Pressure Dependent Elastic and Thermo-Physical Properties of U Ternaries with ZrNiAl Structure Compounds

Abstract

The Thermophysical and ultrasonic aspects of U- ternaries are examined theoretically under high pressure. In order to determine the second- and third-order elastic constants of U- ternaries (URhAl and ThRhAl) compounds under pressure conditions (0-45GPa), the potential model technique has been used. The assessed second-order elastic constants are used along with the pressure-dependent ultrasonic velocities, thermal relaxation time, and other significant and important thermophysical data to determine the orientation. It is observed that thermal relaxation time and mechanical & thermal properties exhibit an increasing trend with increasing pressure for U-ternaries URhAl and ThRhAl compounds. The effect of increasing pressure on the URhAl and ThRhAl compounds shows up as an increase in elastic constants, ultrasonic velocities, ultrasonic attenuation, and Debye temperature. The ratio B/G increases with pressure which indicates that the materials are ductile in nature. We have used the approximate values of SOECs, density, and lattice properties in calculating the melting point, ultrasonic velocity, and thermal conductivity.

Introduction

I. INTRODUCTION

Uranium compounds have a wide range of characteristics Because of the complicated behaviour of their 5f electrons. UTX (T, transition metal; X, non-transition metal) is a large class of uranium ternary equiatomic compounds. The ZrNiAl type, which is an ordered ternary derivative of the Fe2 P type [1], is one of the most common structural types in which such compounds crystallized.  The hexagonal structure is layered, with one form of basal-plane sheet holding all U atoms and some T atoms, and the other containing the remaining T and X atoms. The 5f-band states, which appear near the Fermi energy EF, dominate the electronic structure of the UTX ternaries, as they do in most other uranium intermetallics. The transition metal (T) in d states has greater binding energies and contributes less to the electronic states at EF [2]. In light actinides, the 5 f states have often been close to the boundary between localised and itinerant behaviour. Their sensitivity to external variables and their composition present themselves in a broad range of magnetic properties, which are often extremely strange. [3]. A hard-magnetization axis is equivalent to the chain direction whenever U atoms are coordinated in linear chains (TiNiSi or GaGeLi structure types from UTX compounds), with in-plane anisotropy perpendicular to the chain direction being weaker [3]. In this approach, magnetic anisotropy in U-based substances reflects bonding anisotropy. A large elastic anisotropy was also found in UTX compounds with the ZrNiAl structural type [4]. Many of these compounds are ferromagnetic, with a wide range of Curie temperatures and ordered moment magnitudes [5], and can thus be used to investigate discontinuous phase transitions with changeable magnetic order parameters but a constant crystal structure. The occurrence of discontinuous phase transitions in several of these compounds has recently been established (e.g. UCoAl [6, 7], URhAl, UCoG,a.) On either hand, two members of this group, UPtAl [6] and URhGa [8], showed an initial increase in TC with increasing pressure (in the range of several GPa). It is thus desirable to be able to anticipate how TC behaves under pressure in such compounds.

This study uses Lennard-Jones potential techniques to compute elastic, mechanical and ultrasonic characteristics. Ultrasonic attenuation (UA), which alludes to the specific association between the anisotropic behavior of the proximal hematinic planes and structural motion affinity, is the most important physical parameter used to explain the characteristics of the materials. There is a significant correlation between numerous physical properties, such as thermal energy density, specific heat, thermal conductivity and higher-order elastic coefficients with varying pressures. The information in this work will be helpful for future scientific investigations into the mechanical characteristics of URhAl and ThRhAl compounds as well as for comparing the elastic and ultrasonic properties of the URhAl and ThRhAl) compounds. Although ultrasonic is a non-destructive and practical method with a wide diversity of applications in every field. Ultrasonic characterization of these U- ternaries compounds has been a significant topic of focus for engineers and researchers

II. THEORY

One of the most popular theories for determining the higher order elastic coefficients of    hexagonal wurtzite and HCP shaped compounds is the interaction potential model technique [9, 10]. The formulations of higher-order elastic constants were determined using the second- or third-order strain gradient of elastic energy density.       

A common definition of elastic constants of certain value is the partial derivatives of the substance's thermodynamic potential applied to finite compression. The responsiveness of a material to external stress or the amount of stress required to maintain deformation is described by its elastic constant. The following is the description of the nth order elastic constant.

