The target is devided into $64 \times 64 \times 100$ cells with a side length of $3 \, nm$. Each of it has a state (crystalline/amorphous) and keeps the local carbon concentration. The cell is addressed by a position vector $\vec r = (k,l,m)$, where $k$, $l$, $m$ are integers.
The probability of amorphization is assumed to be proportional to the nuclear stopping power. A local probability of amorphization at any point in the target is composed of three contributions, the ballistic amorphization, a carbon-induced and a stress-induced amorphization. The ballistic amorphization is proportional to the nuclear stopping power as mentioned before. The carbon-induced amorphization is a linear function of the local carbon concentration. The stress-induced amorphization is proportional to the compressive stress originating from the amorphous volumes in the vicinity, the stress amplitude decreasing with the square of distance $d=|\vec r - \vec{r'}|$. Thus the probability of a crystalline volume getting amorphous can be calculated as
The target is devided into $64 \times 64 \times 100$ cells with a side length of $3 \, nm$. Each of it has a state (crystalline/amorphous) and keeps the local carbon concentration. The cell is addressed by a position vector $\vec r = (k,l,m)$, where $k$, $l$, $m$ are integers.
The probability of amorphization is assumed to be proportional to the nuclear stopping power. A local probability of amorphization at any point in the target is composed of three contributions, the ballistic amorphization, a carbon-induced and a stress-induced amorphization. The ballistic amorphization is proportional to the nuclear stopping power as mentioned before. The carbon-induced amorphization is a linear function of the local carbon concentration. The stress-induced amorphization is proportional to the compressive stress originating from the amorphous volumes in the vicinity, the stress amplitude decreasing with the square of distance $d=|\vec r - \vec{r'}|$. Thus the probability of a crystalline volume getting amorphous can be calculated as