Ab-initio Investigation of the Physical features of Pt-Co Intermetallic Compounds
Abstract
This article explores the structural, electronic, mechanical, magnetic, and thermodynamic features of the Pt-Co intermetallic compounds with the help of the FP-LAPW (full-potential linearized augmented plane wave) method in the framework of DFT (density functional theory), as executed through Wien2k code. The negative formation enthalpies and cohesive energies indicate that Pt3Co (L12), PtCo (L10) and PtCo3 (L12) are stable in the ferromagnetic (FM) phase. The calculations of the lattice constants and bulk modulus align fit with existing theoretical and experimental values. The resulting electronic band structure establishes the metallic nature and the magnetic character of all three studied compounds. The DOS at Fermi level, electronic specific heat coefficient γth, polarization P%, and magnetic moment are determined. The investigation of the elastic and mechanical features illustrates that the selected materials are stable and slightly anisotropic. The Pt3Co and PtCo3 materials are inherently ductile and the PtCo is the harder compound. To enhance understanding of these materials, the quasi-harmonic Debye model is applied to scrutinize their thermal features.
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B.S. Mun, M. Watanabe, M. Rossi, V. Stamenkovic, N.M. Markovic, P.N. Ross, J. Chem. Phys. 123, 204717 (2005). https://doi.org/10.1063/1.2126662
Z.M. Liu, L.L. Ma, J. Zhang, K. Hongsirikarn, and J.G. Goodwin, Catal. Rev. 55, 255 (2013). https://doi.org/10.1080/01614940.2013.795455
N.A. Frey, and S. Sun, Inorganic Nanoparticles: Synthesis, Application, and Perspectives, (CRC Press, Boca Raton, 2010), pp. 33–68.
J.M. Montejano-Carrizales, F. Aguilera-Granja, C. Goyhenex, V. Pierron-Bohnes, J.L. Morán-López, J. Magn. Magn. Mater. 355, 215–224 (2014). https://doi.org/10.1016/j.jmmm.2013.10.035
N.L. Lethole, P. Mukumba, and G. Makaka, J. Alloys Compd. 565, 170298 (2023). https://doi.org/10.1016/j.jmmm.2022.170298
D. Weller, A. Moser, L. Folks, M.E. Best, W. Lee, et al., IEEE Trans. Magn. 36, 10 (2000). https://doi.org/10.1109/20.824418
D.J. Sellmyer, M. Yu, R.A. Thomas, Y. Liu, and R.D. Kirby, Phys. Low-Dimens. Struct. 1–2, 155–165 (1998).
D. Kim, J.E. Saal, L. Zhou, S. Shang, Y. Du, Z.-K. Liu, Calphad, 35, 323 (2011). https://doi.org/10.1016/j.calphad.2011.04.005
U.A. Paulus, A. Wokaun, G.G. Scherer, T.J. Schmidt, V. Stamenkovic, V. Radmilovic, N.M. Markovic, and P.N. Ross, Electrochim. Acta, 47, 3787 (2002). https://doi.org/10.1016/s0013-4686(02)00349-3
M.T.M. Koper, Surf. Sci. 548, 1–3 (2004). https://doi.org/10.1016/j.susc.2003.10.045
W. Yu, M.D. Porosoff, and J.G. Chen, Chem. Rev. 112, 5780 (2012). https://doi.org/10.1021/cr300096b
V.R. Stamenkovic, B.S. Mun, M. Arenz, K.J.J. Mayrhofer, C.A. Lucas, G. Wang, P.N. Ross, et al., Nat. Mater. 6, 241 (2007). https://doi.org/10.1038/nmat1840
B.N. Grgur, G. Zhuang, N.M. Markovic, and P.N. Ross, J. Phys. Chem. B, 101, 3910 (1997). https://doi.org/10.1021/jp9704168
J.-S. Kim, D. Seol, J. Ji, H.-S. Jang, Y. Kim, and B.-J. Lee, Curr. Appl. Phys. 59, 131-141 (2017).
