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ULTRASONIC STUDY OF DISLOCATIONS IN CsI
H. Koizumi, I. Iwasa, T. Suzuki
To cite this version:
ULTRASONIC S T U D Y O F DISLOCATIONS I N Cs1
H . K O I Z U M I , 1 . IWASAf AND T . S U Z U K I
Institute of Industrial Science, University of Tokyo, Roppongi, Minato-ku, Tokyo 106, Japan
'Department of Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 11 3 , Japan
Abstract
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The ultrasonic velocity and the attenuation in Cs1 change sensitively with plastic deformation and they recover by y-irradiation. In the amplitude independent region, the measured results of the temperature and frequency dependencesof the change of velocity and the decrement due to dislocations are consistently accounted for by the superposition of the dislocation resonance damping and the relaxation loss of Bordoni type.1
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INTRODUCTIONThe extensible string model of dislocations established by Granato and ~ ü c k e /1/ usually accounts well for the ultrasonic behavior of plastically deformed metals in which electron drag is the main source of dislocation damping. As for ionic crystals, in which electron drag is absent, the ultrasonic study of NaCl by Hikata et a1./2/ revealed that the extensible string model is not consistent with the experimental results below 70K but radiation loss due to the oscillation of kink chains along the Peierls potential accounts for them. The Peierls stress of alkali-halides of NaCl-type is 10-40MPa, as determined by plastic deformation experiments /3,4/. On the contrary, in alkali-halides of CsC1-type Peierls stress is quite small (<lMPa) / 5 , 6 / , so that it can be expected that the extensible string model of ~ranato-LÜcke is applicable to the ultrasonic behavior of CsBr and Cs1 containing dislocations. In this paper will be reported the experimental results on the ultrasonic velocity and attenuation in CsI.
II
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EXPERIMENTAL PROCEDUREThe single crystal of Cs1 was made by Czochralski method in argon, and it contains about 30ppm of monovalent ions and less than lppm of aliovalent impurities (Mg, Ca, The specimens used for the ultrasonic measurements are depicted in Fig.1. BY the compression of about 1% along [1,fi-l,l], dislocations on the slip systems of [100](01i) and [O011 (110) were introduced in the specimens. The ultrasonic velocity and attenuation in the deformed and undeformed specimens were measured
C10-526
JOURNAL
DE
PHYSIQUE
in. the temperature range of 1.5-80K by a pulse echo technique using a
quartz transducer cemented on the compression [Il
fi]
surface by propane. Thelongitudinal wave propagating along
the [l 1
fi]
direction conducts the [3-12;~+i, 2-fi 1 motion of dislocations on the [O011C I , I , ~ ~ I
(110) slip system only. The
deformed specimen was then irradiated tran~ducer by the y-ray of 1 0 = ~ from co60, and
ultrasonic measurements were made
again. Fig. 1. Specimen of CsI.
III
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RESULTSFig. 2. Strain amplitude depen- Fig. 3. Temperature dependence dence of ultrasonic velocitp v in of ultrasonic velocity
deformed Cs1 normalized by the velocity vo at the lowest ampli- tude.
Figure 2 shows the strain amplitude dependence of the ultrasonic velocity v in deformed CsI. In a wide range of the amplitude the velocity is almost independent of the amplitude. The following measurements of velocity and attenuation a were al1 made in this region of amplitude independence. The temperature dependence of v is shown in Fig. 3. Above 20K the three curves in Fig. 3 are almost parallel and independent of frequency w, while below 20K the temperature coefficient of v becomes large by the deformation and agdin smaller by the y-irradiation. In the present measurements, the absolute values of
v are accurate only to 0.5%, so that it is difficult to determine exactly the absolute changes of v exerted by the deformation. If we assume that v at OK does not change by the defor- mation or the y-irradiation, then the relative changes of velocity Av/v can be drawn as in Fig. 5, where Av is the difference between v of deformed (and y-irradiated) crystal and that of undeformed one.
