6.2. Conoscopic mode
6.2.1. Interference Figures
The conical (convergent) shape of light interferes with the sample and the shape of the
interference result is an image (interference figure) that forms somewhere between the analyzer and ocular. In order to bring the interference image closer to the ocular, the Bertrand Lens is used.
An interference figure consists of two dark diffuse intersecting lines (or curves) called isogyres (regions of zero path difference) and circular coloured rings called isochromates, representing regions of identical path difference; The higher the (Δ), the more isochromates there are (e.g.
Fig. 40).
Interference figures for uniaxial crystals
Uniaxial interference figures ideally look like this:
Figure 40: Interference figure for calcite (section perpendicular to the optic axis).
When the section is perpendicular to the optical axis of an uniaxial crystal (e.g. calcite, which is trigonal), the interference figure is a cross (Fig. 40) centred in the middle of the view.
Rotating the stage, the cross, as well the isochromates, do not move. At the intersection of the isogyres is the optic axis (which corresponds to the A3 fold axis of symmetry of the calcite) If the section is oblique to the optic axis, the cross will be out of view and we have to rotate the stage. By rotating the stage, we will observe one vertical “arm” of the cross, moving
horizontally as we rotate the stage, and when it disappears, a horizontal arm will show up, moving vertically (fig. 41).
Figure 41: Interference figure for a uniaxial crystal, section oblique to the optic axis. The optic axis is outside the interference figure but the vertical and horizontal black lines move horizontally and vertically, respectively, as the stage is rotated.
Interference figure for biaxial crystals
Isochromates
Isogyres (regions of zero path difference) Rotation of the stage does not
change the image
Optic axis
Figure 42: Interference figure for a biaxial crystal, section perpendicular to one of the optic axes.
The most useful biaxial interference figures are those for sections perpendicular to the 2V bisectrix (the bisectrix of the acute angle between the two optic axes). In these figures we can see both optic axes (Fig. 43a).
How do we find the section cut most closely perpendicular to the acute bisectrix? Trial and error! Start with the lowest interference colour section you can find and, in the Conoscopic Mode, work your way up until you find the right (i.e., most useful) interference figure.
Determination of the optic sign -using the λ-plate-
The optic sign can be either positive or negative, and this tells us if nγ or nα, respectively, is parallel to the 2V bisectrix.
After finding the interference figure, we introduce the λ-plate. The wavelength introduced by the plate can produce either addition or substraction in the retardation of the isochromates (Fig.
44)!
What does the optic sign mean? It shows the shape of indicatrix in relation to the optic axis of the crystal. For uniaxial crystals: is the optical axis parallel or not with the nγ or nα? For biaxial crystals: is the bisectrix of the acute 2V angle parallel with nγ or nα? See the shape of biaxial indicatrices in Fig. 45.
Figure 43a: Position of the optic axes
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Figure 43b: Movement of isogyres during stage rotation.
From top to bottom, the 2V angle increases.
Figure 44: Determination of the optic sign
Observe the upper right or lower left quadrant:
Add the λ-plate
-Constructive (addition) colours indicate a positive optic sign;
-destructive (subtraction) colours indicate a negative optic sign.
Figure 45: Positive and negative optical sign
a) Crystal biaxial positive : Acute bisectrix: nγ nα and nβ T acute bisectr, δ > 0 b) Crystal biaxial negative Acute bisectrix: nα nβ and nγ T acute bisectr. δ > 0
A quick reference for the determination of the optic sign of minerals with low birefringence (IF 1st order grey-white) is provided in figure 46.
Figure 46: Determination of the optic sign for crystals with low birefringence.
Estimation of the 2V angle
This estimation is an approximation using the interference figures. The best sections are those perpendicular to the acute bisectrix (Fig. 47a). The estimate is done by comparison with images from Fig. 47.
a) 2V=90: one straight line rotating in the opposite direction compared to the rotation of the stage;
b) There is a moderate 2V angle if the isogyres are moderately curved;
c) There is a low 2V angle if the two wings of the cross meet and break slightly as we rotate the stage. The two wings do not leave the interference figure when rotating the stage only if the section is ~ perpendicular to the acute bisectrix (i.e. a uniaxial-like interference figure).
a) Uniaxial to optic axis
c) Biaxial to optic axis b) Biaxial to acute bisectrix
Figure 47: Estimation of the 2V angle (see text). After Shelley (1993).
Is the interference figure good enough for seeing the optical character and determining the optical sign? Interference figures: The Good, the Bad and the Ugly (Fig. 48):
Figure 48: Types of possible sections obtained for biaxial crystals. Which one is good?
