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Hardening and serrated flow behaviour in the 300–500 K range for Eu-doped alkali halides
ha
mefall. Vol. 34, No. 9, pp. 1701-1709,
oool-6160/86 $3.00+ 0.00 Copyright 0 1986 Pergamon Journals Ltd
1986
Printed in Great Britain. All rights reserved
HARDENING AND SERRATED FLOW BEHAVIOUR IN THE 300-500K RANGE FOR Eu-DOPED ALKALI HALIDES? E. OROZCO Instituto de Fisica, Universidad National Autonoma de Mexico, Apartado Postal 20-364, Delegation Alvaro Obregbn, 01000 Mexico D.F.
F. AGULLbL6PEZ Departamento de Optica y Estructura de la Materia and Instituto de Fisica de1 Estado Solido (CSIC-UAM), Universidad Autonoma de Madrid, 28049 Madrid, Spain (Received 20 January 1986) Abstract-The hardening behaviour of Eu-doped alkali halides has been investigated in the 30&5OOK temperature range. The aggregation/precipitation state of the europium has been monitored by means of optical and electron spin resonance spectroscopy. Main attention has been paid to investigate dynamic effects on the yield-stress as well as the occurrence of serrated flow behaviour. In fact, jerky flow, which increases with impurity concentration, has been found for Eu-doped NaCl, KC1 and KBr, although the active temperature range is different for the three systems. This behaviour is characteristic of the impurity in solid solution and disappears or markedly decreases when precipitates are formed. On the other hand, yield-stress (I increases with temperature above RT for NaCl, keeps essentially constant for KC1 and decreases for KBr. The enhancement of (r observed in NaCl has been shown to be a dynamic effect, not related to either impurity aggregation or static strain hardening. These results as well as those on serrated flow are, consequently, discussed in terms of available dynamic strain ageing models. It has been concluded after some numerical estimates, that formation of a Cottrell cloud, probably involving diffusion of cation vacancies, may be an appropriate dynamic aging mechanism to account for the observed effects. On the other hand, the Snoek mechanism of dipolar reorientation, has to be ruled out. R&~III&-NOUS avons Ctudie le durcissement des halogenures alcalins dopes a l’europium entre 300 et 500 K. Nous avons suivi l’etat d’agregation/p&cipitation de l’europium par spectroscopies optique et de resonance de spin Clectronique. Nous avons port6 tout particulierement notre attention sur les effets dynamiques sur la limite elastique et sur l’apparition dun ecoulement hachure. En fait, nous avons trouve un ecoulement hachure qui augmentait avec la concentration en impured dans NaCl, KC1 et KBr dopes a l’europium bien que la domaine de temperatures oti il se produit soit different dans les trois sysdmes. Ce comportement est caracteristique dune impurett en solution solide et il disparait ou diminue notablement lorsqui’il se forme des precipids. Par contre, la limite elastique u augmente avec la temperature au-dessus de la temperature ambiante pour Nacl, reste pratiquement constante pour KC1 et diminue pour KBr. Nous avons montre que l’augmentation de u observQ dans NaCl etait un effet dynamique qui n’etait lie ni 21une agregation de l’impurett ni a un durcissement de deformation statique. Nous discutons ces resultats et ceux de l%coulement hachure en fonction des modeles d’ecrouissage dynamique disponibles. Nous concluons, apt& quelques estimations numeriques, que la formation dun nuage de Cottrell mettant probablement en jeu la diffusion de lacunes cationiques pourrait etre un mecanisme d’ecrouissage dynamique correct pour rendre compte des effets observes. Par contre, on doit &carter le mecanisme de reorientation dipolaire de Snoek. ZusanunenfassunI-Das Verfestigungsverhalten Eu-dotierter Alkalihalogenide wurde im Temperaturbereich xwischen 300 und 500 K untersucht. Der Zustand der Aggregation oder Ausscheidung wurde mit opt&her und Elektronenspinresonanz-Spektroskopie verfolgt. Im wesentlichen wurden dvnamische Einfliissc auf die FlieBspannung und das Auftreten des ruckw&en FlieDens untersucht. An Eu:dotiertem NaCl, KC1 und KBr wurde tats%chlich ruckweises Fliel3e.n. wenn such in verschiedenen Temoeraturbereichen, gefunden; es nimmt mit xunehmender Dotierung’ zu. Dieses Verhalten ist fur Mischkristalle typisch, es verschwindet oder wird deutlich weniger, wenn such Ausscheidungen bilden. Andererseits steigt die FlieDspannung u mit der Temperatur oberhalb von Raumtemperatur fur NaCl, bleibt im wesentlichen konstant bei KC1 und fillt bei KBr. Die Zunahme von u bei NaCl ist ein dynamischer Effekt, der nichtsmit Verunreinigungsaggregaten oder stat&her Verfestigung zu tun hat. Diese Ergebnisse und die fiir das ruckweise Fliebn werden daher such anhand der vorhandenen Modelle dynamischer Reckalterung diskutiert. Nach einigen numerischen Abschiitxungen wird gefolgert, daB die Bildung einer CottrellWolke, die mciglichenveise Diffusion von kation-Leerstellen umfaBt, ein geeigneter dynamischer Mechanismus xur Erkliirung der beobachteten Effekte ist. Andererseits mul3 der Snoek-Mechanismus der Dipol-Umorientierung ausgeschlossen werden. tThis work was partially supported (Spain).
under a cooperative programme between CONACYT (Mexico) and CSIC 1701
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OROZCO and AGULL6-L6PEZ:
SERRATED FLOW IN ALKALI HALIDES
1. INTRODUCTION
For alkali halide crystals containing divalent cation impurities in solid solution. i.e. forming impurityvacancy dipoles, the curve u (yield-stress) vs T (absolute temperature) consists of four stages [l]. In regime I, which corresponds to the lowest temperature range, the hardening is attributed to the Peierls mechanism. Regime II extends up to 250 K and the hardening results from the short-range elastic interaction between the moving dislocations and the tetragonal stress field of fixed impurity-vacancy dipoles. At and above room-temperature (RT), in regime III, the hardening is often attributed to the Snoek mechanism, which involves the reorientation of elastic dipoles in the stress field of the moving dislocations. In regime IV, at temperatures > 500 K, a decrease in hardening is observed. The situation with regard to stage III is particularly unsatisfactory. The Snoek mechanism invoked by most authors [la] as the responsible hardening mechanism, appears hardly consistent with the essentially athermal behaviour of the yield-stress during that stage. In fact, because of the resonant character of the Snoek effect, one would expect the yield-stress being strongly sensitive to testing temperature. Although for a number of doped systems [1,5,6] the yield stress experiences a certain rise with temperature above RT, this has been generally attributed to the effect of impurity clustering or to static strain hardening. However, recent data [7] on NaCl-Eu point to a dynamic effect during straining and consequently a thermal contribution to u, such as that predicted by the Snoek mechanism, may be, indeed, operative. On the other hand, serrated flow behaviour has been observed [7] during RT straining of NaCl-Eu, which appears indicative of the so-called Portevin-Le Chatelier (PLC) effect. This has, also, been previously found in several doped alkali halide systems [8,9], as well as in other ionic [lo, 111 and, more extensively, in metallic [12-141 materials and usually attributed to dynamic strain aging. This phenomenon, which is quite sensitive to temperature and strain-rate, should also be taken into account for a complete description of stage III hardening. In summary, all those features indicate that the hardening mechanisms above RT are rather complex and not well understood yet. The purpose of this work has been to carry out a systematic study of the PLC effect in NaCl-Eu, including its dependence on temperature and strainrate. Furthermore, in order to clarify the role of the host crystal on the effect, additional experiments have been performed on KCl-Eu and KBr-Eu for comparison purposes. Under appropriate conditions, serrated flow behaviour has been shown to be present for all three systems. On the other hand, the dependence of yield-stress on temperature above RT has, also, been investigated, in order to complete the available information on plastic flow behaviour
