Plastic deformation of amorphous solids by track overlap

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Nucl. Tracks Radiat. Meas., Vol. 19, Nos 1--4, pp. 91-96, 1991 Int. J. Radiat. Appl. lnstrum., Part D Printed in Great Britain

PLASTIC DEFORMATION

OF AMORPHOUS

SOLIDS BY TRACK

OVERLAP

S. Klaumflnzer Hahn-Meitner-lnstitut, Bereich Schwerionenphysik, Posffach 39 01 28 D-1000 Berlin 39, Germany

ABSTRACT Particle tracks in solidsare the sources of mechanical stressesand strains.These stresseslead to macroscopically visible plastic deformation of amorphous materials when the particletracks are wellaligned and overlap each other. The anisotropy of the irreversibledeformation is determined by the track symmetry; the sample dimensions perpendicular to the tracks grow linearly with increasing fiuence whereas the sample dimension along the tracks shrinks.This effectoccurs in all amorphous solids,ranging from high-purity vitreous silicato metallic glasses but not in crystallinesolids.The dependence of this plasticdeformation on electronicstopping power, irradiationtemperature, and various solid-stateparameters will be discussed.The findings emphasize the importance of structural relaxation for a deeper understanding of particletrack formation. KEYWORDS Ion irradiation; particle tracks; plastic deformation; amorphous solids; structural relaxation. INTRODUCTION Although the existence of particle tracks in solids has been known for more than thirty years, the basic mechanisms of track formation are still poorly understood. One of the reasons is that revelation of particle tracks has been mostly studied by chemical etching (Fleischer et al., 1975), which is easy to use but has several disadvantages. First, one has to know an appropriate chemical etchant, which preferentially attacks the distorted material forming the latent track. Second, this method applies only above a certain threshold of the energy deposited by the fast particles as electronic excitations and / or ionizations. Irreversible atomic rearrangements, which may occur as subthreshold precursors of continuous latent tracks, are not detected. Third, this method is easy to use only at or above room temperature. If rapid track fading occurs below room temperature, particle tracks are hard to find with this method. In particular, it is long known that elemental defects in metals and alloys can be highly mobile at very low temperatures, hampering any positive proof of the existence of particle tracks in these materials. In the past only a limited search for particle track effects has been done with metallic conductors (Fleischer et al., 1975). All these room-temperature investigations yielded negative results supporting the widely held belief that atomic rearrangements are not triggered by electronic excitations in metals and alloys. This paper summarizes the research work on metallic glasses (Klaumfinzer and Schumacher, 1983; Klaum~inzer et al., 1985, 1986; Hou et al., 1987, 1990) and insulating glasses (KlaumCmzer et al. 1989a; Benyagoub et al., 1989) irradiated at the VICKSI accelerator in Berlin. These investigations demonstratedfor the first time that particle track effects exist also in solids with metallic conductivity (Klaumttnzer et al., 1986). PRINCIPLES OF THE EXPERIMENT The basis of the experiment profits from the fact that individual particle tracks can be imaged by their stress and / or strain fields (Fleischer et al., 1975). Due to their specific production process these fields have cylindrical symmetry.//particle tracks are produced by a beam of fast ions from a big accelerator these tracks are well-aligned. With increasing fluence significant track overlap will occur leading to a corresponding polarization stress, which extends throughout the sample and reflects the specific symmetry of the irradiation geometry. Thus, the atomic rearrangements, released by the following projectiles, have a preferential direction and may give Hse to some kind of plastic strain. It will not saturate during prolonged irradiation, provided a steady-state structure can be maintained in the target. Consequently, a small effect, i.e. a small deformation yield per projectile ion, can be easily amplified and 91

