Mineralogy M2 PDF

# Mineralogy ## M-2 **Bros. ki kitab** **UNIT-I**  **Classmate Tue.** **Date 20/8/19** **Page** **Shameem Sir** ### Indicatrix 1. Indicatrix is a hypothetical concept having practical implications. 2. **Quartz** - I order grey, yellow, blue (3 types of interference colour). 3. **Biotite**...

# Mineralogy ## M-2 **Bros. ki kitab** **UNIT-I**&#x20; **Classmate Tue.** **Date 20/8/19** **Page** **Shameem Sir** ### Indicatrix 1. Indicatrix is a hypothetical concept having practical implications. 2. **Quartz** - I order grey, yellow, blue (3 types of interference colour). 3. **Biotite** - Light brown, dark brown (two types of interference colour). ### Properties of Minerals - All the properties of minerals are controlled by its structure. - $9_1 = 9_2 = 9_3 ; 9_1 = 9_2 \ne CC $ should be vertical - $d = B = \gamma =90° ; L = B = r = 90°$ 4. **Calcite** has four faces of 3 hardness and two faces of 2 hardness. 5. **Kyanite** has two hardness 5, 7.5. 6. **Indicatrix** is related with R.I. 7. The optical properties of the minerals are controlled by their R.I which itself are dependent upon the structure of the mineral along the crystallographic crystals. If R.I is represented in terms of certain measurements, the variations in the optical properties of the minerals can be easily explained. The concept which explains these properties is called Indicatrix. ### Understanding Indicatrix - When we cut along $a_1$ ($a_1$ becomes perpendicular to the stage). - Variation will be in the crystallographic axis and not the optic axis. - Tetragonal system comes after, $a = b +C ; L=B=V=90°$ - The mineral is considered a spherical object. - Indicatrix is used to pass through the center of that spherical object. - R. I is measured in certain values. - Structure controls the R.I & R.I depends on the velocity of light (constant). #### Visualization of Indicatrix -  - When all the 3 sections are combined together in 3-D, we get a sphere. - $a_3$. Sphere of Rotation, ### Implications of Indicatrix - There will be no change in the optical properties of the mineral irrespective of the axis or section cut, ppl or x-nicol. - In case of indicatrix, section is always be a circle and hence all the radii will be equal. - Indicatrix will be proportional to the R.I. - Smaller radii & smaller R.I. ### Light and Crystal Structure - When light passes parallel to the c-axis, we can not see the vibration along the c-axis. - In Cubic, no change in prep structure of as the velocity of light is constant. - In analyser in "$Cond$" - Cubic's are isotropic. - Every circular section obtained from the indicatrix will be isotropic. - R.I denoted by $\omega$. ### Tetragonal System - $a = b + C; L=B=V=90°$ - In tetragonal system, the variation comes in the 'z dir' of c-axis. - c-axis will always be longer than the other two. -  - In 3D, if we combine those two sections (circle+ ellipse) we will get ellipsoid of 3-D. ### Sections and Ellipsoids - We can have as many sections (ellipsoid) but only one circular section. -  - If we cut vertically $-> a, - We can have as many such sections. - If we cut horizontally. - If we cut obliquely $-> a_1$ $->a_1$ - We get reduced value of E, if we go like this. - $E=E_1= E_2= E_3$. - In tetragonal, if E I stage $-> $ isotropism. - Or circular section parallel to the stage". ### Uniaxial Minerals - The sections containing max. value of R.I are called principle sections. -  - Principle Section $-> R.I -> E, \omega$ - Circular Section $-> R.I->\omega$. - Random Section $-> R.I -> E', E^2, E^3 \ne \omega$ - Circular section - If $E>\omega -> +ve$ - $E<\omega -> -ve$ - Direction - Minerals in which there is no doubt, refraction is called optic axis - Minerals, with one optic axis are called Uniaxial Minerals, - Uniaxial - Tetragonal - - Hexagonal. ### Biaxial Minerals - $(\alpha \beta \gamma).