching process. With increasing quenching temperatures some vacancies are assumed to annihilate during quenching, giving rise to * This extra-resistivity in gold was found to belong to quenched-in vacancies. In the following we want to carry over the reasoning for the case of gold to our experimental results.

t (sec) Fig. 5.

Change of temperature of a UC specimen quenched from 800 “C in liquid nitrogen.

24

W. SCHiiLE

AND P. SPINDLER

values of the electrical resistivity below the extrapolation of the straight line. The concentration

of

vacancies

in

equilibrium

at

the

temperature T is given by the following relation :

energy and

is known.

Qs of

two

The activation energies &I systems undergoing similar

processes are proportional to the temperatures at which the process rate has its highest value if the two materials

c=co exp (-&F/JCT),

(1)

where : co= entropy

assumed

With this relation we obtain for the temperature range from 800 to 600 “C (fig. 2) a formation energy of vacancies of QP= 1.0 & 0.1 eV. Since the quenching rates obtained for uranium carbide (fig. 5) are about a factor 10 to 80 lower than in gold 2, + the migration activation energy of vacancies in uranium carbide has to be much higher than in gold to quench-in all vacancies in thermodynamic equilibrium up to a quenching temperature * of 800 “C. ACTIVATION ENERGY POR MIGRATIONOF VACANCIES For the determination of the migration energy of vacancies several procedures can be used. Unfortunately the “slope change method” is not a very accurate one but in many cases most reliable from the physical point of view. With this method a value of 1.45 f 0.3 eV (fig. 4) was obtained. Another method for estimating this energy is based on a comparison of the isochronal annealing behaviour with another recovery process for which the activation + For the quenching carbide

no thin

wires

experiments

or foils

rather thick plates were available. conductivity that

of UC is about

on

as in gold

uranium but

Moreover

a factor

only

the heat

20 smaller

than

of gold.

* This with energy

further

gold of

[Cl.98 eV

may

comparison be justified

vacancies in gold 2)] and therefore

of our quenching because

the

results

formation

is also nearly 1.0 the concentration

eV of

vacancies in thermodynamic equilibrium are (nearly) equal in gold and UC for the same temperatures.

are treated similarly of defects

The concentration thing from similar

constant ;

Qr = formation energy of vacancies ; k = Boltzmann constant ; T = absolute temperature.

4.2,

the concentrations

of vacancies temperatures

to be comparable

and

are comparable. after yuenhave been

for gold

and for

uranium carbide. There is not much known about the annealing mechanisms of vacancies in uranium carbide. But if the quenched-in vacancy concentration is smaller than the sink concentration vacancies will disappear prcdominantly at sinks and not by forming e.g. divacancies. For gold it is known that for quenching temperatures below 800 “C, vacancies anneal preponderantly at fixed sinks 3). If we compare the results for gold with those for uranium carbide, we obtain Q(UC) about 1.6 eV for the migration energy of vacancies in uranium carbide by taking for the centers of the annealing stages T(UC) = 573 “K (fig. 3) and T(Au) = 313 “K with Q(Au)=0.83 eV 3). This value is higher than the one determined by the “slope change method” (1.45 eV), but constitutes still an estimate in approximate agreement. From plastic flow measurement’s on UC, Chang 4) determined an activation energy of 1.63 eV which he attributed to the migration energy of vacancies. This value is also, within the limits of error, in good agreement with our value indicating that the real activation energy of vacancies in uranium carbide might be somewhat higher than 1.45 eV. Taking this value for the migration energy we can now estimate the average number of vacancy jumps during a normal quenching process. We chose a quenching temperature of 800 “C since we have assumed that at this temperature all vacancies in thermodynamic equilibrium are still frozen-in by our quenching technique. The jump number of vacancies I)er second v is given by: v=

vo

exp ( - &M/kT),

(2)

PROPERTIES

OF VACANCIES

vo WDebye

frequency

QM= migration

activation

T = absolute The temperature

has to

vacancies.

temperature. varies

change in degrees with time (set)

by the following

the following:

be larger than the migration energy of single

with time t according to the plot in fig. 5. Between 800 and 700 “C we approximate the temperature

necessitates

has to be small. 2. The migration energy of divacancies

energy of

T in this relation

25

CARBIDE

1. The binding energy between two vacancies

(6 x 1013/sec) ;

vacancies ; k = Boltzmann constant ;

If the binding energy is small the vacancies remain essentially dissociated during quenching (>300

“C) and

vacancies)

their

annihilation

(as single

occurs at fixed sinks.*

relation:

T = - 1000 t + 1073.

