An Analytical Model for Solute Segregation at Liquid Metal/Solid Substrate Interface
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TRODUCTION
SOLUTE segregation can usually be observed at the interfaces, such as liquid/substrate, solid phase/precipitate, grain boundary (GB), and the surfaces,[1–3] and may significantly affect the properties of the interfaces or surfaces. Solute segregation is highly relevant to many fields of studies in materials science, such as heterogeneous nucleation, welding, wetting, catalysis, electronic properties, GB embrittlement, and joining of dissimilar materials. Recently, scanning transmission electron microscopy (STEM) observation revealed at the atomic-level that the solute segregation at GB was the underlying cause of embrittlement of the intrinsically ductile metals when exposed to certain liquid metals.[4] It is generally believed that solute segregation at the liquid/ substrate interface plays an important role in heterogeneous nucleation[5–7] and the wetting phenomena.[2] Currently, our knowledge on solute segregation at the metallic liquid/substrate interface is very limited. This is mainly due to the fact that it is very difficult to access the liquid metal/substrate interface through direct experimental observations.[8–10] During investigation of wetting between metallic liquids and ceramics, the decrease in contact angle is often attributed to solute segregation at the liquid/substrate interface.[2] However, the measurement of the contact angle may be complicated by many factors,[11,12] e.g., surface oxidation of the liquid, roughness of the substrate, and so on. Therefore, it is important to develop a theoretical analysis for the interfacial segregation of solute in the liquid/substrate systems. HUA MEN, Senior Research Fellow, and ZHONGYUN FAN, Professor, are with The EPSRC Centre-LiME, BCAST, Brunel University, Uxbridge, Middlesex UB8 3PH, U.K. Contact e-mail: [email protected] Manuscript submitted January 6, 2014. Article published online August 20, 2014 5508—VOLUME 45A, NOVEMBER 2014
Generally, equilibrium segregation at the interfaces describes distribution of solutes governed by minimization of total free energy of the systems: bulk plus interface.[13] The Gibbs adsorption isotherm is a very useful method to elucidate the segregation phenomena at the surfaces or interfaces. It is based on the changes of surface or interfacial energy with the bulk activity of the solute.[14] For a dilute solution following Henry’s law, the Gibbs adsorption isotherm can be written as:[14] 1 @c Ci ¼ ; ½1 RT @ ln Xi T;P where Ci is the surface or interfacial excess of the solute with respect to its bulk composition, R is the universal gas constant, c is the surface or interfacial energy, and Xi is the mole fraction of the solute in the bulk. The Gibbs adsorption isotherm reveals that interfacial enrichment of a solute is directly related to the decrease in interfacial energy. However, the calculation of solute segregation at the liquid/substrate interface requires the knowledge about the changes of the interfacial energy with the bulk activity of the solute, which is not usually available in most cases. By min
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