EFFECT OF THE SYMMETRY OF CRYSTALS ON THE PASSAGE OF LIGHT THROUGH THEM.
QUARTZ, CALCITE, AND GYPSUM AS EXAMPLES.
The action of transparent crystals on the rays of light which they
transmit is a subject not only of the deepest interest, but also of the
utmost importance. For it is immediately possible to detect a cubic
crystal, and to discriminate between two groups, optically uniaxial and
biaxial respectively, of the other six systems of symmetry, three
systems going to each group, by this means alone. For a cubic crystal is
singly refractive in all directions. A 60°-prism, for instance, cut from
a cube of rock-salt, for the purpose of obtaining the refractive index
of the mineral by the ordinary method of producing a spectrum and
arranging it for minimum deviation of the refracted rays, affords but a
single spectrum, or a single sharp image of the spectrometer slit when
the latter is fed by pure monochromatic light instead of ordinary white
light. This is true however the prism may have been cut, as regards its
orientation with respect to the natural crystal faces.
But a 60°-prism cut from a crystal belonging to the optically biaxial
group, composed of the rhombic, monoclinic, and triclinic systems of
symmetry, will always afford two images of the slit or two spectra,
corresponding to two indices of refraction; and, when the orientation of
the prism is arranged so that the refracting angle is bisected by a
principal plane of the ellipsoid which represents the optical
properties, and the refracting edge is parallel to one of the principal
axes of the optical ellipsoid, the prism, when arranged for minimum
deviation of the light rays, will at once afford two of the three
refractive indices, α, β, γ, corresponding to light vibrations along two
of the three principal axial directions of the ellipsoid. The two
indices which the prism affords will be (1) the one which corresponds to
vibrations parallel to the refracting edge, and (2) that which
corresponds to undulations perpendicular to the edge and to the
direction of transmission of the light through the prism (the third axis
of the ellipsoid). For the vibrations of the light in the two rays into
which the beam is divided on entering the crystal are both perpendicular
to the direction of transmission and to each other; the two images or
spectra produced owing to the double refraction, that is, owing to the
different velocities of the two mutually rectangularly vibrating rays,
thus correctly afford the means of determining two of the three
principal (axial) refractive indices.
Gypsum, the monoclinic hydrated sulphate of lime, CaSO_{4}.2H_{2}O,
already referred to in connection with the Mitscherlich experiment in
Chapter VII., is an excellent substance to employ for the demonstration
of this fact, by cutting and polishing a 60°-prism out of a clear
transparent crystal of the mineral as above described; and if a Nicol
prism be introduced in the path of the rays, one spectrum or
monochromatic image will be extinguished when the Nicol is arranged at
its 0° position, and the other when the Nicol is rotated 90° from this
position. This proves that the two rays affording the two refractive
indices are polarised in planes at right angles to each other, and,
moreover, enables us to verify that the planes in which the vibrations
of the two rays occur are actually parallel and perpendicular
respectively to the refracting edge of the prism. For the two
extinctions occur when the vibration plane of the Nicol is either
vertical, parallel to the prism edge, or horizontal, perpendicular
thereto.
If a second prism be cut complementarily to the first, that is, so that
the refracting edge is parallel to the third axis of the ellipsoid (the
direction of transmission through the first prism) and the bisecting
plane again parallel to one of the three axial planes of the ellipsoid,
such a prism will also yield two refracted images corresponding to two
indices; one of them, that particular image the vibrations of which are
parallel to the refracting edge, will correspond to that one of the
three principal indices which was not given by the first prism, while
the other one will afford a duplicate determination of one of the two
indices afforded by the first prism. Hence, a couple of such axially
orientated prisms of a rhombic, monoclinic, or triclinic crystal will
enable us to determine all three refractive indices, and one of them in
duplicate, which latter fact will enable us to check the accuracy of our
work.
If the 60°-prism be cut from a crystal of the uniaxial group, that is,
from a hexagonal, tetragonal, or trigonal crystal—quartz or calcite
being admirable examples of the latter and particularly suitable for
demonstration purposes—it will generally afford two spectra in the same
manner as a crystal of the three birefringent systems of lower symmetry.
But there is one special mode of cutting which results in the prism
exhibiting only a single spectrum, namely, when the hexagonal,
tetragonal, or trigonal axis of symmetry, which is also the unique
“optic axis” of the crystal along which there is no double refraction,
is arranged to be perpendicular to the bisecting plane of the 60°-prism.
For then the light is transmitted along this unique axial direction when
the prism is arranged for the minimum deviation of the refracted rays
out of their original path, and as it may vibrate in any direction
perpendicular thereto with equal velocity there is no separation into
two rays, that is, no double refraction, and thus only a single spectrum
is afforded by such a prism in white light, or a single image of the
slit in monochromatic light, and this latter will at once yield the
refractive index which is generally indicated conventionally by the
letter ω, corresponding to light vibrations perpendicular to the axis.
Spectroscopists take advantage of this interesting fact, when they
employ a train of quartz prisms so cut in order to explore the violet
and ultra-violet region of the spectrum; for quartz transmits many of
the ultra-violet rays which glass absorbs. Each prism gives only a
single image like glass, whereas if it were otherwise cut it would give
two spectra, which would so complicate matters as to render quartz
useless for the purpose.
When the prism of quartz or calcite, or of any hexagonal, tetragonal, or
trigonal substance, is cut so that the rays of light are transmitted
through it perpendicularly to the axis, and so that the refracting edge
is parallel to the axis, the light is broken up into two rays, one of
which is composed of light vibrating parallel to the edge and therefore
to the axis, and the other of light vibrating perpendicularly to the
axis. Such a prism consequently affords the two principal extreme
refractive indices of the crystal, ω and ε, the latter letter being
always assigned to the refractive index of a uniaxial crystal
corresponding to vibrations parallel to the axis.
A uniaxial crystal, one belonging to the hexagonal, tetragonal, or
trigonal systems, has thus two principal refractive indices, ω and ε,
while a biaxial crystal, one belonging to the rhombic, monoclinic, or
triclinic systems of symmetry, has three, α, β, γ, corresponding to
vibrations respectively parallel to the three rectangular axial
directions of the optical ellipsoid, which are also the crystallographic
axial directions in the case of a rhombic crystal. The index α is the
minimum, and γ the maximum refractive index,the β index being
intermediate; when the latter lies nearer to α in value, the crystal is
said to be a positive one, but when nearer to γ the crystal is
conventionally supposed to be negative. Similarly, when in a uniaxial
crystal ε is the greater, as it is in the case of quartz, the crystal is
termed positive, but if ω be the greater index, as happens in the case
of calcite, then the crystal is by convention considered negative.
Just as in the case of gypsum, which is a positive biaxial crystal (the
reason for the term biaxial will presently be more fully explained),
when the two spectra afforded by a prism of calcite or quartz cut to
afford both ε and ω are examined in plane polarised light, by
introducing a Nicol prism somewhere in the path of the light, the two
images corresponding respectively to ε and ω will be found to be
produced by light polarised in two planes at right angles to each other.
For when the Nicol is at its 0° position one will be extinguished, and
when it is at 90° the other will be quenched. At the 45° position of the
Nicol both images will be visible with their partial intensities, as
happens also in the cases of biaxial prisms.
This behaviour of 60°-prisms of crystals belonging to the seven
different styles of crystal architecture, as compared with a prism of
glass or other transparent non-crystalline substance, is extremely
instructive. For not only is the optical constant refractive index—the
measure of the power exhibited by the crystal of bending light,
corresponding to its effect in retarding by the nature of its internal
structure the velocity of the light vibrations—the most important of all
the optical constants, but also in the course of its determination we
learn more of the behaviour of crystals towards light than from any
other type of optical experiment.
[Illustration:
FIG. 67.—Experiment to show Rectangular Polarisation of the two
Spectra afforded by a 60°-Prism of a Doubly Refracting Crystal cut
to afford two Indices of Refraction.
]
In Fig. 67 is shown a convenient mode of demonstrating the experiment
with the aid of the electric lantern and one of the large Nicol prisms
of the projection polariscope, already briefly described in Chapter VII.
in connection with the Mitscherlich experiment. The 60°-prism is
arranged on a small adjustable stand nearest the screen; then comes the
Nicol polarising prism of 2½ to 3 inches clear aperture, behind which is
the projecting lens, at the focus of which is placed the adjustable slit
on a separate stand. The slit is filled with light from the condenser of
the electric lantern, and in the lantern front a thick water cell is
arranged, in order to remove sufficient of the heat rays which accompany
the light beam to avoid damage to the balsam joint of the calcite Nicol.
When all the parts are properly arranged a sharp image of the slit
should first be thrown on the screen directly, in the temporary absence
of the 60°-prism, and then on replacing the latter at the proper angle
for minimum deviation, when the light traverses the prism parallel to
its third unused side, a spectrum or pair of spectra—according to the
position of the Nicol and to the nature of the 60°-prism as explained in
the foregoing discussion of the possibilities—will be projected on a
second screen (or the same one if movable) arranged at the proper angle
to receive the refracted rays.
If a single spectrum be afforded, which remains single on rotation of
the Nicol, the prism is of glass or of a uniaxial crystal cut so that
the light passes along the optic axis. If two spectra be shown when the
Nicol is arranged in the neighbourhood of its 45° position, the crystal
is a doubly refracting one, and if orientated so that the single optic
axis, if the crystal be uniaxial, is parallel to the refracting edge,
or, if the crystal be biaxial, so that the refracting edge is parallel
to one of the three principal axes of the optical ellipsoid and its
bisecting plane is parallel not only to this but also to a second
principal axis, then one spectrum, corresponding to one principal
refractive index, will extinguish when the Nicol is rotated to its 0°
position, and the other spectrum, corresponding to a second principal
refractive index, will be quenched on rotation of the Nicol to its 90°
position.
The separation of the two spectra on the screen depends on the amount of
the double refraction, and in the case of calcite this is exceptionally
large, so that the two spectra are widely separated on the screen. They
differ also considerably in dispersion. In the case of quartz the double
refraction is very small, and the spectral images of the slit are
consequently so close together as almost to touch one another. The pair
of spectra afforded by gypsum are similarly very close together, owing
also to weak double refraction. The amount of the double refraction is
measured by the difference between the uniaxial indices ε and ω, or that
between the minimum and maximum biaxial indices α and γ. The two spectra
given by quartz and calcite will correspond to ε and ω, and the greatest
separation of spectra occurs in the case of gypsum when the spectra are
those corresponding to α and γ, and not to α and β or β and γ.
It will now be useful and very helpful to examine more closely into the
nature of the beautiful mineral quartz, in order that a series of
interesting experiments may be described with it, which will assist
largely in rendering the optical characters of crystals clear to us.
_Quartz_, rock-crystal, although perhaps the commonest and best known of
all crystallised substances, the naturally occurring dioxide of silicon
SiO_{2}, is yet one of the most remarkable and fascinatingly
interesting. To begin with, as explained in the last chapter, quartz
belongs to one of the eleven enantiomorphous classes of lower than full
systematic symmetry, those which exhibit two mirror-image forms related
to one another like a pair of gloves. The particular class of the eleven
to which quartz belongs is the trapezohedral class of the trigonal
system, and two typical left-handed and right-handed crystals are shown
in Fig. 68 and Fig. 69 respectively.
