PRESSURE DEPENDENCE OF DAMPING CONSTANT OF DISLOCATION MOTION IN CRYSTALS

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PRESSURE DEPENDENCE OF DAMPING

CONSTANT OF DISLOCATION MOTION IN

CRYSTALS

Y. Hiki, T. Kosugi, T. Kino

To cite this version:

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JOURNAL DE PKYSIQUE

CoZZoque G5, supple5ment au nOlO, Tome 4 2 , octobre 1981 page C5-363

P R E S S U R E DEPENDENCE O F DAMPING CONSTANT O F D I S L O C A T I O N MOTION I N CRYSTALS

Y. H i k i , T . Kosugi and T.

in:

Tokyo I n s t i t u t e of Teehno Zogy, Oh-okayma, Mepro-ku, Tokyo 152, Japan

*

_Faculty_{o f Science, Hiroshima University, Hiroshima 730, Japan}

Abstract.- Ultrasonic attenuation in Harshaw LiF and NaCl crystals in deformed and y-irradiated states has been measured at 5 a 100 MHz under hydrostatic pressure up to 3500 kg/cmz. By analyzing the data on the basis of the vibrating string model of dislocation, the pressure derivative of damping constant for dislocation motion was determined. The results were compared with theories of dislocation damping in crystals and reasonable agreement was obtained.

1. Introduction.- In case of elementary process of dislocation motion, resistive force acting on unit length of the dislocation is usually proportional to the velocity of dislocation, and damping constant S is defined as the proportionality constant. Value of the damping constant can be estimated experimentally by an acoustic method, namely, ultrasonic attenuation in a crystal is measured and the result is analyzed on the basis of the vibrating string model of dislocation (1). However, two other quantities, the pinning length between pinning points on dislocations L and the density of mobile dislocations A, are usually not known and the absolute value of damping constant is generally difficult to be obtained. On the other hand, the dependence of B on hydrostatic pressure applied to the crystal can be determined without knowing the values of L and A. Thus we can anticipate the origins of the damping of dislocation motion in crystals more definitely by making use of such an experimental method and by comparing the result with conclusions of various kinds of theories on dislocation damping. The present authors have made this kind of research on Cu (2) and LiF (3) crystals. In the present study, LiF crystal of higher purity and NaCl crystal were used, and the method of the experiment was further improved.

2. Experimental method.- Procedures of measuring ultrasonic attenuation in crystals under high pressure are essentially the same as described before (2, 3). The high pressure experiment is made by using a simple pressure producing system. The hydraulic fluid (Idemitsu Daphne Oil) in a reservoir is sent into the low-pressure side of an intensifier by a couple of pistons having an area ratio of 17.4, and the pressure is

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C5-364 JOURNAL DE PHYSIQUE

finally applied to the oil filled in the high-pressure cylinder of 10 mm in diameter. A specimen crystal put in a specimen holder and a cal-

ibrated nanganin pressure gauge are inside the cylinder. Steady work- ing pressure up to 4000 kg/cm2 can be applied to the specimen crystal.

Specimens are optical-grade Harshaw LiF and NaCl [l001 crystals 9 mm in diameter and 25 mm in length, and their end faces are polished by hand to be flat and parallel with each other. Specimen crystals are annealed in argon atmosphere at 700 Q 750°C for several hours, and then they are deformed by compression by using a loading machine with a deformation rate of 0.05 mm/min. Amounts of the deformation are not so large, being 0.15% and 0.20% for LiF and NaCl crystals. Ultrasonic measurements under pressure are made for the deformed specimens. Then, they are irradiated by co60 y rays to a total dose of 105 R. The measurements are again made for the irradiated specimens.

Ultrasonic pulse reflection method is adopted for the attenuation measurements. An X-cut 9 MEiz or 10 M H z quartz transducer is bonded to an end of the specimen with the Nonaq stopcock grease or a mixture of silicone high vacuum grease (Toray) and silicone oil (Toshiba) in the case of LiF or NaCl crystal. The electronic apparatus used are an ultrasonic generator and receiver (Matec model 6000

+

760) and a pulse amplitude monitor (Matec model 1235B). Usually four pulse echoes are chosen for the measurement, and the accuracy of the attenuation measurement is better than 0.005 dB/psec.

