film thickness which partially controls the nanocrystalline grain size is an integral part of the size scale. In the thin film review it was found that a Cu/Ti/SiO2/Si film system had a value of c = 60 nm [3]. 0 10 20 30 40 50 100 200 300 400 500 KI th, MPa m 1/2 T, K H- free H Figure 4. Comparison of Eq. (2) to hydrogen-affected threshold stress intensities for Fe3%Si crystals. Here, yield strength was given by [ ] 1/ 2 0 1 − = + h ys β σ σ (3) where σ0 = 400 MPa, β = 0.287 µm1/2 and h = film thickness. With measured values of GIG = 3.6 J/m2 for interface fracture in Cu/Ti/SiO2/Si and E = 120 GPa, it was a simple matter to calculate kIG = (EGIG) 1/2 to be 0.66 MPa-m1/2 and from that determine c = 60 nm at Kc = kIG using Eqn. (2). The fit to all the data using Eqn. (2) with yield strength varying as a function of thickness from Eqn. (3) is shown in Figure 5. Cathodically charging the same copper films at 60 mA/cm2 for 70 s in 1 M NaOH reduced the fracture resistance as shown in Figure 5. By allowing a small decrease in the Griffith stress intensity from 0.66 to 0.59 MPa-m1/2 due to hydrogen, Eqn. (2) also predicts the decrease in strain energy release rate. For the hydrogen case here, it is seen that a 20% drop in the surface energy can lead to a 50% decrease in the practical work of adhesion for the 1 µm size film in Figure 5. What does this approach imply for hydrogen embrittlement mechanisms at different levels of scale? Reexamination of Eqn. (2) reveals several aspects perhaps unappreciated prior to recent studies of thin films:
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