1. Optical Mineralogy Use of the petrographic microscope © John Winter, Whitman College with some slides © Jane Selverstone, University of New Mexico, 2003

2. Why use the microscope?? l Identify minerals (no guessing!) l Determine rock type l Determine crystallization sequence l Document deformation history l Observe frozen-in reactions l Constrain P-T history l Note weathering/alteration © Jane Selverstone, University of New Mexico, 2003

3. The petrographic microscope Also called a polarizing microscope physics of lighttools and tricks In order to use the scope, we need to understand a little about the physics of light, and then learn some tools and tricks… © Jane Selverstone, University of New Mexico, 2003

4. What happens as light moves through the scope? light source your eye light ray waves travel from source to eye wavelength, I = f(A) amplitude, A light travels as waves Frequency = # of waves/sec to pass a given point (hz) f = v/ v = velocity (in physics v = c, but no longer) © Jane Selverstone, University of New Mexico, 2003

5. Electromagnetic spectrum Electromagnetic spectrum & visible portion Violet (400 nm)  Red (700 nm) White = ROYGBV dispersion (can be separated by dispersion in a prism)

6. Refraction Incident ray and reflected ray: 1)  of incidence i =  of reflection r' 2) coplanar “plane of incidence” (  plane of interface) Refracted ray: 1) Slower in water (or glass) 1) Slower in water (or glass) 2)  r   i 2)  r   i Depends on  velocity Incident Reflected air Refracted water i r’ r

7. For a substance x: n x = v air /v x n air = ?? light is slower in water, glass, crystals Is n water greater or less than 1?? Larger n associated with slower V !! Snells Law: n i sin i = n r sin r for 2 known media (air/water) sin i/sin r = n r / n i = const So can predict angle change (or use  to determine n r ) Index of refraction

8. Light beam = numerous photons, each vibrating in a different plane Vibration in all directions ~ perpendicular to propagation direction vibration directions propagation direction What happens as light moves through the scope? Polarized LightUnpolarized Light Each photon vibrates as a wave form in a single plane Light beam = numerous photons, all vibrating in the same plane planes of vibration

9. 1) Light passes through the lower polarizer west (left) east (right) Plane polarized light “PPL” Unpolarized light © Jane Selverstone, University of New Mexico, 2003 light intensity decreases Only the component of light vibrating in E-W direction can pass through lower polarizer – light intensity decreases

10. upper polarizer 2) Insert the upper polarizer west (left) east (right) Now what happens? What reaches your eye? Why would anyone design a microscope that prevents light from reaching your eye??? XPL=crossed nicols (crossed polars) south (front) north (back) Black!! (“extinct”) © Jane Selverstone, University of New Mexico, 2003

11. The Optical Indicatrix vibration Shows how n i varies with vibration direction. Vectors radiating from center Length of each proportional to n i for light vibrating in the direction of the vector Indicatrix Indicatrix = surface connecting tips of vectors (a representational construct only!) Isotropic Isotropic media have all n i the same (by definition) What is the shape of an isotropic indicatrix? spherical Amorphous materials or isometric crystals are (optically) isotropic with a spherical indicatrix

12. The Isotropic Indicatrix A section through the center of an indicatrix  all n for light propagating  the section Conventions: Indicatrix 1) Indicatrix w/ center on interface surface 2) n (radial vectors of circular section in this case) same in all possible vibration directions Incoming light can (and will) vibrate in the same direction(s) it did prior to entry If unpolarized, it will remain so. Only effect is slower velocity (rep. by closer symbol spacing) Fig 6-5 Bloss, Optical Crystallography, MSA

13. Liquids, gases, amorphous solids such as glass, and isotropic minerals (isometric crystal system) stay black in all orientations Review: isotropic XPLextinct Review: With any isotropic substance (spherical indicatrix), when the analyzer is inserted (= “crossed- nicols” or “XPL”) no light passes  extinct, even when the stage is rotated Note: the gray field should also be extinct (glass and epoxy of the thin section are also isotropic), but is left lighter for illustration

