Measurement of Surface Tension of Solid Cu by Improved Multiphase Equilibrium
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NTRODUCTION
IN recent years, attention has been focused on nanotechnology and development of nanomaterials due to their specific physical and chemical properties.[1,2] The phase diagrams of nanoscale systems, which can give practical guidelines for their study, are essential for advancement in the field of material science. Several research groups have investigated the phase diagrams in nanosized metals and alloys theoretically,[3–7] as well as experimentally.[8–13] In the theoretical calculations, the temperature function of surface tension of solid metal is one of the significant physicochemical properties. The formulation of surface tension for solid metals in terms of temperature is a considerably difficult and complicated task due to lack of experimental data, large scatter of data, and a narrow temperature range of measurement.[14–18] For this reason, the temperature dependence of surface tension for solid metals has been derived mainly with reference to the surface-tension data for liquid metals.[3–5,15,18] It is, however, disputable whether such an equation is valid. Therefore, reliable experimental data of surface tension for solid metals, i.e., a measurement method with high accuracy, is strongly desired for assessing the validity of temperature function of surface tension for solid metals based on surface tension for liquid metals, and for constructing the equation of the temperature dependency for solid metals with the corresponding data of solid metals alone. MASASHI NAKAMOTO, Assistant Professor, is with the Graduate School of Engineering, Osaka University, Osaka 565-0871, Japan. Contact email: [email protected] MATTI LIUKKONEN, Researcher, ERKKI HEIKINHEIMO, Chief Engineer, and LAURI HOLAPPA, Professor, Laboratory of Metallurgy, and MICHAEL FRIMAN, Researcher, and MARKO HA¨MA¨lA¨INEN, Supervising Assistant, Laboratory of Material Processing and Powder Metallurgy, are with Helsinki University of Technology, FI-02015 TKK, Espoo, Finland. Manuscript submitted February 6, 2008. Article published online August 12, 2008. 570—VOLUME 39B, AUGUST 2008
Multiphase equilibrium (MPE) is one of the methods commonly used for measuring the surface tension of solids.[19–23] This method consists of the measurements of angles at the interfaces between various phases at equilibrium. Considering the two equilibrated situations, (1) a liquid droplet on a solid polycrystalline substrate with no solubility of liquid and (2) a solid polycrystalline without droplet in Figure 1, the relations between the tensions and the angles at the interfaces lead to the following equations: rSV ¼ rLV cos h þ rSL
½1
rGB ¼ 2rSL cos ðw=2Þ
½2
rGB ¼ 2rSV cos ð/0 =2Þ
½3
rGB ¼ 2rSG cos ð/=2Þ
½4
where rSV is the surface tension of solid in gas atmosphere involving the vapor from a droplet (vapor atmosphere), rLV is the surface tension of the droplet, rSL is the interfacial tension between solid and droplet, rGB is the grain-boundary tension, and rSG is the surface tension of solid in inert atmosphere or reducing atmo
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