A new example of the diffusion-limited aggregation: Ni–Cu ﬁlm patterns Hakan Kockar a, *, Mehmet Bayirli a , Mursel Alper b a Physics Department, Science & Literature Faculty, Balikesir University, 10145 Balikesir, Turkey b Physics Department, Science & Literature Faculty, Uludag University, Go ¨ru ¨kle, 16059 Bursa, Turkey 1. Introduction The growth mechanism of dendrites, semi-dendrite and compact structures in both natural and experiments has attracted scientiﬁc interest for nearly ﬁfty years. The pattern morphology in both symmetrical and complex form is not well understood. Just as the microscopic dynamics can determine macroscopic morpholo- gy, the macroscopic dynamics can reach down and affect the microstructure of the growth process. Therefore, the investigation of the formation mechanism of the microstructure patterns is quite important. Examples of such systems include unitary electrode- position [1], patterns of Zn [2,3] and Cu [4] which are obtained from experiments and the manganese dendrites gathered from natural formation [5]. There are a number of computer models of the simulation in order to study the formation mechanism in reel physical systems. They are based on the Eden model [1], diffusion-limited aggrega- tion (DLA) [6] and deposition-diffusion aggregation (DDA) [7]. These models describe the most important morphological patterns observed in various non-equilibrium systems, such as DLA-like, dendrite, needle, treelike, dense-branching, compact, spiral and stingy structures [1,7–10]. It is also well known that they can be characterized by a universal fractal dimension [11]. However, it is clear that kinetic properties of growing patterns cannot be fully characterized by the fractal dimension alone. A DLA patterns is composed of many tips and fjords, but only a few hottest tips can practically grow toward the outside the pattern, which mainly determines its framework [11]. It was showed how to make the calculation of two dimensional (2D) and three-dimensional (3D) DLA-type pattern for the electrodeposited copper [4] which was not an apparent symmet- rical structure [9]. Matsushita et al. [3] and Grier at al. [4] was reported patterns for the metal electrodeposition in unitary systems. Further studies [10] showed that these conﬁgurations differ substantially from an earlier electrodeposition of single metal. Although the phase diagram for the formation of some metal patterns is proposed [2], their growth mechanisms are still under discussion [1–4]. In recent years, improvements in experimental techniques, such as scanning electron microscope (SEM), permit the investi- gation of the morphology of the patterns on the ﬁlms. Conse- quently, the information gained from the morphological parameters of the materials leads to improve the understanding of the processes underlying the growth phenomena. Applied Surface Science 256 (2010) 2995–2999 ARTICLE INFO Article history: Received 7 June 2009 Received in revised form 18 October 2009 Accepted 23 November 2009 Available online 1 December 2009 Keywords: Ferromagnetic thin ﬁlm growth Monte Carlo Simulations Electrodepositing Fractal dimension ABSTRACT The mechanism of the growth of the dendrites in the Ni–Cu ﬁlms is studied by comparing them with the aggregates obtained by Monte Carlo (MC) simulations according to the diffusion-limited aggregation (DLA) model. The ﬁlms were grown by electrodeposition. The structural analysis of the ﬁlms carried out using the x-ray diffraction showed that the ﬁlms have a face-centered cubic structure. Scanning electron microscope (SEM) was used for morphological observations and the ﬁlm compositions were determined by energy dispersive x-ray spectroscopy. The observed SEM images are compared with the patterns obtained by MC simulations according to DLA model in which the sticking probability, P between the particles is used as a parameter. For all samples between the least and the densest aggregates in the ﬁlms, the critical exponents of the density–density correlation functions, a were within the interval 0.160  0.005–0.124  0.006, and the fractal dimensions, D f , varies from 1.825  0.006 to 1.809  0.008 according to the method of two-point correlation function. These values are also veriﬁed by the mass-radius method. The pattern with a and D f within these intervals was obtained by MC simulations to DLA model while the sticking probability, P was within the interval from 0.35 to 0.40 obtained by varying P (1–0.001). The results showed that the DLA model in this binary system is a possible mechanism for the formation of the ramiﬁed pattern of Ni–Cu within the Ni-rich base part of the Ni–Cu ﬁlms due to the diffusive characteristics of Cu. ß 2009 Elsevier B.V. All rights reserved. * Corresponding author. Tel.: +90 266 6121278; fax: +90 266 6121215. E-mail address: hkockar@balikesir.edu.tr (H. Kockar). Contents lists available at ScienceDirect Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc 0169-4332/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2009.11.063