Table 2 shows that in the pressure range of 0 to 50 GPa, the B is much bigger than the G, showing that the resistance of URhAl and ThRhAl compounds to volume change is greater than that of shape change. This is supported by the hardness in Fig. 2(b). The material is brittle if the B/G ratio is higher than 1.75; otherwise, it is ductile. Indicating that the URhAl and ThRhAl compounds are ductile under high pressure, the value of B/G rises from 1.552 to 1.554 as the pressure is increased from 0 to 50 GPa. The stiffness of the URhAl and ThRhAl compounds improves as Young's modulus increases, as illustrated in Fig 2(a) [29]. Table 2 shows that the B increases significantly with increasing pressure, implying that increasing pressure can better the hardness of the compounds [30]. The hexagonal crystal's melting temperature Tm can be calculated using equation 7 [31]. Figure 3 illustrates the estimated melting points for URhAl and ThRhAl compounds at pressure conditions (c). The pressure increase is evidently caused by the gradual augmentation of the URhAl and ThRhAl compounds of Tm, as seen in Fig. 3(c).

B. Ultrasonic Velocity And Allied Parameters

In this analysis, the mechanical and isotropic properties of the compounds URhAl and ThRhAl have been associated to ultrasonic velocity. VL, VS, VD, and were estimated for the URhAl and ThRhAl. Table.3 depicts the values of the pressure-dependent acoustic coupling constants as well as the thermal energy density (E0), which were calculated using the physical constant and Debye temperatures (DL and DS).

Table.3 Thermal conductivity (K(min)Erg/cm-sec-K) and acoustic coupling constant (DL, DS) of U-ternaries compounds (URhAl and ThRhAl) in table.3 at different pressure.

Debye temperature (?) is an interesting and promising characteristic parameter that is essential to take into consideration while examining concepts in the field of solid-state physics. The melting point, thermal conductivity, and specific heat are corresponding. The correlation between the Debye temperature and a variety of materials' physical properties, such as melting temperature and specific heat, is considerable. Using elastic constants, the Debye temperature can be calculated [32].

The "kmin" values that were estimated using Eq. 12 at various pressures (0–50GPa) are shown in Fig. 3. (a). It is evident from Fig. 3(a) that as pressure increases, kmin of the compounds URhAl and ThRhAl gradually increase.

Table.4 demonstrates conclusively that the values of DL for URhAl and ThRhAl compounds at various pressures are even much higher than DS. This illustrates that shear ultrasonic waves exchange ultrasonic energy into heat energy more slowly than longitudinal ultrasonic waves. One of the most crucial physical properties for condensed substances to be considered when analysing the physical mechanisms underlying heat conduction is their thermal conductivity, which further offers comprehensive data on lattice vibrations in solids [33].

Figures 4–7 show the ultrasonic velocities along of the crystal's z-axis at (0-50 GP) pressures, with the URhAl and ThRhAl compounds' velocity VL increasing with angle. (Fig.4), and in Figure 5, the velocity VS1 is at its minimum at an angle of 300 and its greatest at 450. Figure 6 shows how VS2 velocities increase with increasing angle. The peculiar behaviour of direction dependent velocity is also caused by the presence of SOECs and density. The alignment dependent velocity curves obtained in this study are comparable to the direction dependent velocity curves seen in other U-ternary compounds [34, 35]. Therefore, the URhAl and ThRhAl compounds including an angle-dependent hexagonal structure are completely justified. Figure.9 depicts the fluctuation of Debye average velocity (VD) as a function of angle () with the crystal's z-axis. VD increases with angle () and reaches its maximum at 550 because to the inclusion of the velocities VL, VS1, and VS2 in the estimation of VD for the URhAl & ThRhAl compounds [36, 37]. It appears to be assume that changes in debye average velocity are effected by necessary ultrasonic velocities. A significant increase in all wave velocities results in a maximum value of VD at 55°. The z-axis of this crystal rotates at an angle of 550 degrees, as well as the average sound wave velocity confirms that this is the maximum

.

