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Home , Osmium, Ruthenium

DOI: 10.1595/147106709X430927 Ultrasonic Study of and 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 , 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 - ruthenium-- alloys, Group III nitrides and lave- 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 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, . be used as a non-destructive technique for the Trace amounts of Os are also found in -bear- detection and characterisation of a material’s ing ores in the Sudbury, Ontario region of , properties, not only after production but also dur- and in , 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 velocity and related parameters have been calcu- reduction are used to convert rutheni- lated for use in non-destructive testing (NDT) um chloride, yielding a sponge. The sponge is then characterisation. consolidated by techniques or by . 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 (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 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- of the material and θ is the angle with rect and justified. The bulk modulus of Os is unique axis of the . The 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 , 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 . 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. VD is the Debye average velocity and is calculated from the initial slopes of the three *The sound velocities are obtained from References (17, 18) acoustic branches, Equation (ix):

–1/3 3 Ω calculated results of ultrasonic velocities can be ⎧ 1 1d⎫ VD = Σ ∫ 3 (ix) used for anisotropic characterisation of Os and Ru 3 Vi 4π ⎩ i =1 ⎭ metals. where Ω is angle. The integration is over all Ultrasonic Attenuation and Allied directions and the summation is over the three Parameters acoustic branches. The propagation of the longitu- The predominant causes of ultrasonic attenua- dinal ultrasonic wave creates compression and tion in a solid at room temperature are rarefaction throughout the lattice. The rarefied phonon-phonon interaction (Akhieser type loss) regions are colder than the compressed regions. and thermoelastic relaxation mechanisms. The Thus there is a flow of heat between these two ultrasonic attenuation coefficient ‘(α)Akh’ due to regions. The thermoelastic loss ‘(α)Th’ can be the phonon-phonon interaction mechanism is calculated with Equation (x): given by Equation (vi) (11, 14): 2 2 j 2 5 (α/f )Th = 4 π < γi > KT/2ρV L (x) 2 2 j 2 (α/f )Akh = 4 π (3E0 <(γi ) > j 2 3 The thermoelastic loss for the shear wave has –<γi > CVT )τ/2ρV (vi) no physical significance because the average of the where f is the frequency of the ultrasonic wave; V Grüneisen number for each mode and direction of is the ultrasonic velocity for longitudinal and shear propagation is equal to zero for the shear wave. waves as defined in Equations (iii)–(v); E0 is the Only the longitudinal wave is responsible for ther- j thermal energy density; T is the temperature and γi moelastic loss because it causes variation in is the Grüneisen number: i and j are the mode and entropy along the direction of propagation. direction of propagation. The Grüneisen number The thermal conductivities of the selected met- for a hexagonal structured crystal along the <001> als are taken from the literature (6). The orientation or θ = 0º is a direct consequence of the values of the specific heat per unit volume ‘CV ’ second- and third-order elastic constants. CV is the and energy density ‘E0’ are obtained from specific heat per unit volume of the material. The the American Institute of Physics Handbook (20). acoustic coupling constant ‘D’ is the measure of The thermal relaxation time ‘τ’ and Debye average acoustic energy converted to thermal energy and is velocity ‘VD’ are evaluated from Equations (viii) given by Equation (vii): and (ix) and are shown in Figure 2. The ultrasonic

j 2 attenuation coefficients are calculated from D = 3(3E0 <(γi ) > j 2 Equations (vi) and (x). Calculated acoustic cou- – < γi > CVT )/E0 (vii) pling constants ‘D’ and ultrasonic attenuation When an ultrasonic wave propagates through a coefficients ‘(α/f 2)’ are presented in Table IV. crystalline material, the equilibrium of phonon dis- The angle-dependent thermal relaxation tribution is disturbed. The time taken for time varies between 6.5 ps and 9.55 ps. This re-establishment of equilibrium of the thermal indicates that after the propagation of a wave,

