Ultramicroscopy 3 (1978) 215-226 0 North-Holland Publishing Company

DISCUSSION ON THE LIMITATIONS OF “IN SITU” DEFORMATION EXPERIMENTS IN A HIGH VOLTAGE ELECTRON MICROSCOPE

J.L. MARTIN and L.P. KUBIN Lnboratoire d’optique Electronique du C.N.R.S., 29 rue Jeame Marvig, B.P. 4347, 31055 Toulouse Cedex. France

Received 23 January 1978

Radiation damage as well as surface effects are two possible limitations of the “in situ” straining experiment in a high voltage electron microscope. The optimum experimental conditions and a few approximate criteria to be fulfilled are described, using the data presently available. In these criteria are involved the operating conditions of the microscope, the temperature, the geometry and properties of the material investigated.

1. Introduction

The increasing number of deformation experiments performed “in situ” in the electron microscope and some of their spectacular results should not hide their limitations. The aim of the present paper is to review the data available on defect and surface properties in the HVEM.

This data is used to evaluate critically the reliability of deformation experiments and to determine opti- mum conditions for which the in situ experiment can yield information about the bulk properties. Indeed, the high penetration achievable with high energy elec- trons allows direct observation of defect movements in “thick foils”. These defects can interact with other perturbations (e.g. various defects and precipitates) besides the free surfaces. On the other hand, the energy of the electrons can be sufficient to induce radiation damage: this may lead to undesirable dislocation pin- ning or climb.

We discuss first the depths of penetration which can be achieved without production of radiation dam- age. If larger thicknesses are needed (e.g. because of surface effects), point defect production cannot be avoided; we list the different radiation regimes which are expected during deformation, under these condi- tions. In the last part we estimate the various types of interactions between the foil surface and a stationary or mobile dislocation.

215

2. Radiation effects

Observation conditions at the threshold voltage for radiation damage will be examined first, including the average observable thickness which can be achieved. Defdrmation experiments under irradiation conditions will then be described.

2.1. Threshold voltage for radiation damage

There is no obvious relation between the displace- ment energy which determines the threshold voltage and a simple physical property of the material [ 11. ln addition, single crystals exhibit a large orientation dependence of the threshold voltage due to several dif- ferent processes of atomic displacements [2]. For example, the displacement energy for copper is 27 eV in the ( 100) direction and 18 eV in the (110) direction which corresponds to 390 and 485 kV, respectively, for the threshold voltage. Refs. [l] and [3] review the results in this field.

However, a minimum energy Ei, necessary to induce atomic displacements, can be defined. Experimental values obtained by radiation damage studies carried out in the electron microscope, and by conventional methods, are listed in [4].

It is likely that for certain localized orientations E0 can be much lower than the averages which are usually considered [2,4].

216 J.L. Martin. L.P. Kubin /In situ HVEM deformation experiments

One may also observe subthreshold radiation damage and transmitted fluxes, respectively, and x the foil for various reasons. thickness, we can write

(1) At high temperatures the energy EO is not well defined because of thermal fluctuations [5].

(2) There may be “weak spots” in the crystal, close to a defect or due to the preferential displacement of impurities of low atomic weight [6]. Thts effect may be important in in situ deformation experiments on alloys. In this.case a preliminary study of the thres- hold voltages may be necessary because of the scarcity of the experimental results.

91=doex~-w, (1)

provided that it is possible to define some average absorption coefficient /.L The depth of penetration, 6, can be defined, as in Humphrey’s work [7], as the value of x corresponding to a predetermined value of the ratio &/@J~.

(3) In the same way, light elements of the contami- nation layer, or impurities in the atmosphere surround- ing the specimen, may be implanted into the foil.

Fig. 1 represents, as a function of the atomic num- ber, the threshold values deduced from the displace- ment energy EO, for the most commonly investigated elements. As a whole these voltages increase with increasing atomic weight. For a given atomic weight the body-centered cubic metals have the highest thres- hold values, and the hexagonal metals the lowest ones.

Measurements on our 3 MV microscope, operating at 1 MV, show that under the routine experimental conditions for in situ work, $J~/& - lo-‘, with @o - 3.5 X 10’s e cm-’ s-’ for a photographic plate, and do - 2 X 10 ” e cm-’ s-l for video-recording with an image intensifier. Thus, the image intensifier can be used either to decrease the incident flux (by a factor of about 15) or to increase the observable thickness (by a factor of about 1.6).

Actually, the situation is much more complicated because of the strong orientation dependence of the depth of penetration. Each Bloch wave excited in the crystal has its own absorption coefficient; its relative weight with respect to other Bloc11 waves depends on the crystal orientation and accelerating voltage. As a result, for a given material and given accelerating volt- age, there are specific orientations of good transmissive power [8,13]. Following Hashimoto [ 141, in aluminium at 300 kV, the same transmissive power is achieved with a foil 2.9 pm thick in kinematic orientation and with a foil 10 pm thick in -{ 111) Bragg reflexion.

.2.2. Effective penetration of the electrons

This quantity has been determined experimentally in most of the commonly used materials, and rather good agreement with theoretical estimates [7-121 has been obtained. From these results the following con- clusions can be made.