$ (2 circular section) - Perpendicular to the two optic axis - we have two circular sections. - Two circular sections means two isotropic sections. - In biaxial minerals, - $\alpha$ - Minimum (may have any value). - $\beta$ - Medium (Constant) (not change). - $\gamma$ - Maximum (may have any value). -  - Triaxial Ellipsoid. - Three Principle Sections $-> $ - xz $(\alpha \gamma)$ -> yellow/dark green - XY $(\alpha \beta)$ -> yellow - YZ ($\beta \gamma$) -> green/dark green. ### Neutral Minerals - $\beta$ is in between $\alpha$ & $\gamma$ then it has no sign and called - Semi-random section $-> $ any section in between the principle sections. - Semi-random - Zx' $->$, ( $\beta $ won't change) XZ' $->$ - Yz' $->$, Yx' - Totally random section $->$ - Xz' ( $\alpha' \gamma'$). - Section perpendicular to the Y ($\beta$) will be the circular section whose radius will be equal to the $\beta$ and Y direction will serve as the optic axis. -  - Here two circular sections. - Biaxial +ve $\beta$ is closer to $\alpha$ than to $\gamma$, $\alpha \gamma$ is the BXA. - Biaxial -ve. - Vibration direction are also called as bisectrix (Bx). - Bxa - acute bisectrix - Bxo - obtuse bisectrix - c-s circular section. - **B- +ve. If Bxa = Z, Bx0 = X** - **B- ve. If Bxa = X, Bx0 = Z** -  - **Biaxial (+ve)** ### Conoscopy & Orthoscopy - **(dark)** **(visible)** - Conoscopy & Orthoscopy. - The difference between them is in the arrangement of light. - Orthoscopy - we will use a plane mirror. -  - Orthoscopy, the light is parallel and extinction is always measured in the orthoscopic mode. - Extinction L is always acute angle. - First time birefringence was observed in Calcite. - Locus of E-ray changes. - Augitee's extinction L is 42-48° while others are less than 48.5°. - It is the differential absorption of light during the rotation of stage as light gets incident at different angles and hence we get pleochroism. ### Birefringence - A light is vibrating in two mutually perpendicular directions. - One is extraordinary ray (Ex ray), one is ordinary ray (O-ray). - E- ray has $\epsilon$ & O- ray has $\omega$ R.I. -  - $M = Sin i = Constant (C_1)$. (Snell's Law is not followed by E-ray) - Sin r -  - Propagation direction are different but vibration directions are mutually perpendicular (of E-ray & O-ray). ### Path Difference - We take a slab of thickness 't' and light is incident perpendicular to the basal part. The ray splits into E-ray (slow) & O-ray (fast) and travel within the crystal. - O-ray will pass lineard y & E-ray traverses a different path. - Sin $\omega$ E-ray is slow and hence by the time E-ray emerges on the other side of the slab. O-ray has already travelled a much greater distance in the same time ('t'). -  - $V_F$ - velocity of fast ray - $V_s$ - "$" "slow" - $T_s$ - Time taken by slow ray - $T_F$ - "$" "fast" - Different direction is not very significant. - The angular difference is not very large. - Hence dir. along fast & slow ray will hardy be same. - $\Delta$ = path difference. - $\Delta =C(T_s - T_F)$ - $T_s = \frac {t}{V_s}, T_F = \frac{t}{V_F}$ - $\Delta = t( \frac {C}{V_s} - \frac {C}{V_F})$ - $\Delta= t( \frac {C (-V_F)}{V_s V_F})$ - $\Delta= t ( \frac {E - \omega}{V_F}$ - Path difference depends upon the thickness and birefringence. - Retardation = Birefringence * thickness -  - Interference colour are they have a interference of fast & slow ray and they both have a path difference. - All interfering inphase waves will be extinguished by the Analyser. - Inphase $-> n\lambda$ (whole integer) - Inphase - wave are $->$ in order of (n); n=0, 1, 2,... - Out of phase (half wave) $\lambda$ makes max. intensity of colour they have vibration direction parallel to the vib dir of the analyser. - Interference occurs at analyser. - Wedge shape means pointed part $-> $ minimum thickness while max. is in between the contact. - All the circular sections are isotropic. -  - This component of PUD, of will allow the light to pass through it. - This component will allow the light to pass through it, of PUD2 - This much will allow the light will allow to through it (of the mineral). - Inphase wave will not pass through the analyser - Outphase will $->$ pass but the intensity