INTERNAL FRICTION IN THE ALKALI METALS

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INTERNAL FRICTION IN THE ALKALI METALS

F. Hammerschmid, H. Kirchner, G. Schoeck

To cite this version:

F. Hammerschmid, H. Kirchner, G. Schoeck. INTERNAL FRICTION IN THE ALKALI METALS.

Journal de Physique Colloques, 1981, 42 (C5), pp.C5-31-C5-36. �10.1051/jphyscol:1981503�. �jpa-

00220959�

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JOURNAL DE PHYSIQUE

CoZZoque C5, supplgment au nO1O, Tome 42, octobre 1981 page c5-31

INTERNAL F R I C T I O N I N THE A L K A L I METALS

F. Hammerschmid, H.O.K. Kirchner and G. Schoeck

I n s t i t u t fiir Festksrperphysik der UniversitEt Wien, BoZtzmmzngasse 5, A-1 090 Austria

Abstract.- Internal friction measurements in the alkali metals show that in Potassium there exists a y-peak around 50K at about 10 kHz. It is due to the double kink formation in screw dislocation and has an activation enthalpy of AH=0.046

+

0.003 eV. In Sodium and Lithium which undergo low temperature phase transfor- mations there is no evidence of a similar peak above their resp.

transformation temperature. This suggests in Sodium and Lithium a different structure of screw dislocations.

1. Introduction.- It is now accepted that the special plastic properties of the transition metals is an intrinsic property of the bcc lat- tice (1) where the atomic arrangement around the core of a/2 (111) screw dislocations has threefold symmetry (2). This makes glide in a single plane difficult and requires the formation of double kinks by thermal activation. The question arises if this peculiar deformation behaviour is ahcharacteristic for the bcc alkali metals with their simple electronic structure. The alkali metals are highly anisotropic and two of them

(g

and E ) undergo a low temperature phase change to a faulted hcp/fcc structure (3). The plastic behaviour of single crystals of the alkali metals shows characteristic differences: At one hand K is very similar to the bcc transition metals (4,5): Below a critical temperature T %20K (or .06 T ) there is a strong increase

C m

in flow stress and asymmetry in tension and compression, the activation volume is small ( s 5 0 b 3 ) . This is characteristic for the formation of double kinks in screw dislocations. At the other hand Na ^and Li behave differently: In

g

(6) below To=150K (or .4 Tm) the flow stress increases moderately, the activation volume of a few thousand b3 is too large for a double kink mechanism, but there is asymmetry in tension and compression. In

&&

⁽⁷⁾the increase in flow stress starts below To=250K (.5 Tm). The activation volume of a few thousand b3 and comparison with TEM observations (8) indicate that intersec- tion of the dislocation forest is rate con troll in^, though again asymmetry in tension and compression exists.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981503

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C5-32 JOURNAL DE PHYSIQUE

The present investigation should clarify the intrinsic behaviour of dislocations in the alkali metals by the measurement of internal friction ( I.F.). Previous measurements of I.F. by Gulden and Shyne (9) on rather impure 5 and above 77 K in the kHz range showed no maximum in

=.

^In^& upon heating a small unstable maximum around 160 K was found which annealed out at 175 K. It was attributed to oxygen pre- cipitates. There exists no previous I.F. measurement in the alkali metals below 77 K.

2. Experimental procedure.- Considerable experimental difficulties re- sulted from the high reactivity and extreme softness of the samples.

All mounting and handling had to be done in a glove box with an atmos- phere of high purity argon. Cylindrical single crystals (diameter .7 cm, length 6 cm) of high purity where grown after vacuum destilla- tion by condensation in stainless steel molds. Chemical analysis showed impurity contents ( 0 , N, C, Pb) of 1 ppm. The samples were mounted at the central cross section by three spring loaded pins in a cryostat which allowed in situ deformation by tension. The I.F. measurements were taken in the first and third longitudinal mode which were exci-

ted electrostatically at frequencies of about 10 kHz and 30 kHz, resp.

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-

3. Experimental results.

-

^Fig.1 shows the damping Q-I versus temperature for two crystals with various deformations in

s.

A broad peak is centred around 50 K, the background damping rises above 150 K. The scattering of the data points is due to the softness of the samples which made mounting difficult.Dumrny samples of do not show this

scatter.

Fig. 1 Internal Friction in ,g Crystal C

(0) deformed.3% at 5 K (A) total deformation 2%

Crystal G

(a) total deformation 3.9%

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A typical variation of Q-I with deformation is shown in Fig.2. Strai- ning at 5 K (below T ) increases the peak effectively, sucessive strai-

C

ning at 77 K (above Tc) decreases the peak. In the second harmonic the peak maximum shifts to higher temperatures and decreases its height.

Fig. 2 Fig. 3

Fig.2 Internal Friction in

K,

crystal F, ( n ) deformed .5% at 5K;

(0) deformed further by .5% at 77 K;(A) second harm0ni.c-

Fig.3 Internal Friction in IZ, crystal G I ( 8 ) slightly deformed at 77K;

(0) deformed 1 % at 77 K; ( + ) deformed 1% at 5 K; (A) further deformed .5% at 77 K, (G) further deformed -5% at 5 K.

