OF POINT DEFECTS IN Au, Ag AND Cu
PROEFSCHRIFT
TER VERKRUGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL TE DELFT OP GEZAG VAN DE RECTOR MAGNIFICUS IR. H.J. DE WUS, HOOGLERAAR IN DE AFDELING DER MUNBOUW-KUNDE, VOOR EEN COMMISSIE UIT DE SENAAT TE VERDEDIGEN OP WOENSDAG 24 JUNI 1964 DES.
NAMIDDAGS TE 2 UUR
DOOR
HENK IWAN DAWSON NATUURKUNDIG INGENIEUR
GEBOREN TE PARAMARIBO
DIT PROEFSCHRIFf IS GOEDGEKEURD DOOR DE PROMOTOR PROF. DR. M.
J.
DRUYVESTEYN.1. De conclusie van Takamura c. S., dat de puntfouten, die bij plastisch rekken van Au bij 77 of 900K ontstaan, voornamelijk bestaan uit vacatures, berust op geen enkel positief argument.
J.Takamura, K.Furukawa, S.Miura en P.H.Singu,. J.Phys.Soc.Japan 18 suppl. UI (1963) 7.
2. Bij de analyse van maxima in de herstel snelheid van roosterfouten als functie van de temperatuur, dient men rekening te houden met het feit, dat indien er in een bepaald temperatuurgebied 2 herstelprocessen optreden,
er in dat gebied 3 maxima kunnen ontstaan. 1. W.Henderson en J.S.Koehler,. Phys.Rev. 104 (1956) 626. A. van den Beukel, • Dissertatie Delft (1962).
3. De veronderstelling van van Aller, dat de oorzaak van het door hem gemeten effect van een verandering van de elastische spanningstoestand op het herstel van de elec-trische weerstand, uitsluitend gezocht moet worden in een dislocatiemechanisme, is onjuist.
G. van Aller,. Dissertatie Delft (1962).
4. Bij de bestudering van het mechanisme van de vermoeiing van metalen, is onvoldoende aandacht besteed aan het herstel van de door vermoeiing geintroduceerde rooster-fouten.
A. 1. Kennedy,. "Processes of Creep and Fatigue in Metals" , Oliver and Boyd, Edingburg and London 1962.
5. De veronderstelling dat stikstof (en misschien ook water-stof) in Au oplosbaar is, wordt door Jeanotte en Machlin aangevoerd om het verschil te verklaren tussen de half-waardetijd
7"t,
die zij gevonden hebben voor het herstel van Au afgeschrikt in een 80% He + 20% 02 atmosfeer, en de waarde van Tt gemeten door Bauerle en Koehier aan Au dat werd afgeschrikt in lucht. Het feit dat T! van vele andere factoren afhangt, is een reden om dezJ veronderstelling met r-eserve te bezien.D.Jeanotte en E.S.Machlin,. Phil.Mag.ê. (1963) 1835. 1.E.Bauerle en J.S.Koehler,. Phys.Rev, 107 (1957) 1493.
6. Het boekje, Grondbeginselen der Hedendaagse Natuur-kunde, van Prins is veel beter geschikt als compendium dan als leergang of inleiding.
J. A. Prins,. "Grondbeginselen der Hedendaagse Natuurkunde". Tiende druk. 1. B. Wolters, Groningen 1963. (Zie ook het voorbericht bij de achtste druk) •
7. Door het gebrek aan theoretisch inzicht in het gedrag van de electrische eigenschappen van ordenende en pre-cipiterende legeringen, kunnen metingen van deze eigen-schappen vaak slechts van qualitatief belang zlJn, en meestal alleen dienen om de resultaten van metingen van andere eigenschappen te ondersteunen.
8. Door de gebruikelijke wetenschappelijke training die de nadruk legt op zelfkritiek en technische bedrevenheid, worden originaliteit en verbeeldingskracht soms te ge-m'akkelijk onderdrukt.
9. Het gebruik van veiligheidsriemen zou in lesauto' s
ver-plicht gesteld moeten worden.
STELLINGEN BEHORE:\DE BIJ HET PROEFSCHRIFT
This work is part of the research programme of the Re-search group "Metals F. O. M. - T. N. 0." of the "Stichting voor Fundamenteel Onderzoek der Materie" (Foundation for Fundamental Research of Matter - F. O. M.) and was also made possible by financial support from the "Nederlandse Organisatie voOr Zuiver Wetenschappelijk Onderzoek"(Nether-lands Organization for pure Research - Z. W. 0.).
-CONTENTS
page Chapter 1. Introduction and Summary
Chapter Il. Experimental Procedure a. Materials
b. Resistivity measurements c. Small deformations
d. Cold rolling e. Annealing
f. Apparatus for measuring stress-strain curves Chapter lIl. Experimental Results
Part I: Recovery of P ..;lllt Defects a. Introduction
b. Results on Au, Ag and Cu c. Results on the alloys.
d. Comparison between pure metals and alloys e. Activation energy determination
f. Discussion of some additionaJ results 1. "Reaction order of stage lIl" 2. Repeated deformation
Chapter lIl. Experimental Results Part Il: Production of Point Defects a. Introduction
b. Resistivity-strain relations c. Stress-strain relations
d. Comparison of the experimental data with Saada's relation
Chapter IV. Literature on Point Defects in Au, Ag and Cu
a. Intröduction
b. Measurements of equilibrium concentrations of cancies at elevated temperatures and quenching
7 12 12 13 13 15 16 16 18 18 18 25 31 36 42 42 44 46 46 46 51 54 59 59 va- ex-periments 59
c. Annealing of radiation damage 64
d. Production of point defects during plastic
defor-mation 69
e. Annealing of cold worked Au, Ag and Cu 73 Chapter V. Discussion and Interpretation of the
-6-a. Introduction
b. On the analysis of the experiments
c. On the identification of stage c and of stage d d. Discussion of possible mechanisms for stage band
of stage TI (stage a)
e. Discussion of resistivity changes in the alloys
Samenvatting Refercnces page 78 78 88 90 95 99 101
INTRODUCTION AND SUMMARY
In a metal the regular periodic arrangem_~nt of atoms does
not extend everywhere ,2ver the crystal but is disturbed by J/..'1- j lattice imperfections. Experimentally, the nature and
prop-erties of these imperfections or defects can be studied by measuring physical quantities that depend on them, as for instance the electrical resistivity.
During the past decade an abundant amount ofboth theoretical and experimental work concerning this subject has been pub-lished by many investigators. For a general survey of pre-sent k!l0wledge in this field the reader may consult(the book byJvan Bueren1). Excess defect concentrations can be intro:... duced into a metal by cold work, by quenching from high
temperatures, or by high energy irradiation. As Molenaar
and Aarts2) have demonstrated, plastic deformation of some metals at a low temperature gives an increase of the elec-trical resistivity, part of which disappears during subsequent
warming up of the specimen to about room temperature.