Different definitions of the depth of penetration are used and this leads to an apparent dispersion of the experimental results. If Go and $I are the incident

4 UkV

..1500

. . 1000

0 f.c c a bC.C a h.c.p

Nb. do

x Cd . . 500

V. CONI x Pb

.=qu, .Sn

T ; Fe Al

X4S.l 0 M9 20 40 60 ep 2

Fig: 1. Threshold voltage of the most commonly investigated elements as a function of atomic number 2.

In what follows we sketch very roughly some val- ues for the depths of penetration. These values refer

’ 6100kV /rm -1.5

I Al

.l

-0.5

0 ,a0 2 J Fig. 2. Average values of the depths of penetration at 100 kV as a function of atomic number 2 (see section 2.2).

J.L. Martin, L.P. Ku bin /In situ H VEM deformation experiments 211

to kinematic orientations, for orientations correspond- on the type of contrast needed. Letters A to H refer ing to a good transmissive power of the electrons, the to minimum thicknesses necessary for various in situ observable thicknesses can be about three times larger experiments. These values have been determined exper- and their dependence upon accelerating voltage can be imentally and are connected to the various surface complex [ 131. effects discussed in section 3.

Two kinds of absorption processes are usually con- sidered: electron-phonon interactions give top a 2’ dependence [ 151, Z being the atomic number. For light elements, such as aluminium, delocalized inelastic processes are probably responsible for most of the absorption [9].

This estimate is rather pessimistic since eq. (3) yields a ratio 6 1 Mev/6 roekv - 3, whereas more sophis- ticated descriptions together with experimental results indicate that this ratio is between 3 and 5. Further- more, as mentioned above, some orientations exhibit much higher values of 6.

Fig. 2 plots average values of 6 at 100 kV as a func- tion of the atomic number. For light elements the depth of penetration is close to that of aluminium @Al 100 kV - 1.3 pm). For heavier elements 6 can be written, using eq. (l), as

As a rule, however, the light elements exhibit the highest penetration depths at the threshold voltage, despite their low threshold voltages. This can be explained by a saturation of the depth of penetration as the voltage increases.

It therefore seems possible to deform light elements in situ at voltages ranging between 200 and 400 kV, provided the observable thickness is sufficient (see section 3).

6 =A~10g(102),

where &,/#r = 102. In fig. 2 the value of A has been determined by fit-

ting the curve with commonly accepted values of the depth of penetration at 100 kV. These values of 6 refer to room temperature. At low temperatures, the decrease in electron-phonon interactions induces an increase of 6, which depends on the Debye tempera- ture of the material considered, and which can be as much as twice between 300 and 10 K [ 16,171.

2.3. Penetration at the threshold voltage

It has been shown [18,19] that the coefficient A in eq. (2) is proportional to (c/v)~, where v is the veloc- ity of the electrons. The gain in effective penetration at high voltages can be estimated using the well-known relationship between electron velocity and accelerating voltages (see [20] for instance):

3x2 _ 1)1’2, with x = 1 + 1.957 x 1o-6 v, (3)

where the accelerating voltage, V, is expressed in volts. Fig. 3 is a plot of the estimated effective penetra-

tion at the threshold voltage for various materials, com- puted with relations (2) and (3). The full curve refers to microphotography under the average conditions defined above. The dotted curve corresponds to video recording. These values are orders of magnitude and strongly depend on the orientation of the crystal and

2.4. Experiments above the threshold voltage

In-situ experiments may be performed under such conditions for various reasons.

Fig. 3. Depth of penetration, 6, at the threshold voltage as a function of atomic number and minimum thicknesses required for some in situ experiments (A to H). - Photographic plate;. . . image intensifier. 6 = kinematic orientation, 6’ - 36 = orientation of optimum penetration, A - Subgrain properties, creep of light elements [40,54,67], B - Dynamic dislocation behaviour in Al, Fe-S [ 541, Work-hardening cell formation in Al, Fe-S [ 541, C - Dislocation glide in MO, Nb, Ta at low temperatures, [ 721, D - Dislocation tangles in W [ 771, E - Martensitic transfor- mation in CU-Al [ 541, F - Dislocation density in Al [ 541, G - Dislocation density in Fe [ 541, H - Annealing of tetra- hedrainAu [71].

218 J.L. Martin, L.P. Kubbz /In situ HVEM deformation experiments

(1) To investigate the interaction of moving disloca- tions with radiation defects: dislocation channeling. [21,22], hardening or softening under irradiation [23].

2.4.2. High temperature regimes

(2) To achieve larger penetrations at higher voltages. The electron flux is adjusted as low as possible so as to reduce the production rate of point defects [24]. In such conditions, point defect clusters/are usually too small to be visible, and their influence is observed indirectIy. Thus, we have deformed aluminium at 50 K during observation at 600 keV with an image intensi- fier: dislocation motion is completely impeded after a few seconds.

In the following, we describe the various radiation regimes which may occur in a thin foil, compared to the bulk material and list a few criteria characterising an in situ experiment with respect to these regimes.

Interstitials are now always mobile, while the possi- bility for vacancies to be mobile depends on the tem- perature considered. The mobile defects can be attracted by three kinds of sinks. (i) External sinks, namely the free surfaces which exert an image force. (ii) Internal sinks, i.e. the linear and extended defects already pres- ent in the crystal and dislocation loops and clusters created during irradiation. These interactions are usu- ally evaluated in terms of size effects. (iii) The Frenkel pairs can also annihilate by mutual recombination. For each type of sink is thus defined a strength, i.e. the magnitude of its effective capture distance for each type of point defect. According to the experi-

2.4.1. Low temperature irradiation regime The foil and the bulk material will behave in the

same way since the point defects created have a low mobility. The upper limit of this range is the tempera- ture at which interstitial annealing occurs (beginning of stage 1). For all the face-centered cubic and body- centered cubic metals (except iron), this temperature is below that of liquid nitrogen. For iron and hexago- nal metals, it is between 77 and 110 K approximately P51.

