Predicting Amorphous Content of Crystalline Systems

It is desired to derive equations relating crystal phase, amorphous phase, and total composition of systems studied. The derivation is simpler if it is assumed that one mole of K2O is contained in a total system and is divided between crystalline and amorphous phases  

For ease of calculation consider two moles of KPO3 as K2O P2O5. Add z moles of P2O5 to two moles of KPO3 to adjust the ratio, /  

One mole of K2O is distributed between crystalline phases and amoiphous phases. Therefore 

When it is assumed that [KPOaJn is the only crystalline phase, then the amoiphous phase must contain at least z moles of P2O5. Therefore the amorphous phase must contain 

When = 0.5, y = z and the total system is amorphous. This agrees with experimental results. The phase status of a solidified melt is controlled by the K2O-P2O5 ratio, and a sample s thermal history. Recalling that z is moles of P2O5 added per two moles of KPO3, it can be shown that 

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