The stress-strain curve,however, was observed to be con-tinuous after annealing, indicatingthat the resistivity decrease does not reflect the beginning of recrystallization, a pro-cess involving the disappearance of dislocations. The most
~ interpretation of this observation is that defects small-er than dislocations i. e. point defects, which by supposition do not affect the stress-strain curve, are also introduced during deformation. During subsequent warming up they dis-appear by diffusion mechanisms, resulting in the resistivity decrease, which we call recovery. In general, if a physical property associated with lattice defects changes upon annealing we say that the property recovers or anneals. The
pion-eering experiment of Molenaar and Aarts was followed by
the investigations of Manintveld 3), who studied the
tempera-ture dependence of the resistivity decrease in greater detail. This decrease was observed to take place in two tempera-ture intervals. Manintveld ascribed theserecover;y stages to the disappearance at dislocations of interstitial atoms (lower stage) and of lattice vacancies (upper stage).
From th at moment on interest in the defect structure has grown rapidly. Balluffi et al. 4) have published an exhaustive
-8-survey of current knowledge concerning point defect production and annealing in f. c. c. metals.
More information has become available from quenching ex-periments and from measurements of equilibrium defect concentrations at elevated temperatures. These experiments have led to more precise knowledge of vacancy-type defects. Annealing studies of irradiated metals also provide impor-tant data. For a comprehensive review the reader is re-ferred to the report of the Venice Symposium 5) •
Theoretical work is as yet unlikely to provide precise values concerning point defect properties in metals and there is still a great need for careful and systematic experiments under well-known circumstances. At present we know th at the picture of Manintveld 3) represents a gross
oversimpli-fication, but in spite of the substantial amount of work during the past ten years Baluffi et al. 4) in their recent survey,
come to the rather discouraging conclusion that no point defect has as yet been positively identified as taking part in any portion of the _ annealing spectrum of a cold worked metal.
In section b, of part I of chapter 111 we will present the experimental results of a systematic investigation concer-ning the recovery of point defects, varying the degree of deformation down to strains of less than 10/0 in liquid nitro-gen for pure Au, Ag and Cu.
The experimental procedure will be described in chapter 11.
It will beshown that the recovery of the electrical
resist-. ivity of Au, Ag and Cu as a function of temperature shows the same behaviour. After strains of abl)ut
lt%
there are clean separations between sharp recovery stages, at tem-peratures between -100 and +200 oC. We have called the stages a, b, c, and d. On increasing the deformation the separations vanish and the stages merge gradually leading to a rather continuous recovery which one can divide into the extensive sJages known from literature as 11, 111 and IV. The unraveling of such a complicated annealing in itself is extremely difficult and it is clear th at we must begin with understanding the relatively simple recovery spectrum after small deformations. Such an attempt will be made in chapter V, where we shall also present an interpretation of some other effects observed.In addition, we have investigated the recovery behaviour of the alloys Au+4,64at%Cu, Au+3,6at%Ag, Ag+15,4at%Au and Cu+3,92at%Au aftel' small deformations and annealed in exactly the same way as were the pure metals. These results are described in section c, part I of chapter lIl. In these alloys an increase of the resistivity is observed during annealing, which can be interpreted as an increase of short range order. Comparison of the curves of the pure metals with the recovery of the alloys (section d, part I of chapter lIl) provides the additional information whether the various defects migrating at the different temperatures in the pure metals are capable of increasing the degree of short range order when becoming mobile in the alloys. It is observed th at the c and d defects can change the degree of order. This information will prove to be helpful in deciding the mechanism involved ineach recovery stage.
For Au and Au+4,64at%Cu we have extended the experi-ments to strong deformations by rolling in liquid nitrogen. Qualitatively the annealing behaviour is the same as after stretching but there are some marked differences as weil. Activation energy determinations by the slope intersection method after relatively large deformations (unfortunately the effects aftel' smal! deformations were too smail for this), reveal, as is shown in section e, part I of chapter lIl, a range of energies from 0,4 to 0,8 eV for stage IU of Au. For Ag and Cu the first part of stage lIl, does not have a single energy (0,2 to 0,5 eV for Ag; 0,5 to 0,7 eV for Cu). whereas the second part reveals to be uniquely activated (0,55 eV for Ag and 0,72
ev
for Cu). Stage IV in Ag has an energy of 0,89 eV. Jn Cu the effect of stage IV was too smal! to determine the activation energy involved.From our annealing curves of Au, Ag and Cu we have deduced resistivity-strain relations for the resistance of point defects. In a separate test we have measured stress-strain curves of the pure metals and the alloys. In part II of chapter III we shal! present these results and compare them with Saada 's theoretical formula giving arelation between the production rate of point defects and work hardening6). Our results wil! appeal' to fit this theoretical relation in a semi q~an titative way.
A large and still growing amount of literature concerning the production and annealing of point defects exists. In order to obtain insight into the defect structure of a metal one has
-10-to study the annealing behaviour af ter different ways of introducing defects. In addition, measurements of different properties are indispensable for a general picture of the annealing process. As a case in point we may mention that from electrical resistivity measurements only, we do not learn much ab out the role dislocations play in the recovery process of point defects, whereas the change of Young's modulus for instance, provides the additional information whether or not the defects arrive at dislocations to impede their motion. In chapter IV some aspects of the literature concerning point defect properties in Au, Ag and Cu are reviewed bri.efly. The results of quenching experiments and of measurements of equilibrium concentrations of vacancies at elevated· temperatures are summarized in section b. A brief discussion of the evidence coming from the annealing
behaviour of radiation damage is given under c. It is
shown that stage III in the experiments of Burger c. s. 7) after fast neutron irradiation of Au, Ag and Cu is closely analogous to the corresponding cold work stage in these me-tals as it appears in our experiments. Section d is concerned with some aspects of plastic deformation and the annealing of cold worked Au, Ag and Cu. Some headlines of Saada's theory on the production rate of point defects are summa-rized and some results of annealing stur;ies af ter cold work are dicussed.
Finally. chapter V is devoted to the discussion and interpre-tation of our observatj.ons. The chapter is arranged as follows: After an introduction we discuss in section b the analysis of the experimental results . It is shown that stage lil in Au can be described by 3 basic processes b, c and d which overlap. In Ag and Cu stage III consists of the 2 overlapping basic processes band c. The argument of the second order reaction kinetics for stage III in cold worked Au, Ag and Su, as judged by the linear relationship between the reclprocal value ofthe extra resistivity and time, for an isothermal curve is criticized. There is also a criticism passed on the ap-plication of the Meechan-Brinkman method8) for the deter-mination of energies for the recovery processes of a cold worked metal. In section c it is shown that stages c and d can be interpreted in a straightforward manner in terms ofthe migration ofdivacancies and monovacancies respectively. A discussion of stage b (and of stage II) is given under d. It appears that çmr experimental information on stage b is not adequate to identify this stage definitely with a certain process. There is some evidence that the defect respon-sible is an interstitial, but there are also questions as to
the precise mechanism involved. Three alternative pos si-bilities are discussed. It is suggested that stage III after electron irradiation may consist only of the defects of stage b. Section e is concerned with resistivity changes observed in the alloys. It is concluded that the binding energy of a single or a divacancy with a solute atom in Au (Ag). Au (Cu) and Cu (Au) is very small. A greater interaction may exist between a Cu-Cu pair and a vacancy in Au (Cu).
CHAPTER II
EXPERIMENTAL PROCEDURE
a. Materials
The metals used in this investigation were always in the form of 0,20 or 0,25 mm diameter wire. Measurements were made on polycrystalline Au, Ag, Cu and on the alloys listed in tabel 1.