In this case, the defect production rate is /3. SINK STRENGTH l~m-~l

dc/dt = Ra@ , (4)

where Cp is the electron flux, u the displacement cross section of the order of a few ten barns for high energy electrons, and (1 - R) the recombination rate of Fren- kel pairs. Accurate estimates of the cross sections are available ([26], and [27] for light elements). In alumi- nium, for instance, observed at 1 MeV, with a flux of 2X1017ecm-2s~‘andwithR-1,12ppmofFren- kel pairs are created per second.

!mxl

1500

Near and above the upper limit of the temperature range considered here, it is often assumed that the recombination rate is 90% (R = 0.1) [28] ; as described below, however, the situation is more complicated. At low temperatures values of R can be determined as a a function of flux, using the description given by Wol- lenberger [29].

I MUTUAL RECOMBINATION I

I I I bl 100 IO9 10’0 IO” 40’2

8, SINK STRENGTH ~,R-~I

Then, using eq. (4), it is possible to determine the production rate of point defects which can act as dis- location pinning points.

Fig. 4. Various regimes of equilibrium point defect concentra- tion in a Ni foil under irradiation. After [ 301. Foil thickness 0.5 pm. Dashed lines refer to equal fractional loss of point defects. (a) Influence of generation rate, G at 450°C; (b) influ- ence of temperature, G = lo-’ dpa/s. (Courtesy, J. Nucl. Mater.)

J.L. Maitin, L.P. Kubin /In situ HVEM deformation experiments 219

mental conditions (foil thickness, rate of defect pro- duction, temperature, internal sink density), each of the three kinds of sinks can dictate the defect concen- trations and three corresponding irradiation regimes occur. This is illustrated in fig. 4a,b, after Yoo and Mansur [30], where the fractional concentration losses due to the three types of sinks are indicated for various experimental conditions and in a temperature range where vacancy mobility has to be considered. At temperatures where vacancies are not mobile, the sink mechanisms affect only interstitials but in a simi- lar way.

We describe now the three regimes of point defect losses; the most troublesome during an in situ experi- ment is of course the one where point defects diffuse towards dislocations inducing spurious motion by climb.

(a) Pair recombination domain. The interaction of point defects with free surfaces is not considered here and point defect concentrations can be estimated using an approach of the chemical kinetics type. These treat- ments generally include the interaction with internal sinks [3 l-331. Schematically, at average temperatures the recombination of Frenkel pairs is the main process and only a small fraction of the point defect density interacts with dislocations. The situation is reversed at higher temperatures and the transition between both regimes corresponds to the relation

E = (A’ + uoy ,

with K = production rate of the defects; yv = vacancy mobility; s = sink density; h = jump distance of a vacancy (lo-” cm); and v. = vacancy concentration at thermal equilibrium.

The sink density is here the density of dislocations under irradiation and deformation conditions plus the impurity concentration if necessary [33]. Its value is usually assumed to range from 10” to 10” cm”‘. To use this criterion, the migration energy of vacancies is needed; values are given in refs. [28,33,34].

For instance, for a copper specimen in an in situ experiment with a 10” e cm-’ se1 flux of 1 MeV elec- trons, the production rate of point defects is 10M6 s-’ (u = 90 barns). If the equilibrium vacancy concentra- tions are calculated from the estimates of Seeger and Mehrer [35], with a migration energy of 1 eV for vacancies, the transition temperature between the two

regimes is of the order of 700 K. (b) Thin foil behaviour. In a thin film and under

favourable experimental conditions, preferential migra- tion of interstitials and vacancies (when mobile) towards the free surfaces can occur. A denuded zone is thus formed in which mobile defect concentrations are depleted [30,32,33]. Its thickness, z, may be of ’ the order of a few thousands angstroms.

When vacancies are not mobile, the transition between thin foil and bulk behaviour can be evaluated from the estimates of Bourret [33], Makin [28] and Goringe [32] : z is proportional to

h[+ exp( -s)]“4 ,

E,i being the migration energy of the interstitial and h the preference factor of the point defects between internal sinks and surface sinks. This thickness z can be appreciably reduced if the material contains impu- rities in strong interaction with point defects [33].

This influence of thin foil effects can be evaluated using a dimensionless surface diffusion parameter P introduced by Goringe [32] : P Q: (z/h)‘, where h is the thickness of the specimen. Defect concentrations have been calculated as a function of this quantity. It appears that for P 5 0.1, the material behaves as a bulk, while surface effects are predominant for P 2 1.

For higher temperatures, when vacancy mobility has to be considered, the surface effects influence the defect concentrations within a depth z which is now dictated by the migration energy of the vacancies, E,,,,, in the same way as described above. In this domain, as in the preceding one, it appears that it is important, during an in situ experiment at high temperatures, to determine whether vacancies are mobile or not. This can be established for a large variety of materials with help of the results of Kiritani et al. [36] on radiation damage effects in the HVEM.

