Atomistic-Scale Computational Materials Science on Surface and Interface Phenomena for Materials Development

NIPPON STEEL & SUMITOMO METAL TECHNICAL REPORT No. 114 MARCH 2017 Technical Report UDC 669 . 14 : 539 . 24 : 681 . 3 Atomistic-scale Computational Materials Science on Surface and Interface Phenomena for Materials Development Koji MORIGUCHI* Yoichi MATSUZAKI Abstract Functionalities of materials usually originate from the spatial inhomogeneity in the associated systems. The phenomena on the surface are, therefore, expected to induce essentially different physical properties from ones in bulk systems. One of the most important missions of the recent computational materials science is to create universal concepts on the functionalities of practical materials based on the basic physical science. In this article, we review our recent theoretical research activities on some surface and interface phenomena associated in the technologies of “protection against metal dusting”, “molecular design of organic corrosion inhibitors”, “graphite anodes for lithium-ion secondary batteries”, and “SiC single crystal growth”, using the atomistic-scale computational materials science. 1. Introduction and other actions that develop in the nanoscale regime. In addition, In a material as a system, local inhomogeneity such as a defect a surface or interface is a boundary at which the external phase in the parent phase, surface, interface, and nanostructure often as- comes into contact with the internal phase, serving as a place for sumes an important role in the development of the functionality of particles and energy to be transferred and received. Therefore, the the material. The scientific phenomenon at a surface or interface physical properties at surfaces and interfaces are expected to be es- without spatial homogeneity is utilized for engineering purposes in sentially different from those in a homogeneous bulk system. This a broad range of fields including material engineering, corrosion also opens up the possibilities for a material with new functionality protection engineering, semiconductor engineering, electrochemis- added. try, and catalytic engineering. For this reason, the research on the ar- One of the most important missions of computational materials eas of surfaces and interfaces is deemed as extremely interdisciplin- science is to reproduce realistic material phenomena in computers ary and one that is required to elicit as much of the functionality of a based on the basic laws of physics (fundamentals and principles), material as possible.1) The atomistic-scale computational materials and to analyze the behavior under a particular set of conditions, science collectively refers to theoretical simulation technologies in- thereby creating new universal laws and functionality development tended for nanoscale phenomena, which has become an indispens- concepts. In this article, examples of Nippon Steel & Sumitomo able tool for the research and development in a variety of engineer- Metal Corporation's research activities in which the atomistic-scale ing fields along with the remarkable recent progress in hardware/ computational materials science rapidly progressed in recent years software.2–4) has been applied to the surface phenomena are outlined including For transition metal alloys including steel materials in which the practical materials, in the hope that this article will be of some help electronic d-band states around the Fermi level are strongly local- to readers taking a panoramic view of the ties going forward be- ized, the concept of chemical bond formation can be applied between a variety of material development and computational materi- tween constituent atoms. There are atoms that do not form bonds als science. with other atoms even at the surfaces of materials having strong interatomic bonds in a bulk state (i.e. dangling bonds), which leads to 2. Application of Computational Materials Science a chemically activated state with locally high internal energy. For to Surface Phenomena of Metallic Structural this reason, most phenomena of deep interest at surfaces and inter- Materials faces are influenced by the interactions between a few atomic layers This chapter starts with an overview of the Friedel model theory, * Chief Researcher, Ph.D. in Engineering, Mathematical Science & Technology Research Lab., Advanced Technology Research Laboratories 20-1 Shintomi, Futtsu City, Chiba Pref. 293-8511 - 81 - NIPPON STEEL & SUMITOMO METAL TECHNICAL REPORT No. 114 MARCH 2017 which is useful for foreseeing intuitively the relations between the pation of electrons. However, it is explained based on electronic bulk cohesive properties and surface physical properties of a transi- theory that with nd > 5, the bonding force decreases as electrons oc- tion metal, which is followed by research examples on electronic cupy the anti-bonding state.5) state calculations that made a contribution primarily to the construc- At the