Platinum Metals Rev., 2009, 53, (2) 94 Fig. 2 Plot of Debye average velocity ‘VD’ and thermal relaxation time, ‘τ’ against angle 1010 10 with unique axis ‘θ’ of osmium and ruthenium 1 – OsOs-VD – VD RuRu-VD – VD 99 9 Thermal relaxation time, OsOs-Relax. – τ RuRu-Relax. – τ , km s

D 88 8 V

77 7

66 6 ) and Relax time(ps) -1

ms 55 5 τ 3 , ps (10

D 44 4 V Debye average velocity, Debye average velocity,

33 3 00 102030405060708090 θ Angle,Angl e

the distribution of phonons returns to the equi- attenuation due to phonon-phonon interaction is librium position within 6.5–9.5 ps. The values of directly related to the acoustic coupling constant the thermal relaxation time in Pd and Pt are 8.8 and thermal relaxation time. Os has a lower ps and 13.4 ps, respectively (16). The thermal thermal relaxation time than Ru, while the acoustic relaxation time of the chosen metals is directly coupling constant of Os is greater than that of Ru affected by their Debye average velocity and the due to its low value of CV/E0. Thus total attenua- of these metals. tion is mainly affected by the acoustic coupling The total attenuation is given by Equation (xi): constant. Total attenuation at the nanoscale in Pd –15 2 –1 2 2 2 2 and Pt has been reported as 2.98 × 10 Np s m (α/f )Total = (α/f )Th + (α/f )L + (α/f )S (xi) and 7.38 × 10–15 Np s2 m–1, respectively (16). 2 where (α/f )L is the ultrasonic attenuation coeffi- These reported values are larger than those of Os 2 cient for the longitudinal wave and (α/f )S is the and Ru. The total attenuation in the Ru ultrasonic attenuation coefficient for the shear Mo20Ru54Rh15Pd11 has been found to be 2 –15 2 –1 wave. The value of (α/f )Total is greater for Os 1.044 × 10 Np s m (11). A comparison of than for Ru. The dominant mechanism for total total attenuation indicates that these metals are attenuation is phonon-phonon interaction. The more durable and ductile in alloy form than in

Table IV Acoustic Coupling Constants, D, and Ultrasonic Attenuation Coefficients, (α/f 2), of Osmium and Ruthenium

Value Parameter Units Os Ru

D L – 56.002 55.825 D S – 1.532 1.473 2 –15 2 –1 (α/f )Th 10 Np s m 0.002 0.002 2 –15 2 –1 (α/f )L 10 Np s m 1.598 1.509 2 –15 2 –1 (α/f )S 10 Np s m 0.158 0.144 2 –15 2 –1 (α/f )Total 10 Np s m 1.758 1.655

Platinum Metals Rev., 2009, 53, (2) 95 their pure form. The performance of Ru as an alloy Conclusions component for durability and ductility might be The adopted method for theoretical study of better than that of Os due to its lower ultrasonic higher-order elastic constants is justified for the attenuation. pgms. The high values of the elastic constants of The pulse echo technique (PET) can be used the h.c.p. metals Os and Ru provide evidence of for the measurement of ultrasonic velocity and their low adhesive power and high . The attenuation of materials, because it avoids heat results of the elastic constants substantiate the loss and scattering loss. This method provides superiority of h.c.p. metals over f.c.c. metals in this results with good accuracy and would provide regard. The anisotropic characterisation of the useful information when combined with the the- chosen metals can be carried out on the basis of ory presented here. For Ru, PET can be used directional ultrasonic velocity and thermal relax- directly for measurement. The high precision ation time. The phonon-viscosity mechanism is the indirect approaches such as resonant ultrasound dominant cause of total attenuation in these met- spectroscopy (RUS) and novel digital pulse echo als. The acoustic coupling constant is a governing overlap techniques can be used for the measure- factor for total attenuation. The mechanical behav- ment of ultrasonic velocity in Os (21). By iour of Ru is expected to be better in terms of ultrasonic velocity measurements, the anisotropic durability and ductility than that of other pgms due mechanical properties of a material can be under- to its low attenuation. stood as they are related to velocity. This enables The results obtained in this investigation can be quality assurance of products made with these used for further study of these metals. Our whole materials in combination with other materials to theoretical approach can be applied to the evalua- be carried out by measurements of ultrasonic tion of ultrasonic attenuation and related attenuation, not only after production but also parameters to study the microstructural properties during processing. of h.c.p. structured metals.