in that temperature range. The data obtained show systematic differences on moving from NaCl to KBr. One main advantage of the experiments described in this paper, is that optical and electron-spin resonance (ESR) spectroscopy techniques are used to monitor the aggregation/precipitation state of the impurity. This has allowed to ascertain under what conditions the europium is in the form of isolated dipoles and elucidate the role of aggregation/precipitation processes on the reported phenomena. 2. EXPERIMENTAL The experiments were performed on europium doped NaCl, KC1 and KBr crystals which were grown by the Czochralski method in an inert atmosphere following the same procedure as the one described previously [7]. The samples for the mechanical tests with typical dimensions 2.5 x 2.5 x 8 mm, were annealed at 800 K for 1 h and then quenched by dropping them on a copper block at room temperature. In some cases, thermal treatments to induce precipitation of the impurity were performed by heating the samples in air using conventional. furnaces. The concentration of europium in crystals varied from 20 to 100 ppm for NaCl-Eu*+, 70 to 200 ppm for KBr-Eu*+ and was 230 ppm for KCl-Eu2+. It was determined from the corresponding optical absorption spectrum of the doped samples following the same procedure as that described elsewhere [7]. The optical and fluorescence spectra were taken with a Cary 17 spectrophotometer and Jobin Yvon model JY 305 spectrofluorimeter, and the EPR spectra with a Varian E-12 X-band spectrometer. The mechanical tests were carried out in compression along the (100) direction in a Instrom table model machine with a furnace adapted to cover the temperature range 3Oc 500 K. In all cases when the system had stabilized at a given temperature, the sample was introduced in the furnace and kept for N 10 min at this temperature before testing. The cross-head velocities employed were 8.3 x IO-‘m s-i, 1.67 x 10-6m s-’ and 3.35 x 10d6 m s-‘. The macroscopic yield stress was obtained at the intersection of the elastic and easy-glide regions of the stress-strain curve. 3. RESULTS
3.1. Hardening in the 300-500 temperature range Figure 1 shows the data Q vs T in the temperature range 28&470 K for pure and freshly quenched Eudoped NaCl, KC1 and KBr. In all three cases, the low enough europium concentration in the doped samples assures that the impurity is forming isolated Eu+*vacancy dipoles. For NaCl and KBr, this is, indeed, inferred from the dependence of the height of the Eu+* EPR signal on concentration for freshly quenched samples, Fig. 2. The loss of linearity in the plot marks the onset of appreciable clustering effects
OROZCO and AGULLbL6PEZ:
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SERRATED
FLOW IN ALKALI HALIDES
o NoCl-Eu2*t53~wn)
0
KCl-Eu2+
. NaCl
n
KC1 (pure)
(pure)
(13Oppm)
1703
A KBr-Eu2+(198ppm)
(pure)
A KBr
I
I
I
I
I
I
300
330
360
390
420
450
I 470
Temperature(K)
Fig. I. Dependence of the yield-stress on testing temperature for Eu-doped NaCl, KC1 and KBr. Data for nominally pure samples are also included for comparison purposes.
immediately after quenching. For concentrations inside the linearity region the impurity should be forming isolated dipoles with cation vacancies. On the other hand, the luminescence spectra corresponding to the tested samples did not show any of the emission bands attributed [15-17] to precipitated phases and summarized in Table 1. As illustrated in Fig. 1, the hardening behaviour is different depending on crystal host, since d increases with T for NaCl, remains constant for KCI and decreases above 375 K for KBr. The data for NaCl
$1
NaClfu2+
/
I .J-
IL_-
1
0
100
Impurity
200
concentration
300
(ppm)
are in accordance with those already reported for this system and follow the same trend observed for other doped systems such as NaCl-Ca, NaCl-Mn and NaCl:Sr. The effect of Eu-concentration on the yieldstress behaviour is displayed in Fig. 3(a) for NaCl and Fig. 3(b) for KBr. These data confirm that the variation of yield-stress with temperature is, indeed, related to the presence of europium. The effect of strain-rate i on a(T) for Eu-doped NaCl and KBr was investigated by performing the experiments at two rates il = lop4 s-l and i2 = 10m3s-‘, Fig. 4. The data show the same a(T) dependence except for an enhanced athermal contribution in the latter case. Unfortunately, the covered range is rather small to draw definite conclusions. In order to check whether the rise in u for NaCl-Eu is due to impurity clustering or static strain aging, the effect of these two mechanisms was experimentally investigated. The absence of any relevant influence of clustering on yield-stress is evidenced by the data summarized in Table 2. The G values for samples tested at RT are compared with those ob-
Table I. Emission bands associated to the various aggregation/ precipitation states of Eu+* in several alkali halides Crystal host NaCl
KC1
loo
700
Impurity
concentration
(ppm)
KBr
Fig. 2. Dependence of the height of the Eu*+ EPR signal on impurity concentration for samples measured immediately after quenching.
Emission band peak (nm)
Assignment of emission bands
427 410 439 485 419 427 410 439 478 423 421 433 459
Dipoles and small aggregates Stable E&I, Metastable phase:( 111)platelet EuCI, Met&able phase:(310) platelet EuCI, Dipoles and small aggregates Suzuki phase Stable E&I, Metastable phase Metastable phase Dipoles and small aggregates Stable EuBr, Suzuki phase Metastable phase
OROZCO and AGULL&L6PEZ:
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FLOW IN ALKALI HALIDES
(a)
I
%
x
o1 273
330
390
460
V KBr-&+ l KErfu2+ 0 KBr-Eu2+
0 ; 80
( wrd (196ppmI (66ppm)
.-_.-.
273
330
390
Temperature
450 (K)
Fig. 3. Effect of the europium concentration on the yield-stress vs temperature dependence for Eu-NaCI and Eu-KBr. tained by straining at a higher temperature and those corresponding to samples strained at RT after a previous annealing treatment similar to that involved in the high temperature testing. It is clear that the RT Table 2. Yield-stress values measured at 298 and 398 K for quenched and quenched/annealed samples for NaCl doped with various divalent cations (Mn, 150 ppm; Eu, 100 ppm; Ca, 230 ppm)
system
K
Fig. 5. Experiment showing the effect of successive testing at a high (423 K) and low (293 K) temperature.
: t
NaCI:Mn’+ NaCl:Ca*+ NaCl:Eu*+
T.421
Deformation
YI
Host
f.423K
Yield stress at 298 K (kg/cm*)
Yield stress at 398 K (kg/cm’)
88 * 1 232 + 3 68 + 5
91+2 261 k5 82 + 2
I
Yield stress at 298 K after 10 min annealing at 398 K (kg/cm2) 84k3 227k4 67+3
3.2. Serrated flow behaviour Serrated flow behaviour is observed for freshly quenched NaCl:Eu in the temperature range 300500 K. A typical record of the effect is illustrated in Fig. 6 for a sample deformed at T = 423 K and strain-rate ( g 10m4s-l. At the start of the straining, the emission band corresponding to dipoles is exclusively observed (inset in Fig. 6). The flow oscillations are observed during a rather large strain range from the onset of the plastic stage. Their amplitude increases slightly up to 0.2 and then decreases. It
.
NoCl-Eu2itS3ppm)
1: 273
yield-stress is essentially independent of that prior annealing, showing that the induced clustering is not at all responsible for the enhanced Q observed at the higher temperatures. This result is also consistent with the observed fact [18] that no change in yield stress is brought about when dipoles aggregate into small clusters. The role of static strain aging was investigated by subjecting samples to successive testing at RT and a higher temperature. Results are illustrated in Fig. 5 for testing at 293 and 423 K. The d values at RT are essentially independent of previous testing at high temperature which should introduce some strain hardening. Therefore the observed increase in 0 with T cannot be associated to static strain hardening.
300
330
420
Temperature
450
470
(K)
Fig. 4. Effect of strain-rate ( on the yield stress vs temperature dependence for pure and Eu-doped NaCI.