The Good: Section to the acute bisectrix
The Bad: Section oblique to the acute bisectrix
Another Good one: Section ± to OA The Ugly: “Flash Figure”
Section to the obtuse bisectrix (biaxial minerals) or parallel to the OA (uniaxial minerals): confusion guaranteed.
Useful charts for mineral identification: the Tröger Chart
A (sometimes dangerous) shortcut to identify minerals with the petrographic microscope involves using the Tröger Chart, which has the refractive index on the x axis and birefringence values on the y axis. The zero value of birefringence (isotropic crystals) positioned at the middle of the chart, so that the birefringence values increase from zero up but also decrease from zero down in the chart. In the upper part are found minerals with positive optical sign, while in the lower part of the chart are minerals with negative optical sign. To make a distinction between uniaxial and biaxial crystals, the uniaxial are represented with bold circles.
The steps to take are:
a) Check refractive index (n)/chagrin (low, medium, high); for n(RI)<1.65 use part one of the chart (Fig. 49a) and for n>1.65 use part two of the chart (Fig. 49b)
b) Check the maximum birefringence (birefringence colour; then estimate the value of birefringence using the Michel-Levy chart)
c) Determine the optic character (uni- or biaxial) and the optic sign
d) Find the region on the Tröger Chart corresponding to these determined values e) Check the optical characteristics of minerals occurring in that region
f) Check the likelihood of the determined mineral occurring in the rock type investigated g) Don‟t forget: there are more mineral species than shown on the charts!
Figure 49a: Tröger Chart part 1 (refractive indexes from 1.45 to 1.65)
Figure 49b: Tröger Chart part 1 (refractive indexes from 1.65 to 2.80)
27 Key mineral species
It is useful to know the key optical characteristics for the minerals listed below (the common rock-forming minerals).
1. Quartz 2. Plagioclase*
3. K-feldspar* 4. Cordierite*
5. Biotite* 6. Tourmaline*
7. Amphibole* 8. Muscovite
9. Talc 10. Chlorite*
11. Garnet* 12. Spinel*
13. Staurolite 14. Rutile
15. Chloritoid 16. Calcite/Dolomite
17. Titanite 18. Zircon/Monazite
19. Olivine* 20. Cpx*
21. Opx* 22. Epidote*
23. Apatite 24. Kyanite
25. Sillimanite 26. Andalusite
27. Nepheline
Key Characteristics of common minerals: Speeding up mineral identification
Many common mineral phases have unique characteristics (or combinations of two or three) which make them unmistakable.
Examples
Quartz: low RI (~like the resin); low birefringence (1st order IF colour); uniaxial positive; no (visible) twins.
Plagioclase: low RI and birefringence (~like Qtz); lamellar twinning; biaxial positive or negative.
Staurolite: pale yellow pleochroism; high RI; frequently idiomorphic.
Carbonates: very high birefringence, relief changes when you turn the stage; uniaxial negative.
Identify the key characteristics and note them in your mineral catalogue.
A few hints for the relationship between chemical composition - optical properties
Some cations from the Transition Elements in the Periodic Table (including Fe, Cr, V, Ti, etc.) which have several possible valence states in rocks, produce more intense but variable absorption of light, and are called chromophores. The result is that minerals rich in these elements will be more strongly coloured in thin sections (in PPL mode): Fe2+ gives gray, yellow to greenish colours, depending on its concentration and on the absorption produced by other cations (e.g. in olivine, pyroxene, amphibole, chlorite). Fe3+ gives brown colours (in oxydated hornblende = brown hornblende) or green in oxydized biotite. Cr3+ gives pale green colours (e.g. in spinels, Cr-diopside, fuxite (Cr-mica), Cr-staurolite, Cr-cordierite); Ti produces reddish-brown colours (such as in Ti-rich biotite).
In addition to the strong selective absorption, the presence of these cations also increases the refractive indices of the mineral, causing higher relief. This is useful in composition estimations for minerals that are part of solid solutions. For example, in olivine or pyroxene, Fe2+ shares a structural position with Mg2+ (so Fe2+ can substitute for Mg in any proportion).
The Mg-rich end member of the solution will be colourless, but the solid solution becomes more coloured and the refractive index increases as it has more Fe2+ instead of Mg. The Fe2+
end members will be green with higher relief.
When dealing with silicates (as we usually are in rocks), coloured minerals as seen in PPL can be expected to have a positive relief (have refractive indices superior to the resin). There are few exceptions: the bluish hauyine and nosean from the sodalite group have negative relief, but the bluish colour is given by the absorption produced by small amounts of the [SO4] molecule.
The silicates with Al, Ca, Mg, or with Ca, Na, K (note the absence of chromophores) are typically colourless (e.g. all feldspars, feldspathoids, white mica).
