Change of the resistivity of some face centered cubic metals after cold-working at liquid air temperature

CHANGE OF THE RESISTIVITY OF

SOME FACE CENTERED CUBIC METALS

AFTER COLD-WORKING AT LIQUID

AIR TEMPERATURE

PROEFSCHRIFT

TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAP AAN DE TECHNISCHE HOGESCHOOL TE DELFT, OP GEZAG VAN DE RECTOR MAG-NIFICUS Dr O. BOTTEMA, HOOGLERAAR IN DE AFDELING DER ALGEMENE WETEN-SCHAPPEN, VOOR EEN COMMISSIE UIT DE SENAAT TE VERDEDIGEN OP WOENSDAG

26 MEI 1954, DES NAMIDDAGS TE 4 UUR

DOOR

/0/2

^ ^ " ' ^

JAN ADRIANUS MANINTVELD

NATUURKUNDIG INGENIEUR GEBOREN TE DELFT

,OOH0S32q^

!i^HBH05»HH03i

D I T P R O E F S C H R I F T IS G O E D G E K E U R D DOOR DE PROMOTOR: P R O F , DR M . J , D R U Y V E S T E Y N

J

This work i s p a r t of the research programme of the Researchgroup "Metals P,O.M. - T , N , 0 . " of t h e " s t i c h t i n g voor Fundamenteel Onderzoek der Materie" (Foundation for Fundamental Research of Matter - F.O.M.) and was also made p o s s i b l e by financial support

from the "Nederlandse O r g a n i s a t i e voor Zuiver-Wetenschappelijk Onderzoek" (Netherlands Organization for Pure Research - Z.ÏÏ.O.).

C O N T E N T S

Chapter 1. Introduction and summary 7 Chapter 2. Description of experiments and r e s u l t s 13

A. Increase of the r e s i s t i v i t y of Cu, Ag, Au and Pt due to cold-working by s t r e t c h i n g wires a t l i q u i d a i r temperature and i t s recovery a f t e r

subsequent tempering 13 B. Increase of the r e s i s t i v i t y of Cu due to

cold-working by r o l l i n g wires at l i q u i d a i r temper-a t u r e temper-and i t s recovery temper-a f t e r subsequent

tem-pering 22 C. Calculation of a c t i v a t i o n - e n e r g i e s 33

D. Some experimental information about the i n

-fluence of the i n i t i a l condition of the metal. 37 Chapter 3. I n t e r p r e t a t i o n of the observed phenomena . . . . 41

A. Some a s p e c t s of t h e d i s l o c a t i o n - t h e o r y of

p l a s t i c flow in metals 41 B. A n a l y s i s of t h e r e c o v e r y with a s i m p l i f i e d

model for the diffusion of defects 44 C. Mechanism of the second recovery-step . . . . 48

D. Review of some ways of generation of vacancies

by p l a s t i c flow and t h e i r a n n i h i l a t i o n . . . . 51 E. P o s s i b l e mechanisms for t h e f i r s t r e c o v e r y

-step 55 F. A more detailed comparison of the experiments

with the theory developed 59 Chapter 4. Review of some r e l a t e d experiments from l i t e r a t u r e 65

A. Cold-working experiments at low temperatures . 65

B. Quenching experiments 70 C. Experiments on i r r a d i a t i o n of metals with high

energy-particles at low temperatures 71 D. Stored energy-measurements a f t e r cold-working. 77

C h a p t e r 1

I N T R O D U C T I O N A N D S U M M A R Y

The e l e c t r i c a l r e s i s t i v i t y of a metal i s changed by cold-working. When a metal i s deformed p l a s t i c a l l y a t roomtemperature, t h e r e s i s t i v i t y appears t o i n c r e a s e r e l a t i v e l y to i t s value in t h e undeformed c o n d i t i o n . Only one example of work on the e f f e c t of p l a s t i c deformation on the r e s i s t i v i t y w i l l be given. A more com-p l e t e d i s c u s s i o n of l i t e r a t u r e has r e c e n t l y been com-p u b l i s h e d by T. Broom ^.

Taiiman and Dreyer ^ cold-worked Cu, Ag, Au, P t and Pd by r o l l i n g a t roomtemperature. For a value of deformation characterized by a r e l a t i v e decrease in c r o s s - s e c t i o n of the specimens of about 98% in a l l cases a r e l a t i v e i n c r e a s e of the r e s i s t i v i t y of about 2% was found. At the same time they studied the mechanical proper-t i e s of proper-the meproper-tals during deformaproper-tion by measuring proper-the hardness. An i n c r e a s e of t h i s property was found with i n c r e a s i n g amount of cold-working. After the deformation annealing a t higher tempera-t u r e s was a p p l i e d . The r e s u l tempera-t of tempera-t h i s annealing was s tempera-t u d i e d by the authors by measuring the value of the r e s i s t i v i t y as a func-t i o n of func-time for d i f f e r e n func-t anneal i n g - func-t e m p e r a func-t u r e s . A p a r func-t i a l recovery of the e l e c t r i c a l p r o p e r t i e s was found, accompanied by a resoftening of the metal due to the same tempering treatment. In the case of Cu, for example, t h i s recovery mainly took place a t tenpering temperatures between 100 and 200 °C for annealing times of half an hour. The r a t e of the recovery appeared to be l a r g e r a t h i g h e r tempering t e m p e r a t u r e s . Analogical e f f e c t s have been obtained for a l l o y s by the same authors ^.

The i n c r e a s e of the r e s i s t i v i t y being caused by a higher degree of d i s t u r b a n c e of the l a t t i c e , i t s p a r t i a l recovery will be due t o a d i s a p p e a r a n c e of a p a r t of the i n t r o d u c e d d i s t o r t i o n s t o places where t h e i r influence on the r e s i s t i v i t y i s l o s t , a t l e a s t p a r t l y .

An increase of the resistivity and its partial recovery being essential features of plastic deformation, it was

M.J.Druyve-1. T, Broom; Adv. Phys. 3, no 9, 26, 1954.

2. G.Tamraan and K.L.Dreyer; Ann.d.Phys, 16, 111, 1933. 3. G.Tamman and K.L.Dreyer; Ann.d.Phys. 16, 657, 1933.

s t e y n ' s s u g g e s t i o n t o look f o r an e x p e r i m e n t a l answer t o t h e following question:

I s the i n c r e a s e of the r e s i s t i v i t y produced by the same de-f e c t s t h a t cause the work-hardening?

This question could moreover be extended as follows:

I s the value of the increase of the r e s i s t i v i t y measured a t room-temperature, caused by a l l defects produced in the l a t t i c e during cold-working or has a p a r t of these d e f e c t s already disappeared from t h e l a t t i c e by a kind of recovery which may take p l a c e in very s h o r t times a t roomtemperature?

The answer to t h i s question was given by Molenaar and Aarts * who showed experimentally t h a t the l a t t e r p o s s i b i l i t y was undoubtedly r e a l . To get d e f i n i t e information i t was necessary to deform a metal a t a low temperature and to study whether recovery occurred a t roomtemperature.

Molenaar and A a r t s cold-worked copper and s i l v e r by s t r e t c h i n g wires of 0.20 mm diameter in a bath of l i q u i d a i r . Before deform-ation t h e i r wires had been vacuum-annealed. Measuring the change of r e s i s t a n c e and t h e r e l a t i v e e l o n g a t i o n of t h e wire a f t e r s t r e t c h i n g , for Cu the increase of the r e s i s t i v i t y p was o b t a i n -ed a s a f u n c t i o n of t h e e l o n g a t i o n . The r e a l i t y of a complex mechanism i s shown very c l e a r l y by the following

recovery-experiment Molenaar and Aarts c a r r i e d out.

Ap/p was measured as a function of AZ/I a t - 183 °C, p represents the r e s i s t i v i t y of the undeformed Chi a t 183 °C, M/l the r e l a t -ive elongation of the wire. Ap i s the increase of p due to cold-working. Ap i s independent of temperature according to the r u l e of Mathiessen *.