There is one principal form which is common to both the hexagonal and
trigonal systems, namely, the hexagonal prism, and this is the chief
form exhibited by quartz crystals. They are terminated by an apparently
hexagonal pyramid, but which really consists of a pair of complementary
rhombohedra, which are purely trigonal forms; three upper faces of each
rhombohedron are developed at one end of the prism which may be regarded
as the upper, and the three lower faces of each of the two individual
rhombohedra likewise at the lower end of a fully developed doubly
terminated crystal. The rhombohedron is the characteristic form of the
trigonal system of crystal symmetry, the systematic crystallographic
axes being parallel to its edges. It is like a cube deformed by
extension or compression along a diagonal, which latter is arranged
vertically, and becomes the trigonal axis of symmetry (not a
crystallographic axis), as shown in Fig. 70.
[Illustration:
FIG. 68.
]
[Illustration:
FIG. 69.
Left-handed and Right-handed Crystals of Quartz.
]
When two rhombohedra are equally developed, one being rotated with
respect to the other 60° round the vertical trigonal axis of symmetry,
they together resemble a hexagonal pyramid, and crystals of quartz thus
terminated at both ends are not uncommon, so that at first sight a
quartz crystal might be mistaken for a hexagonal prism doubly terminated
by the hexagonal pyramid, and the mineral considered, in error, to
belong to the hexagonal system.
[Illustration:
FIG. 70.—The Rhombohedron and its Axes.
]
But one alternate set of three faces of the hexagonal pyramid at one
end, and the oppositely alternate set of three similar faces at the
other end, will usually be found to be much less brilliant (indeed often
quite dull) than the other alternate three, and very frequently also the
amount of development is markedly different, both facts indicating that
the terminal faces belong to two different but complementary
rhombohedral forms, and that the system of symmetry is the trigonal and
not hexagonal.
But there is much stronger evidence than this for trigonal symmetry. For
the little faces marked _s_ and _x_ on Figs. 68 and 69 are
characteristic of the trapezohedral class of the trigonal system, and it
will be observed that on one crystal, Fig. 68, these faces occupy and
modify a left-hand corner or solid angle on the crystal, while on the
other crystal, Fig. 69, they occupy and replace a right-hand solid
angle. Now, if a plate be cut out of the former crystal perpendicularly
to the axis of the hexagonal prism, that is, to the optic axis of the
trigonal uniaxial crystal, it will be found to rotate the plane of
polarisation to the left, the direction in which the small faces are
situated; while if a similar plate be cut out of the right-handed
crystal shown in Fig. 69, that is, one which has the small faces on the
right, it will be observed to rotate the plane of polarisation to the
right.
As quartz possesses the symmetry of the trigonal system and is thus
optically uniaxial, its optical properties are expressed, in common with
those of all trigonal, tetragonal, and hexagonal crystals, by an
ellipsoid of revolution, an ellipsoid the section of which perpendicular
to the principal axis—that of revolution, the maximum or minimum
diameter of the ellipsoid—is a circle. The optical properties are
consequently the same in all directions round this axis, which has
already been referred to by its common appellation of the “optic axis.”
The optic axis is identical in direction with the trigonal axis of
symmetry in the case of quartz or other trigonal crystal, and in the
cases of hexagonal and tetragonal crystals with the axes of hexagonal
and tetragonal symmetry, these three axes of specific symmetry being the
distinctive property of these three respective systems, which are thus
known in common as optically “uniaxial.”
Consequently, no double refraction is suffered by a ray transmitted
parallel to the optic axis, and the refractive index is equal in all
directions perpendicular to the optic axis, that is, for all rays
vibrating perpendicularly to the axis; hence the value of the refractive
index obtained along any such direction is one extreme value for the
whole crystal, and as already mentioned is distinguished by the letter
ω. The refractive index along the direction of the axis itself is the
other extreme value, and is labelled ε. It must be clearly appreciated,
however, that it is not the direction of transmission but that of
vibration perpendicular thereto, that is meant when it is said that, for
instance, the direction of the axis corresponds to the index ε. That is
to say, a ray the _vibrations_ of which occur parallel to the optic axis
of a uniaxial crystal is refracted to an amount which corresponds to the
refractive index ε, while a ray the vibrations of which occur
perpendicularly to the axis affords ω. The difference between ε and ω is
the measure of the double refraction of the crystal.
In the case of quartz ε is the greater, being 1.5534 for sodium light,
quartz being thus positive according to the convention already alluded
to; while ω is the smaller, namely, 1.5443. In the case of the other
widely distributed trigonally uniaxial mineral calcite, carbonate of
lime CaCO_{3}, the opposite is the case, ω being the greater, having the
value 1.6583 for sodium light, and ω the less, namely, 1.4864, calcite
being thus a negatively uniaxial substance. The amount of the double
refraction in the cases of the two minerals is very different, ε-ω for
quartz being 0.0091, and ω-ε for calcite being as much as 0.1719.
Calcite is indeed a mineral endowed with an especially large amount of
double refraction, a property which renders it so eminently suitable for
use in demonstrating the phenomenon, and for the construction of the
Nicol polarising prism, in which one of the two mutually perpendicularly
polarised rays, that which affords the index ω, is got rid of by total
reflection at a balsam joint, a large rhomb of calcite being cut in half
along a particular diagonal plane and the two halves cemented together
again with Canada balsam; the other ray, which affords ε (but not at its
minimum value), is transmitted as a beam of perfectly polarised light.
The result of this difference in the amount of the double refraction of
the two minerals quartz and calcite is very interesting as regards their
behaviour with polarised light. A thin plate of quartz, such as is often
found in the slices of rock sections employed for microscopic
investigation, of muscovite granite or quartz porphyry for instance, and
which is usually about one-fiftieth of a millimetre in thickness, shows
brilliant colours in a parallel beam of polarised light, the Nicol
prisms of the polarising microscope being crossed for the production of
the dark field before the introduction of the section-plate on the
stage. This is only true, however, when the plate has not been cut
perpendicularly to the axis, for such a thin plate thus cut does not
perceptibly affect the dark field, there being no double refraction of
rays transmitted along the axis, and the interference colours afforded
by crystal plates in polarised light being due to the interference of
the two rays produced by double refraction, one of which is retarded
behind the other so as to be in a different phase of vibration. Also,
the plate, even when cut obliquely, and best of all parallel, to the
axis, has to be rotated in its own plane (perpendicular to the optical
axis of the microscope), to the favourable position for the production
of the most brilliant colour. This especially favourable position is
halfway between (at 45° to) the positions at which darkness is afforded
by the plate. For on rotating the plate between the crossed Nicols it
becomes four times dark during a complete revolution, and at places
exactly 90° apart, known as the “extinction positions,” whenever, in
fact, that plane perpendicular to the plate which contains the optic
axis is parallel to the plane of polarisation of either the polarising
or analysing Nicol. At the intermediate 45° positions the maximum colour
is produced.
The colour owes its origin, as already mentioned, to the interference of
the two rays, corresponding to the two refractive indices, into which
the light is divided on entering the crystal in any direction except
along the axis. For one of the rays is retarded behind the other owing
to the difference in velocity which is expressed reciprocally
(inversely) by the refractive indices, and thus a difference of phase is
produced between the two light-wave motions, with the inevitable result
of interference when the vibrations have been reduced to the same plane
by the analyser; light of one particular wave-length is then
extinguished, and the plate therefore exhibits a tint in which the
complementary colour to that extinguished predominates. The light which
leaves the polarising Nicol is vibrating in one plane, but on reaching
the crystal this is resolved into two rays vibrating at right angles to
each other, and at 45° on each side of its previous direction of
vibration, supposing the crystal to be arranged for the production of
most brilliant colour. On reaching the analysing Nicol, the function of
which is to bring the two vibrations again into the same plane, these
two rays are each separately resolved back to the planes of vibration of
the two Nicols, and that pair (one from each ray) vibrating parallel to
the analysing Nicol are transmitted, while the other pair are
extinguished. The two former rays thus surviving, one individual ray of
the two having one refractive index and the other individual the other
index, are thus in a position to interfere; for they are composed of
vibrations in the same plane and of practically the same intensity, and
differ only in phase. Extinction occurs when this amounts to half a
wave-length, or an odd multiple of this, to which, however, requires to
be added half a wave difference of phase which is introduced by the
operation of the analyser. This explanation is a general one, applicable
to thin plates of crystals belonging to all the six systems of symmetry
other than the cubic. For plates of the latter, unless they are in an
abnormal condition of strain, do not polarise.
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.
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).
[Illustration:
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.
[Illustration:
_PLATE XIV._
FIG. 72.—Crystal Plate cut perpendicularly to the Axis.
Uniaxial Interference Figure afforded by Calcite (Trigonal) in
Convergent Polarized Light, with Crossed Nicols.
]
[Illustration:
FIG. 73.—Crystal Plate cut perpendicularly to the Bisectrix of the
Acute Optic Axial Angle.
Biaxial Interference Figure afforded by Aragonite (Rhombic) in
Convergent Polarised Light, with Nicols crossed and parallel to the
Vibration Directions of the Crystal.
]
[Illustration:
FIG. 74.—The same Plate as for the previous Figure.
The same when the two Nicols have been rotated in the same direction
for 45°, still remaining crossed.
CHARACTERISTIC UNIAXIAL AND BIAXIAL INTERFERENCE FIGURES IN CONVERGENT
POLARISED LIGHT.
(Reproductions of direct Photographs by the author.)
]
On rotating the crystal plate in its own plane, while no change occurs
with the calcite, the aragonite figure changes as regards the black
cross, which breaks up into hyperbolic curves currently spoken of as
“brushes,” until when the plate has been rotated 45° the appearance is
that shown in Fig. 74, the eye being supposed to have followed the
rotation. Or, keeping the eye still, the effect shown in Fig. 74 is
equally produced by the simultaneous rotation of both Nicols for 45°.
The vertices of the hyperbolæ now mark the positions of the optic axes,
and the angle between them is the apparent angle of the optic axes as
seen in air, which is considerably different from the true angle between
the optic axes within the crystal, owing to the very different
refraction of light in air and in the crystal substance.
Now some crystals exhibit a very different optic axial angle at
different temperatures, and one of the most beautiful experiments which
have ever been performed is the Mitscherlich experiment with gypsum,
which has already been described in Chapter VII. in connection with the
work of Mitscherlich, and illustrated in Plate XII., Figs. 52 to 55.
Other substances, on the other hand, show a marked change of optic axial
angle as the wave-length of the light is changed, and such a case has
already been described in Chapter VIII. and illustrated in Plate XIII.,
Fig. 58. The figure afforded by such a substance in ordinary white light
is, however, a complicated one, quite different from the normal one of
Fig. 73 afforded by aragonite, as will be clear on reference to the
interference figure shown at _f_ in Fig. 58, which represents the figure
given by ethyl triphenyl pyrrholone in white light.
