Short Notes K179

phys. stat. sol. (a) 2, K179 (1971)

Subject classification: 10.1; 21.1

Department of Solid State Physics, Charles University, Prague (a), and Physics Department of the City University, London (b)

"0 The Critical Resolved Shear Stress of Cd-Zn Single Crystals at 4.2 K

BY P. LUKA8 (a) and L.D. WILL (b)

Introduction The most probable mechanism controlling the low temperature

solid solution hardening of f. c. c. metals is assumed to be that given by Friedel and

Haasen (I to 3). According to this model a rigid dislocation moves in a zig-zag

form. Then the critical resolved shear stress at 0 K, %

with the solution concentration, c, following the relation

0 should increase linearly ,

0,

W z =- 0 2b3 ,

where W is an interaction energy between dislocations and solute atoms,

However, Scharf et al. (4) investigating the solid solution hardening of magnesium

single crystals alloyed with cadmium find that the critical resolved shear stress at

+ 1 . 2 5 ~ 1 0 ~ c2l3. Likewise &tar and Teghtsoonian (5) have found that zo is not a

s i m s e linear function of the solute concentration for Mg-Zn alloy single crystals.

They concluded that the low temperature solid solution hardening occurs in two

stages, z being linear functions of c1/2 in both, but the slopes being different.

Both for Mg-Cd (4) and for Mg-Zn (5) the critical resolved shear stress at 0 OK was

obtained by extrapolation of the temperature dependence of critical resolved shear

stress for various alloys.

0 OK does not follow the relation (1). Their results can be described by z = zo(Mg)+ 0

0

To overcome the objections to extrapolation over a wide temperature range, in

the present work the influence of zinc as solute on the critical resolved shear stress

of cadmium sihgle crystals was investigated at 4.2 K. 0

Results and discussion Single crystals of diameter 4 mm were grown in a glass

tube using a modified Bridgman method. The handling of the sample before the de-

formation is described elsewhere (6). Orientations were determined by the Laue

back reflection technique. The values of X and A. (where X o and h are the 0 0

K180 physica status solidi (a) 5

Fig. 1

Fig. 1. Critical resolved shear stress vs. solute concentration at 4 . 2 OK

Fig. 2. Critical resolved shear stress linearly dependent on c213 (present results)

angles between specimen axis and basal plane and between axis and slip direction

respectively) were both between 44 and 60 . The specimens of Cd-Zn (with the

concentration of zinc up to 0.5 at%) were deformed at liquid helium (4.2 K) on an

Instren machine :ddel TM-M-L, with an initial strain rate of 6x10

0 0

0

-4 -1 s .

Fig. 1 shows the plot of the critical resolved shear stress against c, where c

is the concentration of zinc in atomic percent. It is seen that the concentration de-

pendence is not linear. Thus we have a similar result to those obtained for Mg-Cd

single crystals by Scharf et al. (4) and also for Mg-Zn by Akhtar and Teghtsoonian(5).

If the critical resolved shear stress is plot- Mg-Zn

ted against c213 a straight line is obtained

(Fig. 2). This can be expressed in the empirical

relation z = z (Cd) + S c ~ ' ~ , where the

T = O X

0 0

m- Fig. 3. Critical resolved shear stress linearly dependent on c2I3 for Mg-Zn alloys plotted by

L I I I the present authors from results of Akhtar and ff 007 002

c2/3 --- Teghtsoonian (5)

Short Notes K181

slope S = 0.6~10 p/mm . The slope of this concentration dependence for Cd-Zn is

of the same order as that for Mg-Cd. It is interesting to note that the z o values for

Mg-Zn determined by Akhtar and Teghtsoonian (5) can also be plotted against c

and give a straight line passing through the value of z for pure Mg (Fig. 3). Again

the slope of the zo vs. c2’3 plot for Mg-Zn is of the same order as is estimated

in this work. Hence it can be concluded that the relation (1) given by Friedel (1) is

not applicable on the case of hexagonal alloys.

4 2

213

0

Acknowledgements

search financially possible. We are grateful to Dr. P. Kratochvh for his critical

remarks.

We wish to thank the F.D. Edwards Scholarship Trust, which made this re-

References

(1) J. FRIEDEL, Dislocation, Pergamon hress , Oxford 1964.

(2) P. HAASEN, Z. Metallk. 55, 55 (1964).

(3) P. HAASEN, in: Physical Metallurgy, Ed. R. W. CAHN, North-Holland Publ.

Co. , Amsterdam 1965.

(4) H. SCHARF, P. LUKAE, M. BOEEK, and P. HAASEN, 2. Metallk. 3, 799 (1968).

(5) A. AKHTAR and E. TEGHTSOONIAN, Acta metall. g, 1339 (1969).

(6) P. L d e and Z. TROJANOVA, Z. Metallk. 58, 57 (1967).

(Received May 10, 1971)