After a c e r t a i n amount of deformation a t l i q u i d a i r temperature the wire was removed from i t s cold bath and allowed t o stay a t roomtemperature for some time. After t h i s tempering treatment the wire was put i n t o the l i q u i d a i r again and the value of Ap/p was measured under the same circumstances as before the annealing. All measurements were c a r r i e d out with the wire u n s t r e s s e d . The r e s u l t of t h i s experiment i s shown i n the f i g u r e 1 by t h e f u l l l i n e .

* For Cu no deviations from this rule have been found ' . For Ag small deviations were obtained. The order of magnitude, however, is much smaller than the measured differences in Ap.

4. J,Molenaar and W.H.Aarts; Nature, 166, 690, 1950. 5. C.W. Berghout; Physica, 18, 978, 1952.

% P 2ü Cu kg/mm^ ^'"^ y ^ . ^ / ^^ / ^ / t" / ^ / /' > -16 ^ ' / • > ^ y j ^ • j r • v ^ • / / 8 X ' / >• y^ y^ y/^ • >^ y j / ^ y J f ^ / ^^ ^y^ 10% Figure i

Cu stretched a t liquid air temperature to 8% extension, allowed to warm up to 20 oc and kept there for 3 hours,

then drawn further at - 183 oc again. full line: Ap/p versus elongation. dotted line: tension versus elongation.

(after Molenaar and Aarts)

The d i s c o n t i n u i t y in the Ap/p curve i s caused by the applied tem-p e r i n g treatment a t roomtemtem-perature. I t c l e a r l y shows a tem-p a r t i a l recovery of the i n i t i a l increase of the r e s i s t i v i t y . After tem-p e r i n g the measurement of Atem-p/tem-p as a function of f u r t h e r elonga-tion was continued in liquid a i r .

Another e s s e n t i a l f e a t u r e of the d e f o r m a t i o n - e f f e c t s could be given by Molenaar and A a r t s as they measured a l s o the s t r e s s -s t r a i n curve for the applied deformation. The r e -s u l t of t h i -s me-chanical measurement i s shown by the dotted l i n e in figure 1. The s t r e s s in kg/mm^ i s p l o t t e d against the elongation in %. The most remarkable f a c t o c c u r r i n g i s t h a t t h e s t r e s s s t r a i n -curve remains continuous a f t e r the a p p l i e d h e a t - t r e a t m e n t a t a temperature of 20 °C. So i t was found by Molenaar and Aarts t h a t whereas the change of the e l e c t r i c a l p r o p e r t i e s due to c o l d -working p a r t l y r e c o v e r by a h e a t - t r e a t m e n t as a p p l i e d - the change of the mechanical p r o p e r t i e s , due to the same deformation, i s not i n f l u e n c e d by t h i s a n n e a l i n g or i t must be w i t h i n t h e accuracy of t h e i r measurements. This shows t h a t i n no way t h e changes of the e l e c t r i c a l and mechanical p r o p e r t i e s due to p l a s t -i c deformat-ion are caused by e s s e n t -i a l l y the same d e f e c t s . Ana-logical e f f e c t s have been found for Ag and Al. I t may be expected according t o measurements l i k e those of Tamman and Dreyer

t h a t a t r e l a t i v e l y higher temperatures a further p a r t i a l recovery of t h e i n c r e a s e d r e s i s t i v i t y w i l l t a k e p l a c e , probably accomp-anied by a recovery of the s t r a i n - h a r d e n i n g of the metal.

In t h i s t h e s i s w i l l be described how the e f f e c t s found by Mole-naar and Aarts were studied in d e t a i l . The dependence on time and temperature of the occurring recovery was obtained experimentally and analysed.

I t w i l l be evident t h a t , among the experimental data of any kind which may give valuable information about atomic processes occur-r i n g duoccur-ring defooccur-rmation, these occur-r e s i s t i v i t y - e f f e c t s can be taken into account.

In the next chapter the experiments which were c a r r i e d out w i l l be described. F i r s t l y p o l y c r i s t a l l j n e wires of Cu, Ag, Au and P t were, a f t e r annealing in vacuo a t one c o n s t a n t temperature and for one constant time, s t r e t c h e d a t l i q u i d a i r temperature. The r e l a t i v e i n c r e a s e of the r e s i s t i v i t y Ap/p, due t o t h i s deforma-t i o n was o b deforma-t a i n e d and i deforma-t s p a r deforma-t i a l recovery a deforma-t deforma-t e m p e r a deforma-t u r e s in the range between l i q u i d a i r temperature and roomtemperature was studied as a function of the time and temperature of a subsequent annealing treatment.

A second s e r i e s of measurements was c a r r i e d out to get the ef-f e c t s a ef-f t e r a s t r o n g e r deef-formation. This was obtained by r o l l i n g wires of copper a t l i q u i d a i r t e m p e r a t u r e . Analogical e f f e c t s were found as in the case of s t r e t c h i n g of copper. A much higher v a l u e of t h e r e l a t i v e i n c r e a s e of r e s i s t i v i t y i s found by t h e rol 1ing-deformation.

After both ways of deformation i t i s found t h a t recovery of Ap/p t a k e s p l a c e i n two subsequent s t e p s in the t e m p e r a t u r e - r e g i o n which has been examined. When i t i s assumed t h a t one s i n g l e p r o -cess i s responsible for each step of recovery i t appears t h a t the r e l a t i o n between time '^ and t e m p e r a t u r e T which a r e t o g e t h e r necessary to give a c e r t a i n amount of recovery can be given by an equation of the general form:

t = A exp (-A) .

In this formula Q represents the energy necessary to activate the recovery-process; k is the constant of Boltzmann and A a factor which will be considered later.

The activation-energies for both steps of the recovery are found from the results of the measurements with the aid of the expres-sion given.

Essentially different values of Q were found for the two occur-ring steps, the value of Q for one step being constant. For Cu equal values of the activation-energy were found after stretching and rolling. A difference in recovery between these two ways of cold-working reveals i t s e l f in a r e l a t i v e l y higher rate of re-covery after rolling.

At the end of the next chapter experiments are described which show that the original increase of the r e s i s t i v i t y and the feat-ures of the occurring recovery-process are influenced r a t h e r strongly by the i n i t i a l condition of the metal wire, as defined by the vacuum-annealing or by any unaccounted deformation of the wire before the actual measurements.

In the third chapter a theoretical interpretation is suggested for the phenomena observed. F i r s t l y a short review is given of the recent theories of p l a s t i c deformation as based upon the existence and interaction of dislocations moving through the l a t t i c e . Assuming that defects in the l a t t i c e , produced by coldworking, are responsible for the observed increase of the r e s i s t -ivity and assuming that the recovery of the electrical properties by subsequent tempering is due to the disappearance of these defects to places where their influence upon p decreases, a very simplified model of diffusion of these defects i s given. This gives an impression of the factors contained by A in the general recovery-equation put forward in the foregoing. By a quantitative analysis of the r e s u l t s obtained i t is found t h a t the second recovery-step - i . e . the step occurring in the highest temperatureregion or with the largest activationenergy can be a t -tributed to a diffusion of vacant l a t t i c e s i t e s , produced by cold-working. A review from l i t e r a t u r e i s given of some ways of generation of vacancies by p l a s t i c flow. From this follows that i t might be possible as well that i n t e r s t i t i a l atoms are produced in the l a t t i c e during cold-working.

Possible mechanisms are given for the part of the increase of p, which disappears in the f i r s t recovery-step. Probable processes are: the diffusion of i n t e r s t i t i a l atoms and the diffusion of pairs of vacancies. Another possibility, although less probable,

is taken into account: the recombination of vacancies and inter-s t i t i a l atominter-s. No definite concluinter-sion can be drawn although i t i inter-s probable that a diffusion of i n t e r s t i t i a l atoms occurs.

The l a s t part of the third chapter deals with a more detailed comparison of the experiments with the explanations suggested.