OROZCO and AGULL6-L6PEZ:
3 0.6 d
_
SERRATED
NoCl-Et?+ (60 wrn)
t
Wavelength
(nm)
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FLOW IN ALKALI HALIDES
Eu, the serrated flow is markedly suppressed on precipitation, although the flow oscillations are still clearly observed when the luminescence band associated to the Suzuki phase is predominant (Fig. IO). For quenched samples, the effect decreases monotonically during straining and no precipitation phenomena have been detected. It is to be noted that the temperature range wherein the effect is apparent is much shorter than that for NaCl-Eu, extending only from 293 to 373 K, Fig. 11. Finally, as for NaCl the amplitude of the flow oscillations is drastically reduced on increasing strain-rate by a factor 4. 4. DISCUSSION The main conclusions inferred from the reported data are: serrated flow behaviour is clearly observed for Eu-doped NaCI, KC1 and KBr during straining around RT. The magnitude of the effect is directly related to the concentration of europium. In the same
I I I Deformation
Fig. 6. Load vs deformation curve for NaCl-Eu strained at 388 K (k = 10m4s-l) showing the serrated flow pattern. The emission band at 427 nm, characteristic of dipoles, is shown in the inset.
has been shown that during straining the dipoles aggregate and give rise to the formation of metastable precipitated phases as evidenced by the growth of the corresponding luminescence bands. The serrated flow is very sensitive to strain-rate C and testing temperature T, as illustrated in Fig. 7. It increases with temperature from 293 to 433 K and then keeps constant or even decreases. On the other hand, the amplitude of the oscillations practically disappears when the strain-rate is multiplied by 4 from the intitial value of i z 10-4s--‘. A very relevant feature is the enhancement of the effect with europium concentration, Fig. 8, indicating that it is, indeed, related to the presence of the impurities. In order to determine the role of the aggregation/precipitation state on serrated flow behaviour, experiments were performed on samples, which had been previously aged so as to develop precipitated phases. It has been found that the presence of metastable and stable precipitates practically eliminates jerky flow. This effect is illustrated in Fig. 9, where no appreciable flow oscillations appear for a crystal mostly showing the luminescence bands corresponding to metastable precipitates (see inset of the figure). On the other hand it is not appreciably influenced by the formation of small aggregates from the dipoles. Serrated flow is also observed for KCl-Eu and KBr-Eu. Systematic experiments have been carried out on KBr-Eu crystals, containing, either isolated dipoles or Suzuki phase precipitates. As for NaCl-
i=
10-q
5-1
NoCI-Eu’+
/‘I (6Oppm)
T=393K
i.10-4s-l
i=zx10-4s-’
0.005cm
i=4x10-4
s-1
1
Fig. 7. Effect of temperature and strain-rate on serrated flow pattern. The load and deformation units are respectively shown in the higher left and lower right corners. The arrows indicate the location of 8.5% strain.
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OROZCO and AGULL&L6PEZ:
SERRATED FLOW IN ALKALI HALIDES
Wavelength
(nm)
6-
5+-Change 4 0.01
I 002
I 0.03
I
QO4
I 0045
Deformation
of I 0.05
scaleI QO55
I _ 1x16
(cm)
Fig. 9. Serrated flow pattern corresponding to a NaCl-Eu sample mostly containing precipitated phases as inferred from the luminescence spectra in the inset (T = 388 K, i = lo-’ s-r): (1) dipoles, (2) EuCl,, (3) and (4) metastable phases.
strain aging as, at least partially, responsible for the serrated flow (Portevin-Le Chatelier effect). In order to qualitatively account for the behaviour described for the europium-doped alkali halides, one Fig. 8. Effect of impurity concentration on the serrated flow pattern of NaCl-Eu (T = 413 K, i = 10m4s-l). The appropriate load and deformation units are indicated at the higher left corner. The arrows indicate the locations of c = 8.5% strain.
temperature range, the yield-stress may increase with temperature (NaCl) or remain constant (KC1 and KBr). For the latter material, the serrated flow disappears at N 373 K as the yield-stress starts decreasing with temperature. Serrated flow behaviour may occur via a dynamic strain aging effect, associated to the dynamic formation of impurity clouds (either Cottrell or Snoek) during straining. Alternatively, it may appear as a consequence of the intrinsic instability of plastic flow during the easy glide stage i.e. due to glide band broadening. This latter effect has been apparently considered responsible for the serrated flow reported for pure alkali halides [19], and it has been also invoked to account for the similar behaviour found in heavily y-irradiated NaCl. On the other hand, the observed enhancement of Q with testing temperature in NaCl-Eu during stage III has been clearly shown to be a dynamic effect, that should be associated to strain aging. Therefore, one should consider dynamic
400
420 Wavelength
440
460
(nm)
Fig. 10. Serrated flow pattern at 4% strain for KBr-Eu containing dipoles (1) or Suzuki-phase precipitates (2) (T = 343 K, i = 10e4 s-l). The corresponding luminescence spectra are shown in the lower half plot.
OROZCO and AGULLbL6PEZ:
SERRATED
(140 ppm)
Fig. 11. Dependence of the serrated flow pattern on testing temperature for KBr-Eu (E = 4% at the position of the arrow). Appropriate load and deformation units are shown at the higher left comer.
may recourse
to the available strain-aging models such as the one recently discussed by Schoeck [20]. This approach considers that the average velocity of the mobile dislocations is controlled by the waiting time t, at local obstacles, such as the trees of the dis-
location forest piercing the glide plane. It is also assumed that during the dynamic strain aging, impurities move to the stopped dislocation core and form a cloud around it (Cottrell mechanism). This diffusion process is controlled by a characteristic diffusion time t, = /Ib’/D, D being the bulk diffusion coefficient, b the Burgers vector of the dislocation and
Normal
flow
-t Dynomlc
sfram
hardening
II) ._> ‘: z w
. (kl),
1
(tw), p 1
4
P2
5
T2
.
. . -iI- -tw + P
-
T
Fig. 12. Plot illustrating the a,(T) dependence under the assumption of a dynamic strain aging contribution, aceording to Ref. [20].
FLOW
IN ALKALI
HALIDES
1707
fl is a number around 100 which corresponds to a cloud radius of 10 b. Alternatively, for doped alkali halides in solid solution one expects that the existing impurity-vacancy dipoles reorientate in the stressfield of a nearby dislocation and lead to a lowering of the energy of the system (Snoek effect). Here, a characteristic time tR can also be defined. In both cases, either Cottrell or Snoek, the formation of that cloud increases the strength of the obstacle, so that the energy U required for overcoming it, is higher than that U, in absence of aging. The analysis of this situation leads to an increase of the effective dynamic stress cr, whose dependence on t, for a fixed strainrate i is as illustrated in Fig. 12. The effective a,(T) curve can be considered as the superposition of the normal G (T) dependence corresponding to the nonaged material and a contribution associated to the hardening induced by the formation of the cloud. An anomalous region with positive slope da/dt, results around t, = to (to is the characteristic time, either t, or tR), indicating that the waiting time is appropriate for an effective formation of either type of impurity cloud. As discussed in detail by Schoeck, that region between (t,), and (tw)2 shows a negative strain-rate sensitivity and induces unstable flow i.e. the PLC effect. Instead of t, one may use more convenient parameters in the plot of Fig. 12, such as the average dislocation velocity v or, even better, the average moving dislocation density p. They are related to t, through the simple kinetic relationships: v = l/tw and p = C t,llb, 1 being the average distance among obstacles in the glide plane. The role of temperature can also be discussed with reference to Fig. 12, since a change in T implies a relative shift in the two component curves making up the effective a,(T). Consequently, a rise in temperature can be described as a displacement of the operating point in the curve towards longer t, or higher dislocation density p. Therefore, one could define a temperature region T,-T, associated to the
interval p,-p2, where jerky or unstable flow occurs. Depending on the plastic flow characteristics of the material and aging processes, one may have a specific a,(T) curve and PLC interval T,-T,. Within the above scheme, one can try to understand the observed features in the hardening behaviour of NaCl-Eu. If the working point for RT testing lies at or near the start (p, or t,,) of the instability region, one should observe a rise in yield-stress with temperature as experimentally found. Moreover, this should be accompanied by an extended PLC zone. On the other hand, it can be argued that the instability region for KBr-Eu is shorter and that the working point at RT lies near the end of the interval. In such a case, a decrease in cr should be found on rising temperature accompanied by the disappearance of the jerky flow behaviour. This is in accordance with the experimental data. The differences in the o,(T) dependence on moving from NaCl to KBr, should be more likely attributed to corresponding
1708
OROZCO and AGULL&L6PEZ:
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differences in the plastic flow dynamics of the host, and not to differences in impurity aging kinetics. In fact, marked differences in the type of glide have been reported for the various alkali halides [ 191 and related to the serrated flow behaviour found in pure crystals.