In order to understand such biaxial interference figures thoroughly,
they should be studied in monochromatic light, when one obtains a clear
and sharp figure consisting of black curves as well as the cross or
brushes, and very sharp vertices to the brushes when the crystal is
arranged as in Fig. 74. The optic axial angle can then be measured for
each important wave-length of light in turn, and the variation for
wave-length followed throughout the whole spectrum. For this purpose it
is very convenient to have a source of monochromatic light of any or
every wave-length always at hand, and the author some years ago devised
a spectroscopic monochromatic illuminator,[17] for use with any
observing instrument, and which is particularly convenient for use with
the polariscopical goniometer which is employed in practice for the
measurement of optic axial angles. It is shown, along with the latter
instrument, in Fig. 75. The spectroscope has a single but very large
prism of heavy but colourless flint glass, and the spectrum produced—the
electric lantern being the source of light, its rays being concentrated
on the slit—is filtered through a second slit at the other end of the
spectroscope, where the detachable eyepiece is situated when the
instrument is used as an ordinary spectroscope, and for the calibration
(with the Fraunhofer solar lines) of the circle on which the prism is
mounted. The escaping narrow slit of monochromatic light includes only
the 250th part of the spectrum, so is monochromatic in a high sense of
the word. It impinges on a little ground glass diffuser carried in a
very short tube in front of this exit slit, and the optic axial angle
polariscope is brought up almost into contact with the ground glass, and
is thus supplied with an even field of pure monochromatic light. With
this apparatus it is easy to observe the exact crossing wave-length in
all cases of crossed-axial-plane dispersion such as that illustrated in
Fig. 58; for the reading of the graduated circle on which the prism is
mounted, and which is rotated in order to cause monochromatic light of
the different wave-lengths in turn to stream through the exit slit,
affords the exact wave-length with the aid of the calibration curve once
for all prepared. This calibration of the graduations is readily carried
out by using sunlight, and determining the readings corresponding to the
adjustment of the principal Fraunhofer lines in the middle of the exit
slit.
[Illustration:
FIG. 75.—Optic Axial Angle Goniometer and Spectroscopic Monochromatic
Illuminator.
]
Having thus rendered clear the nature of ordinary interference figures
afforded by crystals of the two types, uniaxial and biaxial, in
convergent polarised light, we may pass on to see what happens when we
take a number of plates of quartz of different thicknesses, cut
perpendicularly to the optic axis in all cases, instead of a plate of
calcite. We will examine first a fine pair of hexagonal quartz plates so
cut, each 1 millimetre thick exactly, and about 2 inches in diameter.
One was cut from a right-handed hexagonal prism, and the other from a
similar left-handed one.
Employing the lantern projection polariscope shown in Fig. 71, arranged
for convergent light just as for the Mitscherlich experiment, and with
the Nicols crossed, we will now see what happens when each of these
plates in turn is placed at the focus of the light rays, between the two
convergent systems of lenses. On the screen we observe in each case a
somewhat similar interference figure to that given by calcite, a black
cross and rainbow coloured circular rings, the smallest ring, however,
being very large relatively to the innermost ring given by calcite, and
the other rings being also further separated from each other. Moreover,
the black cross appears broadened out, this spreading of both rings and
cross being due to the thinness of the plate combined with the low
double refraction of quartz. Further, the right-handed and left-handed
plates both afford apparently identical figures. In order to obtain a
sharp figure like that of calcite we require to add a fourth lens, kept
in reserve for such cases, to each of the two similar convergent lens
systems, one on each side of the crystal plate, in order to increase the
convergence of the light rays. The figure then obtained with one of the
two plates is reproduced in Fig. 76, Plate XV.
[Illustration:
_PLATE XV._
FIG. 76.
Interference Figure afforded by a Quartz Plate, 1 Millimetre thick, in
strongly Convergent Polarised Light.
]
[Illustration:
FIG. 77.
Interference Figure afforded by a Quartz Plate, 3·75 Millimetres
thick, in moderately Convergent Polarised Light.
]
[Illustration:
FIG. 78.
Interference Figure (Airy’s Spirals) afforded by two superposed Quartz
Plates, 3·75 Millimetres thick, one of Right-handed Quartz and the
other of Left-handed Quartz, in moderately Convergent Polarised
Light.
INTERFERENCE FIGURES IN CONVERGENT POLARISED LIGHT AFFORDED BY QUARTZ
PLATES CUT PERPENDICULARLY TO THE AXIS.
]
Let us now observe, however, what occurs when a thicker plate of quartz
is used. Taking one of 7.5 mm. thickness, and placing it in the focus of
the converging rays, after removing the two extra lenses, we see on the
screen quite a different effect, an attempt to reproduce which
photographically in black and white is made in Fig. 77 on the same Plate
XV. The rings are closer together (using the same degree of
convergence), and the innermost is smaller; moreover, within it all
signs of the central part of the black cross have disappeared, and
instead a brilliant violet colour is shown, which alters to bright red
of the first order spectrum with the least rotation of the analysing
Nicol in one direction from its crossed position with respect to the
polarising Nicol, while if the rotation be in the opposite direction the
deep blue of Newton’s second order is produced. The arms of the cross,
however, appear towards the margin of the field. The violet colour shown
for the exact position of crossing of the Nicols is the tint of passage
between the first and second orders of Newton’s spectra, and this
illumination of the central part of the interference figure is obviously
the effect of the optical activity of quartz, for the tint is the same
as is produced with the plate in ordinary parallel plane polarised
fight, and is, in fact, due to the central axial rays of the convergent
cone being practically parallel.
On rotating the analysing Nicol for a few more degrees to the right we
observe that the innermost ring widens out and that the red passes into
orange and yellow, the quartz plate being a right-handed one. But when a
similar plate cut from a left-handed quartz crystal is used instead, the
inner ring closes up somewhat for the same rotation of the analyser,
moving inwards instead of outwards, and the blue colour given with the
first slight rotation passes into green and yellow as the rotation is
continued. Moreover, the circular character of the rings is altered, and
so much so that when the rotation has proceeded as far as 45° the shape
of the rings has changed almost to a square. These alterations in the
interference figure are characteristic of the two varieties of quartz
crystals. A useful rule to remember is, that for a right-handed crystal
rotation of the analyser to the right causes the colours to appear in
the order of their refrangibility, namely, the least refrangible red
first, then orange, yellow, green, blue and violet in their order; while
for a left-handed crystal the converse is true when the direction of
rotation of the analyser is the same, that is, to the right, clockwise;
obviously also the colours appear in the opposite order when the
rotation of the analyser is to the left.
It will now prove of interest to examine the effects produced by two
plates of opposite varieties of quartz of half this thickness, namely,
3.75 mm. The phenomena are very similar to those just described, but the
rings are a little wider, and the larger area within the innermost ring
is now filled with yellow light instead of violet, when the analyser is
exactly crossed to the polariser. It passes into a bright green when the
analyser is rotated slightly on one side, and into orange when the Nicol
is rotated in the reverse direction. But the most interesting thing of
all is to observe what occurs when these two plates of 3.75 mm.
thickness, one of right-handed quartz and the other of left-handed, are
superposed and placed in contact together as one plate, of double the
thickness, 7.5 mm., at the convergent focus. A beautiful spiral figure
is produced on the screen, composed of the celebrated “Airy’s spirals”
as if the black cross were being reproduced in the central part, but
with each of its bars distorted into the shape of the letter S, as shown
in Fig. 78 at the foot of Plate XV. The contrary effects of the two
opposing rotations are thus extraordinarily indicated visually in the
interference figure afforded by the composite plate.
Now, it is of great practical interest that certain quartz crystals are
found in nature which show Airy’s spirals directly, on cutting a plate
7.5 mm. thick or thereabouts, perpendicular to the optic axis. For
instance, one in the author’s collection of quartzes, a single plate of
an apparently homogeneous and perfectly limpid crystal, shows the
spirals exceedingly well and clearly defined. As a matter of fact, it is
a twin, a right and a left-handed crystal being twinned together with an
invisible plane of composition, which is only revealed on examining the
crystal in polarised light, as will be demonstrated in the next chapter
by the use of parallel polarised light. The fact of such a plate of
quartz affording Airy’s spirals in convergent polarised light is,
however, of itself an excellent proof of the twinning of two crystal
individuals of the opposite varieties.
Now the very shape of these spiral figures suggests screw action of the
molecular structure of the crystals on the waves of light passing
through them, and moreover, of the action of two screws of opposite
directions of winding, one clockwise and the other anti-clockwise, thus
remarkably confirming the supposition that the point-systems of the
structure of the right and left-handed varieties of quartz are of a
helical nature and respectively of opposite modes of winding.
Another experiment, devised by Reusch, which still further enhances the
probability that this supposition as to the structure of quartz crystals
is correct, may next be introduced. A thin film of biaxial mica has been
cut into twenty-four narrow strips, which have been laid over each other
at angles of 60°, so that a screw-shaped pile has been formed of the
central overlapping parts, consisting of four complete rotations; that
is, there are four repetitions of the “pitch” of the screw, each
composed of six films. On placing this composite plate of mica at the
convergent focus of the lantern polariscope, so that the overhanging
ends of any four identically superposed strips occupy the focus, the
ordinary biaxial interference figure of mica—two sets of rings and
hyperbolic brushes, very much like Fig. 52, Plate XII.—is observed on
the screen. But when the plate is moved so that the central part comes
into the focus, where all the twenty-four films overlap in their six
different orientations 60° apart, and so that all the light rays have to
traverse the whole helical pile of the twenty-four films, a uniaxial
figure exactly like that of quartz is produced, namely, one composed of
circular rings, with a black cross only visible, however, at the
marginal part, and with the inner ring filled with brightly coloured
light. Moreover, on slightly rotating the analysing Nicol the innermost
ring moves outwards or inwards and the colour changes to blue or red,
according to the direction in which the helix had been wound, in exact
accordance with the rule stated above for quartz.
If now a second such helical pile of mica films, but one for which the
opposite manner of winding has been adopted, anti-clockwise if the first
had been clockwise, be examined at the convergent focus, precisely the
same appearance will be observed with crossed Nicols, but the opposite
changes will occur on rotating the analyser. Finally, to complete the
interesting proof of the helical nature of quartz crystals, when these
two oppositely wound composite mica plates are superposed—each being
marked carefully to indicate the direction of the helix and the proper
mode of superposition in order to effect precise oppositeness of
arrangement, mirror-image symmetry, in fact, about the plane of
contact—and placed in the convergent beam near its focus, there is at
once seen on the screen a magnificent display of Airy’s spirals, as
perfect as those afforded by the fine natural twin last experimented
with. Hence, there can be no doubt whatever that the remarkable optical
behaviour of quartz is due to its point-system being of a helical
nature, a right or a left-handed screw structure being apparently
produced in nature with equal facility. The circumstances of environment
during the formation of the crystal probably determine which variety
shall be produced, and when the nature of the environment becomes
changed during the operation of formation either twins are produced of
the two varieties, or separate individual crystals.
This may well conclude our experiments in convergent polarised light,
which—including the beautiful Mitscherlich experiment described in
Chapter VII., of exhibiting the crossing of the optic axial plane in the
case of gypsum, and the production of all the types of interference
figures in succession, as the crystal becomes warmed by the heat rays
accompanying the beam of convergent light—will have introduced the
reader to a typical series of such experiments, and such as were
actually exhibited by the author to the British Association at Winnipeg.
We may pass, therefore, in the next chapter to the consideration of an
equally interesting series in which a parallel beam of polarised light
will be used, which will still further elucidate the internal structure
in the especially instructive case of quartz crystals, and that of
crystals in general.
