Practical Electron Microscopy and Database

As an example, assuming Ti (titanium) film is first deposited on a Si substrate, the free energy of the system will change if the Ti atoms react with the Si atoms to form titanium silicide (TiSi₂) film. To form a TiSi₂ layer in thickness t, 0.4t of the Ti film and 0.9t of the Si substrate need to be consumed. Therefore the free energy change ΔG to form the TiSi₂ layer is,
          ΔG = A [(G_0TiSi2 - 0.4G_0Ti - 0.9G_0Si)t + γ_TiSi2+ γ_TiSi2/Si - γ_Si] = AΔγ ----------------------------- [144]
where,
          G_0TiSi2 -- The volume term of TiSi₂,
          G_0Ti -- The volume term of Ti,
          G_0Si -- The volume term of Si,
          Δγ -- The surface/interface term of the Gibbs free energy change,
          γ_Si -- The Si substrate surface energy,
          γ_TiSi2/Si -- The TiSi₂/Si interface energy
          γ_TiSi2 -- The TiSi₂ surface energy.

Note that the driving force for the C49 to C54 transition is the energy differences of G_0TiSi2, γ_TiSi2/Si, and γ_TiSi2. for the two phases.