In particular, flow in NaCl appears to be much more localized inside narrow glide bands than in KC1 and KBr. This implies higher average dislocation velocities (at a fixed C) and smaller average moving dislocation densities, so that it is conceivable that for NaCl the working point at RT may lie at the start of the rate-sensitive region. In summary, the dynamic strain-hardening model discussed by Schoeck [20] can be used to rationalize the observed behaviour and, in particular, to provide an unified description of the PLC effect and the evolution of yield-stress above RT. A key point in the model is the nature of the operating aging mechanism. In order to decide between the Snoek or Cottrell possibilities some numerical estimates can be now made. From the basic kinetic relationship i = p (I/t,)b, one may easily obtain t, between 5 x 10m4 and 5 x 10m3s for a typical strain-rate i = 10m4 and assuming p = 105lo6 cm-’ and I = lo-’ cm. The reorientation time tR for Euz+-vacancy dipoles in NaCl and KBr can be now reliably estimated from the recent data obtained by means of the ionic thermocurrent method (ITC) for a variety of alkali halides [21]. For T = 400 K it comes out tR = 5 x 10e5 s for NaCl-Eu and t, = 3 x 10m5s for KBr-Eu. These times are one or two orders of magnitude shorter in comparison to the expected t,, as estimated above. The difference between estimated and expected t, values is even more marked at T 1500 K, where the dipole reorientation time is w 10v6 s, whereas high-amplitude flow oscillations are still observed. Therefore one should very likely exclude Snoek reorientation as an operative mechanism. Although static strain aging experiments by Appel [22] on NaCl-Ca, yielded an activation energy for aging close to the value reported for dipole reorientation (similar for most doped alkali halides), the reported aging times, of the order of seconds at RT, are, again, very long to support a dipolar reorientation mechanism. To analyze the Cottrell mechanism, the mean square distance R travelled by the diffusing impurities during t, should be estimated. Random walk theory yields R2 = 6Dt,. Although, no data are apparently available for Eu+’ diffusion in alkali halides the diffusion parameters [23] D, = 2.30 x 10e3 cm2 s-’ and E,,, = 0.925 eV (activation energy) for Sfi+ having very similar ionic radius in NaCl can be used. Fort,=lO-‘sandT=400K,oneobtainsR-l& which is too short to induce any appreciable formation of the Cottrell cloud around the dislocation core. In fact, the static strain aging data by Brown and Pratt [8] on NaCl-Cd2+ indicated that much longer times (minutes and even hours) are required for such an effect. However, it is to be recalled that a fraction
FLOW IN ALKALI HALIDES
of the cation vacancies associated to the divalent cation impurities (either Eu2+ or St+) are isolated [23] and present a higher diffusion coefficient [24]. A similar calculation to that mentioned above has been carried out of the case of vacancy diffusion leading to R =200A for t,= lo-‘s and T=40OK. This value appears much more reasonable to permit efficient diffusion to the dislocation core during waiting times. In fact, this process may be related to the observations by Okada and Suita [93, where the oscillations in the flow-stress were associated to the oscillations in the electric current and therefore in the charge transport during straining [25] (GyulayHartley effect). It may be that the diffusion of vacancies to the stopped dislocations during the waiting time, enhances the charge to be dragged along on resuming motion. This should cause current oscillations correlated with the serrated flow. In view of the results by Brown and Pratt [8], it may occur that in static aging experiments, involving longer times and maybe higher temperatures, a second region of Cottrell aging, involving impurity diffusion, may set in. The above numerical estimates have not taken into account that impurities and even vacancies may diffuse at a much faster rate in strained than in unstrained materials, so that appropriate diffusion coefficients and not the reported bulk values, should be used. In fact, the importance of this point is clearly illustrated by the results obtained in this work for NaCl-Eu, where efficient aggregation/ precipitation phenomena are induced during straining, even at rather low strain levels. Anyhow all these analyses are of a qualitative nature and more detailed experimental data are necessary to evaluate the different contributions to the flow stress at and above RT. In particular, some work on monovalent cation doped crystals would be in order, to ascertain the role of cation vacancies in the dynamic aging processes. REFERENCES W. Skrotzki and P. Haasen, J. Phys. 42, C3-119 (1981). G. Schoeck and A. Seeger, Acrn merall. 7, 469 (1959). W. Frank, 2. Narurf. (a) 22, 377 (1967). F. Friihlich, P. Grau and M. Suszynska, Physica srarus solidi (a) 34, 165 (1976). 5. P. L. Pratt, R. P. Harrison and C. W. A. Newey, Din. Fur. Sot. 38, 212 (1964). 6. R. P. Harrison and C. W. A. Newey, Phil. Mug. 17,525
1. 2. 3. 4.
(1968). 7. E. Orozco, J. Soullard, C. Zaldo and F. Agull&Lbpez, Phil. Mug. 50, 425 (1984). 8. L. M. Brown and P. L. Pratt, Phil. Mug. 5, 717 (1963).
9. T. Okada and T. Suita, Tech. Rept. Osaka Univ. 16,265 (1965). 10. M. Srinivasan and T. G. Stoebe, Mater. Sci. Engng 25, 165 (1976). 11. A. Dominguez-Rodriguez and J. Castaing, Scripta metall. 9, 551 (1975). 12. J. Guillot and J. Grilbe, Acra metall. 20, 291 (1972). 13. R. A. Mulford and V. F. Kocks, Acra merall. 27, 1125 (1979). 14. R. B. Schwarz and L. L. Funk, Acra merall. 33, 295 (1985).
OROZCO and AGULL&L6PEZ:
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15. F. J. L6pc.2, H. S. Murrieta, J. A. Hemindez and J. 0. Rubio, Phys. Rev. B 22, 6428 (1980). 16. M. G. Aguilar, J. 0. Rubio, F. J. L6pez, J. Garcia SolC and H. S. Murrieta, Solid St. Common. 44, 141 (1982). 17. H. Murrieta, J. A. Hemrindez and J. 0. Rubio, Kinam 5, 75 (1983). 18. C. Zaldo, J. Garcia Soli: and F. Agull&Mpez, J. m&v. Sci. 17, 1465 (1982). 19. S. N. Komnik, V. Z. Bengus and E. D. Lyak, Physica. status solidi 19, 533 (1967).
FLOW IN ALKALI HALIDES
1709
20. G. Schoeck, Acta metall. 32, 1229 (1984). 21. J. HemBndez, H. Murrieta, F. Jaque and J. Rubio, Solid St. Commun. 39, 1061 (1981). 22. F. ADD& Mater. Sci. Emwe SO. 199 (1981). 23. H. ?&cl&a and W. J.“FFede;icks, ‘J. Pj?ysique 37, C7-385 (1976). 24. Point l3efecrs’in Solids (edited by J. H. Crawford and L. M. Slifkin), Vol. I. Plenum Press, New York (1972). 25. R. ~itwo~h, Ado. Phys. 24, 203 (1975).
mefall. Vol. 34, No. 9, pp. 1701-1709,
oool-6160/86 $3.00+ 0.00 Copyright 0 1986 Pergamon Journals Ltd
1986
Printed in Great Britain. All rights reserved
HARDENING AND SERRATED FLOW BEHAVIOUR IN THE 300-500K RANGE FOR Eu-DOPED ALKALI HALIDES? E. OROZCO Instituto de Fisica, Universidad National Autonoma de Mexico, Apartado Postal 20-364, Delegation Alvaro Obregbn, 01000 Mexico D.F.
