optical min2

8/18/2019 Optical Min2

1/27

Optical Mineralogy in a Nutshell

Use of the petrographic microscope in

three easy lessons

Part II

© Jane Selverstone, University of New Mexico, 2003


2/27

Quick review

• Isotropic minerals –velocity changes as light enters mineral,but then is the same in all directions thru xtl;no rotation or splitting of light.

• Anisotropic minerals –light entering xtls is split andreoriented into two planepolari!ed components thatvibrate perpendicular to one another and travel w"different speeds.

• #niaxial minerals have one special direction along which lightis not reoriented; characteri!ed by $ %Is .

• &iaxial minerals have two special directions along which lightis not reoriented; characteri!ed by ' %Is .

(hese minerals are characteri!ed by a single %I)because light travels w" same speed throughout xtl*


3/27

+eve talked about minerals as magicians now lets prove it-

calcite

c a l c i t e

c a l c i t e

c a l c

i t e

ordinaryray, ω

)stays stationary*extraordinary

ray, ε)rotates*

calcite


4/27

• single light ray coming into cc is split into two• rays are refracted different amounts• rays have different velocities, hence different %Is• stationary rayordinary, rotating rayextraordinary• because refraction of ε is so large, cc must have hiδ ( remember/ δ . n hi n lo )

0onclusions from calcite experiment

If we were to look straight down caxis, we would see

only one star – no splitting-

0axis is optic axis )true for all uniaxial minerals, but unfortunately not for biaxial minerals*

1ore on this in a few minutes2


5/27

&ack to birefringence"interference colors

3bservation/fre4uency of lightremains unchangedduring splitting,regardless of material

5 6"λ if light speed changes,

λ must also change

λ is related to color; if λ changes, color also changes

mineralgrain

plane polari!edlight

fast ray)low n*

slow ray)high n*

lower polari!er

∆retardation

d


6/27

• 7ight waves may be in phase or out of phase when theyexit xtl

• +hen out of phase, some component of light gets

through upper polari!er and displays aninterference color

• +hen one of the vibration directions is parallel to thelower polari!er, no light gets through the upperpolari!er and the grain is 8at extinction9 )black*

Interference phenomena

:ee esse p.


7/27

mineralgrain

plane polari!edlight

fast ray)low n*

slow ray)high n*

lower polari!er

∆retardation

d

At time t, when slow ray =st exits xtl/:low ray has traveled distance d5ast ray has traveled distance d@∆

time distance"rate

:low ray/ t d"6slow

5ast ray/ t d"6fast @ ∆"6air

(herefore/ d"6slow d"6fast @ ∆"6air

∆ d)6air"6slow 6air"6fast*

∆ d)nslow nfast*

∆ d δ

∆ thickness of t.s. x birefringence


8/27

&irefringence"interference colors

%etardation in nanometers

( h i c k n e s s i n m i c r o n s

birefringence


9/27

%emember determining optic sign last week with the gypsum plate

s l o w

blue in B )@*

Cypsum plate has constant ∆ ofD'E nm =storder pink

Isogyres black/ ∆E&ackground gray/ ∆=EE

Add or subtract D'E nm/

D'E@=EE>'E nm blue )@*D'E=EE


10/27

7ets look at interference colors in a natural thin section/

ote that different grains of the same mineral showdifferent interference colors – why

ol

ol

ol

olol

ol plagplag

plag

plag

plag

plag

Fifferent grains of same mineral are in different orientations

If every grain of the same mineral

looks different, how are we ever goingto be able to identify anything


11/27

(ime for some new tricks/ the optical indicatrix

(hought experiment/

0onsider an isotropic mineral )e.g., garnet*

Imagine point source oflight at garnet center;

turn light on for fixedamount of time, then mapout distance traveled bylight in that time

+hat geometric shape is defined by mapped light rays


12/27

Isotropic indicatrix

:occer ball)or an orange*

7ight travels the samedistance in all directions;n is same everywhere,thus δ nhinlo E black