Some quantitative conclusions can be drawn which support the mechanisms put forward in the foregoing.

The fourth chapter contains a summary of recent later literature about experiments closely related to the measurements described. It appears that other cold-working experiments have recently been carried out the results of which are in agreement with the de-scribed deformation-studies.

An experiment is given in which a gold wire has very quickly been quenched from a high temperature to the temperature of liquid air. This quenching gives rise to an increase of the resistance of the Au-wire which appears to decrease again by subsequent tem-pering. The authors suggest that this recovery is due to a dif-fusion of vacant lattice-sites frozen in by quenching. The re-sults show, however, some aspects which decrease the reliability of this explanation.

The following part of the last chapter deals with a kind of ex-periment as is frequently carried out today. Defects of the lattice are introduced by an irradiation of the specimens with neutrons or charged particles with high initial kinetic energy. The results of measurements like these together with subsequent annealing-treatments at relatively higher temperatures show that - at least partly - the same defects are introduced in the lat-tice as by cold-working.

Finally an experiment is described in which the energy, stored in the metal during cold-working, is measured. The results of this measurement are in agreement with the fact that at least vacant lattice-sites are produced by plastic deformation.

C h a p t e r 2

D E S C R I P T I O N O F

E X P E R I M E N T S A N D R E S U L T S

A. Increase of the resistivity of copper, silver, gold and plati-num due to cold-working by stretching wires at liquid air tem-perature and its recovery after subsequent tempering

I t was f i r s t l y studied how the r e s i s t i v i t y of p o l y c r i s t a l l i n e Cu, Ag, Au and P t changed with i n c r e a s i n g deformation when wires of t h e s e metals were s t r e t c h e d a t the temperature of l i q u i d a i r . Before the a c t u a l experiments a long wire of the metal which had to be i n v e s t i g a t e d was annealed d u r i n g 1.5 hour a t 550 °C in a vacuum of about 10"* mm Hg. Pieces of t h i s wire having a diameter of 0.20 mm in a l l cases were used as specimens. The same anneal-ing was always applied to obtain specimens with I d e n t i c a l i n i t i a l conditions for one metal. For t h i s purpose a vacuum-furnace was c o n s t r u c t e d . The a c t u a l furnace i s formed by a Pyrex g l a s s tube with an i n n e r diameter of 5 mm. This tube was surrounded by a s p i r a l of kanthal-wire through which e l e c t r i c a l h e a t i n g could be applied. Thermal i s o l a t i o n around the tube was c a r r i e d out with asbestos-paper and glass-wool. The ends of the tube were widened and could be closed with rubber s t o p s and Apiezon. In these wide ends small d i s k s could be p l a c e d p o s s e s s i n g four small h o l e s through which four wires of about 700 mm, being the length of the oven, could be s t r a i g h t e n e d . By s p e c i a l winding of t h e h e a t i n g s p i r a l around t h e tube the t e m p e r a t u r e could be kept c o n s t a n t within 10 °C. Measuring of the temperature was c a r r i e d out with the aid of three Chromel-Alumel thermocouples c a l i b r a t e d for t h i s purpose. Pieces of the annealed wire could then be s t r e t c h e d . The length of the samples was about 170 mm. The wire was fixed to one arm of a balance as shown in a schematic way in the figure 2. The wire was surrounded by a Dewar f l a s k D, f i l l e d with l i q u i d a i r . Near W another wire C of the same metal was put e l e c t r i c a l l y in s e r i e s with W. This wire C was not stretched and served by i t s r e s i s t a n c e , as i n d i c a t o r of t e m p e r a t u r e - v a r i a t i o n s of the cold bath.

Measurement of the extension of the wire by s t r e t c h i n g happened o p t i c a l l y v i a a mirror M on the balance, the p o s i t i o n of which was fixed with a telescope T from a lightened s c a l e S. Stretching

i t s e l f was c a r r i e d out by t u r n i n g a wheel A which moved the arm 13

S i

4iFCr3

Schematic situation of the stretching apparatus and equipment.

of the balance t o which the wire W was fixed v i a a s t e e l wire B. This wire B was fixed to the other arm of the balance. The r e l a t -ive increase of the length of the wire W, hi/1, could thus be de-termined, I i n d i c a t e s the length of the wire in the undeformed c o n d i t i o n a t l i q u i d a i r temperature, whereas M r e p r e s e n t s t h e increase of I by s t r e t c h i n g a t the same temperature,

The change of r e s i s t a n c e of the wire a f t e r deformation was ob-tained by measuring the change of v o l t a g e between two fixed p o i n t s on the wire, the c u r r e n t through the wire being c o n s t a n t during the measurements. All measurements took p l a c e with the wires s t r a i g h t but u n s t r e s s e d . Fixing of the v o l t a g e - p o i n t s on the wire was obtained by soldering t h i n copper threads of 0.05 ram diameter on i t . The same was done with the comparing wire C. By i n v e r t i n g the d i r e c t i o n of the c u r r e n t i t was checked t h a t no important thermo-voltages between any wire and the threads occur-red. The e l e c t r i c a l measurements were c a r r i e d out with a Diesel-h o r s t p o t e n t i o m e t e r by a compensation-metDiesel-hod u s i n g a Zernike double-coil-galvanometer and a l i g h t e n e d s c a l e as equipment t o define compensation. Every h a l f a minute the r e s i s t a n c e s of the potentiometer, necessary to obtain compensation, were read a l t e r -n a t i v e l y a-nd c a l l e d r e s p e c t i v e l y R a-nd R for the u-ndeformed a-nd deformed w i r e . As the temperature of the l i q u i d a i r i n c r e a s e s with time t h e r e s i s t a n c e s of the w i r e s w i l l i n c r e a s e t o o . All r e s i s t a n c e - v a l u e s measured were normalised a t one temperature. Therefore i t was assumed t h a t the temperature varied l i n e a r with time. When R , R , R', and R ' r e p r e s e n t four r e s i s t a n c e - v a l u e s

measured after each other, R' was brought back to the temperature of R by the relation:

R R : =

R' R'

From the f i g u r e 3, where the dependence of R^ and R a r e given schematically as a function of tem-p e r a t u r e , i t i s e v i d e n t t h a t t h e t r a t i o R/R^ depends on t h e t i m e ,

^ ^ when i t i s assumed t h a t the temper-a t u r e i n c r e temper-a s e s l i n e temper-a r with time. The d i s t a n c e between the two l i n e s being very small in the case of the deformation by s t r e t c h i n g , t h i s de-pendency could be n e g l e c t e d . This was checked experimentally.

«> t a m p t r a t u r *

Figure 3

R^ and R as a function of temperature.

Using the expression:

for the undeformed wire and:

R = D-r

R + AR = (p + Ap) I 4 M d + Ad

for the deformed condition it can easily be derived that:

Ap P

f-(2^.

if)'}

whai i t i s assumed t h a t the volume of the wire remains constant *. After measuring the values of M/l and of AR/R the corresponding value of Ap/p can thus be obtained from formula ( 1 ) .

In the figure 4 the r e s u l t s of these s t r e t c h i n g experiments are shown. The value of Ap/p in % i s given as a function of the elong-ation of the wire in %.

The value of Ap/p contains a p o s s i b l e e r r o r of about 6%, mainly caused by the e r r o r made in the measurement of I.

The quadratic terms in formula (1) could not be neglected which can be seen from an example. When for AZ/i and AR/R measured values are used respectively of 7.75% and 19.40%, for Ap/p a value of 3.38% is obtain-ed when the terms are neglectobtain-ed. Taking into account these terms Ap/p appears to be 2,85%,

P I i 3 2 O 0 1 2 3 4 5 6 7 9 9 10 11 12 13"*

-t

Ap/p of Cu, Ag, Au and Pt as a function of Aï/I after stretching wires at liquid a i r temperature *.