CHAPTER XIV
EXPERIMENTS WITH QUARTZ AND GYPSUM IN PARALLEL POLARISED LIGHT. GENERAL
CONCLUSIONS FROM THE EXPERIMENTS WITH QUARTZ.
In order to rearrange the projection polariscope for experiments in
parallel light, we simply remove the three lenses on separate stands
(Fig. 71), and the convergent systems of lenses on their special
adjustable stand with goniometrical crystal holder, from between the two
Nicol prisms, and replace them by two other separately mounted lenses,
acting together as an achromatic projecting objective, and a rotatable
object stage. The whole arrangement as thus altered for experiments in
parallel polarised light is shown in position in Fig. 79. The change is
readily made, a gap in the plinth-bed guides near the analysing Nicol
enabling it to be effected without removing either of the prisms, the
analyser being simply drawn along a few inches nearer the end in order
to expose the changing gap. The pair of lenses consists of a
plano-convex lens of 5 inches focus and 2¼ inches diameter, and another
plano-convex lens of 8½ inches focus and 2 inches aperture, with their
convex faces turned towards each other. Together they produce on the
screen an excellent image of the object on the stage, and the size of
the image can be varied at will by regulating the relative positions of
the two lenses with respect to each other and to the object stage. If
found more suitable for the particular screen distance available, the
5–inch lens may be replaced by a 6–inch lens also provided as an
alternative.
[Illustration:
FIG. 79.—Projection Polariscope arranged for Parallel Light.
]
When the analysing Nicol is arranged with its vibration direction
parallel to that of the polariser, we obtain bright light on the screen
on actuating the electric lantern, and the image of an object on the
stage can thus be projected on the screen on a bright ground. But when
the analyser is crossed to the polariser, that is, rotated to the
position 90° from this parallel position, the two planes of vibration of
the Nicols being then at right angles, the screen is quite dark. Before
continuing in this dark field our experimental study of quartz, which is
obviously a type of the more exceptionally behaving substances owing to
its special structure, it will be wise to examine a more ordinary kind
of crystalline substance. For this purpose gypsum—better known in
optical work as selenite, hydrated sulphate of lime, CaSO_{4}.2H_{2}O,
crystallising in beautifully transparent and often large crystals
belonging to the monoclinic system, a typical one of which has been
illustrated in Fig. 9 (page 14), and which we have already referred to
in connection with the Mitscherlich experiment described in Chapter
VII.—is especially suitable, on account of its clear and colourless
transparency, the large size of crystals available, and the brilliancy
of the polarisation colours which they afford when adequately thin. A
very perfect cleavage being developed parallel to the symmetry plane,
the clinopinakoid {010}, such thin films, of even thickness throughout,
can be readily prepared.
Such a very thin cleavage plate, about 1½ inches in its longest
dimension, is mounted with Canada balsam between a pair of circular
glass plates 1⅞ inches in diameter, the standard size of object plates
for the projection polariscope; the double plate is then supported in a
mahogany frame also of the standard size—4 by 2¼ inches, with clear
aperture of 1⅝ inches diameter and supporting rabbet for the plate 1⅞ to
2 inches diameter—on the rotating stage by a pair of spring clips. The
Nicols being arranged with their vibration directions parallel, in order
to permit light to travel to the screen, and the lenses being arranged
properly for a sharply focussed picture of suitable size, the outline of
the crystal plate will be seen on the screen, and the whole area of the
crystal will either at once appear coloured, or will do so on more or
less rotation of the stage carrying the crystal, which rotates the
latter in its own plane. The crystal outline is of the character shown
in Fig. 80, which also gives the positions of the crystal axes a and c,
and a simple stereographic projection of the faces of the crystal, from
which the nature of the faces bounding the section-plate will be clear.
[Illustration:
FIG. 80.—Section of Gypsum Crystal showing the Extinction Directions.
]
On rotating the Nicol analyser the colours change, and appear at their
maximum brilliancy when the field is dark and the Nicols crossed.
Leaving the analyser crossed to the polariser, and rotating the stage
and therefore the crystal, the colours again change, and at certain
positions 90° apart during the rotation, marked by the two strong lines
in Fig. 80, they disappear altogether, and the crystal becomes dark like
the rest of the field, while the positions of maximum brilliancy of
colour are found to be situated at the 45°-positions intermediate
between these positions of “extinction.” When the quenching occurs the
vibration planes of the two rays, travelling by virtue of double
refraction through the crystal, are parallel to the planes of vibration
of the rays transmitted through the two Nicols, and the fact is a very
important one, enabling us to determine the directions of light
vibration in the crystal. In the case of our gypsum plate, the cleavage
of gypsum being parallel to the unique plane of symmetry of the
monoclinic crystal, these two positions are the directions of the two
axes of the optical ellipsoid which lie in the symmetry plane, and they
correspond to the vibration directions of rays affording the refractive
indices α and γ. The direction corresponding to γ is that of the “first
median line,” the bisectrix of the acute angle between the optic axes;
while α corresponds to the obtuse bisectrix or “second median line.”
These directions are clearly marked by the strong lines in Fig. 80. The
third axis of the optical ellipsoid is obviously perpendicular to the
plate and to the symmetry plane, and corresponds to the intermediate
refractive index β. Thus this simple observation of the extinction
directions in such a case as gypsum enables us at once to fix completely
the orientation of the optical ellipsoid, a fundamental optical
determination.
A second thin plate of gypsum may next be examined, similarly prepared
and mounted. It is clearly a composite one, being composed of a pair of
twins. For when placed on the stage in the dark field of the crossed
Nicols, and rotated to the position for maximum brilliancy of colour, it
shows different colours in the two halves, as indicated by different
shading in Fig. 81. If, however, the analysing Nicol prism be withdrawn
from the plinth-bed and removed altogether the crystal appears in its
natural colourless condition as a single one, with no indication
whatever of any line of division.
[Illustration:
FIG. 81.—Twin of Gypsum as seen in Parallel Polarised Light.
]
Some exceedingly brilliant polarisation effects are afforded by a number
of objects exhibited by the author in his lecture at Winnipeg, composed
of selenite (gypsum) twins and triplets, some arranged to cross one
another like the mica films of Reusch described in the last chapter, but
only for a single rotation, three twin strips going to a rotation, at
angular distances of 120°; others are arranged in geometrical patterns,
and in circles overlapping one another, and the whole series afford the
most gorgeous and variegated display of colour imaginable, the colours,
moreover, altering either on rotation of the stage or of the analysing
Nicol, and thus passing through every tint conceivable.
Having thus demonstrated the usual effect afforded by a doubly
refracting crystal plate in parallel polarised light, we may next
illustrate two special cases, which will lead us up to the case of
quartz once more. The first relates to a crystal belonging to the cubic
system, which is theoretically singly refractive or “isotropic”; the
second concerns a plate of a uniaxial crystal cut perpendicularly to the
optic axis, the unique direction of single refraction of such a crystal.
A plate of fluorspar affords a good example of the first case. When
placed on the stage of the polariscope it shows no colour at all in
polarised light, whatever be the position of the two Nicols with respect
to each other, and the field remains dark when they are crossed, the
crystal, in fact, behaving just like so much glass.
A word of caution, however, is here necessary, for natural mineral
crystals are not infrequently formed under conditions of considerable
strain, at high temperatures or under great pressure, as in the case of
the diamond for instance. So that we must be careful to choose a normal
and well-formed crystal of fluorspar for our experiment. This point may
be well illustrated by placing on the stage a thick circular plate of
glass, an inch or more in diameter, which has been purposely heated and
then suddenly cooled in order to evoke such a condition of strain.
Crossing the Nicols so as to obtain the dark field, there is at once
produced on the screen a black cross and circular concentric
spectrum-coloured rings, resembling with wonderful simulation the
interference figure, shown in Fig. 72, Plate XIV., afforded by calcite
or other uniaxial crystal in convergent polarised light. Artificial
double refraction has been produced in the glass by the strained
conditions, in a fashion concentrically symmetrical to the axis of the
cylinder, an interference figure being afforded symmetrical about the
axis of the cylinder as if it were an optic axis.
The diamond crystallises in the cubic system, in octahedra, hexakis
octahedra, or hexakis tetrahedra, and should, therefore, theoretically
be without effect on polarised light. Yet it is rare to find a diamond
which does not show more or less colour in the dark field, owing to the
condition of strain in which it exists. It is notorious that the strain
is occasionally so great that a diamond explodes into powder shortly
after removal from its enveloping matrix of blue clay. The author, by
the great kindness of Sir William Crookes, was enabled to show on the
screen, both in a lecture at the Royal Society and in the Evening
Discourse to the British Association at Winnipeg, the images of ten
magnificent large diamonds, natural, perfectly formed crystals uncut and
unspoilt by the lapidary. They were mounted between two circular glass
plates of the usual 1⅞ inches diameter, the diamonds being attached by
balsam to one of them; each plate was held in a mahogany frame of 1⅝
inches circular aperture, the two frames being then attached face to
face to form a single one, an enclosing cell, which could be placed on
the rotating stage as an object-slide for the projection polariscope.
The appearance of the diamonds on the screen in ordinary light is
reproduced in Fig. 82, Plate XVI., as well as is possible without their
natural colour, for while several of them are brilliantly colourless,
others are tinted, one being a bright green diamond. On producing the
dark field by crossing the analysing Nicol with respect to the
polariser, the darkness was dispelled by brilliant polarisation colours,
at once revealing the diamonds and outlining them clearly against the
dark background. On rotating the analyser the colours changed in the
usual manner of polarising objects, and bright colours were shown by all
the diamonds even when the Nicols were parallel.
It is obvious, then, that both a transparent non-crystalline substance
such as glass, and a cubic crystal, must be free from strain in order
that it shall exhibit no colour in polarised light and, indeed, no
polarisation effects whatever, and behave as an isotropic substance.
[Illustration:
_PLATE XVI._
FIG. 82.—Ten Diamonds exhibiting Natural Faces, mounted for the
Lantern Polariscope, to show Polarisation Colours due to Internal
Strain.
]
[Illustration:
FIG. 121.—Doubly Refracting Liquid Crystals of Cholesteryl Acetate,
projected on the Screen in the Act of Growth (see p. 281).
TWO FIGURES ILLUSTRATING THE HARDEST (DIAMOND) AND THE SOFTEST (LIQUID
CRYSTALS) OF CRYSTALS.
]
The second special case to which attention may be called, that of a
plate of an ordinary uniaxial crystal such as calcite, cut
perpendicularly to the optic axis, is also obviously subject to the same
proviso, that the crystal must be free from strain in order to exhibit
the normal phenomena. Such a perfectly normal plate remains quite
obscure in the dark field in parallel light, producing neither colour
nor interference figure, even on rotation of the object stage with the
crystal, in its own plane. For the light traverses the crystal along the
optic axis, the axis of single refraction, and the vibrations occur with
equal velocity in all directions perpendicular to it. Hence there is no
division into two rays, one retarded behind the other on account of less
velocity of vibration, and therefore no interference colour.