AHoy AHoy composition (atomie 0/0)
Au (Cu) Au (Ag) Ag (Au) Cu (Au) 95.36 Au 96.4 Au 84.6 Ag 96.08 Cu 4.64 Cu 3.6 Ag 15.4 Au 3.92 Au Table 1: composition of the alloys used in
this investigation.
In the following discussions the symbols of the alloys as given in the first column of the table will be used.
The Au, Ag and Cu wires, with a stated purity of 99,9990/0, were supplied 'by Johnson - Matthey; the alloys by Drijfhout. The Au (Cu) is the same material as used by Korevaar 9) who reports the following impurity contents:
Ag
<
0,5 0/00Si <0,05 Fe <0,02 Mg <0,02
The impurity content of the other alloys is not exactly known, but it is, in relation. to the concentrations of the composing metals, certainly very small.
The diameter of the Au and Ag (Au) wires was 0,25 and 0,20 mm respectively. The Cu, Ag, Au (Cu) and Cu (Au) wires had an initial diameter of 0,50 mm which has been reduced to 0,20 mm (Cu) or 0,25 mm (Ag, Au (Cu) and Cu (Au) by drawing through widia dies. The Au (Ag) wire has been drawn from 0,30 to 0,25 mmo
Prior to the deformation the wires were always annealed for 1 hour at 450°C in vacua (10-Smm Hg), with the excep-tion of Au which was annealed in air. The resistivities at -195° C of the specimens after this annealing treatment are collected in table 2 together with the approximate grainsizes.
specimen Au Ag Cu Au (Cu) Au (Ag) Ag (Au) Cu (Au) grainsize (mm) 0,1 - 0,2 0.05 - 0,1'" 0,1 0, Ol 0,04 0,02 0,005 resistivity 0,45 0,27 0,21 2,22 1,51 S,13 2,12 (micro-ohrn-cm)
Table 2: Approximate grainsizes and reSlStlVmeS of the metals at -l9SoC af ter annealing treatment. (l hour at 4S00C).
b.
Resistivity measurements
The specimen resistance was
always
measured in stirred liquid nitrogen by a conventional method. using a Diessel-horst-type potentiometer in combination with a Kipp galvan-ometer. The smallest <;ietectable change in resistivity was less than 10-11 ohm-cm. For variations in the thermal part ofthe resistance. arising from small temperature fluctuations of the liquid nitrogen. a correction was made by means of a well annealed dummy of the specimen material. which was kept constantly in the nitrogen Dewar.c.
Small deformations
In order to give a wire in liquid nitrogen an elongation of a few per cent or less. a support as shown in figure 1 was used. B is a small block of brass into which the end a of the specimen Scan be clamped. To B one of the current leads is soldered. D is a drawbar. on the end of which a smallioop L of copper wire. with a diameter varying from 30 to 250 /.lm, is fixed. The end c of the specimen passing with a sharp bend through this loop is soldered to a second current lead. The potential probes, Pl and P2 of 50 /.lm
diameter platinum or copper wire. are spotwelded to the specimen at about 160 mrn apart. Current and potential leads are led out through the tube T which is made of perti-nax. to prevent a large heat conduction from the outside into the liquid nitrogen.
-14-T
I 5
160mm
Figure 1. Schematic sketch of specimen support holding a specimen before deformation
After placing the specimen support into a Dewar filled with liquid nitrogen, the sample is deformed by pulling the draw-bar upwards until the loop L breaks. The strenght of the loop determines the degree of deformation, which is meas-ured as the difference in length of the specimen between the potentiiil probes before and after stretching. A strain of less than 0,2% is still measurable.
It is possible to mount the specimen in the support, without giving the wir~ any plastic deformation. For this purpose the drawbar is pulled up until the distance LB is larger than the specimen length ab. Now the specimen is hooked into the loop and the drawbar pushed down in order to clamp the end a into the bloek B, after which current and potential connections are made. If the wires are mounted carefully in"" this way, the ratio of the lengths between the potential probes of two wires of the same material is consistent with
the corresponding ratio of the electrical resistance, proving that the wires were not deformed plastically during the mounting procedure. In the actual construction 4 specimens are mounted in one support. Af ter stretching the 4 wires to different degrees of deformation, they are annealed si-multaneously.
For the experiments for the determination of activation en-ergies, a special specimen frame, having very little heat capacity, was used.
d. Cold rolling
Rolling was done in liquid nitrogen (in one case in pentane of -450 C) with an apparatus as described by Manintveld 3).
To minimize any unaccounted recovery, the mounting of the cold rolled sample also took place in liquid nitrogen. Using a frame as shown in figure 2, mounting is very easy. The
POTENTlAL LEAD CURRENT / LEADS SPECIMEN A i 1 0 . - - - ' -" 10 cm ---~
Figure 2. Frame used to hold cold rolled specimen
frame consists of 2 parts A, made of pertinax. When the cold rolled samp~e is placed in between. them they can be clenched by means of the screws S. The two pairs of small strips B of brass, serving as current contacts are connected with the current leads, which together with the potential leads are led out through thé pertinax tube T. The parts of the specimen, sticking out of the frame, serve as poten-tial' probes and are soldered to the connections P, which project above the surface of the liquid nitrogen during this operation.
-16-e.
Annealing
·After deformation. the specimens were annealed by trans-ferring the support containing the specimen to a tempera-ture controlled bath for a certain interval of time. For the different temperature regions. thermostat baths as given in table 3 were used. When the support is transferred from the liquid nitrogen into the annealing bath. the temperature of the bath decreases by about 0.1° C or less.
Temperature region -130 to 200e 20 100 100 250 thermostat bath pentane distilled wa ter propylene glycol Table 3: Thermostat baths used for annealing
controlled to :!:. oe 0,1 0,01
0,03
After a measured interval of time the support containing the specimen was removed from the annealing bath and transferred back to the nitrogen Dewar for measurement of the resistance.
f.
Apparatus for measuring stress-strain curves
Figure 3 shows a sketch of the apparatus designed for meas-uring stress-strain curves. Al and A2 are the two arms of a balance. On Al a bar B is hanged in a cup and cone construction. On A a sliding weight M is fixed. S is a support which can Ge translated up and down by means of the wheel W. One end of the specimen ab is clamped into the block c on the support. The other end is fixed to the end of the bar. If at the beginning of the experiment the balance is in equilibrium (indicated by the arrows) the length ab is 120 mm and there is no stress on the wire. The wire can . become strained if we put a stress on it by translating M towards the left by mèans of a· worm and gear in a careful construction in order not to disturb the free motion of the balance. The strain of the wire can be compensated by translatingthe support S downwards until the balance is again in its equilibrium position. The translation of S gives th~ elongation of the· wire which can be determined with at! ac-curacy of 0.1 mmo Given the value of M. the position of the weight along A 2 is a measure for the force acting on the wire. All measurements were done with !he specimen in liquid nitrogen.
-'-NI TROG E.:,.:N _ _ -1I DEWAR
I
I
I
a bFigure 3. Apparatus for measuring stress-strain curves
t
•
CHAPTER III
EXPERIMENT AL RE SUL TS
Part I: Recovery of point defects
a.
Introduction
The annealing of the extra resistivity, introduced by low temperature deformation, was isochronally studied as a function of temperature, af ter strains varying from less than 0,2 to about 100/0. The wa.y the small deformations were applied has been described in chapter U.
