Ising Model Surface Roughening

In the Ising surface model the crystal fluid phase is partitioned at the interface between the solid and fluid, with the crystal interface considered as a gradient in solid and fluids cells, going from complete solid to a complete fluid phase. Using the concepts introduced by Onsager, the dimensionless Ising temperature (dyk) that corresponds to the order-disorder phase transition can be calculated  

The essential feature of any growth model is the recognition of the importance of steps in the growth process. The surface is not perfectly flat but will be covered with steps arising from various processes. Attachment involves the interaction of the absorbed growth entity with these steps.The growth rate is 

The principal difference between the above theories is the way in whieh attachment is treated to either a flat or rough surface. Aggregates of molecules on the surface form a nucleus for growth and will ultimately form a step growth will also be possible at a dislocation. 

5 Sources of Nucleation Sites on Surfaces, Steps and Dislocations 

Any factors that can affect either the formation or movement of the growth entity will influence the type of morphology that is created, and therefore is a fundamental issue when considering crystal growth. 

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The essential influence of surface roughening is also present in this model. Grand canonical Monte Carlo calculations were used to generate adatom populations at various temperatures up to Chemical potentials corresponding to those in the bulk LJ crystal were used, and these produced adatom densities that increased with temperature and roughly approximated the values observed in Ising model simulations below T. ... 

This surface tension /int(T, H) is singular at the roughening transition temperature 7r, as well as at the bulk critical temperature Tc of the Ising model. 

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