Ultrasonic study of fission products precipitated in the nuclear fuel A.K. Yadav a, ⁎ , R.R. Yadav a , D.K. Pandey b , Devraj Singh b a Department of Physics, University of Allahabad, Allahabad-211002, India b Department of Applied Physics, Amity School of Engineering and Technology, Bijwasan, New Delhi-110 061, India Received 26 June 2007; accepted 19 February 2008 Available online 23 February 2008 Abstract The Mo–Ru–Rh–Pd alloys are ɛ-phase hexagonal structured inclusion material in irradiated nuclear fuels. The ultrasonic parameters have been calculated in these alloys at room temperature for the characterization. The orientation dependent ultrasonic velocity has been also evaluated for determination of anisotropic behaviour. Nonlinear elastic constants of the alloys at room temperature are calculated using the interaction potential model for the determination of the ultrasonic attenuation and velocity. Acoustic coupling constants, thermal relaxation time and other related parameters are evaluated for the determination of the ultrasonic properties. Behaviour of the ultrasonic properties have been discussed in correlation with the microstructural phenomenon like phonon–phonon interaction and the other thermophysical properties. © 2008 Published by Elsevier B.V. Keywords: Metals and alloys; Elastic properties; Ultrasonic attenuation 1. Introduction Ultrasonic properties provide important diagnostic for microstructural properties as well as deformation processes in a material, controlling material behaviour based on the physical mechanism to predict future performance of the materials. A number of fission products in irradiated fuels are produced and they affect the fuel performance. Especially the fission products precipitated in the nuclear fuel matrix, such as oxide and metallic inclusions, have great influence on the thermal, mechanical and consequently the ultrasonic properties of the fuel. It is therefore useful to understand all these properties and their correlations. For the metallic inclusions composed of Mo– Tc–Ru–Rh–Pd alloys have been observed in irradiated fuels [1–3]. Yet the thermodynamic, chemical and thermophysical properties of the alloys have been studied till now [4–7], but information on the ultrasonic properties is rarely reported. The structural study of binary, ternary and quaternary alloys made by the combination of the Mo, Pd, Rh and Ru can be seen in literature [6,7], which implies that the structure in different forms of these alloys are different. In the present study, therefore, the ultrasonic attenuation at room temperature and ultrasonic velocities with the related parameters particularly elastic constants, Grüineisen numbers, acoustic coupling constants and the thermal relaxation time for the alloys Mo 35 Ru 31 Rh 9 Pd 25 : alloy-1; Mo 20 Ru 54 Rh 15 Pd 11 : alloy-2; Mo 30 Ru 43 Rh 14 Pd 13 : alloy-3 and Mo 43 Ru 34 Rh 12 Pd 11 : alloy-4 are calculated and discussed. All the chosen alloys have hexag- onal closed packed structure (ɛ-phase hexagonal structure), which is confirmed by powder X-ray diffraction patterns at room temperature [6,7]. 2. Theory 2.1. Theory for the ultrasonic velocity The anisotropic properties of the material are well related to the ultrasonic velocities as they are related to higher order elastic constants. There are three types of acoustical wave velocities in hexagonal structured crystals as one longitudinal (V 1 ) and two transverse (V 2 , V 3 ) wave velocities [8–10]. The Debye average velocity (V D ) can be calculated from the initial slopes of these three acoustical branches [11]. Available online at www.sciencedirect.com Materials Letters 62 (2008) 3258 – 3261 www.elsevier.com/locate/matlet ⁎ Corresponding author. Tel.: +91 532 2460987; fax: +91 532 2460993. E-mail address: akyadav83@rediffmail.com (A.K. Yadav). 0167-577X/$ - see front matter © 2008 Published by Elsevier B.V. doi:10.1016/j.matlet.2008.02.036