F. AGULLbL6PEZ Departamento de Optica y Estructura de la Materia and Instituto de Fisica de1 Estado Solido (CSIC-UAM), Universidad Autonoma de Madrid, 28049 Madrid, Spain (Received 20 January 1986) Abstract-The hardening behaviour of Eu-doped alkali halides has been investigated in the 30&5OOK temperature range. The aggregation/precipitation state of the europium has been monitored by means of optical and electron spin resonance spectroscopy. Main attention has been paid to investigate dynamic effects on the yield-stress as well as the occurrence of serrated flow behaviour. In fact, jerky flow, which increases with impurity concentration, has been found for Eu-doped NaCl, KC1 and KBr, although the active temperature range is different for the three systems. This behaviour is characteristic of the impurity in solid solution and disappears or markedly decreases when precipitates are formed. On the other hand, yield-stress (I increases with temperature above RT for NaCl, keeps essentially constant for KC1 and decreases for KBr. The enhancement of (r observed in NaCl has been shown to be a dynamic effect, not related to either impurity aggregation or static strain hardening. These results as well as those on serrated flow are, consequently, discussed in terms of available dynamic strain ageing models. It has been concluded after some numerical estimates, that formation of a Cottrell cloud, probably involving diffusion of cation vacancies, may be an appropriate dynamic aging mechanism to account for the observed effects. On the other hand, the Snoek mechanism of dipolar reorientation, has to be ruled out. R&~III&-NOUS avons Ctudie le durcissement des halogenures alcalins dopes a l’europium entre 300 et 500 K. Nous avons suivi l’etat d’agregation/p&cipitation de l’europium par spectroscopies optique et de resonance de spin Clectronique. Nous avons port6 tout particulierement notre attention sur les effets dynamiques sur la limite elastique et sur l’apparition dun ecoulement hachure. En fait, nous avons trouve un ecoulement hachure qui augmentait avec la concentration en impured dans NaCl, KC1 et KBr dopes a l’europium bien que la domaine de temperatures oti il se produit soit different dans les trois sysdmes. Ce comportement est caracteristique dune impurett en solution solide et il disparait ou diminue notablement lorsqui’il se forme des precipids. Par contre, la limite elastique u augmente avec la temperature au-dessus de la temperature ambiante pour Nacl, reste pratiquement constante pour KC1 et diminue pour KBr. Nous avons montre que l’augmentation de u observQ dans NaCl etait un effet dynamique qui n’etait lie ni 21une agregation de l’impurett ni a un durcissement de deformation statique. Nous discutons ces resultats et ceux de l%coulement hachure en fonction des modeles d’ecrouissage dynamique disponibles. Nous concluons, apt& quelques estimations numeriques, que la formation dun nuage de Cottrell mettant probablement en jeu la diffusion de lacunes cationiques pourrait etre un mecanisme d’ecrouissage dynamique correct pour rendre compte des effets observes. Par contre, on doit &carter le mecanisme de reorientation dipolaire de Snoek. ZusanunenfassunI-Das Verfestigungsverhalten Eu-dotierter Alkalihalogenide wurde im Temperaturbereich xwischen 300 und 500 K untersucht. Der Zustand der Aggregation oder Ausscheidung wurde mit opt&her und Elektronenspinresonanz-Spektroskopie verfolgt. Im wesentlichen wurden dvnamische Einfliissc auf die FlieBspannung und das Auftreten des ruckw&en FlieDens untersucht. An Eu:dotiertem NaCl, KC1 und KBr wurde tats%chlich ruckweises Fliel3e.n. wenn such in verschiedenen Temoeraturbereichen, gefunden; es nimmt mit xunehmender Dotierung’ zu. Dieses Verhalten ist fur Mischkristalle typisch, es verschwindet oder wird deutlich weniger, wenn such Ausscheidungen bilden. Andererseits steigt die FlieDspannung u mit der Temperatur oberhalb von Raumtemperatur fur NaCl, bleibt im wesentlichen konstant bei KC1 und fillt bei KBr. Die Zunahme von u bei NaCl ist ein dynamischer Effekt, der nichtsmit Verunreinigungsaggregaten oder stat&her Verfestigung zu tun hat. Diese Ergebnisse und die fiir das ruckweise Fliebn werden daher such anhand der vorhandenen Modelle dynamischer Reckalterung diskutiert. Nach einigen numerischen Abschiitxungen wird gefolgert, daB die Bildung einer CottrellWolke, die mciglichenveise Diffusion von kation-Leerstellen umfaBt, ein geeigneter dynamischer Mechanismus xur Erkliirung der beobachteten Effekte ist. Andererseits mul3 der Snoek-Mechanismus der Dipol-Umorientierung ausgeschlossen werden. tThis work was partially supported (Spain).
under a cooperative programme between CONACYT (Mexico) and CSIC 1701
1702
OROZCO and AGULL6-L6PEZ:
SERRATED FLOW IN ALKALI HALIDES
1. INTRODUCTION
For alkali halide crystals containing divalent cation impurities in solid solution. i.e. forming impurityvacancy dipoles, the curve u (yield-stress) vs T (absolute temperature) consists of four stages [l]. In regime I, which corresponds to the lowest temperature range, the hardening is attributed to the Peierls mechanism. Regime II extends up to 250 K and the hardening results from the short-range elastic interaction between the moving dislocations and the tetragonal stress field of fixed impurity-vacancy dipoles. At and above room-temperature (RT), in regime III, the hardening is often attributed to the Snoek mechanism, which involves the reorientation of elastic dipoles in the stress field of the moving dislocations. In regime IV, at temperatures > 500 K, a decrease in hardening is observed. The situation with regard to stage III is particularly unsatisfactory. The Snoek mechanism invoked by most authors [la] as the responsible hardening mechanism, appears hardly consistent with the essentially athermal behaviour of the yield-stress during that stage. In fact, because of the resonant character of the Snoek effect, one would expect the yield-stress being strongly sensitive to testing temperature. Although for a number of doped systems [1,5,6] the yield stress experiences a certain rise with temperature above RT, this has been generally attributed to the effect of impurity clustering or to static strain hardening. However, recent data [7] on NaCl-Eu point to a dynamic effect during straining and consequently a thermal contribution to u, such as that predicted by the Snoek mechanism, may be, indeed, operative. On the other hand, serrated flow behaviour has been observed [7] during RT straining of NaCl-Eu, which appears indicative of the so-called Portevin-Le Chatelier (PLC) effect. This has, also, been previously found in several doped alkali halide systems [8,9], as well as in other ionic [lo, 111 and, more extensively, in metallic [12-141 materials and usually attributed to dynamic strain aging. This phenomenon, which is quite sensitive to temperature and strain-rate, should also be taken into account for a complete description of stage III hardening. In summary, all those features indicate that the hardening mechanisms above RT are rather complex and not well understood yet. The purpose of this work has been to carry out a systematic study of the PLC effect in NaCl-Eu, including its dependence on temperature and strainrate. Furthermore, in order to clarify the role of the host crystal on the effect, additional experiments have been performed on KCl-Eu and KBr-Eu for comparison purposes. Under appropriate conditions, serrated flow behaviour has been shown to be present for all three systems. On the other hand, the dependence of yield-stress on temperature above RT has, also, been investigated, in order to complete the available information on plastic flow behaviour
