INVESTIGATION OF MICROSCOPIC AND OPTICAL CHARACTERS OF MINERALS.
▄Characters of Opaque Minerals▄, observed by _reflected_ light.
The minerals which remain perfectly opaque in thin rock sections have
usually metallic lustre and are very minute in size, as is the case with
the iron ores.
When the metallic minerals of a rock specimen are distinctly seen with
the unaided eye, it is rarely necessary to make a section for their
determination, as this can more easily be done by any of the well known
blowpipe methods.
Form, Lustre, Color, Cleavage, etc., are recognized in the same way as
in the case of macroscopic specimens. In order to make the observations
by reflected light alone, the beam of light from the reflector-mirror
must be cut off by holding the hand over the mirror or by moving the
mirror.
▄Characters of Transparent Minerals▄, observed by _transmitted_ light.
The petrographical microscope for these observations is supposed to be
in the condition of an ordinary microscope, both nicols being out of the
field and a strong beam of light coming up through the transparent
section from the reflector below.
The characters are considered in the order in which they would most
naturally appear to the observer during a complete investigation with
the microscope.[27]
[Illustration:
FIG. 4.—Idiomorphic augite crystals in camptonite. The section is
about at right angles to the vertical axis _ć_, and shows the
intersecting cleavages parallel to the prism of 87° 06′. Keene
Valley, N. Y.
]
[Illustration:
FIG. 5.—Allotriomorphic quartz _q_, showing no “relief,” plagioclase
_p_ and decomposed feldspar _o_ in granite. As seen with crossed
nicols.
]
(_a_) ▄Form.▄[28] _Crystals bounded by planes_, _i. e._, crystals that
have formed when conditions were favorable for complete development.
Such crystals are often called _idiomorphic_ or _automorphic_, see Fig.
4. Crystals that are large in comparison with other accompanying
crystals may be called _Phenocrysts_. Of course crystals, which are not
wholly contained within the rock section, will only show the outline of
the bounding planes cut by this particular section. In some cases, by a
careful study of the outline of several sections of the same mineral and
by a measurement of the angles, it is possible to determine the common
“crystallographic forms” of the mineral. Very misleading outlines may,
however, be observed; as for example the triangular outline of a section
of a cube, with the corner truncated. For measuring the angles have the
stage accurately centered, then bring the vertex of the angle to be
measured to the intersection of the cross-wires in the eye-piece. Bring
one of the sides in coincidence with one of the cross-wires. Note the
reading of the graduated circle and rotate the section until the other
side is in coincidence with the same wire. Take the reading again and
the difference will be the angle required.
_Crystals without bounding planes_, whose surfaces are more or less
determined by those of adjacent crystals. Such crystals are frequently
called _allotriomorphic_ or _xenomorphic_,[29] see Fig. 5. This
allotriomorphic form must not be confounded with the worn or rounded
boundaries of the component grains in clastic rocks.
[Illustration:
FIG. 6.—Corroded sanidine crystal in perlite.
]
_Corroded Crystals_,[30] whose fretted outline is undoubtedly due to
corrosive action of the magma, see Fig. 6.
_Broken or Strained Crystals._ In some cases what were formerly larger
individuals have been broken or shattered by dynamic action into much
smaller fragments, see Fig. 7, showing crushed rim of fragments
surrounding feldspar “auge.” In other cases an actual bending or
distortion of the crystal has taken place, and again sometimes the
effect of mechanical stress is only shown by the so-called “wavy”
extinction. See p. 31 and Fig. 7, showing a carlsbad twin of feldspar
that has been bent and therefore shows marked “wavy” extinction.
[Illustration:
FIG. 7.—Orthoclase “auge” (Carlsbad twin), showing bending and “wavy”
extinction, surrounded by crushed rim of mineral fragments. As seen
with crossed nicols. “Augen-gneiss,” Bedford, N. Y.—B. 13.
]
[Illustration:
FIG. 8.—Crystallites and Microlites _a_. Skeleton Forms _b_.
]
_Crystallites_, in general those incipient forms of crystals which have
not yet reached a stage of development sufficient to show double
refraction, see Fig. 8, _a_. Quite a number of names are used to
describe the different forms that occur.
_Microlites_, more or less completely defined microscopic crystals,
which usually show double refraction, but cannot be always specifically
determined, see Fig. 8, _a_.
_Skeleton Forms_, resulting from rapid cooling of the magma occur in
some lavas, see Fig. 8, _b_.
(_b_) ▄Color.▄ It must be remembered that the colors observed are always
due to transmitted light and may be called “_absorption tints_.”
Minerals which in hand specimens are opaque are often colored in
sections; and minerals which are commonly colored may appear colorless
in sections. At times color may be given to a section simply by the
presence of a great number of minute inclusions.
[Illustration:
FIG. 9.—Olivine crystal in basalt showing “high relief” and cleavage.
]
(_c_) ▄Index of Refraction.▄ _n_ = sin _i_/sin _r_. This can be
approximately determined by the appearance of the surface and outline of
a mineral, that is by its _relief_. The descriptive terms are of course
relative, but in common practice minerals are said to have _medium_
refraction when the refractive index is between that of balsam (1.54)
and that of calcite (1.60), _strong_ refraction when higher than 1.60
and _weak_ refraction when lower than 1.54. In the case of uniaxial and
biaxial minerals the mean value of the indices of refraction is used.
A mineral which has _strong refraction_ appears to have _high relief_,
_i. e._, distinct dark contours and a rough or “shagreened” surface,[31]
which has bright illumination and appears to stand out above the
surfaces of the surrounding minerals with weaker refraction, see Fig. 9.
A mineral with _medium refraction_ does not show any _relief_, hence has
a smooth surface and no dark contours, see Fig. 5.
A mineral with _weak refraction_ may also appear to have a rough
surface, but not so marked as in the case of a mineral with very strong
refraction, due to the smaller contrast in indices between the mineral
and balsam.
The practical way of testing for the approximate index of refraction or
the _relief_ of a mineral is to make use of the lens for convergent
light, which is placed on top of the lower nicol immediately below the
section.
By lowering[32] the lens the character of the relief of a mineral
section is made very apparent.