92

S. KLAUMONZER

measured by using high ion fluences so that multiple track overlap occurs. In addition, since plastic deformation is irreversible by virtue, the ion irradiation can be performed at any desired temperature, preferentially at low temperatures to avoid thermal annealing, whereas the measurement of the plastic strain can be done conveniently at room temperature. Like the polarizationstressthe strain tensor has to reflectthe symmetry of the irradiationgeometry, provided no complications arise from additionalcrystallographicanisotropies.Hence, amorphous targets are superior to crystallineones. A strain tensor, the symmetry of which is compatible with ionbeam irradiation with uniform energy deposition,allows the following dimensional changes (KlaumCtnzer and Benyagoub, 1991): i) an isotropicswelling or compaction, which leads to a decrease or increase of the mass density;ii)a growth of the dimensions perpendicular to the beam, accompanied by a corresponding shrinkage of the sample dimension parallel to the beam in such a way that the mass density remains unaltered. In the following the lattereffectwill be denoted as ion-beam-induced plasticdeformation. An experiment comprises the following steps. In order to ensure uniform energy deposition thin (i.e. projected ion range ~> target thickness) glassy solids have to be irradiated homogeneously by beam sweeping to fluences so that considerable track overlap occurs. Two different irradiation geometries have to be applied. The first one is standard, i.e. the thickness t of a specimen is orientated parallel to the beam and the other two dimensions (length e and width b) are orientated perpendicularly to the beam (see Fig. 1), In the second irradiation geometry, the sample is tilted by an angle of 45" so that both t and b subtend an angle of 45" with the beam axis. The length e is still perpendicular to the beam (see Fig. 1). In addition to length and width, the mass density or a physically related quantity has to be measured.

Fig. 1.

scanned ion

| 9o~,~

beam

geometry @

geometry 0

The two irradiation geometries applied in this work to demonstrate the occurrence of ionbeam-induced plastic deformation. The dark bar represents the cross-section (width × thickness) of a thin sample.

Let us assume that compaction or swelling do not occur. Then, ifeffect(ii)exists,the following equations for the relativedimensional changes hold (Klaumtlnzer and Benyagoub, 1991): (Ae/e),

=

(Ablb) I = - - 0 . 5 ( A t / t ) I

(1}

for irradiation geometry 1 (subscript 1) and (Ae/e) a =

tae/e) 2 =

-

2 (Ablb)2 = - 2 (At/t)2

(2)

for irradiation geometry 2 (subscript 2). Consequently, a clear trace of ion-beam-induced plastic deformation is a width shrinkage in geometry 2, which is half of the width growth of geometry 1. VITREOUS

SILICA

In Fig. 2 the relative dimensional changes of high-purity synthetic vitreous silicaare plotted versus fluence d~tfor irradiation with 360-MeV Xe ions below 150 K for the two irradiationgeometries. For the Xe ions the electronicenergy lossSe is about 15 keV/nm, which is well above the threshold of about 4 keV/nm for creation of etchable tracks in vitreous silica.Below lx1013 Xe/cm2 the dimensional changes are independent of the irradiation geometry and due to an isotropiccompaction of vitreous silica.This compaction saturates at lx1013 Xe/cm2 with a m a x i m u m density increase of about 3 % leading to an isotropicshrinkage of the specimen dimensions of about 1%. These findings are quantitatively supported by measurements of the index of refraction,which additionallyindicates a structural steady state above 1013 Xe/cm2. It isobvious from Fig. 2 that above ~t - Ixl013 Xelcm2 the changes in length and width for the two irradiationgeometries obey the equations (1) and (2),respectivelywhen the compaction is taken into account. Hence, ion-beam-induced plasticdeformation occurs in vitreous silica.

PLASTIC DEFORMATION OF AMORPHOUS SOLIDS

93

It can be shown that the deformation rate, A = e -1 de/d(~bt), is a direct measure of the deformation yield per ion (Hou et al., 1990). This quantity is plotted versus Se in Fig. 3. The deformation rate is very small below 2.5 keV/nm whereas above this value A increases linearly with Se. Obviously, for ion-beam-induced plastic deformation there exists an apparent threshold in Se which is less than that for the formation of etchable tracks. This result is not very surprising because the formation of etchable tracks requires a continuous trail of distorted material for a single projectile whereas ion-beaminduced plastic deformation requires only cylindrical symmetry of the distorted regions. The spatial connection of the latter follows automatically by high-fluence irradiation until the steady state is reached. In Fig. 4 the deformation rate A normalized to its low-temperature value Amax after 360-MeV Xe irradiation is plotted versus irradiation temperature T. Obviously, A/Amax decreases with increasing T. In this context it should be noted that 50% track fading occurs in vitreous silica after annealing at 560 K for i h (Fleischer et al., 1975). At this temperature A/Amax has decreased by about a factor of 3 in comparison with its low-temperature value.