Another sample is shown in Fig.3.The alignment of the original sample for electrostatic exitation involved a slight deformation, resulting in a small peak. Deformation of 1% at 77 K produces a peak of moderate height. Most effective is a deformation at 5 K, successive deformation at 77 K decreases the peak heightla slight successive deformation increases then the peak considerably. Annealing for 3 days at 77 K prac- tically eliminated the peak.

In some samples there was a slight indication of a secondary peak between 20 and 30 K. The same tendency shows up in the modulus defect AM/M= 1/2. Av/vo where vo is the resonance frequency (Fig.4). Due to the high damping the resonance is wide and vo could not be determined very reliably. Nevertheless a drop i n ~ ~ a r o u n d 50 K and a smaller drop between 20 and 30 K can be distinguished. The peak shift with temperature in four samples yielded the activation enthalpy AH=.046+.003 eV and the preexponential time constant r, =3. 10-lo sec. The width was a- bout three times the width of a Debye peak. No indication of an impurity peak around 160 K (9) was found, indicating that the samples were pure.

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C5-34 JOURNAL DE PHYSIQUE

Fig. 4 Ficj. 5

Fig.4 Resonance frequency of crystal G. (x) total deformation 1.4%;

(A) total deformation 2.6%, second harmonic;(o)total deformation 3.9%.

Fig.5 Internal Friction in Na.(o) deformed slightly at 77 K;

(A) deformed 1.5% at 50 K.

The internal friction in N a is shown in Fig.5. Below 45 K the samples underwent a martensitic phase change and could not be excited any more.

There is no indication of any peak but the same rise of the background above 150 K. After 1.5% deformation this rise shifted by 10 K to lower temperatures. In that temperature region the macroscopic work hardening coefficient decreases sharply because of recovery and climb (6).

&

above its transformation temperature of 77 K, where there is also no indication of a low temperature peak but a steep rise in background above 200 K (11).

4. Discussion.- According to the nomenclature of the relaxation peaks in bcc metals (12,13) there seems to be little doubt that the observed peak in 5 is a y-peak associated with the formation of double kinks in screw dislocations. The apparently low activation enthalpy of

AH=.046eV has to be put against the effective shear modulus

u= 1/3(C44+Cll-C12) which is two orders of magnitude smaller in 5 (14) than in the transition metals. In first order the energy of a double kink Edk is expected to be proportional to pb 3

.

In the table we list experimental values of AHpfrom the literature and their reduced values. As can be seen

g

fits well into the data of the transition metals :

Fe(15,16) Ta(12) W(12,17) K L i Na AH (eV)

3

^.6-.7 ^1.0 ^1.5 ^.046

vb (eV) 6.9 9.0 20.9 .51 .63 .59

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The large width of the peak can result from the fact that there are three different energies for double kink formation (13) and that it depends on the internal stress oi through the Pare condition (18) aiveEdk where v is the activation volume. When we take for oi the value of the flow stress of about 1 0 - ~ ~ at 5K and for v = 50b (4) we 3 find o . v = .025 eV which is of the same order as AH

1 Y '

The value of the preexponential factor r,= 3.10-lo sec is in agreement with the experimental values for the transition metals ( considering

the larger Debey frequency for the alkali metals) and of the order expected from theoretical estimates (19). For kink migration (a' peak) the preexponential would be expected to be larger by at least 2 orders of magnitude (13). Systematic variation of the amplitude was not made however the third harmonic could only be excited weakly. The fact that in this mode the peak was smaller indicated some nonlinear effects.

The smaller peak height could result from the fact that due to a lower applied stress fewer dislocations were brought into the Park condition The most convincing argument in support of the double kink mechanism is the fact that deformation at 5 K which forms screw dislocations increases the peak height while subsequent deformation at 77 K which forms dislocations of random orientation decreases the height. Whether the small peak between 20 and 30 K is an indication of an a or a'mechanism (13) cannot be ascertained.

The fact that neither in

5

nor in

&

(11) there is a peak is rather as- tonishing. According to the values of &3 in the table the activation enthalpy for double kink formation in these metals should be slightly higher than in 5 , everything else being the same peaks would be expected at or above 50 K.

Even if the peaks should lie below the transformation temperatures, their wings should be observable in the region of experiment. The ab- sence of such an increase in damping suggests that the formation of double kinks in and is different from the transition metals.The fact that these metals have the highest anisotropy factors of the alkali metals and undergo a phase change indicate that the binding for- ces have special properties (5). As a consequence it has been sugges- ted (20) that screw dislocations might have a second equilibrium posi- tion in these metals which would reduce the kink energy considerably.

Acknowledgement.- The financial support of the Fonds zur FBrderung der wissenschaftlichen Forschung and the Hochschuljubilaumsstiftung der Stadt Wien is gratefully acknowledged.

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JOURNAL DE PHYSIQUE

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