The shape of the isochronal curves depends upon the degree of deformation. For sufficiently small strains one obtains recovery curves which show discrete recovery stages, whereas for large deformations recoverybecomes continuous, as will be shown in section b, for Au, Ag and Cu. Some preliminary results have been published alreadylO).
For Au we have extended the measurements to large defor-Jllations by rolling in liquid nitrogen. The results are qualitatively the same as af ter stretching but there are
_s"ome marked differences as weIl.
The isochronal curves for the alloys stretched at -195° C will be described under c, where also some data on cold rolled Au(Cu) are discussed.
In section d we will compare the curves for the pure metals with the corresponding curves for the alloys, only as far as is necessary for better understanding of the experimental results, as the main discussion will be deferred to chapter V. Section e is concerned with the determination of acti-vation energies for some parts of the recovery curves for Au, Ag and Cu. Finally, under f, some results on the "reaction order of stage IU", and on the influence of a second deformation are discussed.
b.
Results on Au, Ag and Cu
The results of subsequent isochronal anneaiings for 5-minute periods in 10-degree intervals, after different degrees of
deformation are shown in figures 4, 6 and 7 for Au, Ag and Cu respectively. The deformation increases for the successive curves in upward direction. Along the vertical scale, the resistivity increase, fj,p, is plotted as a per-centage of the final value p , at the end of each run. This p is not the same value fa~ each curve, the differences are
h~wever only a few tenths of ane per cent. For clarity's sake
we have shifted the zero levels for fj,p of the different curves with respect to each other. fj,Po is the resistivity difference. between the beginning and the end of the run. Table 4 lists some numerical data for the curves after stretching.
Au (figure 4) Ag (figure 6) Cu (figure 7) .'
E ,,/0 -,,/0 t1po E 0/0 -,,/0 t1po E ,,/0 t1po -0/0
Pe Pe Pe 0,8 0,06 0,2 0,03 0,5 0,05 1,5 0,12 1,8 0,12 1,3 0,08 3,7 0,25 2,2 0,19 3,0 0,21 5,5 0,40 3,9 0,39 3,7 0,27 5,6 0,49 7,0 0,92 4,6 0,39 6,6 0,63 6,0 0,49 7,9 0,82 9,7 1.23
Table 4: Values for E and the corresponding values for
t1po
- for Au, Ag and Cu. Pe
Let us begin by considering the curves of figure 4 for Au. Starting with E
=
0,8%, the deformation increases up to9,7%. The curve corresponding with the smallest deformation (0,8%) reveals only one stage at about 50°C, which we have called d. For temperatures between 100 and 2000C there is no observable recovery. For E
=
1,5% the resistivityde-creases in 4 stages called a, b, c and d. For this defor-mation the stages a, band c are still very small but become more pronounced when E increases up to 5, 6%. For, E =
6,6% the upper two stages c and d, are no longer separated but merge. For stilllarger deformations the separation be-tween band c also disappearsgradually, and finally one ob-tains a curve as is shown for E = 9,7%, consisting of only two parts. This type of curve was found earlier by ather investigatars 3,9,11)., and fallowing van Bueren 12) and current custom, we have labelled the stages:
"n"
(at temperatures below _600 C) and"nI"
(between -60 and 1000 C)..
.!~~'l09~____ _
t23 ..."
~---0.82 - - ... ~---0~3-,
',n
, ,
,
0.49 - -- - - ---'_
-20-Oa--- ___
a 0.40 - ... :::-, ==---"""'I'~~-o-.J-_ Au (99.999) E% 9.7 a - - - 7.9 --0-4-"'6.6 --o--c ... ~ 5.6 -0-.., ... 5.5 o 0 03.7~5---~~îI~b~--~c~~~
~---0.12 - - --.t>=--f-<~--_+~-_+__
+:::::::
b ~ _ _ _ _ _ _ _ _ _ _ _ _ _ ...o-... ___ -J."..:--'~'--Jo_...~r_'I:l._lo__:..~....:::IOo-o--,,--U--o 1.5 0.06 0.8 -200 -150 - - - Tlmperaturl!°C Figure 4. Typical set of curves for Au for isochronal annealiug for 5 min,Jtes at eachof the temperatures specified (10-degree intervals). Note that for each curve
~ p = 0 at the end of the run.
At the end of the run some of the Au wires were annealed for 1 hour at 450°C. Af ter this treatment the resistivity was measured at -195°C. The resistivity difference before and after this annealing, being the effect of stage V, was of the same magnitude as the total resistivity of point defects. Af ter stretching Cu at -195°C, Berghout 13) also found the resistance recovering in stage V to be about half of the total resistance increase.
We have also measured the recovery of Au rolled in liquid nitrogen. The elongation of the wire, expressed as a percen-tage of the initial length, fc ' is chosen as a measure for
the degree of deformation. Results are plotte.d in figure !),
for Ec =' 6, 46 and 1100/0. The isochronal time is 5 minutes
at each of the temperatures specified, (IO-degree intervals). The unit of the vertical scale is not the same for the
dif-r~=530%~-, "60 , , , n \ \ AuI99.999' 33.8 r"_ ... " \ \ \ \ 1I\ 4.90----_ ...
.
" -200 -100 -SOFigure 5. Isochronal curves of cold rolled Au.
SO 100 ISO 200 250
- Temp.raturf ·C
Holding time 5 minutes (IO-degree intervals).(For the vertical scalesee text).
ferent curves. Along this scale the difference of the resist-ivity at some point of the annealing curve and the final value (after annealing up to 60° C) is plotted as a percentage of this final value. The figures next to the scale indicate the differences of the resistivity after cold rolling and after annealing up to 600C, expressed as a percentage of the value at 60°C. For Ec = 6% we observe the resistivity to decrease in a similar manner as af ter a strain of 5,6% (see figure 4) i. e. in 4 annealing stages a, b, c and d. Stage a below -60° C, b between -60 and 0° C, c between 0 and 30°C and stage d between 30 and 70° C. It is surr::rising however, that the total resistance of these stages is larger by a factor of about 10 compared to the stages after 5,6% stretch-ing and still the stages a, b, c and d are. more or less separated. Another remarkable point is the fact that the magnitude of stage b, with respect to the total resistivity
22
-change, is larger after 60/0 cold rolling than af ter 5,6% stretching. For E c = 46 and 110% we observe the stages II (bel ow -70° C) and III (between -70 and 60°C). Stage III is larger than stage II by a factor 2, 6 for E c = 46%, and for E c = 110% this factor becomes 3, 5 as compared to 1,4 for the annealing curve af ter a strain of 9,7% (see figure 4). It is not likely that part of the stage II defects are lost during cold rolling or during mounting the specimen in the frame. Annealing of the specimen, cold rolled by 110% was continued until recrystallization (stage V) had finished
i. e. at 250°C. In this case the effect of stage V is 30% of the total resistivity change, whereas after stretching this is 50%. We will not attempt to interpret the differences between the stretched and the cold rolled curves since more detailed work on these points will be needed to clarify the situation.
