Biaxial Minerals EENS 2110 Tulane University Mineralogy Prof Stephen A Nelson Biaxial Minerals This document last updated on 04 Nov 2011 All minerals that crystallize in the orthorhombic monoclinic or triclinic crystal systems are biaxial Biaxial crystals have 2 optic axes and this distinguishes biaxial crystals from uniaxial crystals Like uniaxial crystals biaxial crystals have refractive indices that vary between two extremes but also have a unique intermediate refractive index Biaxial refractive indices are as follows The smallest refractive index is given the symbol or X The intermediate refractive index is given the symbol or Y The largest refractive index is given the symbol or Z All biaxial minerals have optical symmetry equivalent to 2 m2 m2 m But in each of the crystal systems the optical directions have different correspondence to the crystallographic directions In orthorhombic crystals the optical directions correspond to the crystallographic axes i e the X direction and its corresponding refractive index can be either the a b or c crystallographic axes the Y direction and can be parallel to either a b or c and the Z direction or can be parallel to either a b or c In monoclinic crystals one of the X Y or Z directions or indices is parallel to the b crystallographic axis and the other two do not coincide with crystallographic directions In triclinic crystals none of the optical directions or indices coincide with crystallographic directions although in some rare case one of the indices might coincide with one of the crystallographic directions The Biaxial Indicatrix The biaxial indicatrix like the isotropic and uniaxial indicatrices diagrammatically illustrates the refractive index for vibration directions of light It is shown in the diagram below Page 1 of 17 11 4 2011 Biaxial Minerals The biaxial indicatrix has three principle axes labeled and Directions that have refractive indices between and are referred to as Directions with refractive indices between and are referred to as Note that the direction also must occur in the plane that includes and Similarly if we were to draw all other possible planes that include the direction would have to occur in each of these as well This results in two sections that would be circular with a radius equivalent to the refractive index These two sections are referred to as the circular sections In the diagrams below we see the two circular sections each having a radius equal to the refractive index In the left hand diagram some of the other possible planes that include are shown In the righthand diagram these planes are removed to show only the circular sections Lines drawn perpendicular to the circular sections are the optic axes This is why minerals that exhibit these optical properties are called biaxial The acute angle between the optic axes is called the 2V angle Just like in uniaxial minerals if one is looking down one of the optic axes light traveling along the optic axis will be vibrating in the direction and thus the mineral would be extinct for all rotation positions The three principal planes of the biaxial indicatrix are shown here The plane containing the and directions also contains the optic axes which are perpendicular to the directions This plane is called the optic axial plane or OAP The other two principal planes contain the and directions and the and directions respectively Page 2 of 17 11 4 2011 Biaxial Minerals Optic Sign of Biaxial Minerals The optic sign of biaxial minerals depends on whether the refractive index is closer to that of or to There are several ways that this can be stated so we will look at all of them Biaxial Positive A mineral is biaxial positive if is closer to than to In this case the acute angle 2V between the optic axes is bisected by the refractive index direction Thus we say that is the acute bisectrix BXA because it bisects this angle If a table of optical properties of minerals reports the 2V angle it usually refers to this acute angle But some tables report the 2V as 2V or 2V Note that in the case of a biaxial positive mineral 2V is the acute bisectrix while 2V bisects the obtuse angle between the optic axes called the obtuse bisectrix BXO Biaxial Negative A mineral is biaxial negative if is closer to than to In this case the acute angle 2V between the optic axes is bisected by the refractive index direction Thus we say that is the acute bisectrix In the case of a biaxial negative mineral 2V is the acute bisectrix while 2V is the obtuse bisectrix Note that 2V 2V 180o If 2V 90o the mineral has no optic sign If 2V 0o the mineral is uniaxial Optical Orientations of Biaxial Crystals Just like in uniaxial crystals we can move the indicatrix around in a crystal so long as the indicatrix is kept parallel to the optical directions and use this as an aid to determining the Page 3 of 17 11 4 2011 Biaxial Minerals optical directions in the crystal Several orientations are possible the most general are shown in the diagram below Note that in this diagram we have not shown the crystallographic axes because different minerals will show different relationships between optical directions and crystallographic directions as discussed above If a crystal oriented on the microscope stage with its vibration direction perpendicular to the stage then the and vibration directions will be the two privileged directions in the crystal as for the face labeled A in the diagram below With such a face it would be possible to determine the and refractive indices by using the Becke line method and various oils when either of these privileged directions is oriented parallel to the polarizer Just as in uniaxial minerals the crystal would be extinct with the analyzer inserted when either of the privileged directions are parallel to the polarizer At any other orientation of the two principal vibration directions the crystal would exhibit an interference color that reflects the thickness of the crystal and the birefringence for this orientation Note that this would not be the maximum interference color for this crystal If a crystal face such as B in the diagram above is parallel to the microscope stage one would be looking down the direction in the crystal In this orientation the optic axial plane OAP would be parallel to the stage and the and refractive indices could be determined using the Becke line method and various oils Because the direction in this orientation is perpendicular to or normal to the OAP the direction