Extinction-angle distribution of plagioclase feldspars in clastic sediments

An extinction-angle distribution was computed for randomly oriented grains of plagioclase feldspar with a known An-composition. Expressed by a histogram with eighteen columns, the results are shown by an 18×19 data array for nineteen types of low-temperature plagioclase. In a mixture of grains with various An-compositions, the extinction-angle distribution is given by a linear combination of the obtained data matrix with the frequencies of An-composition. If we have a sample containing randomly oriented grains of plagioclase feldspars, a frequency distribution of those with An-composition can be calculated after measuring their extinction angles. By taking into account the constraints of inequalities, the calculation is treated with the dual method of linear programming. The procedure provides for a simpler and more expedient method for determining the frequency distribution of An-composition. This method was tested by applying it to a model sample containing randomly oriented plagioclase grains with known An-composition frequencies, whose extinction-angle distribution was determined by the Monte Carlo method. An example of application of this method to Permian sandstones from central Japan is presented.