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Anisotropic materials

Anisotropic materials. Differences isotropic

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Anisotropic materials

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    1. Anisotropic materials Nesse, 1991 Chapter 5, p. 37-52

    2. Anisotropic materials Differences isotropic & anisotropic mineral Velocity of light varies depending on the direction of travel through the mineral Anisotropic minerals double refraction Light that enters anisotropic materials splits into 2 rays with different velocities. Ray with lower RI fast ray & higher RI slow ray The 2 rays vibrate at right angles to each other Each anisotropic material has 1 or 2 directions, called optic axes, where the light behaves as if it were isotropic

    3. Double refraction Use clear calcite rhomb (along cleavage plane) on paper with dark dots The mark will be repeated looking through the calcite rhomb When the calcite rhomb is viewed through a polaroid plate only one row of points is seen

    4. Double Refraction Note the vibration direction of the polarizing plate. When the plate is rotated 90 degrees the other row of points becomes visible This shows that the point is transmitted through the rhomb by 2 differently polarized rays

    5. DOUBLE REFRACTION

    6. DOUBLE REFRACTION

    7. Interference When an anisotropic mineral is placed between crossed polars it may show vivid colors. These are called INTERFERENCE COLORS, also known as BIREFRINGENCE How do interference colors form? First consider monochromatic light.

    8. Interference When monochromatic light with velocity V enters the anisotropic mineral, it is split into two rays that vibrate at right angles and have different velocities Amplitude of each ray can be determined by vector addition

    9. Interference Because of the difference in velocity, the slow ray lags behind the fast ray The distance that the slow ray lags behind when both excite the crystal is called Retardation D

    10. Interference Magnitude of retardation depends on the thickness of the crystal d and the difference between the velocity of the fast ray Vfast and the slow ray V slow The time it takes the slow ray to traverse the crystal is ts

    11. Interference ts=d/Vs - for slow ray (distance/velocity) During time ts the fast ray traverses the crystal but also travels the additional distance equal to retardation D ts = d/Vf + D/V Or d/Vs = d/Vf + D/V

    12. INTERFERENCE So d/Vs = d/Vf + D/V Rearranging: D = d (V/Vs V/Vf) V is speed of light in air is essentially the speed of light in vacuum. Remember: Definition of refractive index: nm=V/Vm Substituting D = d (ns nf) Where ns nf is birefringence (d) or Difference between the refractive index of the slow and the fast ray

    13. Interference a) If the retardation (D) is one wavelength. ? = i? (i is an integer) NOTE: When the vector components of the 2 rays are resolved in the vibration direction of the upper polar, they are in opposite directions and cancel out

    14. Interference b) If the retardation (D) is one-half wavelength or ? = (i + ) ? Vector components of both rays resolved in the vibration direction of the upper polar, they are in the same direction so they constructively interfere

    15. Interference Consider the interference pattern formed by quartz wedge with monochromatic light. Where the retardation is a whole number of wavelengths, the slow and fast ray destructively interfere at the upper polar and a dark band is seen. Where the retardation is 1+ wavelength the 2 rays constructively interfere and light passes with maximum intensity

    16. Interference Using polychromatic light: Every wavelength will have a different place where total cancellation will occur The colors that result after the interference by the upper polar are called interference colors The interference colors depend on: 1/ the path length or thickness of the mineral, t 2/ the difference in Refractive Index between the fast & slow rays (also known as the birefringence), nf - ns

    17. Interference If a quartz wedge is placed between crossed polars: At the thin end thickness and retardation are 0 and the color is black As the thickness increases the color changes from gray, to white then to yellow and red and then repeating the sequence of blue-green yellow and red The color produced depends on which colors pass through the polars and which are canceled

    18. Michel Levy Color Chart

    19. INTERFERENCE Remember D = d (ns nf) D (nm) = d (nm) x (ns nf) 1nm=10=10-6mm d (nm) = D / (ns nf) d = 315/0.009 = 35000nm or 0.035mm

    21. Extinction Anisotropic minerals will go dark (extinct) between crossed polars every 90? of stage rotation (unless the Optic Axis is vertical).

    22. Extinction Measuring extinction angles: 1/ Align crystal length direction or cleavage parallel to cross hair. 2/ Note the angle (degrees) on the rim of your stage. 3/ Cross the nicols and rotate until the grain becomes extinct. 4/ Note the number of degrees on rim of stage and deduct from previous value. 5/ Angle of rotation is the extinction angle.

    23. Extinction Categories of extinction a) parallel extinction b) inclined extinction c) symmetrical extinction d) no extinction angle

    24. Fast & Slow Ray Which vibration direction is the fast or the slow ray?

    25. Using Polarized light Sample in 45o position Path difference after sample D1 Accessory plate with fixed path length DA Slow ray // slow ray yields additional path difference. Path difference after accessory plate D2 = D1+ DA or addition Interference color will be higher

    26. INTERFERENCE

    27. Using Polarized light Sample in 45o position Path difference after sample D1 Accessory plate with fixed path length DA Slow ray // fast ray yields lesser path difference. Path difference after accessory plate D2 = D1- DA or subtraction Interference color will be lower

    28. INTERFERENCE

    29. INTERFERENCE

    30. Relief Remember the Becke-line Test ? In this test, the bright line goes to the higher refractive index material Now there are 2 Refractive Indices, a fast ray & a slow ray It is now possible to have one refractive index higher than balsam or oil (positive relief) and one lower than the balsam (negative relief)

    31. Relief This is called changing relief Example: Calcite Oil n=1.550 Fast ray n=1.57, so low relief Slow ray n= 1.658, so high relief

    32. Pleochroism Change of color on rotation of the stage in plane polarized light (so only one vibration direction passes) This is when the nicols are not crossed and only the lower polar in place. This effect is known as Pleochroism Examples: Chlorite (dark green to light green) and biotite (dark brown to light brown)

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