Atomic displacements in low temperature irradiated chromium crystals

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Atomic displacements in low temperature irradiated chromium crystals

M. Biget, F. Maury, P. Vajda, A. Lucasson, P. Lucasson

To cite this version:

M. Biget, F. Maury, P. Vajda, A. Lucasson, P. Lucasson. Atomic displacements in low temperature irradiated chromium crystals. Journal de Physique, 1979, 40 (3), pp.293-298.

�10.1051/jphys:01979004003029300�. �jpa-00209108�

Atomic displacements ^{in low} temperature irradiated chromium crystals

M.

Biget,

^F. Maury, ^P.

Vajda,

^{A. Lucasson} (*) ^{and P. Lucasson}

Bât. 350 (**), Université Paris XI, ^F 91405 Orsay, ^France (Reçu ^{le 26} septembre 1978, accepté le 23 novembre 1978)

Résumé. ²⁰¹⁴ Nous avons irradié des échantillons monocristallins de chrome parallèles ^aux plans (100), (110) ^et (111),

avec des électrons d’énergie comprise ^{entre 0,48 et} 1,7 ^{MeV. Nous avons trouvé} que l’énergie ^{seuil de} déplacement atomique ^est sensiblement la meme dans les deux directions cristallographiques ~100~ et ~111~ ^bien

que

^les

mécanismes de déplacement soient vraisemblablement différents. Nous avons étudié le recuit des défauts créés, après irradiation à 0,525 ^MeV (jusqu’à ⁶⁰ K), 0,5 ^et 0,75 MeV. L’anisotropie ^des premières sous-étapes ^{de recuit} présente plusieurs points communs avec le recuit du tungstène dans le même domaine de température. ^Nous suggérons ^une interprétation des différentes sous-étapes jusqu’à ^{40 K.}

Abstract. ²⁰¹⁴ Monocrystalline specimens ^of chromium, ^cut parallel ^{to the} (100), (110) ^and (111) planes, ^{have been}

irradiated with electrons in the energy range 0.48-1.7 MeV. The threshold energy for atomic displacement ^{is found}

to be about equal ^{in the two} crystallographic directions ~ 100~ and ~ ^111~ , although the mechanisms for displa-

cement may be quite ^{different in the two cases.} The recovery of the defects has been studied _up to 60 K, ^{and after} irradiations at 0.5,0.525 and 0.75 MeV. The anisotropy ^{of the different} substages appears ^to bear some resemblance to the low temperature recovery of tungsten. ^A tentative attribution is given for the various substages ^{up to 40 K.}

Classification Physics ^{A bstracts} 61.80F - 61.70E

1. Introduction. - This work is part ^{of an extensive} study of Frenkel defect creation and _recovery in bcc metals [1]. ^This study has been undertaken in order to obtain some information on the threshold _energy surface for atomic

displacements

^{in bcc}

crystals,

^and

check whether this surface would

depend

^{on the}

particular

metal under consideration. Results have been obtained in the ^cases of Mo [2, 3], ^a-Fe [4], ^Ta [5]

and W [6]. ^{For all these metals,} the threshold _energy for atomic

displacement

has been found to be mini-

mum in the ( 100 > direction in agreement ^{with the} first

experimental

^{data of Lomer and} Pepper

[7]

^as

well as with the results of the Brookhaven

computation

group [8]. ^{On the other} hand, the threshold _energy in the ( 111 > direction has always been found to be

relatively

lower than that

predicted

by the compu- tations on iron

[8],

the ratio

Td’ IT100> varying

from 1.05 in the case of W to 1.3 in the case of Mo.

The ratio of the threshold

energies

^{in the} ( 100 )

and ( 111 ) directions is a

significant

parameter which

might

^{account, at least}

partly,

^{for the} differences in the stage 1 recovery spectrum, ^{observed in different} bcc metals : it _may directly ^{influence the relative}

populations

^{of the various} substages. ^{Moreover, it}

may be

indirectly

^{related to the} stage 1 recovery spectrum by ^{the fact} that, like the interaction between interstitial and _vacancy

specific

^{to each Frenkel}

pair configuration,

^it

originates

^{from the} interatomic

potential particular

^to each metal. Very ^{little is}

known about low temperature irradiated chromium.

