journal article·2021-01-29Open access

Accurate simulation of surfaces and interfaces of ten FCC metals and steel using Lennard–Jones potentials

Krishan Kanhaiya, Seonghan Kim, Wonpil Im, Hendrik Heinz

npj Computational Materials· Volume 7· Issue 1

Abstract

Abstract The earlier integration of validated Lennard–Jones (LJ) potentials for 8 fcc metals into materials and biomolecular force fields has advanced multiple research fields, for example, metal–electrolyte interfaces, recognition of biomolecules, colloidal assembly of metal nanostructures, alloys, and catalysis. Here we introduce 12-6 and 9-6 LJ parameters for classical all-atom simulations of 10 further fcc metals (Ac, Ca (α), Ce (γ), Es (β), Fe (γ), Ir, Rh, Sr (α), Th (α), Yb (β)) and stainless steel. The parameters reproduce lattice constants, surface energies, water interfacial energies, and interactions with (bio)organic molecules in 0.1 to 5% agreement with experiment, as well as qualitative mechanical properties under standard conditions. Deviations are reduced up to a factor of one hundred in comparison to earlier Lennard–Jones parameters, embedded atom models, and density functional theory. We also explain a quantitative correlation between atomization energies from experiments and surface energies that supports parameter development. The models are computationally very efficient and applicable to an exponential space of alloys. Compatibility with a wide range of force fields such as the Interface force field (IFF), AMBER, CHARMM, COMPASS, CVFF, DREIDING, OPLS-AA, and PCFF enables reliable simulations of nanostructures up to millions of atoms and microsecond time scales. User-friendly model building and input generation are available in the CHARMM-GUI Nanomaterial Modeler. As a limitation, deviations in mechanical properties vary and are comparable to DFT methods. We discuss the incorporation of reactivity and features of the electronic structure to expand the range of applications and further increase the accuracy.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Machine Learning in Materials Science · nanoparticles nucleation surface interactions · Calcium Carbonate Crystallization and Inhibition

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (100+)

Show source-provided references
1. Dreaden, E. C., Alkilany, A. M., Huang, X. H., Murphy, C. J. & El-Sayed, M. A. The golden age: gold nanoparticles for biomedicine. Chem. Soc. Rev. 41, 2740–2779 (2012).10.1039/C1CS15237H ↗
2. Huang, X. Q. et al. High-performance transition metal-doped Pt3Ni octahedra for oxygen reduction reaction. Science 348, 1230–1234 (2015).10.1126/science.aaa8765 ↗
3. Li, M. F. et al. Ultrafine jagged platinum nanowires enable ultrahigh mass activity for the oxygen reduction reaction. Science 354, 1414–1419 (2016).10.1126/science.aaf9050 ↗
4. Heinz, H. et al. Nanoparticle decoration with surfactants: molecular interactions, assembly, and applications. Surf. Sci. Rep. 72, 1–58 (2017).10.1016/j.surfrep.2017.02.001 ↗
5. Murphy, C. J. et al. Anisotropic metal nanoparticles: synthesis, assembly, and optical applications. J. Phys. Chem. B 109, 13857–13870 (2005).10.1021/jp0516846 ↗
6. Auyeung, E. et al. DNA-mediated nanoparticle crystallization into Wulff polyhedra. Nature 505, 73–77 (2014).10.1038/nature12739 ↗