(3)

The integration of eq. (2) from t = 0 to t=0.2 set (from 800 to 700 “C) yields about 105 jumps, if QM= 1.45 eV (for 1.60 eV the jump number is only 2 x 103). The number of vacancy jumps while the sample is cooling from 700” to 300” is negligible as compared to the jump number between 800 and 700 “C as a further integration easily shows. We conclude that the sink concentration has to be smaller than 1O-5 (molar fraction) otherwise all vacancies could not have been quenchedin. This result is in agreement with the results known from well annealed metals and alloys, where the sink concentration is usually less

4.2.1.

URANIUM

This explanation

where

than

IN

10-G. Consideration

of d&vacancies

In many isochronal annealing curves an increase of electrical resistivity of about 0.5% is observed before the actual recovery stage starts. Such a behaviour was already found in the stage II recovery of gold (120-180 “K) after deformation at low temperatures 5). This increase was attributed to the dissociation of di-interstitials since two separated interstitials contribute more to the electrical resistivity than one di-interstitial. Also the electrical resistivity due to divacancies is smaller than that of two separated single vacancies. Therefore one explanation of our observed increase of electrical resistivity would be the assumption that divacancies which are formed during the quenching become dissociated by annealing at temperatures up to 300 “C.

4.2.

IDENTIFICATION

In

OF C-VACANCIES

THEIR

ELECTRICAL

table

1

AND

RESISTIVITY

all the values

for

carbon

and

uranium diffusion in UC reported in the literature are tabulated. The self-diffusion coefficients vary considerably. But the activation energies determined by the various groups appear, on the whole, consistent if one takes into account the evaluated temperature range of diffusion. For U-diffusion at high temperatures values of about 3.8 eV are found.e-10) At low temperatures a value near 1.35 eV was found for material which was stoichiometric or sub-stoichiometric 6). For carbon diffusion the average activation energy in the low temperature range is 2.4 eV whereas that at higher temperature is 3.6 eV 7, g). Lee and Barrett a) found that the diffusion coeflicient of C in UC varies with stoichiometry, whereas Bentle 7) reported that the self-diffusion of C in UC coefficient is nearly independent of stoichiometry. It is also found (table 1) that C-diffusion is always a factor 102 to lo3 larger than Udiffusion. This implies that C- and U-diffusion proceed on separate ways i.e. in the sublattices of C and U, respectively.

*

During

vacancy

quenching from 800 “C only about

jumps

formation

would

since

at

be necessary 800 “C

vacancies in thermodynamic mately

c”=~O-~

migration

the

concentration

equilibrium

(800 “C, CO=& Qr=l.O

energy

of vacancies

would

104

for divacancy of

is approxieV).

If the

be nearer to

1.60 eV than to 1.45 eV no significant annihilation of single vacancies

due to formation

of divacancies

could occur during quenching from 800 ‘C.

26

w . SCHiiLE

AND

P.

TABLE

1

1 Tracer

Matrix

/

Low

Activation

SPINDLER

/ i TJC4.83 1

1

U U

UC438

’

uc4.9

’

U U

UC4.8 UC4.82 uc4.s :

U

UC432 UC5.00 UC5.10 UG.60

1.21

G x 10-l’

1.43

10-12

1000-1400

6 x 10-e

1400-2000

8)

800-1600

3.04

2x10-4

1600-2100

6)

3.37

!