will depend on the path difference.. - Retardation of the gypsum plate $-> 550$ nm (Red Colr). - I order will finish at 550 nm - We can get different order of colours in the same mineral. - Bec order depends on the value of retardation. - Red colour can be genrated by the retardation of 550°. - Wedge - Use get this with flaky minerals - Thickness inceases, Less Resistant, mineral will not maintain uniform thickness. - Retardation will increase this side, and hence interference colour will change. We will get the true body colour at the edge. - Conoscopy - We will use concave mirror - for isotropic minerals study. - It should be medium power objective or high power objective - We will $->$ use Bertrand use. - If Bertrand lens is not there in a microscope then, we will remove the eyepiece. - $ S_1 $ slow one $-> S_2 $ slow $-> F_1 $ fast one -  - $S_2$ will superimpose on F_1 and there will be a no. of such waves. - The ray that will strike the analyser, will be a composite of slow & fast rays. - While in phase will not ever pass to the analyser while out of phase will reach the analyser. - Interference Figure - These dark or bright regions are isochromes or cones of retardation, provided we use monochromatic light. -  - O.A / Melatope $-> $ Isogyres. - Isochromes - Optic axis centred figurs (Isotropic Section) (O.A Istag) - These if we use sunlight / whitalight, then bands of concentric or circular bands of different colours and the set of colours will repeat themselves. (separated by a ring of red colour). - As, we move away from melatope towards margins we will get high order colours & low order colours is towards the mulatope. - Melatope intersection of two isogyres. - Melatope - position of optic axis. - 0.85 - Highest power magnification. - OAC Figure $->$ O'A at the centre of cross-wires. - Basal Section $->$ I c axis. - Prismatic $->$ O'A II to the stage / c axis -II. - Pyramidal section $->$ c-axis inclined. -  - Basal Section $->$ Pyramidal section $->$ Prismatic Section - Random Section - If, we increase the magnification we will get large and barger no. of isochromes. -  - Off-centred O'A figure. - Principle Section (O'A II to the stage) $->$ - But makes an L with the cross wires (or, vibration direction of the microscope) - Diffused grey figure - we will get when O. A is II to any of the Cross-wire (Stage के II तो है ही) -  - Diffused Grey 2 - 2-3' rotation - Dark lines. - OA II to the x-wires. $->$ Highly Intense Colours. - Flash figure - (We get this at 2-3° rotation of O'A) - (We get high intensity colours) - This method is useful in distinguishing different crystal sections. ie isotropic, uniaxial and biaxial sections. - Uniaxial or Biaxial? (R.I.) -  - This is the cone of illumination. - The components of Ray 1 & Ray 2 on resolution overlap each other and hence we can say that these rays are moving perfectly II to each other. - These rays will stuck the analyser and there will be a path difference and whenever there will be a path difference interference will occur. (The corner rays will travel max. distance, maybe correct) - Ray 1. $\Delta = t,x Birefringence $ - $ = t,x \omega - \epsilon' $ (for uniaxial is same). - Ray 2. Retardation will be less since thickness has redueced and as we move towards O.A, Bire-fringence decreases and along O'A no birefringence. - Isochromes are so called becz we get so single colour for same Retardation, Or chromes of equal Retardation in 3-D. -  - As we move tawands O.A retardation decreases as Birefringence decreases as well as thickness also decreases. -  - Red light is the starting point. - Different / one order of interference order. - Alternate circular bands / monochromatic light tones of bright & dark colour. - Isochromes / cone of equal retardation ( these are the base of the cone. Cones are the composite cones)" - Inclined rays will resolve within the crystal. - As the $\delta$(retardation) increases, cone of equal "retardation" increases. - All the inphase waves of the order of black colour are extinct as