in that temperature range. The data obtained show systematic differences on moving from NaCl to KBr. One main advantage of the experiments described in this paper, is that optical and electron-spin resonance (ESR) spectroscopy techniques are used to monitor the aggregation/precipitation state of the impurity. This has allowed to ascertain under what conditions the europium is in the form of isolated dipoles and elucidate the role of aggregation/precipitation processes on the reported phenomena. 2. EXPERIMENTAL The experiments were performed on europium doped NaCl, KC1 and KBr crystals which were grown by the Czochralski method in an inert atmosphere following the same procedure as the one described previously [7]. The samples for the mechanical tests with typical dimensions 2.5 x 2.5 x 8 mm, were annealed at 800 K for 1 h and then quenched by dropping them on a copper block at room temperature. In some cases, thermal treatments to induce precipitation of the impurity were performed by heating the samples in air using conventional. furnaces. The concentration of europium in crystals varied from 20 to 100 ppm for NaCl-Eu*+, 70 to 200 ppm for KBr-Eu*+ and was 230 ppm for KCl-Eu2+. It was determined from the corresponding optical absorption spectrum of the doped samples following the same procedure as that described elsewhere [7]. The optical and fluorescence spectra were taken with a Cary 17 spectrophotometer and Jobin Yvon model JY 305 spectrofluorimeter, and the EPR spectra with a Varian E-12 X-band spectrometer. The mechanical tests were carried out in compression along the (100) direction in a Instrom table model machine with a furnace adapted to cover the temperature range 3Oc 500 K. In all cases when the system had stabilized at a given temperature, the sample was introduced in the furnace and kept for N 10 min at this temperature before testing. The cross-head velocities employed were 8.3 x IO-‘m s-i, 1.67 x 10-6m s-’ and 3.35 x 10d6 m s-‘. The macroscopic yield stress was obtained at the intersection of the elastic and easy-glide regions of the stress-strain curve. 3. RESULTS
3.1. Hardening in the 300-500 temperature range Figure 1 shows the data Q vs T in the temperature range 28&470 K for pure and freshly quenched Eudoped NaCl, KC1 and KBr. In all three cases, the low enough europium concentration in the doped samples assures that the impurity is forming isolated Eu+*vacancy dipoles. For NaCl and KBr, this is, indeed, inferred from the dependence of the height of the Eu+* EPR signal on concentration for freshly quenched samples, Fig. 2. The loss of linearity in the plot marks the onset of appreciable clustering effects
OROZCO and AGULLbL6PEZ:
0 273
SERRATED
FLOW IN ALKALI HALIDES
o NoCl-Eu2*t53~wn)
0
KCl-Eu2+
. NaCl
n
KC1 (pure)
(pure)
(13Oppm)
1703
A KBr-Eu2+(198ppm)
(pure)
A KBr
I
I
I
I
I
I
300
330
360
390
420
450
I 470
Temperature(K)
Fig. I. Dependence of the yield-stress on testing temperature for Eu-doped NaCl, KC1 and KBr. Data for nominally pure samples are also included for comparison purposes.
immediately after quenching. For concentrations inside the linearity region the impurity should be forming isolated dipoles with cation vacancies. On the other hand, the luminescence spectra corresponding to the tested samples did not show any of the emission bands attributed [15-17] to precipitated phases and summarized in Table 1. As illustrated in Fig. 1, the hardening behaviour is different depending on crystal host, since d increases with T for NaCl, remains constant for KCI and decreases above 375 K for KBr. The data for NaCl
$1
NaClfu2+
/
I .J-
IL_-
1
0
100
Impurity
200
concentration
300
(ppm)
are in accordance with those already reported for this system and follow the same trend observed for other doped systems such as NaCl-Ca, NaCl-Mn and NaCl:Sr. The effect of Eu-concentration on the yieldstress behaviour is displayed in Fig. 3(a) for NaCl and Fig. 3(b) for KBr. These data confirm that the variation of yield-stress with temperature is, indeed, related to the presence of europium. The effect of strain-rate i on a(T) for Eu-doped NaCl and KBr was investigated by performing the experiments at two rates il = lop4 s-l and i2 = 10m3s-‘, Fig. 4. The data show the same a(T) dependence except for an enhanced athermal contribution in the latter case. Unfortunately, the covered range is rather small to draw definite conclusions. In order to check whether the rise in u for NaCl-Eu is due to impurity clustering or static strain aging, the effect of these two mechanisms was experimentally investigated. The absence of any relevant influence of clustering on yield-stress is evidenced by the data summarized in Table 2. The G values for samples tested at RT are compared with those ob-
Table I. Emission bands associated to the various aggregation/ precipitation states of Eu+* in several alkali halides Crystal host NaCl
KC1
loo
700
Impurity
concentration
(ppm)
KBr
Fig. 2. Dependence of the height of the Eu*+ EPR signal on impurity concentration for samples measured immediately after quenching.
Emission band peak (nm)
Assignment of emission bands
427 410 439 485 419 427 410 439 478 423 421 433 459
Dipoles and small aggregates Stable E&I, Metastable phase:( 111)platelet EuCI, Met&able phase:(310) platelet EuCI, Dipoles and small aggregates Suzuki phase Stable E&I, Metastable phase Metastable phase Dipoles and small aggregates Stable EuBr, Suzuki phase Metastable phase
OROZCO and AGULL&L6PEZ:
1704
SERRATED
FLOW IN ALKALI HALIDES
(a)
I
%
x
o1 273
330
390
460
V KBr-&+ l KErfu2+ 0 KBr-Eu2+
0 ; 80
( wrd (196ppmI (66ppm)
.-_.-.
273
330
390
Temperature
450 (K)
Fig. 3. Effect of the europium concentration on the yield-stress vs temperature dependence for Eu-NaCI and Eu-KBr. tained by straining at a higher temperature and those corresponding to samples strained at RT after a previous annealing treatment similar to that involved in the high temperature testing. It is clear that the RT Table 2. Yield-stress values measured at 298 and 398 K for quenched and quenched/annealed samples for NaCl doped with various divalent cations (Mn, 150 ppm; Eu, 100 ppm; Ca, 230 ppm)
system
K
Fig. 5. Experiment showing the effect of successive testing at a high (423 K) and low (293 K) temperature.
: t
NaCI:Mn’+ NaCl:Ca*+ NaCl:Eu*+
T.421
Deformation
YI
Host
f.423K
Yield stress at 298 K (kg/cm*)
Yield stress at 398 K (kg/cm’)
88 * 1 232 + 3 68 + 5
91+2 261 k5 82 + 2
I
Yield stress at 298 K after 10 min annealing at 398 K (kg/cm2) 84k3 227k4 67+3
3.2. Serrated flow behaviour Serrated flow behaviour is observed for freshly quenched NaCl:Eu in the temperature range 300500 K. A typical record of the effect is illustrated in Fig. 6 for a sample deformed at T = 423 K and strain-rate ( g 10m4s-l. At the start of the straining, the emission band corresponding to dipoles is exclusively observed (inset in Fig. 6). The flow oscillations are observed during a rather large strain range from the onset of the plastic stage. Their amplitude increases slightly up to 0.2 and then decreases. It
.
NoCl-Eu2itS3ppm)
1: 273
yield-stress is essentially independent of that prior annealing, showing that the induced clustering is not at all responsible for the enhanced Q observed at the higher temperatures. This result is also consistent with the observed fact [18] that no change in yield stress is brought about when dipoles aggregate into small clusters. The role of static strain aging was investigated by subjecting samples to successive testing at RT and a higher temperature. Results are illustrated in Fig. 5 for testing at 293 and 423 K. The d values at RT are essentially independent of previous testing at high temperature which should introduce some strain hardening. Therefore the observed increase in 0 with T cannot be associated to static strain hardening.
300
330
420
Temperature
450
470
(K)
Fig. 4. Effect of strain-rate ( on the yield stress vs temperature dependence for pure and Eu-doped NaCI.
