The Free Energy of Surface Segregation in Binary Systems
The Langmuir-McLean equation for segregation, when using the regular solution model for a binary system, is valid for surface segregation (although sometimes the equation will be written replacing with ) . The free energy of surface segregation is . The enthalpy is given by
where and are matrix surface energies without and with solute, is their heat of mixing, Z and are the coordination numbers in the matrix and at the surface, and is the coordination number for surface atoms to the layer below. The last term in this equation is the elastic strain energy, given above, and is governed by the mismatch between the solute and the matrix atoms. For solid metals, the surface energies scale with the melting points. The surface segregation enrichment ratio increases when the solute atom size is larger than the matrix atom size and when the melting point of the solute is lower than that of the matrix .
A chemisorbed gaseous species on the surface can also have an effect on the surface composition of a binary alloy. In the presence of a coverage of a chemisorbed species theta, it is proposed that the Langmuir-McLean model is valid with the free energy of surface segregation given by, where
and are the chemisorption energies of the gas on solute A and matrix B and Θ is the fractional coverage. At high temperatures, evaporation from the surface can take place, causing a deviation from the McLean equation. At lower temperatures, both grain boundary and surface segregation can be limited by the diffusion of atoms from the bulk to the surface or interface.
Read more about this topic: Segregation In Materials, Theories of Segregation
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