14. relief Mineral properties in PPL: relief relativen Relief is a measure of the relative difference in n between a mineral grain and its surroundings Relief is determined visually, in PPL Relief is used to estimate n garnet:n = 1.72-1.89 quartz:n = 1.54-1.55 epoxy:n = 1.54 Quartz has low relief Garnet has high relief

15. relief Mineral properties in PPL: relief relativen Relief is a measure of the relative difference in n between a mineral grain and its surroundings Relief is determined visually, in PPL Relief is used to estimate n olivine plag olivine:n = 1.64-1.88 plag:n = 1.53-1.57 epoxy:n = 1.54 - Olivine has high relief - Plagioclase has low relief © Jane Selverstone, University of New Mexico, 2003

16. What causes relief? n xtl > n epoxy n xtl < n epoxy n xtl = n epoxy Hi relief (+)Lo relief (+)Hi relief (-) Difference in speed of light (n) in different materials causes refraction of light rays, which can lead to focusing or defocusing of grain edges relative to their surroundings © Jane Selverstone, University of New Mexico, 2003

17. thin section Now insert a thin section of a rock in XPL west (left) east (right) Light vibrating E-W How does this work?? Unpolarized light Light vibrating in many planes and with many wavelengths Light and colors reach eye! north south © Jane Selverstone, University of New Mexico, 2003

18. Conclusion has to be that minerals somehow reorient the planes in which light is vibrating; some light passes through the upper polarizer But, note that some minerals are better magicians than others (i.e., some grains stay dark and thus can’t be reorienting light) Minerals act as magicians!! olivine plag PPLXPL

19. O E Double images: Ray  2 rays with different propagation and vibration directions Each is polarized (  each other) Fig 6-7 Bloss, Optical Crystallography, MSA Anisotropic crystals Calcite experiment double refraction Calcite experiment and double refraction O-ray O-ray (Ordinary) Obeys Snell's Law and goes straight  Vibrates  plane containing ray and c-axis (“optic axis”) E-ray E-ray (Extraordinary) deflected in Vibrates in plane containing ray and c-axis..also doesn't vibrate  propagation, but we'll ignore this as we said earlier

20. Both rays vibrate parallel to the incident surface for normal incident light, so the interface x-section of the indicatrix is still valid, even for the E-ray Thus our simplification of vibration  propagation works well enough From now on we'll treat these two rays as collinear, but not interacting, because it's the vibration direction that counts O E Fig 6-7 Bloss, Optical Crystallography, MSA IMPORTANT: A given ray of incoming light is restricted to only 2 (mutually perpendicular) vibration directions once it enters an anisotropic crystal privileged directions Called privileged directions Each ray has a different n  = n o  = n E in the case of calcite  <  …which makes the O-ray dot appear above E-ray dot

21. Some generalizations and vocabulary isotropic l Amorphous materials and isometric minerals (e.g., garnet) are isotropic – they cannot reorient light. These minerals are always extinct in crossed polars (XPL). anisotropic l All other minerals are anisotropic – they are all capable of reorienting light (acting as magicians). anisotropic not l All anisotropic minerals contain one or two special propagation directions that do not reorient light. oneuniaxial s Minerals with one special direction are called uniaxial twobiaxial s Minerals with two special directions are called biaxial © Jane Selverstone, University of New Mexico, 2003

22. n > 1 for anisotropic substances n = f(vibration direction) Indicatrix no longer a sphere Indicatrix = ellipsoid Note: continuous function, smooth ellipsoid. Hexagonal and tetragonal crystals have one unique crystallographic axis (c axis)  2 identical ones The optical properties reflect this as well: ellipsoid of rotation about c (optically uniaxial) and c = the optic axis Fig 6-10 Bloss, Optical Crystallography, MSA