In figure 6 a typical set of curves for Ag for deformations ranging from 0, 2 to 7, 0% is illustrated. Just as in the case of Au, for sufficiently small deformations, Ag shows only one detectable stage centered at about 35°C, (see the curve for E
=
0,2% of figure 6), which on the analogy of Au wehave called d. No recovery occurs between 100 and 200° C. When E increases annealing occurs in 4 stages, which
again, we have called a, b, c and d as in the case of Au. Such curves are shown for E = 1,8 and 2,2%. A further increase of the deformation leads to a rather continuous recovery (E
=
3,9%) and for E=
7,0% annealing is presentat all temperatures investigated. One can divide this con-tinuous recovery rather arbitrarily into three extensive stages, known as stage II, III and IV 14). Stage II annealing .
takes place at temperatures below -100° C, and stage III running from -100 up to OOC is followed smoothly by what is called stage IV.
Unlike the results of Au and Ag, for Cu we failed to find even after deformations of less than 0,2% only one stage, though the stages below OOC were very small. Typical curves for Cu are plotted in figure 7. The curve corresponding with E = 0,50/0 reveals pronounced recovery at about 35 and
170°C. There is also some slight recovery at temperatures bel ow OOC. The isochronal curves for E = 1,3 and 3,0%
here also consist of 4 stages, which again wf5 have cailed a, b, c and d. Obviously, the two weil defined stages. at 35 and 170°C of the curve for E = 0,5% are the stages c and d respectively. On the curves for E = 3,7 and 4,6% one can hardly recognize aseparation between band c
I
6 Po/ P100% 0.920-,
,
,
\ \ \ 0.390.., ",
0.190. __ 0.120- __ \ \ \,
, n
\,
\, ,
"-a --\ \ 0.D3~--- --lSO -100 Ag (99.999) (% 7.0 39 21 1.8 0.2 •Figure 6. Typical set of curves for Ag. (See also the legend of figure 4)
and for still larger deformations (E
=
6,00/0), 3 extensiveannealing stages, known from literature 13), have been
observed, labelled:
"n"
(below -40°C),"rn"
(-40 to 60°C) and"rv"
(60 to 200°C). The separations between the stages are not clear therefore the temperatures given aresome-what arbitrary.
Summarizing the results for Au, Ag and Cu deformed by stretching, it may be said that af ter sufficiently small strains Au and Ag show only oae detectable stage d, operating
~ I '<t' C'J I Ap . 0 Ap lp 0 P200 .490- - _ _ °l 200 Yo
11039~
____ --'-"
'-,
...-
... 0.270- -- __ ... __ _ 0.210--- ______ _ Cu{99.999 ) E% 6.0 4.6 3.7OD.~---_----~~~_:t!:
1:::1:
::-.-o-.-.-:~-: ::~
0.050 -~goon03.0 -200 -lSO -100 -50just above room temperature. For a deformation of 0,5%, 80% of the resistivity decrease caused by the disappearance
of point defects of Cu is due to stages c and d. For a strain
of about 1,5%, in all three metals there are the 4 stages, a. b, c and d. Approximate temperature intervals at which they occur are listed in table 5.
stage II III IV a b <; d smal! deformations Au Ag below -60 below -100 -60 to -10 -100 to -40 -10 25 -40 0 25 100 0 80 large deformations below -60 -60 to 100 below -100 -100 to 0 o 80 Cu below -40 -40 to 0 o 60 120 200 bel ow -40 -40 to 60 60 200 Table 5: Approximate temperatures (oC) for the
dif-ferent recovery stages of Au. Ag and Cu.
When E increases the separations between the stages become less clear and the recovery ever more continuous. In Au the stages c and d first merge as E increases. and latter on the separation between band c also vanishes. The three stages b. c and d make up stage III of Au. In Ag and Cu. when E increases, band c merge, making up stage lIl, which is followed gradually by stage IV annealing. Af ter large deformations, of Au. Ag and Cu, recovery takes place at all temperatures investigated and is of an essentially continuous nature.
c.
Results on the alloys
Af ter. one hour annealing at 450° C in vacua (10-5 mm Hg).
the alloys were deformed in liquid nitrogen and then annealed for 5-minute periods in 10-degree intervals just as were the pure metals. The results of this treatment are plotted in figures 8 to 13. After stretching, each curve shows a minimum value Pmin of the resistivity p, which is chosen, somewhat arbitrarily, as zero level for t:.p. For Au(Cu) the minimum occurs at -20, for Au(Ag) at 10. for Ag(Au) at -100 and for Cu(Au) at 20° C. Along the vertical scale
-26-,6.p is plotted as a percentage of p min. For a certain aHoy
P min has not exactly the 'same value for each curve. since
P min depends on the degree 'of deformation .. The differences are however only a few tenths of one per cent or less. Again. for clarity's sake. we have shifted the zero levels for ó,p for the different curves with respect to each other.
Looking at the plots of the Au(Cu) aHoy (figure 8). we see
(% 10.2 ~--o-<>-o9.2 6.0 '----0--.5.5 ..,0--0-.,>-0 4.6 P.".-I!20% P·20 0205 ... - - - ' Au + 4.64.t % Cu 0.159 0--- -- ___ ... .. " ,
~~::
==
=
=
=
~ =
=
=
--
~~ ~ ~
:
----.--.>-1----_1.-0---0.047 <>- __________ _____ ~_'-'!,,---+----...!-.A 0.034 < > - - - ---= ...
~"'-..-""__1,...--0.021 0 - - - -... ..---+0 _ _ _ ... -" 0.009 0- - - -- - - -- - -- - - -_ - - . , ...-+-____ -+ ___ ___
0.000 0 - - - + ____ + ______ -0.000 <>--- - - ----<>-<>--<>_-+-___ <>--<>-+-____ -<>-... _--0---200 -150 -100 -50 50 - - - - TemperJituri oeFigure 8. Isochronal curves of Au(Cu) af ter stretching. Holding time 5 minutes (10 -degree intervals).
3.4 2.8 1.6
0.5
0.2
that after deformations of 0.2 and 0.5% there is no change in resistivity. up to 20°C. For higher temperatures there is a resistivity increase. For E
=
1.6% or more. the increasealready starts at -10° C. whereas at lower temperatures the resistivity decreases in two stages. one below -60°C. and one between -60 and -20°C. as can be seen clearly for deformations between 2.8 and 6.0%. For deformations larger than 1.6% the resistivity increase goes through a maximum
(p max ). Some numerical data are listed in table 6.
The type of curves corresponding with large deformations was observed earlier by Korevaar 9) on an Au+7at%Cu
P-195 -P-20 Pmax -P-20 E 0/0 0/0 0/0 P -20 P- 20 1,6 0,009 0,623 2,8 0,021 0,686 3,4 0,034 0,688 4,6 0,047 0,700 5,5 0,056 0,688 6,0 0,066 0,682 9,2 0,159 0,628 10,2 0,205 0,610
Table 6. Some numerical data for the curves of figure 8 (A u(Cu)). P-19S-P-20 represents the total resistivity decrease and Pmax - P-20 the total resistivity increase.
aHoy af ter an elongation of 15% in liquid nitrogen. The in-crease is ascribed to an inin-creased degree of short range order.
Figure 9 shows typical results obtained for the isochronal
~ ___ ro-""'"",,_ 33 59 Au + 4.64 .t ,. Cu 153 -200 -150 -100 -50 50 100 - -___ T.mper.tur. ec
Figure 9. Isochronal curves for cold rolled Au(Cu) Holding time 5 minutes (10-degree intervals).
