Optical Mineralogy Part II Lecture PDF

Optical Mineralogy Part II Compiled By: Prof. Fathy Hassan  OPTICAL MINERALOGY Introduction to Mineral Module...

Optical Mineralogy Part II Compiled By: Prof. Fathy Hassan  OPTICAL MINERALOGY Introduction to Mineral Module Identification Plane- Basic Concepts Polarized light Crossed- Petrological Nature of Light Microscope Polarized light Shape Refractive Absorption Cleavage Relief Colour Index Scheme Interference Interference of Light Extinction Twinning Birefringence Indicatrix Figures  Observation with Analyzer Inserted (Crossed-polarizers Mode) Observation with Analyzer Inserted (Crossed-polarizers Mode) Extinction behaviour: The rotation of a birefringent crystal section between crossed polarizers involves a periodic change between a bright image and a dark image. A full rotation of the stage involves four extinction positions separated by 90° and four bright images in between. The four orientations of maximum brightness are also referred to as diagonal positions. Extinction positions and diagonal positions of a quartz grain during a 360° rotation of the stage. Observation with Analyzer Inserted (Crossed-polarizers Mode) In the extinction position the E-W vibrating waves leaving the polarizer are exactly parallel to one of the two possible vibration directions of the crystal Hence, the waves are not split up and pass the mineral without any change in vibration direction as E-W vibrating waves which propagate with the velocity specific to that direction in the crystal. Taking the optically uniaxial quartz as an example, either the E- or the O-waves with the refractive indices ne' resp. n0 are parallel to the polarizer. After leaving the crystal, the E-W vibrating waves are blocked by the N-S oriented analyzer, and the crystal appears black. If the crystal is rotated out of the extinction position, the plane of polarization of the light entering the crystal is no longer parallel to any of the principal vibration directions in the crystal. The E-W vibrating waves leaving the polarizer are therefore split up in the crystal into two orthogonally vibrating waves with refractive indices ne' and nx’ ,in the general case of an anisotropic mineral.  At time t, when slow ray 1st exits xtl:  =retardation Slow ray has traveled distance d Fast ray has traveled distance d+  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 Grain  = d(Vair/Vslow - Vair/Vfast) Plane  = d(nslow - nfast) Polarized light  = d*  = thickness of Thin Section x birefringence Lower Polarizer  Observation with Analyzer Inserted (Crossed-polarizers Mode) As the light waves enter the analyzer, two extreme cases can be distinguished: Case A: If the retardation of the two waves corresponds to a phase shift of zero or whole number multiples of , the condition of complete destructive interference is realized. The components of this particular wavelength vibrate in opposite directions and hence obliterate each other. No light is passing the analyzer. Case B: If the retardation of the two waves corresponds to a phase shift of l /2 or odd-number multiples of l /2, the condition of maximum constructive interference is realized. The components of this particular wavelength vibrate parallel (“in phase”) and thus are superimposed to form an interference wave of maximum amplitude (i.e., maximum light intensity). The light is completely transmitted by the analyzer.  Original ♣ If retardation is an integer number of wavelengths: polarized ♣ Components resolve into vibration direction same as original direction direction ♣ All light is blocked by analyzer  = 1,2,3…  Privileged direction of Resolved vibration analyzer direction – Identical to original direction All light blocked =  = 1, 2, 3…  extinct Resolvedvibration Resolved vibration direction direction  Original ♣ If retardation is half integer of wavelength polarized ♣ Components resolve into vibration direction 90º to direction original ♣ Light passes through analyzer Privileged direction of Resolved analyzer vibration directions 90º to original direction All light  = ½, 3/2, 5/2…  passes Difference between our 2 rays ♣ Apparent birefringence –  ♣ Maximum birefringence & retardation when c axis is parallel to stage – difference in refractive ♣ Birefringence & retardation = 0 when c axis is index (speed) between the 2 perpendicular to stage (optic axis) rays ♣ Intermediate birefringence & retardation for ♣ Retardation –  → distance intermediate orientation separating the 2 rays ♣ Still talking about monochromatic light ♣ If retardation is an integer number of ♣ Retardation therefore is a wavelengths: function of the apparent ♣ Components resolve into vibration direction same birefringence and the as original direction ♣ All light is blocked by analyzer thickness of the crystal → ♣ If retardation is half integer of wavelength ideally all thin sections are ♣ Components resolve into vibration direction 90º to 0.3 mm, but mistakes do original ♣ Light passes through analyzer happen… Interference Colours In contrast to monochromatic light, the use of white light provides a full spectrum of wavelengths (spectral colours) which, for a given retardation, is modified in the analyzer through interference such that certain wavelengths are transmitted at full intensity; others are reduced to a variable degree or are obliterated entirely. White light exiting a colourless anisotropic crystal comprises an infinite number of wave couples corresponding to all spectral colours, each wavelength represented by a wave couple with mutually orthogonal vibration directions that are fixed by the crystal's orientation. Any specific retardation, generating a characteristic wavelength spectrum and wave amplitude pattern, which in combination produce a unique interference