Crystals

by A. E. H. Tutton

When we take a plate of calcite of the same small thickness as that of the quartz in a rock section, thinner than a sheet of thin paper, we find that the calcite does not polarise. So great is the retardation of one of the two rays behind the other in calcite, that a plate excessively thin is required in order that colour shall be observed. For the colours of crystal plates under the polariscope, due to double refraction, are subject to the same laws as the colours of thin films, namely, that as the thickness increases—introducing more and more retardation in the case of a crystal, just as in a thin film greater length of path is introduced with increase of thickness—the various tints of all the seven orders of Newton’s spectra are exhibited in turn, each spectrum differing by one further wave-length of retardation, and after the seventh the white of the higher orders (white light mixed with colour, the latter thus appearing only as a faint tint) gives place to true white light, colour being no longer perceptible. Hence with calcite, owing to the extremely powerful double refraction, and therefore very considerable retardation of the slower ray behind the quicker, a plate a fiftieth of a millimetre only in thickness already shows the white of the higher orders, that is, appears only very feebly tinted with colour, and a plate of calcite very much thinner still is required to show brilliant colours. A plate of calcite, therefore, cut obliquely or parallel to the optic axis, of the thickness of a rock section or thicker, simply appears four times dark and four times light alternately, at positions 45° apart, as the section-plate is rotated in its own plane perpendicular to the axis of the polariscope.

When a plate of either quartz or calcite one-fiftieth of an inch thick, cut perpendicularly to the optic axis, is examined under the polariscope or polarising microscope, the dark field is unaffected by its introduction on the stage, remaining dark on a complete rotation of the crystal plate in its own plane. Moreover, the calcite plate continues to behave similarly however much the thickness is increased, the field remaining dark. But when quartz is examined as regards the effect of thickness an extraordinary thing happens. As the plate is thickened, that is, as a series of plates of gradually increasing thickness are successively placed on the stage, the dark field begins to brighten, and eventually colour makes its appearance. Moreover, rotation of the plate in its own plane—supposing the latter to be strictly perpendicular to the axis of the polariscope and the plate itself to have been truly cut perpendicularly to the optic axis of the quartz crystal—produces no change whatever, the colour remaining the same and evenly distributed over the plate, thus differing from the previous phenomena of interference due to double refraction. When monochromatic light is employed, yellow sodium light for instance, it is found that if the plate be not too thick, say a millimetre in thickness, the dark field is restored when the analyser is rotated in a particular direction, either to the right or to the left, for a specific angle, which is 21° 42′ for a plate of quartz one millimetre thick. Moreover, if the plate has been cut from a crystal showing the distinctive trapezohedral-class faces s and x on the right (Fig. 69) the analysing Nicol requires to be rotated to the right; whereas if the plate has been cut from a crystal showing these little determinative faces on the left (Fig. 68) the analyser has to be rotated to the left in order to quench the light.

It is obvious, therefore, that the colours of these thicker plates of quartz are due to the phenomenon of “optical activity.” The original plane of polarisation of the light received from the polarising Nicol is rotated by the quartz plate, and to an extent which is directly proportional to the thickness. When white light is used a particular colour is extinguished for each position of the analyser, and the complementary colour therefore predominates in the tint actually exhibited. Now the most intensely luminous part of the spectrum is about wave-length 0.000550 millimetre in the yellow, and in the case of a plate of quartz 7.5 millimetres thick this colour is extinguished when the Nicols are crossed, while a plate of half this thickness, 3.75 mm., actually exhibits the colour under crossed Nicols and extinguishes it under parallel Nicols. For the angle of rotation of the plane of polarisation for light of this wave-length is 90° for a plate 3.75 mm. thick, so that the analyser has to be turned through a right angle from the crossed position, that is, placed parallel to the polariser, in order to extinguish this colour. A plate of double the thickness, 7.5 mm., will require the analyser to be rotated through 180°, the angle of rotation for this thickness of plate, in order to extinguish this yellow ray. But 180° rotation simply brings the Nicol again to the crossed position, so that no rotation is really necessary at all.

Now the complementary colour to the yellow of wave-length 0.000550 mm. is the transition violet tint, the well-known “tint of passage” between the brilliant red end of the first order spectrum of Newton and the deep blue of the beginning of the second order. Hence, this violet tint is afforded by a plate of 7.5 mm. thickness when the Nicols are crossed, and by a plate of 3.75 mm. thickness when they are parallel. When, therefore, these plates are examined respectively under crossed and parallel Nicols, and the analysing Nicol is turned ever so little, the tint changes remarkably rapidly into brilliant red or blue, according to the direction of the rotation of the Nicol and the nature, whether right or left-handed, of the quartz. Moreover, when two complementary plates of each thickness are thus examined, one of each pair being cut from a right-handed crystal and the other from a left-handed one, the colour will be red in one case and blue in the other for the same direction of rotation of the analyser.

