The petrographic or polarizing microscope is a very useful device
for determining the optical properties (differences) between
various minerals which makes it a useful device for classifying
different rock types. Its primary function is to yield an
enlarged image of a mineral thereby revealing identifiable
features that are otherwise not apparent in hand sample. The
optical properties of different minerals are further revealed
with the aid of plane and crossed polarized light (explained
below). Magnification of a mineral is achieved by a combination
of two sets of lenses; the objective and ocular.
The objective provides a sharp clear image of the mineral while
the ocular further enlarges and improves the clarity of the
mineral image provided by the objective. Most petrographic
microscopes include three objectives that differ in light
gathering power between low (a magnification of 2 times), medium
(10 times) and high (50 times). Although each polarizing
microscope has only one ocular (or one pair of oculars) they also
come in a range different magnifications (5, 7 and 10 times). The
total magnification of the mineral image can be determined my
multiplying the objective magnification by the ocular
magnification. Oculars usually have cross hairs (one
oriented north-south, the other oriented east-west) which provide
a reference to orient individual mineral grains under different
magnifications. A light condenser is located below the microscope
stage and can be adjusted to make light converge which is
particularly useful to illuminate minerals under high
magnification for observation of mineral interference figures (explained
below). A diaphragm, also located below the microscope
stage, can be adjusted to control the intensity of light entering
the mineral. The polarizing microscope utilizes two polars, a low
polar and upper polar. The lower polar or Nicol
prism (usually found on older microscopes) is located in the
sub-stage condenser and it transmits light in the N-S plane of
the microscope (see below for an explanation of polarization).
The upper polar or analyzer is fitted above the stage in
the upper microscope tube. It is also a prism oriented so that it
only transmits light in the E-W plane of the microscope. The
lower polar (Nicol prism) remains in position always, while the
analyzer (upper polar) can be removed from the optical path. When
both polars are in place, the polars (the lower and the upper)
are said to be crossed. The Bertrand Lens is used
to observe mineral interference figures (explained below). An accessory
plate can be inserted into the microscope to determine the
optic signs of a minerals (explained below).
Aggregates of minerals are commonly studied in thin section, slices of rock material 0.03 mm thick (with lateral dimensions between 10 to 20 mm wide and 20 to 30 mm long). These thin slices of rock are usually mounted on a glass slide and cemented to the slide with a mounting compound of known refractive index. The most common mounting compound used is Canada balsam with a refractive index of 1.54 (explained below). Mineral grains within thin sections have been ground to a thickness of 0.03 mm, a thickness at which most minerals allow light to be transmitted through them. This standardization of thicknesses of different mineral grains in a thin section slide allows the accurate comparison of optical characteristics of different minerals. This is useful in the identification of different minerals leading to characterization of mineral aggregates as different rock types.
The majority of minerals are
transparent to light in thin section with the exception of
metallic minerals which are opaque.
Most transparent minerals are
colourless in thin section. Some minerals (calcite, augite) show
colour changes as they are rotated on the plane of the microscope
stage in plane polarized light (Pleochroism).
The form of crystals and the
arrangement of cleavage planes within them are useful for
identification.
Some minerals often contain
smaller inclusions of other minerals.
All other microscope related
properties used to identify minerals in thin section relate to
the refraction of light transmitted through crystals.
Visible light is part of the
electromagnetic spectrum. Light emitted by an object travels in a
straight line from and vibrates perpendicular to the direction of
its propagation (in all directions) in a transverse wave motion.
Light, traveling as a wave, has a wavelength (L) defined by the
distance between successive wave crests (or troughs) and a travel
velocity (c, the speed of light). The number of waves passing a
fixed point per second (a function of its velocity) defines the
frequency of light (f = c/L).
Visible light is composed of all
wavelengths between 0.0004 (violet) and 0.0007 cm (red), a very
narrow range within the total electromagnetic spectrum
(wavelengths between 0.0000000001 and 1000 cm). These different
wavelengths of light produce the different colours as visually
perceived by our eyes. Colour is the result of sensations
produced by different wavelengths of light on pigments in the
retina of our eyes. The three main pigments in the cones of our
eye’s retina respond individually to the different
wavelengths of the visual spectrum of light. Absorption in those
three pigments are the fundamental mechanism of colour sensation
in that the total sensation of colour is associated with the
absorption characteristics of these pigments acting together.
