1. Thermodynamic data A tutorial course Session 6: Modelling Surface Tension Alan Dinsdale “Thermochemistry of Materials” SRC

2. General Conclusions Based on the approach of Tanaka Using the Butler equation to estimate the surface tension from bulk thermodynamic properties Tested with success for metallic and ionic melts Assumes an equilibrium between the bulk liquid and the surface liquid Generalised and extended in this project to cover multicomponent systems Tested in detail for solder systems – Uses the new database for solders – Makes use of Brian Keene’s review of experimental surface tension data for tin and lead free solders (1993) Surface tension is affected by surface active components such as O and S Concentration of soluble O and S is affected by other elements but this will also be determined from the thermodynamic model

3. Model for surface tension (1) As originally presented: This relates the surface tension of the binary alloy to the surface tension of the pure components and the thermodynamic properties of the bulk and the surface monolayer

4. Model for surface tension (2) These equations can be transformed into: and expresses that the chemical potential of the components is equal in the bulk and surface layer The thermodynamic properties of the bulk are well represented by standard thermodynamic models

5. Model for surface tension (3) The thermodynamic properties of the surface layer is given by: where A 1 is the surface area of component 1,  1 is the surface tension of component 1 N 0 is the Avogadro number and V 1 the molar volume of component 1

6. Model for surface tension (4) There is an empirical relationship between G mix, the excess Gibbs energy of mixing, for the surface and G mix for the bulk Gibbs energy of surface layer given by: The surface tension, , is calculated to be the value which just brings the surface into equilibrium with the bulk. This allow the model to be generalised to any number of components

7. Sample calculations: Bi-Sn 608 K

8. Surface composition: Bi-Sn 608 K

9. Ag-Sn 1273 K

10. Ag-Sn 40%Sn : effect of temperature

11. Sn-Ag-Cu: variation with temperature

12. Surface tension of pure Sn

13. Surface tension of pure Pb