In order to become familiar with the way in which the “relief” or
appearance of the surface indicates the strength of the refractive
index, the student may use a long glass slide on which are embedded in
balsam (1.54) small fragments of different minerals, for example:
Sodalite (1.483), orthoclase (1.523), quartz (1.547), topaz (1.620),
hornblende (1.631), augite (1.70), epidote (1.751), zircon (1.95) and
rutile (2.712).
Determinations of refractive indices in sections by the methods of
Chaulnes,[33] Sorby,[34] or total reflection are accompanied by many
difficulties and may fail to give satisfactory results. The Becke
method, however, often furnishes a convenient means of determining the
_relative_ values of the refractive indices of adjoining minerals or of
minerals embedded in balsam. This is of especial service when one of the
minerals is known and hence its refractive index.
BECKE METHOD.[35]
Suppose two adjoining minerals, in a thin rock section, to be singly
refracting and to have their plane of contact vertical, _i. e._,
parallel to the optic axis of the microscope.
Let _A_ and _C_, Fig. 10, be two such sections with the plane of contact
_OO′_ vertical, _A_ having a lower refractive index than _C_, and
consider only the direction of the rays within the section, neglecting
the refractive effect of the air, glass and balsam.
A beam of transmitted light contains besides normal rays convergent
rays, which pass through the section as indicated in Fig. 10. Consider
now the cone of light rays _GBI_. The rays _O′G_ on meeting the plane of
contact _OO′_ will be somewhat concentrated and deflected by the higher
refractive index of _C_ and will continue as the cone _EF_. Some rays as
_O′H_ will, on meeting the contact plane, be totally reflected and will
continue as the cone _OE_, while the rest of the rays _HI_ will be
dispersed and deflected by the weaker refractive index of _A_,
continuing as the cone _OD_. Hence, more light rays will emerge on the
side of the contact plane where the substance of higher refractive index
lies, and there will be a concentration of illumination on this side
producing the so-called “bright line.”
[Illustration:
FIG. 10.
]
In practically making the test with a petrographical microscope remove
the polarizer, analyzer and condensing lens,[36] and introduce below the
section a small light-stop, to reduce in size the cone of incident
light.[37] The adapter, holding this light-stop, should be adjustable so
that the stop can be lowered sufficiently to produce the best results.
The smaller the contrast between the indices of refraction the smaller
the incident cone of light should be, as best results are obtained when
this cone is little larger than twice _O′H_, Fig. 10, all the _O′H_ rays
being then totally reflected. The more of the _HI_ rays that pass
through, the brighter will be the _OD_ cone and the less sharp the
contrast in illumination. A high power objective[38] should be used, as
those with small aperture and great focal length do not give good
results. Focus on the dividing plane and adjust until equal illumination
is observed on both sides and the trace of the plane resembles a fine
thread, the focal plane being at _MN_. Then _raise_ the _objective_
slightly, thus moving the focal plane to _ST_, when a _bright line_ or
band will appear on the side of the _stronger refracting_ substance, the
width of the line depending on the contrast between _n_ and _n′_,
becoming narrower as _n_ and _n′_ approach each other in value. On
raising the objective still further the line broadens and finally
disappears. If the objective is lowered instead of raised the reverse
phenomenon will take place, the bright line appearing on the side of the
weaker refracting substance.[39] When the indices are nearly the same a
bright line will appear on both sides and it is important then to make
the cone of incident light as small as possible and to select the
_brighter_ line.
With doubly refracting minerals, each set of doubly refracted rays would
suffer total reflection under somewhat different conditions and there
would be no one point _B_ (as in isotropic minerals) where no bright
lines would appear. However, if the cone of incident light is small
enough in diameter, the test will be practically obtained as described.
The Becke test can often be made with a medium power objective[40]
without removing the polarizer and condensing lens, provided the
condensing lens be lowered sufficiently. It may also prove convenient to
turn the reflector a little sideways.
The thinner the section the more distinct will be the phenomenon. The
contact plane must be clear and not coated with opaque decomposition
products.
When the plane of contact _OO′_ deviates considerably from parallelism
with the optic axis of the microscope a disturbance of the phenomenon
may be expected and no satisfactory results be obtained. In general
under these conditions the “bright line,” both on raising and lowering
the objective, will remain on the side of the overlapping substance,
without regard to the relative values of the indices.
The refractive index of the cementing material should not be very much
lower than that of either of the thin sections, as the result would then
be to disperse the emerging rays too much and dim the effect. In the
case of distinguishing between minerals of high refractive power, such
as augite and garnet, methyliodide is recommended instead of balsam.
In the case of doubly refracting crystals, the lower nicol (polarizer)
must be retained, if it is desired to obtain the relative refractive
index of one of the two rays, either with respect to the balsam or to a
ray in an adjoining crystal with a parallel vibration direction. For
determining vibration directions of rays and the faster and slower rays
in two adjoining sections see later, pp. 31 and 33.
The method of _Schrœder van der Kolk_[41] can also be employed for the
same purpose as the Becke test. The ordinary objective (Seibert No. II)
is used, and the method essentially consists of darkening a portion of
the field by means of the finger or a plate inserted below the
polarizer. The condenser lens must be lowered beyond the sharp focus of
the edge of the shadow (on raising the condenser the following phenomena
are _reversed_). As the shadow approaches the contact between two
minerals a bright line will appear on the edge of the “far” mineral, if
its refractive index is the higher, and a dark line on this same edge if
its index is lower than that of the “near” mineral. The indices of the
two rays in doubly refracting minerals must be determined by the aid of
the polarizer.
[Illustration:
FIG. 11.—Biotite, showing perfect cleavage, in rhyolite.
]
(_d_) ▄Cleavage▄,[42] which appears as more or less distinct and regular
lines or cracks, see Figs. 11 and 12. These cleavage cracks may be
parallel or intersect, depending on the position of the section relative
to the cleavage planes of the crystal.
[Illustration:
FIG. 12.—Augite _a_, showing good cleavage, and plagioclase _p_ in
diabase. The plagioclase shows “polysynthetic” twinning between
crossed nicols.
]
[Illustration:
FIG. 13.—Garnet in mica schist, showing fracture. Franconia, N. Y.
