On extinction angles cΛZ´ of monclinic and rhombic pyroxenes in random sections

Abstract

In the orthoscopic observation, we usually observe pyroxenes at random orientation, and therefore, we get extinction angles measured on that random section. Calculation of an extinction angle on a given section is necessary, if we observe statistically arbitrary extinction angles of numerous pyroxenes, especialy in groundmass of volcanic rocks, in which both monoclinic and rhombic pyroxenes are present. General formulas for an extinction angle on a given section of pyroxenes are given in this paper. Some optical features commonly described in many textbooks can be explained as special cases of these formulas. Formulas (1), (2) and (3) are for monoclinic pyroxenes (b=Y), (1), (5) and (6) are for rhombic ones. The symbols used here are as follows : c∧Z=δ, c∧Z';=φφ, θ_x, θ_y, θ_z:, are the angles between a normal to a given section and X-, Y-, and Z-axes respectively. If the normal to a given section is plotted on the axial plane ZX, then the angle between this plotted line and the c-axis is ρ, which corresponds to longitude. Also if we plot two angles between c-axis and two optical axes on a given section, then plotted angles are represented by ζ and ζ ', respectively. The results of calculation of φ by given values of c∧Z and 2Ω in the formulas (2) and (6) are shown in Fig. 2 for monoclinic pyroxenes and Fig. 3 for rhombic pyro-xenes. The figures are indicated by stereographic projections of lines of equal extinction angle.