The substitution of Ca for Na in plagioclase solid solutions produces no colour change, but does induce an increase in the refractive index (relief) and the extinction angle. Michel-Levy proposed a method to estimate the Ca-end member (Anorthite CaAl2Si2O8) in a plagioclase, based on the extinction angle.
The carbonates always show twinkling (a modification of relief from positive to negative) when the stage is rotated. Together with the high order birefringence (4th order), the twinkling is diagnostic for carbonates.
Tips for discriminate between different mineral groups All cubic minerals are isotropic.
All orthorhombic minerals, as well as all uniaxial minerals (medium symmetry: trigonal, tetragonal, hexagonal), have parallel extinction (except for basal sections, which have symmetrical extinction).
All monoclinic and triclinic minerals have oblique extinction (except for basal sections which have symmetrical extinction).
All phyllosilicates have parallel extinction and perfect basal cleavage; the extinction is not total (smooth) but „rough‟ (small bright coloured spots are present across its entire surface).
All orthosilicates have relatively high refractive indices (relief) All tectosilicates have low or medium-low refractive indices (relief) Sulphates (e.g. gypsum) have usually negative refractive indices (relief)
Heavy elements (down periods in the periodic table) produce high relief (Ba, U, REE etc) in their host mineral
Sulphides are all opaque (as some of the oxides: magnetite, hematite, ilmenite); yellowish-brown alterations on fissures (no pleochroism, no birefringence) are usually Fe-hydroxides (goethite, lepidocrocite etc) or hematite (dark reddish).
Mineral associations: helpful in identifying minerals
Not all minerals can be naturally associated in a rock. Most rocks have 2-5 abundant minerals and a few other minerals as possible accessories or alteration. The natural association of minerals in rocks is controlled by their stability, which mainly depends on chemistry, pressure (including water pressure), and temperature.
-olivine and quartz are never found together in equilibrium in the same thin section (one is undersaturated in SiO2, the other is super-saturated in SiO2, respectively).
-feldspathoids (nepheline, sodalite, cancrinite, etc.) are never found together with quartz (same explanation as above);
-if olivine has been recognised (medium-high relief, no cleavage, strong chagrin, high birefringence), it is frequently associated with pyroxenes (no chagrin, good cleavage, similar relief, parallel extinction = orthopyroxene; oblique extinction (30-45°) = clinopyroxene) and/or amphiboles (longer prisms, stronger pleochroism, typical basal sections with 120° angle between cleavages, medium relief, lower extinction angle), and/or plagioclase (colourless, low birefringence first order, polysynthetic twinning)
-grid twinning is typical for microcline (K-feldspar), and is commonly associated with quartz and (sodic) plagioclase
-perthitic textures - fine lamellae of albite (relief zero or negative) in a host of K-feldspar (stronger negative relief than albite); perthites are typical for K-feldspar (orthoclase, microcline, rare in sanidine).
Mineral Identification – A Beginner’s Guide
to Identifying the Common Rock-Forming Minerals using Transmitted Light Microscopy Is your mineral?:
COLOURLESS? COLOURED?
ISOTROPIC? low relief? hole in slide, or basal section of a non-isotropic mineral
ISOTROPIC? green? spinel
high relief? garnet black? “opaque” (oxides, sulphides)
NON-ISOTROPIC? NON-ISOTROPIC?
UNIAXIAL? UNIAXIAL?
LOW RELIEF? (relief masked by mineral colour)
positive? quartz pleochroic brown, green, orange
(pseudo-uniaxial or very low 2V)?
biotite
negative? nepheline, scapolite pleochroic pale brown to colourless? phlogopite
MODERATE RELIEF? BIAXIAL?
positive, usually as laths muscovite, talc very pale green to colourless, very weakly pleochroic?
cpx, chlorite, chloritoid, muscovite, serpentine
HIGH RELIEF? pleochroic pale pink to pale green to
colourless?
hypersthene Positive-negative (“relief
pleochroisme”, with distinct cleavages calcite pleochroic yellow-brown to colourless? staurolite
BIAXIAL? pleochroic distinctly green, brown,
blue-green?
hornblende, tourmaline LOW RELIEF?
may have polysynthetic twinning feldspars, cordierite pleochroic brown to colourless, often euhedral, very high δ?
titanite
HIGH RELIEF? reddish-brown needles, very high δ? rutile
conchoidal fracture? olivine pleochroic blue, purple? riebeckite, glaucophane
idio- to subidioblastic, in a metamorphic rock?