And now this leads us back to quartz, for this mineral is also uniaxial,
and we will investigate in the same manner in parallel polarised light
the plates of the mineral cut perpendicularly to the optic axis, which
have already been referred to in connection with the experiments
concerning the interference figures produced in convergent polarised
light. Suppose we take first the large plate of quartz 7.5 mm. thick and
over 2 inches in diameter. Placing it on the stage—instead of finding
the dark field to be unaffected by the introduction of the plate, and to
remain so on rotation of the latter in its own plane, as should
theoretically be the case if quartz were a normal uniaxial crystal, and
as calcite has been actually shown to do—we observe that it polarises in
brilliant colour, the whole hexagonal outline of the plate, clearly
focussed on the screen, being filled with an evenly brilliant violet
tint, the tint of passage, just as the central part of the interference
figure, within the innermost ring, had been coloured in the convergent
light experiment with the same plate. The colour changes with the
slightest rotation of either of the Nicols, passing into red for one
direction of rotation and into blue and green when the Nicol is rotated
in the other direction. The tint also alters when the section-plate is
rotated about its vertical diameter, by rotating the upper adjustable
part of the supporting column of the stage within its outer fixed
tubular column; this latter change is equivalent to a thickening of the
plate, the light beam having to traverse a longer path through the
quartz during such oblique setting of the plate.
This colour is due to the same fact which produced colour in the central
part of the interference figure, namely, the optical activity of quartz,
the fact that the plane of vibration of a beam of plane polarised light
transmitted along the axis of quartz is rotated to the right hand or to
the left. The amount of this rotation is precisely equal, although
opposite in direction, for the two varieties of quartz, but the rotation
varies very considerably for different rays of the spectrum. It also
varies directly proportionally to the thickness of the plate. A plate
one millimetre thick cut perpendicularly to the axis rotates the plane
of polarisation for red hydrogen light (C of the spectrum) to the extent
of 17° 19′, for yellow D sodium light 21° 42′, and for greenish-blue F
hydrogen light 32° 46′. The rotation is a maximum for plates
perpendicular to the axis, and the effect is inappreciable in directions
at right angles thereto. It is clearly due to the oppositely spiral
winding of the regular-point-system of the crystal structure, round the
direction of the optic axis, the trigonal axis of symmetry of the
crystal, a structure which we have proved to be characteristic of quartz
by the beautiful experiments with the helical piles of mica plates,
absolutely reproducing the polarisation effects with quartz, as
described in the last chapter.
The opposite optical rotation of the two varieties of quartz can be well
shown by constructing a “biquartz.” Two plates of equal thickness,
preferably either 7.5 mm. or 3.75 mm., are cut, one from a right-handed
and the other from a left-handed crystal, each exactly perpendicular to
the optic axis. The two edge-surfaces to be subsequently joined together
are also cut, ground and polished as true planes perpendicular to the
plate surfaces, and the two plates are then cemented together with
Canada balsam by these two prepared edge-surfaces, taking care that the
broad plate-surfaces of the two halves are absolutely continuous as if
the whole were a single parallel-surfaced plate of quartz. Such a
composite plate or “biquartz,” is one of the most useful aids to the
study of optical activity, being much used for enhancing the
sensitiveness of the determination of the angle of rotation.
When the image of such a 7.5 mm. biquartz, mounted in the usual mahogany
frame and placed on the object stage of the projection polariscope, is
thrown on the screen—the Nicols being crossed for production of the dark
field, and the stage and crystal plate being strictly perpendicular to
the parallel beam of polarised light—the whole of the screen covered by
the image of the plate appears uniformly coloured with the violet tint
of passage. But the moment the analysing Nicol is rotated for a very few
degrees, one-half turns red and the other blue and then green. If the
Nicol be turned back again to the crossing position with the polariser,
and then rotated further in the opposite direction to the former
rotation, the appearances on the two sides of the sharply focussed fine
line of demarcation between the two halves are inverted, the side which
formerly turned red now becoming green, and _vice versa_. The two
varieties of quartz are thus oppositely affected, and it will be obvious
that the biquartz is a very delicate test for the exact crossing of a
pair of polarising prisms, or for the determination of the mutual
extinction of two rectangularly polarised beams of light in general.
A very striking and beautiful mode of exhibiting this opposite and equal
rotation of the plane of polarisation by the two varieties of quartz may
next be described, an experiment which we owe to Prof. S. P. Thompson. A
composite plate of mica is constructed out of 24 sectors of 15° angle
each, the whole making up a complete circular plate. They are cemented
between two circular glass plates of the usual 1⅞ inch size, with
balsam; the sectors are laid down in succession on one of the plates
first, side by side, with the edge of every one in turn in close contact
with the edge of the next in order, so as to radiate from a common
centre. The second glass plate is only cemented after the arrangement
has been allowed to set for some days, when there is less risk of
disturbing the mounting of the sectors. The latter have all been cut
from the same film of mica, which has a thickness corresponding to a
retardation of one of the two rays produced by the double refraction of
the crystal behind the other equal to one and a half waves. Each sector
is so cut that the line bisecting the 15° angle is parallel to the line
joining the positions of emergence of the two optic axes of the crystal.
[Illustration:
FIG. 83.—A Disc _b_ of 24 Mica Sectors under Crossed Nicols, showing
Effects at _a_ and _c_ of Introduction of Left and Right-handed
Quartz Plates.
]
On placing this wheel of mica on the polariscope stage, the Nicols being
crossed, the effect shown at _b_ in Fig. 83 is observed on the screen.
The four sectors 90° apart, the bisecting lines of which are vertical
and horizontal respectively, parallel to the vibration planes of the
Nicols, appear as a jet black cross; the sectors next to them appear
pale brown, and the next again a still paler delicate shade of sepia,
while the central diagonal ones of each quadrant, at 45° to the black
cross, are brilliantly white.
On now introducing behind or in front of the stage a right-handed quartz
plate one millimetre thick, one of the pair of large ones described in
one of the convergent light experiments of the last chapter, the black
cross is observed to be deflected one sector to the right, as shown at
_c_ in Fig. 83; whereas when the left-handed companion plate is
introduced in like manner the cross moves over one sector to the left,
as indicated at _a_ in Fig. 83. The two quartz plates are mounted on the
same mahogany object frame, a specially long one with two large
apertures carrying the quartzes, so that first one and then the other
can be placed in or out of position, and when this is done rapidly the
movement of the cross from right to left and back again is very marked.
Occasionally a natural biquartz is obtained, on cutting a plate out of a
crystal of quartz perpendicularly to the axis. For it is not uncommon to
find a crystal which, while apparently a single crystal, is really a
twin, the two right and left individuals being joined by an invisible
plane of contact, or “plane of composition” as it is called, so
beautifully have the two grown together. Figs. 84 and 85 show two kinds
of twins of quartz. The former consists of two obviously different
individuals, with the little _s_ and _x_ faces indicating right or
left-handedness clearly developed in an opposite manner. The crystal
shown in Fig. 85, however, appears to be a single individual, yet
differs from either a right-handed or a left-handed crystal in showing
the _s_ and _x_ faces developed on both right and left solid angles. It
is a case of complete interpenetration.
In both cases the plane of twinning is parallel to the optic axis, and
to a pair of faces of the hexagonal prism of the second order,
perpendicular to a pair of the actual first order prism faces shown by
the crystal. They are examples of the well-known “Brazilian twinning” of
quartz, so called because many quartz crystals found in Brazil display
it.
[Illustration:
FIG. 84.—Pair of Brazilian Twins of Quartz.
]
[Illustration:
FIG. 85.—Completely Interpenetrated Brazilian Twins of Quartz.
]
A natural biquartz of 3.75 millimetres thickness cut from such a crystal
as is shown in Fig. 85, the plate having a hexagonal outline just as if
the crystal were really a single one, may next be projected on the
screen. The Nicols being crossed, the outline of the crystal is seen
sharply defined, the whole area of the crystal being coloured a uniform
yellow, there being absolutely no trace of any dividing line. But the
moment one commences to turn the analysing Nicol different shades,
orange and green respectively, begin to develop on the two sides of the
line indicating the plane of composition of the twin, the hexagon being
divided by a diametral line joining two corners, which have been
arranged in mounting the plate in its carrier frame to be above one
another, so as to bring the line of composition vertical, as will be
clear from Fig. 86. On rotating the analyser further the difference is
still more marked, and we have blue on one side and orange red on the
other, developing still deeper into red and purple as the analyser
approaches the parallel position with respect to the polariser; when
this latter position is attained the transition violet tint is developed
evenly over the whole plate, and the dividing line has again
disappeared.
[Illustration:
FIG. 86.—A Natural Biquartz in Parallel Polarised Light.
]
Another natural biquartz, also shown in the author’s lecture at
Winnipeg, introduces us to a new phenomenon. For when the Nicols are
crossed we observe a black band down the centre of the plate, marking
the line of division of the twins. When the analyser is rotated until it
is parallel to the polariser this black band changes to a white one, the
sequence of colours on the different sides of the band, that is, in each
half of the plate, being the same as just described. The effect with
crossed Nicols is more or less simulated in Fig. 87, Plate XVII., which
is a reproduction of a direct photograph of the screen picture. The
reason for this black band in the dark field, and for the white one in
the bright field, is that the two halves of the twin overlap at the
centre, the plane of junction of the two individual crystals being
oblique to the plate, instead of exactly perpendicular thereto as was
the case with the first natural biquartz. We are, in fact, beginning to
get the effect of two superposed wedges of quartz.
[Illustration:
_PLATE XVII._
FIG. 87.—Natural Biquartz exhibiting the Black Band (Nicols crossed)
at the Oblique Junction of the Right-handed and Left-handed Parts.
]
[Illustration:
FIG. 88.—Artificial Biquartz, the two parts being obliquely joined in
order to produce the Black Band.
DIRECT PHOTOGRAPHS OF PICTURES PROJECTED ON THE SCREEN BY THE LANTERN
POLARISCOPE, USING PARALLEL LIGHT.
]
When the obliquity is greater, or the crystal thicker, a white band
appears on each side of the black central one, the Nicols being crossed,
and when the thickness is as great as 6 to 7.5 mm. a spectrum band
appears on each side of the white one.
That this obliquity of the surface of contact of the two intergrown
individuals (not the plane of twinning, which remains parallel to a pair
of faces of the hexagonal prism of the second order) is the true
explanation can be readily proved by reproducing the effect
artificially. A thick double plate of quartz is constructed, as shown in
Fig. 88, composed of two halves of respectively right-handed and
left-handed quartz, each 6 to 7 millimetres thick, and each of which has
had the edge-face of junction ground and polished obliquely at an angle
of 30° or so, and oppositely so, instead of perpendicularly to the
plates; the two halves are then cemented together in the usual manner
for a biquartz, with Canada balsam, in order to make a continuous plate.
On placing the plate of this construction possessed by the author on the
stage of the projection polariscope, the two halves exhibit on the
screen respectively brilliant red and green colour, with a vertical
central black band, and on each side of it first a white strip and then
a spectrum band, all the bands being parallel to each other, and the
whole effect being precisely what was observed with the thickest natural
biquartz.
Thus, we have imitated the oblique junction of the twin parts of the
second and third biquartzes, and proved that this obliquity is the
reason for the phenomena of bands, the black band occupying the centre
where the two opposite rotations of the right and left quartz are
precisely neutralised. The dark field of the crossed Nicols consequently
prevails along this central strip, for the rotatory effect of the first
individual crystal on the light passing through it is exactly undone by
the subsequent passage of the rays through the other individual. On
either side of this neutral strip there is a little preponderance of
right-handed quartz on one side, and of left-handed quartz on the other,
and the usual effect of a thin plate of quartz is therefore seen,
namely, no colour but a little light, while further accretions of
thickness of the preponderating variety give all the colours of the
spectrum in turn, as with growing thicknesses of ordinary single quartz
plates, thus producing the spectrum band.