S t r e t c h i n g measurements were c a r r i e d out on Cu, Ag, Au and P t , The p u r i t i e s of the metals used were the following:

Cu: O.P,H,C, Ag: 99,92 % Au: 99.93 %

Pt: unknown

The stretching curves being representative for the change in the electrical properties of the metal after deformation, it could be studied whether any recovery occurred at temperatures higher than that of liquid air. Molenaar and Aarts found a recovery at room-teraperature which for Cu and Ag respectively took place in about 30 and 10 minutes. Annealing during a longer time at this temper-ature did not give any further recovery neither did a subsequent heat-treatment at 150 °C in the case of Cu. So the interesting temperaturegion in which recovery of the increase of the re-sistivity takes place is expected to be the interval between liquid air- and roomtemperature.

To apply tempering treatments the wire had to be brought - after the cold-working at - 183 °C - as quickly as possible to a higher temperature at which it must be kept for a certain known time. Such a treatment was applied with the aid of a kind of "thermo-state", constructed for this purpose. This apparatus is shown in the figure 5.

* I am indebted to Mr.B.Korevaar who carried out all measurements on Pt.

Figure 8

"Thermostate" for recovery-treatments after stretching.

A heavy massive copper beam c o n s i s t s of two halves A and B which can be j o i n e d t o g e t h e r . In t h e d i r e c t i o n of the a x i s a h o l e i s l e f t . The length of the beam i s 170 mm, the other two dimensions being 40 mm. In the hole which has a diameter of about 8 ram two wires W and C can be placed, i s o l a t e d e l e c t r i c a l l y from the t h e r m o s t a t e . The two wires are put in s e r i e s with each other a t one end of the beam.

The wire C which a c t s again as t e m p e r a t u r e - c o r r e c t i n g wire i s fixed i s o l a t e d a t t h e o t h e r end of the t h e r m o s t a t e . The wire W comes f r e e l y out of t h e hole and i s fixed t o a l i t t l e l e v e r L which has the form of a circle-segment. S t r e t c h i n g of the sample i s c a r r i e d out by turning t h i s l e v e r .

To measure the v o l t a g e - c h a n g e s on the wires between two fixed points again t h i n copper threads were soldered on W and C in the same way as in the balance-method. These p o t e n t i a l - t h r e a d s were led out of t h e t h e r m o s t a t e through very small h o l e s G. Three other small holes T served as c a r r i e r s for three thermo-couples. With t h e s e couples t h e temperature a l o n g s i d e the wire could be measured. Copper-Constantan j u n c t i o n s were used. The thermo-e l thermo-e c t r i c powthermo-er in mV/°C was known from l i t thermo-e r a t u r thermo-e ^ togthermo-eththermo-er with c a l i b r a t i o n - p o i n t s at the temperature of b o i l i n g nitrogen and of dry ice (CO^).

A schematic view of the s i t u a t i o n in the " t h e r m o s t a t e " i s given in the figure 6.

After f i x i n g of the vacuum-annealed wires W and C with p o t e n t i a l probes and thermo-couples in the thermostate the whole could be 7. Temperature; I t s Measurement and Control in Science and Industry

(Reinhold Publ. Cooperation, Kew York. 1941) p, 206 - 227.

0 o o * Q

h 1

Schematic view on the situation in the stretch ing-thermostate.

placed in a box which could be f i l l e d with l i q u i d a i r . This box was i s o l a t e d thermally with asbestos and glass-wool. During the p r e p a r a t i o n for the measurements a t t e n t i o n must be paid to not deforming the sample as t h i s might influence the actual r e s u l t s . Some d e t a i l s about t h i s i n f l u e n c e of an unaccounted degree of deformation of the wire will be given in part D of t h i s chapter. So s t r e t c h i n g of the wire W at l i q u i d a i r temperature could be a p p l i e d . After deformation t h e value of AR/R was measured. R means the value of the r e s i s t a n c e of the wire (between the p o t -e n t i a l - j u n c t i o n s ) in th-e und-eform-ed s t a t -e at l i q u i d a i r t-eni)-era- teni)era-t u r e . AR r e p r e s e n teni)era-t s teni)era-the increase of R due teni)era-to s teni)era-t r e teni)era-t c h i n g a teni)era-t teni)era-t h i s temperature. The value of Ap/p could be obtained h e r e a f t e r using t h e r e s u l t s of the balance-method, as t h i s experiment gave the r e l a t i o n between AR/R and M/l for the same material.

Hereafter recovery-measurements could be c a r r i e d out.

Generally the recovery of Ap/p as a function of time and tempera-ture of the annealing treatment can be measured in experimentally three d i f f e r e n t wa^ys:

a. a s a function of the temperature for d i f f e r e n t constant times using d i f f e r e n t wires for each temperature.

b. as a function of time a t d i f f e r e n t constant temperatures (isothermally), using one wire for each temperature. c. isothermally for subsequent d i f f e r e n t tempering

tempera-tures during some time on one and the same wire.

These methods leading to the same r e s u l t s the thermostate-method i n the way c a l l e d a. was chosen as i t was expected t h a t in t h i s case a fundamental view could be obtained of the r e c o v e r y f e a t -18

ures in the whole t e m p e r a t u r e - r e g i o n s t u d i e d . An experimental disadvantage of a. compared with t h e other methods i s formed by the fact t h a t for each temperature a new wire had t o be used. A wire, fixed in the t h e r m o s t a t e for measurements a t one c e r t a i n temperature could not be used again for an i d e n t i c a l measurement a t another t e m p e r a t u r e . The r e c o v e r y a t the f i r s t t e m p e r a t u r e might influence t h a t a t the second in a complicated way. So the procedure followed was:

The l i q u i d a i r being removed a f t e r s t r e t c h i n g the t h e r m o s t a t e with i t s c o n t e n t s was warmed up as quickly as p o s s i b l e to a c e r -t a i n -tempera-ture where i -t was kep-t for a d e f i n i -t e -time. Then -the box was f i l l e d again with l i q u i d a i r and t h e value of AR/R was measured a f t e r t h i s tempering t r e a t m e n t . All measurements were carried out in liquid a i r with the wires unstressed. The same ex-periment could then be repeated for some e x t r a time a t the same temperature. For recovery-measurements a t another tempering tem-perature the wire had to be replaced by a new undeformed one. The high heat-capacity of the apparatus made i t possible to main-tain any temperature of the thermostate during 45 minutes without many d i f f i c u l t i e s . As regards the warming up, the apparatus need-ed of course a r e l a t i v e l y long t i m e . Taking i n t o account t h i s fact the recovery-time i t s e l f had t o be chosen r e l a t i v e l y long with regard to the time necessary to warm up. Warming up was c a r -ried out by infra-red i r r a d i a t i o n of the beam Pid by blowing warm a i r on i t with a föhn *.

I t appeared t h a t to reach tempering t e m p e r a t u r e s in the whole region between l i q u i u a i r - and roomtemperature warming up - times had to be used up t i l l 5 minutes. For t h i s reason recovery-times were chosen of respectively 15 and 45 minutes a t each temperature of the annealing treatment. Special a t t e n t i o n had to be paid to not blowing warm a i r with the föhn d i r e c t l y through the hole of the thermostate, as t h i s would spoil the measurement as unaccoun-ted high temperatures of the wire might be a t t a i n e d .

For each recovery-me?surement a t a c e r t a i n temperature always the same amount of deformation was applied as well as p o s s i b l e . Snail d e v i a t i o n s of the acquired amount of s t r e t c h i n g could be taken into account as i t appeared t h a t always the same r e l a t i v e value of recovery occurred in t h a t case.

Another factor which might influence the increase and the recov-ery of the r e s i s t i v i t y was the r a t e of s t r e t c h i n g . Attention was

* Warming up of the "thermostate" could also be applied by e l e c t r i c heating of the beam. As the method followed appeared to work well, this electric heating has not been carried out.

therefore paid to use in pll experiments about the same rate of stretching. To get an idea of this influence upon the increase of the resistivity stretching rates of 3 and 1/3 mm pro second were apilied using the balance-method. The rate of deformation actual-ly used in all experiments was 1 mm pro second. No change of the increase of resistivity Ap/p could be found when these different rates were applied,

The recovery-temperature of the thermostate could easily be kept constant for 45 minutes within 1 °C, When the temperature started to increase a very small amount of liquid air was added to the box which by its evaporation made decrease the temperature again, The whole temperature-region was investigated in the way describ-ed.