(c) Radiation-induced climb of dislocations. This effect is to be avolded if possible &uing in situ experi- ments and corresponds to the regime where the major losses in point defect concentrations arise from elastic interaction with dislocations. Experimentally these interactions are clearly evidenced during irradiation, mainly when interstitials only are mobile: formation of denuded zones around dislocations and subbound- aries [37,38] dislocation climb and helix formation

220 J.L. Martin, L.P. Kubin /In situ HVEM deformation experiments

[37,39]. For instance, in the case of the 01-3 at.% Al alloy, at 473 K, the climb velocity is close to 6 W. s-l under irradiation with 1 MeV electrons and a flux of 2 X 10” e cm-’ s-’ [37]. Since this velocity is a linear function of flux, at low fluxes, it seems possible to evaluate spurious climb velocities in a deformation experiment by changing the flux values [40], provided that there is no associated temperature change, or using the data on loop annealing kinetics (for a review see [38], also [al ,421). Weak-beam examination of the specimens after deformation may also be useful [43]7

The various mechanisms involved during dislocation climb under such conditions have been semi-quantita- tively evaluated in simple situations [44,45]. It appears that an important parameter of the climb velocity is the ratio of the mean-free path of the point defect along the dislocation to the average distance of jogs at equilibrium [45]. According to the temperature, either the jogs or the whole dislocation act as a perfect sink for point defects. (A perfect sink is able to main- tain an equilibrium concentration of point defects in its vicinity, i.e. it does not saturate.)

At last, when both interstitials and vacancies are mobile, the problem is again more complicated, but it seems that the mutual recombination of point defects at the sinks may limit the spurious effects of irradia- tion [46,47]. In summary, we notice that the incidence of dislocation-radiation defect interactions during straining experiments is difficult to evaluate theoreti- cally, but can be detected during or after the experi- ments.

2.5. Radiation effects: conclusion

For a given in situ deformation experiment it seems possible to determine the best values of the parameters involved in an approximate but simple way. These parameters are the thickness, the accelerating voltage, the temperature and, when possible, the material.

When point defect creation cannot be avoided during deformation, because large thicknesses are required, the behaviour of mobile dislocations with respect to these point defects can be only roughly predicted. Some irradiation conditions are to be avoided; they correspond to temperatures at which vacancies are immobile and interstitials diffuse prefer- entially towards dislocations.

Assuming that some acceptable experimental con- ditions have been achieved, it is necessary to check that the optimum thickness is high enough to mini- mize the interactions of dislocations with the foil sur- faces. This point is discussed below.

3. Surface effects

Two main effects govern the interaction between a dislocation and a foil surface: the image force and a pinning mechanism at the dislocation ends. The relative importance of these two effects during in situ experi- ments is now examined.

3.1. Image forces

3.1.1. Definition and estimation A dislocation next to surface interacts with it: its

stress field is different from that in an infinite crystal since it has zero value at the surface. It can be evaluated in the following way.

l In the simple case of a screw dislocation lying parallel to a free surface bounding the crystal in vacu- um, the problem can be solved exactly by introducing an image dislocation, symmetrically placed with respect to the surface, of opposite Burgers vector, in an iden- tical crystal. Under these conditions, the dislocation is attracted to the surface by a force [48] :

F = Gb2/4nl , (6)

where G = shear modulus, b‘= Burgers vector, and I= distance between the surface and the dislocation.

l For an edge dislocation under the same conditions, the superposition of the image annihilates all the stress components at the surface, except one. Two image dislocations are generally necessary [SO].

l For a linear dislocation of mixed character meet- ing a free surface at an arbitrary angle, the stress field is also known: it includes the image stress field plus another one which has been computed exactly [Sl].

l For non-linear dislocations, the problem is very intricate and usually only the image stress field is con- sidered [49].

The thin foil situation has also been considered [50,52]. Quite often an oxide layer at the foil surfaces has to be taken into account which leads to the inter- action of the dislocation with the two surfaces bound- ing the crystal, the oxide layer and the vacuum [48].

J. L. Martin, L.P. Kubin /In situ HVEMdeformation experiments 221

By analogy with relation (6), the dimensionless parameter h~/Gb (7 = flow stress of the material, h = thickness of the foil) should be as high as possible in order to minimize the influence of image forces.

3.1.2. Consequences (a) Dislocation density in the foil. During thin foil

preparation a certain number of the dislocation seg- ments near the surface will move out. In the same way, during in situ deformation the annihilation rate of dis- location will be higher than in the bulk material because of the losses at the surface. According to the rule 6 = ~,,,bF(t is the strain rate of a crystal in which disloca- tions of density, P,,, , move with an average velocity V), V is larger in the thin foil, as well as the applied stress for a given strain-rate.

As an example, in a stainless steel foil deformed in situ at 100 kV [53], the stresses reach a value of 130 MN/m* as estimated from the radius of curvature of the dislocations. This corresponds to stresses necessary to deform a bulk sample in the work-hardened state.

Since the very first observations of defects using a high voltage electron microscope, dislocation densities have been measured as a function of the foil thickness for various materials. In aluminium samples, for instance (purity 99.99%) after a 6% elongation and an 8% thickness reduction by rolling, the dislocation den- sity is constant for thicknesses larger than 0.8 pm. .W’hen dislocation cells are formed (after 13% straining), the critical thickness is 0.2 Pm [ 541. In pure iron sam- ples, after a 6% deformation at -1 10°C, the disloca- tion density does not depend on foil thickness. In a copper-silica alloy deformed in situ at 1 MV, the dis- location density in the foil is 1Oa cm-* because of the particles and the rupture strain in the microscope is much larger than for pure copper in the same condi- tions [SS].