The black band is also afforded when the plate is cut somewhat
obliquely, out of a twin crystal with a junction plane truly
perpendicular to the equatorial section, instead of cutting it truly
perpendicularly to the axis, the junction plane being then oblique to
the plate. The polarisation colours are not so strong, however, unless
the plate be made thicker.
[Illustration:
_PLATE XVIII._
FIG. 89.—Black Central Band and equidistant Spectrum Bands on each
side, afforded by Babinet’s Composite Plate of two Quartz Wedges,
one parallel and the other perpendicular to the Axis. (Direct
Photograph of Screen Picture as projected by Lantern Polariscope.)
]
[Illustration:
FIG. 94.—Section-plate of Amethyst, natural size, as seen directly in
Ordinary Light, showing Alternate Violet Sectors (see p. 223).
]
This effect of a black band with flanking spectra is very similar to
that obtained, due to double refraction and not to optical activity,
when two thin wedges of quartz are cemented together to form a parallel
plate, one wedge being cut so that the optic axis is parallel to the
edge of the wedge, and the other with the optic axis perpendicular to
the edge. When such a composite plate of quartz, often known as a
Babinet plate from the name of its first constructor, is placed on the
stage of the polariscope, and rotated to the 45° position with respect
to the planes of vibration of the crossed Nicols, there is observed on
the screen a deep black band in the centre parallel to the edge of the
wedge, and a number of spectrum bands on each side, separated by white
equal interspaces, the rainbow coloured bands showing the orders of
Newton’s spectra. The effect, as seen on the screen, is reproduced
photographically in black and white in Fig. 89, Plate XVIII.
These experiments lead us naturally to the study of a great variety of
quartz twins, involving some of the most beautiful and gorgeously
chromatic phenomena which it is possible to produce on the screen with
the projection polariscope. They will eventually bring us to the study
of amethyst quartz, in which the twinning is repeated so often that the
laminations of alternate right and left quartz are sometimes countless,
and almost approach molecular dimensions.
The Brazilian twinning of quartz, parallel to a pair of faces of the
second order hexagonal prism {11̄20}, often occurs in a very erratic
manner, as regards the arrangement of the portions of the composite
crystal belonging to the two varieties, the surfaces of contact and
character of the interpenetration being frequently very irregular, and
often remarkably so. Thus Fig. 90, the upper figure of the coloured
frontispiece, gives some faint idea of the appearance presented on the
screen by a very beautiful quartz plate, one-half of which is entirely
composed of left-handed quartz, giving a rich even rose-red colour when
the Nicols are crossed, not very far from the violet transition tint,
the plate being nearly 7.5 mm. thick, while the other half consists of
an alternation of strips of right and left-handed quartz, joined
obliquely to the surface of the plate, the black band and its
accompanying white ones and spectrum bands being repeated two or three
times before the edge is reached. This is a very instructive case, for
it shows in this half of the plate, on a large scale, what occurs in
amethyst in a more minutely structural manner, the broad strips, the
sections of plates upwards of a quarter of an inch thick, of alternating
character becoming in amethyst thin lines, the sections of laminæ or
films of microscopic tenuity, their number being correspondingly
enormously increased.
It may be interesting to state how this Fig. 90, and the lower Fig. 97
of the frontispiece representing the projection on the screen of benzoic
acid in the act of crystallisation, were produced. The pictures on the
screen were directly photographed on the latest Lumière autochrome
plates, a transparency in the actual natural colours being thus obtained
in each case. These transparent colour-photographs were then used as
originals wherewith to reproduce the effects on paper by the most recent
improved three-colour photographic process.
[Illustration:
_PLATE XIX._
FIG. 91.—Sectorial 60° or 120° Intrusive Twinning of Right and
Left-handed Quartz, showing Ribbons with Central Black Band where
Oblique Overlapping occurs.
]
[Illustration:
FIG. 92.—Irregular Intrusive Twinning of Right and Left-handed Quartz.
DIRECT PHOTOGRAPHS OF REMARKABLE SCREEN PICTURES AFFORDED IN PARALLEL
POLARISED LIGHT BY SECTIONS OF TWINS OF RIGHT AND LEFT QUARTZ.
]
Two other typical cases of irregular quartz twinning may also with
advantage be demonstrated. The first is a plate in which there are
repeated 60° V-shaped or 120° wedge-shaped intrusions of one variety
into a greater mass of the other variety. The border of the V or 120°
wedge is composed of a ribbon, the outer edges of which are
spectrum-coloured and the central line of which is formed by the deep
black band, which is separated on each side from the spectra by a white
strip. Some idea of the beauty of this quartz plate, which was
generously lent to the author by Prof. S. P. Thompson, as projected on
the screen under crossed Nicols, may be gathered from Fig. 91, Plate
XIX., the upper homogeneous part of the plate being coloured a brilliant
green, and the lower part red.
The second is an irregular interpenetration of one variety into the
other, in repeated V-shapes occupying the lower half of the image of the
plate as seen on the screen in the dark field of the projection
polariscope, like a range of sharp mountain peaks, the black bands being
so rapidly repeated as to be nearly continuous. These darker portions
thus appear to form the bulk of the mountains, while the upper untwinned
half of the crystal shows a clear and even sky blue; to make the
resemblance to a range of Alpine mountains even more complete, the wavy
line of demarcation between the twinned and non-twinned portions of the
plate is bordered by a white ribbon, of varying width, giving the
appearance of a snow-cap to each peak, which shows up clearly against
the blue sky. It will be obvious that this quartz plate affords an
altogether very beautiful series of phenomena in parallel polarised
light on the screen, for the colours change with every movement of the
analysing Nicol from the crossed position, the appearance for which has
just been described. Fig. 92, Plate XIX., gives only the faintest idea
of the beauty of the screen picture afforded by this section-plate. The
effect chosen as best for photographic reproduction purposes is one
afforded when the analysing Nicol is rotated somewhat away from the
crossed position with respect to the polariser.
And now we arrive finally at amethyst quartz, three very beautiful
hexagonal plates of which—cut perpendicularly to the optic axis as usual
for quartzes intended to display optical activity, from an apparently
single hexagonal prism in each case—will be taken as typifying the
phenomena exhibited by this especially interesting variety of quartz on
the screen in parallel polarised light. The smaller one affords a screen
picture, with Nicols not quite crossed, such as is portrayed in Fig. 93,
Plate XX. We observe that the area of the hexagon is roughly divisible
into six 60°-sectors, and that alternate ones are uniformly coloured,
indicating that they belong to wholly right-handed or left-handed
quartz; whereas the other alternate sectors are most beautifully marked,
as if by line shading parallel or inclined at 30° to the edges of the
hexagon, by a considerable number of equally spaced dark or slate
coloured bands, close together but separated by white bands, with a
trace of spectrum colours along the middle of the latter. If we rotate
the analysing Nicol somewhat we can readily find a position, which is
not always that of crossed Nicols, for which these parallel bands of
laminar twinning are most clearly defined, as shown in the illustration,
the colours of the other sectors ever changing during the rotation.
[Illustration:
_PLATE XX._
FIG. 93.—Section-plate of Amethyst Quartz, showing Sectorial Repeated
Twinning of the Right and Left Varieties.
]
[Illustration:
FIG. 95.—Section-plate of large Amethyst Quartz Crystal, showing
relatively large Area of Sectorial Repeated Twinning of Right and
Left-handed Quartz (see p. 225).
DIRECT PHOTOGRAPHS OF SCREEN PICTURES OF AMETHYST PROJECTED BY THE
LANTERN POLARISCOPE IN PARALLEL LIGHT.
]
It is obvious that we have here to do with the same phenomenon as was
illustrated by the parallel bands shown on the large scale by the
section illustrated in Fig. 90 of the coloured frontispiece, the black,
white, and spectrum-coloured bands being simply repeated very many more
times in the same space, and in alternate sectors of the crystal.
The twinning of amethyst in 60°-sectors is very characteristic of this
variety of quartz, and it is an interesting fact that the sectors which
show the laminar bands in polarised light often appear purple coloured
in ordinary light, the tint from which amethyst derives its name. This
is not necessarily or always so however, and the section just described
and illustrated in Fig. 93 appears quite colourless throughout on casual
inspection in ordinary light, in fact as a clear colourless hexagonal
section of ordinary simple quartz; a trace of the amethyst colour
becomes, however, apparent on closer examination when held obliquely, in
the sectors where the bands become visible in polarised light.
The second plate of amethyst is a magnificent section 9 millimetres
thick and 2½ inches in diameter, of which alternate 60°-sectors are
deeply amethyst coloured, the tint being a pure violet of about the
wave-length of the hydrogen line near G of the spectrum. Moreover, even
to the naked eye when the specimen is held in the hand up to the light,
in certain positions the laminæ become visible as more deeply shaded
violet line markings. On placing it on the stage of the polariscope but
with the analysing Nicol removed, so as to observe the natural
appearance of the section in white light (for, although polarised by the
polarising Nicol, being unanalysed the section exhibits no polarisation
effects), these facts become clear to everyone in the room. The violet
staining of alternate sectors appears very deep, and traces of
lamination in the violet parts are just apparent on close scrutiny, the
other alternate sectors appearing colourless and unmarked except by a
few flaws almost always present in so large a section-plate of amethyst.
The natural appearance of this plate is shown in Fig. 94, Plate XVIII.
(facing page 218), as far as is possible photographically, the violet
sectors being clearly demarcated.
On replacing the analysing Nicol the colourless sectors are seen to
polarise uniformly in brilliant colours, indicating a homogeneous
variety of quartz in each, either right or left-handed. Moreover,
whenever two of these naturally colourless parts touch each other, which
they do as the margin of the plate is approached, an irregular ribbon is
produced, composed of the black band in the centre, with first white and
then spectrum-coloured flanking strips on each side, the spectra forming
the edges of the ribbon. The violet sectors show the laminated twinning,
but, owing to the great thickness of this plate, in too complicated
(overlapping) a manner to be easily followed, a thinner plate being
required to show such fine laminations clearly.
Finally, the third section is such a thinner plate, about 3.5 mm. thick
and nearly 1½ inches in diameter. This section of amethyst is probably
the most beautiful of all, for it not only shows the laminated twinning
to perfection, in three alternate 60°-sectors and in all six in the
middle part of the plate, but also these alternate sectors are
distinctly violet even to the eye when the specimen is held in the hand
against a white background; and the laminations are likewise also
clearly visible on holding the section obliquely up to the light. In
polarised light, either with crossed or parallel or anyway arranged
Nicols, the phenomena on the screen are of the most superb character.
The whole of the middle part of the plate appears made up of six
sectors, _all_ showing the fine laminar bands parallel to the edges of
the second order hexagonal prism {11̄20}, that is, at 30° to the edges
of the section, the crystal being a first order hexagonal prism {10̄10}.
