Journal of Crystal Growth 237–239 (2002) 14–20 Statistical mechanics of vicinal surface with adsorption Noriko Akutsu a, *, Yasuhiro Akutsu b , Takao Yamamoto c a Faculty of Engineering, Osaka Electro-Communication University, Hatsu-cho, Neyagawa 572-8530, Japan b Department of Physics, Graduate School of Science, Osaka University, Machikaneyama-cho, Toyonaka, Osaka 560-0011, Japan c Department of Physics, Faculty of Engineering, Gunma University, Kiryu, Gunma 376-0052, Japan Abstract We have made a statistical mechanical study of a vicinal surface with adsorption with coverage Y being less than 1. In the case of Langmuir adsorption, where the lateral interactions among the adsorbates are absent, the universal behavior of a vicinal surface—Gruber–Mullins–Pokrovsky–Talapov (GMPT) behavior—persists although the step tension, the step stiffness and the roughening transition temperature are modified by adsorbates. The effect of lateral attraction among adsorbates is the emergence of the inter-step attraction mediated by the density fluctuation of the adsorbate, which causes non-GMPT behavior such as first-order transition in equilibrium crystal shape and thermal step bunching. r 2002 Elsevier Science B.V. All rights reserved. PACS: 05.70.Np; 68.35.Rh; 05.50.+q; 68.35.Md Keywords: A1. Adsorption; A1. Impurities; A1. Low dimensional structures; A1. Phase equilibria; A1. Roughening; A1. Segregation 1. Introduction It has been known that adsorbates often change surface energetics and surface kinetics [1–5]. In order to explain (or predict) thermodynamic behavior of a surface with adsorption from a structure of atomic scale, we have to carry out statistical mechanical calculations which connect quantities of atomic scale and those of mesoscopic scale. In this article, we show results of our recent statistical mechanical study of a vicinal surface with adsorption [6–8]. The aim of our study is to clarify the entropic effect caused by adsorption to the vicinal surface and step quantities. 2. Model Hamiltonian 2.1. The decorated RSOS model We want to know the effect of the adsorption monolayer to the surface configuration—steps, islands, and negative islands—on a substrate. From this point of view, a kink in a step is the most elementary excitation on a surface. On a real surface, a kink should be defined on the basis of the unit cell of the reconstructed surface [9,10]. We consider a solid-on-solid (SOS) model on a square lattice with nearest-neighbor (nn) interac- tions to treat steps, islands, and negative islands on a substrate. The position of each SOS column, i; is expressed in terms of a pair of integers as i ¼ ðm; nÞ: The height of the column is denoted by h i ð¼ hðm; nÞ). *Corresponding author. Tel.: +81-72-824-1131(2267); fax:+ 71-72-824-1140. E-mail address: nori@phys.osakac.ac.jp (N. Akutsu). 0022-0248/02/$-see front matter r 2002 Elsevier Science B.V. All rights reserved. PII:S0022-0248(01)01842-5