The reco\rery of Ap/p of Cu, Ag, Au and Pt after stretching at liquid air temperature was obtained as a function of the temper-ing temperature for constant recovery times of 15 and 45 minutes, The results of the measurements are shown in the figures 7, 8, 9 and 10 respectively for Cu, Ag, Au and Pt,

% 3.5 3.0 £p P n 2.0 10 0 -150 -100 -50 0 50 100 ^ tsmpcraturt (^C) Figure 7

Recovery of Ap/p of Cu.

I t i s very e v i d e n t t h a t for a l l t h e s e m e t a l s t h e r e c o v e r y of Ap/p in the examined temperature-region occurs e s s e n t i a l l y in two subsequent s t e p s . The end value of recovery due to the two s t e p s i s indicated in the figures by e.v.

Cu

O 15mJnut«s racovtry-tima • 45 minutts r«covtry-time

% 2.0 £p P 1.5 10 0.5 -150 -100 o 15 minutes recovery-ttms • tSminutes recov*ry-tim« - 5 0 O 50 — » • temperature ( • € ) 100 Figure 8

Recovery of Ap/p of Ag.

o 15 minutes recovery-time i 45 minutes recovery-time

—r—

-150 -100 - 5 0 0

Figure 9

Recovery of Ap/p of Au.

50 - 1 100 - ^ temperature ( C)

The recovery-step which takes p l a c e a t the lower temperatures i s c a l l e d the f i r s t s t e p , the second s t e p being the following one. The d i f f e r e n t t e m p e r a t u r e - i n t e r v a l s in with both recovery-proces-ses were found to occur, are given in t a b l e I.

The most important f e a t u r e s of these r e s u l t s have been published in a short note in Nature together with some headlines of a poss-i b l e poss-i n t e r p r e t a t poss-i o n of the e f f e c t s obtaposs-ined ^ ' ' .

8, M.J.Druyvesteyn and J.A.Manintveld: Nature, 168. 868. 1951. 9. J.A.Manintveld; Nature, 169, 623, 1952.

% 2.5 r £p P 11 20 1.5 1.0 Pt o 5 minutes recovery-time • 15 minutes r e c o v e r y - t i m e A 45 minutes recovery-time -150 -100 -50 50 - • • temperati're C O Figuur 10 Recovery of Ap/p of Pt. Table I

Temperature-intervals of the recovery-steps.

100 metal Cu Ag Au Pt first step - 150 °C till - 70 °C - 190 °C till -100 °C - 120 °C till - 30 °C - 150 °C till - 70 °C second step - 40 °C till + 40 °C - 70 °C till 0 °C - 10 °C till + 50 °C - 10 °C till + 70 °C

I t was found t h a t during the whole recovery-process of the r e s i s t i v i t y no change of the mechanical p r o p e r t i e s occurred in the deformed metals. This was checked with the balance-method. No change of t h e y i e l d - p o i n t a f t e r the a p p l i e d tempering was observed.

B. Increase of the resistivity of copper due to cold-working by rolling wires at liquid air temperature and its recovery after subsequent tempering.

I t could be expected t h a t , compared with s t r e t c h i n g a heavier de-formation l i k e drawing through d i e s or r o l l i n g might have a much s t r o n g e r influence on the r e s i s t i v i t y of the specimen. I t might furthermore be p o s s i b l e t h a t new conclusions could be drawn from the r e s u l t s of subsequent tempering treatments. As r o l l i n g seemed e:g)erimentally to be the e a s i e s t wajr t h i s kind of deformation was

Figure li

The roller.

chosen. A small roller was constructed. As the same wires were to be used as in the stretching experiments the size of this instru-ment could be kept small preventing at the same', time unnecessary evaporation of liquid air. In figure 11 the roller is shown which has the dimensions of a common matchbox.

The apparatus was constructed of steel plated with a double layer of copper and nickel respectively for conservation. The rolls themselves were made of hardened steel. A solution for the bear-ing-problem was found in the material Akulon, a production of the A.K.U. at Arnhem. It appeared to have excellent properties for it purpose. The distance between the rolls could easily be vari-ed by turning the cog-wheels on top of the instrument. The appar-atus could be placed upon the bottom of the brass box which also served as container of the liquid air ?n the stretching experi-ments. It could be fixed to the bottom of the box. Driving of the rolls was carried out by a thin rod of brass the end of which was hollow. At this end the driving rod could be fxxed to the steel axis of the lower roll which moved by its rotation the upper roll by cog-wheels on both ends of the rolls. By a hole in the box the rod was led out from the liquid air bath through another hollow little brass rod, soldered on the box. Good fitting prevented the liquid air from getting lost.

To get a straight rolling it appeared to be necessary to guide

the wire. This happened with the aid of four thin plates of ebo-nit, placed in the box perpendicular to the rolling direction of the wire. Being led through cuts in these plates the wire could be kept straightened during the rolling, as moving in only one direction was possible. Electrically in series with the specimen another wire which was not rolled was put near it and served again as temperature-correcting resistance. The amount of deform-ation now being much higher the dependency of the ratio of the resistance-values in the rolled and in the undeformed condition upon temperature could not be neglected. This dependency was ob-tained experimentally which made correction possible. Two thin copper threads of 0.05 mm diameter were soldered on the sample again to serve as potential-probes. Rolling was only applied to a part of the piece between the potential-junctions. The resistance between these points - which is the measured one - consists of the contribution of a rolled part and an unrolled piece. After obtaining the resistance in the (totally) undeformed and in the (partly) deformed condition the value of the relative change in resistivity Ap/p could be obtained when all changes of dimensions of the wire due to rolling were known, p represents, as always, the resistivity of the undeformed wire at the temperature of liquid,air, whereas Ap means the absolute increase of p after a certain treatment, Ap is independent of temperature according to the rule of Mathiessen. For the calculation of Ap/p from AR/R and the changes of dimensions of the wire it was again assumed like in the stretching procedure that the volume of the wire remained constant after rolling. In the figure 12 a schematic view is given of the wire in the undeformed and deformed condition.

I

u

r'

4

• 1

On.'eformed and rolled wire with potential-probes.

When l^ represents the length of the distance between the potent-ial-junctions Pj and Pj in the unrolled condition, when Z' is the length of the part which is rolled and when the unrolled parts of the piect I are called l^ and Zj, for the resistances in the

un-rolled and un-rolled condition of the wire it can be written respec-tively:

I

R = p -2- '

o

d and p representing the area of cross-section and the resist-ivity of the undeformed wire, and

(1,^1,) Z' R - P o — ^ — ^ p jr

o

a r e a of c r o s s - s e c t i o n and r e s i s t i v i t y of the r o l l e d wire c a l l e d d' and p ' .

Prom t h i s follows:

^ = (a^ + ap) ^ + a ^ - 1 (2) p R

when a i s s u b s t i t u t e d for d ' / d and where p r e p r e s e n t s the r a t i o (Zi+ Z 2 ) / Z ' . The c r o s s - s e c t i o n of the deformed wire not having e x a c t l y the shape of a r e c t a n g l e , a m u l t i p l i c a t i o n of measured breadth and t h i c k n e s s with a micrometer will give a value for d' which appeared to be r a t h e r i n a c c u r a t e . A r e l a t i v e e r r o r in a of 20% can be o b t a i n e d in t h i s way. Assuming t h a t the wire-volume remained c o n s t a n t a f t e r r o l l i n g a r e p r e s e n t s a l s o the r a t i o of the length of the deformed p a r t and the length of t h i s same p a r t before deformation. Measuring of t h e s e l e n g t h s g i v e s a h i g h e r accuracy as the r e l a t i v e e r r o r s a r e s m a l l e r . The lengtiis them-selves being of the order of 30 mm were measured with a p o s s i b l e e r r o r of 0.2 mm. The r e l a t i v e e r r o r i n a obtained in t h i s way i s about 5%.

