Multifunctional Bulk Metallic Glass: An Ab Initio Study on Pd₃₉Ni₁₀Cu₃₀P₂₁ for Enhanced Mechanical Strength and Optical Shielding
Abstract
Bulk metallic glasses (BMGs) are a type of solid material with amorphous atomic structures that exhibit favorable mechanical, thermal, and functional properties. This study presents the attributes of the glass, examining first-principles details of the Pd₃₉Ni₁₀Cu₃₀P₂₁ bulk metallic glass structure, its elastic properties, thermodynamics, and electronic–optical performance. Density functional theory calculations were performed for a comparison with the amorphous atomic configuration and energy–volume relation through a third-order Birch–Murnaghan equation of state. The very high bulk modulus of approximately 159 GPa and >6 pressure derivatives demonstrated uniformity, resistance, and strong pressure strengthening. All three elastic moduli, Poisson’s ratio, and Pugh’s criterion are constantly demonstrating ductile mechanical response dependent on shear transformation zone–mediated plasticity. The results of the thermophysical examination show stable anharmonic lattice behavior, a Debye temperature of approximately 395 K, and favorable thermal expansion, indicating good predictability of the thermomechanical response. Electronic studies revealed a very metallic phase with low pseudogap around the Fermi level—mainly the hybridization between transition metal d-states and phosphorus p-states into a stable, amorphous phase. Optical spectra that contain a wide band, excellent reflectivity at low photon energies, and an isotropic optical response are typical of metallic glasses. In conclusion, these results prove Pd₃₉Ni₁₀Cu₃₀P₂₁ as a highly mechanically stable material for progress in various mechanical, optical, and energy applications in a lightweight frame.
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Caroline Pereira dos Santos, Carlos Henrique Prado Silva, Marcelo Franklin da Silva Santos, Érico Raimundo Pereira de Novais, Divanizia do Nascimento Souza, Marcos Vinicius dos Santos Rezende, Andréa de Lima Ferreira Novais, DFT to study the structural, optoelectronic, and mechanical properties of CuNiPd and Cu2PPd2 alloys, Journal of Alloys and Compounds, 1038, 2025, 182830, https://doi.org/10.1016/j.jallcom.2025.182830
Simon Evertz, Denis Music, Volker Schnabel, Jozef Bednarcik, Jochen M. Schneider, Thermal expansion of Pd-based metallic glasses by ab initio methods and high-energy X-ray diffraction. Sci Rep 7, 15744 (2017). https://doi.org/10.1038/s41598-017-16117-7
He, Y., Schwarz, R.B. Synthesis and Properties of Bulk Metallic Glasses in Pd-Ni-P and Pd-Cu-P Alloys. MRS Online Proceedings Library 455, 495–500 (1996). https://doi.org/10.1557/PROC-455-495
Gong, P.; Deng, L.; Jin, J.; Wang, S.; Wang, X.; Yao, K. Review on the Research and Development of Ti-Based Bulk Metallic Glasses. Metals 2016, 6, 264. https://doi.org/10.3390/met6110264
L.Y. Watanabe, S.N. Roberts, N. Baca, A. Wiest, S.J. Garrett, R.D. Conner, Fatigue and corrosion of a Pd-based bulk metallic glass in various environments, Materials Science and Engineering: C, 33(7), 2013,4021-4025, https://doi.org/10.1016/j.msec.2013.05.044
Sharma, A.; Zadorozhnyy, V. Review of the Recent Development in Metallic Glass and Its Composites. Metals 2021, 11, 1933. https://doi.org/10.3390/met11121933
H. Kato, T. Wada, M. Hasegawa, J. Saida, A. Inoue, H.S. Chen, Fragility and thermal stability of Pt- and Pd-based bulk glass forming liquids and their correlation with deformability, Scripta Materialia, 54(12), 2006, 2023-2027, https://doi.org/10.1016/j.scriptamat.2006.03.025.
F.M. Alamgir, H. Jain, R.B. Schwarz, O. Jin, D.B. Williams, Electronic structure of Pd-based bulk metallic glasses, Journal of Non-Crystalline Solids, 274(1–3), 2000, 289-293, https://doi.org/10.1016/S0022-3093(00)00192-7.
