A New Model to Study the Sound Velocity in Liquid Metals

Year 2025, Volume: 38 Issue: 3, 1420 - 1429

Piyush Kuchhal , Narsingh Dass

https://doi.org/10.35378/gujs.1502124

Abstract

This study proposes a new relationship to investigate the behavior of sound velocity as a function of pressure in liquid metals. The suggested relation is applied in liquid metals like Sodium, Potassium, Rubidium, Cesium, Mercury and Bismuth. The computed sound velocity results for each liquid metal are found to be consistent with the experimental data across the entire pressure range, with root mean square deviations on the order of 10-4 in each case. The temperature effect is also introduced by considering the linear dependence of thermal pressure on temperature. The maximum average absolute percentage relative deviation (AARD %) of 0.45 is noted in the case of Bismuth across the entire pressure range at temperatures. The first and second pressure derivatives of sound velocity at ambient pressure and temperature are calculated and found to be in good agreement with the available data. Furthermore, the proposed relationship can predict the variation of the first pressure and temperature derivatives of sound velocity with pressure and temperature.

Keywords

Liquid metals, Sound velocity, Pressure, Temperature

Ethical Statement

The authors declare that this work is original and has not been submitted for publication elsewhere.

Supporting Institution

University of Petroleum and energy Studies, Dehradun, India-248007

Thanks

Dear Sir I am pleased to submit our manuscript titled "A New Model to Study the Sound Velocity in Liquid Metals" for consideration for publication in Gazi University Journal of Science. This study introduces a novel model for understanding the behavior of sound velocity in liquid metals under varying pressure and temperature conditions. Our research focuses on liquid metals such as sodium, potassium, rubidium, cesium, mercury, and bismuth. We have proposed a new relationship to study the sound velocity, which has been validated against experimental data, showing consistent results across the entire pressure range with root mean square deviations on the order of 10-4. Additionally, we have incorporated the temperature effect by considering the linear dependence of thermal pressure on temperature. Key findings of our study include: • The computed sound velocity results are in good agreement with experimental data for all studied liquid metals. • The model accurately predicts the first and second pressure derivatives of sound velocity at ambient pressure and temperature. • The proposed relationship effectively captures the variation of sound velocity and its derivatives with both pressure and temperature. This model's novelty lies in its simplicity and accuracy, requiring only three parameters (A, B, and ξ) to represent the sound velocity across a wide range of pressures and temperatures. Our findings provide significant insights into the thermophysical properties of liquid metals and contribute to the broader understanding of their behavior under different conditions. We believe that our work is a valuable contribution to the field of condensed matter physics and will be of interest to the readers of Gazi University Journal of Science. The manuscript has not been published or submitted for publication elsewhere. Thank you for considering our manuscript for publication. We look forward to your positive response. Sincerely, Piyush Kuchhal UPES, Dehradun India [e-mail]