colour. Evidently, interference colours can only be generated from polychromatic light. Interference Colour Chart ♣ To give a few examples: In the lower range of retardation ( = 0 200 nm) black and grey colour tones dominate. The range  = 400 500 nm shows characteristic orange to light red interference colours, as blue and green wavelengths are suppressed, while longer wavelengths dominate the spectrum. ♣ This situation is reverse in the range  = 600 650 nm. Here, the shorter wavelengths dominate, which results in a blue interference colour. The distinctive purple colour at  = 551 nm ("first-order red") lies in a position where the intermediate wavelengths (green to orange) are "filtered out", while red and blue hues dominate. ♣ Thus, the interference colour spectrum starts with black ( = 0) and progresses through grey, white, yellow, and orange to a succession of intense colours of red → blue → green → yellow → orange → red, which repeats itself with increasing retardation, while getting more and more pale (Michel-Lévy colour chart).  Michel-Lévy Colour Chart The colour sequence is subdivided intoth colour orders using the distinctive purplish reds (in steps of 551 nm). From the 4 order upwards, the interference colours are dominated by alternating greenish and reddish hues. With increasing retardation these fade more and more and eventually approach white. This is referred to as high-order white. The first graphical presentation between retardation, crystal thickness and birefringence [ =d*(nz–nx)] was published by Michel-Lévy (1888). When using interference colours for the determination of minerals it has to be kept in mind that the retardation which accumulates as the waves pass through the crystal is not only dependent on ∆n of that particular crystal section, but also on the thickness of the sample. Therefore, thin sections are prepared with a defined standard thickness (commonly 25 or 30 µm). Let’s look at interference colors in a natural thin section: Reached Eye Light and colours Now insert a thin section of a rock plag ol plag in many phases and with many Light vibrating wavelengths ol ol plag plag plag ol ol Light vibrating E-W East (Right) West (Left) ol plag Unpolarized Light Note that different grains of the same mineral show different interference colors, why? Conclusion has to be that minerals somehow reorient the planes in which light is vibrating; some light passes through the upper polarizer Optical Properties Using Crossed- polarizers Mode (CPL)  Isotropism Most mineral grains change color as the stage is rotated; these grains go black 4 Isotropic minerals: show optical behaviour times in 360º rotation-exactly every 90º that is independent of the direction of light propagation. This means, their optical properties (light velocity, These minerals are refractive index and colour) are identical in all Anisotropic directions. Another important characteristic of optically isotropic materials is that light waves do not experience any change in vibration direction. This means that E-W vibrating plane-polarized light waves maintain their E-W orientation after passing through the isotropic materials (glass, mineral). Therefore, they are blocked by the analyzer, which is a N-S oriented polarizer. Anisotropic minerals: as mentioned before, These minerals are The rotation of a birefringent crystal section between Isotropic crossed polarizers involves a periodic change between a bright image and a dark image. A full rotation of the stage involves four extinction positions separated by 90° and four bright images in between. The four Glass and a few minerals stay black in orientations of maximum brightness are also referred to as diagonal positions. all orientations  Extinction Many grains in a thin section go dark (extinct) every 90º of rotation Cause for extinction is orientation of vibration directions Occurs when principal vibration directions are parallel to vibration directions of upper and lower polarizers Light retains original polarized direction Light blocked by analyzer The angle between a vibration direction and the morphological reference element (crystal edge, cleavage, twin plane) in a crystal section is referred to as the extinction angle (EA). Extinction angles are useful for the characterisation of monoclinic and triclinic minerals. Extinction Types of Extinction and Determination of the Angle Three general types of extinction can be Extinction distinguished: Parallel extinction: the vibration directions lie Types parallel to the morphological reference directions (EA = 0°). Symmetrical extinction: the vibration directions Measuring the Extinction bisect the angles between two equivalent morphological reference directions (EA1 = EA2). Angle Inclined extinction: the vibration directions form any angle (EA ≠ 0°, ≠ 90°) with morphological reference directions. Measuring the Extinction Angle: Rotate the stage so that the reference line coincides with the N-S direction and record the stage reading. The stage is rotated and turned slowly until maximum extinction occurs and record the stage reading. The difference between the two readings is the extinction angle. Extinction Angle (EA) = I - II = 14º Parallel Extinction Inclined Extinction All uniaxial minerals show parallel Monoclinic and triclinic minerals: extinction indicatrix axes do not coincide with Orthorhombic minerals show crystallographic axes. parallel extinction These minerals have inclined (this is because the crystal axes and extinction indicatrix axes coincide) (and extinction angle helps to identify them) CPL Extinction Angle PPL  Extinction Parallel Extinction Angle Extinction behavior c=Z is a function of the relationship n between indicatrix n a=X orientation and b=Y crystallographic orientation Inclined Extinction