]
Cleavage is sometimes best observed by slightly lowering the condensing
lens under the section.
When sections show intersecting cleavage cracks it is often possible to
recognize the mineral by its known cleavage angle, as in the case of
amphibole and pyroxene.
(_e_) ▄Fracture▄, which appears as irregular and non-parallel cracks,
see Fig. 13.
[Illustration:
FIG. 14.—Apatite in feldspar _a_. Garnets in quartz, Branchville, Ct.,
_b_. Liquid inclusions of CO_{2}, some showing gas bubbles, in
quartz _c_.
]
[Illustration:
FIG. 15.—Enstatite showing “Schiller” Structure.
]
(_f_) ▄Inclusions▄, which may be _solid_ (either distinct crystals or
glass), _fluid_ or _gas_, see Fig. 14. These inclusions are
distinguished by the fact that the solid inclusions generally have sharp
contours, the fluid inclusions distinct dark borders, and the gas
inclusions broad dark borders more distinctly marked than those of the
fluid inclusions. The fluid inclusions often contain a bubble of gas.
The inclusions may have a definite or indefinite position in the crystal
in which they occur, and can sometimes be more distinctly seen by using
convergent light or a “spot” lens.
(_g_) ▄Schiller Structure.▄ “Is that in which cavities of definite form
and orientation (‘negative crystals’) are developed along certain planes
and filled or partially filled by material dissolved out of the
enclosing crystal,”[43] see Fig. 15.
Characters Observed by Polarized Light.
The polarized light is obtained by passing the beam of light from the
reflector through the polarizer or lower nicol,[44] which must be in
place below the stage of the microscope. White light is supposed to be
used.
▄Pleochroism▄, that property which all anisotropic minerals have, to a
greater or less extent, of absorbing certain colored rays in certain
directions, thereby showing different colors in different directions by
transmitted light. Uniaxial minerals are dichroic showing two
differences in color, produced by the rays which vibrate parallel to the
direction of the vertical axis _ć_ and the plane of the basal axes.
Biaxial crystals are trichroic showing theoretically three differences
of color produced by rays with vibration directions corresponding very
nearly to those of the three principal vibration directions.[45] Any
given section of a biaxial crystal will, of course, appear only
dichroic.
The practical way of testing for _pleochroism_ is as follows: Revolve
the stage, carrying the section, when a change in the color of the
mineral will be noticed, if it is pleochroic. This pleochroism may
appear as an actual change in color or simply as a change in the shade
of the same color. At times it may be so weak as hardly to be noticed,
when it is best to make the test with the condensing lens in position
immediately under the section, or by rotating the lower nicol instead of
revolving the stage. The color of the light, vibrating parallel to
certain definite crystallographic directions in minerals, is often very
characteristic.
In some cases there may be such strong _absorption_ of one of the rays,
that, when the vibration direction of this ray is over the plane of
vibration of the polarizer, practically no light is transmitted and the
section appears dark. Strong absorption is characteristic of certain
minerals, such as biotite, amphibole, tourmaline and allanite and takes
place parallel to definite directions in these minerals.
Pleochroism may often be noticed with ordinary light in the case of hand
specimens.
Characters Observed with both Polarizer and Analyzer[46] in Position,
that is with “Crossed Nicols.”
When the nicols are accurately crossed, the field should be quite dark,
and if this is not the case the adjustments must be looked to. The
condensing lens should be removed for these tests as they are to be made
with parallel light, but as a matter of convenience instead of removing
the condensing lens, the polarizer with the lens on top may be lowered,
when the results will be about the same as with parallel light. White
light is supposed to be used.
▄Isotropic Character.▄ Sections of isotropic crystals are perfectly dark
and remain so during a complete rotation of the stage through 360°. The
explanation is very simple. Light being transmitted by an isotropic
crystal in all directions without double refraction; it follows that the
light from the polarizer, after having passed through the section, comes
to the analyzer still vibrating in the plane of vibration of the
polarizer. Hence it is entirely cut out by the analyzer.
_Amorphous_ transparent substances act in the same way and remain dark
during complete rotation of the stage.
_Optical anomalies_, _i. e._, double refraction, may occur in isometric
crystals and in amorphous substances that have been subjected to
strains.
▄Anisotropic Character.▄ Sections of anisotropic crystals, having the
property of _double refraction_, produce in general some _interference_
or _polarization color_, except as mentioned later. The popular
explanation is as follows:
[Illustration:
FIG. 16.
]
In Fig. 16, let PP′ be the plane of vibration of the polarizer, and A′A
the plane of vibration of the analyzer. All the light, after it has
passed through the polarizer, is vibrating parallel to PP′ when it
reaches the lower side of the transparent crystal, _cdef_, on the stage
of the microscope. In this transparent section let _ob_ and _oa_ be the
two _directions_ of _vibration_, _i. e._, the only two directions
parallel to which rays of light can vibrate in passing through the
section.
Let _om_ represent the amplitude of vibration of a ray from the
polarizer. When this ray reaches the section it cannot get through it
vibrating in the direction _om_, but is doubly refracted and of the two
resulting rays, one gets through vibrating in the direction _ob_ and the
other vibrating in the direction _oa_. From _m_ draw perpendiculars to
_ob_ and _oa_. Then according to the law of the parallelogram of forces
_ob_ will represent the amplitude of vibration of the ray passing
through the crystal vibrating in the direction _ob_, and _oa_ will
represent the amplitude of vibration of the ray passing through the
crystal vibrating in the direction _oa_. We will thus have two rays
passing through the crystal, polarized at right angles to each other.
[Illustration:
FIG. 17.
]
Consider now the general question of the transmission of the doubly
refracted rays through a plate. Whatever the angle of the parallel
incident rays, each ray as AB, Fig. 17, is resolved, as just described,
into two rays BC and BD, polarized at right angles to each other and
following (usually) different paths in the plate. On emergence these
follow parallel paths. Among the incident rays there are rays EG and FH,
such that one component of FH will emerge at D with one of the
components of AB, and one component of AB and one component of EG will
emerge at C. Hence from every point of the upper surface of the plate
there will emerge two rays and these rays will have travelled through
different paths in the plate with different velocities and will have
their vibrations at right angles to each other.