7. Macfarlane, R. J., Jones, M. R., Lee, B., Auyeung, E. & Mirkin, C. A. Topotactic interconversion of nanoparticle superlattices. Science 341, 1222–1225 (2013).10.1126/science.1241402 ↗
8. Zhu, E. et al. Long-range hierarchical nanocrystal assembly driven by molecular structural transformation. J. Am. Chem. Soc. 141, 1498–1505 (2019).10.1021/jacs.8b08023 ↗
9. Zhu, E. et al. Peptide-assisted 2-D assembly toward free-floating ultrathin platinum nanoplates as effective electrocatalysts. Nano Lett. 19, 3730–3736 (2019).10.1021/acs.nanolett.9b00867 ↗
10. Cao, L. et al. Differential surface elemental distribution leads to significantly enhanced stability of PtNi-based ORR catalysts. Matter 1, 1567–1580 (2019).10.1016/j.matt.2019.07.015 ↗
11. Sarikaya, M., Tamerler, C., Jen, A. K. Y., Schulten, K. & Baneux, F. Molecular biomimetics: nanotechnology through biology. Nat. Mater. 2, 577–585 (2003).10.1038/nmat964 ↗
12. Naik, R. R. et al. Peptide templates for nanoparticle synthesis derived from polymerase chain reaction-driven phage display. Adv. Funct. Mater. 14, 25–30 (2004).10.1002/adfm.200304501 ↗
13. Xia, Y., Xiong, Y., Lim, B. & Skrabalak, S. E. Shape-controlled synthesis of metal nanocrystals: simple chemistry meets complex physics? Angew. Chem. Int. Ed. 48, 60–103 (2009).10.1002/anie.200802248 ↗
14. Dacheux, N., Clavier, N. & Podor, R. Monazite as a promising long-term radioactive waste matrix: benefits of high-structural flexibility and chemical durability. Am. Mineral. 98, 833–847 (2013).10.2138/am.2013.4307 ↗
15. Heinz, H., Vaia, R. A., Farmer, B. L. & Naik, R. R. Accurate simulation of surfaces and interfaces of face-centered cubic metals using 12 − 6 and 9 − 6 Lennard-Jones potentials. J. Phys. Chem. C. 112, 17281–17290 (2008).10.1021/jp801931d ↗
16. Geada, I. L., Ramezani-Dakhel, H., Jamil, T., Sulpizi, M. & Heinz, H. Insight into induced charges at metal surfaces and biointerfaces using a polarizable Lennard-Jones potential. Nat. Commun. 9, 716 (2018).10.1038/s41467-018-03137-8 ↗
17. Feng, J. et al. Influence of the shape of nanostructured metal surfaces on adsorption of single peptide molecules in aqueous solution. Small 8, 1049–1059 (2012).10.1002/smll.201102066 ↗
18. Feng, J. et al. Adsorption mechanism of single amino acid and surfactant molecules to Au {111} surfaces in aqueous solution: design rules for metal-binding molecules. Soft Matter 7, 2113–2120 (2011).10.1039/c0sm01118e ↗
19. Heinz, H. et al. Nature of molecular interactions of peptides with gold, palladium, and Pd-Au bimetal surfaces in aqueous solution. J. Am. Chem. Soc. 131, 9704–9714 (2009).10.1021/ja900531f ↗
20. Roussel, T. J., Barrena, E., Ocal, C. & Faraudo, J. Predicting supramolecular self-assembly on reconstructed metal surfaces. Nanoscale 6, 7991–8001 (2014).10.1039/C4NR01987C ↗
21. Ramezani-Dakhel, H., Ruan, L. Y., Huang, Y. & Heinz, H. Molecular mechanism of specific recognition of cubic Pt nanocrystals by peptides and the concentration-dependent formation from seed crystals. Adv. Funct. Mater. 25, 1374–1384 (2015).10.1002/adfm.201404136 ↗
22. Ruan, L. et al. Tailoring molecular specificity toward a crystal facet: a lesson from biorecognition toward Pt{111}. Nano Lett. 13, 840–846 (2013).10.1021/nl400022g ↗
