Optical Mineralogy Lecture 3 PDF

Optical Mineralogy Part II Compiled By: Prof. Fathy Hassan Accessory (Retardation or Compensator) Plates Ifparallel a birefringent crystal section is in extinction position, the vibration directions Z' and X‘ are to the N-S and E-W directions of the crossha...

Optical Mineralogy Part II Compiled By: Prof. Fathy Hassan Accessory (Retardation or Compensator) Plates Ifparallel a birefringent crystal section is in extinction position, the vibration directions Z' and X‘ are to the N-S and E-W directions of the crosshairs. For a variety of applications, it may be important to know which direction corresponds to the higher, respectively lower, refractive index: o Determination of mineral colour in a specific vibration direction. o Determination of optical sign of optically uniaxial minerals which are elongate in c direction or platy having the basal plane ({001}, {0001}) as the dominant crystal face. o Determination of sign of elongation (l) of acicular to columnar, platy or flaky minerals in elongate crystal sections. For a distinction between vibration directions Z' and X‘, compensator plates are used. These are anisotropic crystal plates of constant or variable retardation with known orientation of the X and Z wave vibration directions (α = nx and = nz). Most commonly, the Gypsum Plate Quartz compensators are inserted Wedge diagonally into the microscope tube below the analyzer. The wave corresponding to nz ( or Z’) vibrates in NE-SW direction, Mica the wave corresponding to nx Plate (α or X’) in NW-SE direction. Accessory (Retardation) Plates Commonly used compensators: plate): a- The first-order red plate (lambda plate, 1  plate, gypsum thick, It consists of gypsum plate that is cut parallel to the optic axis, about 62 µm which shows a first order red Interference colour in diagonal position ( = 551 nm). This colour is found at the boundary between first and second order colours. When introduced, fast and slow rays of the λ-plate will interfere with the those of the mineral, modifying the retardation (Δ). The wave can combine their wavelengths by addition (increasing retardation) or subtraction (decreasing retardation). Increasing or decreasing the retardation can be seen by the changes in the interference colours in the Michel-Levy table (to the left with 550 nm or to the right with 550 nm starting to the interference colours observed for the mineral). Determination of the Vibration Direction: In order to distinguish between the extinction directions X' and Z' (with corresponding refractive indices nx' and nz'), the mineral grain is put exactly in an extinction position and then rotated anticlockwise by 45ｰinto a diagonal position. In this position, the originally E-W vibrating wave is now vibrating NE- SW (in quadrants I and III); the originally N-S vibrating wave is now oriented NW- SE (in quadrants II and IV). Two different optical orientations of the mineral are possible in diagonal position: 1- The NE-SW vibrating wave is the slower wave; its refractive index is n ’. The NW-SE vibrating wave is the faster wave; its refractive index is n ’. z x 2- The NE-SW vibrating wave is the faster wave; its refractive index is n ’. x The NW-SE vibrating wave is the slower wave; its refractive index is nz’. By inserting the first-order red plate into the light path, with the compensator direction Z’ () in diagonal NE-SW orientation, the two different positions 1 and 2 can be distinguished as follows:  Determination of the Vibration Direction: In an anisotropic mineral, the nx' wave advances faster in the crystal plate than the nz' wave. Both waves have different wavelengths. After leaving the mineral, both waves have the same velocity and wavelength, but with an accumulated retardation of Min = d* (nz’- nx’ ). With this retardation, the waves enter the crystal plate of the compensator, whereby the mineral's nx' wave is again the faster wave nx Comp, the original nz' wave transforms to the slower wave nz Comp. Therefore: In Case 1: the retardation accumulated in the mineral is now further increased by the retardation of the compensator. There is an increase of interference colours: Min + Comp = total In Case 2: the retardation accumulated in the mineral is now further decreased by the retardation of the compensator. There is a decrease of interference colours: Min - Comp = total      Qz   Qz Addition and subtraction in the two diagonal positions of a quartz grain cut oblique to its c axis. The E-wave vibrates parallel to c, whereby ne' = nz'; the O-wave vibrates orthogonal to c, with no = nx Suppose we view an anisotropic crystal with o  = 100 nm (1 -order gray) at 45 from extinction st Min + Comp = total Insertion of Compensator 100 + 550 = 650nm  Slow min. || Slow gyp → Addition Original 1st order gray → 2nd order blue Suppose we view an anisotropic crystal with o  = 100 nm (1 -order gray) at 45 from extinction st o Ray in the crystal Comp - Min = total that is parallel to Slowgyp is ahead by 100nm 550 – 100 = 450nm o 550m retardation in gypsum plate → Insertion of 450nm behind Compensator  Fast min. || Slow gyp → Subtraction Original 1st order gray → 1st orange What will happen when you insert the gypsum plate?  Accessory (Retardation) Plates ♣ Construction: ♣Usually gypsum - full wave plate,  = 550 nm ♣Common mica - ½ wave plate,  = 150 nm ♣Retardation is known ♣Orientation of principle vibration directions is known, set at 45º to polarizer and analyzer ♣Fast ray is length of holder, slow ray is perpendicular to holder ♣Interference of accessory plate either adds or subtracts from retardation of mineral ♣With slow ray of mineral parallel slow ray of accessory plate – retardation increases ♣With slow ray of mineral parallel fast ray of accessory plate – retardation decreases ♣ Net result: ♣Accessory plate tells you orientation of fast and slow direction in mineral ♣Important for many optical observations Sign of Elongation The meaning of the sign of elongation is to determine whether the slow or fast component is vibrating in the longest direction of the crystal. If the slow component vibrates in the longest direction of the mineral, the mineral is said to have a positive sign of elongation or is "length-slow". If the fast component vibrates in the longest direction of the mineral, the mineral is said to have a negative sign of elongation or is "length-fast". Addition is observed if the wave with the larger refractive index (n ') vibrates parallel z or at a small angle to the long dimension of the crystal section: l (+) = positive sign of elongation or "length-slow". Examples: acicular-columnar crystals– sillimanite, gedrite, anthophyllite. Subtraction is observed if the wave with the smaller refractive index (n ') vibrates x parallel or at a small angle to the long dimension of the crystal section: l (–) = negative sign of elongation or "length-fast". Examples: acicular-columnar crystals– tourmaline, apatite. For optically uniaxial mineral species with acicular-columnar habit, the sign of elongation corresponds to the optic sign. Platy muscovite showing positive sign of elongation. In muscovite, the slowgyp and slow (ny nz) waves vibrate in identical orientation. Therefore, the retardation adds up and increased interference colours result (total = Min + gyp = 1231 nm; 3rd order blue-green). Prismatic apatite showing negative sign of elongation. In apatite, the fast wave vibrates parallel to the slow wave of the gypsum plate, and the slow wave in apatite parallel to fast wave of the gypsum plate. Hence, retardation is reduced and subtraction results (total = gyp - apatite = 476 nm; 1st -order orange-yellow). Than k