When these doubly refracted rays come to the analyzer, whose plane of
vibration is A′A, they cannot get through vibrating in their present
directions, but components of these rays, such as _ot_ and _os_, can get
through vibrating parallel to the plane A′A.
Hence we have two series of rays coming to the eye, polarized in the
same plane, but one set slightly in advance of the other. These rays
will “interfere” and produce some _interference_ or _polarization_
color.[47] In using white light whenever one of two light rays of the
same color has suffered a “retardation” of just one wave-length (or even
multiple thereof) the color will be extinguished; and when the
“retardation” is one half wave-length (or even multiple thereof) the
color will be intensified. Therefore, some tints will be extinguished
and others intensified, the combination resulting in the production of
some definite interference color. Of course in the case of monochromatic
light the thickness of the section may be such that “destructive
interference” takes place producing no color (darkness).
Now suppose the stage to be rotated until the section _cdef_ takes the
position _c′d′e′f′_. The section will be found to be dark and no
interference color will be seen. This is due to the fact that the
directions of vibration in the section are parallel to the planes of
vibration of the crossed nicols, consequently the light passes through
the section still vibrating parallel to the plane PP′ of the polarizer
and is all cut out by the analyzer. Darkness will occur every 90° and
therefore four times during a complete rotation of the stage. The
interference color is also observed to vary in intensity, but not in
color, and to be at its maximum 45° from the positions of darkness.
Sections of uniaxial crystals at right angles to the optic axis act like
isotropic substances and remain dark during a complete rotation of the
stage. In the biaxial crystals, a section at right angles to an “optic
axis” shows uniform illumination[48] which does not change as the stage
is rotated.
The only way to find out whether sections that remain dark are
isotropic, or uniaxial at right angles to an optic axis, is to test them
with convergent light as described later, see p. 40.
▄Interference Colors.▄ The interference color shown by any mineral
section depends on three factors: 1° the strength of the double
refraction (_γ_ − _α_ = the difference between the refractive indices of
the slowest and fastest rays); 2° the position of the section in the
crystal; 3° the thickness of the crystal section.
To eliminate, so far as possible, the variation due to the optical
orientation of the section, care must always be taken to obtain the
maximum interference color given by the different sections of the same
mineral in the rock section. Sections giving the maximum color are those
parallel to the _ć_ axis in uniaxial minerals and those parallel to the
axial plane in biaxial minerals.[49] Hence such sections in convergent
light never show the emergence of an optic axis or a bisectrix; and
furthermore, other clues, such as crystal outlines, cleavage,
pleochroism, etc., may help to indicate the favorable section.
The influence of the thickness of the section is also important and must
be considered. The interference color will rise in the scale (be higher
in order) as the section becomes thicker. Methods of obtaining the
thickness of a section are given on pp. 35 and 36. When reference is
made to definite interference colors the mineral section is supposed to
have a thickness of 0.03 mm. and to be such as to give the maximum
color; and all mineral sections in a rock section are considered to have
a uniform thickness.
With these precautions in mind the _interference colors_ indicate the
_strength_ of the _double refraction_ as follows:[50] The colors of
minerals with very weak double refraction vary from a bluish-gray to a
grayish-white. As the strength of the double refraction increases the
colors become the very intense bright tints of the spectrum, yellow,
red, blue, green, etc., called the first and second order colors. As the
strength of the double refraction still increases the colors pass
through the tints of the spectrum in sequence (called orders), becoming
paler until finally, when the double refraction is very strong, the
colors become the neutral, almost colorless tints of the higher orders.
The eye must be trained to appreciate the colors of different orders,
and the student is advised to practice with mineral sections, of known
strength of double refraction, and compare the resulting interference
colors with a color chart,[51] or use the interference color diagram at
the end of the book. A convenient test can be made with a one fourth
undulation mica plate to distinguish between the white of the 1° order
and the practically white very high order tint. Introduce the mica plate
in the slot _k_, Fig. 2, and the effect will be to produce a marked
change in the color of the 1° order, while no change will be observed in
the high order color.
The exact order of the color can be determined by the use of a quartz
wedge, as described on p. 35.
_Abnormal Interference Colors_[52] may be brought about in several ways.
In white light strong absorption of part of the light components may not
only alter the color of the mineral but also modify the interference
color. The double refraction may be nearly zero for light of a
particular color so that the mineral is isotropic for that color,
resulting in a change in the interference color, as for example the
indigo of melilite, which is nearly isotropic for yellow light. In
biaxial minerals the axial angle may be zero for light of a particular
color, resulting also in a modification of the interference color, as
the blue in penninite in sections ⟂ _Bx_{a}_. When the bisectrices are
much dispersed there will be no position of darkness between crossed
nicols in white light.
▄Extinction and Extinction Angles.▄ When the section, see Fig. 16, is in
such a position that its directions of vibration are parallel to the
planes of vibration of the nicols, no light can pass through the
analyzer, and the section is dark. Hence the light is extinguished and
this phenomenon is called _extinction_.
_Extinction_ is said to be _parallel_ or _symmetrical_ when the
directions of vibration are parallel to any crystallographic lines or
directions, or bisect the angles between these lines. The
crystallographic lines or directions may be either cleavages or the
similar boundaries of idiomorphic crystals.
This kind of _extinction_ is shown by all sections of tetragonal and
hexagonal crystals, by all sections parallel to the crystal axes in
orthorhombic crystals and also by the sections parallel to the ƃ axis in
monoclinic crystals.
When the _extinction_ is not symmetrical it is called _oblique_, and is
shown by all sections of monoclinic crystals (except those parallel to
the ƃ axis) and triclinic crystals.
Extinction which does not take place over the whole of the section of a
single crystal at the same moment, but passes over the section like a
dark wave or shadow, is said to be “_wavy_”; and indicates that the
crystal has been subjected to mechanical forces producing a change in
the position of the directions of vibration in different parts of the
crystal, see Fig. 7.