References

• [1] Guyue, Bo., Long Ren, Xun Xu., Yi Du. and Shixue Dou., “Recent progress on liquid metals and their applications”, Advances in Physics X, 3: 1, (2018).
• [2] Dubrovinsky, L. S., Dubrovinskaia, N. A., and Le Bihan, T., “Aggregate Sound Velocities and Acoustic Grüneisen Parameter of Iron up to 300 GPa and 1,200 K”, Proceedings of the National Academy of Sciences of the United States of America, 98 (17), 9484–9489, (2001).
• [3] Blairs, S., “Review of data for sound velocity in pure liquid metals and metalloids”, International Materials Reviews, 52(6): 321-344, (2007).
• [4] Blairs, S., “Temperature dependence of sound velocity in liquid metals”, Physics and Chemistry of Liquids, 44(6): 597-606, (2006).
• [5] Das, N., Praharaj, M. K., and Panda, S. ,"Exploring ultrasonic wave transmission in liquids and liquid mixtures: A comprehensive overview", Journal of Molecular Liquids, 403: 124841, (2024).
• [6] Panda, R., Panda, S., and Biswal, S. K., “Acoustic behavior of electrolytes in aqueous dimethyl sulphoxide as a solvent at different temperatures”, J Therm Anal Calorim 149: 4839–4853, (2024).
• [7] Kuchhal, P., Kumar, R., and Dass, N., “Equation of state of liquid metals from sound-velocity measurements”, Phys. Rev. B, 55(13): 8042-8044, (1997).
• [8] Kumar, R., Kuchhal, P. and Dass, N., “The pressure and temperature dependence of the sound velocity in liquid metals”, Journal of Physics. Condensed Matter, 8: 10891-10897, (1996).
• [9] Komabayashi, T., Kato, J., Hirose, K., Tsutsui, S., Imada, S., Nakajima, Y., and Baron, A. Q. R., "Temperature dependence of the velocity-density relation for liquid metals under high pressure: Implications for the Earth’s outer core", American Mineralogist, 100(11-12): 2602-2609, (2015).
• [10] Tatsuhiro, S., Hideki, T., Tadashi, K., Toshihiko, K., Yoichiro, H., Tetsuo, I., and Keisuke, S., “Sound velocity and density measurements of liquid iron up to 800 GPa: A universal relation between Birch's law coefficients for solid and liquid metals”, Earth and Planetary Science Letters, 392, 80-85, (2014).
• [11] Decremps, F., Gauthier, M., Ayrinhac, S., Bove L., Belliard, L., Perrin, B., Morand, M., Marchand, G. Le., Bergame, F., and Philippe, J., “Picosecond acoustics method for measuring the thermodynamical properties of solids and liquids at high pressure and high temperature”, Ultrasonics, 56: 129-40, (2015).
• [12] Huaming, L., Xiaoxiao, Z., Yongli, S., and Mo, L., "Thermodynamic properties of liquid sodium under high pressure", AIP Advances 7, 045305, (2017).
• [13] Huaming, L., Yongli, S., and Mo, L., "Equation of state of liquid Indium under high pressure", AIP Advances, 5: 097163, (2015).
• [14] Davis, L. A., and Gordon, R. B., “Compression of Mercury at High Pressure”, Journal of Chemical Physics, 46: 2650, (1967).
• [15] Shaw, G. H. and Caldwell, D.A., “Sound-wave velocities in liquid alkali metals studied at temperatures up to 150 °C and pressures up to 0.7 GPa”, Physical Review B, 12: 7937, (1985). DOI: https://doi.org/10.1103/PhysRevB.32.7937
• [16] Ayrinhac, S., Gauthier, M., Bove, L.E., Morand, M., Le Marchand, G., Bergame, F., Philippe, J., and Decremps, F., “Equation of state of liquid mercury to 520 K and 7 GPa from acoustic velocity measurements”, Journal of Chemical Physics, 140: 244201, (2014).
• [17] Chang, S., Yonggang, L., Zhigang, W., Wei, S., Paul, D., Asimow, H. T., and Hongsen, X., “Equation of state of liquid bismuth and its melting curve from ultrasonic investigation at high pressure”, Physica B: Condensed Matter, 524: 154-162, (2017).
• [18] William, A., Watkins, W. E., Schevill, E., “Aerial Observation of Feeding Behavior in Four Baleen Whales: Eubalaena glacialis, Balaenoptera borealis, Megaptera novaeangliae, and Balaenoptera physalus”, Journal of Mammalogy, 60(1): 155–163, (2017).
• [19] Mirjalili, S. and Lewis, A., “The Whale Optimization Algorithm”, Advances in Engineering Software, 95: 51-67, (2016).
• [20] Oliv, D., Aziz, M. A. E., and Hassanien, A. E., “Parameter estimation of photovoltaic cells using an improved chaotic whale optimization algorithm”, Applied Energy, 200: 141-154, (2017).
• [21] Kielczyński, P., Szalewski, M., Balcerzak, A., Wieja, K., Rostocki, A., Siegoczynski, R., “Thermodynamic method for measuring the B/A nonlinear parameter under high pressure”, IEEE International Ultrasonics Symposium (IUS), Prague, Czech Republic, 1665-1667, (2013).
• [22] Khadar, J. M., “Acoustic nonlinearity parameter B/A and related molecular properties of binary organic liquid mixtures”, Journal of Molecular Liquids, 100(3): 217-227, (2002).