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Ultrasonic Study of Osmium and Ruthenium DETERMINATION of HIGHER-ORDER ELASTIC CONSTANTS, ULTRASONIC VELOCITIES, ULTRASONIC ATTENUATION and ALLIED PARAMETERS

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Ultrasonic Study of Osmium and Ruthenium DETERMINATION of HIGHER-ORDER ELASTIC CONSTANTS, ULTRASONIC VELOCITIES, ULTRASONIC ATTENUATION and ALLIED PARAMETERS DOI: 10.1595/147106709X430927 Ultrasonic Study of Osmium and Ruthenium DETERMINATION OF HIGHER-ORDER ELASTIC CONSTANTS, ULTRASONIC VELOCITIES, ULTRASONIC ATTENUATION AND ALLIED PARAMETERS By D. K. Pandey*, Devraj Singh** and P. K. Yadawa*** Department of Applied Physics, AMITY School of Engineering and Technology, Bijwasan, New Delhi-110 061, India; E-mail: *[email protected]; **[email protected]; ***[email protected] Ultrasonic properties of two platinum group metals, osmium and ruthenium, are presented for use in characterisation of their materials. The angle-dependent ultrasonic velocity has been computed for the determination of anisotropic behaviour of these metals. For the evaluation of ultrasonic velocity, attenuation and acoustic coupling constants, the higher-order elastic constants of Os and Ru have been calculated using the Lennard-Jones potential. The nature of the angle-dependent ultrasonic velocity is found to be similar to those of molybdenum- ruthenium-rhodium-palladium alloys, Group III nitrides and lave-phase compounds such as TiCr2, ZrCr2 and HfCr2. The results of this investigation are discussed in correlation with other known thermophysical properties. Osmium (Os) and ruthenium (Ru) belong to Buckley (6). Os and Ru both possess a hexagonal the platinum group metals (pgms). Both Os and closed packed (h.c.p.) structure (6). Barnard and Ru are hard, brittle and have poor oxidation resis- Bennett (7) studied their oxidation states. tance. Both metals are mostly produced from The investigation of ultrasonic properties can mines in the Bushveld Complex, South Africa. be used as a non-destructive technique for the Trace amounts of Os are also found in nickel-bear- detection and characterisation of a material’s ing ores in the Sudbury, Ontario region of Canada, properties, not only after production but also dur- and in Russia, along with other pgms. Os oxidises ing processing (8–10). However, none of the work easily in air, producing poisonous fumes, and is the reported in the literature so far is centred on the rarest of the pgms. Ru is also found in ores with ultrasonic study of Os and Ru. Thus, in the pre- other pgms in Russia, and in North and South sent work, we have studied the ultrasonic America. Ru is isolated through a complex chemi- properties of these metals. Ultrasonic attenuation, cal process in which calcination and hydrogen velocity and related parameters have been calcu- reduction are used to convert ammonium rutheni- lated for use in non-destructive testing (NDT) um chloride, yielding a sponge. The sponge is then characterisation. consolidated by powder metallurgy techniques or by argon arc welding. Ru is mostly used in hard Higher-Order Elastic Constants disks and in alloys with platinum for jewellery and The higher-order elastic constants of h.c.p. electrical contacts. It also has increasing use in structured materials can be formulated using the catalysis (1). Os and Ru were discovered in 1804 Lennard-Jones potential, φ(r), Equation (i): (2) and 1844 (3), respectively. m n φ(r)= {–(a0/r ) + (b0/r )} (i) Magnetic measurements of Ru and Os have been made by Hulm and Goodman (4). Savitskii where a0, b0 are constants; m, n are integers and r is et al. (5) investigated the microstructural, physical the distance between atoms (11). The expressions and chemical properties of these metals, and their of second- and third-order elastic constants are mechanical properties have been explored by given in the set of Equations (ii): Platinum Metals Rev., 2009, 53, (2), 91–97 91 4 4 C11 = 24.1 p C' C12 = 5.918 p C' 6 8 C13 = 1.925 p C' C33 = 3.464 p C' 4 4 C44 = 2.309 p C' C66 = 9.851 p C' 2 4 2 4 C111 = 126.9 p B + 8.853 p C' C112 = 19.168 p B – 1.61 p C' (ii) 4 6 4 6 C113 = 1.924 p B + 1.155 p C' C123 = 1.617 p B – 1.155 p C' 6 4 C133 = 3.695 p BC155 = 1.539 p B 4 6 C144 = 2.309 p BC344 = 3.464 p B 2 4 8 C222 = 101.039 p B + 9.007 p C' C333 = 5.196 p B where p = c/a (the axial ratio); C' = χ a/p 5; Os and Ru are given in Table I (6). The calculation 3 3 n + 4 B = Ψ a /p ; χ = (1/8)[{n b0 (n – m)}/{a }]; of higher-order elastic constants was carried out Ψ = – χ/{6 a2 (m + n + 6)}; and c is the height of using the set of Equations (ii), taking appropriate the unit cell. values of m, n and