Tirumala Rao Kotni, Muthu Kumar Sampath, Murali Mohan Seepana, Adarsh Kumar Arya, A Review on Corrosion Characteristics of Bulk Metallic Glasses. J. of Materi Eng and Perform (2026). https://doi.org/10.1007/s11665-025-13123-z.
Chen, M. A brief overview of bulk metallic glasses. NPG Asia Mater 3, 82–90 (2011). https://doi.org/10.1038/asiamat.2011.30.
Chen, M. A brief overview of bulk metallic glasses. NPG Asia Mater 3, 82–90 (2011). https://doi.org/10.1038/asiamat.2011.30.
Mark Telford, The case for bulk metallic glass, Materials Today, 7(3), 2004, 36-43, https://doi.org/10.1016/S1369-7021(04)00124-5.
Yanglin Li, Shaofan Zhao, Yanhui Liu, Pan Gong, Jan Schroers, How Many Bulk Metallic Glasses Are There?, CS Comb—Sci—2017, 19, 11, 687–693, https://doi.org/10.1021/acscombsci.7b00048.
Fu-Fa Wu, K. C. Chan, Song-Shan Jiang, Shun-Hua Chen, Gang Wang, Bulk metallic glass composite with good tensile ductility, high strength, and large elastic strain limit. Sci Rep 4, 5302 (2014). https://doi.org/10.1038/srep05302.
H.X. Li, Z.C. Lu, S.L. Wang, Y. Wu, Z.P. Lu, Fe-based bulk metallic glasses: Glass formation, fabrication, properties and applications, Progress in Materials Science, 103, 2019, 235-318, https://doi.org/10.1016/j.pmatsci.2019.01.003.
Inoue, A., Shen, B., Nishiyama, N. (2008). Development and Applications of Late Transition Metal Bulk Metallic Glasses. In: Miller, M., Liaw, P. (eds) Bulk Metallic Glasses. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-48921-6_1.
Aga, R.S., Morris, J.R. (2008). Modeling: The Role Of Atomistic Simulations. In: Miller, M., Liaw, P. (eds) Bulk Metallic Glasses. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-48921-6_3.
Srivastava, A. Prakash, Pandey, B. Kumar, and Shanker, A. (2026). Pressure-Dependent Structural, Mechanical, and Thermal Behavior of Zr₅₀.₅Ti₄.₈Cu₁₉.₀Ni₁₁.₄Al₁₄.₃ Bulk Metallic Glass: A DFT and Equation of State Study. Physical Chemistry Research, 14(1), 71-85. doi: 10.22036/pcr. 2025.552725.2766.
Shih-Jye Sun, Shin-Pon Ju, Cheng-Chia Yang, Kai-Chi Chang, I-Jui Lee, Effects of Strontium incorporation into Mg-Zn-Ca biodegradable bulk metallic glass investigated by molecular dynamics simulation and density functional theory calculation. Sci Rep 10, 2515 (2020). https://doi.org/10.1038/s41598-020-58789-8.
Gokul Raman Arumugam Kumar, Kanika Arora, Manish Aggarwal, S. Swayamjyoti, Param Punj Singh, Kisor Kumar Sahu, Raghavan Ranganathan, Structure–property predictions in metallic glasses: Insights from data-driven atomistic simulations. Journal of Materials Research 40, 36–68 (2025). https://doi.org/10.1557/s43578-024-01480-9.
Sahni, V. (2004). The Hohenberg-Kohn Theorems and Kohn-Sham Density Functional Theory. In: Quantal Density Functional Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09624-6_4.
Sahni, V. (2004). The Hohenberg-Kohn Theorems and Kohn-Sham Density Functional Theory. In: Quantal Density Functional Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09624-6_4.
Abhay P. Srivastava, Pankaj Sharma, Brijesh K. Pandey, Alok Mishra, Multifunctional Properties of BaTiO3 Across the Cubic–Tetragonal Phase Transition: Implications for Ferroelectric and Electronic Applications. J Inorg Organomet Polym (2026). https://doi.org/10.1007/s10904-026-04390-x.
John P. Perdew, Kieron Burke, and Matthias Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 78, 1396 (1997), https://doi.org/10.1103/PhysRevLett.77.3865.