The value obtained f o r Ap/p being p o s s i b l y dependent on the r a t e and on the amount of cold-working, t h e s e values were kept con-s t a n t acon-s well a con-s p o con-s con-s i b l e when con-subcon-sequent recovery-experimentcon-s had to be c a r r i e d out. To get an impression of t h e influence of the amount of r o l l i n g upon the r e s i s t i v i t y , these increases were measured for some d i f f e r e n t amounts of deformation. The r e s u l t s of t h i s measurement. are given in the figure 13.

For subsequent recovery-measurements always t h e same amount of r o l l i n g was applied c h a r a c t e r i z e d by a r e l a t i v e decrease of the c r o s s - s e c t i o n of the wire of about 60%.

After t h i s r o l l i n g a t the temperature of l i q u i d a i r the recovery was measured i s o t h e r m a l l y according t o method b in c h a p t e r 2, p a r t A. The value of the r e s i s t a n c e between the p o t e n t i a l j u n c -tions was measured a t l i q u i d a i r temperature as a function of the

•fc 220 if 200 P 1 lao 1 160 140 130 100 eo 60 40 20 Cu . . / / / / / / / / / / / / 10 20 30 r«L»trvt r « 40 uctic / • / 50 60 n in ar«a of

X

Dependence of Ap/p on the amount of cold-working by rolling at liquid

air temperature.

time during which the initially deformed wire had been at a cer-tain constant tempering temperature, A whole isothermal recovery-c m , e recovery-can thus be measured with one wire,

The procedure necessary to keep the wire at the annealing temper-ature for subsequent increasing times was now relatively easy, conpared with the stretching-experiments. During a certain time the wire was put in a tempering bath which was formed by a Dewar flask containing a special liquid, cooled down to the temperature wanted. To get recovery-temperatures down to - 80 °C aceton was used, cooled by putting dry ice directly into it. For tempera-tures do*n to - 120 °C pentane was used; the pentane was at first cooled from roomtemperature down to - 80 °C in the same way as the aceton. Further cooling to the temperature wanted was carried out by putting into the liquid a hollow copper cylinder filled with liquid air. About - 130 °C being the freezing point of pen-tano, propane was used for still lower temperatures. After liqui-fication of gaseous propane by cooling the low tempering tempera-ture of the propane wanted could be reached by further cooling with the liquid air-cylinder.

r o l l e r . For t h i s removal the wire was loosened from i t s c u r r e n t -c o n t a -c t s and the t h i n p o t e n t i a l - t h r e a d s from t h e i r outward - con-nections with the potentiometer. The wire thus being free between the r o l l s could be taken out from the r o l l e r always remaining in the l i q u i d a i r during t h i s treatment to avoid any unwanted recov-ery of t h e i n c r e a s e of the r e s i s t i v i t y by r o l l i n g . During t h i s manipulation no deformation of the p a r t of the wire between the p o t e n t i a l - j u n c t i o n s was allowed e i t h e r . This might give r i s e t o unaccounted e f f e c t s . The whole removing-procedure was c a r r i e d out by hand with the aid of tweezers. The wire now l y i n g in the l i -quid a i r alongside the r o l l i n g - a p p a r a t u s was then connected with a p e r t i n a x s t i c k which was used as a w i r e - c a r r i e r d u r i n g t h e t r a n s p o r t of the wire from the l i q u i d a i r to the annealing bath and vice versa. After the wire had been a t the annealing tempera-ture for the time wanted the s t i c k with the wire was plunged i n t o the l i q u i d a i r again, as a l l measurements took place a t the tem-perature of l i q u i d a i r . The pertinax s t i c k with the wire i s shown in the figure 14.

II 'J - ^ w ^

h i — D 0 D Figure li

S i t u a t i o n of the t r a n s p o r t - s t i c k with the wire fixed to i t .

The time necessary to t r a n s f e r the wire from the l i q u i d a i r i n t o the tempering bath and back again must be short enough to prevent any unaccounted recovery. I t was checked t h a t the time which occurred ( 0 . 2 second) was short enough. This was done in the f o l -lowing way: After measuring the value of R after a c e r t a i n recov-ery the wire was transferred to the recovering bath and immediat-ely back to the l i q u i d a i r . As no change of t h e i n i t i a l R-value o c c u r r e d , i t appeared t h a t the t r a n s p o r t - t i m e had been s h o r t enough. The tempering bath was s t i r r e d before every r e c o v e r y -treatment and i t s temperature was measured with the thermo-couple used in the stretching-experiments or with a thermometer for low temperatures. This thermometer was c a l i b r a t e d c a r e f u l l y against a platinum-resistance thermometer.

Repeating the t r a n s p o r t - m a n i p u l a t i o n for known subsequent times in the same tempering bath, followed a f t e r every annealing time by measuring the r e s u l t i n g r e s i s t a n c e at l i q u i d a i r temperature, a whole isothermal recovery-curve was obtained.

To find the end value (e.v.) of the recovered resistance after total recovery in the studied temperature-range the wire was - at the end of the recovery-period - put for 15 minutes in a Dewar containing hot water of about 90 ^C. This time of 15 minutes ap-peared to be sufficiently long to get the end value of recovery after both steps. The resistance-value at the end was measured at last at liquid air temperature again.

At the end of these measurements the change of dimensions of the deformed wire was measured to be able to obtain the values of Ap/p according to formula 2. Measuring of the lengths was done with a mm-scale, the initial cross-section was found by measuring the diameter of the undeformed wire with a micrometer.

Isothermal recovery-experiments like this were carried out at a number of temperatures in the whole recovery-region.

The results of this recovery-study after rolling are shown in the figure 15.

The isothermal recovery is given by plotting of p =(R-Rj,)/(R -R^,) as a function of time during which the wire was kept at different constant annealing temperatures. R means the resistance of the part of the wire between the potential-junctions after a certain recovery. Rg is the value in the total recovered condition where-as R is the resistance before any recovery hwhere-as occurred. The value of the ratio p before any recovery has taken place is talcen to be 100%. The isothermals at aro:nd - 80 "c show a reaching of a kind of end-value whereas at higher temperatures p starts to decrease again.

So it is evident that in the case of rolling the recovery of the increase of the resistivity due to deformation at liquid air tem-perature takes place in two subsequent steps too.

This is shown more clearly when the results are plotted in the same way as was done with the stretching-experiments. The iso-thermal curves being shown in the figure 15, the plotting in the last way is given in the figure 16. The value of p is now given as a function of the annealing temperature with the tempering time as parameter.

Plotting the value of p gives curves which show the features of the recovery as well as direct plotting of Ap/p would do. Using the factor p gives results that are more accurate, as the error

-wi'c

170 «C

Figure 15

Isothermal recovery of the electrical properties of Cu, rolled at liquid a i r temperature, as a function of the time

at different temperatures.

occurring in the measurement of the change of dimensions are not involved in i t .

When a copper wire i s r o l l e d at roomtemperature and when the p , due t o t h i s deformation i s measured a t t h i s t e m p e r a t u r e as a function of time, i t i s found that p decreases with time as shown in the figure 17.

The r e s u l t agrees with the observation t h a t recovery of the s e -cond step occurs a t t h i s temperature.

The existence of two subsequent recovery-steps can be shown in a 29

— 0-0-0-2.5 mingtts racovtiy-timt S minutafi rtt-ortfy-tim» — 4—6-fi- lOminutt» f>'eov«ry~tlmt

^ tamparature t"C)

Figure 16

Recovery of the electrical properties of Cu after rolling at liquid air temperature as a function of the annealing temperature

for different times of tempering.

