Crystals

by A. E. H. Tutton

But it is a remarkable fact, nevertheless, that there are two directions in such a crystal along which the latter is apparently singly refractive, and these two directions are known as the “optic axes,” and the crystals of the three systems of lower symmetry are consequently said to be “biaxial.” These two singular directions are symmetrical to two of the three rectangular axes of the ellipsoid, those corresponding to the extreme indices α and γ, in the plane containing which two axes they lie, and they are perpendicular to the third β. For if we draw the ellipse of which the minimum and maximum axes are represented in length by α and γ, there will obviously be four symmetrical positions on the curve where a line drawn to the centre of the ellipse would be equal to the intermediate value β. If we join opposite pairs of these four points by diameters (lines passing through the centre of the ellipse) we have two directions each of which, together with the perpendicular direction of the β axis, lies on a circular section of the ellipsoid, for all radii from the centre lying in each of these sections are alike equal to β. Consequently, light transmitted along the two directions in the crystal normal (perpendicular) to these two circular sections will suffer no apparent double refraction, the refractive index being the same, namely β, and the velocity of vibration equal in all directions in the crystal parallel to the two circular sections. Hence, we have two directions in biaxial crystals in which the optical properties are similar to those of uniaxial crystals along their singular optic axis. But the optical properties along the two optic axes of a biaxial crystal are advisedly stated to be “similar” to, and not “identical” with those along the optic axis of a uniaxial crystal; for although they are identical to all ordinary experimental tests, they are not quite so when we come to ultimate details, which, however, are beyond the purview of this book, but an account of which will be found in the author’s “Crystallography and Practical Crystal Measurement” (Macmillan & Co., 1911).

Fig. 71.—Projection Polariscope arranged for Convergent Light.

With these prefatory theoretical remarks, which are necessary in order that the experiments now to be described should be understood, we may proceed to consider a graduated series of experimental demonstrations which it is hoped will render clear some of the more important features of crystal structure which have been dealt with in previous chapters. Our principal agent will be polarised light, that is, light which has been reduced to vibration in a single plane by means of the well-known Nicol’s prism. This latter is a rhomb of calcite which has been cut in two parts along a specific diagonal direction, and the two parts of which have been re-cemented together with Canada balsam, in such a manner that one of the two rays, known as the “ordinary” and which corresponds to the ω refractive index, into which the doubly refracting calcite crystal divides the ordinary light which it receives from the lantern or other source of light, is totally reflected at the layer of balsam, while the other ray, known as the “extraordinary” and corresponding to a refractive index of intermediate value between ω and ε, and composed of vibrations at right angles to those of the totally reflected ray, is alone transmitted, as a ray of plane polarised light.

We employ a pair of such Nicol prisms (a very large pair being shown in Fig. 71), together with a convenient system of lenses for focussing either the object-crystal or the phenomena displayed by it, as a “polariscope,” which is the most powerful weapon of optical research on crystals which has ever been invented. When the two prisms are arranged so that the vibration planes of the polarised light which they would singly transmit are parallel, we speak of them as “parallel Nicols,” and light is transmitted unimpeded through the pair thus placed in succession; but when one of them is rotated the light diminishes, until when the vibration planes are at right angles no light escapes at all if the Nicols are properly constructed, there being produced what is known as the “dark field” of the “crossed Nicols.” For the plane polarised light reaching the analyser from the polariser cannot get through the former, its plane of possible light vibration being perpendicular to that of the already polarised beam.

The phenomena exhibited by crystals in polarised light are of two kinds, namely, those observed when a parallel (cylindrical) beam of fight is passed through the crystal, and those exhibited when a converging (conical) beam of fight is employed and concentrated on the crystal, the centre of which should occupy the apex of the cone. The disposition of apparatus in the former case of parallel light will be described in the next chapter and illustrated in Fig. 79. The arrangement for convergent light, as employed for projections on the screen, has already been referred to in connection with the Mitscherlich experiment with gypsum, and illustrated in Fig. 51 (page [92]). The arrangement is shown again here for convenience, in Fig. 71. The parts of the apparatus are briefly as follows: (1) the electric lantern with self-adjusting Brockie-Pell or Oliver arc lamp and a 4½ or 5–inch set of condensers; (2) the water cell; (3) the polarising Nicol with a parallelising concave lens at its divided-circle end; (4) a condensing lens; (5) the convergent system of three lenses closely mounted in succession; (6) the crystal; (7) the collecting system of three lenses equal and similar to the convergent system; (8) the field lens; (9) the projection lens; and (10) the analysing Nicol. The ten parts are separately mounted in the author’s apparatus, which confers greater freedom in experimenting and more power of varying the conditions; the converging and collecting lens systems, however, are mounted in a separately adjustable manner on a common standard, which carries in the centre complete goniometrical adjustments for the crystal.

When we place on the stage of the polariscope, the Nicols being crossed, a plate of a uniaxial crystal cut perpendicularly to the optic axis, and subsequently a similar plate of a biaxial crystal cut perpendicularly to that axis of the optical ellipsoid, either α or γ, which is the bisectrix of the acute angle between the two optic axes, and use the system of lenses which converges the light rays received from the polarising Nicol prism on the crystal, as shown in Fig. 71, we observe in the two cases quite different and very beautiful interference phenomena, which at once distinguish a uniaxial from a biaxial crystal. The two appearances are illustrated in Plate XIV., by Figs. 72, 73, and 74, which are reproductions of the author’s direct photographs. Fig. 72 shows the interference figure afforded by uniaxial calcite, which is the same for all positions of the crystal plate when rotated in its own plane by the rotation of the stage. Figs. 73 and 74 represent the interference figures given by biaxial aragonite, the orthorhombic form of carbonate of lime, calcite and aragonite being the two forms of this substance, which has been shown in Chapter VII. to be dimorphous. The effect shown in Fig. 73 is afforded when the line joining the two optic axes is parallel to the plane of vibration of either of the crossed Nicols, and the interference figure represented in Fig. 74 is given when the stage and crystal (or the two Nicols simultaneously) are rotated 45°.

The uniaxial calcite figure (Fig. 72) consists of circular spectrum-coloured rings resembling the well-known Newton’s rings, but with a dark cross, fairly sharp near the centre but shading off towards the margin of the field, marking the directions of the vibration planes of the Nicols.

The biaxial aragonite figures (Figs. 73 and 74) show two series of rings surrounding the two optic axes and thus locating the positions of their emergence, equidistant from the centre of the field, where the bisectrix emerges. They are not circular, but are curves known as lemniscates, which are complete rings nearest to the two optic axes, but soon pass into figure-of-eight loops, and eventually into ellipse-like lemniscates enveloping both optic axes, and more and more approaching circles in their curvature as the margin of the field is approached. Moreover, when the direction of the fine joining the two optic axes is parallel to the vibration plane of either of the Nicols, as was the case when Fig. 73 was produced and photographed, a black rectangular cross is seen, one bar, which is much the sharper one, passing through the optic axes and the other lying between them at right angles to the first bar, the centre of the cross being in the middle of the field.