Thermodynamics of Melt Growth

Melt growth is the formation of a crystalline solid from a liquid phase that has essentially the same composition as the solid. If the composition of the liquid shows a larger deviation from that of the solid one deals with solution growth. Fundamentals of thermodynamics of melt growth can be found, e.g. in (15). 

Whenever possible, crystals should be grown from melt The main reason is that mass transport is not required. The two most important, most widely apphcable techniques of melt growth are the Czochralski technique and the Bridgman technique, both with a number of special variants. 

The melting point Tm of a solid is the temperature at which solid and liquid are in equilibrium at a given pressure P. The normal melting point of a solid is its melting point at P = 1 bar. For a one omponent system, once the temperature is chosen, the pressure is fixed, and vice versa. 

At the melting temperature Tm discontinuous changes occur in entropy S s), volume V(s) and the enthalpy Hfs) of the solid, the typical characteristics of a first-order phase transition. 

At all temperatures the liquid has a higher enthalpy (internal energy) than the sohd. Therefore, upon crystallization latent heat is released (i.e. solidification from a melt is an exothermic process), the amount of which is equal to the heat of melting, but with opposite sign  

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