To our knowledge ^the only

existing

data have been obtained in our group [9] ^on

polycrystalline specimens.

A

single-step displacement probability

^function P(T)

with a

unique

^{threshold at 28} ± ^{1 eV} could account for the defect

production

^rate up ^{to a} transmitted energy Tm l"to.I 100 eV. The recovery spectrum ^{has been} studied from 10 to 60 K. Distinct peaks ^showed up below 40 K ; yet, ^as for other bcc metals (W, ^for

example),

^{it was not}

possible

^{to determine} exactly

the end of stage ^{1 since no} long range

migration

^was

evident below 60 K.

2. Expérimental. ^{- The}

specimens

^were

prepared

from a zone-refined chromium bar obtained

by

^the

courtesy ^{of J.}

Bigot (CECM-Vitry,

^France)

[10].

Several

grains

with their axes

parallel

to ( 111 ) ^and (110) ^{were detected} by ^a systematic X-ray explo-

ration of the bar and then cut out of it. The

slicing

^was

performed

^{with a}

goniometric

adaptor described in reference [11]. The final thickness was achieved by

mechanical

polishing,

^{followed by}

electropolishing

in a mixture of 95 %

CH3COOH

⁺ 5 % HCI04. ^No

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01979004003029300

294

Table 1. ^- Specimen characteristics

The tickness of the samples ^{was measured at both ends} (xi, x2) and in the middle of the sample (xm) ^{with a} micrometer. A mean thick-

ness was deduced either by weighing ^the sample ^or from its measured resistance. XFOR is ^{the mean} thickness which has been used in the cal- culations. 3l is the measured resistivity ratio between room temperature ^and liquid ^helium.

anneal was

performed

before irradiation. The different characteristics of the samples ^are listed in table I.

An indication of the

purity

^is

given by

^the

resistivity

ratio A (see ^Table I), ^{the main}

impurities being

Fe (10

ppm)

^{and N} (10

ppm) (cf.

^Ref.

[10]).

As can be _seen, the thickness of the

samples

^is

highly

^non uniform, ^the

samples being

^{thinner at both}

ends

(xi, x2)

than in their middle

(xm).

^Since the very ends of the

samples

^{are not} irradiated, ^{this will lead}

to an underestimate of the radiation-induced

resistivity

calculated from the measured resistance.

On the other hand, ^the length ^{of the} (111) sample (4 mm) ^{was shorter than} the total irradiated

length

(5 mm) ; ⁱⁿ consequence, part ^{of the}

sample

^holder (a copper foil of _{50 gm} covered with

superconducting

soft solder) ^was irradiated, ^thus

resulting

^{in an extra}

heating

^{of the}

sample.

^The irradiation temperature

was controlled in a first series of irradiations by

measuring

the resistance of the irradiated poly-

crystalline sample

^{(its mean} temperature

during

^the irradiations,

Ti,

^was

kept

^{around 9} K) ^{and in a}

second series of irradiations

(performed

^{at a lower}

temperature)

by

measuring

^the

resistance

^{of the (111)}

sample

(its ^mean temperature T; ^was kept ^{between 6}

and 7 K). Note that the weak

points

^{at the ends of the}

samples

may be another cause of extra

heating.

Experience proved

(cf. ^section 4) that,

during

^the

first series of irradiations,

samples

^{(100) B and (110) A}

were irradiated at a

higher

temperature ^than

samples

(100) ^{A and} (110 B).

The

annealing

^{studies were}

performed in

^situ

by heating

the entire

sample

chamber and

monitoring

the temperature by ^{means of a}

platinum

^{resistor. All}

resistivity

measurements were made at 4.2 K with a

sensitivity

^{of 1 x} 10- 11 Q cm.

3. Defect production. ^{- 3. 1} EXPERIMENTAL RE- SULTS. ^- Two series of irradiations were

performed

in the energy range 0.48-1.7 MeV. The results of the second one only ^{will be} presented here since a fraction

of the defects was lost

during

^{the first run} (because ^of

overheating).