t~

vitreoussilica {Synsil) 80K(T(150K

I hi I ~s' I

vitreous silica m 6

/

I

gz

oJ

"g0 ~ t

2

o; .t. 0

2

I ¢*

I 6

I $

r~

I

5

i

10

I

15

electronic energy loss [keV/nm)

fluincll i t [ lOllX//cnll)

Fig. 2.

Fig. 3.

Relative dimensional changes of vitreous silica versus Xe ion fluence (length(o) and width (.) for geometry 1; length (v) and width (v) for geometry 2).

Deformation rate A-- e-lde/d (~t) of vitreous silica at about 100 K as a function of the electronic energy loss.

GLASSY METAL Pd8oSi2o As a test material for a glassy metal the classical metallic glass Pd80Si2o was chosen. This glass has an electrical resistivity of about 8x10-sf~ cm at room temperature. This resistivity is more than 7 orders of magnitude smaller than the adopted threshold value of 2xl03f~cm, which separates track forming from non-track forming solids (Fleischer et al., 1975). In Fig. 5 the relative dimensional changes of Pd80Si20 are plotted versus fluence ~t of irradiation with 285-MeV Kr ions. The irradiation temperature was kept below 100 K. No density change was observed within the error limits of -t- 0.5%. Like vitreous silica, for the two irradiation geometries Pd8oSi20 exhibits above lx1014 Kr/cm2 dimensional changes which obey equation (1) and (2), respectively. The mass density, electrical resistivity, and its temperature coefficient do not change in the high fluence region suggesting that the structure is in a steady state. In Fig. 6 the ratios 2A/P for various projectilesare plotted versus Se. The quantity P denotes the total displacement cross-section for atomic displacements via m o m e n t u m transferring collisions (nuclear energy loss Sn). The ratio 2A/P is a measure for the number of rearranged atoms constituting the dimensional changes per fluence increment relative to the number of atoms, which are displaced via Sn, i.e. the standard mechanism of damage creation in metals (Hou et al., 1990). Obviously, ion-beaminduced plastic deformation is essentially driven in Pd8oSi20 by Se, i.e. by electronic excitations and / or ionizations in the wake of the fast projectiles. After a strong nonlinear rise of 2A/P below Se = 25 keV/nm there is a linear increase of 2A/P above this value. The latter behaviour is rather similar to that of vitreous silica (Fig. 3). Hence, the value Se = 25 keV/nm may be taken as an apparent thresh-

94

S. KLAUM~NZER

1.0

'i

I

I

I

I

i

--15

x o


0.8

$ ~I0

0.6

f

geometry 1

o

OJ,

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"

0.2

/

\

~ v ~

°

&

I I

%

I

I

1

I

50

100

500

I

irrndiat'ion temperature[K)

geometry 2

-5 1

2 4 fluence St (101~Kr/cm 2 )

,ooo

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6

Fig. 4.

Fig. 5.

Deformation rates of SiO2 and Pd80Si20 versus irradiation temperature. The normalization values are Amax = 0.Sx10 -15 cm2 and Amax = 5.5x10 -15 cm 2 for SiO2 and Pd80Si20, respectively.