23. Chew, A. K. & Van Lehn, R. C. Effect of core morphology on the structural asymmetry of alkanethiol monolayer-protected gold nanoparticles. J. Phys. Chem. C. 122, 26288–26297 (2018).10.1021/acs.jpcc.8b09323 ↗
24. Bedford, N. M. et al. Elucidation of peptide-directed palladium surface structure for biologically tunable nanocatalysts. ACS Nano 9, 5082–5092 (2015).10.1021/acsnano.5b00168 ↗
25. Ramezani-Dakhel, H., Mirau, P. A., Naik, R. R., Knecht, M. R. & Heinz, H. Stability, surface features, and atom leaching of palladium nanoparticles: toward prediction of catalytic functionality. Phys. Chem. Chem. Phys. 15, 5488–5492 (2013).10.1039/c3cp00135k ↗
26. Zhang, C. et al. Low-temperature charging dynamics of the ionic liquid and its gating effect on FeSe0.5Te0.5 superconducting films. ACS Appl. Mater. Interfaces 11, 17979–17986 (2019).10.1021/acsami.9b02373 ↗
27. Shi, W., Zhang, Z. & Li, S. Quantitative prediction of position and orientation for platonic nanoparticles at liquid/liquid interfaces. J. Phys. Chem. Lett. 9, 373–382 (2018).10.1021/acs.jpclett.7b03187 ↗
28. Meng, C., Liao, L. & Huang, C. Study on failure mechanism of Cu-polyethylene-Cu sandwich structure by molecular dynamics simulation. Comput. Mater. Sci. 154, 315–324 (2018).10.1016/j.commatsci.2018.08.011 ↗
29. Zhu, Z. et al. Reversible hydrophobicity–hydrophilicity transition modulated by surface curvature. J. Phys. Chem. Lett. 9, 2346–2352 (2018).10.1021/acs.jpclett.8b00749 ↗
30. Nathanson, M., Kanhaiya, K., Pryor, A., Miao, J. & Heinz, H. Atomic-scale structure and stress release mechanism in core–shell nanoparticles. ACS Nano 12, 12296–12304 (2018).10.1021/acsnano.8b06118 ↗
31. Liu, J. et al. Understanding chemical bonding in alloys and the representation in atomistic simulations. J. Phys. Chem. C. 122, 14996–15009 (2018).10.1021/acs.jpcc.8b01891 ↗
32. Xu, R. et al. Three-dimensional coordinates of individual atoms in materials revealed by electron tomography. Nat. Mater. 14, 1099–1103 (2015).10.1038/nmat4426 ↗
33. Shi, P. et al. Enhanced strength-ductility synergy in ultrafine-grained eutectic high-entropy alloys by inheriting microstructural lamellae. Nat. Commun. 10, 489 (2019).10.1038/s41467-019-08460-2 ↗
34. Santodonato, L. J. et al. Deviation from high-entropy configurations in the atomic distributions of a multi-principal-element alloy. Nat. Commun. 6, 5964 (2015).10.1038/ncomms6964 ↗
35. Sheng, H. W., Kramer, M. J., Cadien, A., Fujita, T. & Chen, M. W. Highly optimized embedded-atom-method potentials for fourteen FCC metals. Phys. Rev. B 83, 134118 (2011).10.1103/PhysRevB.83.134118 ↗
36. Singh-Miller, N. E. & Marzari, N. Surface energies, work functions, and surface relaxations of low-index metallic surfaces from first principles. Phys. Rev. B 80, 235407 (2009).10.1103/PhysRevB.80.235407 ↗
37. Silvestrelli, P. L. & Ambrosetti, A. Van Der Waals corrected density functional theory simulation of adsorption processes on noble-metal surfaces: Xe on Ag(111), Au(111), and Cu(111). J. Low. Temp. Phys. 185, 183–197 (2016).10.1007/s10909-016-1515-y ↗
38. Ruiz, V. G., Liu, W. & Tkatchenko, A. Density-functional theory with screened van Der Waals interactions applied to atomic and molecular adsorbates on close-packed and non-close-packed surfaces. Phys. Rev. B 93, 035118 (2016).10.1103/PhysRevB.93.035118 ↗
39. Liu, W., Tkatchenko, A. & Scheffler, M. Modeling adsorption and reactions of organic molecules at metal surfaces. Acc. Chem. Res. 47, 3369–3377 (2014).10.1021/ar500118y ↗
40. Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132, 154104 (2010).10.1063/1.3382344 ↗
41. Goerigk, L. & Grimme, S. A thorough benchmark of density functional methods for general main group thermochemistry, kinetics, and noncovalent interactions. Phys. Chem. Chem. Phys. 13, 6670–6688 (2011).10.1039/c0cp02984j ↗
42. Heinz, H., Lin, T.-J., Mishra, R. K. & Emami, F. S. Thermodynamically consistent force fields for the assembly of inorganic, organic, and biological nanostructures: the interface force field. Langmuir 29, 1754–1765 (2013).10.1021/la3038846 ↗
43. Lindorff-Larsen, K., Piana, S., Dror, R. O. & Shaw, D. E. How fast-folding proteins fold. Science 334, 517–520 (2011).10.1126/science.1208351 ↗
44. Dauber-Osguthorpe, P. et al. Structure and energetics of ligand binding to proteins: Escherichia coli dihydrofolate reductase-trimethoprim, a drug-receptor system. Proteins Struct. Funct. Genet. 4, 31–47 (1988).10.1002/prot.340040106 ↗
45. Sun, H., Mumby, S. J., Maple, J. R. & Hagler, A. T. An ab-initio CFF93 all-atom force field for polycarbonates. J. Am. Chem. Soc. 116, 2978–2987 (1994).10.1021/ja00086a030 ↗
46. Huang, J. & MacKerell, A. D. CHARMM36 all-atom additive protein force field: validation based on comparison to NMR data. J. Comput. Chem. 34, 2135–2145 (2013).10.1002/jcc.23354 ↗
47. Jorgensen, W. L., Maxwell, D. S. & TiradoRives, J. Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids. J. Am. Chem. Soc. 118, 11225–11236 (1996).10.1021/ja9621760 ↗
48. Wang, J. M., Wolf, R. M., Caldwell, J. W., Kollman, P. A. & Case, D. A. Development and testing of a general amber force field. J. Comput. Chem. 25, 1157–1174 (2004).10.1002/jcc.20035 ↗
49. Mayo, S. L., Olafson, B. D. & Goddard, W. A. DREIDING: a generic force field for molecular simulations. J. Phys. Chem. 94, 8897–8909 (1990).10.1021/j100389a010 ↗
50. Sun, H. COMPASS: an ab initio force-field optimized for condensed-phase applications - overview with details on alkane and benzene compounds. J. Phys. Chem. B 102, 7338–7364 (1998).10.1021/jp980939v ↗
51. Foiles, S. M., Baskes, M. I. & Daw, M. S. Embedded atom-method functions for the FCC metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys. Rev. B 33, 7983–7991 (1986).10.1103/PhysRevB.33.7983 ↗
52. Daw, M. S., Foiles, S. M. & Baskes, M. I. The embedded atom method: a review of theory and applications. Mater. Sci. Rep. 9, 251–310 (1993).10.1016/0920-2307(93)90001-U ↗
53. Heinz, H. & Ramezani-Dakhel, H. Simulations of inorganic–bioorganic interfaces to discover new materials: insights, comparisons to experiment, challenges, and opportunities. Chem. Soc. Rev. 45, 412–448 (2016).10.1039/C5CS00890E ↗
54. Ghiringhelli, L. M. & Delle Site, L. Phenylalanine near inorganic surfaces: conformational statistics vs specific chemistry. J. Am. Chem. Soc. 130, 2634–2638 (2008).10.1021/ja077817d ↗
55. Pensado, A. S. & Padua, A. A. H. Solvation and stabilization of metallic nanoparticles in ionic liquids. Angew. Chem. Int. Ed. 50, 8683–8687 (2011).10.1002/anie.201103096 ↗
56. Wright, L. B., Rodger, P. M., Corni, S. & Walsh, T. R. GoIP-CHARMM: first-Principles based force fields for the interaction of proteins with Au(111) and Au(100). J. Chem. Theor. Comput. 9, 1616–1630 (2013).10.1021/ct301018m ↗