23. Uniaxial ellipsoid and conventions: (-) crystal:  >   oblate (+) crystal:  >   prolate Fig 6-11 Bloss, Optical Crystallography, MSA

24. l Circular Section  optic axis: all  's l Principal Sections have  and true  : max & min n's Random Sections (  ' and  ) All sections have  !! Any Any non-circular cut through the center of a uniaxial indicatrix will have  as one semiaxis and  ' (or true  ) as the other Fig. 6-12 Depending on light propagation we can have:

25. O E Fig 6-7 Bloss, Optical Crystallography, MSA Fig 6-8 Bloss, Optical Crystallography, MSA Calcite experimentdouble refraction Calcite experiment and double refraction

26. Circular Section: Circular Section: all rays are O-rays and vibrate parallel  Fig 6-13 Bloss, Optical Crystallography, MSA

27. Random Section: Random Section: O-ray vibrates parallel  E-ray vibrates parallel  ' Optic Axis Fig 6-13 Bloss, Optical Crystallography, MSA

28. Principal section: This is essentially the same as random, but here  ' is really true . In this case both rays really do vibrate  propagation & follow same path (as we have simplified the random case) We shall consider random and principal as alike, only the value of  varies. Optic Axis Fig 6-13 Bloss, Optical Crystallography, MSA

29. Essentially 2 possibilities (light coming toward you) 1. Circular section Light prop. || OA All vibration directions  c are the same n O E Fig 6-7 Bloss, Optical Crystallography, MSA Optic Axis Fig 6-13 Bloss, Optical Crystallography, MSA Like isotropic (no unique plane containing ray and c-axis) Only one ray (O-ray) with n =  (doesn’t split to two rays) Extinct with analyzer in and stays that way as rotate stage (behaves as though isotropic) If incident light is unpolarized it will remain so

30. Essentially 2 possibilities (light coming toward you) 2 rays Only 2 privileged vibration directions O-ray with n =  E-ray with n =  ’ or  (depending on section) Does not stay same as rotate (more later) Fig. 6-12 O E Fig 6-7 Bloss, Optical Crystallography, MSA 2. Elliptical section Any orientation other than circular

31. B-C: Polarized parallel  and  Transmits only one ray! Transmits only one ray! (no component parallel to the other privileged direction) Note convention here: Light slows upon entering xl. Since frequency (& color) is about same, the slowing is illustrated by more compressed wave forms (they spend more time in the xl), so vibrate more times (vibrate more per length traveled) A: Unpolarized Ray splits into  and  This figure rotates the light source (we rotate the crystal) Fig 6-17 Bloss, Optical Crystallography, MSA D: Polarized at random angle Resolves into components parallel  and parallel 

32. Rotating the stage Anisotropicwith an elliptical indicatrix section exactly every 90 o Anisotropic minerals with an elliptical indicatrix section change color as the stage is rotated; these grains go black 4 times in 360° rotation-exactly every 90 o Isotropic: Isotropic: glass or isometric minerals or look down optic axis of anisotropic minerals polarizer

33. Consider rotating the crystal as you watch: B = polarizer vibration direction parallel   only E-ray extinct Analyzer in  extinct C = polarizer vibration direction ||   only O-ray extinct also  extinct with analyzer polarizer    

34. Consider rotating the crystal as you watch: D Polarized light has a component of each Splits  two rays one is O-ray with n =  other is E-ray with n =  recombine When the rays exit the crystal they recombine   polarizer

35. REVIEW l Calcite: Fig 6-7 F 2 rays, each polarized  vibrate  each other & in plane of incidence l Indicatrix- uniaxial F Random Section  O-ray vibrates parallel   E-ray vibrates parallel  ' F Principal section F Circular section  ' and  = “privileged vibration directions” Optic Axis O E