surface where the crystal periodicity is broken, there is a tion of a corrosion protection function for metallic structural materi- reduction in the number of coordinated atoms that constitute the als. surface as shown in Fig. 1 (b). This weakens the interaction between 2.1 Friedel model theory regarding the electronic states on the atoms, resulting in reducing the band width W. When this band surf surface of transition metal width reduction is ΔW as shown in Fig. 1 (a), the total energy (Etot ) In most cases, physical properties related to the cohesive force of the surface system is expressed as follows analogically based on and interatomic bonds in transition metals including alloys can be the process of derivation of equation (1). organized by the number of d electrons (n ) per atom in the system. W −ΔW d E surf = − n (10 − n ) (2) The Friedel model provides such behavior simply and clearly in tot 20 d d terms of physics.5) In the Friedel model, the rectangular electronic As the surface energy is equal to the loss from the total energy due density of states (DOS) shown in Fig. 1 (a) is boldly assumed for the to the breaking of bonds, the surface energy per atom (Esurf) is ex- d-band states of the transition metal, thereby examining the cohe- pressed as follows. sion mechanism of the system. Using five d-orbital levels E( atom = ΔW d E ≡ E surf − E bulk = n (10 − n ) (3) W/2) that are degenerated in an isolated atom state as the benchmark surf tot tot 20 d d bulk of the orbital energy, the total energy (Etot ) of the bulk system is In the framework of tight-binding approximation, when the 5) expressed as equation (1) with simple calculation in between, number of coordinated atoms is Nc, the band width W is scaled in 6) W ∝ √N . Accordingly, the band width ratio between the bulk system E bulk = − n (10 − n ) = − E bulk (1) c tot 20 d d coh and the surface system are expressed as follows, with the numbers bulk where, W is the band width of the rectangular DOS, and Ecoh is the of coordinated atoms of these systems respectively denoted as bulk surf cohesive energy of the bulk system. Nc and Nc . surf The important conclusion derived from the Friedel model of the N c W − ΔW = bulk (4) bulk system is that the physical properties of transition metal alloys W Nc related to the cohesive force and interatomic bonds are essentially This derives the following equation for the band width reduction determined by the number of electrons that occupy the d-band and (ΔW) of the surface system. surf the band width. The interatomic bonds in the system are strongest N c ΔW = 1 − W (5) when the number of n is five, and the larger the band width W is, ( bulk ) d Nc bulk the larger the maximum value of the cohesive energy Ecoh becomes. This concept of associating the number of coordinated atoms Nc The d-band state of nd < 5 corresponds to the bonding state. In this with the band width reduction ΔW is often called the bond-cutting regime the interatomic bonding force increases along with the occu- model.6) On the (001) surface of an fcc structure as shown in Fig. 1 (b) as surf bulk an example, the equality Nc /Nc = 8/12 is true in terms of simple surf bulk geometry, obtaining the value 1 − Nc /Nc to 0.2 ( =1/5) or so, and the surface energy of equation (3) can be approximately evaluated using the following equation. surf ΔW N c bulk E = n (10 − n ) = ( 1 − bulk ) E surf d d coh 20 Nc 1 W ≈ E bulk = n 10 − n (6) 5 coh 100 d ( d) Equation (6) is a concept in terms of physics that associates the bulk cohesive physical properties with the surface physical properties, in which the surface energy of the transition metal is considered as approximately 1/5 or so of the bulk cohesive energy. In a system with strong interatomic bonds in the bulk state, the presence of dangling bonds at its surface, which are more highly activated than interatomic bonds in the bulk state, leads to an increase in surface energy. To make a comparison between the Friedel model of the surface system described above and more precise first-principles computa- tion analysis, we plotted relations between the theoretically calculat- ed values 7) of the surface energy of 4d transition metals by Vitos et al. and the number of d electrons (nd) as shown in Fig. 1 (c). Al- though there are some exceptions such as 3d transition metal due to magnetism, the crystal structures in the ground state of the transition Fig. 1 Rectangular DOS in Friedel model for (a) the bulk and surface metal from the left side in the periodic table are changed as hcp → states. (b) Schematic illustration of coordination number reduc- 5) tion for the surface atoms on (001) in fcc structure. (c) Compari- bcc → hcp → fcc → hcp. For the plots with the vertical axis, the son of the surface energies for the 4d metals including Rb and Sr surface energy theoretical values 7) for the close-packed surface based on the first-principles 7) and Friedel model analyses.

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