CHAPTER III.

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.