36. Interference in phase A: Particles in phase if displaced from rest position by same amount in same direction F a 1 - a 2 - a 3 are all in phase F b 1 - b 2 - b 3 are also all in phase (but not with a 1 …) perfectly out of phase l particles perfectly out of phase: equal-but-opposite displacement s b 1 and c 1 are not, since in an instant it won't work Fig 7-1 Bloss, Optical Crystallography, MSA Path Difference  Path Difference (  ) = distance between any 2 points on a wave form  usually expressed as x   between any 2 points in phase = i (i=any integer)   between any 2 points perf. out of phase = ( (2i+1) / 2 ) B: Instant later with a second ray entering composite ray C: Shows algebraic sum  interference  composite ray constructive interference If both waves in phase  constructive interference with amplitude greater than either (intensity = A 2 )

37. Interference Interference of light polarized in perpendicular planes but not in crystals where vibrate independently s This works in air & isotropic media, but not in crystals where vibrate independently big step Now we're ready for a big step Fig 7-2 Bloss, Optical Crystallography, MSA

38. Interference travel at different velocities Plane polarized light enters xl. & resolved into 2 rays (if not || optic axis), which vibrate  each other & travel at different velocities (since have different n) travel diff # of  Will thus travel diff # of (even if frequency same or similar) F So if in phase when enter, won't be when exit!! path dif = t (|  -  '|)  The path diff (  ) between O-ray and E-ray = t (|  -  '|) (t = thickness) s absolute value because the crystal can be (+) or (-) thickness mineral orientation   then = t(N-n) and each mineral has a  unique  and ,  is thus a function of the thickness, the mineral observed, and the orientation Fig 7-3 Bloss, Optical Crystallography, MSA

39. Interference 2 crystals of equal t, but different  n i A: n = 1 / 2 N A: n = 1 / 2 N n=small ref index N=large " " F slow ray requires 2 periods & fast only one polarized in same plane as entered F thus come out polarized in same plane as entered   no transmission by analyzer in XPL E E WW N N S S Fig 7-4 Bloss, Optical Crystallography, MSA

40. Interference 2 crystals of equal t, but different  n i B: n = 3 / 4 N F Slow ray requires 2 periods & fast 1.5   100% transmission by analyzer in XPL E E WW N N S S Fig 7-4 Bloss, Optical Crystallography, MSA

41. Transmission by the Analyzer Determined by: a) Angle between analyzer and polarizer a) Angle between analyzer and polarizer (fixed at 90 o ) b) Angle between polarizer and closest privileged direction of xl  When polarizer || either privileged vibration direction  extinct, since only one ray & it's cancelled s Every crystal goes extinct 4 times in 360 o rotation (unless isotropic)

42. Transmission by the Analyzer c)  = path difference = t (N-n) Fig. 7-4  t(N-n) = 1  0% transmission t(N-n) = 1.5  100% transmission Fig 7-6 Bloss, Optical Crystallography, MSA

43. Transmission by the Analyzer Determined by: d)  of lighta new concept  in part (c)  has been expressed in terms of s...but it's really an absolute retardation, some finite # of nm (or A or miles…) absolutedifferent x/  If the transmitted light is white (mixed), each wavelength will be retarded t(N-n) by the same absolute distance, which will be a different x/

44. Transmission by the Analyzer Example: assume xl has t(N-n) that will retard  = 550  m & viewed 45 o off extinction (max intensity) retardation  550550550550550550 400440489550629733 selected light   400440489550629733 1 3 / 8 1 1 / 4 1 1 / 8 1 7 / 8 3 / 4 1 3 / 8 1 1 / 4 1 1 / 8 1 7 / 8 3 / 4 You can see 550  m gets no transmission & others varying amount

45. retardation  550550550550550550 400440489550629733 selected light  400440489550629733 1 3 / 8 1 1 / 4 1 1 / 8 1 7 / 8 3 / 4 1 3 / 8 1 1 / 4 1 1 / 8 1 7 / 8 3 / 4 interference color no green & more red- violet interference color Fig 7-7 Bloss, Optical Crystallography, MSA

