Integration Controlled Crystal Growth Rate

If the mass transfer of the solute from the bulk solution to the crystal surface is fast enough, the crystal growth is predominantly determined by the steps occurring on the crystal surface, such as surface adsorption, surface diffusion, dehydration, lattice integration, etc. Sometimes, all of the steps occurring on the crystal surface are collectively called "surface integration.'' Since the growth steps on the crystal surface are complicatedly dependent on the supersaturation, it is very difficult to fully describe the surface integration phenomena with mathematics. Fortunately, however, the rate of the overall surface integration is controlled by one step and then it may be simply expressed by a power-law equation.

where kr is the surface integration coefficient and r is the order of the surface integration. Although the power-law expression is too simple to analytically predict all of the steps, it is often used to estimate the crystal growth in industrial crystallization.

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