The ultrasonic attenuation a
7 ( K I Fig. 5. Av/v and A as functions of temperature. soli4 lines are calcu- Fig. 4. Temperature dependence of lated by the dislocation resonance decrement. damping model. Symbols are the sarne
as in Figs. 3 and 4.
changes sensitively with the deformation. Figure 4 shows the decrement A=2nva/w as a function of T. In the deformed crystal
A
increases steeply with increasing T and reaches a small peak at about 15K, and above 20K it has rather weak dependence on T. By the y-irradiation A of deforrned crystal recovers largely as the change of veloc- ity does. These recoveries ofA
and v by y-irradiation mean that the ultrasonic behaviors observed here relate to the motion of dislocations, and we define the dislocation contribution to the decrement, Ad, by subtracting A of undeformed crys- ta1 fromA
of deformed one. In Fig. 5 is shown A against T.d
IV
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DISCUSSIONSFor the present experiment on deformed Cs1 in the amplitude independent region the dislocation break-away damping model /1/ is out of consideration, because this model leads to the amplitude dependence of Av/v and A
.
The dislocation resonance damping model 119 predicts that near OK Ad is propor- tional to w and Av/v is independent of w, because near OK phonon damping constant B is small, thus dislocations make underdamped oscillation. The experimental result below 20K is, however, contrary to this prediction. The small peak observed in
A
-T curves around 15K cannot also be accounted for by the resonanced damping model.
C10-528 JOURNAL
DE
PHYSIQUEwhere O is the Debye temperature. At T=70K, eq. (1) gives ~ ~ 1 . 0 x 1 0 - ~ ~ / c m * s e c . Using this value of B, the appropriate values of A and L were determined so as to fit the data of A and Av/v at 70K. The obtained values are A=6x 1 0 ~ c m - ~ and LZ0.52~. Then Bor these
A
and L the temperature dependences ofAd
and Av/v were calculated by taking into account B(T) of eq. (1). The calcy1at;ed curves shown in Fig. 5 reproduce well the experimental results above 30K. The dislocation density Az6x 1 0 ~ c m - ~ is reasonable for the deformation of about 1% and the average pinning length L=0.52pm may be attributed to the pinning by aliovalent impurities.Below 20K, Av/v increases with decreasing T. This implies that near OK dislo- cations do not oscillate freely. The small peak of A around 15K indicates that a relaxation process occurs around this temperature. ~ t e relaxation time r is given by /8/
T-1 = v o exp (-W/~T )
,
(2) where W is the activation ener y and vo is usually of the order of 10'~sec-'. For the peak position Ti15K and r-'=2nf, f being 5MHz, eq. (2) gives W=0.016eV. If this peak is caused by kink pair formation process (Bordoni peak), W is related to the Peierls stress TP as
W = a T = b . 3 Q
,
(3)where a is the period of the Peierls potential, b the Burgers vector, E the line energy of a dislocation and G the shear modulus. For the above estimate of W, eq. (3) gives Tp^:0.2MPa. This value of rp is nearly equal to the critical shear stress measured at low temperatures(-1.5K) by the plastic deformation tests of the same crystal as used in this work /5/.
In summary, the present experimental results on ultrasonic velocity and attenu- ation in deformed Cs1 are consistently accounted for by the superposition of dislo- cation resonance damping, which is dominant at high temperatures, and relaxation loss of Bordoni type, which is dominant around 15K.
REFERENCES
/1/ Granato, A. and ~ Ü c k e , K., J. Appl. Phys.
z
(1956) 583. /2/ Hikata, A. and Elbaum, C., Phys. Rev.89
(1974) 4529./3/ Suzuki, T. and Kim, H., J. Phys. Soc. Jpn
2
(1975) 1566, (1976) 1703. /4/ Suzuki, T.,
Skrotzki, W. and Haasen, P., phys. stat. sol. ( b ) E (1981) 763. 151 Koizumi, H. and Suzuki, T., phys.stat.so1. (a)- (1982) K101, (a)- (1983) 301. /6/ Koizumi, H. and Suzuki, T., "Dislocations in Solids" ed. Suzuki, H., University of Tokyo Press, 1985, p. 479./ 7 / Ninomiya, T., "Treatise on Materials Science and Technology", Vol. 8, Academic Press. 1975. , D.