When light encounters a mineral
some of it is reflected from the surface of the mineral and some
of the light enters the mineral (crystal lattice). Light entering
the crystal from a less dense medium, like air, experiences a
change in its original path or intersection (the incident light
ray path), due to the ordered arrangements of atoms within the
crystal structure, and is consequently bent or refracted. The
degree of refraction (bending) of the incident light ray depends
on the velocity of the light ray and the angle of the incident
ray. Generally the greater the difference of velocity of the
light ray in air versus the crystal, the greater the refraction
(bending) of the light ray through the mineral from its original
path. As mentioned above, the behaviour of light entering a
crystal is fundamentally controlled by the crystal structure. The
internal symmetry of a crystal is dependent upon the orientation
of atoms. The arrangement of the atoms determines how light
interacts with the crystal which will determine the amount of
refraction that light experiences while transmitting through the
crystal or the refractive index (RI) of the crystal. Therefore,
minerals can be identified by their refractive index or indices
(if doubly refracting).
The refractive index (n)
of a substance is defined as:
n = v / V
Where v is the velocity of light
in a vacuum (or air), and V is the velocity of light in the
substance. It is assumed that the refractive index of light in
air is essentially the same as a vacuum, = 1 (water has a
refractive index of 1.33, Petrologic slide mounting compound,
Canada balsam, has a refractive index of 1.54).
The refractive index of the light
itself entering a crystal increases as the its wavelength
decreases. Therefore, two things determine the refractive index.
Difference in velocity between light in air and light in the
mineral. Also, velocity differs for different wavelengths of
light (RI greater for violet end of light than for red end). This
is called dispersion. All minerals have provide some light
dispersion.
Light slows down when it enters a
mineral, so the refractive index will always be greater than 1.
Most minerals have refractive indices with values between 1.50
and 1.80.
Isotropic crystals (those
belonging to the cubic crystal system) have only one refractive
index (see the explanation below). Under plane polarized light
crystals that have an RI that is different than the thin section
mounting compound (Canada balsam) will be seen to have relief. The greater the difference between the
RI of the mineral and the mounting compound, the more apparent
the relief. A Becke Line test can be used to determine
whether the mineral RI is greater than the Canada balsam RI.
A Becke line is a band or rim of
light visible along a grain/crystal boundary in plane-polarized
light. It is best seen using the intermediate power lens (or low
power in some cases), on the edge of the grain.
When a mineral grain is taken out
of focus by lowering the stage of the microscope, a narrow line
of light will form at the edge of the mineral grain and move
toward the medium of higher refractive index. If the Becke Line
moves into the mineral grain, then the mineral has a higher RI
than the liquid. The single index of refraction is significant
for isotropic minerals.
A Becke line is the result of
minerals in thin sections tending to be thicker in their centre
and thinner towards their edges. This makes them act as lenses
such that if its refractive index is higher than the mounting
medium the rays converge toward the center of the grain; if the
refractive index is lower, the rays diverge towards the edge of
the grain.
Determination of a mineral’s
RI can be made by mounting the slide in liquids (oils) with
different RI values and determining (using the Becke line test)
which liquid (with calibrated RI) the mineral’s RI is most
closely matched. Very accurate refractive index determinations of
minerals are done with monochromatic light and a device called a
refractometer.
The difference between the
refractive indices of the ordinary (slow) and the extraordinary
(fast) rays (N-n) is called birefringence (doubly refracting). This gives rise to interference colors in thin sections when viewed under Cross
Polarized light, a characteristic useful for telling minerals
apart.
Carbonates are among the few
minerals that have a large enough ordinary to extraordinary RI
difference (N-n) to show an effect in regular and plane polarized
light. Calcite spar shows a double refractive image when viewed
through a crystal face parallel to the basal plane. The large RI
difference makes calcite in thin sections appear to
"twinkle" as the stage is rotated under Plane Polarized
Light. Most other anisotropic minerals only reveal their subtle
N-n differences under crossed polarized light as interference
colours.
Mineral Extinction Angles
Isotropic minerals remain dark (extinct)
in all positions under crossed polarized light, which makes them
easy to distinguish from anisotropic minerals in thin section.
Under certain conditions some uniaxial anisotropic minerals show
light extinction (remain dark in some positions) under crossed
polarized light.
The angle between a light ray
(ordinary or extraordinary) vibrational direction and any
specified crystallographic direction (cleavage or crystal face
identified in thin section) is called the extinction angle.
The extinction angle of a mineral is found by first rotating the
mineral into an extinction position then rotating the mineral (by
rotating the stage) until the identifiable crystallographic
feature (cleavage or crystal face) is parallel to the polarizer
and analyzer vibrational directions (as indicated by the ocular
cross hairs). The angle of extinction is the angle between the
position of mineral extinction and the polarizer (or analyzer).