As a rule the dislocation substructure in the foil will be similar to that of the bulk sample, provided that the mean free-path between defects strongly interacting with the moving dislocations is smaller than the foil thickness:

l when frictional forces are high: body-centered cubic metals at low temperatures, semiconductors, etc.;

l when the dislocations are pinned such as in im- pure metals or alloys exhibiting the Cottrell effect, the Suzuki effect, short-range ordering, or reinforced by precipitates.

(b) Position and shape of defects in the foil. During straining both the position and shape of the dislocation depend on the applied stress and the interaction forces with the free surfaces. The corresponding dislocation profile has never been computed. An insight to this problem can however be provided by studying the position of a dislocation into the absence of applied stress. This position is the net result of several inter- actions: the interaction force of the dislocation and its image; the line tension (which is minimum in screw orientation); and the force attracting the dislocation towards its position of shortest length in the foil. This problem has been solved, taking into account elastic anisotropy [56,57], and it has thus been possible to interpret weak-beam images of dislocations in the alloy Cu-10 at.% Al [57,58].

Perfect dislocations: The equilibrium positions have been computed for this alloy as a function of the angle between the Burgers vector and the foil plane. The slip plane is assumed to be perpendicular to the surfaces. The dislocation deviates from the screw orientation all the more as its Burgers vector is parallel to the foil.

-E- 12 3 L 56 9

1 2 3 5 6’

Fig. 5. Equilibrium configurations of partial dislocations in Cu-10 at.% Al. Anisotropic calculation. 7 = 11.5 erg/cm* (after [57]). (a) Geometry;(b) foil thickness SO nm; (c) 100 nm. (Courtesy, Phys. Status Solidi.)

222 J.L. Martin, L.P. Kubin /In situ HVEM deformation experiments

These results are independent of the foil thickness and are valid for dislocations the length of which is mu& larger than the width of splitting.

Imperfect dislocations: The equilibrium shape of the dislocation depends on (i) the interaction of each partial with its image, (ii) the interaction between the two partials, and (iii) the stacking fault energy. The first effect seems to be dominant. For the alloy studied here, it was found that

l the average direction of the ribbon deviates from the foil normal depending on the total Burgers vector orientation; as a rule each partial rotates towards its screw orientation, as close to it as possible, which leads to a trapezoidal splitting;

l dislocations with a strong edge character are dis- sociated at both surfaces, especially when they are long, while screw dislocations exhibit a constriction at one of the surfaces. Consequently, the latter are often observed to cross-slip near that surface [53,58] (see fig. 5).

In an alloy the frictional forces may alter the above computations: in Cu-10 at.% Al the image forces affect the dislocation configurations within 70 nm from the surface at room temperature. In a pure metal the corresponding distance would be lo4 b at the same temperature [58].

3.2. Dislocation pinning or drag at foil surfaces

3.2.1. The pinning effect Apart from the purely elastic interactions reported

above, another effect has to be considered: at the sur- face the dislocation creates a step of height b - n (n = unit vector normal to the foil, see fig. 6a), which

. =fJ 9 c/

Fig. 6. Slip steps at the surface of a cadmium single crystal (after [62]). (a) Free surface; (b) Detachment of a superficial layer;(c) Rupture of the layer. p and n are the slip plane and foil normals, respectively.

involves an energy y (b * n)/sin Q, per unit length of step [48] (7 = surface energy, Cp = angle between foil plane and slip plane). In other words, during slip the end point of the dislocation at a free surface under- goes a frictional force

(7)

Some experimental values of y can be found in [59].

3.2.2. Estimate of the frictional force According to the evaluation of Frank and Stroh

[60] the surface energy at the slip step is close to y - E Cb, with E 5 10-r and the frictional force can be expressed as a function of the line tension T - Gb2/2:

b-n T Ff= 2e--

b sin @ ’ (8)

This force depends on the material through T and b and on the geometry of the active glide systems: the geometrical factor f = (b * n)/(b sin @) is such that 0 G If I < 1. The case f = 0 corresponds to a Burgers vector parallel to the foil plane.

If the surface is covered by an oxide or contamina- tion layer, the frictional force is more difficult to esti- mate (fig. 6b,c) [61].

Under these conditions the dynamic equilibrium shape of the dislocation near the foil surface is the net result of the force Ff, of the line tension, of the applied shear stress, and of the image forces. The only quan- titative estimate known to us applies to the profile of a dislocation loop which glides in a cadmium single crystal which was studied by X-ray topography [62]. Image forces have been neglected here because of the sample thickness (h - 100 pm).

(a) Parallel surfaces (see fig. 7) [62]. l When the force Ff is smaller than the line tension,

* FF FT T

II h ‘tb

T

Fig. 7. Bending of a dislocation in a thin foil (after [62]).