-28-runs of cold rolled Au(Cu), for Ec
=
33, 59 and 153%. Theresistivity of these specimens decreases by annealing to ab out 20°C. At higher temperatures there is an increase followed by a small decrease. The curve for E c
=
330/0 reveals two clearly separated stages below 20° C. The spea-ration occurs at about -60°C. This is less clear for the two other curves for the larger deformations. The stage between -60 and about 20°C grows rapidly with increasing deformation, whereas the magnitude of the stage below -60° C is only slightly deformation dependent. There is not much to be said about absolute values of resistivity changes since the geometry of the cold rolled specimen is not exactly known, and therefore it is impossible to give more quanti-tative data. No attempt will be made to explain the details of these curves since our experimental information on this point is meagre.Figure 10 shows typical results for Au(Ag) for E 3,2, P-~~PIO -071' • __ _ ~
..
I
OD2t ... ---- __ _ 200 '00 50 0 50 100 --Y""p.rotun-CFigure 10. lsochronal curves for Au(Ag) (af ter stretching) Holding time 5 minutes (10 -degree intervals) .
6,2 and 11,1%. These curves reveal a resistivity decrease in two stages followed by an increase. Numerical data for the decreases and the increases are listed in table 7. The annealing results of the Ag(Au) alloy for E
=
2,0 and 3,9% are illustrated in figure 11. Recovery takes place at€ ,,/a P- 195 -PlO ,,/a Pmax - PlO ,,/a
PlO PlO
"3,2 0,028 0,069
6,2 0,061 0,037
11,1 0,218
Table 7: Numerical data for the curves of
figure 10 (Au(Ag». P-195 - PlO
represents the resistivity decrease.
Pmax -PlO the maximum increase
of P above 100e.
temperatures below -100°C. Between -100 and 20°C there
is a gradual increase ~P1' foHowed by a second increase
~P2 (20 to 70° C). For· further data see table 8.
I
-200 -ISO -100 -so -:...--_ _ ~~mpor.lu,,~oo
Figure "u. Isochronal curves for Ag(Au)
Holding time 5 minutes (10 -degree intervals) .
P -195 -P -100 P20 - P -100 P70 - P20
E ,,/a ,,/a "/. ,,/a
P- 100 P-lOO P -100
2.0 0.010 0,007 5 0,010
3,9 0,013 0,007 0,008
Table 8: Numerical data for the curves of figure 11 (Ag(Au»
P-195 - P-100 represents the total resistivitydecrease.
P20 -P-lOO and P70 -P20 the subsequent increases.
Figure 12 shows the results for the Cu(Au) aHoy for E
=
1,4,2.0 and 3.5%. At temperatures below 20° C, the resistivity
decreases in two scarcely separated stages, (separation at
-30-I
I
Cu + 3.92 at"; Au 1!,9SP20 =0.072% 0---_ .... P20 ... , ... , 0.0 - - - --0.0160--- __ -oo-I,+--.o..J...<' oFigure 12. lsochronal curves for Gu(Au) (small strains) Holding time 5 minutes (lO-degree intervals).
E%
2.0 1.4
increase consisting of two parts: .6.Pl between 20 and 100°C and .6.P2 between 120 and 250° C. The magnitude of these increases becomes smaller as E grows, (see table 9).
P-195 -P20 P100 -P20 P250 -P120 E ,,/0 ,,/0 ,,/0 ,,/0 P 20 P20 P20 1,4 0,016 0,04.2 0,062 2,0 0,038 0,039 0,040 3,5 0,072 0,036 0,030 7,1 0,153 0,020 14,0 0,296
Table 9: Numerical data for the curves of figures 12 and 13 (Gu(Au)l P-195 - P20 represents the resistivity
decrease. PlOO - P20 and P250 - P120 the
sub-sequent increases.
For large E the increases even change into decreases, as
is shown in figure 13. First, the increase between 120
and 250°C changes into a decrease (E
=
7,1%), and ÎorE = 14,0%, along the whole curve the resistivity decreases.
Also in these cases ÄP is consistently expressed as a per-centage of thc value of paf ter annealing up to 20° C.
It may be well to compare in the following section the iso· chronal curves of the pure metals and the alloys, since this is linked up directly with the previous discussions. We will not repeat the following discussion in chapter V.
,~.D.ltl'" """ ~ OJSJ'"
-
... ... -200 -lSD -100 -SD 0 50 100 lSD 200 - - - -- Temperature-C (lil; ".0 7.1Figure 13. See the legend of figure 12 (large strains).
d.
Comparison between pu
re me
tals and alloys
The principal difference between the annealing behaviour of the pure metals and the alloys, is that the pure metals always give a resistivity
decrease,
whereas for some parts of the annealing curves of the alloys, the resistivityin-creases .
This is due to an increase of short range order (s. r. 0.) of the alloys. A complete discussion of this pheno-menon would be too long and involved and out of the scope of this thesis. We shall therefore merely point out a few aspects from literature. For more details the reader is re-ferred to the articles by Nix and Shockly 15) , Lipson 16) ,Muto and Takagi l:7) and to the book of Elcock Hl) . In an
ordered state of a binary alloy as, say CuAu, the atoms of different kind are not distributed at random over the lattice points of the crystal. but form some ordered arrangement, adsing from the fact that the attraction between an Au and a Cu atom in the lattice is larger than the attraction between two like atoms.
This tends to a situation by which every Cu atom has as many Au neighbours as possible and vice versa.' In the alloys we investigated, only short range order occurs, i. e. a state by which ·the local order reaches over ju st a few lattice
-32-points, as opposed to long range order, which is extended over the whole crystal, leadlng to a super structure. Hirabayashi 20) and Damask21) have found that short range
order in CuAu alloys causes an increase of resistivity. As the temperature increases the energy of the thermal vibrations ofthe atoms becomes larger which may cause them to change their position, and according to free energy considerations the order at equilibrium, wiH decrease with increasing temperature. In general, the equilibrium order will not be realized within reasonaple times at roomtemperature. How-ever, Brinkman et al. 21) measuring electrical resistivity have demonstrated that the isothermal orde ring rate of CUaAu at 150°C is considerably enhanced oby quenching the aHoy from a temperature in the vicinity of 600°C. Similar results were found on AuCu with atomic percentages of Cu varying from 1,5 to 25,4 by Korevaar9) and on Ag+50at%Au
and Ag+62at%Au by van der Sijde 22). The results obtained are interpreted very satisfactorily in terms of changing the de-gree of order by the migration of quenched-in vacancies. This order-disorder phenomenon can be used to detect defects, which, when becoming mobile, produce consider-able atomic rearrangement, leading to an increase of the degree of s. r. o. of the aHoy. If the increase of the elec-trical resistivity associated with the increased degree of s. r. o. resulting from the
migration
of the defects. is larger than the resistivity decrease associated with thedisappearance
of the defects, one measures a net increase.As has been said, Korevaar9) observed that on annealing of Au+7at%Cu, stretched 15% in liquid nitrogen, there is a resistivity decrease at temperatures below -40° C (stage II), similar to the decrease in pure Au, whereas at ab out room temperature (stage lIl). there is a large increase. From these results Korevaar draws the conclusions, that the defects migrating in stage II cannot be divacancies, since by arguments outlined above, their migration would have an influence on the degree of order, whereas the defects, mig rating in stage III
are
capable of increasing the order, just as do the °quenched-in defects.Another point, somewhat aside from the order-disorder phenomenon, is the fact that compared with the recovery of defects in pure metals, the presence of solute atoms may complicate the annealing kinetics of the defects in the alloys esp,eciaHy when the concentration of solute atoms is large as it is in our Ag(Au) aHoy. This may complicate to some extent the comparison of the data for pure metals and aHoys. Nevertheless this comparison may provide additional
infor-mation which may prove to be helpful in deciding the me-chanism involved in each recovery stage.