If the angle between the crystallographic feature and the
polarizer (or analyzer) vibrational directions is zero, the
mineral is said to have straight extinction. If the angle
is not zero, the mineral is said to have inclined extinction.
The extinction angle can be an
important distinguishing character for different minerals.
However, it is important to note that grains of the same mineral,
in different orientations, will show different kinds of
extinction. If inclined extinction is shown for most of the
mineral's grains it is useful to note the maximum extinction
angle shown.
In general, minerals belonging to
the tetragonal, hexagonal, trigonal or orthorhombic crystal
systems will show straight extinction. Minerals belonging to the
monoclinic and triclinic systems usually show inclined
extinction.
Polymorphic minerals, as
the name suggests, are minerals that can form more than one type
of structure. Polymorphism is, usually, a response to changes in
temperature and pressure during crystallization. Displacive
polymorphism is a function of temperature. After the mineral
crystallizes at a certain temperature, further stabilization of
the mineral structure (at a lower temperature) may require the
rearrangement of atoms. Achieving a more stable crystal structure
may be as simple as a readjustment of bond angles between atoms
(rather than the breaking of bonds which requires more energy).
The bond angle "kinking" that results in a reduction of
crystal symmetry can produce two structural atomic arrangements
separated by a twin plane (twinning).
Twinning is a prominent
feature of plagioclase feldpars which often show a stripey pattern in
thin section. The crystal in thin section is observed to have
black and white narrow lamellae which alternate in orientation.
These are caused by lamellae of one orientation (the black
lamellae) being in an extinction position, while the other (the
white lamellae) is not.
More about Uniaxial and Biaxial Anisotropic Minerals
Anisotropic minerals are subdivided into two groups: uniaxial
and biaxial.
Hexagonal and tetragonal crystal
system minerals are characterized by two or three equal (in
length) crystal axes (a-axis) in the plane perpendicular to the
optic axis (c-axis) of a different length (greater or less than
the a-axis). The refractive indices of the ordinary and
extraordinary refracted rays of minerals in these crystal systems
are characterized by the two different crystal axis lengths. In
these cases, where light is split into an ordinary and
extraordinary rays along two crystal axes, there is one optical
axis along which all light rays travel with the same velocity
(zero birefringence) and, therefore, these anisotropic minerals
are referred to as uniaxial.
Orthorhombic, monoclinic and
triclinic crystal system minerals have three crystal axes (a, b,
c) of unequal length. The RI values of the light rays refracted
through minerals in these crystal systems are characterized by
the three different crystal axis lengths. Note, in these cases
light is split along two of the three possible crystal axes at a
time depending on the orientation of the mineral's crystal axes
in thin section. There are two planes in these anisotropic
minerals perpendicular to which refracted light rays travel at
the same velocity (have the same RI) and, therefore, show zero
birefringence (they appear dark under crossed polarized light
when rotated). These anisotropic minerals that have two optic
axes are referred to as biaxial.
Interference Figures
Mineral interference figures are produced by converging light
(conoscopic light) under crossed polars. Interference
figures are resolved by the Bertrand Lens which is a
converging lens that allows the observation of interference
figures projected to the back focal plane of the objective and,
subsequently, not resolved by the high power objective.
The convergence of polarized
light with the same wavelengths causes destructive interference
where the light is extinguished parallel to the microscope
polarizers. Under crossed polarized light a black cross (isogyre)
figure is produced.
Uniaxial minerals oriented with
their optic axes perpendicular to the plane of the thin section
show centered isogyres. In other cases where the minerals being
viewed are oriented such that their optic axes are at an angle to
the plane of the thin section, the isogyres appear uncentered.
Biaxial minerals (with two optic
axes) viewed under conoscopic light also produce isogyre
interference figures. However, biaxial mineral isogyres separate
into two hyperbolic isogyres as the stage of the microscope is
rotated. The angle between the two optic axes of a biaxial
anisotropic mineral is the optic angle (2V). A biaxial mineral
has an acute bisectrix (a plane that bisects the acute
optic angle) and an obtuse bisectrix (a plane that bisects
the obtuse optic angle).
Mineral Optical Signs
If the ordinary ray of a uniaxial mineral is determined to have a greater
velocity than the extraordinary ray, the mineral is said to be
uniaxial positive, and uniaxial negative if the extraordinary ray
is determined to have the greater velocity.