OROZCO and AGULL6-L6PEZ:
3 0.6 d
_
SERRATED
NoCl-Et?+ (60 wrn)
t
Wavelength
(nm)
1705
FLOW IN ALKALI HALIDES
Eu, the serrated flow is markedly suppressed on precipitation, although the flow oscillations are still clearly observed when the luminescence band associated to the Suzuki phase is predominant (Fig. IO). For quenched samples, the effect decreases monotonically during straining and no precipitation phenomena have been detected. It is to be noted that the temperature range wherein the effect is apparent is much shorter than that for NaCl-Eu, extending only from 293 to 373 K, Fig. 11. Finally, as for NaCl the amplitude of the flow oscillations is drastically reduced on increasing strain-rate by a factor 4. 4. DISCUSSION The main conclusions inferred from the reported data are: serrated flow behaviour is clearly observed for Eu-doped NaCI, KC1 and KBr during straining around RT. The magnitude of the effect is directly related to the concentration of europium. In the same
I I I Deformation
Fig. 6. Load vs deformation curve for NaCl-Eu strained at 388 K (k = 10m4s-l) showing the serrated flow pattern. The emission band at 427 nm, characteristic of dipoles, is shown in the inset.
has been shown that during straining the dipoles aggregate and give rise to the formation of metastable precipitated phases as evidenced by the growth of the corresponding luminescence bands. The serrated flow is very sensitive to strain-rate C and testing temperature T, as illustrated in Fig. 7. It increases with temperature from 293 to 433 K and then keeps constant or even decreases. On the other hand, the amplitude of the oscillations practically disappears when the strain-rate is multiplied by 4 from the intitial value of i z 10-4s--‘. A very relevant feature is the enhancement of the effect with europium concentration, Fig. 8, indicating that it is, indeed, related to the presence of the impurities. In order to determine the role of the aggregation/precipitation state on serrated flow behaviour, experiments were performed on samples, which had been previously aged so as to develop precipitated phases. It has been found that the presence of metastable and stable precipitates practically eliminates jerky flow. This effect is illustrated in Fig. 9, where no appreciable flow oscillations appear for a crystal mostly showing the luminescence bands corresponding to metastable precipitates (see inset of the figure). On the other hand it is not appreciably influenced by the formation of small aggregates from the dipoles. Serrated flow is also observed for KCl-Eu and KBr-Eu. Systematic experiments have been carried out on KBr-Eu crystals, containing, either isolated dipoles or Suzuki phase precipitates. As for NaCl-
i=
10-q
5-1
NoCI-Eu’+
/‘I (6Oppm)
T=393K
i.10-4s-l
i=zx10-4s-’
0.005cm
i=4x10-4
s-1
1
Fig. 7. Effect of temperature and strain-rate on serrated flow pattern. The load and deformation units are respectively shown in the higher left and lower right corners. The arrows indicate the location of 8.5% strain.
1706
OROZCO and AGULL&L6PEZ:
SERRATED FLOW IN ALKALI HALIDES
Wavelength
(nm)
6-
5+-Change 4 0.01
I 002
I 0.03
I
QO4
I 0045
Deformation
of I 0.05
scaleI QO55
I _ 1x16
(cm)
Fig. 9. Serrated flow pattern corresponding to a NaCl-Eu sample mostly containing precipitated phases as inferred from the luminescence spectra in the inset (T = 388 K, i = lo-’ s-r): (1) dipoles, (2) EuCl,, (3) and (4) metastable phases.
strain aging as, at least partially, responsible for the serrated flow (Portevin-Le Chatelier effect). In order to qualitatively account for the behaviour described for the europium-doped alkali halides, one Fig. 8. Effect of impurity concentration on the serrated flow pattern of NaCl-Eu (T = 413 K, i = 10m4s-l). The appropriate load and deformation units are indicated at the higher left corner. The arrows indicate the locations of c = 8.5% strain.
temperature range, the yield-stress may increase with temperature (NaCl) or remain constant (KC1 and KBr). For the latter material, the serrated flow disappears at N 373 K as the yield-stress starts decreasing with temperature. Serrated flow behaviour may occur via a dynamic strain aging effect, associated to the dynamic formation of impurity clouds (either Cottrell or Snoek) during straining. Alternatively, it may appear as a consequence of the intrinsic instability of plastic flow during the easy glide stage i.e. due to glide band broadening. This latter effect has been apparently considered responsible for the serrated flow reported for pure alkali halides [19], and it has been also invoked to account for the similar behaviour found in heavily y-irradiated NaCl. On the other hand, the observed enhancement of Q with testing temperature in NaCl-Eu during stage III has been clearly shown to be a dynamic effect, that should be associated to strain aging. Therefore, one should consider dynamic
400
420 Wavelength
440
460
(nm)
Fig. 10. Serrated flow pattern at 4% strain for KBr-Eu containing dipoles (1) or Suzuki-phase precipitates (2) (T = 343 K, i = 10e4 s-l). The corresponding luminescence spectra are shown in the lower half plot.
OROZCO and AGULLbL6PEZ:
SERRATED
(140 ppm)
Fig. 11. Dependence of the serrated flow pattern on testing temperature for KBr-Eu (E = 4% at the position of the arrow). Appropriate load and deformation units are shown at the higher left comer.
may recourse
to the available strain-aging models such as the one recently discussed by Schoeck [20]. This approach considers that the average velocity of the mobile dislocations is controlled by the waiting time t, at local obstacles, such as the trees of the dis-
location forest piercing the glide plane. It is also assumed that during the dynamic strain aging, impurities move to the stopped dislocation core and form a cloud around it (Cottrell mechanism). This diffusion process is controlled by a characteristic diffusion time t, = /Ib’/D, D being the bulk diffusion coefficient, b the Burgers vector of the dislocation and
Normal
flow
-t Dynomlc
sfram
hardening
II) ._> ‘: z w
. (kl),
1
(tw), p 1
4
P2
5
T2
.
. . -iI- -tw + P
-
T
Fig. 12. Plot illustrating the a,(T) dependence under the assumption of a dynamic strain aging contribution, aceording to Ref. [20].
FLOW
IN ALKALI
HALIDES
1707
fl is a number around 100 which corresponds to a cloud radius of 10 b. Alternatively, for doped alkali halides in solid solution one expects that the existing impurity-vacancy dipoles reorientate in the stressfield of a nearby dislocation and lead to a lowering of the energy of the system (Snoek effect). Here, a characteristic time tR can also be defined. In both cases, either Cottrell or Snoek, the formation of that cloud increases the strength of the obstacle, so that the energy U required for overcoming it, is higher than that U, in absence of aging. The analysis of this situation leads to an increase of the effective dynamic stress cr, whose dependence on t, for a fixed strainrate i is as illustrated in Fig. 12. The effective a,(T) curve can be considered as the superposition of the normal G (T) dependence corresponding to the nonaged material and a contribution associated to the hardening induced by the formation of the cloud. An anomalous region with positive slope da/dt, results around t, = to (to is the characteristic time, either t, or tR), indicating that the waiting time is appropriate for an effective formation of either type of impurity cloud. As discussed in detail by Schoeck, that region between (t,), and (tw)2 shows a negative strain-rate sensitivity and induces unstable flow i.e. the PLC effect. Instead of t, one may use more convenient parameters in the plot of Fig. 12, such as the average dislocation velocity v or, even better, the average moving dislocation density p. They are related to t, through the simple kinetic relationships: v = l/tw and p = C t,llb, 1 being the average distance among obstacles in the glide plane. The role of temperature can also be discussed with reference to Fig. 12, since a change in T implies a relative shift in the two component curves making up the effective a,(T). Consequently, a rise in temperature can be described as a displacement of the operating point in the curve towards longer t, or higher dislocation density p. Therefore, one could define a temperature region T,-T, associated to the
interval p,-p2, where jerky or unstable flow occurs. Depending on the plastic flow characteristics of the material and aging processes, one may have a specific a,(T) curve and PLC interval T,-T,. Within the above scheme, one can try to understand the observed features in the hardening behaviour of NaCl-Eu. If the working point for RT testing lies at or near the start (p, or t,,) of the instability region, one should observe a rise in yield-stress with temperature as experimentally found. Moreover, this should be accompanied by an extended PLC zone. On the other hand, it can be argued that the instability region for KBr-Eu is shorter and that the working point at RT lies near the end of the interval. In such a case, a decrease in cr should be found on rising temperature accompanied by the disappearance of the jerky flow behaviour. This is in accordance with the experimental data. The differences in the o,(T) dependence on moving from NaCl to KBr, should be more likely attributed to corresponding
1708
OROZCO and AGULL&L6PEZ:
SERRATED
differences in the plastic flow dynamics of the host, and not to differences in impurity aging kinetics. In fact, marked differences in the type of glide have been reported for the various alkali halides [ 191 and related to the serrated flow behaviour found in pure crystals.