^{The first}

thing

^{to note is that} the pro- duction rate remained constant (within ^the measuring

sensitivity),

with the incident electron fluence, ^{even at}

the lowest electron energies. ^{This means that the sub-}

threshold defects play ^a

negligible

^{role in the total}

damage

production. Moreover, - 85 % ^{of the defects}

recovered below 40 K after irradiation ^at 0.5 MeV ; this percentage ^{decreased to -} 60 % ^after

irradiating

at 0.75 MeV : these numbers are

quite

comparable

to what is usually obtained in other metals when no

subthreshold damage is observed

(see

e.g. Ref.

[2]).

The

experimental production

^{rates are}

plotted

ⁱⁿ

figure

^{1 for the four}

samples

(100) A, (100) B, (110) ^B

and (111), ^{as a} function of the electron energy. The

production

^{curve measured for the}

polycrystalline

sample reproduced closely ^that obtained before [9]

and is not

given

here. The

uncertainty

^{due to the}

electrical measurements lies between 1 and 2 %.

Most of the

uncertainty

^{on the}

experimental points

comes from

possible

variations of the electron beam

profile

ⁱⁿ conjunction with the thickness inhomo-

geneity

^{of the}

samples,

^and from uncontrolled

overheating (particularly

^{for the} (111)

sample).

3.2 DATA ^{ANALYSIS. -} Since the radiation-induced

resistivity

may be underestimated

(by

^{an amount}

which _{may vary} from one sample ^{to the} other) ^{due to}

a wrong evaluation of the

shape

factor for the irradia- ted part ^{of the}

sample,

^{it would be}

meaningless

^to try

to determine the exact

shape

of the threshold _energy surface, ^{and even to} try ^to determine the relâtive

opening

of the lenses

(regions

^{of low threshold ener-}

gies

^{around the main}

crystallographic

directions) ^{in a}

classical

geometrical

^model. Therefore, ^we adopted ^a

threshold _energy surface which has been

directly

deduced from the results of

Erginsoy et

^al.

[8]

^{on iron,}

the same that we had used for Mo [3].

Two

regions

of low threshold _energy were consi- dered around the ( 100 ) and 111 ) directions, ^and treated like _square

potential

^wells with radii of 22°

Fig. ^{1. - Induced} resistivity change ^{rates as a} function of the incident electron _energy for four samples ; ^the crosses are the experimental points, ^the curves are calculated with :

The PF values used for normalization are indicated on the figure.

296

and 240

respectively.

Outside of these

100 )

^and ( 111 ) lenses, the threshold _energy was

arbitrarily

fixed at 95 eV (which

corresponds

^{to an incident}

electron _energy of 1.1 MeV). ^{The exact} value of this parameter ^{is of little}

importance,

since it will influence the calculated production ^curves only ^at high energies where, ⁱⁿ any case, the model is not

supposed

^{to be as}

valid because of the occurrence of

multiple displa-

cements. Thus we remain with two parameters

only,

which are the threshold

energies

ⁱⁿ thé ( ^{100 ) and} 111 > directions,

T¿100>

^and

T¿lll>, plus

^{a norma-}

lization factor for each

production

^curve which should be

equal

^to the Frenkel

pair resistivity,

pF ^- if the radiation-induced

resistivity

has been estimated cor-

rectly ^{- or less than} PF ^- if it has been underestimated

(cf. ^section 2).

The calculation of the

displacement

cross-sections with this model has been described in detail in refe-

rences [3] ^and [4].

The calculated

production

^{curves are drawn in}

figure

^{1 with 3 sets of} parameters :

The calculated curves have been normalized to the

experimental

^ones in the medium energy range where the model is

supposed

^to be still valid (not ^too many

multiple displacements)

^{and the} corrections for _energy loss and beam

straggling

^{are not too}

important.

We can see that

Td"’>

^{= 29 eV leads to}

production

rates

definitely

^{smaller than the}

experimental

^{ones at}

low

energies

^{for the} (100) samples; ^{in the same} way

Td "’ >

^{= 27 eV leads, for the (111)} sample ^{and at}

low

energies,

^to

production

^rates

systematically larger

^{than the measured ones.}

The best fit is obtained with

Td’00> =

^{27.5 ± 1 eV}

and

Td"’> =

^{28.5 ± 1 eV. These two values are}

nearly

equal,

^{as in the case of W} [6]. This result will not depend ^{much on the} assumed threshold _energy surface, ^{but the}

general shape

^{of the curves will}

depend

^{on it. The} agreement ^{between the}

experimental

and calculated data is

surprisingly

good,

especially

for the (100) samples : ^{it is to} be noted that the calcu- lation reproduces ^even the difference in the shape ^of

the

production

^{curves for the two} (100)

samples

between - 0.5 and 0.7 MeV, ^{as a} consequence of their different mean thicknesses.

