INTERNAL FRICTION IN BARIUM

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INTERNAL FRICTION IN BARIUM

F. Hammerschmid, G. Schoeck

To cite this version:

F. Hammerschmid, G. Schoeck. INTERNAL FRICTION IN BARIUM. Journal de Physique Collo-

ques, 1985, 46 (C10), pp.C10-301-C10-304. �10.1051/jphyscol:19851067�. �jpa-00225451�

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INTERNAL FRICTION I N BARIUM

F. HAMMERSCHMID and G. SCHOECK

Institut

fiir

Festkorperphysik der Universitat Wien, Boltzmannqasse, 5 , A-1090 Wien, Austria

Abstract - Internal f r i c t i o n in Ba has been measured in longitudinal resonance a t about 14 kHz in the temperature range between 10 K and 300 K. There exist t w o peaks around 37 K and 223 K resp. which are tentatively identified as a-peak and y -peak w i t h an activation energy o f H = 0.38 eV and Ha = 0.047 eV.

Y I - INTRODUCTION

I t has been demonstrated by a large number o f computor simulations t h a t in bcc metals the core o f a a/2 <I11

>

screw dislocation has a nonplanar structure w i t h three- fold symmetry (1). This limits the mobility o f the screw dislocations and gives rise t o a large increase o f the flow stress a t low temperatures where the movement o f screw dislocation occurs by the formation of kink-pairs (and their subsequent seperation) with the aid o f thermal activation. The atomic structure o f these kinks is s t i l l under discussion. Wheras atomic calculations (2,3) assumed the existence o f a simple kink (i.e. a dislocation crossing from one Peierls valley t o a neighbouring one), analysis o f defor- mation experiments lead Seeger (4) t o postulate the existence o f double kinks (i.e. a kink crossing over two Peierls hills).

The formation and the movement o f kinks can be studied by internal f r i c t i o n (IF) measurements. In the nomenclature now generally accepted in bcc metals (5) the internal f r i c t i o n maximum associated w i t h the kink-pair formation in screw dislocations is called 7-peak, the maximum assosciated with the kink-pair formation on 71° dlsloca- tions is called %peak and the maximum associated w i t h the movement o f kinks (primarily in screw dislocations) is called '-peak.

Most IF investigations on the Y-peak in bcc metals have been made on the transi- t i o n metals (6). Since the kink produces a considerable modification o f the core (inclu- ding possibly reversals o f the polarity) the kink energy is large and the y-peak occurs a t relatively high temperatures in these metals. In the group V metals w i t h a high solubili- t y f o r foreign interstitials the results have been masked by the interaction o f hydrogen w i t h dislocations.

The only non-transition metals w i t h bcc structure in which detailed IF measurements have been made so f a r are the alkali metals K , N a and L i (7) which have a simple electronic structure. Among these alkali metals potassium shows a broad y-peak (centered around 50 K at about 10 kHz) extending up t o 90 K. On the other hand lithium and sodium do not show any indication o f a y-peak in the temperature range accessible for I F measurements. These t w o metals transform around 77 K ( L i ) o r 50 K (Na) t o a closed-packed structure, but scaling based on the value o f the shear modulus

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19851067

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C10-302 JOURNAL DE PHYSIQUE

and the lattice parameter indicates t h a t above the transformation temperature kink-pair formation should occure w i t h a corresponding rise in internal f r i c t i o n when i t is assumed that the core configuration is similar as in potassium. Since no such increase in IF is observed one must conclude t h a t the kink energy in L i and Na is considerbly 1owe.r than in K. Based on these observation it has been suggested t h a t the core structure in these t w o metals might be different and might have a twofold symmetry which must result when the dislocation core o f a screw dislocation coincides w i t h an atomic row (8).

I t is therefore interesting t o look whether other non-transition metals do show a y-peak w i t h the normal characteristics. In the present study we report on internal f r i c t i o n measurements in barium which is a earth-alkali m e t a l and has also a bcc structure.

