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Biaxial optics

Biaxial optics. Nesse, 1991 Chapter 7, page 77 to 108. Biaxial Minerals. Minerals in orthorhombic, monoclinic and triclinic specify length of unit cell along all three crystallographic axes Also specify three indices of refraction named a, b, and g ( in book called n a , n b and n g)

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Biaxial optics

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  1. Biaxial optics Nesse, 1991 Chapter 7, page 77 to 108

  2. Biaxial Minerals • Minerals in orthorhombic, monoclinic and triclinic • specify length of unit cell along all three crystallographic axes • Also specify three indices of refraction named a, b, and g (in book calledna, nb and ng) • Where na < nb < ng so maximum birefringence is ng- na

  3. Biaxial minerals • 3 indices of refraction: na < nb < ng • Light still broken into two rays, one fast & one slow • Both rays are extraordinary • Slow ray is always ng’, with ng >ng’ > nb • Fast ray is always na’, with na <na’<nb

  4. Biaxial Indicatrix Similar to uniaxial indicatrix Main difference - 3 principal indices instead of 2 The 3 indices are plotted on 3 mutually perpendicular axes n is always plotted on X-axis n plotted on Y-axis n plotted on Z-axis The Biaxial indicatrix is a Triaxial Ellipsoid (elongate along the Z-axis)

  5. Biaxial Minerals • X-Y, • X-Z, and • Y-Z plane 3 Principal sections na nb ng na ng nb

  6. Biaxial Minerals • The biaxial indicatrix has 2 circular sections with radius nb • The 2 optic axes (O.A.) are perpendicular to these circular sections • The angle between the 2 O.A.’s is called 2V • Axis bisecting acute angle is acute bisectrix or Bxa • Axis bisecting obtuse angle is obtuse bisectrix or Bxo

  7. Optic Sign? Z=acute bxa = optically positive Z=obtuse bxo = optically negative 2V Obtuse bisectrix Z Z 2Vx Acute bisectrix

  8. Example: Normal incidence parallel to an optic axis Produces isotropic section (remains dark on rotation between crossed polars)

  9. Random section Indicatrix section is an ellipse with R.I. values of n’ & n’ Section - Partial birefringence

  10. Fig 7.7 REMEMBER: The axes of the biaxial indicatrix indicate the refractive indices and the vibration directions Example: Normal incidence parallel to an indicatrix axis

  11. Relationship between crystallographic axes and indicatrix axes • Orthorhombic minerals • Crystallographic axes and indicatrix axes coincide

  12. Monoclinic minerals • b-axis coincides with one of the indicatrix axes b

  13. Triclinic minerals • None of crystal axes coincides with indicatrix axes

  14. Biaxial Interference Figures Interference figures obtained in same manner as uniaxial ones: Conoscopic light High power objective Condenser lens & Bertrand lens Cross polars Biaxial interference figures are distinctly different from uniaxial figures Can be used to distinguish biaxial or uniaxial mineral

  15. Biaxial acute bisectrix figure - when acute bisectrix oriented perpendicular to the microscope stage isochrome Optic plane oriented E-W Optic plane in 45º position 7.12 45 degree position 0 degree position melatopes

  16. Optic plane Optic Normal isochrome isogyre

  17. 2V>60 7.17 Use change of isogyres of acute bisectrix with rotation of the stage NOTE: If melatopes rotate out ~ 30º of rotation THEN 2V > 60o

  18. Centered Optic Axis Figure when one of the optic axes is vertical, the melatope will be under the cross-hair other melatope in field of view if 2V < 30º Optic plane in 45° position

  19. Estimating 2V on the basis of the curvature of the isogyre in a centered optic axis figure If both melatopes in field of view, the 2V can be estimated. When 2V is zero, figure is a uniaxial cross Both melatopes in FOV Fig 7.32 One melatope in FOV

  20. Extinction in orthorhombic minerals REMEMBER: Extinction angle is the angle between a cleavage trace + extinction position. This angle varies depending on crystal orientation. Fig 7.33 parallel extinction Cut parallel to c-axis-prismatic cleavage random section - inclined extinction symmetrical extinction - cut parallel to (001) NOTE: Usually, cleavages are parallel to 3 crystallographic axes (100)(010) & (001) are pinacoidal cleavages - common in Biaxial minerals.

  21. Extinction in monoclinic minerals For Monoclinic minerals, 1 axis of indicatrix is parallel to the b crystallographic axis Fig 7.34 parallel extinction - prismatic cleavage inclined extinction

  22. Sign of elongation Length fast or negative elongation Length slow or positive elongation Length fast or length slow? Elongate minerals When z-axis is parallel to the length - length slow (+ve) When X-axis is parallel to the length - length fast (-ve) + or - + or - positive Platy minerals

  23. Determining the optical properties of an oriented mineral.Section (100), (010), and (001)

  24. (100) perpendicular to a-axis so b and c-axis in field of view • Draw grain and determine color and relief • Cross polars and determine fast and slow direction • Make interference figure One ray is fast and other slow The optic direction towards you is // to a-axis, bxa, bxo or ON

  25. (010) perpendicular to b-axis, so a and c-axis in field of view • Draw grain and determine color and relief • Cross polars and determine fast and slow direction • Make interference figure One ray is fast and other slow The optic direction towards you is // to a-axis, bxa, bxo or ON

  26. (001) perpendicular to b-axis, so a and c-axis in field of view • Draw grain and determine color and relief • Cross polars and determine fast and slow direction • Make interference figure One ray is fast and other slow The optic direction towards you is // to a-axis, bxa, bxo or ON

  27. Now you know which optical direction is parallel to the a, b, and c-axis • With your interference figure you can estimate the 2V. • Draw all the information on a block diagram

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