Some idea of the arrangement will be afforded by Fig. 95, Plate XX. The
marginal parts develop into alternately right and left-handed sectors or
half-sectors, polarising in different and very brilliant colours, and
showing the ribbon bands at every junction. On rotating the analysing
Nicol the changes are remarkably beautiful, particularly for the
positions of the analyser when the laminar bands take on their deep
slate colour, with white and marginally spectral interstrips. The whole
phenomena, indeed, afforded by this plate of amethystine quartz, are the
most magnificent which the author has ever seen on the screen, in the
whole of his crystallographic experiences.
The Brazilian twinning law of quartz, according to which the plane of
twinning is parallel to a pair of faces of the second order hexagonal
prism {11̄20}, appears capable of explaining all these varieties of
right and left-handed twins, the interpenetration of the intimate kind
shown in Fig. 85 (page 215) usually resulting in sectorial portions of
space being occupied by each kind, the surfaces of junction of
oppositely optically active parts being, however, very varied in their
distribution and character. Where they happen to be more or less
horizontal, a plate cut perpendicularly to the axis to include both
kinds would show Airy’s spirals in convergent polarised light, as may
readily be demonstrated by such a plate, one of several, in the author’s
collection. Where they are oblique, a plate cut at right angles to the
axis would, as we have seen experimentally, afford the black, white and
spectral ribbon bands in parallel polarised light. Where, however, the
mode of interpenetration is still more intimate, we have the rapidly
alternating laminæ of the two varieties, right and left-handed, building
up the beautiful structure of amethyst in thin layers. A section-plate
of such an intimate blending of the two varieties, cut as usual
perpendicular to the axis in order that any phenomena of optical
activity shall be exhibited at the maximum, affords no indication
whatever of optical rotation, the two varieties simply neutralising each
other’s effects, and the plate behaves as an ordinary uniaxial crystal,
affording in convergent polarised light a black cross like calcite,
complete to the centre. In parallel polarised light it shows of course
the laminated structure, but the tendency to remain dark under crossed
Nicols is shown by the fact that the tints exhibited by the laminations
are slates, greys, and even black, when the Nicols are crossed, the
delightful other colours only making their appearance when the analysing
Nicol is rotated. Thus the simple law of Brazilian twinning is quite
capable of explaining the whole of the phenomena exhibited by composite
crystals of the two varieties of quartz, and such an explanation is the
one accepted by von Groth, in the excellent description of quartz in the
last edition of his _Physikalische Krystallographie_.
[Illustration:
FIG. 96.—Plan of Amethyst Crystal.
]
An interesting crystal of amethyst very similar to the third of those
just described, the one illustrated in Fig. 95, was described by Prof.
Judd in the year 1892 to the Mineralogical Society.[18] The plan of the
crystal is given in Fig. 96. The wedges marked _x_, _y_, _z_, are of a
pale yellow colour, as are also the three strips, sections of plates,
proceeding from the wedges and meeting at the centre _o_. The wedge _y_
exhibits left-handed polarisation, and the wedge _z_ right-handed. The
large wedge _x_ is composite, the part marked _x__{r} being right-handed
and that marked _x__{l} left-handed. The surface of junction of the two
parts is not perpendicular to the plate, so where the two varieties
overlap, the part marked _x__{rl}, a ribbon band is shown in parallel
light and Airy’s spirals in convergent polarised light. The yellow parts
of the crystal exhibit ordinary rotatory polarisation colours, even
tints; but in the remaining sectors of the crystal, the lines of
division of which are indicated by the radial lines A, B, C, no trace of
circular polarisation is displayed, and the central part, where the
lamellæ are very well developed, gives the ordinary calcite-like
uniaxial interference figure. The more marginal portions, however, show
complicated interference figures, somewhat resembling those of biaxial
crystals, owing to irregular distribution of the two varieties of
quartz, and probable displacement of the optic axis by distortion.
An ingenious theory of the formation of the lamellæ is put forward by
Prof. Judd in the same memoir. He had already shown that quartz is
endowed with planes of gliding, parallel to the rhombohedral faces, and
suggests that the lamellation is the result of the effect of high
pressure and possibly high temperature on the quartz crystal after its
formation. The lamellæ appear to be frequently parallel to the
rhombohedral terminal faces of the crystal, as if they were indeed glide
plane effects. It is quite conceivable that the gliding of layers of
molecules, which when permanent usually involves rotation and inversion
of the molecules, might result in alternately right and left structural
arrangements, and there is considerable evidence that the development of
the purple tint occurred subsequently to the growth of the crystal. It
is probably due to change in the state of oxidation of the trace of
manganese present as a minute impurity in the quartz crystal, and which
is concentrated between the lamellæ, just as the yellow tint is due to a
slight trace of iron (ferric) oxide. The theory is an interesting one,
and throws considerable light on the possible nature of intimate
lamellar twinning.
One last experiment may now be referred to, the concluding experiment of
the Winnipeg lecture, and which is very reminiscent of the beautiful
slate colour of the lamellæ of amethyst. It is the actual
crystallisation, projected on the screen, of a thin film of melted
benzoic acid, which affords radiating closely packed long and narrow
crystals, shooting out on the screen from centres near the margin of the
field, very much like the individual crystals of repeatedly twinned
quartz in the beautiful amethyst crystal illustrated in Fig. 95.
Provided the film of melted benzoic acid be thin enough, the crystals
appear on the screen in parallel polarised light, under crossed Nicols,
tinted with the same beautiful shades of slate colour as amethyst, the
intermediate low-order tint between the black and the grey of Newton’s
first order spectrum. Some idea of the appearance on the screen is
afforded by Fig. 97, the lower of the two coloured figures in the
frontispiece. As in the case of Fig. 90, the screen picture was
photographed directly on a Lumière autochrome plate, and the
transparency in the actual colours thus obtained was employed as an
original wherewith to reproduce the picture on paper by the latest
three-colour photographic process.
In carrying out the experiment a few of the flaky crystals of benzoic
acid are placed on one of the circular glass object plates of the
standard 1⅞-inch size for the projection polariscope; they are covered
by a second similar one, and the two plates are then held in a pair of
tongs and gently warmed over a small spirit lamp, or miniature Bunsen
lamp. As soon as the crystals have fused, and the melted substance is
evenly spread as a thin film between the two glass plates, the latter
are rapidly transferred to a special mahogany object frame, fitted with
a side slide to press the double-plate edge just sufficiently to hold it
in position in the frame, which is then at once placed on the rotating
stage of the polariscope. The screen appears quite dark at first, the
Nicols being crossed, but in a second or two as the slide cools the
benzoic acid begins to crystallise out at the sides, brilliant colours
and the deep greys being both developed, the former chiefly near the
edges of the crystals, rendering the crystallisation wonderfully
distinct and beautiful on the black background. Then long needle
crystals shoot out from various quarters one after another or
simultaneously, in lovely shades of slate or grey tinted with brilliant
colours at the margins and tips, the growing point cutting its way along
like a sharp brilliantly coloured arrowhead. Eventually an arch is
formed of such acicular crystals, radiating simultaneously from many
centres, gorgeously coloured in parts, but showing the yet more æsthetic
slates and greys in the main. Finally, the whole screen picture fills up
with a mass of interlacing yet ever distinct crystals, the last few to
crystallise in the centre usually doing so with a burst of especially
bright colour, as the thickness increases adequately for the double
refraction retardation to reach the more brilliant second order
spectrum, a concluding effect which evokes the emphatic delight of even
the most phlegmatic philosopher, inured to scenes of beauty in natural
phenomena.
The series of experiments with quartz described in this and the previous
chapter, culminating with those revealing the alternate repetition of
extremely fine layers of right and left-handed quartz in amethyst, will,
it is hoped, have illustrated and rendered intelligible the important
structural principle of enantiomorphism or mirror-image symmetry. We
have only to imagine the layers to become thinner and thinner until we
approach ultimately the neighbourhood of the minute dimensions of the
chemical molecule, without as yet penetrating within the range of the
molecular forces; the two such oppositely constructed and intimately
blended structures, built up by atoms arranged oppositely screw-wise,
clockwise and anti-clockwise, will now form an ultramicroscopic mixture
of the two varieties in equal quantities, that is, in equal molecular
proportions.
Such a structure will exhibit the symmetry of the system to which the
two individuals belong, but instead of only displaying that of the
enantiomorphous class of that system, possessing lower than the full
symmetry, as each variety does when crystallised alone, it will now
display the full holohedral symmetry of the system. That is, the
symmetry is enhanced by this intimate blending of the two complementary
enantiomorphous forms, the two together supplying all the possible
elements of symmetry of which the system is capable. Moreover, as we
have seen in the case of the lamellar portion of the amethyst crystals
represented in Figs. 95 and 96, there will now be no sign of optical
activity, for the two opposite rotations are equal and destroy each
other.
Hence, such a compound crystal shows the holohedral symmetry of the
system, and is optically inactive. In such cases we are, in fact,
confronted with the phenomenon of pseudo-racemism, as defined in Chapter
XI. For we know that the two varieties are still present intact,
polarised light revealing them in the case of their grosser development
such as is found in amethyst, and the system of symmetry being clearly
the same, the forms developed being merely the sum of those of the two
individual varieties.
Amethyst thus affords us a gross demonstration of the nature of
pseudo-racemism, and as such has proved an exceedingly illuminating
study.
We can carry the process further, however, in imagination, until the two
differently helical molecules are themselves juxtaposed face to face,
right molecule to left molecule. When, however, this occurs, we have
entered into that most fascinatingly interesting region, the range of
molecular forces, a mysterious sphere of activities of which we are only
just beginning to learn something. Within this region of larger activity
the two oppositely constructed molecules are often known to combine
chemically to produce a molecular compound, just as potassium sulphate
molecules, for instance, will combine with those of magnesium sulphate
to form the well-known double salt. The double molecule now furnishes
the representative point of the space-lattice, in other words, a new
space-lattice is now erected, the units of which may be taken to be the
representative points of the double molecules. Such a space-lattice will
of necessity be of a totally different character to the old one
corresponding to the single molecule of either variety (for each variety
has the same space-lattice, the points, however, representing
differently, enantiomorphously, orientated atomic details). That is to
say, we shall have an entirely new kind of crystal produced, in all
probability belonging to a different crystal system. It is known as a
racemic compound, as described in Chapter XI.
This is exactly what happens in the case of tartaric acid, the two
varieties, dextro or right-handed tartaric acid and lævo or left-handed
tartaric acid, not forming pseudo-racemic crystals of like but enhanced
(holohedral) symmetry, but a truly molecular compound, the well-known
inactive racemic acid, in which the phenomenon of “racemism” was first
discovered and from which it took its name.
Now a molecular compound is notoriously regarded by chemists as a type
of chemical compound of low stability, molecular attraction or affinity
not being nearly so powerful as atomic affinity. Hence, under suitable
conditions it may be possible to induce the two component varieties to
crystallise out separately from the solution of the racemic compound. In
the case of racemic acid itself this does not readily happen, but in the
cases of certain of its metallic salts, sodium ammonium racemate, for
instance, specific conditions are known under which the two varieties of
crystals, right and left-handed respectively, may be separately
crystallised out from the solution, some of which conditions were
referred to in Chapter XI. Racemic acid itself, however, crystallises
quite differently to the two tartaric acids, namely, in triclinic
prismatic crystals. These are, in fact, absolutely different from the
monoclinic crystals of the dextro and lævo varieties of ordinary
tartaric acid, for racemic acid takes up also a molecule of water of
crystallisation on separating from its aqueous solution. There are
certain chemical differences also, due to the chemical union of the two
enantiomorphous molecules into a single double molecule, such, for
instance, as greater facility of reduction by hydriodic acid to succinic
acid.