57. Born, M. Eine Thermochemische Anwendung der Gittertheorie. Verh. Dtsch. Phys. Ges. 21, 13–24 (1919).
58. Hirschfelder, J. O., Curtiss, C. F. & Bird, R. B. Molecular Theory of Gases and Liquids (John Wiley, 1954).
59. Lide, D. R. CRC Handbook of Chemistry and Physics, 96th edn. (CRC Press, 2015).
60. Tyson, W. R. & Miller, W. A. Surface free-energies of solid metals - estimation from liquid surface-tension measurements. Surf. Sci. 62, 267–276 (1977).10.1016/0039-6028(77)90442-3 ↗
61. Keene, B. J. Review of data for the surface tension of pure metals. Int. Mater. Rev. 38, 157–192 (1993).10.1179/imr.1993.38.4.157 ↗
62. Mills, K. C. & Su, Y. C. Review of surface tension data for metallic elements and alloys: part 1 - pure metals. Int. Mater. Rev. 51, 329–351 (2006).10.1179/174328006X102510 ↗
63. Jha, K. C., Liu, H., Bockstaller, M. R. & Heinz, H. Facet recognition and molecular ordering of ionic liquids on metal surfaces. J. Phys. Chem. C. 117, 25969–25981 (2013).10.1021/jp4032404 ↗
64. Emami, F. S. et al. Force field and a surface model database for silica to simulate interfacial properties in atomic resolution. Chem. Mater. 26, 2647–2658 (2014).10.1021/cm500365c ↗
65. Pramanik, C., Gissinger, J. R., Kumar, S. & Heinz, H. Carbon nanotube dispersion in solvents and polymer solutions: mechanisms, assembly, and preferences. ACS Nano 11, 12805–12816 (2017).10.1021/acsnano.7b07684 ↗
66. Chen, J. et al. Building two-dimensional materials one row at a time: avoiding the nucleation barrier. Science 362, 1135–1139 (2018).10.1126/science.aau4146 ↗
67. Heinz, H., Koerner, H., Anderson, K. L., Vaia, R. A. & Farmer, B. L. Force field for mica-type silicates and dynamics of octadecylammonium chains grafted to montmorillonite. Chem. Mater. 17, 5658–5669 (2005).10.1021/cm0509328 ↗
68. Lee, J. et al. CHARMM-GUI input generator for NAMD, GROMACS, AMBER, OpenMM, and CHARMM/OpenMM simulations using the CHARMM36 additive force field. J. Chem. Theory Comput. 12, 405–413 (2016).10.1021/acs.jctc.5b00935 ↗
69. Jo, S., Kim, T., Iyer, V. G. & Im, W. CHARMM-GUI: a web-based graphical user interface for CHARMM. J. Comput. Chem. 29, 1859–1865 (2008).10.1002/jcc.20945 ↗
70. Zhou, J. et al. Observing crystal nucleation in four dimensions using atomic electron tomography. Nature 570, 500–503 (2019).10.1038/s41586-019-1317-x ↗
71. Mehl, M. J. & Papaconstantopoulos, D. A. Applications of a tight-binding total-energy method for transition and noble metals: elastic constants, vacancies, and surfaces of monatomic metals. Phys. Rev. B 54, 4519 (1996).10.1103/PhysRevB.54.4519 ↗
72. Schneemilch, M. & Quirke, N. Free energy of adsorption of supported lipid bilayers from molecular dynamics simulation. Chem. Phys. Lett. 664, 199–204 (2016).10.1016/j.cplett.2016.10.010 ↗
73. Menon, S. K. & Martin, P. L. Determination of the anisotropy of surface free energy of fine metal particles. Ultramicroscopy 20, 93–98 (1986).10.1016/0304-3991(86)90174-9 ↗
74. Flueli, M. & Borel, J.-P. Surface energy anisotropy measurements on a small cuboctahedron of gold observed by high resolution electron microscopy (HREM). J. Cryst. Growth 91, 67–70 (1988).10.1016/0022-0248(88)90368-5 ↗
75. Lee, W. H. et al. The equilibrium shape and surface energy anisotropy of clean platinum. J. Catal. 126, 658–671 (1990).10.1016/0021-9517(90)90028-I ↗
76. Mezey, L. Z. & Giber, J. The surface free-energies of solid chemical elements - calculation from internal free enthalpies of atomization. Jpn. J. Appl. Phys. Part 1 21, 1569–1571 (1982).10.1143/JJAP.21.1569 ↗
77. Osman, M. A. & Keller, B. A. Wettability of native silver surfaces. Appl. Surf. Sci. 99, 261–263 (1996).10.1016/0169-4332(96)00101-8 ↗
78. Heinz, H., Jha, K. C., Luettmer-Strathmann, J., Farmer, B. L. & Naik, R. R. Polarization at metal-biomolecular interfaces in solution. J. R. Soc. Interface 8, 220–232 (2011).10.1098/rsif.2010.0318 ↗
79. Dharmawardhana, C. C. et al. Reliable computational design of biological-inorganic materials to the large nanometer scale using interface-FF. Mol. Sim. 43, 1394–1405 (2017).10.1080/08927022.2017.1332414 ↗
80. Mark, L. O., Zhu, C., Medlin, J. W. & Heinz, H. Understanding the surface reactivity of ligand-protected metal nanoparticles for biomass upgrading. ACS Catal. 10, 5462–5474 (2020).10.1021/acscatal.9b04772 ↗
81. Kosevitch, A. M., Lifshitz, E. M., Landau, L. D. & Pitaevskii, L. P. Theory of Elasticity 3rd edn, Vol. 7 (Butterworth-Heinemann, 1999).
