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·Materials Characterization and testing
Ultrasonic Characterization of IntermetallicsRaja Ram Yadav and Devraj Singh
Department of Physics, University of Allahabad, India
e-mail . physics @ nde.vsnl.net.in
In the low temperature region and in metals the most important factor contributing to ultrasonic attenuation is the electron-phonon interaction [1,2,3].
Although a number of studies have been made in metals at low temperature region, only few results are available in intermetallics. The Rare - earth monopnictides RX (X = N, P As, Sb, Bi) are quiet interesting as the observed anomalous physical properties of these semimetallics have attracted much attention in recent year [4-8]. In order to study the behaviour of ultrasonic attenuation, we have taken GdP, GdAs single crystals. When ultrasonic wave is passed through a solid, the coupling between conduction electron and acoustical phonon occurs below 80K. In this investigation electron-lattice interaction characterizing the compounds GdP, GdAs have been studied with the help of electrical resistivity and elastic parameters.
The attenuation due to shear and compressional viscosity of the lattice at the low temperatures are 
|he||stands for electron - viscosity|
|VL||velocity of longitudinal wave|
|VS||Velocity of Shear wave|
|f||frequency of the wave|
|r||density of the material|
|h||Planck's constant divided by 2p|
We have computed the temperature dependence of second order elastic constants SOEC (C11, C12, C44) for the evaluations of velocity of the ultrasonic wave with method described by Mori and Hiki .
|T (K)||R(10-8W m)||he(10-4 Kg/ms)||(a/f2)L(10-15 Nps2/m)||(a/f2)S( 10-15 Nps2/m)|
|Table 1: Electrical resistivity (R), Viscosity (he), (a/f2)L for longitudinal wave and (a/f2)S for shear wave of GdP at temperature (T) region from 2K to 80K.|
|T (K)||R(10-8Wm)||he(10-4 Kg/ms)||(a/f2)L(10-15 Nps2/m)||(a/f2)S( 10-15 Nps2/m)|
|Table 2: Electrical resistivity (R), Viscosity (he), (a/f2)L for longitudinal wave and (a/f2)S for shear wave of GdAs at temperature (T) region from 2K to 80K.|
Obviously from eqn. (3) he is inversely proportional to R-resistivity. As the intermetallic compounds GdP and GdAs have fewer carrier electron, the electrical resistivity values are quite high and he evaluated are small in general for all compounds. The ultrasonic attenuation both for longitudinal and Shear waves is directly proportional to he. Thus ultrasonic attenuation in these semimetallics is very low in comparison to pure metals as expected due to large resistivities of the substances. Due to smaller number of free carrier electrons available the ultrasonic attenuation arising from election-phonon interaction in GdP and GdAs is very small is general. The four curves for ultrasonic absorption coefficients over frequency square as a function of lower temperature (< room temperature) are qualitatively similar. At low temperature the ultrasonic absorption firstly decrease rapidly with increasing temperature and shows a kink at just above the Neel temperature TN (fig 1-4). At higher temperature the absorption is linear with temperature. The Neel temperature as determined from the derivative ¶r/¶T are found to be 15.9, 18.7K for GdP and GdAs respectively. Although for GdP and GdAs electrical resistivity kniks in the curve of R vs. T, appear exactly at Neel temperature TN 15.9 and 18.7K  but in plot of ultrasonic attenuation is T, kinks appear just above the Neel temperature approximately at 20K (fig 1-4) because here elastic behavior can be seen with SOEC values also affect the attenuation accordingly.
|Fig 1: (a/f2) long. of Gdp vs. temperature||Fig 2: (a/f2) ) shear. of Gdp vs. temperature|
|Fig 3: (a/f2) long. of GdAs vs. temperature||Fig 4: (a/f2) shear. of GdAs vs. temperature|
It can be understand with the tables 1-2 that shear wave attenuation (a/f2)S in GdP and GdAs single Crystal is greater than the (a/f2)L. Thus Although the attenuation in these compounds is smaller than pure metals, yet the trend of temperature dependence of (a) is of the same nature as for metal except some anomalous kinks due to anomalous physical parameters observed in Rare earth monopnictides.
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