Thus our experiments with quartz have afforded us the means of acquiring
a clear idea of the nature of this most interesting type of crystal
structure which involves the principle of mirror-image symmetry. Racemic
acid and its similar structures, racemic compounds in general, are known
as “externally compensated” structures, the reflective principle here
acting externally to the single enantiomorphous molecule. It is but
another step, however, to imagine internal compensation of
enantiomorphous parts of a molecule, by mirror-image combination of such
parts, such as in all probability occurs in the case of the truly
inactive fourth variety of tartaric acid, in order to comprehend how the
principle enabled the 165 types of homogeneous structure involving this
kind of repetition to be arrived at, and thus, together with the 65
regular point-systems already known, to afford us the complete set of
230 types of homogeneous structures possible to crystals.
CHAPTER XV
HOW A CRYSTAL GROWS FROM A SOLUTION.
One of the most deeply interesting aspects of a crystal, especially from
the point of view of the history of crystallographic investigation,
concerns the mysterious process of its growth from a solution (in a
solvent) of the substance composing it. The story of the elucidation, as
far as it has yet been accomplished, of the nature of crystallisation
from solution in water is one of the most romantic which the whole of
scientific progress can furnish. Again we are struck with the
parallelism between crystals and living objects. For just as the
discovery of bacteria, the infinitesimal germs of life, has given an
immense impetus to our knowledge of disease and been blessed with most
beneficent effects in combatting the ravages of the latter, so the
discovery that crystal-germs of most common crystallised substances, of
no larger size than bacteria, are floating about in our atmosphere, and
ready at any time to drop into our solutions and, if the latter are in
the proper receptive condition, to set them crystallising, is little
less marvellous, and has had as profound an effect on our knowledge of
the process of crystallisation. A true story, told to the Royal Society
the other day, may serve to illustrate the point. A new chemical
compound had been discovered, and at the time there could obviously be
no crystal-germs, minute crystallites of the dimensions of possibly only
a comparatively few chemical molecules, of this hitherto unknown
substance floating about in the air. It was found impossible to obtain
the deposition of crystals in the ordinary way, from solutions of the
substance in its ordinary solvent, although they were in the condition
of proper receptivity above referred to, on account of the absence of
such germs in the air. But later on, when the air of the laboratory had
become impregnated with such germs, on account of the daily handling of
the substance in the laboratory, no difficulty was any longer found in
obtaining good crystals quite readily from these solutions.
We are at first inclined to wonder whether such extraordinary statements
can possibly be sober facts. Yet such is, indeed, the case, and it will
be very well worth devoting a chapter to the story of how we have at
length arrived at definite knowledge concerning the process of
crystallisation from the state of solution in water. For water is the
ordinary solvent from which we obtain our crystals, that is, such as are
prepared artificially in the laboratory. The laws which have been
discovered to hold for aqueous solutions are, however, equally
applicable to the cases where other solvents are used, such for instance
as the usual organic solvents like alcohol, ether, chloroform, and
benzene.
The conditions under which crystallisation occurs from the liquid state,
or from solution of the substance in a solvent, have been accurately
determined experimentally by H. A. Miers,[19] and they bear out in the
main the predictions from theoretical considerations which were made by
Ostwald.[20] Taking first the case of crystallisation from solution,
there are two distinct curves representing the degree of solubility of
the solid substance and of supersolubility. The well-known ordinary
solubility curve is obtained by taking the temperature for abscissæ and
concentration for ordinates, so that any point on the curve indicates
the amount of the solid substance which the solvent can hold in solution
at that particular temperature. Now the fact that supersaturation may
occur has long been established, the phenomenon being of frequent
occurrence; and it is common knowledge that a supersaturated solution
may be preserved for a long time without crystals being deposited from
it, provided the liquid be maintained quietly at rest. Obviously,
therefore, this condition of supersaturation ought to be represented by
a second curve a few degrees lower as regards temperature than the
solubility curve, and its conditions were fairly fully predicted by
Ostwald, after collecting together and analysing the results of the
experiments of Gernez, Lecoq de Boisbaudran, J. M. Thomson, de Coppet,
Lefebvre, and Roozeboom. It was reserved for Miers, however, to discover
a means of experimentally tracing this curve, by observations of the
refractive index of the solution. The point at which the deposition of
crystals from the supersaturated solution occurs is immediately
indicated by a sudden change in the refraction of the liquid, the
refractive index attaining its maximum value at the temperature of
spontaneous crystallisation, and then dropping suddenly the moment the
crystals begin to fall. Moreover, the solution at the same time records
its own strength, for the refractive index varies directly as the amount
of salt dissolved. The determination of the strength of the solution at
the critical moment itself had previously proved an impossibility by
ordinary methods.
Fig. 98 gives a general diagrammatic representation of Miers’ results
for a typical crystalline substance soluble in water. S is the ordinary
solubility curve, which may also be termed the “curve of crystallisation
by inoculation.” For as soon as the solution reaches this condition of
normal saturation it is liable to be caused to commence crystallising if
a germ crystal, that is, a miniature crystallite floating in the air as
dust, of the substance itself or of one isomorphous with it or capable
of forming parallel growths with it, fall into the solution from the
air. It has been a revelation to us that such minute crystallites of all
common substances are scattered broadcast in our atmosphere, and that
sooner or later one will introduce itself into any solution set to
crystallise which is not sealed up or placed in a vessel with a
filtering plug of cotton-wool in its neck or other aperture.
[Illustration:
FIG. 98.—Diagram illustrating the Conditions for Crystallisation from
Solution or the Liquid State.
]
SS is the supersolubility curve, situated approximately 10° to the left
of the solubility curve as regards temperature, but about as much above
as regards concentration, so that the two curves usually run diagonally
and more or less parallel to each other across the diagram. This
supersolubility curve may be also called the “curve of spontaneous
crystallisation,” for it represents the conditions under which alone
crystals may begin to form without the initiating impulse of inoculation
by a germ-crystallite. On the suggestion of Ostwald it is also termed
the “metastable limit,” and the whole area between the solubility and
supersolubility curves is named the area of metastability, that which
represents the “metastable” condition of the solution. Within this area
the conditions are those for the start of crystallisation by
inoculation. The area beyond the supersolubility curve represents the
“labile” state, in which the conditions are those for spontaneous
crystallisation, inoculation being no longer necessary. These precise
results will, it is hoped, be quite clear with the aid of Fig. 98.
Hence, when a cooling solution not quite saturated at the higher
starting temperature is stirred in an open vessel a slight shower of
crystals, started by inoculation, appears when the saturation point is
reached, which Miers calls a “metastable shower,” corresponding to the
ordinary solubility curve; the liquid then goes on cooling without
depositing the main bulk of the excess which that curve indicates ought
to be deposited, if it represent the whole truth. But when the
temperature of the supersolubility curve about 10° lower is reached, a
much more copious shower falls by spontaneous crystallisation, the
“labile shower.”
In a closed vessel, such for instance as a glass tube sealed with the
aid of the blowpipe after the introduction of the solution, on cooling
after heating to a temperature superior to that of saturation, the first
shower never falls at all, no amount of shaking inducing the deposition
of crystals at the ordinary saturation point, proving that the slight
shower of the experiment in the open vessel is due to crystal-germs
introduced from the atmosphere. The second shower of crystals falls at
the lower temperature just as before, however, at the temperature of the
supersolubility curve, indicating that this shower is due in both cases
to spontaneous crystallisation. Solutions thus enclosed in sealed tubes,
to which inoculating dust crystals cannot have access, can never be made
to crystallise at any temperature higher than that given by the
supersolubility curve, however agitated, although they immediately do
crystallise, if shaken, as soon as that temperature is reached during
the cooling. If allowed to remain absolutely quiet, however, the
temperature may fall considerably lower before any crystallisation
occurs, the labile region being frequently well penetrated before this
happens. When crystallisation does supervene, the temperature usually
rises somewhat. After the labile shower has been deposited, the crystals
continue to grow steadily further, until the metastable region has been
traversed, and the saturation state is eventually reached, when final
equilibrium is produced.
The proof that the crystals deposited in the metastable condition were
started by the advent of atmospheric germ crystals—that is, by
infinitesimal but perfectly structurally developed crystals, carried by
their very lightness like the particles of dust which are only revealed
in the path of a sunbeam as seen against a dark background—was afforded
by a series of experiments with a mixture of two rare organic chemical
preparations, salol (phenyl salicylate) a substance melting at 42.5°,
and betol (β-naphthol salicylate) another melting at 92°, which Miers
assumed were not likely to be present in ordinary air. The assumption
proved well grounded, and the first shower never fell at all in the
earlier experiments in which mixtures of these two substances were
allowed to cool in open vessels, from the state of fusion. But very soon
the air of the laboratory became impregnated with crystallites of both
substances, due to the very operations themselves being carried on in
contact with the air, and in the later experiments the first shower of
crystals did fall. The experiments were really designed to effect the
determination of the solubility curve for salol and betol in each other,
that is, the freezing-point curve of their mixtures, and the discovery
of the so-called “eutectic” point at which a mixture of constant
composition solidifies at a definite temperature. But incidentally the
experiments also served to establish similar laws for the production of
crystals from the liquefied state, by cooling below the melting point,
to those applying to crystallisation from solution. In the case of the
mixtures of the substances the one of lower melting point acted as a
solvent for the one of higher melting point, just as water does for
salt. Two curves corresponding to the ordinary freezing point and to the
limit of superfusion were established, analogous to the solubility and
supersolubility curves. Pure salol alone proved to crystallise
spontaneously at 33°, 9½° below its melting point, and the refractive
index attained a maximum for this temperature. Betol spontaneously
crystallised at 79°, 13° below its melting point.
Two general cases of crystallisation are shown by the dotted curves ABCD
and ABE in Fig. 98. The first, represented by ABCD, is the case of a
supersaturated solution, made by adding the salt to hot water, being
allowed to cool slowly while stirred. The solution cools from A to B
without anything visibly happening, no crystal-germ falling into the
solution until B is reached, somewhere well within the metastable
region. When the germ has fallen in, however, crystals begin to appear
as a slight shower at B, and from B to C they continue to grow slowly.
On reaching the labile condition at C a cloud of crystals, the heavy
shower, is deposited, and the concentration falls rapidly to D on the
solubility curve, generally with slight rise of temperature.
The second case is the important one employed by the author in the
investigations which will be found described in his “Crystalline
Structure and Chemical Constitution” (Macmillan & Co., 1910), for the
purpose of producing crystals of high perfection for goniometrical
investigation. The method can be confidently recommended as the one best
adapted to afford good measurable crystals, and is of quite general
application. The solution is made up so as to be in the metastable
condition, that is, only slightly supersaturated for the ordinary
temperatures. Eventually, while the solution is at rest in a protected
place, free from draughts or vibration, and after it has cooled to the
temperature of the air, a crystal-germ enters, followed probably by
others; each forms a centre of crystal growth, which proceeds very
slowly and deliberately, keeping pace with the evaporation in such a
manner that the labile condition is never reached. The natural result is
the production of very well-formed crystals bounded by excellent faces,
truly plane and free from striation or distortion.