46. retardation  800800800800800800 800 400426457550581711 800 selected light  400426457550581711 800 21 7 / 8 1 3 / 4 1 1 / 2 7 / 8  1 / 8 1 2 1 7 / 8 1 3 / 4 1 1 / 2 7 / 8 1 / 8 1 no red or violet & more green Dashed curve: no red or violet & more green Fig 7-7 Bloss, Optical Crystallography, MSA

47. Color chart Colors one observes when polars are crossed (XPL) Color can be quantified numerically:  = n high - n low

48. Color chart Shows the relationship between retardation, crystal thickness, and interference color 550  m  red violet 800  m  green 1100  m  red-violet again (note repeat  ) 0-550  m = “1 st order” 550-1100  m = 2 nd order 1100-1650  m = 3 rd order... Higher orders are more pastel

49. 1) Find the crystal of interest showing the highest colors (  depends on orientation) 2) Go to color chart thickness = 30 microns use 30 micron line + color, follow radial line through intersection to margin & read birefringence Suppose you have a mineral with second-order green What about third order yellow? Estimating birefringence

50. Example: Quartz  = 1.544  = 1.553   1.553 1.544 Data from Deer et al Rock Forming Minerals John Wiley & Sons

51. Example: Quartz  = 1.544  = 1.553 Sign?? (+) because  >  birefringence  maximum  -  = 0.009 called the birefringence (  ) = maximum interference color (when seen?) What color is this?? Use your chart.

52. Color chart Colors one observes when polars are crossed (XPL) Color can be quantified numerically:  = n high - n low

53. Example: Quartz  = 1.544  = 1.553 Sign?? (+) because  >  birefringence  maximum  -  = 0.009 called the birefringence (  ) = maximum interference color (when see this?) What color is this?? Use your chart. For other orientations get  ' -   progressively lower color Rotation of the stage changes the intensity, but not the hue Extinct when either privileged direction N-S (every 90 o ) and maximum interference color brightness at 45 o 360 o rotation  4 extinction positions exactly 90 o apart

54. orthoscopic So far, all of this has been orthoscopic (the normal way) All light rays are ~ parallel and vertical as they pass through the crystal Orthoscopic viewing Fig 7-11 Bloss, Optical Crystallography, MSA l xl has particular interference color = f(biref, t, orientation) l Points of equal thickness will have the same color l isochromes l isochromes = lines connecting points of equal interference color l At thinner spots and toward edges will show a lower color l Count isochromes (inward from thin edge) to determine order

55. What interference color is this? If this were the maximum interference color seen, what is the birefringence of the mineral?

56. Conoscopic Viewing condensing lenBertrand lens A condensing lens below the stage and a Bertrand lens above it Arrangement essentially folds planes of Fig 7-11  cone Light rays are refracted by condensing lens & pass through crystal in different directions Thus different properties Only light in the center of field of view is vertical & like ortho Interference Figures  Interference Figures Very useful for determining optical properties of xl Fig 7-13 Bloss, Optical Crystallography, MSA

57. How interference figures work (uniaxial example) Bertrand lens Sample (looking down OA) sub-stage condenser Converging lenses force light rays to follow different paths through the indicatrix WE-W polarizer N-S polarizer What do we see?? nn nn nn nn nn nn nn nn Effects of multiple cuts through indicatrix © Jane Selverstone, University of New Mexico, 2003

58. Uniaxial Interference Figure Fig. 7-14 O E isochromes l Circles of isochromes l Note vibration directions:   tangential   ' radial & variable magnitude isogyres l Black cross (isogyres) results from locus of extinction directions melatope l Center of cross (melatope) represents optic axis l Approx 30 o inclination of OA will put it at margin of field of view