The angle between a direction of vibration in the section and some known
crystallographic direction (as a cleavage or crystal outline) is called
an _extinction angle_, and is measured in the following way: Find the
positions of the directions of vibration in the section, which must be
parallel to the cross-wires when extinction takes place. Note the
reading on the graduated circle of the stage, then remove the upper
nicol, in order to get a more distinct view of the field, and rotate the
stage until you bring some known crystallographic line into parallel
position with the cross-wire selected as a reference line. Take the
reading of the graduated circle again, and the difference between these
two readings will be the _extinction angle_.
It can readily be seen that depending on which way the section is
rotated, either a small or a large extinction angle will be obtained,
the two angles being complements of each other. The extinction angle
generally recorded is that between the nearest direction of vibration
and the vertical axis _ć_.
In monoclinic minerals the maximum value of the extinction angle (the
angle of real value in distinguishing the mineral) can only be obtained
from a section parallel to the clino pinacoid (010); but in practice
sufficiently accurate results can generally be obtained by measuring the
extinction angles of all sections of the same mineral, which seem to be
about parallel to the vertical axis _ć_, and then taking the maximum
value obtained. Amphibole and pyroxene can easily be distinguished in
this way.
_Extinction_ is generally tested for by revolving the stage, carrying
the section, until darkness is observed. The principal difficulty,
however, is caused by the eye failing to appreciate the position of
maximum darkness. Hence it is better to revolve the stage until the
section just becomes dark (or fades out) and then revolve further until
the section just begins to lighten up again. The mean of the readings,
in these two positions, will be the one to use.
A gypsum test-plate, so prepared as to give some definite interference
color, as red of the 1° order, may be introduced between the two nicols,
and the section revolved until this color is exactly matched. This
perfect matching of color is only possible when the directions of
vibration of the section are exactly parallel to the planes of vibration
of the nicols, as otherwise some interference color would be produced by
the section and the true color of the test-plate would not appear. The
most favorable condition is when the section is colorless and only
covers a part of the field of view, as then the rest of the field shows
the color of the test-plate and the exact matching of color is an easy
matter. This method of testing can be employed to recognize the very
weak double refraction of some minerals, whose interference colors are
such dark grays as not to be noticed without this test. After the
test-plate has been introduced, some slight variation in the color will
be observed when the stage carrying the doubly refracting section is
rotated. There are other methods[53] for locating these directions of
vibration. They depend generally on substituting changes of color for
degrees of darkness or on changes in interference figures, and consist
in the use of color test-plates or Klein’s quartz-plate, or of special
oculars prepared by Bertrand, Calderon, etc.
METHOD OF TESTING FOR THE VIBRATION DIRECTIONS OF THE FASTER AND SLOWER
RAYS, _A′_ AND _C′_, IN A MINERAL SECTION.
A mica or gypsum plate can be used to make this test, the directions of
vibration of the faster and slower rays on these plates being known and
marked.[54]
The crystal section to be tested is placed on the rotating stage,
between crossed nicols, and turned to the position of extinction, when
these directions of vibration will be parallel to the cross-wires in the
eye-piece. The section is then turned 45°, when the interference color
will be at its maximum, and these directions of vibration will make
angles of 45° with the planes of vibration of the nicols and the
cross-wires in the eye-piece.
Now introduce[55] the test-plate, between the section and the analyzer,
so that its known directions of vibration also make angles of 45° with
the cross-wires in the eye-piece.
When the test-plate is introduced a new interference color will be
noticed which is either higher or lower in the color scale[56] than the
original interference color of the mineral section. When the known
directions of vibration of the test-plate are superposed over
corresponding directions in the mineral section, the effect is to
thicken the section and the interference color rises in the scale.
When the directions of vibration of the test-plate are superposed over
directions of vibration in the mineral section which are not
corresponding, the effect is to thin the section and the interference
color sinks in the scale.
For minerals which have very strong double refraction, as zircons, so
that the interference colors are of the higher orders, it is advisable
to use the method of testing with a quartz wedge.[57]
If a wedge is inserted between crossed nicols and its _c_ direction
inclined at 45° to the planes of vibration of the nicols, then
successive interference colors will be seen commencing with the gray of
the first order and passing through the colors as shown by a color
chart. If now the crystal section lies with its vibration directions
also in the diagonal position, the color of any portion of the quartz
wedge will be changed where it covers the section, the new color being
that of a thicker part of the wedge if the _c_ direction in the section
lies under the _c_ direction of the wedge. Also where the wedge overlaps
the section the displacement of the color fringes in the section will be
towards the thin edge of the wedge. On the other hand the new color will
be that of a thinner part of the wedge when the _a_ direction in the
section lies under the _c_ direction of the wedge. In this case the
displacement of the color fringes will be towards the thick part of the
wedge.
This method is very convenient when the crystal section has in any place
sloping edges, showing prismatic color fringes. The movement of these
fringes (as previously described) is towards the thin edge of the wedge
when the vibration directions correspond and away from this edge when
they do not correspond.
If the wedge when inserted finally “compensates” the color of the
crystal section (_i. e._, practically produces an absence of color,
darkness), then the a in this section must lie under the c in the wedge,
as the effect of the wedge has been to continually thin the section.
DETERMINATION OF ORDER OF INTERFERENCE COLOR.
This can be determined by use of a quartz wedge or a v. Federow mica
wedge.[58] Have the vibration directions of the given section in the
diagonal position, then gradually insert the wedge between the crossed
nicols so that the corresponding vibration directions in the section and
wedge are crossed, that is so that the colors are run down until finally
dark gray or black is obtained. Count the number of times the original
interference color reappears, if _n_ times, then the color is a red,
blue, green, etc., of _n_ + 1 order.[59]
It is often easier to insert the wedge until compensation of the color
is obtained; then as the wedge is pulled out the direct count of the
recurrence of the original color will give the order of that color.
METHOD OF MEASURING THE STRENGTH OF THE DOUBLE REFRACTION BY VON FEDEROW
MICA WEDGE.[60]
“The wedge[61] consists of fifteen superposed quarter undulation mica
plates, each about two mm. shorter than the one beneath it and with
their directions of vibration parallel. The series is mounted on a strip
of glass and covered with a cover-glass.