With this as background we will now consider together the isochronal curves of the pure metals and of the alloys. In figures 14, 15, 16 and 17 we have drawn two curves of nearly the same deformation: one for the pure metal and one for the corresponding aHoy. It will be shown in part II of this chapter that if different metals are stretched to the same e, th is does not necessarily involve equal defect concentrations. Therefore our comparison here wiH be qualitative. Along the vertical scale of the figures the ab-solute value of the resistivity change is plotted. For the convenience of comparing the curves we have put ~p equal to zero at the beginning of each run.
Figure 14 indicates the recovery of Au and Au(Cu) for E
t
- 0 -Au + 4.64 at % Cu --Au (99.9991o --- .... - ... _ _ ~~~~-_...__
-200 -ISO -100 -SO o SO 100 ISO 200
-Temperoture 'C
Figure 14. Comparison between Au and Au(Cu) (very small deformation)
E = 0,4 and 0,5% respectively. Up to 20°C there is neither
in the aHoy nor in the pure metal, any observable change of resistivity. Just above room temperature the curve of the aHoy goes up, whereas in the pure metal we observe the resistivity to decrease in one stage caHed d. From this picture it is obvious that the defects mobile at stage d of Au are capable of increasing the degree of s. r. o. when migrating in Au aHoyed with a few atomic percent of Cu. When the observed recovery' in Au has finished, at 70° C, the resistivity of the aHoy continues to increase and later on it decreases. In chapter V we will suggest an interpre-tation for this observation.
-34-In figure 15 we have drawn isochronal curves for Au and Au(Cu), for a deformation of 5,5%, and part of the curve
-0--Au + 4.64at%Cu -6-Au + l.6oto/.Ag - Au (gg.9991 -1 -100 -150 -100 -50 50 (% 55 100 -r:;;peroture cc
Figure 15. Comparison between Au. Au(Cu) and Au(Ag).
of Au(Ag) for E = 6,20/0. The pure metal reveals the stages
a, b, c and d, as discussed in section b. At temperatures below -200 C the resistivity of the alloys decreases in two
stages, in a similar manner and at the same temperature intervals as do the stages à. and b in pure Au (this part of the curve for Au(Ag) is not shown, since it is not essentially different from the other curves). On the analogy of Au, the lower two stages of the alloys are also called a and b. In the temperature range where the stages c and d occur. in Au, we ~bserve an increase of the resistivity of the alloys in one step. This increase is larger for Au(Cu) than for Au(Ag). On comparing figures 14 and 15, the con-clusion is at hand that in the curves of figure 15, both· the c and d defects contribute to the increase of s. r. o. in the aHoys, though we cannot separate the contributions of the different defects because stages c and d are very close to each other. The resistivity decrease (stages a and b). in Au(Cu) is larger than the total decrease of a and b in pure Au. For the Au(Ag) aHoy this decrease is slightly less compared to the corresponding effect in Au.
Au(Cu) (figure 9), lE'aving stage V recovery aside, one can see that from 20°C on, the aHoy resistance starts to increase whereas the decrease of the resistance of Au goes on up to 60° C. The defects migrating in th is tem~erature range, being part of the c defects and the d defects, cause an increase in the degree of order of the aHoy.
It is likely that the c defects in Au(Cu) are already mobile below 20°C, but the effect of the increased degree of order on the resis"tÏvity might become obscured by the large re-sisbvity decrease associated with the disappearance of de-fects, sincE' the defE'ct concentrations are large in this case. Figure 16 shows two curves: one for Ag (E
=
2, 20/0) and one for Ag(Au) (E=
2,0%). For tE'mperatures above -100°C the aHoy resistjvity increases in two stages ÀP1 and ÀP2'0.5 - 0 -Ag+ 15.40t% Au ... Ag (99.999) (=2.0% ~ ... (=2.2% -200 -150 -100 -50 0 50 100 -Temperoture ·e
Figure 16. Comparison between Ag and Ag(Au)
It is clear that the stage d defects. cause ÀP2' The incr~ase. f::. PI takes place over a braad temperature range where'
stages band c recovery occurs in the pure metal. The resistivity decrease below -100°C is larger for the aHoy than for the pure metal.
Annealing curves for Cu (E = 3,0%) and Cu+3, 92 at%Au (E
=
3,5%) are iHustrated in figure 17. At temperatures above 20° C the curve of Cu shows the stages c (between 0 and 60°C) and d (between 120 and 200° C), whereas from 20°C on the resistivity of the aHoy increases in two stages f::.P1 (20 to 100°C) and f::. P2(120 to 230°C). Thus the migration of the defects which are mobile in pure Cu at the stages c and d causes the resistivity increases f::.p 1 and f::.p 2res-pectively in Cu(Au). The observation that the increase starts at a slightly higher temperature than the onset of stage c in Cu may be a result of the large effect of disappearing defects in Cu(Au) obscuring part of the increase. The re-sistivity decrease (stages a and b) of the aHoy is 6 times
o --- __ , , -1 -1.5
"' ,
, " ,,
,,
, ,,
" -200 -150 -100 -50 -36-o __ Cu+ 3.92at%Au - C u 50 100 150 200 250 • remperature oeFigure 17. Compàrison between Cu and Cu(Au)
larger than the decrease of resistivity by annealing up to 20°C of pure Cu. This large effect cannot be ascribed to the slightly larger deformation of the alloy.
We may summarize the results of this section as follows: 1. The defects, mobile in Au, Ag and Cu at the stages c and d, are capable of increasing the degree of s. r. o. when be-coming mobile in the alloys Au(Cu) and Au(Ag). Ag(Au), and Cu(Au).
2. Atlowertemperatures (stages a and b) we always measure a net resisitivity decrease (with the exception of stage b of Ag(Au)); (see also chapter V). The decrease in the alloys occurs in a similar manner as in the corresponding elements. The ratio of the resistivity decrease of stages a and b to the resistivity increase at c and d, depends strongly upon the degree of deformation of the alloys.
3. For q certain small value of E stage a+b in Au(Cu) and
Cu(Au) is larger than in Au and Cu respeetively. In Au(Ag), stage a+b is somewhat smaller than the corresponding effect in Au. At stage b of Ag(Au) a net increase is observed. For the same &mall strain the effect of stage a is larger in Ag(Au) than in Ag. These points will come up again for discussion in part II of this chapter.
e.