Gypsum and quartz accessory plates (lenses) may be used in
conjunction with a uniaxial isogyre to determine the optic sign
of a uniaxial mineral. These accessory plates have a specific
orientation of their ordinary (slow) and extraordinary (fast)
rays and, therefore, they either add to (retard) or deplete
(compensate) the amount of interference produced by the mineral
(evident as a colour shift).
The gypsum plate is useful in
determining the optical sign of uniaxial minerals that show very
low (dull grey) interference colours in their isogyre
quadrants. The gypsum plate is essentially a red filter (the
black isogyre appears red). If the slow direction of the plate
(usually marked on the plate) in position is parallel to the slow
direction of the mineral then the order of the interference
colour increases (the plate further retards or interferes with
the mineral fast ray). The colour in the isogyre quadrants in
line with the gypsum plate slow ray direction is blue shifted
(according to the Interference colour chart), and the mineral is
identified as uniaxial positive where the velocity of the
ordinary ray is greater than that of the extraordinary ray.
Alternatively, if the slow direction of the plate in position is
parallel to the fast direction of the mineral then the
interference colour is compensated (the plate reduces
interference with the mineral slow ray). The colour in the
isogyre quadrants in line with the gypsum plate slow ray
direction is yellow shifted (according to the Interference Colour
Chart), and the mineral is identified as uniaxial negative
where the velocity of the extraordinary ray is greater than that
of the ordinary ray.
The quartz plate is useful in
determining the optical sign of uniaxial minerals that show high
interference colours in their isogyre quadrants. The quartz plate
is actually a wedge that varies in thickness along its length.
The thickness variation produces a variation in colour (colour
bands) in the isogyre quadrants that are ordered according to the
Interference Colour Chart. Inserting the quartz wedge into the
microscope thin edge first (where its thickness increases as the
wedge is further inserted) has the effect of increasing the
interference of the ordinary and extraordinary rays produced by
the mineral, similar to the effect you would get when the
thickness of the mineral is increased. When a quartz wedge is
slowly inserted in the path of the optic axis of a uniaxial
negative mineral (extraordinary ray faster than the ordinary ray)
the colour bands in the northwest and southeast isogyre quadrants
move towards the center of the isogyre (and disappear) while the
colour bands in the northeast and southwest isogyre quadrants
move towards the edge of the isogyre field. This reinforcement
(center movement) of the interference colours in the NW and SE
quadrants of the uniaxial negative mineral, in conjunction with
the increasing retardation associated with the gradual insertion
of the quartz wedge, corresponds to the situation where the slow
direction of the plate (usually marked perpendicular on the
wedge) is parallel to the fast direction of the mineral. The
opposite effect occurs for uniaxial positive minerals.
Most uniaxial minerals have a
negative optical sign.
Biaxial Optical Signs
The optic sign of a biaxial
mineral is easiest to determine with the aid of accessory plates
when both (the acute bisectrix interference figure) or only one
of the optic axis figures (isogyres) are observed for the
mineral.
By definition, the velocity of
all light rays moving along an optic axis have a constant
velocity. For a negative biaxial mineral the velocity of light
rays in the acute bisectrix plane are slower than the velocity of
light rays traveling in the obtuse bisectrix plane of the
mineral. When a gypsum plate (with slow ray oriented parallel to
the obtuse optic plane) is inserted into the path of the light
emerging from a negative biaxial mineral the slow direction of
the plate in position is perpendicular to the slow direction of
the mineral (traveling in the acute bisectrix plane). In this
case the gypsum plate reduces the interference (subtraction) on
the slow moving light rays and a yellow colour is produced on the
convex side of the isogyre. Insertion of a gypsum accessory plate
in the light path of a biaxial positive mineral results in the
production of a blue colour on the convex side of the
interference isogyres.
The quartz wedge may also be used
to determine the optic sign of biaxial minerals, particularly for
highly birefringent minerals. For a biaxial negative mineral,
insertion of a quartz wedge results in the outward movement (away
from the center) of colour bands on the convex side of the
isogyres (interference subtraction) and inward movement (toward
the center) of colour bands on the concave side of the isogyres
(additional interference). The opposite behaviour is seen for
positive biaxial minerals.
Optical Mineralogy
References
Klein, C. and Hurlbut, C.S. Manual
of Mineralogy (21st Ed.). John Wiley & Sons, New
York. (1993). 681 pp.
Shelley, D. Manual
of Optical Mineralogy. Elservier, Amsterdam (1981). 239
pp.
Stoiber, R.E. and Morse, S.A. Microscopic
Identification of Crystals. Krieger, New York. (1981).
278 pp.