1.3x10-3

2.78

I /

I 2.73

7)

1600-2100

“)

1523-1847

9) / 1”)

1280-1700

1.75 3.2

j j

12&F-2050

1450-1980

1;

x IO-’

2.34

2.95 x 10-z

1200-1600

1.95

2.76 x lo-3

1200-1600

“) “) 3.86

1450-1800

“)

uc4.4

2.2

1075-1475

3.6

1475-1900

7)

UC4.6

2.2

1075-1475

3.6

1455-1900

7)

UC4.8

2.2

1075-1475

3.6

1475-1900

UC4.9

2.2

1075-1475

3.6

1475-1900

‘) 7)

uc4.7

/

Ref.

3.9

! I

2.39

temp. rango W) I1

I

I

U

High

Activation

energy (evJ i Wcm2/sec)

,

_ /

/

I

It is assumed that the following relation holds for single vacancy di~usion in each sublattice: &M+Qr=Qn,

(4)

QF ==formation energy vacancies) ;

(for

either

C- or U-

Q~=migration energy vacancies) ;

(for

either

CL or U-

Qn = self-diffusion activation C- or U-diffusion).

energy (for either

From our data we obtain 2.45 eV for Qn, as defined in eq. (4). This value is very close to the average value 2.4 eV for the results summarized in table 1 for the case of carbon diffusion in the low temperature range. This leads us to the conclusion that the vacancies we obtain after quenching are carbon vacancies. From an extrapolation of the solid line in fig. 2 to l/T + 0 we find for @“co about 104 ,uuSLcm, where COis the entropy constant and ev the electrical resistivity per vacancy, In this treatment the assumption is implicit that the quenched-in resistivity is proportional to the concentration of vacancies. In metals and alloys the electrical resistivity percent vacancies is approximately proportional to the residual resistivity. Assuming that this proportionality is also true for uranium carbide, a

32

/

compound with metallic behaviour, then we find by a comparison with gold a), for example, that the resistivity for carbon approximately 18 $Joml%.

vacancies

is

Childs and Ruckman 11) measured the electrical resistivity per percent carbon vacancies by irradiating substoichiometric uranium carbide. They obtained 6.7 ,uGom/% carbon vacancies, a value that differs from our estimate of 18, but is nevertheless also very high.

The concentration

of divacancies

c,

increases

with increasing temperature according relation : cVV m cycV exp ( f B/kT) = = const. exp {(-2&r + B)/(kT)},

to the

(5)

where cy is the concentration of single vacancies in thermodynamic equilibrium at temperatures T, and B is the binding energy between two vacancies. Since the formation energy of carbon vacancies (QF= 1.0 eV) is small an appreciable ooncentratio~~ of carbon divacancies at high temperatures is expected according to eq. (5). The activation energy for diffusion by suoh a divacancy mechanism in the carbon sublattice may be written as follows:

PROPERTIES

OF

VACANCIES

&D~~=~&F~--B+&M~, where

2Qrv - B

is the

formation

(6) energy

of

divacancies as can be seen from eq. (5), and where QMVVis the divacancy migration energy. In the previous the activation

chapter we have shown that

energy

of 2.45 eV for carbon

diffusion is very likely due to a single vacancy diffusion mechanism. This activation energy is found below about 1600 “C!. Above this temperature the activation energy amounts to about 3.6 eV (table 1). We suppose that this activation energy can be attributed to a divacancy diffusion With our formation energy of mechanism. 1.0 eV for single carbon vacancies we obtain &n~-- B= 1.6 eV using eq. (6). QMVVand B cannot be determined separately by experimental methods. But from our experiments, discussed in the previous chapter, we were led to the assumption that QMVVhas to be larger than Qnv (1.45 eV) and that B has to be very small. This result is in agreement with our supposition of a divacancy diffusion mechanism, since Q$v is even a little larger than 1.6 eV if a positive value is taken for the binding energy B (B < 1.0 eV). 4.4.