Activation energy determination
If the migration of a certain defect is a thermally activated process with a single energy of activation E, the rate of
disappearance of this defect at temperature T (OK) is gen-erally assumed to follow an equation of the form8):
dn/dt = f{n, ql' q2' .... qn) exp··E/kT (1)
where n is the defect concentration and the q's represent properties of the specimen independent of tand T leading to the annihilation of the defect, k is Boltzmann constant. If the associated extra electrical resistivity is a single valued function of n, which is areasonabIe assumption for n sufficiently small, then it follows that
d.6p/dt
=
F{.6p, ql' q2'· .. · qn) exp-E/kT (2) The important quantity E can be determined by the so called slope intersection method, i. e. by. changing the isothermal annealing temperature Tl suddenly to T2 and by studying the change in annealing rate:(d.6P/dt)1
- - - =
exp{E/k) (I/T2 - I/Tl) (d.6p/dt)2(3) In many cases however, separated single processes do not occur therefore this picture is olten too simpIe. Looking for instance at the recovery of Au following large defor-mations we observe two extensive recovery stages II and lIl. Looking at figure 4 we see that as the deformation in-creases, the 3.processes b, c and d merge, and make up stage III and therefore this stage is essentially not a single process. After deformations of a few per cent or ,less, the annealing curves do reveal well separated stages. Un-fortunately however, these effe cts are too small to deter-mine activation energies and detailed kinetics. If one still wants to know something ab out the activation energies one will have to study the complicated recovery curves af ter large defo-rmations, involving large defect concentrations, and one will have to apply formally equation (3), leading to apparent activation energies'~). We have done this for Au, Ag and Cu, keeping in mind the picture of the development of the extensive stage.s (lI, III and IV) out of the small well defined steps a, b, c and d. The accuracy of the E deter-minations is
±
0,03 eV with the exception of the E for stage IV of Ag. In this case where the resistivity effect 0) There is still another possibility to obtain information about the activation energiesof stages c and d, af ter small deformations by studying the recovery kinetics of the
-38-is small the accuracy -38-is
±
0,06 eV. lf the slope inter-section method reveals formally a range of E value s as recovery proceeds, th is implies complicated kinetics. lf E is constant in a certain range, equation (3) may hold.Figures 18 to 22 illustrate the results of such studies on Au, Ag and Cu. Along the vertical scale ~p is plotted in arbitrary units. The figures on the left side of the curves
indicate the isothermal annealing temperatures and the figures
on the right give the values obtained for the apparent acti-vation energies. The dotted lines are isochronal lines.
Figure 18 shows results for Au. Curve A was obtained on a
specimen rolled in 1lquid nitrogen. (Ec
=
580/0). Before an-nealing at -51,0° C the specimen was held for 5-minuteperiods in 15-degree intervals from -100 to -70°C, in order
to anneal-out stage Il. A continuous range of activation
energiesfromO,42 to' 0,76 eV is observed in the'temperature range from -51,0 to 20,8° C. The final value of the
resist-A, Ar'itr." .... it.
I
-" A 'w ... , ... ~.r . . l ... t .... .Figure 18. Actlvation energies for stage III of Au
Curve A: Ec
=
58"/0 at -195°C Curve B : E c = 83"/0 at -45°Civity Pe, was obtained after the specimen was annealed for 15 minutes at 60°C. Schüle et al. 11) claim to have found a
single activation energy of 0, 71
±
0, 02 e V for the migration of the stage III defects of Au. However, they rolled their specimens at -40°C. In an attempt to reproduce this resultwe have rolled Au in pentane of -45°C to 83% and used the slope intersection method to determine E, which reveals a range from 0,60 to 0,81 eV (curve B). However, Schüle et al. determined E using the Meechan-Brinkman method,8) which is as fo11ows: One of two identical specimens (same history, same deformation), is isothermally annealed at temperature Tc (OK), the other one isochrona11y for Dot mlnutes at each of the temperatures Ti (OK), (i
=
1,2,3, .•. ). The change of resistivity in the iIh isochronal pulse beingDop. By comparing the isochronal data with the isothermal ruri one can find the time tj, requireà at Tc to bring about the same Dop .• Together with equation (2) it now fo11ows that:
I
or
In . t· I
=
C - E /kT 1 (4)with
C
=
In Dot + E/kTca plot of ti versus I/Ti gives a straight line the slope of which determines E. Needless to say that this method only holds if the ti versus I/Ti points essentia11y from a straight line. It is doubtful whether this is the· case with the points of SchUle et al.
Figure 19 shows the results for stage III of Ag stretched 100/0 (in tension) in liquid nitrogen. Before starting annealing at -90,0° C, stage II is anneá1ed-out by holding the specimen for 10 minutes at -100<' C. The first part of stage III (fron:
-90,0 up to 44,5°C), corresponding with stage b (-100 to -40°C) reveals activation energies which range from 0.18 to 0,50 eV. The second part between -44.5 and -2.7°C, corresponding with stage c (-40 to 0° C), has a constant energy of 0,55 eV.
Activation energies of stage IV annealing of Ag are given in figure 20 for E = 10%. Before starting the measurements,
stage II and UI are annealed-out by holding the specimen for 5-minute periods in 10:degree intervals at temperatures I;>etween -100 and 10° C. The resistivity effect of stage IV is very sma11, therefore the accuracy in this case is only
± 0,06 eV. On the dotted· line representing the isochronal curve for 1 minute one can clearly see stage IV, fo11owed
6p
Arbltrary
urllts
t
-40-Isothermol onneollng time
Figure 19. Activation energies for the first and second part of stage III of Ag (E
=
100/0)gradually by stage V annealing (only partly shown). The activation energy of 1,04 eV belongs to the very beginning of this stage. The average value for stage IV is 0,89 eV. Figure 2] shows values for E of Cu for temperatures between -98,0 and 12,OoC for a strain of 10%. A continuous range of energies from 0,21 up to 0,72 eV is found. The values up to -40,7° C belong to stage Il. The recovery of the first part of stage lil (-40,7 to 2, lOC) corresponds with stage b (-40 to OOC). The value E
= 0,72 eV is measured at
tem-peratures where stage c (0 to 60° C) occurs.In figure 22 the. data for the second part of stage III of Cu (from 2,1 to 49, 5°C) corresponding with stage c (0 to 60° C) are illustrated. This annealing reveals a constant activation energy of 0,72 eV. The effect of stage IV of Cu was toa small determine E.
6p Arbitrory units q Ta =25.5't \ , , , lmin Ag {99.999I 1.04 \ \ \ \ \ 82_5 , , \
-Isothermol onn.allng timeFigure 20. Activation energy for stage IV of Ag (E
=
10"10)A.rbi~/:'ry To=-98.dt
UOIts
I
E.071.v
n
Figure 21. Activation energies for part of stage n and for the fim part of stage III of Cu. (E = 100/0)
t:.p Arb,trory
units
42
-Isothermol onneol,ng t ,me
Figure 22. Activation energy for the second part of stage lil of Cu (E
=
10',/0)f.
Discussion of some additional results
1. "Reaction order of stage lIl"
For some simple situations the rate equation (2) may be written as:
d~p/dt = -A' Äpr exp-E/kT (5)
where r represents the order of the process and A I a constant.
Atomistically, a first order process (r=l) reflects the action of a single defect, a second order (1'=2) or higher order process, reflects tl!e combined action of two or more defects. For a second order process integration of equation (5) yields:
(
-B
f
dto
where B = A' exp-E/kT is a constant for an isothermalrun, and ~pc represents the initial resistivity due to the defects, or
