Iron catalytic nanoparticle formation

ME574(W13) TEAM 4

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Introduction

Theory

Numerical Method

Modeling

Result

Conclusion

Code/Ref.

Modeling

For simplification we assume vacuum condition during annealing. Also we limit the study to only one particle formed from a 2 nm long film in this model rather than a continuous thing film.

Node selection

By using the symmetry, we initially set 5 nodes as follows:

The initial setting of distance between nodes is 0.5 nm. In order to not conflict between nodes and simulate the smooth surface shape, the nodes are removed when the distance between them goes less than 0.05 nm and added when the distance is larger than 0.3 nm during the program code running. A small number was added to the non J diagonal terms to reduce singularity of the matrix and large values were added to end nodes to desired x or y coordinate and to not allow flux (see code for size of values, see class notes for guidelines on small number).

Parameter setting

Since we assume that there is no vapor phase during the annealing process, the evaporation-condensation effect is negligible. Therefore we set L λ ² /M = 10⁻⁶ with λ =1 (nm) in the numerical simulation according to the lecture note (n9 at page 58).

Then the normal velocity of the surface can be changed to

W is considered zero, v can also be described,

If we assume MΩ²ϒ as a constant, then the annealing time t* in this simulation is related to the real time t as,

We arbitrarily set the surface tension as 1 and mobility M was set to be the diffusion coefficient from Ref 2, using the 790 as the temperature transition between the two sections;