13/27

anisotropic minerals - uniaxial indicatrix

4uart!

calcite

caxis

caxis

7ets perform the same thought experiment2


14/27

Uniaxial indicatrix

caxiscaxis

:paghetti s4uash uniaxial )@*

tangerine uniaxial )*

4uart!

calcite


15/27

0ircular section is perpendicular to the stem )caxis*

Uniaxial indicatrix


16/27

Uniaxial indicatrix(biaxial ellipsoid)

nε

nω a=X

c=Z

b=Y

nε

a=X

c=Z

nωb=Y

+hat can the indicatrix tell us aboutoptical properties of individual grains


17/27

nω nω Etherefore, δE/ grain stays black

)same as the isotropic case*

nε

nω a=X

c=Z

b=Y

nω

nω

Gropagate light along the caxis, note whathappens to it in plane of thin section


18/27

Crain changes color upon rotation. Crain will go black whenever indicatrixaxis is B+ or :

nε

nω

(his orientation will show the maximum δ of the mineral

n ε

n ω

n ε

n ω

n ε

n ω

n ε

n ω

nε nω H Etherefore, δ H E

:

+ B

ow propagate light perpendicular to caxis


19/27

anisotropic minerals - biaxial indicatrix

clinopyroxenefeldspar

ow things get a lot more complicated2


20/27

iaxial indicatrix(triaxial ellipsoid)

O! O!

"#$

Y

X

Z

nβ

nγ

nαnβ

nβ

nγ

nα

nγ

nβ

nαnβ

(he potato-

$6!

(here are $ different ways to cut this and get a circle2


21/27

Alas, the potato )indicatrix* can have any orientationwithin a biaxial mineral2

c

a

b

Z

X

Y

Y

aZ

bX

colivine augite


22/27

2 but there are a few generali!ations that we can make

(he potato has ' perpendicular principal axes of

different length – thus, we need ' different %Isto describe a biaxial mineral

direction nα )lowest*J direction nβ )intermed; radius of circ. section*K direction nγ )highest*

• 3rthorhombic/ axes of indicatrix coincide w" xtl axes• 1onoclinic/ J axis coincides w" one xtl axis• (riclinic/ none of the indicatrix axes coincide w" xtl axes


23/27

O! O!"#$

Y

X

Z

nβ

nγ

nα

$6/ a diagnostic property of biaxial minerals

• +hen $6 is acute about K/ )@*• +hen $6 is acute about / )*

• +hen $6LEM, sign is indeterminate

• +hen $6EM, mineral is uniaxial

$6 is measured using an interference figure21ore in a few minutes


24/27

Now interference figures work )uniaxial example*

&ertrandlens

:ample)looking down 3A*

substagecondensor

0onverging lenses force lightrays to follow different pathsthrough the indicatrix

+ B

: polari!er+hat do we see

n ω

n ε

n ω

n ε

n ω n

ε

n ω n

ε

Bffects of multiple cuts thru indicatrix


25/27

&iaxial interference figures

(here are lots of types of biaxial figures2 well concentrate on only two

=. 3ptic axis figure pick a grain that stays dark on rotation

+ill see onecurved isogyre

determine $6 from curvature of isogyre

LEM >EM


26/27

$. &xa figure )acute bisectrix* obtained when you are looking straight

down between the two 3.A.s. Nard to find, but look for a grain withintermediate δ.

&iaxial interference figures

#se this figure to get sign and $6/

)@* $6$EM $6EM

:ee esse p. =E=

O! O!

"#$

Y

X

Z

nβ

nγ

nα


27/27

Quick review/

Indicatrix gives us a way to relate optical phenomena tocrystallographic orientation, and to explain differencesbetween grains of the same mineral in thin section

O! O!

"#$

Y

X

Z

nβ

nγ

nα

hi δ

O! O!

"#$

Y

X

Z

nβ

nγ

nα

lo δ

Isotropic #niaxial &iaxial :ign $6All of these help us to uni4uely identify unknown minerals.

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