References 1 P. Ahlberg, ‘Development of the metathesis method 10 “Ultrasonics”, ed. P. D. Edmonds, Methods of in ’, Advanced information on the Experimental Physics, Vol. 19, Academic Press, 2005, The Royal Swedish New York, U.S.A., 1981 Academy of Sciences, Stockholm, 2005; 11 A. K. Yadav, R. R. Yadav, D. K. Pandey and http://nobelprize.org/nobel_prizes/chemistry/ D. Singh, Mater. Lett., 2008, 62, (17–18), 3258 laureates/2005/chemadv05.pdf (Accessed on 21st 12 A. S. Darling, Platinum Metals Rev., 1966, 10, (1), 14 February 2009) 13 F. Occelli, D. L. Farber, J. Badro, C. M. Aracne, 2 W. P. Griffith, Platinum Metals Rev., 2004, 48, (4), 182 D. M. Teter, M. Hanfland, B. Canny and B. 3 V. N. Pitchkov, Platinum Metals Rev., 1996, 40, (4), Couzinet, Phys. Rev. Lett., 2004, 93, (9), 095502 181 14 D. K. Pandey, D. Singh and R. R. Yadav, Appl. 4 J. K. Hulm and B. B. Goodman, Phys. Rev., 1957, Acoust., 2007, 68, (7), 766 106, (4), 659 15 J.-C. Zheng, Phys. Rev. B, 2005, 72, (5), 052105 5 E. M. Savitskii, V. P. Polyakova and N. B. Gorina, 16 R. R. Yadav and D. K. Pandey, Mater. Lett., 2005, 59, Platinum Metals Rev., 1979, 23, (2), 57 (5), 564 6 D. H. Buckley, NASA Technical Note, 1967, 17 Web Elements, Osmium, Physical Properties: D-4152, 1: http://ntrs.nasa.gov/ (Accessed on 15th http://www.webelements.com/osmium/physics.html March 2008) (Accessed on 16th April 2008) 7 C. F. J. Barnard and S. C. Bennett, Platinum Metals 18 Web Elements, Ruthenium, Physical Properties: Rev., 2004, 48, (4), 157 http://www.webelements.com/ruthenium/physics. 8 S. K. Kor, Nature, 1958, 181, (4621), 1462 html (Accessed on 16th April 2008) 9 S. K. Kor, R. R. Yadav and D. Singh, Mol. Cryst. Liq. 19 S. Yamanaka and K. Kurosaki, J. Alloys Compd., Cryst., 2002, 392, 75 2003, 353, (1–2), 269

Platinum Metals Rev., 2009, 53, (2) 96 20 “American Institute of Physics Handbook”, 3rd 21 C. Pantea, I. Mihut, H. Ledbetter, J. B. Betts, Edn., ed. D. E. Gray, McGraw-Hill, New York, Y. Zhao, L. L. Daemen, H. Cynn and A. Migliori, U.S.A., 1972, pp. 4–44 Acta Mater., 2009, 57, (2), 544

The Authors D. K. Pandey is a Lecturer in the Devraj Singh is a Lecturer in the Department of Applied Physics, AMITY Department of Applied Physics, AMITY School of Engineering and Technology, School of Engineering and Technology, New Delhi, India. His main activities are in New Delhi. His research interest is the the field of ultrasonic characterisation of ultrasonic non-destructive testing (NDT) condensed materials and nanofluids. characterisation of condensed materials.

P. K. Yadawa is a Lecturer in the Department of Applied Physics, AMITY School of Engineering and Technology, New Delhi. His major field of interest is the ultrasonic characterisation of structured materials.

Platinum Metals Rev., 2009, 53, (2) 97