A composite plate is frequently found very useful in work in connection with optical rotation, and is known as a “biquartz,” two plates of opposite rotations being cemented together by Canada balsam, the plane of junction being made perpendicular to the plate so as to be almost invisible when the plate is examined normally. When polarised light is employed, the least rotation of the analyser from exact crossing with the polariser, for which the violet transition tint is evenly produced over the whole composite plate, causes the half on one side of the plane of junction (appearing as a fine line) to turn red and the other half to turn blue or green.

This, in essence, is the nature of the optical activity of quartz, and the secondary effects derived from it influence all the optical phenomena afforded by this interesting mineral. Owing to the fact that quartz crystals are practically unendowed with any facility for cleavage, the natural rhombohedral cleavage being very imperfectly developed and rarely seen, it is possible to cut, grind, and polish large plates of this beautiful, colourless, and limpidly transparent mineral without a trace of flaw. Such quartz plates of large size, adequate to fill the field of a large projection polariscope, the stage aperture of which is nearly 2 inches in diameter, form magnificent polarising objects for the projection on the screen of the effects observed in polarised light. As many of the optical properties of crystals may be illustrated with their aid, it is proposed in the next two chapters to describe a few of the more interesting screen experiments which can be performed with quartz, first (Chapter XIII.) in convergent polarised light, and then (Chapter XIV.) in parallel polarised light, and thus to illustrate the facts relating to the connection between optical activity and the internal structure of crystals in a manner which will at the same time be interesting and will lead to their much clearer comprehension.

The experiments described are largely those with which the author illustrated his lecture to the British Association for the Advancement of Science during their 1909 meeting at Winnipeg.

CHAPTER XIII
EXPERIMENTS IN CONVERGENT POLARISED LIGHT WITH QUARTZ, AS AN EXAMPLE OF MIRROR-IMAGE SYMMETRY AND ITS ACCOMPANYING OPTICAL ACTIVITY.

It has already been shown that crystals are optically divisible into two classes characterised respectively by single and by double refraction. Singly refractive crystals belong exclusively to the system of highest symmetry, the cubic. They afford obviously only one index of refraction, which is generally symbolised by the Greek letter μ, the value of this constant being the same for all directions throughout the crystal. Crystals of the other six systems of symmetry are all doubly refractive. Those of the trigonal, tetragonal, and hexagonal systems have been shown in the last chapter to possess two refractive indices, a maximum and a minimum, one represented by ε corresponding to light vibrating parallel to the singular axis of the system, the trigonal, tetragonal, or hexagonal axis of symmetry, and another signified by ω corresponding to light vibrations perpendicular to that axis. For the properties are identical in all directions around this axis, which is thus the optic axis as well as the predominating crystallographic one. Such crystals are consequently known as “uniaxial.” When ε is the larger refractive index the crystal is positive, while if ω be the maximum the crystal is said to be negative. It has been shown in the last chapter that quartz belongs to the positive category, while calcite is negative. Along the one direction of the optic axis these uniaxial crystals behave like singly refractive crystals do in all directions.

Crystals of the rhombic, monoclinic, and triclinic systems of symmetry have also a minimum refractive index, symbolised by α, and a maximum index indicated by γ, corresponding to light vibrating parallel to two directions at right angles to each other; the third direction perpendicular to both these and normal to their plane does not afford an index of refraction equal to either of these, however, as in the case of a uniaxial crystal, but one of an intermediate value, for which the second letter β of the Greek alphabet is reserved. Whether this value β is nearer to the minimum α or to the maximum γ determines the conventional optical sign of the crystal, whether positive or negative. In the case of the rhombic system the three rectangular directions in question are identical with the three rectangular crystallographic axes. In the monoclinic system the single symmetry axis normal to the unique plane of symmetry is identical in direction with either the α, β, or γ optical direction, but in the triclinic system there are no coincidences between the crystal axes and those of the optical ellipsoid. Along none of these axial directions of the optical ellipsoid which can be imagined to express graphically the refractive index—an ellipsoid known as the optical “indicatrix,” and which has been shown by Fletcher to be a more convenient mode of expressing the optical characters of a crystal than the vibration-velocity ellipsoid of Fresnel—do the optical properties resemble those of a uniaxial crystal along the optic axis, or of a cubic singly refractive crystal, the crystal being doubly refractive along all three axes.