b0. The values of the second- and The basal plane distance ‘a’ and axial ratio ‘p’ of third-order elastic constants are shown in Table II. The Young’s modulus ‘Y’ and bulk modulus Table I ‘B’ were evaluated using the second-order elastic Basal Plane Distance, a, and Axial Ratio, p, for constants presented here. It is obvious from Osmium and Ruthenium* Table II that there is good agreement between Value the calculated values from this study and the pre- viously reported values for the Young’s modulus Parameter Units Os Ru and the bulk modulus (6, 12, 13). It is observed a Å 2.729 2.700 that the higher-order elastic constants of Os and p – 1.577 1.582 Ru are analogous to those of gallium nitride and *All values obtained from Reference (6) indium nitride, respectively (14). All the second- Table II Second- and Third-order Elastic Constants for Osmium and Ruthenium Second-order Value, 1011 Nm–2 Third-order Value, 1011 Nm–2 elastic constant Os Ru elastic constant Os Ru C11 8.929 6.279 C111 –145.620 –102.400 C12 2.193 1.542 C112 –23.088 –16.236 C13 1.774 1.255 C113 –4.550 –3.220 C33 7.938 5.654 C123 –5.783 –4.093 C44 2.128 1.506 C133 –26.815 –19.098 C66 3.166 2.463 C344 –25.139 –17.904 B 4.119 2.911 C144 –6.738 –4.768 * B 3.800 2.920 C155 –4.491 –3.178 ** B 4.110 – C222 –115.219 –8.026 Y 5.525 3.971 C333 –93.777 –67.211 Y * 5.600 4.300 – – – Y *** 5.620 4.220 – – – *Reference (12); **Reference (13); ***Reference (6) Platinum Metals Rev., 2009, 53, (2) 92 and third-order elastic constants for Ru are Equations (iii)–(v) (14), where V1 is the longitudi- found to be higher than those of Mo-Ru-Rh-Pd nal wave velocity, V2 is the quasi-shear wave alloys (11). Thus we conclude that our calculated velocity and V3 is the shear wave velocity; ρ is the higher-order elastic constants and theory are cor- density of the material and θ is the angle with rect and justified. The bulk modulus of Os is unique axis of the crystal. The densities of Os and found to be higher than that of its nitride and Ru are taken from the literature (6). The angle- carbide (15). The values of C11 for the face cen- dependent ultrasonic velocities in the chosen tred cubic (f.c.c.) structured pgms, Pd and Pt, are metals were computed using Equations (iii)–(v) 1.8 × 1011 Nm–2 and 2.2 × 1011 Nm–2, respective- and are shown in Figure 1. ly (16). The high elastic modulus reveals that Os The longitudinal ultrasonic velocities of Os and and Ru have low adhesion power and high hard- Ru (see Figure 1) for wave propagation along ness. Thus these metals are suitable for unique axis are given in Table III, together with applications such as sliding electrical contacts, their sound velocities (17, 18). The nature of the switches, slip rings, etc. ultrasonic velocity curves in these h.c.p. metals is similar to other h.c.p. structured materials (11, 14, Ultrasonic Velocities 19). Comparison with these sources verifies our The anisotropic properties of a material are velocity results. The anomalous maxima and min- related to its ultrasonic velocities as they are ima in the velocity curves are due to the combined related to higher-order elastic constants. There are effects of the second-order elastic constants. The three types of ultrasonic velocities in h.c.p. angle-dependent velocities of Ru are greater than crystals. These include one longitudinal and two those of Mo-Ru-Rh-Pd alloys (11) due to the shear wave velocities, which are given by higher values of the elastic constants for Ru. Thus 2 2 2 2 2 2 2 2 V 1 = {C33 cos θ + C11 sin θ + C44 + {[C11 sin θ – C33 cos θ + C44 (cos θ – sin θ)] 2 2 2 1/2 + 4 cos θ sin θ (C13 + C44) } }/2ρ (iii) 2 2 2 2 2 2 2 2 V 2 = {C33 cos θ + C11 sin θ + C44 – {[C11 sin θ – C33 cos θ + C44 (cos θ – sin θ)] 2 2 2 1/2 + 4 cos θ sin θ (C13 + C44) } }/2ρ (iv) 2 2 2 V 3 = {C44 cos θ + C66 sin θ}/ρ (v) Fig. 1 Plot of ultrasonic velocity ‘V’, against angle 7.5 with unique axis ‘θ’ of osmium and ruthenium 7 1 6.5 – 6.5 6 , km s V ) 5.5 -1 5 Os – V Ru – V1 Os – V2 ms 5 Os-V1 1 Ru -V 1 Os -V2 3 Ru -V– 2V2 OsOs-V3 – V3 RuRu-V3 – V3 4.5 V (10 4 3.5 Ultrasonic velocity, Ultrasonic velocity, 3 2.5 00 102030405060708090 Angle,Angle θ Platinum Metals Rev., 2009, 53, (2) 93 Table III phonon distribution is called the thermal relaxation time ‘τ’ and is given by Equation (viii): Longitudinal Ultrasonic Velocities, V1, and Sound 2 Velocities* of Osmium and Ruthenium τ = τS = τL/2 = 3K/CV V D (viii) –1 Value, km s where τL is the thermal relaxation time for the τ Parameter Os Ru longitudinal wave; S is the thermal relaxation time for the shear wave; and K is the thermal conductiv- V1 5.9 6.7 Sound velocity 4.9 6.0 ity.
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