II - EXPERIMENTAL PROCEDURE

Due t o the relatively high melting point (998 K ) and i t s high reactivity the handling o f Ba samples poses considerable difficulties. There is no crucible material f o r molten Ba available t o which i t does n o t stick. Growth o f single crystals w i t h cylindrical cross section by the Czochralski-technique i n vacuum is d i f f i c u l t because the high volatility prevents optical observation. Therefore polycrystalline Ba rods w i t h nominal purity 99.9

+

from the Metallschmelzgesellschaft (BRD) were machined down t o cylindrical shape o f 0.6 c m diameter and 6 cm length. Machining had t o be done under a protective kerosene f i l m . Further handling was done in a glove box under protective oxigen-free atmosphere. Prolonged storage (>1 month) even under paraffin o i l produced visable surface oxidation.

Oxidation i n kerosen was even faster and occured within a few days.

The ends of some o f the samples were f i t t e d with short pots o f aluminium o r brass t o ensure plane, parallel non-oxidizing endsurfaces required f o r electrostatic exitation.

The internal f r i c t i o n measurement were made in the same equipment used previously f o r alkafi metals (7). Longitudinal resonance was excited i n the temperature range between 10 K and 300 K in the f i r s t harmonic (ca 14 kHz) and the second and t h i r d harmonic.

The temperature was measured w i t h a Si diode w i t h an error o f less than 0.5 K .

In situ deformation in the IF cryostat was d i f f i c u l t , since the samples showed a tendency to necking close t o the end pots ( w h ~ c h served as grips f o r the tensile deformation). Because the flow stress increased strongly a t low temperatures the deformation which was o f the order o f 1% t o 2% could only be made a t room temperature.

1 1 1 - EXPERIMENTAL RESULTS

Fig. 1 (run E4) shows the IF spectrum in sample E a f t e r machining t o the required dimensions. Above a background weakly increasing w i t h temperature there exist t w o IF peaks, one around 37 K and a second one around 223 K. In this temperature range the resonance frequency decreased typically from about 14 kHz t o 13.6 kHz. A f t e r resting 5 days a t room temperature a strong increase in IF occured above 200 K. A typical example is shown in Fig. 2. This strong increase in IF occured originally above 300 K but s h i f t e d w i t h increasing oxidation t o lower temperatures and caused then some problems in studying the peak a t 223 K. Very probably this increase in IF is due t o a back ground and n o t associated w i t h a larger peak a t higher temperatures.

The low temperature peak stayed a t 32 K a f t e r 1% deformation b u t shifted w i t h the second harmonic t o 39 K (run E8) and w i t h the t h i r d harmonic t o 40 K ('run E10).

Similar results were also obtained f r o m sample D. In d i f f e r e n t runs this peak had typically a half-width o f about 1,5 t o

3

times the Debye half-width.

The influence o f deformation on the hight o f this peak could not be observed in detail. Already a f t e r 1% tensile strain the samples showed some necking near the end pots and thf st,rain was inhomogeneous. This is compatible with the observation that the value o f 10 Q - increased from 1 a t the f i r s t harmonic t o 1,8 at the second and 2,5 a t the third. ~ h ? ~ $ e a s o n might be t h a t in the higher harmonics the oszillating strain maxima occure closer t o the end.

The results o f a l l runs on peak 1 are represented in Fig.3 where we have plotted the reciprocal peak temperature versus the resonance frequency. A variation in resonance frequency could be obtained either by variation in the mass o f the end-pots o r by exciting higher harmonics. The values obtained for the activation enthalpy H

and @e p r e e x p q ~ n t i a l t i m e coqgtant rm1 were HI = 0,047

*

^{0,005 eV} ^{w i t h} ^rml ⁼ ^{4 5} ^{10- s}

and 10 s

<

roo,

<

10- s.

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sample introduced in the quartz tube had t o be covered w i t h kerosene in oder t o prevent oxidation. This resulted in a high IF background a t low temperatures. The high temperature maximum disappeared due t o annealing but reappeared a f t e r 2% deformation.

The data on all runs on peak number 2 are represented in F i g d . The values which were obtained f o r t h e activation enthalpy Hz and pre-exponential t i m e constant T

; are H, = 0.48 f 0.1 eV w i t h T-, "1.6.10-16s and 10-18s< r m 2 <

IV - DISCUSSION

When as we believe the peaks are o f intrinsic nature i t is reasonable t o associate the 223 K maximum (number 2) w i t h a y -peak and the 37 K maximum (number 1 ) w i t h an a-peak. Though the chemical i m p u r ~ t i e s o f the sample are unknown the introduction o f oxigen caused a large increase in IF occuring somewhere above 200 K.

