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STRAIN AMPLITUDE DEPENDENT DAMPING IN ZINC SINGLE CRYSTALS
N. Igata, T. Yokoyama
To cite this version:
N. Igata, T. Yokoyama. STRAIN AMPLITUDE DEPENDENT DAMPING IN ZINC SIN- GLE CRYSTALS. Journal de Physique Colloques, 1985, 46 (C10), pp.C10-187-C10-190.
�10.1051/jphyscol:19851043�. �jpa-00225427�
JOURNAL DE PHYSIQUE
Colloque CIO, supplément au n012, Tome 4 6 , décembre 1985 page C10-187
STRAIN AMPLITUDE D E P E N D E N T D A M P I N G IN Z I N C S I N G L E CRYSTALS
Department o f M a t e r i a l s S c i e n c e , U n i v e r s i t y o f ~ o k y o , T o k y o 1 1 3 , Japan
F a c u l t y o f S c i e n c e and T e c h n o l o g y , Meijo U n i v e r s i t y , Nagoya 4 6 8 , J a p a n
&su& - L' amortissement en fonction de 1' amplitude de contrainte e s t étudié A l ' a i d e des vibrations en flexion dans une garmne de température entre 100 e t 300 K. L'effect hysterésique e s t o b s d aux tm&ratures plus hautes que 270 k, mais non pas à $les plus basses que 170 k. On peut considerer que ce phén&e e s t entrainé par l a mise en désordre de l a plygonisation par 1'amplitude de contrainte.
Abstract - The strain-amplitude-dependent àamping i s studied by flexural vibrations i n a t m p r a t u r e range between 100 and 300 K. m e hysteresis effect is observed a t temperatures above 270 K r but not below 170 K. This phenornenon is considered to be caused by the disorder of plygonization due to s t r e s s anplitude.
1 - ~ D ~ I O N
The studies of the hysteresis effect on the anplitude-dependent damping of zinc crystals were carried out a long the ago by Read /1/, Read and Tyndall /2/, Swift and Richardson /3/ and Wert /4/. Recently, two straight linssof the Granatc-Lücke p l o t i h m b e e n r e p r t e d by Bortollotti e t aZ./5/ and they have explained t h i s phe- nomenon by the changing of loop length distribution, using the theory of Tmtt and B i r r b a u m /6/. Yokoyama /7/ has r e p r t e d that the hysteresis effect disappeared by cold working and was seldm obçerved i n the 2nd-order pyramidal s l i p planes. In the present e x p r k t , the hysteresis e f f e c t is studied below rocan temperature.
II - EXPEFCUGNCAL PROCEDURE
The purity of zinc crystals i ç 99.999 wk%
with Cd (5 p p ) and Fe (1 p p ) as the major impurities. Single crystal rectangular bars
(0.3X0.5X6%8 cm) are prepared and the orientation i s chosen so t h a t the s t r e s s on the basal s l i p system is maximized by ori- enting the (0001) plane a t an angle of about 45O with respect to the axis of the sample.
The Schmid factor i ç 0.45%0.49 i n a l 1 the samples. Etch-pit studies of basal s l i p dis- locations are studied on a side plane of the sample, a s s h m i n Fig.1. The w a n dislo- cation d a s i t y i ç about 6.5 X 105/cm2, and there mixed plygonizations and disloca- tions of low density ( 4 X 10 '/cm2 ) . The in-
1
ternal f r i c t i o n Q - l i s measured by the free
decay method in free-free flexural vibra- Fig. 1 - Photqraph of etch-pits on tion between 100 and 300 K. a side plane (1120) of a specimen.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19851043
CIO-188 JOURNAL DE PHYSIQUE
MAXIMUM STRAlN AMPLITUDE
In as-annealed crystals, an example of the hysteresis lcop measured a t r m temper- ature is shown in Fig.2. The 'breakpoint' atwhich the decrernent becoies amplitude dependent begins a t the maximum s t r a i n amplitude of 3 X 10-6, but the r a t e of in- crease of decrement decreases a t 5 X 10 -'and reachg a saturation value above 1 X 10-'.
In the decreasing run, the decrement begins to decrease a t 7 X 10-5 a f t e r keeping the saturation values, and depicts a hysteresis lmp. This behavior is in agreement with the r e s u l t s obtained by Read /1/ and others /2,3,4/. The area of t h i s l m p be- canes narrower with decreasing temprature and only a l i t t l e hysteresis i s observed a t the anplitude around 3X 10 -' a t 231.6 K. M hysteresis l m p is found a t tempera- tures b e l w 170 K. A t lm temperatures the b r e a k p i n t begins a t lm amplitude of 1 X 10-6 -and the decrements increase much steeper than the one m s u r e d a t r m tem- perature.
Fig. 2 - The behaviors of interna1 f r i c t i o n vs maxirmrm strain-amplitude for one sample a t 292.5 ( c i r c l e s ) , 251.5 (triangles), 231.6 (inverse triangles) and 99.1 K
(çquares) .
- IO?
- ior
v
Z 2 1 0 3 :
2 a
LL.
J a z a
W l-
z
l o 5 q
MAXIMUM STRAIN AMPLITUDE
Fig. 3 - The change of hysteresis l m p for the s p e c h measured a t r m temperature, the 1st run (circles) , the 2nd run (triangles) and 3rd run (squares) .
IO IO* IO-= i O-&
O 111-1
O-. Z92.5K O 1
a - - - 251.5 K o-- r 231.6K
O---. 99.1 K 9'
4 ~ W ~ , $ : O ? .A;.* u -
= vv9$=a
- vv=;..:opa
. 1 vs<,i.p%." ,,y
Fx&ldd ,o,600
lo-47a-? = .:-. b .:ii$..n
: > ***" o.o. *
1 , . . .