In particular, flow in NaCl appears to be much more localized inside narrow glide bands than in KC1 and KBr. This implies higher average dislocation velocities (at a fixed C) and smaller average moving dislocation densities, so that it is conceivable that for NaCl the working point at RT may lie at the start of the rate-sensitive region. In summary, the dynamic strain-hardening model discussed by Schoeck [20] can be used to rationalize the observed behaviour and, in particular, to provide an unified description of the PLC effect and the evolution of yield-stress above RT. A key point in the model is the nature of the operating aging mechanism. In order to decide between the Snoek or Cottrell possibilities some numerical estimates can be now made. From the basic kinetic relationship i = p (I/t,)b, one may easily obtain t, between 5 x 10m4 and 5 x 10m3s for a typical strain-rate i = 10m4 and assuming p = 105lo6 cm-’ and I = lo-’ cm. The reorientation time tR for Euz+-vacancy dipoles in NaCl and KBr can be now reliably estimated from the recent data obtained by means of the ionic thermocurrent method (ITC) for a variety of alkali halides [21]. For T = 400 K it comes out tR = 5 x 10e5 s for NaCl-Eu and t, = 3 x 10m5s for KBr-Eu. These times are one or two orders of magnitude shorter in comparison to the expected t,, as estimated above. The difference between estimated and expected t, values is even more marked at T 1500 K, where the dipole reorientation time is w 10v6 s, whereas high-amplitude flow oscillations are still observed. Therefore one should very likely exclude Snoek reorientation as an operative mechanism. Although static strain aging experiments by Appel [22] on NaCl-Ca, yielded an activation energy for aging close to the value reported for dipole reorientation (similar for most doped alkali halides), the reported aging times, of the order of seconds at RT, are, again, very long to support a dipolar reorientation mechanism. To analyze the Cottrell mechanism, the mean square distance R travelled by the diffusing impurities during t, should be estimated. Random walk theory yields R2 = 6Dt,. Although, no data are apparently available for Eu+’ diffusion in alkali halides the diffusion parameters [23] D, = 2.30 x 10e3 cm2 s-’ and E,,, = 0.925 eV (activation energy) for Sfi+ having very similar ionic radius in NaCl can be used. Fort,=lO-‘sandT=400K,oneobtainsR-l& which is too short to induce any appreciable formation of the Cottrell cloud around the dislocation core. In fact, the static strain aging data by Brown and Pratt [8] on NaCl-Cd2+ indicated that much longer times (minutes and even hours) are required for such an effect. However, it is to be recalled that a fraction
FLOW IN ALKALI HALIDES
of the cation vacancies associated to the divalent cation impurities (either Eu2+ or St+) are isolated [23] and present a higher diffusion coefficient [24]. A similar calculation to that mentioned above has been carried out of the case of vacancy diffusion leading to R =200A for t,= lo-‘s and T=40OK. This value appears much more reasonable to permit efficient diffusion to the dislocation core during waiting times. In fact, this process may be related to the observations by Okada and Suita [93, where the oscillations in the flow-stress were associated to the oscillations in the electric current and therefore in the charge transport during straining [25] (GyulayHartley effect). It may be that the diffusion of vacancies to the stopped dislocations during the waiting time, enhances the charge to be dragged along on resuming motion. This should cause current oscillations correlated with the serrated flow. In view of the results by Brown and Pratt [8], it may occur that in static aging experiments, involving longer times and maybe higher temperatures, a second region of Cottrell aging, involving impurity diffusion, may set in. The above numerical estimates have not taken into account that impurities and even vacancies may diffuse at a much faster rate in strained than in unstrained materials, so that appropriate diffusion coefficients and not the reported bulk values, should be used. In fact, the importance of this point is clearly illustrated by the results obtained in this work for NaCl-Eu, where efficient aggregation/ precipitation phenomena are induced during straining, even at rather low strain levels. Anyhow all these analyses are of a qualitative nature and more detailed experimental data are necessary to evaluate the different contributions to the flow stress at and above RT. In particular, some work on monovalent cation doped crystals would be in order, to ascertain the role of cation vacancies in the dynamic aging processes. REFERENCES W. Skrotzki and P. Haasen, J. Phys. 42, C3-119 (1981). G. Schoeck and A. Seeger, Acrn merall. 7, 469 (1959). W. Frank, 2. Narurf. (a) 22, 377 (1967). F. Friihlich, P. Grau and M. Suszynska, Physica srarus solidi (a) 34, 165 (1976). 5. P. L. Pratt, R. P. Harrison and C. W. A. Newey, Din. Fur. Sot. 38, 212 (1964). 6. R. P. Harrison and C. W. A. Newey, Phil. Mug. 17,525
1. 2. 3. 4.
(1968). 7. E. Orozco, J. Soullard, C. Zaldo and F. Agull&Lbpez, Phil. Mug. 50, 425 (1984). 8. L. M. Brown and P. L. Pratt, Phil. Mug. 5, 717 (1963).
9. T. Okada and T. Suita, Tech. Rept. Osaka Univ. 16,265 (1965). 10. M. Srinivasan and T. G. Stoebe, Mater. Sci. Engng 25, 165 (1976). 11. A. Dominguez-Rodriguez and J. Castaing, Scripta metall. 9, 551 (1975). 12. J. Guillot and J. Grilbe, Acra metall. 20, 291 (1972). 13. R. A. Mulford and V. F. Kocks, Acra merall. 27, 1125 (1979). 14. R. B. Schwarz and L. L. Funk, Acra merall. 33, 295 (1985).
OROZCO and AGULL&L6PEZ:
SERRATED
15. F. J. L6pc.2, H. S. Murrieta, J. A. Hemindez and J. 0. Rubio, Phys. Rev. B 22, 6428 (1980). 16. M. G. Aguilar, J. 0. Rubio, F. J. L6pez, J. Garcia SolC and H. S. Murrieta, Solid St. Common. 44, 141 (1982). 17. H. Murrieta, J. A. Hemrindez and J. 0. Rubio, Kinam 5, 75 (1983). 18. C. Zaldo, J. Garcia Soli: and F. Agull&Mpez, J. m&v. Sci. 17, 1465 (1982). 19. S. N. Komnik, V. Z. Bengus and E. D. Lyak, Physica. status solidi 19, 533 (1967).
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1709
20. G. Schoeck, Acta metall. 32, 1229 (1984). 21. J. HemBndez, H. Murrieta, F. Jaque and J. Rubio, Solid St. Commun. 39, 1061 (1981). 22. F. ADD& Mater. Sci. Emwe SO. 199 (1981). 23. H. ?&cl&a and W. J.“FFede;icks, ‘J. Pj?ysique 37, C7-385 (1976). 24. Point l3efecrs’in Solids (edited by J. H. Crawford and L. M. Slifkin), Vol. I. Plenum Press, New York (1972). 25. R. ~itwo~h, Ado. Phys. 24, 203 (1975).