J. KUMAR ET AL.
48
The temperature variation of non-linearity constant is
presented in Figure 2 along <100> direction. The value
of Dl/Ds along <100> direction is about 5.34 which is
expected for this type of crystals. We can see that ratio of
non-linearity constants Dl/Ds increases with temperature.
The D is a measure of acoustic energy converted to
thermal energy under the relaxation process, thus the
increase in Dl/Ds with temperature shows that longitudi-
nal loss increases with temperature and vice versa along
<100> direction. Along other two directions also the
values of Dl and Ds decreases with temperature in a
manner which shows that longitudinal loss increases with
temperature.
Studies of the ultrasonic absorption in crystals and its
dependence on the direction of propagation and wave
mode (polarization of the elastic displacement vector) are
important from the standpoint of the further development
of the theory of sound wave-lattice interactions. The
thermal ultrasonic attenuation along different directions
is presented in Figure 3. We can see from the figure that
thermal attenuation increases with temperature along all
these directions and of the order of 10–18 Nps2/m which is
expected for the type of crystal under inspection. At any
particular temperature the thermal attenuation along
<100> direction is more and is less along all other direc-
tions, hence <100> is more suited for the study of ther-
mal ultrasonic attenuation. Figures 4-6 represent the
ultrasonic attenuation due to phonon-phonon interaction
along <100>, <110> and <111> crystallographic direc-
tions respectively. Along all these directions the ultra-
sonic attenuation increases with increase in temperature,
the situation is little different for shear wave along
<110> direction (pol.<110>) for which the ultrasonic
attenuation decreases with temperature. Among all these
three directions the attenuation along <111> direction
changes sharply with temperature so the study along
<111> crystallographic direction is more reliable for the
characterization. From the attenuation values along dif-
ferent directions it is evident that the ultrasonic attenua-
tion is different along different directions i.e. varies with
the orientation of the crystal.
5. Conclusions
From the above results one can reach to the conclusion
that the thermal relaxation time, ultrasonic wave veloci-
ties and attenuation are the properties which depends on
the crystallographic directions or one can say that these
properties are orientation dependent which strongly sup-
ports the results given by other investigators [14,15] for
the same type of crystals that all these properties are
strongly dependent on direction of polarization. The
study of ultrasonic attenuation for longitudinal wave
along <100> is more important in characterization of the
crystal since its magnitude is more along this direction.
The rapidly increase in ultrasonic attenuation at higher
temperature is interpreted mainly due to increase of den-
sity of dislocations. The results obtained in this study can
be used for further investigations [16,17] and industrial
research and development purposes.
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