the vibration dir. will be II to the polarizer. - More the divergence, more the travel distance. - More divergence, more variation, more the thickness. -  - Thickness varies and Birefringence also varies & hence retardation varies. Principle axis will have R.I ( $\omega$ ). One ray will be fast and another will be slow. -  - We will geta locus of circle and infinite no of points. - Sinu, this an inverted cone, hence it is called cone of equal retardation. - The Birefringence and thickness decreases as we move from the boundary of the circle to the centre. $\epsilon$, at the O.A. the light is incident normally. - With the help of this we can determine the sign of the mineral. -  - To know the vib dir. of a microscope and the position of the bisti. - ll to the cross-wire and the priaxial. - In case of tourmaline the lighest colour will tell about the vibration dir. of the polarizer. - Sign of the mineral. - E along the vad ip - Substraction -  - *(-ve) sign* - $\lambda$ 550 $-> n$ 100 $-> n$ 1650 - Path difference of order=n$\lambda$ $-> $ extinction - Path difference (n+1) x $\lambda$ $-> $ brightness - Approximate radii of the circles corresponding to the retardation of 2$\lambda$, 3$\lambda$, 4$\lambda$, are 1.2r, $1.5r$, $1.5r$ - No. of isohcromes & Birefringence (High birefringence possess more isochrones than the low birefringence - No of isochcromes & thickness (more thick $-> $ more isochcromes) - To obsure the interference figy use the Bert van lens or remove the oudative. - Th higher the numeral aperture of the objective used, the wider the angle of the con of light from the crystal that enter the objective. - Melatope means the position of the O.A and not the inteusection of the cross-wires. - Two melatopes. - Biaxial Minerals $-> $ Thicker than uniaxial minerals. -  - Bxa actue bisectrix, (2V<45°) (z or x). -  - In Bx0 $-> $ obtuse bisectrix melatopes will be outside the field of view. - Diff. btw Uniaxial & Biaxial - The isogyres will be significantly thinner than the other one. - (z or x) - Just by looking, we cannot tell about the central line (axis) i.e whethaitis the z axis or x-axis. -  - Z will be the BXA actute bisectrix - In alkaline Hbl, as $Na^+$ increase the yellow colour of the Hbl varnishes and becomes green - If Na' content in any mineral increases colour becomes good. - If there is only one isogyre and on rotation it passes through the intersection and become II to one of the cross wire. In that case we cannot determine whether the optic figure is Biaxial or uniaxial. - Highly curve $->$ Biaxial mineral. - Lightly curve isogyre $->$ Uniaxial mineral. -  - Aeqerine, Glaucophane, Riebeckiter they have more or less same optic colour, pleochroism, other properties. - Pleochroism- light green, dark green, light blue-dark blue. - We determine the 2' angle and then we determine the refractive indices and for & R.I we need the vibration direction. - Circular Section से कं determine करते हैं (min. intensity) - Principle $-> $ " " $-> $ " " (max. intensity) - In Conoscopic, - If, we get Centred O.A, then we will have the circular section of the tetragonal, crystal system. - Now go back to the orthoscopic arrangement to get the R.I. - Off Centred O.A fig. sirf Uniarid में होती है या Biaxial में? - How to find R.I? < Oblique Illumination - (In Orthoscopy) - Becke-line method - use TIR(Total internal reflection - Take a mineral so that the boundary is visible - Close the diaphragm - Raise the tube or lower the stage. - Becke line increases towards the high R.I mineral - We use liquids of known R.I, we can precisely determine the R.I. - Staining - It is a v. simple technique by which every mineral can be identified. - It requires certain chemicals - Chiefly used in sedimentary rocks. - Especially for K-Feldspars (orthoclase) Anorthoclase) are difficult to identify in microscope. Cordierite is sometimes mistaken for plagioclase. - Plagioclase forms by magmatic differentiation. - Staining $->$ based on visual interpretation. - It is also used for the identification