Relative dimensional changes for Pd80Si2o versus Kr ion fluence (length (o) and width (o) for geometry 1; width (V) for geometry 2).

old, above which the deformation yield per ion becomes very large. This threshold for Pd8oSi2o is by one order of magnitude larger than that for vitreous silica. Whether this finding reflects a fundamental difference between insulators and metals is currently not clear. In Fig. 4 the normalized deformation rate of Pd80Si20 after irradiation with 360-MeV Xe ions and 285MeV Kr ions, respectively, is plotted versus irradiation temperature. Like for vitreous silica, A]Amax decrases monotonically with increasing T. However, the decrease for Pd8oSi2o lies almost completely below room temperature and occurs in the same temperature region in which significant defect annealing occurs (Klaumfinzer and Petry, 1982). It is concluded that both the insulating vitreous silica and the electrically conducting glass PdsoSi2o show ion-beam-induced plastic deformation. Therefore, it is suggestive that particle tracks exist even in glassy Pd8oSi2o but probably anneal out below room temperature (cf. also S. Klaumfinzer et al., 1990). In addition, as can be concluded by a comparison of Figs. 3 and 6, the formation of a continuous latent track in PdsoSi20 probably requires electronic stopping powers more than 20 keV/nm. L

120

I

/

PdaoSi2o T<50K

v

~00 o

o: e0 60

I

/

/

•-'2 /*0

Fig. 6.

E

Deformation rate of Pd80Si20 normalized to the total displacement cross-section P as a function of the energy loss Se.

o 20

10 20 30 LO electronic energy toss [keVInm)

PLASTIC DEFORMATION OF AMORPHOUS SOLIDS

UNIVERSALITY

95

AND M O D E L

Extensive irradiation experiments have revealed that ion-beam-induced plastic deformation occurs probably in all amorphous materials (S. Klaumcmzer et al., 1989b; S. Klaum~tnzer, 1989). However, it is completely absent in crystallinematerials.The deformation rate varied from 0.8 × 10-15 cm2 for vitreous silicato 15.3 × 10-15 cm2 for glassy Fe32Ni36CrI4PI2B6. N o correlationsbetween A and the electricalresistivityand the elasticmoduli exist,although the lattertwo quantitiesare considered to be of some importance for track formation (Fleischeret aL, 1975). A rough correlation seems to exist between A and the glass transition temperature Tg; the higher Tg is the smaller is A. Thus, due to its high glass transition temperature of about 1500-K, vitreous silicahas the smallest deformation rate ever measured. A better relationexistsbetween A and the freevolume of a glass.This finding corroborates the absence of ion-beam-induced plasticdeformation in crystalsbecause the freevolume is nil in these materials. Obviously, the more looselypacked structure of the amorphous materials allows irreversible atomic relaxation processes,which do not existin crystals. Recently, a model has been devised which accounts semi-quantitatively for all experimental findings (S. Klaumttnzer et al., 1989b; S. Klaumttnzer, 1969). This model assumes that a high transient shear stress arises around an ion'strajectoryfrom a short-time (a few femtoseconds) Coulomb explosion. It should be noted that the distinctionbetween conductors and insulatorson a time scale of femtoseconds is meaningless because m a n y electronsare in excited statesin the track core.Because of ~liquid-like" cellsin all amorphous materials (Grest and Cohen, 1981) irreversiblestructuralrearrangements will appear, which ultimately lead to plastic deformation. The expression 'liquid-likecells"means that there are structural regions in which the atoms can extremely rapidly (~ 10-13s)and irreversibly(final configuration has almost the same energy than the previous one) rearrange under the action of a shear stress.In fact,a calculationof the concentration of liquid-likecells(= shear sites)on the basis of the free-volume theory (Grest and Cohen, 1981) explains the variation of the deformation rate during 360M e V Xe irradiationbelow 50 K in various (Fe, Ni)l-xBx alloysalthough P and Se are constant (Fig. 7).

15

!1o

( Fe.Ni11.1Bx

Fig. 7.

,=

I

5 10 concentrntion of shear sites nollO"~1

"

15

Variation of the deformation rate of various (Fe, Ni)l.x Bx alloys for 360MeV Xe irradiation below 50 K as a function of the concentration of shear sites. The full line corresponds t ? an effective track radius of about 24 A.