82. Simmons, G. & Wang, H., eds. Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook 2nd edn (MIT Press, 1971).
83. Hertzberg, R. W. Deformation and Fracture Mechanics of Engineering Materials, 3rd edn. (John Wiley & Sons, 1989).
84. Mishra, R. K., Fernández-Carrasco, L., Flatt, R. J. & Heinz, H. A force field for tricalcium aluminate to characterize surface properties, initial hydration, and organically modified interfaces in atomic resolution. Dalton Trans. 43, 10602–10616 (2014).10.1039/C4DT00438H ↗
85. Liu, J. et al. Interpretable molecular models for molybdenum disulfide and insight into selective peptide recognition. Chem. Sci. 11, 8708–8722 (2020).10.1039/D0SC01443E ↗
86. Blanca, E., Rodriguez, C. O., Shitu, J. & Novikov, D. L. Degree of localization of the exchange-correlation hole and its influence on the ground-state (structural and magnetic) properties of d. Met. J. Phys. Condens. Mat. 13, 9463–9470 (2001).10.1088/0953-8984/13/42/307 ↗
87. Mahoney, M. W. & Jorgensen, W. L. A five-site model for liquid water and the reproduction of the density anomaly by rigid, nonpolarizable potential functions. J. Chem. Phys. 112, 8910–8922 (2000).10.1063/1.481505 ↗
88. O. Oyj. Handbook of Stainless Steel (Outokumpu Oyj, Espoo, Finland, 2013).
89. Ledbetter, H. & Austin, M. Effects of carbon and nitrogen on the elastic constants of AISI type 304 stainless steel. Mat. Sci. Eng. 70, 143–149 (1985).10.1016/0025-5416(85)90275-7 ↗
90. Heinz, H. & Suter, U. W. Atomic charges for classical simulations of polar systems. J. Phys. Chem. B 108, 18341–18352 (2004).10.1021/jp048142t ↗
91. Coppage, R. et al. Exploiting localized surface binding effects to enhance the catalytic reactivity of peptide-capped nanoparticles. J. Am. Chem. Soc. 135, 11048–11054 (2013).10.1021/ja402215t ↗
92. Grimsby, D. V., Wu, Y. & Mitchell, K. A LEED analysis for the Ni (111)−(2× 2)−O surface structure: evidence for oxygen-induced relaxations of both vertical and lateral types in the close packed surface layer of nickel. Surf. Sci. 232, 51–55 (1990).10.1016/0039-6028(90)90586-W ↗
93. Narusawa, T., Gibson, W. & Törnqvist, E. Structure study of oxygen-adsorbed Ni (111) surface by high energy ion scattering. Surf. Sci. 114, 331–348 (1982).10.1016/0039-6028(82)90475-7 ↗
94. Batra, I. P. & Kleinman, L. Chemisorption of oxygen on aluminum surfaces. J. Electron Spectrosc. Relat. Phenom. 33, 175–241 (1984).10.1016/0368-2048(84)80020-1 ↗
95. Martinson, C., Flodström, S., Rundgren, J. & Westrin, P. Oxygen chemisorption on aluminum single crystals: site determination by LEED studies. Surf. Sci. 89, 102–113 (1979).10.1016/0039-6028(79)90597-1 ↗
96. Ramezani-Dakhel, H. et al. Nature of peptide wrapping onto metal nanoparticle catalysts and driving forces for size control. Nanoscale 9, 8401–8409 (2017).10.1039/C7NR02813J ↗
97. Briggs, B. et al. Atomic-scale identification of Pd leaching in nanoparticle catalyzed CC coupling: effects of particle surface disorder. Chem. Sci. 6, 6413–6419 (2015).10.1039/C5SC01424G ↗
98. Basinski, Z. S., Hume-Rothery, W. & Sutton, A. The lattice expansion of iron. P. Roy. Soc. A Math. Phy. 229, 459–467 (1955).
99. Skriver, H. L. & Rosengaard, N. Surface energy and work function of elemental metals. Phys. Rev. B 46, 7157 (1992).10.1103/PhysRevB.46.7157 ↗
100. Aghemenlo, H., Iyayi, S. & Avwiri, G. Surface relaxation and surface energy of face–centered cubic. Met. J. Appl. Sci. Environ. Manag. 10, 37–42 (2006).