J.L. Martin, L.P. Kubin /In situ HVEMdeforrnation experiments 223

the dislocation is pinned at the surface and bends un- der the applied stress. When the resolved shear stress is larger than r, = WJGh, the dislocation drags its ends along the surfaces. In the present case, T, = 5 X lo-’ MN/m2.

l When Fr is larger than the line tension the dislo- cation ends are futed. For stresses above the critical value 71, = 2T/bh the dislocation loop is composed of a half circle linked at its end points by two straight segments running along the surface. In the present case, 7: = 3 X 10S2 MN/m2 because of a superficial layer due to the polishing treatment.

(b) Wedge crystal [62]. The force Ft is the same as above, but tne drag force on the dislocation ends depends on the angle f of the intersections of the foil surfaces and the considered slip plane and also on the distance x between the loop and the edge of the hole.

l When Ff < T sin t, i.e. when { is large enough for a given crystal, the dislocation loop is attracted by the hole where it disappears irrespective of the values of x and of the applied stress. For a cadmium crystal with free surfaces, the corresponding critical value for { is 1 l”5.

0 When T sin 5 < Ff < T, the dislocation stays at an equilibrium position x0, given by

I

xo =~-&[~cosJl -($jsinc]. (9)

For a given stress, if the dislocation is somewhere between x0 and the hole edge, it remains there with an equilibrium curvature. If it is beyond x0, it drags its end points down to the x0 position.

l When Ff > T, the dislocation reaches an equilib- rium position at

x= Tcosr zi$

by dragging two segments along the surfaces. (c) Dislocation pile-up in a wedge crystal [62].

Using a similar method, the equilibrium positions of several dislocations emitted by the same source have been computed and compared with experiment. An order of magnitude can be obtained for the quantity Ft/T which determines the type of behaviour of the dislocation ends at the foil surfaces. In the present case, Ft/T - 0.6, which indicates a strong pinning effect, i.e. a superficial layer again.

Similar estimations and measurements would be helpful for different materials and thinner foils, taking image forces into account.

3.3. Discussion

In the light of the various types of dislocation-foil surface interactions, the choice of shape and geometry of the specimen should be guided by the following criteria.

l The microsample should have an uniform thick- ness because of the interaction of dislocations and wedges.

l For the choice of the tensile axis and foil normal of a single crystal, the preceding results indicate that the S&mid law is no longer valid for a flat and thin specimen. The active glide system in this case must fulfil several requirements: (1) a resolved shear stress different from zero; (2) a glide step at the surface as narrow as possible; and (3) an easy activation of sources near or at the surface. Points (1) and (2) can be satisfied. Surface multiplication is a frequent phe- nomenon [63,64], but is not explained, up to now, in terms of image forces. Because of the lack of results in this field, one can only refer to the geometries which have been experimentally tested [65].

l The strain given by a dislocation loop expanding inside a thin foil is proportional to the area of slip plane enclosed between the foil surfaces. In other words, for a given tensile axis the experimental work hardening rate also depends on foil orientation through the active slip plane [65,66].

l Obviously, the foil thickness should be as large as possible. The minimum required thicknesses have been mentioned in section 3.1.2; some of them require observation voltages larger than the threshold voltages, and in this case one has to deal with different radiation effects. To choose the best observation conditions, we have plotted on the curve of the observable thicknesses at the threshold voltage (fig. 3), the minimum required thickness for the in situ study of a certain number of phenomena. To study for instance the cell formation during an in situ creep test in aluminium or in an alu- minium alloy, several independent experiments have shown that a thickness of at least 3 pm is necessary to avoid surface effects [54,40,67] ; this necessitates volt- ages higher than the threshold voltage.

224 J.L. Martin, L.P. Kub in/i h situ H VEM deformation experiments

- 16lmm -

1 t

1 h- ---2.?lmm - ----I

-

Fig. 8. Distribution of local flow stresses over the cross section of a Cu tensile specimen (after [ 731).

. At last, the plastic deformation of the external layers of a cylindrical copper single crystal has been studied by complementary methods [68,73]. By chem- ically machining the sample and comparing the flow stress measured for each cross section one can compute the flow stress of the surface layer. Fig. 8 shows that it increases from the outside to the inside within a 200 pm thickness, then becomes constant. In addition, by Berg-Barret observations and by dislocation pinning under load, it is shown that defect configurations exhibit a larger work hardening inside the sample, after deformation experiments at 78 K.

Since the observed thicknesses in electron micro- scopy are much smaller than 200 pm, work-hardened states will not easily be achieved during in situ experi- ments. Nevertheless such a state can be reached in a conventional deformation test, and the microsample machined out of the strained sample with a parallel tensile axis [67].

4. Conclusion

We have attempted to estimate the effects of the two principal hazards of in situ dynamic experiments: radiation damage and surface effects. In the light of

theoretical estimates and of some related experiments the influence of each effect has been approximately evaluated. Simple criteria define the conditions in which they can or cannot be troublesome. These cri- teria are summarized in figs. 3 and 4. However, in most cases, it is advisable to check the optimum experi- mental conditions before undertaking in situ work.

These are not the only limitations. Others include the difficulty of contrast experiments, uncertainty about the states of stress and strain in the observed area, the local temperature because of the possibility of beam heating, the smoothness of the straining device at a fine scale. The heterogeneity of deformation and the wide variety of simultaneous microscopic defect interactions also have to be taken into account.