Conclusion

In the current investigation, the Lennard-Jones potential approach was used to evaluate the elastic, mechanical, and thermophysical aspects of the URhAl and ThRhAl compounds at pressures ranging from 0 to 50 GPa. The analysis yields the following finding: 1) The elastic constant, which plays a vital role in establishing essential points of mechanical and dynamic behaviour. The higher order elastic constants in the URhAl and ThRhAl compounds verify our theory. The URhAl and ThRhAl compounds\' assessed elastic coefficients fulfil the criteria, indicating that they are mechanically stable under the pressures applied. 2) Furthermore, reports have been made on the B, G, Y (Young\'s modulus), Poisson\'s ratio (?), and Hardness of URhAl and ThRhAl compounds under various pressures (Hv). In particularly, the estimated B/G values show that URhAl and ThRhAl compounds are brittle in the pressure range of 0–50 GPa. Applying increasing pressure can made it more ductile since it becomes more brittle the more pressure is applied. URhAl exhibit better mechanical response with increasing pressure in comparison to ThRhAl. 3) Moreover, data has been provided regarding the melting point, thermal conductivity, and specific heat capacity of URhAl and ThRhAl compounds under various pressures. As pressure is increased, the thermal conductivity (kmin) of the compounds of URhAl and ThRhAl gradually increases. The pressure which causes the melting point of the compounds of URhAl and ThRhAl to gradually increase. 4) The \"?” value for URhAl and ThRhAl compounds is found to be in the order of picoseconds, supporting their hexagonal shape. The period for the re-establishment of symmetry propagating of phonons will be the shortest for wave propagation in this direction since \" has the least value along = 550 at all pressures. 5) The most important element in determining thermal conductivity is UA, which governs total attenuation and is carried on by the p-p interactions. URhAl and ThRhAl compounds exhibit their best performance with higher pressure, and their increased ductility is supported by the minimum UA under higher pressure. 6) URhAl exhibit better response with increasing pressure in comparison to ThRhAl. The research could help with laves phase URhAl and ThRhAl compounds processing and non-destructive characterization. The current study is expected to contribute significantly to a comprehensive understanding of U-ternary compounds and provide guidance for such applications. Funding; No