One _may wonder why ^{so crude a} model leads to such a good ^{fit. We see two reasons} for that : ^- at low

energies,

^{the beam is so}

widely spread

^{that - in the}

directions of _easy

displacement

^{- it covers the whole}

of the

corresponding

lens ; ^thus

taking

^{a mean value}

of the threshold _energy for the whole lens will be a

good

approximation.

^The

approximation

^{should not}

be

quite

^as good ^{for the} (110) sample.

At high energies ^the equality ^{of the two thre-}

sholds

Td’00>

^and

T¿lll>

(which ^{means that the} crystal ^is fairly

isotropic)

^{is a} very favourable case,

allowing ^mutual

compensations

^when

multiple displa-

cements take place.

The obtained value for _PF lies between 25 and 39 gÇl cm/at

%

F.P., ^{the most}

likely being

- 37 gn cm/at %. ^{Of course,} this value will

depend

much on the threshold _energy surface and will decrease if one increases the size of the low-threshold _energy

regions.

These conclusions are in good agreement ^{with the}

polycrystalline

^results. There, ^{we had found that a}

displacement probability

^function

with _PF ⁼ 40 gfl cm/at %,

fitted well the

experimental production

^{rates in the}

energy range 0.5-1.1 MeV. The

quantity

^0.6 represents the fraction of the total solid

angle

(4 7r) ^{which is} open to atomic

displacements

in the medium energy range ; it corresponds, ^{in the} present model, ^{to the total}

opening

^of thé ( 100 ) and ( lll ) lenses, ^which

amounts to 0.55 x 4 TE in our model. Thus, ^{this first} step ^{of the} P(T ) ^{function must include} both 100 ) and ( 111 )

displacements,

contrary ^{to the case of} Mo [3, 12] ^for example, ^{for which the two thresholds}

Ta loo>

^and

Td"’>

stood much more apart.

4. Recovery. ^- 4. 1 EXPERIMENTAL RESULTS. ^-

Isochronal anneals (At ^{= 10} min.) ^were

performed

after

^{three runs of the} first series of irradiations

(7§ -

⁹ K) ^{at the}

energies

^{0.525 MeV}

(Fig.

2),

0.75 MeV

(Fig.

3) ^{and 0.5 MeV}

(Fig.

4) ^{and after}

one run ^{of the} second series of irradiations

(6

K ii

^{7 K) at 0.5 MeV}

(triangles

ⁱⁿ

Fig.

4).

Only

^{the curves}

corresponding

^{to the} (100) ^and (111) samples ^have been drawn on the

figures,

^{the curves}

Fig. ^{2. -} Isochronal _recovery spectra (At ^{= 10} min.) for the two orientations (111) ^and (100) (0 : sample (100) A, + : sample (100) B) after an irradiation at 0.525 MeV ; the curves have been normalized to the radiation-induced resistivity recovery between 8 and 40 K.

Fig. ^{3. -} Isochronal _recovery spectra (AI ⁼ 10 min.) for the two orientations (III) ^and (100) (0 : sample (100) A, ^{+ :} sample (100) B) ^{after an} irradiation at 0.75 MeV ; the curves have been normalized to the radiation-induced resistivity recovery between 8 and 40 K.

Fig. ^{4. -} Isochronal _recovery spectra (At ^{= 10} min.) for the two

orientations (111) ^and (100) (0 and t::. : sample (100) A, + : sample (100) B) ^{after two} different irradiations at 0.5 MeV. The triangles

refer to the second irradiation. The curves have been normalized to the radiation-induced resistivity recovery between 8 and 40 K.

obtained with the (110) samples being intermediate.