59. Uniaxial Figure F Centered not F Centered axis figure as 7-14: when rotate stage cross does not rotate F Off center: melatope F Off center: cross still E-W and N-S, but melatope rotates around center F Melatope outside field: F Melatope outside field: bars sweep through, but always N-S or E-W at center F Flash Figure: F Flash Figure: OA in plane of stage Diffuse black fills field brief time as rotate Fig. 7-14

60. Accessory Plates We use an insertable 1-order red (gypsum) plate

61. Accessory Plates l We use an insertable 1-order red (gypsum) plate N l Slow direction is marked N on plate l Fast direction (n) || axis of plate 550nm retardation The gypsum crystal is oriented and cut so that  = (N-n)  550nm retardation N n  it thus has the effect of retarding the N ray 550 nm behind the n ray If insert with no crystal on the stage  1- order red in whole field of view Fig 8-1 Bloss, Optical Crystallography, MSA

62. Accessory Plates Suppose we view an anisotropic crystal with  = 100 nm (1-order gray) at 45 o from extinction Addition If N gyp || N xl  Addition further retarde F Ray in crystal || N gyp already behind by 100nm & it gets further retarded by 550nm in the gypsum plate  100 + 550  650nm F What color (on your color chart) will result? 2 o blue  Original 1 o grey  2 o blue N

63. Accessory Plates Now rotate the microscope stage and crystal 90 o  N gyp || n xl (  still = 100 nm) Subtraction N gyp || n xl  Subtraction ahead F Ray in the crystal that is parallel to N gyp is ahead by 100nm  550  m retardation in gypsum plate  450nm behind F What color will result? F 1 o orange N

64. N What will happen when you insert the gypsum plate?

65. N

66. Optic Sign Determination allin normal to For all xls remember  ' vibrates in plane of ray and OA,  vibrates normal to plane of ray and OA How would you do that? 1) Find a crystal in which the optic axis (OA) is vertical (normal to the stage). How would you do that? 2) Go to high power, insert condensing and Bertrand lenses to  optic axis interference figure (+) (+) crystal:  ’ >   faster so  faster O E  '  '  '  '    

67. Fig 7-13 Bloss, Optical Crystallography, MSA

68. Optic Sign Determination Inserting plate for a (+) crystal:  subtraction in NW & SE where n||N  addition in NE & SW where N||N Whole NE (& SW) quads add 550nm s isochromes shift up 1 order Isogyre adds  red In NW & SE where subtract s Each isochrome loses an order Near isogyre (~100nm) s get 450 yellow in NW & SE (100-550) s and 650 blue in NE & SW (100+550) (+) (+) crystal:  ’ >   faster so  faster  '  '  '  '     add add sub sub N

69. (+) OA Figure with plate Yellow in NW is (+) (+) OA Figure without plate

70. Optic Sign Determination Inserting plate for a (-) crystal:  subtraction in NE & SW where n||N  addition in NW & SE where N||N Whole NW (& SE) quads add 550nm s isochromes shift up 1 order Isogyre still adds  red In NE & SW where subtract s Each isochrome loses an order Near isogyre (~100nm) s get 650 blue in NW & SE s and 450 yellow in NE & SW (-) (-) crystal:  ’ <   slower so  slower  '  '  '  '     add sub add sub N

71. (-) OA Figure with plate Blue in NW is (-) (-) OA Figure without plate (same as (+) figure)

72. Can determine the refractive index of a mineral by crushing a bit up and immersing the grains in a series of oils of known refractive index. When the crystal disappears perfectly n mineral = n oil The trick is to isolate  and true  by getting each E-W (parallel to the polarized light) Orienting crystals to determine  and 

73. To measure  only (if all grains of a single mineral): low interference colors- ideally a grain that remains extinct as the stage is rotated 1) Find a grain with low interference colors- ideally a grain that remains extinct as the stage is rotated 2) (check for centered OA figure) 3) Determine optic sign while you're at it (for use later) 4) Back to orthoscopic : all rays are  5) Compare n xl to n oil Orienting crystals to determine  and 