I. Galanakis, M. Alouani, and H. Dreyssé, J. Magn. Magn. Mater. 320, 221(2002). https://doi.org/10.1016/s0921-4526(02)00687-7
K. Aledealat, B. Aladerah, A. Obeidat, M. Gharaibeh, Heliyon, 7, e08639 (2021). https://doi.org/10.1016/j.heliyon.2021.e08639
M. Futamoto, M. Nkamura, M. Ohtake, N. Inaba, and T. Shimotsu, AIP Adv. 6, 085302 (2016). https://doi.org/10.1063/1.4960554
K.M. Krishnan, C. Nelson, C.J. Echer, R.F.C. Farrow, R.F. Marks, and A.J. Kellock, J. Appl. Phys. 83, 6810 (1998). https://doi.org/10.1063/1.367815
S.C. Tsang, C.H. Yu, H. Tang, H. He, V. Castelletto, I.W. Hamley, T. Narayanan, et al., Chem. Mater. 20, 4554 (2008). https://doi.org/10.1021/cm801068j
Y. Wang, X. Zhang, Y. Liu, Y. Jiang, Y. Zhang, and J. Yang, J. Mater. Sci.: Mater. Electron. 70, 528 (2014).
M. Neamtu, C. Nadejde, V.D. Hodoroaba, R.J. Schneider, L. Verestiuc, and U. Panne, Sci. Rep. 8, 6278 (2018). https://doi.org/10.1038/s41598-018-24721-4
T.S. Rodrigues, A.G.M. da Silva, and P.H.C. Camargo, J. Mater. Chem. A, 7, 5857 (2019). https://doi.org/10.1039/c9ta00074g
L.M. Rossi, N.J.S. Costa, F.P. Silva, and R. Wojcieszak, Green Chem. 16, 2906 (2014). https://doi.org/10.1039/c4gc00164h
A.M. Alssad, A.A. Ahmed, H.A. Qattous, Heliyon, 5, e02433 (2019). https://doi.org/10.1016/j.heliyon.2019.e02433
A. Obeidat, B. Aladerah, M.-K. Qaseer, J. Alloys Compd. 559, 169501 (2022). https://doi.org/10.1016/j.jmmm.2022.169501
H. Okamoto, J. Phase Equilib. Diffus. 40, 743 (2019). https://doi.org/10.1007/s11669-019-00760-w
J. Cui, Y. Zeng, Q. Zheng, Q. Peng, F. Yu, X. Wang, N. Xie, et al., Fuel, 142, 292 (2025). https://doi.org/10.1016/j.ijhydene.2025.05.394
R. Wu, J. Zuo, L. Zhao, Z. Zhu, Q. Li, X. Niu, and J.S. Chen, Chem. Commun. 61, 5742 (2025). https://doi.org/10.1039/d5cc00736d
Y.-L. Mai, X.-S. Xie, Z.-D. Wang, C.-F. Yan, and G.-H. Liu, Trans. Nonferrous Met. Soc. China, 50, 114–121 (2022).
H. Li, D. Wei, C. Shi, Q. Long, L. Zhou, H. Jin, J. Yu, et al., J. Alloys Compd. 985, 119089 (2025). https://doi.org/10.1016/j.jelechem.2025.119089
J. Shen, C. Chen, L. Song, L. Zhong, K. Shan, Y. Guo, W. Zhan, et al., Wang, Appl. Surf. Sci. 379, 133066 (2025). https://doi.org/10.1016/j.fuel.2024.133066
Z. Qin, L. Wu, R. He, Z. Meng, J. Pan, and J. Zeng, Appl. Surf. Sci. 475, 143675 (2024). https://doi.org/10.1016/j.electacta.2023.143675
H. Wang, J. Liu, K. Du, X. Wang, X. Li, Y. Liu, C. Min, at al., J. Power Sources, 616, 235127 (2024). https://doi.org/10.1016/j.jpowsour.2024.235127
J. Zou, Y. Du, R. Fang, X. Duan, Y. Liu, J. Mao, L. Yu, et al., Fuel, 307, 121794 (2022). https://doi.org/10.1016/j.fuel.2021.121794
