A NEW METHOD TO EVALUATE FRACTIONAL CRYSTALLIZATION IN IGNEOUS ROCKS

A new method to evaluate the role of fractional crystallization is presented in this paper, based on the Rayleigh Law for trace elements. A major element "j" (x) and a trace element "i" (y) of a set of samples (with constant bulk distribution coefficient D(i)) are plotted on a logarithmic diagram. This diagram uses transformate variables (x, y) such as x = log[log(M(o)j - M(e)j) - log(M(l)j - M(e)j)] nad y = log[log(C(l)i/C(o)i)], where (M(l)i, C(l)i) = the concentration of major and trace elements in any sample, (M(o)i, C(o)i) = concentration of major and trace elements close to the most differentiated sample, and M(e)j = the concentration of major elements in the fractionate. In this plot, the slope is equal to one and the y intercept is log(D)(i) - 1). We can fit the data set by the least squares method setting several values of M(e)i until the slope is equal to one. In this way, D(i) and M(e)j are determined, permitting: (i) the calculation of D(i) for all available trace elements; (ii) the determination of the chemical composition of the fractionate, and (iii) the calculation of remnant magma fraction values for any sample on the trend.