Spontaneous formation of a surface dislocation loop

The corresponding work done against the background elastic deformation field due to mismatch is 

The total work done in forming the dislocation is then 

For very small values of R/h, the behavior of the function is dominated by W R), and W R) increases from fF(0) = 0 with increasing R/h. On the other hand, for large values of R/b, the behavior is dominated by and W R) decreases to ever more negative values. The function assumes a maximum value at some intermediate value of R this maximum value represents the activation energy that must be supplied through random thermal fluctuations in order to nucleate a dislocation in the form of a surface half loop. The value of R at which this maximum occurs, say i2max satisfies the equation iF (i2max) = 0 which implies that 

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