THE QUENCHINGRESULTS OF ORIFFITHS

Further support for the idea that U- and Cvacancies move independently in uranium carbide can be gained from reconsidering the implications of the quenching results obtained by Griffiths 1) who did not measure the quenching rate. He quenched the uranium carbide specimens to room temperature in a helium stream. His method probably differed from ours in that our gas stream was cooler being at liquid nitrogen temperature. Thus his quenching rate mainly below 600 “C must be low compared to ours resulting in a condition that defects which are mobile below a temperature of 600 “C could not be frozen in. This means that the defects which were quenched in by Griffiths were perhaps less mobile (i.e. different) that those quenched-in in the present experiments. In our case the center of the recovery stage

IN

URANIUM

27

CARBIDE

after quenching

was found to be near 310 “C

(fig. 3), whereas

in the case of Griffiths

the

recovery stage appeared in the vicinity of 600 “C to 700 “C, i.e. at an appreciably higher temperature. recovery

we

From

this temperature

would

estimate

an

of rapid activation

energy of 2.2 eV. However, Griffiths determined an activation

energy of 1.1 eV for the recovery

of electrical resistivity

at 600 “C!. An energy of

1.1 eV implies that vacancies would make in average about 1011 jumps 1) during their lifetime. This jump number appears to be several orders of magnitude too high since the sink concentration for point defects is surely not smaller than lo-* in a well annealed material. Therefore we doubt that the value of 1.1 eV given by Griffiths for the migration activation energy of vacancies is right, even though we do not doubt the existence of the recovery stage he reports. The temperature range from which Griffiths quenched his specimens (1250-1500 “C) was higher than our temperature range of quenching. Also the formation energy of vacancies he determined (2.8 eV) was much higher than our value. With a formation energy of 2.8 eV and assuming CO= 5 the vacancy concentration in equilibrium at the highest thermodynamic temperature (T = 1710 “K) from which he quenched amounts to only 2 x 10-s. This concentration we believe is much too low to give rise to the high resistivity changes measured. For his pre-exponential factor one obtains a value of log ,uL’cm. This is several orders of magnitude too high to represent the electrical resistivity per percent vacancies in uranium carbide. From the previous consideration it is clear that the activation migration and formation energies determined by Griffiths lead to some implausible implication. It appears to us that Grifliths observed a vacancy type defect which is different from the kind of defect we obtained, i.e. that he observed U-vacancies.* *

The defects quenched-in by Griffiths may also (U- and C-atoms exchange-

have been vacancy clusters

28

W. SCHOLE AND P. SPINDLER On the basis of this supposition

we shall

reinterpret Griffiths data as follows: The electrical resistivity of U-vacancies should

be

Assuming U-vacancy

larger

than

that

that the electrical

of

C-vacancies.

resistivity

of a

is a factor of two larger than that

of a C-vacancy

we obtain

energy of U-vacancies

for the formation

a value between

1.4 to

stage (stage I), centered at about 150 “C is found and attributed to the annihilation of single uranium interstitials with uranium vacancies. The second stage which according to Bloch and Mustelier la) appears only after a relative high neutron dose is centered at about 500 “C. Its interpretation

is not unambiguous.

Childs et al. 13) originally attributed this stage to

1.7 eV (using the upper and lower resistivity

the annihilation

changes found by Griffiths by quenching). The estimation of the migration activation energy for the recovery process on the basis of a comparison of the temperature range ofrecovery with our recovery stage yields 2.2 eV. The sum of the estimated formation energy 1.4 to 1.7 eV and the migration energy (w 2.2 eV) yields

interstitial. Bloch and Mustelier assumed that the annihilation of uranium interstitials occurs by formation of clusters of interstitials. The third recovery stage found only after a heavy neutron irradiation was noted by Bloch and Mustelier 14) and by Griffiths 15). It was centered at about 800 “C and was attributed to vacancy annihilation at sinks

values between 3.6 and 3.9 eV. For the activation energy of uranium self-diffusion a value in the vicinity of Qn = 3.7 eV is reported in the literature (table 1). This agreement supports our reinterpretation of Griffiths results. 4.5.