Nevertheless, the unique advantage of the method is the possibility of(i) dynamic observation and record- ing of the interaction processes between a dislocation and various types of obstacles, with a good resolution, and (ii) quantitative measurements at the dislocation scale: defect densities and velocities, radii of curvature, waiting times at a given obstacle. As shown by several reviews [69-711 and recent publications [24,72], the method is being used successfully for the investigation of various deformation mechanisms. The subjects of investigation now in progress are the following: in BCC metals and their alloys at low temperatures, the study of the large friction forces acting on the screw disloca- tions which move by the double kink mechanism, of defect mobilities and substructures as a function of temperature, strain and alloying content and of the various slip systems, dislocation multiplication and intersection; similar work is being done in various types of semiconductors; in FCC metals the observation of microscopic glide on planes other than { 111) above room temperature, of the cross slip mechanism involv- ing the Washburn process; in some FCC concentrated alloys, the study of collective dislocation glide and slip band propagation in the presence of the Cottrell effect or short range order; in the field of creep, the study of dynamic properties of subboundaries and grain boundaries and their influence on the creep rate; in biphased alloys (reinforced by particles or fibres) the interaction of defects and strong obstacles with emphasis on the role of interfaces; the interaction between plasticity and irradiation.

Since the artifacts studied above cannot always be evaluated accurately nor evidenced unambiguously,

J.L. Martin, L.P. Kubin /In situ HVEM deformation experiments 225

in situ experiments should not be used alone, but complemented with mechanical testing experiments, conventional observations in electron microscopy, and when possible with other methods of defects observa- tion under load such as the pinning technique [73,74] or dynamic Lang techniques [62,75], or dynamic etch-pit experiments [76a,b].

Acknowledgements

The authors are indebted to Dr. B. Jouffrey for many stimulating discussions and valuable comments on the manuscript. Suggestions by the reviewer, Dr. H. Mughrabi, are acknowledged with thanks.

References

111

121

131 [41

T.E. Mitchell, G. Das and E.A. Kenik, in: Fundamental Aspects of Radiation Damage in Metals, M.T. Robinson and F.W. Young Jr., eds. (USERDA, Conf. 751006 P2, 1975)I 73. M. Wilkens, Radiation damage in crystalline materials, Vth Int. Conf. on HVEM, Kyoto 1977, to be published. P. Lucasson, in: ref. [ 11, 1. 42. K. Urban, in: Microscopic Electronique i Haute Tension, B. Jouffrey and P. Favard, eds. (S.F.M.E., Paris, 1976) p. 164.

151 R.J. Beeler and M.F. Beeler, in: ref. [ 11, I 21. (61 W. Bauer and A. Sosin, J. Appl. Phys. 35 (1964) 703. (71 C.J. Humphreys, Phil. Mag. 25 (1972) 1459. [S] C.J. Humphreys, L.E. Thomas, J.S. LaUy and R.M.

Fisher, Phil. Mag. 23 (1971) 87. [ 91 A. Rocher, D. Thesis, Universite Paris Sud, Centre

d’Orsay (1973).

[ 1 l] C. Roucau, Thesis, Universitd Paul Sabatier, Toulouse (1975).

[lo] A. Rocher, R. Ayroles, A. Mazel, C. Mory and B. Jouf- frey, in: High Voltage Electron Microscopy, P.R. Swann, C.J. Humphreys and M.J. Goringe, eds. (Academic Press, London, 1974) p. 436.

[ 121 C. Roucau and R. Ayroles, Phil. Mag. 34 (1976) 517. [ 131 B. Jouffrey, in: Electron Microscopy and Materials

Science, E. Rued1 and U. Vald&, eds. (Commission of the European Communities, 1973) p. 981.

[ 141 H. Hashimoto, J. Appl. Phys. 35 (1964) 277. [ 151 C.R. Hall and P.B. Hirsch, Proc. Roy. Sot. London A286

(1965) 158. [ 161 H. Boersh, 0. Bostanjoglo and H. Niedrig, Z. Phys. 180

(1964) 407. [ 171 S. Ikeno, Phys. Status Solidi (a) 36 (1976) 317. [18] A. Howie, J. Phys. Sot. Jap. 17 (1962) 118.

[19] H. Yoshioka, J. Phys. Sot. Jap. 12 (1957) 618. [ 201 R.D. Heindenreich, Fundamentals of Electron Micro-

scopy (Wiley Interscience, 1964), p. 119 and 394. [ 211 H. Saka, K. Noda, K. Matsumoto and T. Imura, in: ref.

[4], p. 325. [22] E. Johnson and P.B. Hirsch, Acta Met., to appear. [ 231 L.P. Kubin, F. Louchet, P. Croh and F. Vanoni, in:

Proc. 4th Int. Conf. on the Strength of Metals and Alloys (Nancy, France, 1976) 11 814.

[ 241 D. Caillard and J.L. Martin, in: ref. [23], I 105. [ 251 J.S. Koehler, in: ref. [ 11, I 397. [ 261 O.S. Oen, ORNL 4897-UC34 (1973). [27] W.A. McKinley and H. Feshbach, Phys. Rev. 74 (1948)

1759. [28] M.J. Makin, Jernkont. Ann. 155 (1971) 509. [ 291 H.J. Wollenberger, in: Vacancies and Interstitials in

Metals, A. Seeger, D. Schumacher, W. Schilling and J. Diehl, eds. (North-Holland, Amsterdam, 1970) p. 215.

[30] M.H. Yoo and L.K. Mansur, J. Nucl. Mater. 62 (1976) 282.

