Optical Mineralogy in a Nutshell Use of the petrographic microscope in three easy lessons Courtesy of Jane Selverstone University of New Mexico Part II © Jane Selverstone Quick review • Isotropic minerals –velocity changes as light enters mineral, but then is the same in all directions thru xtl; no rotation or splitting of light. These minerals are characterized by a single RI (because light travels w/ same speed throughout xtl) • Anisotropic minerals –light entering xtls is split and reoriented into two plane-polarized components that vibrate perpendicular to one another and travel w/ different speeds. • Uniaxial minerals have one special direction along which light is not reoriented; characterized by 2 RIs. • Biaxial minerals have two special directions along which light is not reoriented; characterized by 3 RIs. Determining if mineral is uniaxial or biaxial or uniaxial biaxial If uniaxial, isogyres define If biaxial, isogyres define curve that cross; arms remain N-S/E-W rotates with stage, or cross that as stage is rotated breaks up as stage is rotated Reminder about how to get an interference figure 1. Find a grain that stays dark as stage is rotated 2. Go to highest power objective 3. Insert Bertrand Lens 4. Look down scope and rotate stage Determining optic sign Now determine the optic sign of the mineral: 1. Rotate stage until isogyre is concave to NE (if biaxial) 2. Insert gypsum accessory plate 3. Note color in NE, immediately adjacent to isogyre -- Blue = (+) Yellow = (-) uniaxial (+) (+) biaxial We’ve talked about minerals as magicians - now let’s prove it! c a l c i t e c a lc it e c alc ite calcite calcite ordinary ω ray, extraordinary (stays stationary) ray, ε (rotates) Conclusions from calcite experiment • single light ray coming into cc is split into two • ε ray is refracted - changes direction & speed • rays have different velocities, hence different RIs • stationary ray=ordinary, rotating ray=extraordinary • because refraction of ε is so large, cc must have hi δ (remember: δ = nhi -nlo) If we were to look straight down c-axis, we would see only one dot – no splitting! C-axis is optic axis (true for all uniaxial minerals, but unfortunately not for biaxial minerals) More on this in a few minutes… Birefringence/interference colors birefringence Thickness in microns Retardation in nanometers Back to birefringence/interference colors ∆=retardation Observation: frequency of fast ray light remains unchanged (low n) during splitting, regardless of slow ray material (high n) d F= V/λ mineral if light speed changes, grain λ must also change plane polarized light λ is related to color; if λ changes, color changes • waves from the two rays can be in lower polarizer phase or out of phase upon leaving the crystal Interference phenomena • When waves are in phase, all light gets killed • When waves are out of phase, some component of light gets through upper polarizer and the grain displays an interference color; color depends on retardation • When one of the vibration directions is parallel to the lower polarizer, no light gets through the upper polarizer and the grain is “at extinction”(=black) At time t, when slow ray 1st exits xtl: Slow ray has traveled distance d Fast ray has traveled distance d+∆ ∆=retardation time = distance/rate fast ray (low n) Slow ray: t = d/Vslow slow ray (high n) Fast ray: t= d/Vfast + ∆/Vair d Therefore: d/Vslow = d/Vfast + ∆/Vair mineral ∆ = d(Vair/Vslow -Vair/Vfast) grain ∆ = d(nslow -nfast) plane polarized ∆ = d δ light ∆ = thickness of t.s. x birefringence lower polarizer Determining optic sign with the gypsum plate - what happens? blue in NE = (+) Gypsum plate has constant ∆ of 530 nm = 1st-order pink ow sl Isogyres = black: ∆=0 Background = gray: ∆=150 Add to/subtract from 530 nm: 530+150=680 nm = blue = (+) 530-150=380 nm = yellowish = (-) Addition = slow + slow Subtraction = slow + fast Let’s look at interference colors in a natural thin section: plag ol plag ol Ifol everyplag grain of the same mineralplag looks