The wave-length of a middle color may be taken as 560 μμ (millionths of
a millimeter); hence each quarter undulation mica plate may be
considered to possess a phase difference or retardation of 140 μμ. If,
then, between the polarizer and analyzer we insert the mica wedge, so
that its direction of vibration of the slower ray, _c_, is at right
angles to that of the mineral under examination, we subtract from the
phase difference of the mineral an amount equal to _n_ times 140 μμ, in
which _n_ represents the number of superposed mica plates in the field.
When the mineral appears dark the value evidently corresponds closely to
the phase difference of the mineral.[62]
From the expression Δ = _eX_, in which Δ is the phase difference or
retardation, _X_ the double refraction, and _e_ the thickness in
millionths of millimeters, the thickness can be deduced when the double
refraction is known or _vice versa_. If a mineral of known double
refraction can be found in the section near the mineral under
investigation,[63] the double refraction of the latter can be deduced by
measuring the phase difference of the known mineral, whence e results,
and this substituted in the above formula yields _X_.”
METHOD OF DETERMINING MINERALS AND THICKNESS OF SECTION, BY USE OF TABLE
OF DOUBLE REFRACTION (MAXIMUM) AND DIAGRAM.[64]
Select some easily recognized mineral in the rock section and note the
maximum interference color given by any of its sections.[65] The
strength of the double refraction of this mineral being known, look up
on the diagram the diagonal line corresponding to this double refraction
and follow along this line toward the left hand lower corner until the
observed interference color is reached, when the horizontal line will
indicate the thickness of the section. The thickness is given in
hundredths of millimeters. Then in the case of the unknown mineral pick
out the section giving the highest interference color and carry along
the same horizontal line until this new color is located,[66] then pass
up to the right along the diagonal line to the numbers indicating the
strength of the double refraction of the unknown mineral. Turn to the
table where the minerals will be found having about this strength of
double refraction.
_Example:_ In a section of granite (biotite-granite) a grain of quartz
was selected, which gave the brightest color. This color was a bright
yellowish white and the known double refraction of quartz is 0.009.
Following down on this diagonal line until the interference color was
reached it was seen that the thickness of the section was about 0.03 mm.
(a very thin section). The section of the undetermined mineral, giving
the highest order color, showed a bright 2° order purple-blue. Passing
along the 0.03 horizontal line until this color was reached and then up
along the diagonal line, it was seen that the double refraction of this
mineral must be about 0.04. The table gives muscovite and ægerite as
having about this double refraction. The mineral was proved to be
muscovite by its absence of color and relief and by the characteristic
cleavage and parallel extinction.
[Illustration:
FIG. 18.—Sanidine crystal _f_, showing Carlsbad twin (which, as it
consists of two parts only, may be called _simple_), and quartz _q_
in rhyolite. Crossed nicols.
]
Structure:
(_a_) _Twinning_, generally noticed by the parts of the twin not
extinguishing at the same time. It may also be observed, without crossed
nicols, just as in the case of macroscopic minerals.
Twinning may be described as: _simple_, Fig. 18; _polysynthetic_, due to
repeated twinning after the same law, Fig. 12; and _crossed or
“gridiron,”_ due to repeated twinning after two laws, Fig. 19.
[Illustration:
FIG. 19.—Microcline, showing crossed or “gridiron” twinning. Crossed
nicols.
]
(_b_) _Zonal_ structure, often only made visible by the zones
extinguishing at different times. It may, however, be noticed by the
zones being of slightly different color, or by the zonal distribution of
inclusions. In the case of the feldspars the zonal structure may be
caused either by the crystal being formed of zones of different chemical
composition (the successive zones in the plagioclases growing more acid
towards the exterior), or by ultra-microscopic twinning,[67] Fig. 20.
[Illustration:
FIG. 20.—Zonal feldspar (Carlsbad twin) in trachyte. Crossed nicols.
]
(_c_) _Aggregate_ structure, being a confused mass of separate little
crystals, scales or grains all extinguishing at different times, Fig.
21.
[Illustration:
FIG. 21.—Sphærulites in felsite. Ground mass shows aggregate
structure. Crossed nicols.
]
(_d_) _Sphærulitic_ structure, produced by the aggregation, in a radiate
form, of crystals or crystallites. It is generally easily perceived by
the dark cross, resulting from the extinguishing of the light in those
crystals whose directions of vibration are parallel to the planes of
vibration of the nicols. When the stage is revolved the arms of the
cross do not rotate, Fig. 21.
[Illustration:
FIG. 22.—Olivine decomposed to serpentine. The pseudomorphism has been
almost complete, only small portions of the original olivine
remaining. The outline of the parent crystal can be quite distinctly
seen. Crossed nicols.
]
(_e_) _Pseudomorphic_ structure, which may be partial or complete and is
noticed by the changed portions producing different optical effects from
those of the original mineral. Sometimes, although the pseudomorphism
has been almost complete, the form of the original mineral or crystal
may still be seen, Fig. 22.
Characters Observed by Convergent Polarized Light.
_Convergent light_ is obtained by passing the rays of polarized light
through a strong condensing lens, which generally fits like a cap over
the top of the polarizer. By means of a suitable adjustment the
condensing lens can be brought very close to the lower surface of the
section on the stage. The lens thus sends a cone of light through the
section, and used in connection with _crossed nicols_ a series of
optical phenomena, called _interference figures_,[68] are produced.
Each direction in which rays are sent is traversed by a minute bundle of
parallel rays and these rays extinguish and produce interference colors
as already described for parallel light. Hence each direction yields a
spot or picture in the field of view and from all these spots combined
there results an “interference figure” or picture, depending upon the
structure of the section for all the directions traversed by the rays.
A very high power objective[69] must be used, and when the eye-piece is
removed, a small image of the interference figure will be seen. In some
microscopes an arrangement is made for getting a magnified image of the
interference figure, by retaining the eye-piece and using an additional
Bertrand lens.
In order to get good results care must be taken to have strong
illumination and the condensing lens close up under the section. The
tests are best made with monochromatic light, but with white light the
effects are substantially the same, the only difference being that the
rings and curves are variously colored instead of being simply light and
dark.
_Isotropic_ substances show no _interference figures_.
Uniaxial Interference Figures.