S. Wang, W. Xu, Y. Zhu, Q. Luo, C. Zhang, S. Tang, and Y. Du, J. Mater. Sci. 13, 827 (2020).
C. Luo, K. Wan, J. Wang, B. Li, D. Yang, P. Ming, and C. Zhang, Renew. Sustain. Energy Rev. 679, 165 (2025). https://doi.org/10.1016/j.jcis.2024.10.063
D. Fu, Z. Hu, J. Xun, X. Yu, L. Wang, S. Zeng, and F. Li, Fuel, 396, 135250 (2025). https://doi.org/10.1016/j.fuel.2025.135250
B. Ravichandran, N. Narayanan, H. Liu, W. Zhang, N. Bhuvanendran, and H. Su, J. Power Sources, 402, 136040 (2025). https://doi.org/10.1016/j.fuel.2025.136040
V. Domin, M. Prokop, T. Bystron, M. Gatalo, L. Pavko, N. Hodnik, B.F. Gomes, et al., Appl. Catal. B: Environ. 536, 146707 (2025). https://doi.org/10.1016/j.electacta.2025.146707
M. Kim, H.E. Bae, J. Song, T.B.N. Huynh, T.T. Pham, S.K. Cho,T. Lim, et al., Curr. Opin. Electrochem. 52, 101934 (2025). https://doi.org/10.1016/j.mtener.2025.101934
U. Guevara, R. López, J. Blanco, and J. Núñez, Mater. Res. Express, 6, 096514 (2019). https://doi.org/10.1088/2053-1591/ab2c50
S. Karoui, H. Amara, B. Legrand, and F. Ducastelle, J. Phys.: Condens. Matter, 25, 056005 (2013). https://doi.org/10.1088/0953-8984/25/5/056005
X. Gonze, J.-M. Beuken, R. Caracas, F. Detraux, M. Fuchs, G.-M. Rignanese, L. Sindic, et al., Comput. Mater. Sci. 25, 478 (2002). https://doi.org/10.1016/s0927-0256(02)00325-7
R. Boulechfar, Y. Khenioui, S. Drablia, H. Meradji, M. Abu-Jafar, S. Bin Omran, et al., Solid State Commun. 273, 23 (2018). https://doi.org/10.1016/j.ssc.2018.02.005
A.T. Khodja, R. Boulechfar, H. Meradji, Y. Akeb, R. Chemam, S. Ghemid, and X. Wang, Solid State Sci. 100, 107651 (2020). https://doi.org/10.1016/j.jmgm.2020.107651
A. Front, B. Legrand, G. Tréglia, C. Mottet, Surf. Sci. 679, 128 (2019). https://doi.org/10.1016/j.susc.2018.08.024
J.P. Perdew, and Y. Wang, Phys. Rev. B, 45, 13244 (1992). https://doi.org/10.1103/physrevb.98.079904
R.V. Chepulskii, and W.H. Butler, Phys. Rev. B, 86, 155401 (2012). https://doi.org/10.1103/physrevb.86.155401
Z.-B. Li, K. Xiong, C.-C. Jin, Y.-J. Sun, B.-W. Wang, S.-M. Zhang, J.-J. He, et al., Rare Met. 40, 1208 (2021). https://doi.org/10.1007/s12598-020-01656-2
J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). https://doi.org/10.1103/physrevlett.78.1396
L. Zosiak, C. Goyhenex, R. Kozubski, and G. Tréglia, J. Phys.: Condens. Matter, 27, 455503 (2015). https://doi.org/10.1088/0953-8984/27/45/455503
S.-M. Zhang, K. Xiong, C.-C. Jin, Z.-B. Li, J.-J. He, and Y. Mao, Rare Met. 40, 1020 (2021). https://doi.org/10.1007/s12598-020-01651-7
K. Aledealat, B. Aladerah, and A. Obeidat, J. Alloys Compd. 363, 115112 (2023). https://doi.org/10.1016/j.ssc.2023.115112
M.A. Rahman, K. Mousumi, M.L. Ali, R. Khatun, M.Z. Rahman, S.S. Hasan, W. Hasan, et al., Results Phys. 44, 106141 (2023). https://doi.org/10.1016/j.rinp.2022.106141