SUMMARY In summary, there is evidence that the creation of overlapping well-aligned particle tracks by heavy ion irradiation leads to macroscopically visible plastic deformation in amorphous materials, i.e. the sample dimensions perpendicular to the beam grow whereas the dimension parallel to the beam shrinks. This effect occurs in insulating as well as in metallic glasses. Therefore, the detection of particle track effects is primarily not a matter of insulating or metallic behaviour of the target but rather depends on the possibility whether the electronically triggered atomic rearrangements can escape a backward relaxation in order to yield measurable effects. The available data strongly suggest that particle tracks can be detected in metallic glasses at low temperatures. It should be noted that discontinuous particle tracks have been identified quite recently by transmission electron microscopy in crystalline Ni-Zr compounds (Barbu et al., 1990; Barbu et al., 1991).

96

S. KLAUMI~NZER

REFERENCES Barbu, A., A. Dunlop, D. Lesueur, R.S. Averback, R. Spohr and J. Vetter (1990). First transmission electron microscopy observation of latent tracks in a metallic compound. 15. Int. Conf. on Particle Tracks in Solids, Marburg, Sept. 3-7.These proceedings. Barbu, A., A. Dunlop, D. Lesueur and R.S. Averback (1991). Latent tracks do existin metallic materials. Submitted to Europhysics Letters. Benyagoub, A., S. L6ffler,M. Rammensee and S. KlaumCinzer (1989). Ion-beam-induced plasticdeformatSon in vitreous silica.Rad. Eft. Def. Solids, 11.0,217-219. Fleischer, R.L., P.B. Price and R.M. Walker (1975). Nuclear Tracks in Solids. University of California Press, Berkeley. Grest, G.S. and M.H. Cohen (1981). Liquids, glasses and the glass transition:a free-volume approach.

Adv. Chem. Phys., 48,455-525. Hou, M.D., S. Klaum~inzer and G. Schumacher (1987). Inelastic deformation of metallic glasses induced by the electronic e n e r ~ loss of fast ions. Nucl. Instr. Meth., B19/20, 16-20. Hou, M.D., S. Klaum~inzer andS. Schumacher (1990). Dimensional c ~ of metallic glasses during bombardment with fast heavy ions. Phys. Rev. B41, 1144-1157. Klaum~inzer, S. (1989). Ion-beam-induced plastic deformation: a universal phenomenon in glasses. Rad. Eft. Def. Solids, 110, 79-83. Klaumttnser, S. and W. P'e-~'y(1982). Electron radiation damage in amorphous PdsoSi20 at 4.6 K. Phys. Lett., 87A, 314-316. Klaumttnzer, $.-'a'nciG. Schumacher (1983). Dramatic growth of glassy Pd80Si20 during heavy-ion irradiation. Phys. Rev. Lett., 51, 1987-1990. Klaumlinzer, ~., G. Schumac-~er, M.D. Hou andG. Vogl (1985). Radiation-induced growth of metallic glasses. In: Rapidly Quenched Metals (S. Steeb and IT. Warlimont, ed.) Vol. I, pp. 895-898. North-Holland, Amsterdam. Klaumiinzer, S., M.D. Hou and G. Schumacher (1986). Coulomb explosions in a metallic glass due to the passage of fast heavy ions? Phys. Rev. Lett., ~ 850-853. Klaumfmzer, S., Li Changlin, S. L6ffler, M. Rammensee and G. Schumacher (1989a). Plastic flow of vitreous silica and Pyrex during bombardment with fast heavy ions. Nucl. Instr. Meth., B39,665669. Klaumfinzer, S., Li Changlin, S. LSffier, M. Rammensee, G. Schumacher and H.C. Neitzert (1989b). Ion-beam-induced plastic deformation: a universal behaviour of amorphous solids. Rad. Eft. Def. Solids, 108, 131-135. Klaumttnzer, S., W. Petry and G. Schumacher (1990). A search for particle tracks in the metallic glass Pd80Si2o. 15. Int. Conf. on Particle Tracks in Solids, Marburg, Sept. 3-7. These proceedings. Klaumiinzer, S. and A. Benyagoub (1991). Phenomenology of plastic flow of amorphous solids induced by heavy-ion bombardment. Phys. Rev. B, in print.