Application of principle component analysis–artificial neural network for simultaneous determination of zirconium and hafnium in real samples

Determination of zirconium and hafnium were done by applying singular value decomposition and a feed forward Neural Network Algorithm with back propagation of error. The determination of trace amounts of mixtures of Zr(IV) and Hf(IV) in various matrices (river, tap and industrial wastewater) were investigated by PC–ANN using the complexes formed between Alizarin Red S, Zr and Hf. The results showed that measurement is possible in the ranges of 0.03–3.4 and 0.2–7.0 μg ml−1 for Zr(IV) and Hf(IV), respectively. The detection limits were 0.02 and 0.08 μg ml−1 for Zr(IV) and Hf(IV), respectively. The results also show very good agreement between true and predicted concentration values and have the ability to use in routine analysis.