(_a_) Sections perpendicular to the optic or vertical axis _ć_ show a
dark cross, with or without colored rings, Figs. 23 and 24. The figure
is symmetrical to the center, as the optical behavior of uniaxial
crystals is symmetrical to the optic axis.
[Illustration:
FIG. 23.
]
[Illustration:
FIG. 24.
]
The arms of the cross are parallel to the planes of vibration of the
nicols, and the figure does not move when the stage carrying the section
is rotated.[70]
(_b_) Sections oblique to the optic axis show a portion of a dark cross,
with or without colored rings, Fig. 25. The centre of the cross is not
in the axis of rotation, and as the stage bearing the section is
revolved, the centre of the cross describes a circle, the arms always
maintaining parallel positions.
If the section is still more oblique to the optic axis the centre of the
interference cross may be outside the field of view, and only portions
of the dark arms will be seen.
Sections parallel to the optic axis show a vague dark cross, which, on
rotating the stage, dissolves into hyperbolic curves (suggesting biaxial
figure), which very rapidly disappear in the direction of the optic
axis. When the interference figure shows colors, these colors are lower
in order in the quadrants containing the optic axis. Knowing thus the
position of the optic axis the optical character can be obtained by the
method for parallel light, p. 43.
[Illustration:
FIG. 25.
]
Sections which are thick and have strong double refraction will show the
cross and rings clearly and sharply defined, there being quite a number
of rings crowded close together. Sections which are very thin and have
weak double refraction show only a broad dark cross and no rings. The
interference figures will vary between these extremes, depending on the
thickness of the section and the strength of the double refraction.
To obtain the most characteristic figures, observations must be made on
sections about perpendicular to the optic axis, that is sections which
remain dark or nearly dark during complete rotation between crossed
nicols in parallel light.
▄Optical Character, Positive or Negative.▄ After having obtained an
uniaxial interference figure, test it by means of a ¼ undulation mica
plate. This plate must be introduced between the objective[71] and the
analyzer in such a way that its vibration direction c, marked on the
plate, makes an angle of 45° with the planes of vibration of the nicols.
When this is done the interference figure changes, or may more or less
disappear, two dark spots or blotches being brought prominently into
view. If rings are still seen it will be noticed that they have expanded
in the quadrants occupied by the dark spots, and have contracted in the
remaining quadrants. This movement of the rings may make it possible to
determine the optical character of a section, which is so oblique to the
optic axis that the dark spots are not seen after the introduction of
the mica plate.
[Illustration:
FIG. 26.
]
[Illustration:
FIG. 27.
]
If the optical character is _positive_ the line joining these dark spots
is perpendicular to the direction c of the mica plate, see Fig. 26.
If _negative_ the line joining the dark spots coincides with the
direction c of the mica plate, see Fig. 27.
The (+) and (−) character is easily determined by remembering that the
line, joining the dark spots, makes the + and − sign respectively with
the direction c of the mica plate. The direction c of the mica plate
(represented in the figures by an arrow) is of course not seen, but its
position must be borne in mind when making this test. This test can be
made with either monochromatic or white light.
If the mica plate does not give satisfactory results, which will be the
case when the double refraction of the crystal to be tested is very weak
or when the section is very thin, use a selenite plate, cut the proper
thickness to give the red color of the first order.
This plate must be introduced with its vibration direction a (previously
determined) making an angle of 45° with the planes of vibration of the
nicols. Instead of the dark spots being seen there will appear two blue
and two red quadrants. The diagonally opposite quadrants being of the
same color.
In determining the (+) and (−) character consider the blue quadrants as
the equivalent of the dark spots in the preceding case. This test must
be made with white light.[72]
Biaxial Interference Figures.
[Illustration:
FIG. 28.
]
[Illustration:
FIG. 29.
]
(_a_) Sections perpendicular to an optic axis exhibit the interference
figures shown in Figs. 28 and 29, the curves being nearly circular and a
straight black bar bisecting these curves, whenever the trace of the
plane of the optic axes coincides with the vibration direction of either
nicol. As the stage, carrying the section, is rotated the bar changes
into one arm of a hyperbola and back again into a bar. This arm or bar
will rotate in the opposite direction to the motion of the stage.
As previously stated sections of biaxial crystals, perpendicular to an
optic axis, do not remain dark during rotation of the stage between
crossed nicols in parallel light. On the contrary these sections remain
uniformly illuminated.[73]
(_b_) Sections perpendicular to the acute bisectrix (see p. 5), exhibit
interference figures like those shown in Figs. 30 and 31.
[Illustration:
FIG. 30.
]
[Illustration:
FIG. 31.
]
Fig. 30 shows the appearance of the interference figure when the plane
of the optic axes is parallel to the plane of vibration of either nicol,
and Fig. 31 shows the appearance when this plane is inclined 45° to the
planes of vibration of the nicols.
As the stage, carrying the section, is rotated the dark cross seems to
dissolve into two branches of a hyperbola, which again unite to form a
cross.
In sections perpendicular to a bisectrix, with a large axial angle, the
figure will appear, during a rotation of 90° (in the direction of the
hands of a watch), as in Fig. 32, top row. When the section is somewhat
oblique to an “optic axis,” the figure appears as in middle row; and
when still more oblique, as in bottom row.
The black centres[74] of the small ellipses and the black hyperbolic
curves mark the points of emergence of the optic axes, and therefore
indicate approximately the size of the _axial angle_, 2_E_.
Sections in other positions, relative to the optic axes, give
interference figures less definite in appearance than those just
described; and the same conditions affect the appearance of all figures
as in the case of uniaxial crystals. Very thin sections, of weak double
refraction, may only show indistinct dark crosses or hyperbolic curves,
without any ellipses.
The section perpendicular to the acute bisectrix, which gives the most
characteristic interference figure, cannot generally be recognized
except by an examination in convergent light. It is never, however, the
section giving the maximum interference color. The interference colors
in different sections, normal to the optical elements, grade downward in
the following order: (1) optic normal, (2) obtuse bisectrix, (3) acute
bisectrix, (4) optic axis. Sometimes cleavage may furnish a clue as to
the best section to test as in Topaz and Mica, where the acute bisectrix
is normal to the cleavage.