The temperature ^{interval was OT = 1.5 K,}

allowing

the observation of more details than in the poly- crystalline

experiment.

^{The same} peaks appear ^{at ’"} 16

and at 21 K but with an

asymmetric

structure at least for the second _one; the existence of at least three

substages ^{has to} be assumed in the temperature range 26-35 K if one compares the recovery ^curves of the different orientations.

The _recovery between 40 and 60 K has been studied

only

after the 0.525 MeV run. It is rather constant and small in that _range,

exhibiting

^{no well defined}

structure as can be seen on

figure

2, ^which _suggests that it already

belongs

^to stage ^II.

4.2 DISCUSSION. ^- 4. 2.1 Recovery between 10 and 25 K. - This temperature range contains two main

substages ^{centred at - 16 and 21} K,

although

^the

first one has been

partially

suppressed ^{in a number of}

cases due to too

high

^an irradiation temperature (see

for

example figure

4).

Comparing figures

^{3 and 4, it}

appears clearly ^{that the relative}

amplitudes

^{of both} substages increase with the incident electron _energy whatever the

sample

orientation _may be. This

implies

that the

corresponding

^{defects are} created with a

threshold _energy

slightly higher

^{than the minimum}

one. Moreover, ^the

substage

^{at 21} K, ^{which is}

larger

at low

energies (Fig.

4, A) ^{for the} (111)

sample

(in

spite

^{of a}

higher

irradiation temperature) and, ^at

high energies (Fig.

3), ^{for the} (100) sample, ^{can be attributed}

to Frenkel

pairs

^{created via}

displacements taking

place ^near the ( lll ) direction.

Nothing

^definite

can be said of the first substage, since its relative

amplitude

^is

highly dependent

^{on the} irradiation temperature. ^{At low} energy, and for the only ^irra-

diation

performed

well below 10 K

(Fig.

4, A) ^{it is} larger ^{for the} (100)

sample

and almost invisible in the

(111)

sample ;

^this suggests ^{that it could stem from}

pairs produced

ⁱⁿ thé ( 100 ) ^direction.

In many respects

(energy dependence,

orientation

dependence

^{of the second} substage), ^the recovery between 10 and 25 K in Cr appears similar to that in W, which takes place ⁱⁿ

roughly

^{the same} tempera-

ture range (8-20 K) [6]. ^{As in} W, ^the peak correspon-

ding

^{to the}

pairs

created in thé ( l ll ) ^direction

(substage I2)

^{has a} complex ^structure

(in

^{both cases,}

W [13] ^and Cr, ^a bump ^is clearly ^{visible on the}

high

temperature

side).

^{Let us note that if the}

analogy

stands on real

physical grounds,

^{an internal friction}

relaxation

peak

should be observed in Cr as it has been observed in W [14, 15] ^{and Mo} [16], which would anneal

during

substage I2, dislocation

pinning taking place

^{in the same} temperature range.

As concerns the first substage, ^{it seems} (see

Fig.

⁴

and

Fig.

3) ^to shift towards the

higher

temperatures when

increasing

the energy. Most

likely

this shift is the mere result of the

higher

temperature ^{of the} 0.75 MeV irradiation, ^which suppresses the low temperature part ^{of the} peak.

4.2.2 Recovery ^between 25 and 40 K. ^- This is the most

important

part ^{of the recovery at low}

energies

for all orientations and thus it should correspond ^to

defects produced ^with the lowest threshold

energies.

298

At least four substages ^{must be}

distinguished

^{in that}

temperature range, centred at - 28.5 K, ³¹ K, ^{33 K} and 36 K (the ^{curves of}

figures

2, ^{3 and 4} have been drawn on this

assumption).

^{An even more}

complex

structure is not excluded.

A tentative attribution of these

peaks

is the follo-

wing :

- The 31 K peak whose relative

amplitude

^is’

maximum at low

energies

^{for the} (100) orientation and at

high energies

^{for the} (111) orientation would

correspond

^{to Frenkel}

pairs

created in the ( 100 )

direction.

- The 28.5 K and 33 K

peaks

which exhibit the

same orientation

dependence (they

^are larger ^{at low}

energies

^{for the} (111)

sample

^{and at}

high energies

^for

the (100)

samples)

^would correspond ^{to Frenkel}

pairs

created in the ( 111 ) ^direction.