of the Carbonates (limestones). - Staining is always, preceded by Etching. - Etching $->$ the roughness of the surface of the mineral so that the minerals can readily react with the stain chemicals. - Etching can be done by two acids L.H.C. - 52% HCl - for all sort of Carbonates. - 52% HF - for all the silicate minerals. - HF is the best etching agent. - Etching can be done using the slides but the rock should not be covered by the coverslip. - If the rock is very porous, we use an additional adhesive paraffin, (lake side cement, epoxy, resin) (used under especial conditions). - (Paraffin is used for porous rocks.) - AX has to be a bottle filled with HF, is left open and the slide is kept upside down over the opening of the HF bottle. - Eq. Gvanite = K-Feldspar + Plagiodase Feldspar + Quartz. - For staining we need - (i) Bal₂ - (ii) Sodium Cobaltinit rite - (iii) Rhodhizonic Acid. - Rinse the etched mineral with water. - Immerse in BaCl₂ sot" for 2-3 times. - Re-Rinse - Immerse it in Sodium Cobaltinitrite stor sot". - If we yst get light yellow colour. - This means the mineral is K_Feldspar. - Now cleanly wash the mineral and rime it into the Rhodhizonic acid sol". - If we get brick red spot colour, The mineral is plagioclase feldspar. - The unstained part of the rock is Quartz (N.sta) - Quartz can never be stained by any combination of reagents. - If the plag. is pure albite it will not give brick red colour, there has to be atleast 3% anorthite to get a brick red colour. - For Orthoclase & others.. - Wash the slide and put the slide over 80°C, so that it becomes a bit gong powdery for gercy. - Cool it and vince it in Call, soi" (acts as a catalyst for stain) and then BaCl₂ sol" and then Na Cobaltinitrite sot" and dry the sol. - Light Grey - plagioclase - Umstained Quartz - Light yellow-Orthodave. - Plagioclase - Anorthoclase $->$ Granitic rock - (untwinned plagioclase) Cordierite -> Mtm. rock - Sanidine -> Sodic Rock. - Eg. We we Amainth solution. We have to rinse it with water and then we dip it into BaCl₂ and then again rinse it & dip it into Amaranth sol". Then, if - Light Red $-> $ Plagioclase - Greyish Cherry Red $-> $ Anorthoclase - Deep Red $->$ Cordierite - Sanidine does not respond to Amaranth sol". Then that part is Sanidine. - Pure Albite is also unstaind. - Carbonates. - Etching & done with cold dil. HCl. -> Brisk effervescence - Brisk effervescence (3 min) - Dragonite, calite, or witherite. - No effervescence - all other carbonates, Do etching with hot Hce for 1 to 3 min - Now we need different sol's - - Alizarine Red S - FEIGL'S sol' - Rhodizonic sol' - MAGNESON - TROPAEOLINOO - Potassium Ferricynide - Potassium Hydroxide. - Ammonium Sulphide & Copper Sulphate. - ARS. - (i) Purple Stains -> - (ii) Deep Red Stains $->$ - (iii) No colour $-> $ - (i) For purple: E+ ARS + 30% NaOH and boil - Dark Purple: Ankerite. - Douk Red Brown -> Cerrusite - No Color $->$ Strontianite - (Revets to colorless mineral). - (ie Purple turns coloculess mineral). - (ii) Deep Red Stains - Now apply FEIGL'S SOL". - Black - Anhydrite, Aragonite - Colorless / No Colour $-> $ - if colourless it has to be treated with 30% NaOH+bål. - Purple Colour $-> $ High Mg Calcite. - Orange Red $-> $ witherite - No Colour $-> $ NC- Calcite. - (ii) E + ARS - NC. Colour - Treat with 30% NaOH and boil. - No Colour $->$ (Anhydrite) - Dark Brown $->$ (Siderite) - Purple (5% NaOH+ boil) - Purple (Treat with Magneson + 30% NaOH ). - No Colour $-> $ (Smithsonite) - (Troppeolin 00+ 1.5% H2S04+12% Ferricyanide). - No Colour $-> $ (Magnesite) - Yellow $->$ (Smithsonite) - Secondary Rad", Excited e remains in it's own orbit. - Backscattered Rad" - energy reflectid back - Characteristic Rad" - energy exites the e so that it leaves it's orbit and jump to higher level. - Chemical/ Point Analysis, - Analysis - Secondary Rad", Excited e remains in it's own orbit. - Backscattered Rad" - energy reflectid back. - Characteristic Rad" - energy exites the e so that it leaves it's orbit and jump to higher level.