Cu

25 minutes

Fia 17

P as a function of time measured at roomtemperature after rolling

at roomtemperature,

very spectacular way when an experiment i s c a r r i e d out according t o method c in chapcer 2, p a r t A. This measurement c o n s i s t s of subsequent annealing treatments at constant temperatures i n c r e a s -ed a f t e r each s h o r t isothermal measurement. This experiment i s

carried out on one wire. Starting at a low temperature the recov-ery of Ap/p was measured for some time after a tempering treat-ment at a low recovery-temperature. Then the temperature of the recovering bath was increased and for some time the recovery of the same wire was measured after this annealing.

This was followed again by an isothermal measuring of the recov-ery at a still higher temperature and so on. All actual measuments were carried out at the temperature of liquid air. The re-sult of such an experiment is given in the figure 18. The value of Ap/p after rolling in liquid air is shown as a function of

time for subsequent increasing temperir? temperatures.

' igure 18

Recovery of Ap/p of Cu as a function of time at sabsequenl increasing temperatures.

It is very clear that at about - 70°C the first recovery-step dies out whereas at somewhat higher anneal?ng temperatures a sec-ond process of recovery starts to work.

A measurement according to method c as described can very well be used for preliminary investigations of the electrical recovery-behaviour of metals of which this recovery-behaviour is not yet known. One wire of the metal is sufficient and the measurement can be ried out in a relatively short time. Such an experiment was car-ried out on Ni. The result is shown in the figure 19 in the same way as was done for Cu, It is evident that at about - 65 °C a saturation of recovery is attained, followed by a subsequent recovery-step at higher temperatures. For the lower

r e c o v e r y t h e a c t i v a t i o n - e n e r g y comes out t o be about 0.34 eV whereas t h i s energy a p p e a r s t o have a v a l u e of 0.9 eV a t t h e h i g h e r r e c o v e r y - t e m p e r a t u r e s . These e n e r g i e s were c a l c u l a t e d a s described in p a r t C of t h i s chapter. RQ-RE 42 41 40 39 38 37 \ - i n " c \ . 0 - a 3 2 a V X^se'c ^ -.0-0.36aV X l i ^ C Ni - _ ^ 1 ^V^2»C --«Q-aB9aV \ - 3 8 ° C \ o . a a 3 a v Y20°C 0 2 A 6 B 36 iO minutCf ••r«covtry-timt Figure 19

Recovery of p of Ni as a function of time at subsequent increasing temperatures of

anneal ing.

Resuming it can be said that after stretching and rolling of a face centered cubic metal like copper at liquid air tem-perature an increase of the resistivity is found. Moreover this increase disappears after heat-treatments at higher temperatures. This occurs - at least qualitatively - in an identical way for both types of cold-working, the occurrence of two subsequent recovery-steps being essential for this recovery of the increased resistivity.

A difference between the stretching and rolling data which is evident at once is the much higher increase of the resistivity after rolling and a relatively higher rate of recovery in this case.

kept at a certain temperature T - is plotted against 1/T, for one certain value of the recovered resistivity, a straight line is obtained. This same feature can be found in the temperature-dependency of the coefficient of self-diffusion D.

Comparing this feature of the recovery with its analogical occur-rence in the case of diffusion it is reasonable to suggest that Ap/p can be written as:

P '^

T being a temperature-dependent parameter, given by the equation T = exp (—) .

t

For a constant value of recovery — has to be constant.

exp

y

So the relation between time t and temperature T, both necessary to obtain this recovery-valre, can be written as:

t = A exp {^ (3)

Q has the physical meaning of an a c t i v a t i o n - e n e r g y , necessary t o put t h e mechanism which causes recovery i n t o a c t i o n , k i s t h e constant of Boltzmann.

The assumption t h a t each process i s c h a r a c t e r i z e d by one s i n g l e a c t i v a t i o n - e n e r g y i s j u s t i f i e d by t h e e x p e r i m e n t s a s w i l l be shown in the next s e c t i o n of t h i s chapter. The more d e t a i l e d fea-t u r e s of fea-t h s occurring processes will be represenfea-ted in fea-the fac-t o r A which w i l l c o n fac-t a i n some funcfac-tion of Ap/p, This f a c fac-t o r A will be analysed in an approximate way in chapter 3, section B of t h i s t h e s i s . Taking A indepenaent of temperature the e n e r g i e s which might a c t i v a t e each r e c o v e r y - p r o c e s s for t h e d i f f e r e n t metals can e a s i l y be obtained from the equation 3.

C. Calculation of activation-energies

As the experiments show, the same values of recovery of the r e -s i -s t i v i t y a f t e r cold-working a t l i q u i d a i r temperature are ob-tained by d i f f e r e n t couples of t and T. This ic r e a l i s e d graphic-a l l y by drgraphic-awing h o r i z o n t graphic-a l l i n e s in the f i g u r e s 7, 8, 9, 10 graphic-and 16. The i n t e r s e c t i o n - p o i n t s with the r e c o v e r y - c u r v e s give t h e values for t and T.

In t h i s way two e x p r e s s i o n s are o b t a i n e d for one and the same value of recovery, using equation 3:

and

tl = A exp i-^)

t , = A exp ( ^

Dividing the first formula by the second one, it follows: Q = k-T T • ^ 1 ' '•2 T , - T , In (4) I t T -T i s evident t h a t t h e This e r r o r i s of 1 ' • 2 ' ' 2

From t h i s equation Q can be c a l c u l a t e d , e r r o r in Q i s mainly caused by e r r o r s in the order of 10%,

For several values of the recovered r e s i s t i v i t y for each step and for each metal a value of Q has been obtained which appears to be a c o n s t a n t one for the whole s t e p . This value of Q i s given in the following t a b l e I I in eV.

Table II Activation-energies in eV metal Cu Ag Au Pt first step St. 0.20 ± 0.03 ro. 0.25 ± 0.03 St. 0.18 ± 0.02 St. 0.29 ± 0.03 St. 0.22 ± 0.03 1 second step 0.88 ± 0.09 0.82 ± 0,08 0,69 ± 0,07 0.69 ± 0.06 0.99 ± 0.091

The way of deformation i s given by s t . and r o . meaning s t r e t c h i n g and r o l l i n g .

r e s p e c t i v e l y

As r e g a r d s the r o l l i n g - e x p e r i m e n t s the a c t i v a t i o n - e n e r g i e s can a l s o be obtained i n a somewhat d i f f e r e n t way. Equation 3 can be written as:

I n . t _kT

P l o t t i n g l o g . t against i/T for constant values of recovery, Q can be found from the r e s u l t i n g curves. This p l o t t i n g i s c a r r i e d out in the figures 20 and 21 for the f i r s t and the second s t e p . In appears t h a t s t r a i g h t l i n e s are obtained the slope of which give t h e a c t i v a t i o n - e n e r g y . For one whole s t e p the l i n e s a r e p a r a l l e l to each o t h e r . This shows t h a t each s t e p i s c h a r a c t e r

-figure 20

1/T against log. t (first step)

Figure 21

1/T against log. t (second step)

ized by one single value of Q. The values thus obtained are, of course, equal to those calculated from equation 4.

Still another way of calculation of the energies for the recovery after rolling can be applied to the results of the third way of measuring, called method c in the foregoing. The results of a measurement like this were given in the figure 18.

Por this purpose it has to be realized that the recovery can also be given by the equation:

where B i s again some function of Ap/p *.

For t h e c a l c u l a t i o n of Q t h e s l o p e s of two i s o t h e r m a l s i n a t r a n s i t i o n - p o i n t P have to be o b t a i n e d fron. the f i g u r e 18. As both isothermal curves have the same value of B in the t r a n s i t i o n p o i n t , Q can be calculated with the known values of the tempering temperatures. This has been c a r r i e d out for some couples of i s o -thermals in each s t e p . Examples are given in the f i g u r e s 22 and 23 for the f i r s t and second recovery-step.

% 135 p 130 125 0 1 2 3 4 5 6 7 8 0 lOmiHitee Figure 22

Subsequent Isothermal recovery-curves for the calculation of Q (first step).