Kresse, G., & Furthmüller, J. (1996). Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Physical Review B, 54(16), 11169–11186. https://doi.org/10.1103/PhysRevB.54.11169 .
Blanco, M. A., Francisco, E., & Luana, V. (2004). GIBBS: isothermal-isobaric thermodynamics of solids from energy curves using a quasi-harmonic Debye model. Computer Physics Communications, 158(1), 57–72. https://doi.org/10.1016/j.cpc.2003.10.003 .
Srivastava, A.P., Pandey, B.K., Gupta, A.K. et al. A New Approach to Evaluate Pressure of Solids at High Compression. Natl. Acad. Sci. Lett. 47, 713–718 (2024). https://doi.org/10.1007/s40009-024-01409-0.
Srivastava, A. Prakash, and Pandey, B. Kumar (2026). A Computational Study of Pressure-Induced Melting in LaFeO₃: Using DFT and Semi-Empirical Model. Physical Chemistry Research, 14(1), 1-7. https://doi.org/10.22036/pcr.2025.537079.2712.
Srivastava, A.P., Pandey, B.K. DFT-based evaluation of covalent organic frameworks for adsorption, optoelectronic, clean energy storage, and gas sensor applications. J Mol Model 31, 302 (2025). https://doi.org/10.1007/s00894-025-06535-0.
Chen Feng, Cheng Wei, Bao-long Fang, Hong-yi Fan, A Deduction of the Hellmann-Feynman Theorem. Int J Theor Phys 59, 1396–1401 (2020). https://doi.org/10.1007/s10773-019-04362-7.
Karl F. Shamlaye, Jörg F. Löffler, Synthesis and characterization of Mg-based bulk metallic glasses in the Mg–Ag–Y–(Cu) system, Journal of Alloys and Compounds, 859, 2021, 157803, https://doi.org/10.1016/j.jallcom.2020.157803.
Abhay P. Srivastava, Brijesh K. Pandey, Abhishek K. Gupta, Explore the fascinating realm of comparing metal melting curves by applying the equation of state and Lindemann's law, Computational Condensed Matter, 40, 2024, e00952, 2352-2143, https://doi.org/10.1016/j.cocom.2024.e00952.
Abhay. P. Srivastava, B.K. Pandey, A. K. Gupta, et al. Comparing Melting Curves of Metals Using the Equation of State and Lindemann's Law. Iran J Sci (2024). https://doi.org/10.1007/s40995-024-01748-z.
Abhay. P. Srivastava, B.K. Pandey, A constructive approach to formulating pressure-dependent binding energy using the equation of state. Ionics (2025). https://doi.org/10.1007/s11581-025-06183-7.
Abhay. P. Srivastava, B. K. Pandey, & M. Upadhyay (2024). Anticipating Pressure Changes in Halides under Compression. East European Journal of Physics, (3), 333-339. https://doi.org/10.26565/2312-4334-2024-3-37.
Lin-jun Huang, Jian-guo Tang, G.Y. Liang, Yao Wang, D.C. Wu, Microstructural investigation and electrochemical property of Mg63Ni27Nd10 amorphous alloy, Journal of Power Sources, 189(2), 2009, 1247-1250, https://doi.org/10.1016/j.jpowsour.2008.12.001.
Fenger Sun, Guowei Zhang, Xiaoyan Ren, Mingjie Wang, Hong Xu, Yizheng Fu, Yunqing Tang, Dongyang Li, First-principles studies on phase stability, anisotropic elastic and electronic properties of Al-La binary system intermetallic compounds, Materials Today Communications, 24, 2020, 101101, https://doi.org/10.1016/j.mtcomm.2020.101101.
Srivastava, A.P., Pandey, B.K. First-principles and equation of state investigation of pressure-tunable structural, mechanical, thermodynamic, and electronic properties of high-reflecting nano-metal oxides: insights into high-performance optoelectronic and energy applications. Appl Nanosci 15, 47 (2025). https://doi.org/10.1007/s13204-025-03124-8.