74. Now look at the other crystals of the same mineral: If the crystals are randomly oriented in a slide or thin section you may see any interference color from gray- black (OA vertical) to the highest color possible for that mineral (OA in plane of stage and see  and true  ). Orienting crystals to determine  and 

75. To measure  : 1) Find a grain with maximum interference colors 2) (Check for flash figure?) 3) Return  orthoscopic at lower power 4) Rotate 45 o from extinction (either direction) 5) Figure out whether  is NE-SW or NW-SE & rotate it to E-W extinction 6) Then only  coming through! Oils are then used  n must redo with each new oil as get closer! Ugh! Orienting crystals to determine  and  (+) xl  >  so  faster (-) xl  >  so  faster Thus whole grain will gain a color when N xl || N gyp i.e. slow direction is NE-SW

76. absorption color in PPL l Changes in absorption color in PPL as rotate stage (common in biotite, amphibole…) l Pleochroic formula:  Example: Tourmaline:  = dark green to bluish  = colorless to tan Can determine this as just described by isolating first  and then  E-W and observing the colorPleochroism

77. Hornblende as stage is rotated

78. Biotite as stage is rotated

79. Biaxial Crystals Orthorhombic, Monoclinic, and Triclinic crystals don't have 2 or more identical crystal axes F The indicatrix is a general ellipsoid with three unequal, mutually perpendicular axes F One is the smallest possible n and one the largest   = smallest n(fastest)   = intermediate n   = largest n(slowest) principal vibration directions xyz The principal vibration directions are x, y, and z ( x || , y || , z ||  )  ' <  '<  By definition  ' <  '<  Fig 10-1 Bloss, Optical Crystallography, MSA

80. Biaxial Crystals If  <  <  then there must be some point between  &  with n =  Because =  in plane, and true  is normal to plane, then the section containing both is a circular section Has all of the properties of a circular section! If look down it:  all rays =  F no preferred vibration direction F polarized incoming light will remain so F unpolarized ““““ F thus appear isotropic as rotate stage   Looking down true  = 

81. Biaxial Crystals If  <  <  then there must be some point between  &  with n =    Looking down true  =   optic axis by definition OA

82. Biaxial Crystals If  <  <  then there must be some point between  &  with n =   optic axis by definition Biaxial And there must be two!  Biaxial Orthorhombic, Monoclinic, and Triclinic minerals are thus biaxial and Hexagonal and tetragonal minerals are uniaxial   Looking down true  =  OAOA

83. Biaxial Crystals Nomenclature: Optic Axial Plane (OAP) 2 circular sections  2 optic axes Must be in  -  plane = Optic Axial Plane (OAP) optic normal Y ||  direction  OAP = optic normal Fig 10-2 Bloss, Optical Crystallography, MSA Acute angle between OA's = 2V acute bisectrix B xa The axis that bisects acute angle = acute bisectrix = B xa obtuse bisectrix B xo The axis that bisects obtuse angle = obtuse bisectrix = B xo

84. Biaxial Crystals B(+) B(+) defined as Z (  ) = B xa Thus  closer to  than to    Looking down true  =  OAOA

85. Biaxial Crystals B(-) B(-) defined as X (  ) = B xa Thus  closer to  than to    Looking down true  =  OA OA

86. Let's see what happens to unpolarized light travelling in various directions through a biaxial crystal Light will propagate with normal incidence to: Both = O-rays Both polarized, and vibrate  each other (as uniaxial) One ray vibrates || Z and has n =  and the other vibrates || Y and n = ...or Z and X or Y and X 1) Principal Plane - Includes 2 of the 3 true axes or principal vibration directions Fig 10-11C Bloss, Optical Crystallography, MSA

87. Let's see what happens to unpolarized light travelling in various directions through a biaxial crystal Light will propagate with normal incidence to: This is identical to uniaxial: 1 O-ray and 1 E-ray  and  ' or  and  '... vibration in incident plane so indicatrix works! 2) Semi-random Plane Includes one principal vibration direction Fig 10-11B Bloss, Optical Crystallography, MSA