In the present experiment, transmission of sound from both ends of the specimen into the hydraulic fluid causes an apparent sound attenuation. The problem has been treated precisely by the present authors

( 4 ) , and only a brief description will be given here. We use the acous-

tic assembly as shown in Fig. 1. Note the electrode with grooved face. The purpose of this is to stabilize the attenuation by sound transmission from the left end of the specimen, and also to simplify the acoustic condition of the sound transmission. There is of course the transmission of sound from the right end of the specimen too. The

apparent attenuation can be calculated from sound transmission coef- @ _{ficients, which are represented as}

functions of acoustic impedance of specimen, hydraulic oil, and bonding @ liquid @ specimen @ bonding material. The attenuation is also

changed by pressure due mainly to the

@ transducer @ electrode _{density change of hydrqulic oil.}

Fig. 1 : Assembly used for The result of the calculation shows acoustic measurement.

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fairly large; its amount is strongly dependent on pressure; the dependence is not linear. We use the calculated results in the analysis as described in the following section.

3. Results and analysis.- Ultrasonic attenuation a in a specimen is firstly measured in air as a function of sound frequency f for the deformed and the irradiated states, and examples of the data are shown in Fig. 2. The rapid increase at low frequencies originates from the diffraction effect, and the gradual increase at high frequencies is due

-

Fig. 2 : Attenuation vs

frequency measured in air both materials. The solid curves for deformed and irradiated represent the theoretical relation

0.8 0.6

-

Y

U) 0.4i

B

Y 8 0.2- LiF crystal. 2 2 A = AUT/ (1

+

w T ) ; (1) o LiF

1

2 2 T = n l B L / n C, NaCI (3

and here w is the angular frequency

I I I _ LiF o deformed

-

irradiated

/"I

P

-

\69eQ90y o / O

-

7:

f

6 h* \*b\II--Se-*'*

-

10 of the sound, R is the orientation

factor, G is the shear modulus, b is

5 the Burgers vector, C is the effec-

S _{tive line tension of dislocation, n}

and n' are constants depending on

2 the distribution of pinning points.

to the thermoelastic damping. The difference of a between the deformed and the irradiated states corre- sponds to the dislocation damping, since the dislocations are consid-

ered

state. to be The immobile values of in decrement the latter A

( = ac/f; where a is the attenuation

in Np/cm, c is the sound velocity in cm/sec, and f is the sound frequency in Hz) due to the dislocations thus obtained are plotted in Fig. 3. The

Oo

I I I .

50 100 150

I

L

I

Two quantities A and T are regarded

overdamped resonance peak due to dis-

I

,

, ,

,

, ,

, l

l

as parameters in fitting the theo-

l 1 0 20 50 100 200 retical formula to the data. f (MHt)

The attenuation measurements

f (MHz) _{locations can obviously be seen in}

Fig. 3 : Decrement due to

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C5-366 JOURNAL DE PHYSIQUE

irradiated specimens under pressure, and the results are illustrated in Fig. 4. The data for the deformed specimens and for the irradiated specimens are respectively fitted to the relations

a

deform = "0 + "trans + (dade£orrn /~P)P, ( 4

C1 - 1

irrad - a0 + atrans (P) + (dairrad/dP)Pr ( 5 ) where a and a O 1 are constant attenuation values arising from technical

0

reasons, a

trans is the attenuation arising from the sound transmission from the ends of the specimen. The values of atrans can be calculated numerically as described before. We consider here that (dadisl/dP) =

(dadef orm /dP)

-

(dairrad/dP), where adisl is the attenuation due to the dislocation damping. Then the values of the derivative (dadisl/dP) can be determined from data fitting as shown by solid curves in Fig. 4. The obtained pressure derivatives of the decrement due to dislocations are plotted in Fig. 5 against sound frequency for LiF and NaCl crystals, where A , represents the decrement at P = 0.

The theoretical expression for the pressure derivative of the decrement can be obtained from Eq. (1) as a function of frequency:

0.8-

Fig. 4 : Attenuation vs Fig. 5 : Pressure derivative

pressure for deformed and of decrement vs frequency

irradiated LiF and NaCl for LiF and NaCl crystals.

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By fitting the formula to the data shown in Fig. 5, we can determind two quantities (l/Ao) (2A/aP) and (l/Ao) (aA/aP)

.

The values of A. from the measurements in air are used to be inserted into the factor w ~ o in Eq. (6). The solid curves in Fig. 5 are the fitted ones. From Eqs.