Srivastava, A. Prakash, and Pandey, B. Kumar (2026). A Computational Study of Pressure-Induced Melting in LaFeO₃: Using DFT and Semi-Empirical Model. Physical Chemistry Research, 14(1), 1-7. https://doi.org/10.22036/pcr.2025.537079.2712.
Dadi, D.G., Shura, M.W., & Gochole, F. DFT analysis of structural, electronic, and optical properties of Ni and Zn doped CoS counter electrode for dye sensitized solar cells. Sci Rep 15, 35486 (2025). https://doi.org/10.1038/s41598-025-19663-7
Maurya, D., Pandey, B.K. & Srivastava, A.P. Mechanically robust and optically active Mg80Ni10Nd10 metallic glass: first-principles evidence for next-generation optical coatings. Opt Quant Electron 58, 28 (2026). https://doi.org/10.1007/s11082-025-08615-0.
Srivastava, A.P., Pandey, B.K. Ab initio design of Zr-based bulk metallic glass for high-strength and optical coating applications. Opt Quant Electron 57, 561 (2025). https://doi.org/10.1007/s11082-025-08467-8.
Horsley, S., Artoni, M. & La Rocca, G. Spatial Kramers–Kronig relations and the reflection of waves. Nature Photon 9, 436–439 (2015). https://doi.org/10.1038/nphoton.2015.106.
Selvam Mathi, Hanan Akhdar, Ranjan S. Shetti, Tarfah Alinad, Abdullah N. Alodhayb, Kunal Mondal, Nagaraj P. Shetti, Amorphous electrocatalysts for oxygen and hydrogen evolution reactions: Advances in hydrogen production, Materials Today Sustainability, 32, 2025, 101223, https://doi.org/10.1016/j.mtsust.2025.101223.
Akbar Abbas, Saad Tariq, Hussain J. Alathlawi, Fadiyah Antar Makin, Areej Al Bahir, M. Musa Saad H․-E․, High-pressure computational analysis of CsCdF₃: Structural stability, electronic transitions, and thermodynamic properties, Physics Letters A, 541, 2025, 130429, https://doi.org/10.1016/j.physleta.2025.130429.
H. W. Sheng, W. K. Luo, F. M. Alamgir, J. M. Bai, E. Ma, Atomic packing and short-to-medium-range order in metallic glasses. Nature 439, 419–425 (2006). https://doi.org/10.1038/nature04421.
Akihisa Inoue, Stabilization of metallic supercooled liquid and bulk amorphous alloys, Acta Materialia, 48(1), 2000, 279-306, https://doi.org/10.1016/S1359-6454(99)00300-6.
Anjani K. Pandey, B.K. Pandey, Rahul, Theoretical prediction of Grüneisen parameter for bulk metallic glasses, Journal of Alloys and Compounds, 509(11), 2011, 4191-4197, https://doi.org/10.1016/j.jallcom.2010.11.120.
Knowles, K.M. Necessary and Sufficient Elastic Stability Conditions for Single Crystals. J Elast 157, 19 (2025). https://doi.org/10.1007/s10659-025-10112-0.
Dalsaniya, M.H.; Upadhyay, D.; Patel, P.; Jha, P.K.; Kurzydłowski, K.J.; Kurzydłowski, D. Pressure-Dependent Thermal and Mechanical Behavior of a Molecular Crystal of Bromine. Molecules 2024, 29, 4744. https://doi.org/10.3390/molecules29194744.
Yamada, Y., Kanemitsu, Y. Electron-phonon interactions in halide perovskites. NPG Asia Mater 14, 48 (2022). https://doi.org/10.1038/s41427-022-00394-4.
Mara, J.; Bodnár, A.-E.; Trif, L.; Telegdi, J. Development of Effective Infrared Reflective Coatings. Appl. Sci. 2023, 13, 12903. https://doi.org/10.3390/app132312903.
N. Mattern, M. Stoica, G. Vaughan, J. Eckert, Thermal behavior of Pd40Cu30Ni10P20 bulk metallic glass, Acta Materialia, 60(2), 2012, 517-524, https://doi.org/10.1016/j.actamat.2011.10.032
Copyright (c) 2026 Sangita Gupta, Amit Kumar Chaubey, Sarita Chaudhary, Kapil Bhardwaj, Abhay P. Srivastava
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