- t-* o-o-o .--- -0-0.0-0-0-
-
:
' ' ' I " " I I . , .
In well-annealed specimens, the damping a t r m temperature keeps a constant value u n t i l the amplitude of 6 X 10-' (see Fig.3) , but rapidly increases up t o the Q-'value of 2.9 X 10 -'at the amplitude of 2.5 X 10-Y The damping on the decreasing amplitude shows a plateau over the amplitude range frcan 2 X 10-'to 2 X 10 -5. The second measure- ment i s carried out after about 18 hours. The form of the loop resembles the behav- i o r of hysteresis indicated in Fig.2 rather than t h a t in the 1st run of Fig.3. On the subsequent measurement, the decrement runs on the same values a s those of the fonner decreasing run, a s shawn i n Fig.3. This behavior is consistentwith the re- s u i t reported by Wert /4/.
IV- DISCUSSICN
The amplitude dependent internal f r i c t i o n 9;: i s expresseci a s a function of mxhm s t r a i n amplitude,
Q;; = A (ErnaxIn + B (1)
where A and B are constants obtained by the e x _ p e r h t and the exponent n is 0.7 Q,
1.3. This expnent n i s a parameter of both temperature and amplitude. Q;; is a value under a non-hcmqeneous s t r e s s distribution i n samples, so t h a t Q& could be changed to the true internal f r i c t i o n 6(€,) under a homogeneous s t r e s s distribution according t o Asano's method /8/. F u r t h m r e , the dislocation velccity v i s able to be obtained £rom the true interna1 f r i c t i o n with the formula /9,10/
n+ 4 )
f (n+2) fT r ' ~
= -.A. - - E"+l
Pb 2 b l h 3 (2)
where f is the vibration frequency; p, the density of movable dislocation; b, the Burgers vector: Vn) the Gamna function.
F r a the contribution to the amplitude dependent damping, the dislocation density p i s estimated t o be 1X105/cm2. The dislocation velocities are dekxmined f r m the data of Q;: *thin the amplitude E,,, (8 X 10- Q, 2 X 10- 5, a t various temperatures.
Then, the s t r a i n i s transfonned into the resolved shear s t r e s s with the Schmid fac- t o r and Young's moduius. Hence the dislocation velccity is plotted against the re- solved shear s t r e s s a t temperatees of 292.5, 251.5, 231.6, 169.1 and 99.1K , a s
RESOLVED SHEAR STRESS (MPo)
Fig. 4 - Dislocation velocity vs resolved shear stress a t temperatures of 292.5, 251.5, 231.6, 169.1 and 99.1 K.
C10-190 JOURNAL D E PHYSIQUE
indicated in Fig.4. Since the dislocation velocities estimated at w a t u r e s be- tween 145.0 and 251.5 k are larger than those at other temperatures, the disloca- tions are deduced to be movable easily at this t-ature range.
It has recently been reprted by Yokoyama /Il/ ,that the interaction between disloca- tions and vacancies disappears at about 250 K. The decrease of the dislocation ve- locity at temperatures belm 170 K is deduced £rom unpinning of dislocations £rom point defects proposed by the Granato-Lücke d e l /12/, and it is difficult to re- lease dislocations £rom polygonized dcaiiainç. At r o m temperature, m s t of vibration energies in well-annealed samples are probably spent by the disorder of polygoni- zations at high amplitude, so that the dislocation velccity is slow. The difference between the decrements on increasing amplitude and those on decreasing amplitude is probably due to increase of dislocation density by releasing frcin polygonized do- mains.
The anplitude-dependent damping at temperatures above 300 K has already been studi- ed by Yokoyama / 7 / . The hysteresis effect was observed in the taperature range be- tween 300 and 385 Kr but not above 400 K. The dissolution of polygonization seems to occur at high temperatures above 400 K and no hysteresis effect can also be ob- served. F r a these exp.rimental results, the hysteresis effect is found to occur in the temperature range between 250 and 385 K. In the samples subjected to cold work or in those defonned preferentially on the Lnd-order slip plane, hystexesis loop has not been observed /7/. In the former case, polygonization becmes probably loose, ming to the action of cold work, and in the latter case, polygonization due to the 2nd-order slip dislocation has not yet been found.
v - CONCLUSION
The hysteresis effect of zinc crystals is observed over the temperature range be- tween 250 and 385 K, and it is caused by the redistribution of dislocations frcin polygonization by altemating stress.
/l/ Read, T. A., Phys. Rev. 58 (1940) 371.
/2/ Read, T. A. and Tyndal1,Ë. P. T., J. Appl. Phys. (1946) 713.
/3/ Swift, 1. H. and Richardson, J. E., J. Appl. Phys. (1947) 417.
/4/ Wert, C. A., J. Appl. Phys. 20 (1949) 29.
/5/ Bortollotti, A., ~artineili,G. and Passari, L., Internai Friction and Ultra- sonic Attenuation in Crystalline Solids II:, Springer-Verlag. (1975) 507.
/6/ Trott, B. D. and Birnbaum, H. K., J. Appl. Phys. 41 (1970) 4418.
/7/ Yokoyama, T., Jr. de Phys. supplement au nOIO, 42-(1981) c5-375.
/8/ Asano, S., Phil. Mag., 0 (1974) 1155.
/9/ Açano, S., J. Phys. Soc. Japan. 29 (1970) 952.
/10/ Asano, S., Bulletin of Japan 1nstTit. 19 (1981) 21.
/il/ Yokoyama, T., to be published in ~ c r i p t a ~ t . (1985).
/12/ Granato, A. and Lücke, L., 27 (1956) 98.