INTERSTITIALS IN URANIUM CARBIDE

The data for recovery of electrical resistivity, and density of uranium lattice parameter, carbide after neutron irradiation are manifold and no clear cut explanation of these results can be given at this time. However, some of the experimental data appear to be well established and their interpretation by Childs et al. 11712713) appears to be reasonable. In order

of a second kind of uranium

because the recovery stage after quenching found by Griffiths 1) appeared in the same temperature region. The center of our recovery stage after quenching is situated at 350 “C (fig. 3) and is well-distinguished from the three other recovery stages observed upon neutron irradiation (at 150, 500 and 800 “C). If stage I recovery is attributed to the recombination of uranium interstitials with uranium vacancies -the carbon interstitials are supposed to have been annihilated already below room temperature with carbon vacancies 13)-the stages due to the annihilation of

the indication from the resistivity increase of 0.5 eV%

either uranium or carbon vacancies are not expected to be large or to appear at all after irradiation. A temperature shift of a recovery stage due to a difference in point defect concentration occurs only, if the reaction order is two, i.e. interstitials recombining with vacancies. Such an effect was found for the stage I recovery by Bloch and Mustelier i4) but it amounts to only a few degrees. Therefore the attribution of the recovery stage found after quenching at 310 “C to the annihilation of carbon vacancies is not in contradiction to

which was often

these results.

to integrate our results into this picture we have to discuss the whole matter again. After neutron irradiation, one large recovery able) which were either present

in thermodynamic

equilibrium at high temperatures or which were formed during quenching from single vacancies. The formation energy of 2.8 eV could then represent the formation energy

of a trivacancy

(three times the formation

energy of a single vacancy minus the binding energy of the trivacancy).

But from our experiments we got observed

before the begin of the

recovery stage that the binding energy between two vacancies is so low that above 300 “C all divacancies are dissolved into single vacancies. And of course the possibility

for the formation

of trivacancies

above

300 “C is still much smaller than that of divacancies.

Acknowledgements The authors wish to thank Prof. Dr. R. Lindner for the support of the present work

PROPERTIES

and for stimulating

OF

discussions.

VACANCIES

We also thank

IN

9

Dr. Sonder of the ORNL for his critical reading of the manuscript were gratefully

and for his suggestions which accepted.

One of us (P.S.) acknowledges a scholarship

of

the

also

to

the receipt of

Deutsche

Forschungs-

gemeinschaft. We

have

Chemistry

g,

Service

of

thank

the

CCR

ISPRA

Analytical for

t,he

analysis. 12)

References L. B. GrifXths, Phil. Mag. 7 (1962) 827 J. E. Bauerle and J. S. Koehler, Phys. Rev. 107 (1957) 1493 W. Schiile, A. Seeger, D. Schumacher and K. King, Phys. Stat. Sol. 2 (1962) 1199 R. Chang, J. Appl. Phys. 33 (1962) 858

13) Id) 15)

URANIUM

CARBIDE

29

D. Schumacher and A. Seeger, Phys. Letters 7 (1963) 184 R. Lindner, G. Riemer and H. L. Scherff, J. Nucl. Mat. 23 (1967) 222 G. G. Bentle, private communication W. Chubb, R. W. Getz and C. W. Townley, J. Nucl. Mat. 13 (1964) 63 H. M. Lee and L. R. Barrett, Proc. Brit. Ceram. Sot. 7 (1967) 159 P. Villaine and J. F. Marin, CEA MET-12/67 B. G. Childs and J. C. Ruckman, New nuclear materials, including non-metallic fuels 2 (IAEA, Vienna, 1963) p. 1 B. G. Childs, A. Ogilvie, J. C. Ruckman and J. L. Whitton, IAEA, Symposium on Radiation damage in solids and reactor materials 4 (1963) p. 241 B. G. Childs, J. C. Ruckman and K. Buxton, Carbides in nuclear energy 2 (1964) 869 J. Bloch and J. P. Mustelier, J. Nucl. Mat. 17 (1965) 350 L. B. Griffiths, J. Nucl. Mat. 4 (1961) 336