Qj and Qj representing again the energies for the first and

sec-It was found as equation 3:

t = f ( — ) exp (-^ kT' Differentation gives: d ( ^ ) 1 = f {-^) — e x p {—-J P' dt kT' or '(^) . —'— = exp , dt f'(.^ ^"^ (•^) = B exp (-f )

115.0 ie -J- 110J) I I 105.0 loao o 2 4 6 B 10 12 14 16 ie 20 minutes ^ t i m e Figure 23

Subsequent isothermal recovery-curves for the calculation of Q (second step)

ond r e c o v e r y - s t e p , values were obtained in t h i s way of Qj = 0. 26 eV and Q2=0.80 eV. These values agree with the values a l r e a d y found for the r o l l i n g experiments.

The value of Q found in t h i s way i s very s e n s i t i v e to e r r o r s made in the determination of the slopes.

I t i s q u i t e evident t h a t the a c t i v a t i o n - e n e r g i e s found for both ways of cold-working, s t r e t c h i n g and r o l l i n g a t l i q u i d a i r temperature, are the same for copper. From t h i s i t might follow t h a t the occurring mechanisms of the recovery do not depend upon the applied way of deformation - a t l e a s t as regards s t r e t c h i n g and r o l l i n g .

An e s s e n t i a l d i f f e r e n c e between t h e f e a t u r e s of the r e c o v e r y a f t e r t h e two ways of cold-working i s to be found in the r a t e with which t h i s recovery takes p l a c e . This w i l l be discussed in d e t a i l in section F of chapter 3.

D. Some experimental information about the influence of the initial condition of the metal

The metals t h a t have been studied were always annealed in a vacuo of about lO""* mm Hg at 550 °C during 1.5 hour. So for one metal

equal iiitial conditions, as regards those defined by annealing, were obtained.

Another important factor which might influence the results to be obtained is any deformation applied before the actual cold-working, thus in a way also defining the initial conditions of the wire.

A few experimental examinations of the effect of these two fac-tors which might have an influence upon the results were carried out to get an impression of their severity.

In the first place different temperatures of the vacuum-anneal ing treatment before the measurements were applied. For this purpose gold wires were annealed at temperatures of 150 °C, 250 °C and 350 °C in the same vacuum as in the case of the annealing at 550 °C. The resulting features of the effects of the resistivity could thus be compared with those of the 550 °C-treatment. With the aid of the balance-method as described in the foregoing it was studied how the Ap/p depended upon the extension AZ/Z applied by stretching at the temperature of liquid air. The results of these measurements are shown in the following figure 24 together with the behaviour of the 550 °C-metal already known.

if p 3 3S0OC /C-"^^ 150 ISO'C 10 n 1 2 " * 2U Figure

Influence of the temperature of the vacuum annealing treatment on the relation between Ap/p of Au and Al/T

after stretching at liquid air temperature.

It is quite evident that the effect of cold-working on the re-sistivity is influenced rather strongly by the temperature of the

vacuum annealing. The resistivity of the gold which had been vacuum annealed at 150 °C does not show any increase after de-formation and fraction of the wire occurs quickly. The Au of the 250 °C-treatment shows an increase of the resistivity which is relatively larger than the metal which has been annealed at a temperature of 550 °C. The annealing at 350 °C, however, appears to give rise to corresponding values of Ap/p which are relatively smaller.

The results show the necessity to normalise the vacuum annealing treatment rather carefully.

That this necessity is very real is shown moreover when the re-covery is studied. It appeared that the rere-covery of Ap/p was in-fluenced also rather strongly by the temperature of the vacuum annealing. This is shown clearly in the figure 25 where the re-covery is plotted as a function of the tempering temperature at a constant tempering time of 15 minutes and for different tempera-tures of the vacuum annealing together with the curves for the 550 °C already obtained. Especially the results for the 350 °C annealing show a strong deviation. When the activation-energies for the metals, annealed at 250 and 350 °C, are calculated it appears that this energy is independent of the annealing temper-atures of the vacuum-treatment. The energies for the first recov-ery-step are respectively 0.27 and 0.30 eV, those of the second step 0.71 and 0.66 eV.

To get an idea of the influence of any deformation before the actual cold-working, stretching was applied to two copper wires. One wire was initially deformed purposely at roomtemperature to an elongation of about 8%, being of course a rather strong de-formation. It appeared that the prestrained copper showed a sub-sequent increase of the resistivity due to stretching of 3.06% after an elongation of 4.64%. The undeformed Cu gave- a value for Ap/p of 1.30% after the same stretching. So this experiment shows a much higher increase of the resistivity for the prestrained metal. The difference between the two samples is evident. The in-fluence on the recovery was revealed by having the annealed and prestrained wires totally recovered after deformation, i.e.

ap-lying a recovering-treatment by which both recovery-steps have taken place. The total recovery for the prestrained Cu appeared to be 35% of the initial value of Ap/p after deformation. The same recovery for the soft metal was 27%.

if.

5:

Recovery of Ap/p of Au for different temperatures of the i n i t i a l l y applied

vaeuura-annealing.

This shows t h a t the i n i t i a l amount of deformation before the actual measurements i s important too for the e f f e c t s t o be obtained. I t shows the necessity of avoiding any unaccounted amount of cold-working.

The i n v e s t i g a t i o n of the influence of t h e i n i t i a l c o n d i t i o n of the metal as defined by, for i n s t a n c e , the vacuum annealing and by any cold-working before the actual measurements would form a study on I t s e l f .

The experiments of t h i s section were only c a r r i e d out t o give an idea of t h i s influence.

C h a p t e r 3

I N T E R P R E T A T I O N O F T H E O B S E R V E D P H E N O M E N A

A, Som^ aspects of the dislocation-theory of plastic flow in metals

In t h i s chapter i t will be t r i e d to explain the experiments de-scribed i n the foregoing chapter.

In the f i r s t place the increase of r e s i s t i v i t y due t o cold-work-ing has to be explained. Therefore i t w i l l be necessary t o know what happens in the l a t t i c e during deformation. A s h o r t review w i l l t h e r e f o r e be given of the r e c e n t i d e a s about t h e mechanism of p l a s t i c deformation. A complete and modern treatment of t h i s s u b j e c t can be found in the r e c e n t works of C o t t r e l l ' " and of Read ^ ' .

I t i s now g e n e r a l l y assumed t h a t the s l i p by which the deform-ation of a face centered cubic metal takes place i s mainly caused by the motion of a type of l a t t i c e - d i s t o r t i o n called d i s l o c a t i o n . This s p e c i a l kind of d i s t o r t i o n being reasonable from the n a t u r e of p l a s t i c flow, has been i n i t i a l l y introduced t o e x p l a i n t h e value of the c r i t i c a l s h e a r - s t r e s s necessary t o put the p l a s t i c deformation i n t o a c t i o n . As i t was evident from experimental d a t a s l i p should in most cases occur by the moving of one p a r t of the l a t t i c e along another p a r t r e l a t i v e l y t o a closest-packed plane. I t was f i r s t l y suggested t h a t t h i s took place in an ideal l a t t i c e . As i t appeared t h a t the c r i t i c a l s h e a r - s t r e s s was a f a c t o r 10 larger than the one experimentally observed, a kind of defect was looked for, c l o s e l y r e l a t e d t o the plane along which s l i p took p l a c e , which might account for the small value of t h e c r i t i c a l s t r e s s observed. The type of disturbance of the l a t t i c e which ap-peared to have the required q u a l i t i e s i s c a l l e d a d i s l o c a t i o n . I t appeared t h a t most of the phenomena accompanying p l a s t i c de-formation can be explained by the d i s l o c a t i o n - t h e o r y - a t l e a s t in a q u a l i t a t i v e way.

10. A.H. Cottrell; Dislocations and plastic flow in crystals, 1953. 11. W.T.Read; Dislocations in crystals, 1953.