M.N. Sadat, M.A. Rahman, D.C. Roy, M.A. Rahman, M.Z. Hasan, I. Ahmad, S. Chowdhury, et al., Physica B, 672, 415402 (2024). https://doi.org/10.1016/j.physb.2023.415402
Z. Wei, Y. Xie, Y. Xiao, J. Chen, J. Xue, N. Qu, and J. Zhu, J. Mater. Res. 1–11 (2025). https://doi.org/10.1557/s43578-025-01596-6
P. Rani, M.K. Kashyap, R. Singla, J. Thakur, and A.H. Reshak, J. Alloys Compd. 835, 155325 (2020). https://doi.org/10.1016/j.jallcom.2020.155325
M. Islam, M.S.I. Sarker, T. Nakamura, M.K.R. Khan, F.A. Khan, M.A. Islam, and S. Sato, Mater. Chem. Phys. 269, 124727 (2021). https://doi.org/10.1016/j.matchemphys.2021.124727
Z. Zine, N. Meftah, Phys. Solid State, 66, 416–423 (2024). https://doi.org/10.1134/s1063783424601115
Z. Zine, N. Meftah, and B. Daoudi, Solid State Commun. 396, 115769 (2025). https://doi.org/10.1016/j.ssc.2024.115769
S. Imada, T. Muro, T. Shishidou, S. Suga, H. Maruyama, K. Kobayashi, and T. Kanomata, Phys. Rev. B, 59, 8752 (1999). https://doi.org/10.1016/s0921-4526(97)00234-2
J.M. Sanchez, J.L. Moran-Lopez, C. Leroux, and M.C. Cadeville, J. Phys. C: Solid State Phys. 21, L1091–L1096 (1988). https://doi.org/10.1088/0022-3719/21/33/004
J.M. MacLaren, R.R. Duplessis, R.A. Stern, and S. Willoughby, J. Appl. Phys. 41, 4374 (2005). https://doi.org/10.1109/tmag.2005.854755
A. Kootte, C. Haas, R.A. de Groot, J. Phys. : Condens. Matter, 3, 1133 (1991). https://doi.org/10.1088/0953-8984/3/9/009
A. Alam, B. Kraczek, D.D. Johnson, Phys. Rev. B, 82, 024435 (2010). https://doi.org/10.1103/physrevb.82.024435
P. Blaha, K. Schwarz, F. Tran, R. Laskowski, G.K.H. Madsen, and L.D. Marks, J. Chem. Phys. 152, 074101 (2020). https://doi.org/10.1063/1.5143061
O.K. Andersen, Phys. Rev. B, 12, 3060 (1975). https://doi.org/10.1103/physrevb.12.3060
J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, and C. Fiolhais, Phys. Rev. B, 46, 6671 (1992). https://doi.org/10.1103/physrevb.46.6671
F.D. Murnaghan, Proc. Natl. Acad. Sci. USA, 30, 244 (1944). https://doi.org/10.1073/pnas.30.9.244
R.G. Hennig, A.E. Carlsson, K.F. Kelton, and C.L. Henley, Phys. Rev. 71, 100 (2005). https://doi.org/10.1103/physrevb.71.144103
D. Zhou, J. Liu, S. Xu, and P. Peng, Comput. Mater. Sci. 51, 409 (2012). https://doi.org/10.1016/j.commatsci.2011.07.012
D. Zhou, J. Liu, S. Xu, and P. Peng, Comput. Mater. Sci. 86, 24 (2014). https://doi.org/10.1016/j.commatsci.2014.01.007
R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser, and K.K. Kelley, Selected Values of the Thermodynamic Properties of Binary Alloys, ASM, Metals Park, OH, 1973.
Z. Li, K. Xiong, Y. Sun, C. Jin, S. Zhang, J. He, and Y. Mao, Comput. Condens. Matter, 23, e00462 (2020). https://doi.org/10.1016/j.cocom.2020.e00462
W.B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys, (Pergamon Press, Oxford, 1964).