Al2SiO5: andalusite, sillimanite, kyanite
AMORPHOUS (no optic sign)
granular, with anomalous 1st order colours?
clinozoisite, epidote opaque interior, brown at thin edges chromite up to 2 distinct cleavage directions opx, cpx, wollastonite, all
amphiboles other than
red hematite
A Birefringence Primer
Interference colours (birefringence) produced when the polariser and analyser are both “in” (crossed nicols, or crossed polars).
For mineral diagnostic purposes, the colours refer to “maximum birefringence”, produced only when mineral grains are aligned perpendicular to their c-axis (i.e., many grains will show interference colours below the maximum, but the „average” or typical colour seen in a thin section is usually close enough.
In strongly-coloured minerals, interference colours may be masked by the mineral colour; if the apparent interference colour looks “odd”, compare it with the actual mineral colour in plane-polarised light, to avoid confusion.
Birefringence
If a mineral is black, does that mean it is automatically “1st order Black”?
Not necessarily; it could also be
o an opaque mineral (light is not transmitted through it), so it is also black under plane-polarised light (i.e., with analyser “out”)
o an isotropic mineral is always black under cross-polars; it has no birefringence and is therefore not “1st order” per se
o basal-orientated sections (looking directly down the c-axis, in general) can be 1st Order black, but this is not the maximum birefringence for that particular mineral.
o a hole in the slide, often the result of “plucking” of certain minerals, or where there are void spaces (not uncommon in volcanic rocks and sediments); it will have “very low relief” and no crystal shape or other properties.
Got it narrowed down yet?
Yes? – Good! Now go look up the detailed properties of the possible minerals, and match them to the observed properties & associated minerals and textures.
No? – Is it similar to anything? (probably); There may be some common “similar” minerals not listed here in related mineral groups, other solid solution end-members, etc., so start with the mineral(s) it looks the most similar to, and work from there.
Still stumped? Follow the identification Table for Common Minererals in Thin Sections. If still stumped....Ask a petrologist…
Identification Tables for Common Minerals in Thin Section
These tables provide a concise summary of the properties of a range of common minerals. Within the tables, minerals are arranged by colour so as to help with identification. If a mineral commonly has a range of colours, it will appear once for each colour.
To identify an unknown mineral, start by answering the following questions:
(1) What colour is the mineral?
(2) What is the relief of the mineral?
(3) Do you think you are looking at an igneous, metamorphic or sedimentary rock?
Go to the chart, and scan the properties. Within each colour group, minerals are arranged in order of increasing refractive index (which more or less corresponds to relief). This should at once limit you to only a few minerals. By looking at the chart, see which properties might help you distinguish between the possibilities. Then, look at the mineral again, and check these further details.
Notes (refer to notations and observations in the tables below):
(i) Name: names listed here may be strict mineral names (e.g., andalusite), or group names (e.g., chlorite), or distinctive variety names (e.g., titanian augite). These tables contain a selection of some of the more common minerals. Remember that there are more than 4000 minerals, although 95% of these are rare or very rare. The minerals in here probably make up 95% of medium and coarse-grained rocks in the crust.
(ii) IMS: this gives a simple assessment of whether the mineral is common in igneous (I), metamorphic (M) or sedimentary (S) rocks. These are not infallible guides - in particular many igneous and metamorphic minerals can occur occasionally in sediments. Bear this in mind, even if minerals are not marked as being common in sediments.
(iii) Colour in thin sections (TS): the range of colours for each mineral is given, together with a description of any pleochroism. Note that these are colours seen in thin-section, not handspecimen.
The latter will always be much darker and more intense than thin section colours.
(iv) RI: the total range of refractive index shown by the mineral with this coulour is shown: This covers any range due to compositional variation by solid solution, as well as the two or three refractive indices of anisotropic minerals.
(v) Relief : is described verbally, followed by a sign indicating whether the relief is positive or negative (ie greater or less than the mounting medium of the thin-section - 1.54). Minerals with refractive indices close to 1.54 have low relief, those with much higher or lower refractive indexes will have high relief.
(vi) Extinction: angles are only given where minerals usually show a linear feature such as a cleavage and/or long crystal faces. For plagioclase feldspars (stippled) the extinction angles given are those determined by the Michel-Levy method (see a textbook for details).
(vi) Int. Figure: this gives details of the interference figure. Any numbers given refer to the value of 2V (normally a range is given), followed by the optic sign. For uniaxial minerals the word "Uni" is given, followed by the sign. Your course may or may not have covered interference figures. If not, ignore this section!
(vii) Birefr: Birefringence is described verbally. In some cases the maximum is given as a colour, in other cases you will need to cross-refer to an interference colour chart.
(viii) Twinning etc.: a few notes about twinning, or other internal features of crystals may be given. If no
Tables for Common Minerals in Thin Section