[Illustration:
FIG. 32.—Biaxial Interference Figures (from Reinisch). Top row: Almost
perpendicular to bisectrix, large axial angle. Middle row: Somewhat
oblique to an “optic axis.” Bottom row: More oblique to an “optic
axis.”
]
It must be remembered that this uncertainty, in the choice of sections
for testing, does not exist in uniaxial crystals; where the best
sections are indicated by the fact that they remain dark or nearly so
during complete rotation between crossed nicols.
The uniaxial or biaxial character of a mineral section, which only shows
an indistinct bar, may be determined as follows: A bar (one arm of the
cross) of a uniaxial interference figure moves in the same direction as
the rotating stage, and always remains straight, while the biaxial bar
rotates in the opposite direction to the stage and becomes curved.
▄Optical Character, Positive or Negative.▄ When the axial angle is very
small, so that the interference figure approaches that of a uniaxial
crystal, the methods used for testing uniaxial figures are employed.
When, however, the axial angle is large, the following method can be
used:
After having obtained an interference figure, from a section as nearly
at right angles to the acute bisectrix[75] as possible, the stage is
rotated until the plane of the optic axes (the trace of which on the
plane of the section is the line joining the points of emergence of the
two optic axes) makes an angle of 45° with the planes of vibration of
the crossed nicols or the cross-wires in the eye-piece.
A quartz wedge[76] is now pushed in between the mineral section and the
analyzer,[77] so that its axis _ć_ = c (previously determined and marked
on the wedge) is either at right angles or parallel to the plane of the
optic axes of the mineral section.
The optical character of the mineral is _positive_ when the ellipses,
surrounding the points of emergence of the two optic axes on the convex
sides of the hyperbola, appear to expand or open out towards the centre
when the quartz wedge is pushed in with its axis parallel to the plane
of the optic axes.
The optical character is _negative_ when the ellipses appear to expand
or open out when the wedge is pushed in with its axis at right angles to
the plane of the optic axes.
As the ellipses expand they move from the points of emergence of the
optic axes towards the centre of the interference figure, and finally
open into lemniscates which move outward from the plane of the optic
axes.
Even when the section is very thin and the double refraction very weak,
only the black hyperbolas without ellipses being seen, the test can be
made; and colored ellipses will appear, after the pushing in of the
quartz wedge, which will act in the same way as the ellipses of the
interference figure.
In a section at right angles to the _obtuse bisectric_ these results are
all reversed.
When the section is perpendicular to one optic axis, rotate the section
until the plane of its optic axes is 45° to the planes of vibration of
the nicols. The interference figure will now have the appearance as
shown in Fig. 29, the hyperbola being convex towards the acute
bisectrix. Insert the ¼ undulation mica plate, so that its direction c
is parallel to the plane of the optic axes. If the optical character is
positive the hyperbola will move towards the acute bisectrix and if
negative away from it. When the gypsum plate is used the blue color will
appear on the convex side for (+) and on the concave side for (−)
minerals.
▄Determination of the Axial Angle.▄[78] This can be approximately
determined with a petrographical microscope, if equipped with a
micrometer eye-piece. Have the axial plane of the crystal section in the
diagonal position, Fig. 31; and measure the distance _d_ from the centre
to either hyperbola with a micrometer (or average the distance to both).
Then sin _E = d/C_, in which _C_ is a constant for the same combination
of lenses and is obtained by using a crystal section (mica cleavage) of
known axial angle. For example, in a mica with 2_E_ = 91° 50′ and _d_ =
41.5 divisions on the micrometer scale, _C = d_/sin _E_ = 57.78 for that
special combination of lenses. The true axial angle can be obtained from
the equation sin _V = d/βC_.
▄Optical Distinctions between Orthorhombic, Monoclinic, and Triclinic
Crystal Sections (perpendicular to acute and obtuse bisectrices).▄ The
interference figures are always symmetrical in shape and distribution of
color to the planes and axes of symmetry of the crystal system; hence
are most symmetrical in the orthorhombic, less so in the monoclinic and
still less so in the triclinic system.
_Orthorhombic crystals_ show the figures always in two of the pinacoids
and in white light the color distribution will be symmetrical to the
trace of the axial plane and the line through the centre at right angles
to this trace and also to the central point.
_Monoclinic crystals_ show the figures in the clino pinacoid or in
sections at right angles to this. In white light the color distribution
is never symmetrical to two lines, but is symmetrical either to the
trace of the axial plane (_inclined dispersion_[79]), or to the line
through the centre at right angles to this trace (_horizontal
dispersion_), or to the central point (_crossed dispersion_).
_Triclinic crystals_ show in white light figures with distribution of
color unsymmetrical to any line or point.
In white light the “color fringes” of the hyperbola are due to the
“_dispersion_”[79] of the optic axes and bisectrices. That is, for each
color (for light of each wave-length) there is a particular interference
figure; the overlapping of these superposed figures producing the color
fringes.
When the axial angle is larger for red light than for violet, the
dispersion is said to be ρ > ν and the interference figure, in the
position of Fig. 31, will show the hyperbolic curves fringed with red
towards the centre (inside). In general the color with the larger axial
angle is nearer the centre of the field. This is due to the
extinguishing of light of each color at the axial points, the resulting
colors at these points being produced by white light minus the absorbed
color. When the dispersion is ν > ρ the reverse distribution of color
fringes will take place.
By measuring the axial angle in red and blue light, this dispersion of
the optic axes can also be obtained.
RESUMÉ OF THE USES OF PARALLEL AND CONVERGENT POLARIZED LIGHT.
_Parallel_ light is used to detect pleochroism, to distinguish between
isotropic and anisotropic substances, to study interference colors, to
determine the strength of the double refraction, to locate directions of
vibration, to measure extinction angles, to find the directions of
vibration of the faster and slower rays, to determine the relative value
of the indices of refraction of the two rays, and to investigate the
crystal structure in general.
_Convergent_ light is used to distinguish between uniaxial and biaxial
crystals, to determine whether a section that appears to be isotropic is
really so or only perpendicular to an optic axis and to determine the
optical character, grade of symmetry (system), axial angle and
dispersion.