[ 311 A.C. Damask and G.J. Dienes, Point Defects in Metals (Gordon and Breach, London, 1971).

[32] M.J. Goringe, Radiat. Eff. 10 (1971) 159. [ 331 A. Bourret, Radiat. Eff. 5 (1970) 27. [ 341 W. Schilling, G. Burger, K. Isebeck and H. Wenzl, in:

ref. [ 291, p. 255. [ 351 A. Seeger and H. Mehrer, in: ref. [ 291, p. 1. [ 36) M. Kiritani, N. Yoshida, H. Takata and Y. Maehara, in:

Electron Microscopy, vol. 1, J.V. Sanders and D.J. Good- child, eds. (Canberra, 1974) p. 444.

[ 37) N. Sumida, M. Kiritani and H. Fujita, in: ref. [4], p, 233. [38] R.W. Ballufi, in: ref. [ 11, p. 852. [ 391 F. Louchet and L.P. Kubin, Radiat. Eff. 26 (1975) 67. [40] M. Henderson Brown and K.F. Hale, in: ref. [lo], p. 206. 1411 J. Washburn, in: Plastic Deformation of Materials, J.C.M.

Li and A.K. Mukherjee, eds. ASM Mats./Metalworking Techn. Series no. 4 (Amer. Sot. Metals, 1975) p. 337.

1421 J. Powell and J. Burke, Phil. Mag. 31 (1975) 943. [43] W.M. Stobbs, Phil. Mag. 27 (1973), 257. [44] J.P. Hirth and J. Lothe, Theory of Dislocations (McGraw-

Hill, New York, 1968) p. 484 and 524. [45] R.W. Ballufi, Phys. Status Solidi 31 (1969) 443. [46] K.C. Russell, Acta Met. 19 (1971) 753. (471 J.C. Katz and H. Wiedersich, J. Chem. Phys. 55 (1971)

1414. [48] J. Friedel. Dislocations (Pergamon Press, Oxford, 1964)

p. 44 and 46. [49] J.P. Hirth and J. Lothe, Theory of Dislocations,

(McGraw-Hill, New York, 1968) p.-82 and 129. [SO] A.K. Head, Proc. Phys. Sot. London B 66 (1953) 793. 1511 E.H. Yoffe, Phil. Mag. 6 (1961) 1147. 1521 J.D. Eshelby and A.N. Stroh, Phil. Mag. 42 (1951) 1401. [53] M.J. Whelan, P.B. Hirsch, R.W. Horn and W. Bollmann,

Proc. Roy. Sot. A240 (1957) 524. [54] H. Fujita, Y. Kawasaki, E. Furubayashi, S. Kajiwara and

T. Taoka, Jap. J. Appl. Phys. 6-2 (1967) 214. [55] M. Grosbas, M.F. Denanot, E. Dedieu, M. Cahoreau,

D. Caillard and J.L. Martin, in: ref. [23], p. 244.

226 J.L. Martin, L.P. Kubin /In situ HVEMdeformation experiments

[56] A. Korner, P. Svoboda and H.O. Kirchner, Phys. Status Solidi (b) 80 (1977) 441.

1571 A. Korner, H.P. Karnthaler and H.O. Kirchner, Phys. Status Solidi (b) 81 (1977) 191.

[SS] P.M. Hazzledine, H.P. Karnthaler and E. Wintner, Phil. Mag. 32 (1975) 81.

[S9] J. Basterfield, W.A. Miller and G.C. Weatherly, Can. MetaJJ. Q 8 (1969) 131.

[60] F.C. Frank and A.N. Stroh, Proc. Phys. Sot. B65 (1952) 811.

(611 J.C. Grosskreutz and M.B. MacNeil, J. Appl. Phys. 40 (1969) 355.

[62] C. G’Sell, D. Thesis, Nancy University, France (1976). [63] W.G. Johnston and J.J. Gilman, J. Appl. Phys. 31 (1960)

632. [64] D. Vesely, Phys. Status Sotidi 29 (1968) 685. (651 H.J. Kolkman, Ser. Met. 8 (1974) 45. [66] H. Saka and T. Imura, J. Phys. Sot. Jap. 32 (1972) 702. 1671 D. Caillard and J.L. Martin, Ser. Met. 12 (1978) 157.

[68] J.T. Fourie, Phil. Mag. 17 (1968) 735. [69] T. lmura, in: ref. [ 41, p. 293. 1701 R. Lagneborg and B. Lehtinen, In situ experiments in

HVEM, Vtb Int. Conf. on HVEM, Kyoto 1977, to be published.

[71] R.E. Smallmann, Mater. Sci. Eng. 28 (1977) 1. [ 721 F. Louchet, L.P. Kubin and D. Vesely, in: ref. [ 231,

1171. [ 731 H. Mughrabi, J. Microsc. Spectrosc. Electr. 1 (1976) 571. 1741 H. Strunk, J. de Phys. 38 (1977) 377. [ 751 J. di Persio and B. Escaig, Phys. Status Solidi (a) 40

(1977) 393. [ 761 (a) M. Kleintges, R. Labusch, H.G. Brion and P. Haasen,

Acta Met. 25 (1977) 1247. (b) H. Ney, R. Labusch and P. Haasen, Acta Met. 25 (1977) 1257.

[ 771 T. Tabata, H. Mori, H. Fujita and 1. Ishikawa, J. Phys. Sot. Jap. 40 (1976) 1103.