Compatible w i t h our assignement is also the f a c t t h a t the 223 K-peak dissapears by annealing and is reintroduced by cold-work. Against the interpretation o f maximum number 1 as &peak due t o kink migration in screw dislocation speaks the f a c t that its magnitude is not correlated w i t h the y-peak.

Unfortunately exept f o r the bulk modulus B = 10.3 GPa (9) there are no reliable measurements o f elastic constants f o r Ba available. Based on the resonance length (6 cm) and the resonance frequency f = 14 kHz we estimated the Youngs modulus t o be E

= 9.9 GPa. With the value of B we obtain then f o r the shear modulus

u

= 3.7 GPa and the Poisson constant v = 0.34. With magnitude o f the Burgers vector b = 0.43 nm we arrive at a characteristic dislocation energy value pb3

=

1.9 eV. With this the we obtain a characteristic ratio r,= Hz/pb3 ~ 0 . 2 5 . This is large compared w i t h usual values f o r the y-peak where r = H /pb3

=

0.1 (7). In addition the median value o f .rmz is large compared w i t h v%lues reported in the literature (5,6,7). As best probable value we take therefore the lower l i m i t o f our measurements and arrive f o r Ba a t an activation enthalpy

H ^%0.38 eV w i t h r m ~ 1 0 - 1 4 s .

This gives a ratio r =

%

/ub3

=

0.2 whichYis s t i l l larger than "normal". Wether this is a property o f 8aYor whxther this is due t o an error in

u

or H cannot be decided. A decrease in H w i t h a corresponding increase in rm would brTng the values more in agreement w i t h Jther bcc materials. Y

A f t e r assigning the maximum 2 t o an y-peak i t is reasonable to associate the maximum 1 w i t h an a-peak. The pre-exponential t i m e constant is o f the correct order o f magnitude and hence

H = 0.047

+

0.005 eV with roo = 4.1 *lo-12s

This leads t o a ratio ra = H /ub3 = 0.025. I t is dyfficult t o compare t h ~ s value w i t h literature values on oth%r bccametals, since especially in the group V metals there is s t i l l some controversy on the influence o f hydrogen on the so called a-peak. Our p u r i t y is nominally 99.9 + but we do not have information on the nature o f impurities and on the presence of hydrogen in solid solution.

V - ACKNOWLEDGEMENT:

Thanks are due t o Dr. P. Herke and Dr. W. Hollerbauer whose logistic support was essential in sample preparation and t o Dr. H. Mullner f o r maintenance o f the IF equipment. The work was supported by the Fonds zur Forderung der wissenschaftlichen For- schung of Austria.

V I - REFERENCES:

/I/ V. V i t e k , Crystal Latt-Def. 5, 1, (1974) /2/ Ch. Wiitherich, PhilMag. 3 5 , 3 3 7 (1977)

/3/ M.S. Duesbery, A c t a ~ e t 7 1 0 , 1747, 1759 (1982) /4/ A. Seeger, Z.Metallkde. 727369 (1981)

/5/ A. Seeger, C. W u t h e r i c h ~ ~ u o v o Cim. 338, 38 (1976)

/6/ G. Fantozzi, C. Esnont, W. Benoit a n d 7 ~ . Ritchie, Progr.Mat.Sci. 27, 311 (1982) /7/ F. Hammerschmid, H.O.K. Kirchner and G. Schoeck, J.d.Phys. ~ ( C T , 31 (1981) 181 G. Schoeck, Scripta Met.

3,

983 (1980)

/9/ G.C. Carter, Metals Hdbk. 9. ed vol. I l l p. 716

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C10-304 JOURNAL

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PHYSIQUE

Fig. 1 Internal f r i c t i o n in Ba. Sample machined down t o correct size

$0 1 a 8 IS# na ^PISO 1/1 a i l

C%C' ^b

a

O .-KC'

. I * , IS*

. B

E 8 5 - r ~ c b r.rnr$p*rt 6

4 Arrr)r'....4.+*.' ...a-

....

...4.*,*..

...

k . r ( !'

0

I & w e -

....

4,..4.-%..

-

_1m

;

sw

.'

a : & :

...

-.*-."..-n em-... ...I...

-

Fig. 2 Same sample a f t e r 5 days resting

Fig. 3 Temperature s h i f t o f peak maximum Fig. 4 Temperature s h i f t o f peak maximum w i t h frequency o f peak 1. with frequency o f peak 2.