- The 36 K peak ^{is a} candidate for free interstitial

migration

^{like the 47 K}

peak

^of molybdenum [17, 18, 19] ^{or the 115 K}

peak

^{of iron} [4]. However, ^{no indi-} cation exists at the moment to confirm or to invalidate this.

4.2.3

Comparison

^with calculations. ^- Table II

gives

^the calculated percentage of defects created in the

( 100 ) ^{direction as a} function of the electron _energy and sample orientation. The calculations have been

performed

^{with the two sets of} parameters :

(The

percentage of defects created in thc ( 111 )

direction is the mere complement ^{to 100} % ^{of that}

listed).

The

figures

^{obtained are seen to be rather} dependent

on the exact values of the parameters (at ^{least for the} low

energies).

In any ^case, they ^are consistent with the

.previous

attributions.

Table II. ^- Calculated percentages of

defects

^created

in

the

100 > ^direction

Sample orientation and mean thickness

5. Conclusion. ^- A

simple geometrical

^{model in}

which the threshold _energy is assumed to be approxi- mately ^{constant around a few} directions of low indices

(here

100 ) and (111

))

has been found to

reproduce surprisingly

^{well the}

experimental

^results.

The mean threshold

energies

^around the ( 100 ) ^and ( 111 ) directions which are determined in this model are found

practically equal.

^{In that} respect, chromium behaves like tungsten.

An

interpretation

^{has been}

given

^{of the main}

recovery substages ^{below 40 K.} Although ^{a confir-}

mation is needed as concerns the first _recovery

substage centred around 15 K, ^{the low} temperature part ^of the recovery (below ²⁵ K) appears ^to be _very similar to W, ^{i.e. the} defects which anneal at the lowest temperature ^are those which are produced ^with

a

relatively high

^threshold energy. Moreover, ^{as for} W, the recovery in the temperature range 25-40 K is due to the simultaneous recombination of

pairs

produced ⁱⁿ thé ( 100 ) and ( 111 ) directions (and,

in that respect, ^{can be} compared ^to substage ID ^of iron). ^Further

experiments

^are

required

^to

identify

^the long range interstitial

migration.

References [1] BIGET, M., Thesis, Orsay (1978).

[2] BIGET, M., VAJDA, P., LUCASSON, ^{A. and} LUCASSON, P., ^Radiat.

Eff. ²¹ (1974) ^229.

[3] MAURY, F., VAJDA, P., BIGET, M., LUCASSON, A. and LUCAS- SON, P., Radiat. Eff. ²⁵ (1975) ^175.

[4] MAURY, F., BIGET, M., VAJDA, P., LUCASSON, A. and LUCAS- SON, P., Phys. ^{Rev. B 14} (1976) ^5303.

[5] BIGET, M., MAURY, F., VAJDA, P., LUCASSON, A. and LUCAS- SON, P., Phys. Rev., to be published ^{in 1978.}

[6] MAURY, F., BIGET, M., VAJDA, P., LUCASSON, A. and LUCAS- SON, P., ^Radiat. Eff. ³⁸ (1978) ^53.

[7] LOMER, ^{J. N. and} PEPPER, M., ^Philos. Mag. ¹⁶ (1967) ^1119.

[8] ERGINSOY, C., VINEYARD, G. H. and ENGLERT, A., Phys.

Rev. A 133 (1964) ^595.

[9] BIGET, M., VAJDA, P., MAURY, F., LUCASSON, A. and LUCAS- SON, P., Proc. of the Int. Conf. on the Fundamental

Aspects of Radiation Damage ⁱⁿ Metals, Gatlinburg,

USERDA Conf.-751006, ⁶⁶ (1975).

[10] BIGOT, J., Ann. Chim. 5 (1970) ^397.

[11] BIGET, M. and VAJDA, P., J. Phys. ^{E. Sci.} Instrum. 6 (1973)

968.

[12] RIZK, R., VAJDA, P., LUCASSON, A. and LUCASSON, P., Phys.

Status Solidi (a) ¹⁸ (1973) ^241.

[13] DAUSINGER, F., Thesis, Stuttgart (1976).

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