MATS 201B SOLID STATE DIFFUSION Problem Set 4 Due: Dec. 6, 2012

1. The growth of a single phase Al3Ti between Al and Ti follows diffusion growth with x2 = A t where A= 2.0 X10-20 cm2/s at 250 °C. The concentration drop ΔCeq = 1 at %, and G = 4.7. Calculate the interdiffusion coefficient at 250 °C. 2. The feasibility of bonding laminated composites was investigated by cold-roll bonding, followed by diffusion welding of alternating 50 µm layers of Al and Ti at 660 °C for 4 hr (see figures for sample before and after annealing). In other studies of aluminide formation, the diffusion flux ratio for Al to Ti is 13:1 for TiAl3 formation. (The density of Al is 4.21X1022 atoms/cm3 and the density of Ti is 4.16X1022 atoms/cm3.)

(a) For the diffusion-welded sample (after annealing at 660 °C for 4 hr) alternating layers of ~75 µm TiAl3 and ~25 µm Ti were observed as shown below. Explain why the Al-rich layers become wider and Ti layers become thinner with annealing. (b) A new sample is made with alternating layers of Al and Ti each 5 nm thick and heated at 1100 °C until interdiffusion occurs. If the dislocation density of the film is 108 /cm2 and the grain size is 100 nm, what is the ratio of Deff to the lattice diffusivity? (c) A sacrificial barrier of Ti is used between Al and Si to delay Al diffusion into Si (called Al spiking). At 500 °C, Ti reacts negligibly with Si, but reacts with Al to form a continuous and uniform layer of TiAl3. When the Ti is consumed, the sacrificial barrier is also consumed. If a layer of 100 nm Ti is consumed to form TiAl3, by a diffusion-controlled reaction such that the effective diffusion coefficient is D(cm2/s) =0.15exp(-1.85 ev/kT), estimate the lifetime of the barrier (see figures below)

3. MgO-based magnetic tunnel junctions (MTJ) (eg. Fe/MgO/Fe tunnel junctions) are a strong candidate for next generation magnetic random access memory (MRAM) due to the observation of large tunneling magnetoresistance and spin-torque switching for read and write operations, respectively. MgO is an FCC non-stoichiometric semiconducting oxide in which the dominant defects are cation vacancies and holes. (a) Derive an expression for DMg as a function of the oxygen partial pressure. (b) Suppose Fe forms Fe2O3 in the MTJ. Then MgO and Fe2O3 form a diffusion couple, and assuming that the dominant diffusing species are charged vacancies, derive an expression for the interdiffusion coefficient for this system.