different, how are weol ever going to beplag able to identifyol anything?? ol plag Note that different grains of the same mineral show different interference colors – why?? Different grains of same mineral are in different orientations Time for some new tricks: the optical indicatrix Thought experiment: Consider an isotropic mineral (e.g., garnet) Imagine point source of light at garnet center; turn light on for fixed amount of time, then map out distance traveled by light in that time What geometric shape is defined by mapped light rays? Isotropic indicatrix Light travels the same Soccer ball distance in all directions; (or an orange) n is same everywhere, thus δ = nhi-nlo = 0 = black anisotropic minerals - uniaxial indicatrix c-axis c-axis calcite quartz Let’s perform the same thought experiment… Uniaxial indicatrix c-axis c-axis tangerine = uniaxial (-) calcite Spaghetti squash = uniaxial (+) quartz (this is not strictly correct, but works for our purposes…) Uniaxial indicatrix nω nε nω nω Circular section is perpendicular to the stem (c-axis) Uniaxial indicatrix (biaxial ellipsoid) c=Z c=Z nε nε n n ω a=X ω a=X b=Y b=Y What can the indicatrix tell us about optical properties of individual grains? Propagate light along the c-axis, note what happens to it in plane of thin section c=Z nε nω a=X nω b=Y nω nω -nω = 0 therefore, δ=0: grain stays black (same as the isotropic case) Now propagate light perpendicular to c-axis N nε -nω > 0 therefore, δ > 0 n nωnω nω ω WEn nε ω n n ε n n ε ε ε S Grain changes color upon rotation. Grain will go black whenever indicatrix axis is E-W or N-S This orientation will show the maximum δ of the mineral anisotropic minerals - biaxial indicatrix feldspar clinopyroxene Now things get a lot more complicated… Biaxial indicatrix (triaxial ellipsoid) 2Vz Z OA OA 2Vz nγ nβ nβ nα X The potato! nβ Y nγ nγ nα nβ nα nβ There are 2 different ways to cut this and get a circle… Alas, the potato (indicatrix) can have any orientation within a biaxial mineral… c Y c olivine Z augite (cpx) b b Y a X Z a X … but there are a few generalizations that we can make The potato has 3 perpendicular principal axes of different length – thus, we need 3 different RIs to describe a biaxial mineral X direction = nα (lowest) Y direction = nβ (intermed; radius of circ. section) Z direction = nγ (highest) • Orthorhombic: axes of indicatrix coincide w/ xtl axes • Monoclinic: Y axis coincides w/ one xtl axis • Triclinic: none of the indicatrix axes coincide w/ xtl axes 2V: a diagnostic property of biaxial minerals Z OA OA • When 2V is acute about Z: (+) 2Vz • When 2V is acute about X: (-) • When 2V=90°, sign is indeterminate nγ • When 2V=0°, mineral is uniaxial nα X nβ Y 2V is measured using an interference figure… More in a few minutes How interference figures work (uniaxial example) Converging lenses force light Bertrand rays to follow different paths lens through the indicatrix N-S polarizer What do we see?? Sample (looking down OA) ω ε ω ε substage condensor ε ε ω ω Effects of multiple cuts thru indicatrix WE Biaxial interference figures There are lots of types of biaxial figures… we’ll concentrate on only two 1. Optic axis figure - pick a grain that stays dark on rotation Will see one determine sign w/ gypsum plate curved isogyre (+) (-) determine 2V from curvature of isogyre 90° 60° 40° See Nesse or handout Biaxial interference figures 2. Bxa figure (acute bisectrix) - obtained when you are looking straight down between the two O.A.s. Hard to find, but look for a grain with intermediate δ. Z OA OA 2Vz nγ nα X nβ Y Use this figure to get sign and 2V: (+) 2V=20° 2V=40° 2V=60° See handout/Nesse Quick review of why we use indicatrix: Indicatrix gives us a way to relate optical phenomena to crystallographic orientation, and to explain differences between grains of the same mineral in thin section Z OA OA 2Vz hi δ nγ nα X nβ Y Z OA OA 2Vz lo δ nγ nα X nβ Y Isotropic? Uniaxial? Biaxial? Sign? 2V? All of these help us to uniquely identify unknown minerals..