References

[1] Dwight, A.E. in: B.C. Giessen (Ed.), Developments in the Structural Chemistry of Alloy Phases, Plenum, New York, 1969, p. 182. [2] Sechovsky, V., Havela, L. in: K.H.J. Buschow (Ed.), Handbook of ´ calculations. Magnetic Materials, Vol. 11, North-Holland, Amsterdam, 1998, p. 1. [3] Havela, L., Sechovsky, V., de Boer, R.F., Brück, E., and Nakotte, H. Physica B., 1992 vol. 177, p.159. [4] Havela, L., Divis, M., Sechovsky, V., Andreev, A.V., Honda, F., Oomi, G., Méresse, Y., and Heathman, S. J. Alloys Compd. 2001, vol. 322, P.7. [5] Kimura, N., Kabeya, N., Aoki, H., Ohyama, K., Maeda, M., Fujii, H., Kogure, M., Asai, T., Komatsubara, T., Yamamura, T., and Satoh, I., Phys. Rev. B.2015, vol.92, p.35106. [6] Aoki, D., Combier, T., Taufour, V., Matsuda, T.D., Knebel, G., Kotegawa, H., and Flouquet, J. J. Phys. Soc. Japan. 2011, vol.80, p.94711. [7] Shimizu, Y., Braithwaite, D., Salce, B., Combier, T., Aoki, D., Hering, E.N., Ramos, S.M., and Flouquet, J. Phys. Rev. B. 2015, p.91,125115. [8] Míšek, M., Prokleška, J., Opletal, P., Proschek, P., Kaštil, J., Kamarád, J., and Sechovský, V. AIP Adv. 2017, vol.7. [9] Panday, D.K.and Yadav, R. R. Applied Acoustics., 2009,vol. 70, No 3, P. 412-415. [10] Panday, D.K.,and Yadav, R.R. Materials Letters., Vol. 59, No 5, 2005, P 564-569. [11] Fine, M.E. Brown, L.D., and Marcus, H.L. Scripta Metallurgica, 1984, vol.18, 951 (1984). [12] Yousef, E. S., El-Adawy, A., and El-KheshKhany, N., Solid State Commun. 2006, vol. 139, 108. [13] Verma, S. K., Panday, D.K. and Yadav, R.R. Physica B: Condensed Matter, vol. 407, No 18, 15 2012, Pp. 3731-3735 [14] Balla, V. Singh, D., Pandey, D. K., Yadav, C. P. ,International Journal of Thermophysics (2020), p.41:46 . [15] Pillai, S.O. Solid State Physics: Crystal Physics, seventh ed., New Age International Publisher, Chap. 4, 2005, pp. 100–111. [16] Yadav, C. P., and Pandey, D.K. Ultrasonics., 2019,Vol. 96, P. 181-184. [17] Singh, D. and Panday, D.K. Pramana. J. Physics., Vol. 72, No. 2 2009, pp. 389–398 [18] Khan, A. Yadav, C. P., Pandey, D.K., Singh, D., and Singh, D., J. PURE APPL. ULTRASON., 2019, VOL. 41, NO. 1. [19] Dhawan, P. K., Wan, M., Verma, S .K, Pandey, D .K, and Yadav R.R. JOURNAL OF APPLIED PHYSICS, 2015, vol.117, 074307. [20] Havela, L., Divis, M., Sechovsky, V., Andreev, A.V., Honda, F., Oomi, G., Meresse, Y., and Heathman, S. Journal of Alloys and Compounds.2001, vol.322, no.7. [21] Zhang, G., Zhao, Y.X., Hao, Y.J., and Zhang, L. World Scientific, 2018, vol.32, No.1. [22] W. Voigt, (1928). Lehrbuch der Kristallphysik. Teubner Verlag, Leipzig. [23] Reuss, A.Z. ZAMM – Journal of Applied Mathematics and Mechanics, 1929, vol.9, 49. [24] Hill, R. The elastic behaviour of a crystalline aggregate, Proc. Phys. Soc., A. 1952,vol.65, 349. [25] Suetin, T.V., Shien, I.R., Electronic and Mechanical Properties, Phase Stability, and Formation Energies of Point Defects of Niobium Boronitride Nb2BN, Physics of the Solid State, 2017, Vol. 59, p. 1459-1469. [26] Turkdal, N., Deligoz, E., Ozisik, H. and Ozisik, H.B. Ph Transit; 2017, vol.90, p.598. [27] Weck, P.F., Kim, E., Tikare V., and Mitchell, J. A. Dalton Trans.; 2015, vol.44, p.18769. [28] Morelli Donald, T., Slack Glen, A., High lattice thermal conductivity solids in high thermal conductivity of materials, in: S.L. Shinde, J. Goela XVIII (Eds.), Springer Publisher, Chap 2, 2006, p. 37–68. [29] Singh, S. P., Singh, G., Verma, A. K., Jaiswal, A. K., Yadav,R. R., Metals and Materials International 2021, vol.27 p.2541–2549. [30] Yadav, C. P., Pandey, D. K., and Singh, D. Indian J Phys., 2021,vol.93, p.1147. [31] Ivanovskii, A. L. Int. J. Refract. Met. Hard Mater. 2013, vol.36, p.179. [32] Guechi, A., Merabet, A., Chegaar, M., Bouhemadou, A., and Guechi, N. J. Alloys Compd. 2015,vol.623, p.219. [33] Ranganathan, S. I., Ostoja-Starzewski, M. Phys. Rev. Lett. 2008, vol.101, p.55504. [34] Panda, K. B., and Chandran, K. S. Ravi. Comput. Mater. Sci, 2006,vol.35,p.134. [35] G. Singh, S. P. Singh, D. Singh, A. K. Verma, D K Pandey and R R Yadav, Pramana-J. Phys., 2022, p.96:97. [36] Yadav, R. R., and Singh, D. Acoust. Phys. 2003, vol.49, p.595. [37] Singh, D., Kumar, A., Thakur R. K., and Kumar, R., Proc. Natl. Acad. Sci. India A 2020, vol.90, p.177. [38] Verma,S K., Yadav, R. R ., Yadav, A. K., and Joshi, B., Mater. Lett. 2010, vol.64, p.1677. [39] Jyoti, B. Singh, S. P., Gupta, M., Tripathi, S., Verma, A. K., Singh, D., and Yadav, R. R., Acoustical Physics, 2021, Vol. 67, No. 6, pp. 584–589.

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