Diffusion in interfaces on surfaces and along dislocations

1. d Diffusion in interfaces on surfaces and along dislocations Grain Boundary Diffusion : Diffusion along grain boundaries is more rapid than normal lattice diffusion. Packing density in a grain boundary is less than the perfect lattice so atoms can change places more easily.

2. where and Consider the following model of steady state diffusion: JGB JL d d >> : is the GB width ~ 0.5nm Isotope diffusion experiments indicate that When is GB diffusion important? Depends upon GB width δ, grain size d and also DGB / DL.

3. Suppose there are NT atoms per unit time diffusing through a grain of width d with boundary width δ. from Fick’s 1st law – assuming steady state

4. or So obviously Grain boundary diffusion is important for Now recall So that Defining an apparent diffusion coefficient

5. and log D DGB Dapp DL DGB(δ/d) 1 / T Typically At low temperature there is an important contribution of DGB to the flux. The cross-over occurs at ~ 0.75 Tmp.

6. JL Jp following a procedure similar to the gb case Diffusion along Dislocations => Dislocation –core diffusion often referred to as “pipeline diffusion” Dislocation

7. Here g is the sum of the pipe cross-sectional areas per unit area of matrix. For example the core radius is ~ 10 -8 cm and a well-annealed metal contains as 106disl/ cm2 so: Dislocation effects can become important below as 0.5 Tmp.

8. Adatom Ledge adtom kink Terrace vacancy Surface Diffusion at high temp Ds is dominated by adatom migration at low temp Ds is dominated by surface vacancy migration Terrace-ledge-kink surface

9. } } Adatom equil. Pop. Surf vac. equil. Pop. No is the # of terrace sites per unit area. For metals No ~ 1015 cm2.

10. where and The total surface flux contains contributions from vacancies and ad-atoms. :

11. Measurement of Ds: Most measurements have involved so-called mass transfer methods. Da has been measured for tungsten using for FIM W d A(t) Curved arrows indicates mass - flow Sinusoidal profile decay Scratch smoothening

12. W where k is the curvature. vm is the molar volume. Assume the surface has one principal curvature. Assuming g is the isotropic. Grain boundary grooving

13. Grain Boundary Grooving W Sinusoidal profile decay A(t) A positively curved surface has a higher chemical potential than either a flat or a negatively curved surface so mass will flows along surface from the hills to the valleys.

14. A(t) Field Emission Tip Protrusions build up with field on and decay exponentially with field off.