(2) and (3), we obtain the following relation

Here we assumed that the density of dislocations was not changed during each experimental run. This may be true because the change of attenuation with pressure is reversible in the present pressure range. The first and the second terms in RHS of Eq. (7) are determined experimentally, and the other terms can be calculated by using the higher order elasticity theory. Thus the pressure derivative of damping constant can be obtained. The results are shown in Table I for LiF and NaCl crystals. The value for impure LiF crystal (3) is also included in the table. LiF (I) and LiF (11) indicate the impure (Institute for Applied Optics) crystal and the pure (Harshaw) crystal. The purity of crystal is easily predicted by observing the coloration produced by the y-ray irradiation. Analyses of impurities in crystals are now in progress.

Table I Experimental and theoretical pressure derivative 2 of damping constant (l/Bo) (dB/dP) in 10-I' cm /dyn,

2 and theoretical damping constant B in 1 0 - ~ dyn.sec/cm

.

Experiment B + E + M B + E + M + N

(1/Bo ) (dB/dP (l/Bo)(dB/dP) B (1/Bo ) (dB/dP) B LiF (I)

+

200 f 40

LiF (11)

-

32

+

15

NaCl - 2 + 1 0

+

3.7 9.2

+

2.5 12.2

4. Discussion.- A number of theories have been proposed for the origin of intrinsic dislocation damping, namely, the energy dissipation of a uniformly moving dislocation due to frictional force against the motion. They are divided into four categories: theory of phonon scattering by Leibfried (5), Klemens (6), and Brailsford (7) ; thermoelastic effect by Brailsford (7) and Eshelby (8); phonon viscosity by Mason and Bateman

( 9 ) ; fluttering mechanism by Ninomiya (10). We have calculated the

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CS-368 JOURNAL DE PHYSIQUE

constants (11) and calculated fourth-order elastic constants (12) of LiF and NaCl crystals are used. It is considered that the four mechanisms for the dislocation damping mentioned above are independent with each other and their contributions are additive. We choose the expres- sions by Brailsford (B), Eshelby (E), Mason (M), and Ninomiya (N)

,

and sum up the calculated results for the damping constant and its pressure derivative. Obtained values are shown in Table I under the notation B

+

E

+

M

+

N. The values for the case of dropping the last contribu- tion are also shown as indicated B

+

E

+

M.

Experimental values of pressure derivative of damping constant for LiF (11) and NaCl are considered to be in agreement with theoretical values when the experimental uncertainty is referred. About the value of the damping constant, the experiment on direct observation of dislocation velocity by Johnston and Gilman (13) gives B

-

7 X 1 0 - ~ for LiF crystals. In this point, the mechanisms B

+

E

+

M seem to be more favorable. It is added here that no single mechanism is able to result in reasonable values of damping constant and its pressure derivative. We are interested in seeing that the experimental result for impure LiF (I) is very different from that of pure crystal. We are now doing the same kind of experiment to study the effect of impurity on the dislocation damping by using A1 crystals with very high purity and doping them by neutron irradiation, and the results will appear soon.

References

(1) A. V. Granato and K. Lflcke: J. Appl. Phys.

27,

583; 789 (1956). (2) Y. Hiki and T. Maruyama: Proc. 5th Intern. Conf. Internal Friction

and Ultrasonic Attenuation in Crystalline Solids, Vol. 11, p. 201 (1975).

(3) Y. Kogure, T. Kosugi and Y. Hiki: Proc. 6th Intern. Conf. Internal Friction and Ultrasonic Attenuation in Solids, p. 525 (1977). (4) T. Kosugi and Y. Hiki: Jpn. J. Appl. Phys., to be published. (5) G. Leibfried: Z. Physik

127,

344 (1950).

(6) P. G. Klemens: Proc. Phys. Soc. A,* 1113 (1955). (7) A. D. Brailsford: J. Appl. Phys.

43,

1380 (1972). (8) J. D. Eshelby: Proc. Roy. Soc.

e,

396 (1949).

(9) W. P. Mason and T. B. Bateman: J. Acoust. Soc. Amer.

36,

644 (1964).

(10) T. Ninomiya: J. Phys. Soc. Jpn.

2,

399 (1974).

(11) J. R. Drabble and R. E. B. Strathen: Proc. Phys. Soc.

92,

1090 (1967).

(12) S. Mori and Y. Hiki: J. Phys. Soc. Jpn.

45,

1449 (1978).