Shuttleworth, Magnetochemistry, 6, 61 (2020). https://doi.org/10.3390/magnetochemistry6040061
C. Leroux, M.C. Cadeville, V. Pierron-Bohnes, G. Inden, and F. Hinz, J. Phys. F: Met. Phys. 18, 2033 (1988). https://doi.org/10.1088/0305-4608/18/9/021
N.I. Vlasova, G.S. Kandaurova, and N.N. Shchegoleva, J. Magn. Magn. Mater. 222, 138 (2000). https://doi.org/10.1016/s0304-8853(00)00506-0
M.J. Capitan, S. Lefebvre, Y. Calvayrac, M. Bessiere, and P. Cenedese, J. Appl. Crystallogr. 32, 1039 (1999). https://doi.org/10.1107/s002188989900998x
R.J. Soulen Jr., J.M. Byers, M.S. Osofsky, B. Nadgorny, T. Ambrose, S.F. Cheng, P.R. Broussard, et al., Science, 282, 85 (1998). https://doi.org/10.1126/science.282.5386.85
F. Goumrhar, L. Bahmad, O. Mounkachi, and A. Benyoussef, Comput. Condens. Matter, 15, 15 (2018). https://doi.org/10.1016/j.cocom.2018.03.003
R.J. Lange, S.J. Lee, D.W. Lynch, P.C. Canfield, B.N. Harmon, et al., Phys. Rev. B, 58, 351 (1998). https://doi.org/10.1103/PhysRevB.58.351
I. Galanakis, M. Alouani, and H. Dreyssé, Phys. Rev. B, 62, 6475 (2000). https://doi.org/10.1103/physrevb.62.6475
M. Born, and K. Huang, Dynamical Theory of Crystal Lattices, (Clarendon Press, Oxford, 1956).
W. Voigt, Ann. Phys. 38, 573 (1889). https://doi.org/10.1002/ange.18890022003
A. Reuss, Z. Angew. Math. Mech. 9, 49 (1929). https://doi.org/10.1002/zamm.19290090104
R. Hill, Proc. Phys. Soc. Lond. A 65 (1952) 349.
C.H. Jenkins, and S.K. Khanna, Mechanics of Materials, (Elsevier, 2005).
S.F. Pugh, Philos. Mag. 45, 823 (1954). https://doi.org/10.1080/14786440808520496
D.G. Pettifor, Mater. Sci. Technol. 8, 289 (1992). https://doi.org/10.1007/978-1-4615-3382-5_17
X.-Q. Chen, H. Niu, D. Li, and Y. Li, Intermetallics, 19, 1275 (2011). https://doi.org/10.1016/j.intermet.2011.03.026
O.L. Anderson, J. Phys. Chem. Solids, 24, 909 (1963). https://doi.org/10.1016/0022-3697(63)90067-2
Y. Pan, and M. Wen, Vacuum, 156, 419 (2018). https://doi.org/10.1016/j.vacuum.2018.08.010
Nianyi, W. Shangan, Z. Yong, and Z. Xiangyun, J. Alloys Compd. 234, 130 (1996). https://doi.org/10.1016/0925-8388(95)01963-4
Q. Chen, Z. Huang, Z. Zhao, and C. Hu, Comput. Mater. Sci. 67, 196 (2013). https://doi.org/10.1016/j.commatsci.2012.08.010
G. Inden, in: Proc. Int. Conf. on Solid-Solid Phase Transformations, TMS-AIME, (Warrendale, PA, 1983), pp. 175.
J.M. Sanchez, J.L. Moran-Lopez, C. Leroux, and M.C. Cadeville, J. Phys. : Condens. Matter, 1, 491 (1989). https://doi.org/10.1088/0953-8984/1/2/019
S.I. Ranganathan, and M. Ostoja-Starzewski, Phys. Rev. Lett. 101, 055504 (2008). https://doi.org/10.1103/physrevlett.101.055504
X. Luan, Q. Zhang, H. Bao, J. Zhou, B. Zhang, G. Wu, and J. Li, Crystals, 8, 307 (2018). https://doi.org/10.3390/cryst8080307
X. Li, X. Chen, L. Han, C. Ruan, P. Lu, and P. Guan, J. Mater. Res. 31, 2956 (2016). https://doi.org/10.1557/jmr.2016.307
M.A. Blanco, E. Francisco, and V. Luaña, Comput. Phys. Commun. 158, 57 (2004). https://doi.org/10.1016/j.comphy.2003.12.001
P.L. Dulong, and A.T. Petit, Ann. Chim. Phys. 10, 395 (1819).
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