88. Vibration directions of 2 rays in all 3 cases are mutually perpendicular, and || to the longest and shortest axes of the indicatrix ellipse cut by the incident plane This is the same as with uniaxial, only the names change 3) Random Plane No principal vibration directions  2 E-rays One vibrates in the OWZ' plane and || OZ’ with n =  ' The other vibrates in the OWX' plane and || OX’ with n =  ’ Fig 10-11A Bloss, Optical Crystallography, MSA

89. 4) Circular Section (either one) Acts as any circular section: Unpolarized remains so Polarized will pass through polarized in the same direction as entered with n =   extinct in XPL and remains so as rotate stage   Looking down true  =  OAOA

90. Review Fig 10-10 Bloss, Optical Crystallography, MSA

91. black Biaxial Interference Figures B xa figure B xa figure (B xa is vertical on stage) As in uniaxial, condensing lens causes rays to emanate out from O OX  OS  OA results in decreasing retardation (color) as  OA  OT  OU Increase again, but now because    OX  OQ  OP  incr retardation (interference colors) OR is random with  ' and  ' Fig 10-14 Bloss, Optical Crystallography, MSA

92. Biaxial Interference Figures B xa figure Result is this pattern of isochromes for biaxial crystals Fig 10-15 Bloss, Optical Crystallography, MSA

93. Biaxial Interference Figures Biot-Fresnel Rule: Biot-Fresnel Rule: for determining privileged vibration directions of any light ray from path and optic axes Calcite Expt: no longer a single plane containing ray and OA Vibration directions bisect angle of planes as shown Fig 10-9A Bloss, Optical Crystallography, MSA

94. Biaxial Interference Figures Application of B-F rule to conoscopic view B xa figure + = bisectrices of optic axis planes Isogyres are locus of all N-S (& E-W) vibration directions Since incoming light vibrates E-W, there will be no N-S component  extinct Fig 10-16 Bloss, Optical Crystallography, MSA

95. Biaxial Interference Figures Centered B xa Figure Fig 10-16 Bloss, Optical Crystallography, MSA

96. Biaxial Interference Figures Same figure rotated 45 o Optic axes are now E-W Clearly isogyres must swingDemonstration Fig 10-16B Bloss, Optical Crystallography, MSA

97. As rotate Centered Optic Axis Figure Large 2V: B xa Figure with Small 2V: Not much curvature Makes use of B xa awful

98. Always use optic axis figures F Easiest to find anyway. Why? l B xo looks like B xa with 2V > 90 o l Random Figures: Isogyre sweeps through field (not parallel x-hair at intersection, so can recognize from uniaxial even with this odd direction) F Useless if far from OA

99. Biaxial Optic Sign B(-) B(-)a = B xa thus b closer to g Fig. 11-1A add add subtract 100 gray + 550  650 blue 100 gray - 550  450 yellow

100. Biaxial Optic Sign B(-) B(-)  = B xa thus  closer to  (in stage) add subtract add Centered B xa 2V = 35 o With accessory plate

101. Biaxial Optic Sign B(+) B(+)  = B xa thus  closer to  (in stage) Fig. 11-1A sub sub add

102. & Always use Optic Axis Figure & curvature of isogyre to determine optic sign How find a crystal for this? Blue in NW is (-) still works

103. Estimating 2V OAP Fig 11-5A Bloss, Optical Crystallography, MSA

104. Sign of Elongation N  If  || elongation will always add length slow  length slow length fast If  || elongation will always subtract  length fast length slow U(+) will also  length slow length fast U(-) will also  length fast 

105. Sign of Elongation N  If  || elongation length slow Sometimes will add  length slow length fast Sometimes will subtract  length fast    Platy minerals may appear elongated too Can still use sign of elongation on edges