_The Nature of Crystals: Ice and Snow_
WHEN we look round to see what crystals we shall examine by our new
X-ray analysis, the crystals of ice and snow at once strike our
imagination. Water is one of the most obvious substances in the world:
it affects our lives in numberless ways and we are interested in all
the forms which it can assume. And again, from a scientific point of
view we should like to discover the structure built with so simple a
molecule, one oxygen and two hydrogens, and we might find that it was
within our power to do so. But there is one very compelling reason
in the beauty of the snow crystal, with its tracery so delicate and
finished, and of the frost crystals on the windowpane, so quaint and
charming in their outline. It is true that the blocks of ice that come
from the freezing works are not remarkable for grace of outline, though
there is a fascination in watching them slither across the pavement at
the end of the ice-man’s pincers.
[Illustration: PLATE XVII.
(By courtesy of the Chief of the U.S.A. Weather Bureau.)
Snow crystals of various forms.
(From Monthly Weather Review, U.S.A.)]
The manufacture of commercial ice is too rapid to bring out the ice
design: the crystalline structure is there, but the mass contains a
multitude of tiny invisible crystals oriented in all directions, and is
full of bubbles and sheets of air.
If we are to see what Nature will do if left to work out her design
in peace, we must examine the snowflakes that fall in a hard northern
winter. In England, we do not see the best crystals: it is not cold
enough. Observers in other countries such as Sweden and America have
many exquisite drawings, which are to be found scattered through
physical and meteorological publications. Some of them are reproduced
in Plates XVII and XVIII.
We can imagine the way in which the snowflakes grow. One or two
molecules of water become associated in the upper air; molecule after
molecule adds itself to the growing, falling crystal, filling out the
details of the pattern until at last the six-pointed snowflake rests
gently on the ground. If the weather is cold the flake may continue to
grow in the same way, and the crystals develop perfect little facets,
which glitter like diamonds in the sunshine. When the snow crystal
first forms, it is very often feathery; the six arms grow outward
and other little arms grow out from each of them to right and left,
and from these yet smaller arms, and so on, all the arms joining one
another at the angle of 60°, so that the whole is like a six-pointed
star of fine lace. These feathery forms are peculiar to the early stage
of crystallization, and seem to be the consequence of sudden and rapid
freezing. The arms stretch out from the center because they have used
up the nearer molecules that are ready to join up into the structure,
and they must stretch out into new fields. This effect is often found
in other cases of rapid crystallization; a notable example is the
formation of skeleton crystals of iron in the crucible of molten and
cooling metal. If they are to be preserved, the rest of the liquid must
be poured off before the crystal has had time to fill up vacant spaces.
They are called “dendrites,” because they look something like trees,
with trunks, big branches, small branches, and so on, but the angle at
which two branches of an iron crystal join together is a right angle,
not 60°, and the form is far from being as graceful as that of ice.
[Illustration: PLATE XVIII.
(By courtesy of the Dept. of Scientific Research of the Admiralty.)
A. Snow crystals. (From the Monthly Weather Bureau. U.S.A.)
B. Ice flowers growing on the ice floes. C. Bundle of irregular prisms.
(From “The British Antarctic Expedition, 1910-1913.”)]
When the snow crystal has had time to grow, and there is an available
supply of molecules, the gaps fill up, and the crystal becomes a
hexagonal plate (Plate XVII b).
[Illustration: Fig. 41.
The hexagon represents a magnified section of an ice prism. _ABCD_
is a ray passing through it.]
Sometimes, it is supposed, the plates grow in that form from the
beginning. Strange to say, these plates are often connected in pairs
by a hexagonal prism; one plate is generally larger than the other,
and the whole is like a fairy tea-table (Plate XVIII a). The
prism appears also in the curious formations of Plate XVIII c,
which is taken from Wright and Priestley’s _Glaciology_, British
Antarctic Expedition, 1910-1913.
The prisms and plates and “tea-tables” are believed to be the cause of
the mock suns and halos that are observed in high latitudes (Plate XIX).
Suppose that the hexagon in Fig. 41 represents a section of one of
these prisms or plates, and let _ABCD_ be the path of a ray of
light going through it. It is refracted at the points _B_ and
_C_; the ray is on the whole bent through an angle of at least
21° 50', which is, in the language of physics, the angle of minimum
deviation.
[Illustration: Fig. 42.--Shows how the ice halo is formed. For a
description see the text.]
If in Fig. 42 _S_ be a source of light and _E_ the eye, a ray from _S_
is bent in going through _P_, and will enter the eye if _F_ is properly
placed. In the figure the prism is placed symmetrically, in which case
it is known that the deviation _SPE_ has its minimum value. Any prism
lying between _SPE_ and _SP'E_, such as _P{0}_, will bend the ray from
_S_ in such a direction that it cannot possibly get to the eye, no
matter how the prism is placed. The eye cannot receive a refracted ray
from any such prism.
[Illustration: PLATE XIX.
The first picture is due to Mr. G. A. Clarke, and is taken from Mr. F.
J. Whipple’s article on Meteorological Optics in the “Dictionary of
Applied Physics,” Vol. III., p. 529 (by courtesy of Messrs. Macmillan
& Co.). It shows a halo and mock suns. The second picture is from an
interesting original sketch in the possession of the Royal Institution:
it shows the halo and the “sun-pillar.”]
A prism _P{1}_ may send light to the eye, if it has an
unsymmetrical position, as the figure shows; the angle of deviation
has to be more than the minimum, and that is why the prism must be
crookedly placed, as in the figure. If, therefore, an observer at
_E_ stands facing the sun at _S_, light will be seen to come
from the directions _PE_ and _P'E_, and also other directions
outside; but the latter will be relatively feeble, because most of
the deviations are not far from the minimum value--the farther they
are from it, the fewer they are, in accordance with a known law of
maximum or minimum values. Also there is no light at all from within
_PEP'_, and the consequence is that the strong light of the
minimum deviations is the more sharply defined.
This applies to rays coming from all directions round the sun; and so,
on the whole, the observer must see a ring round the sun, sharp on
the inside, rather more diffuse on the outer. For red light the angle
_PEP'_ is rather smaller than for blue, so that the halo is not
quite white, but is colored, red on the inside, blue on the outside.
The halo is observed if there are enough ice prisms in the air, just
as a rainbow is seen if there is a sufficiently large number of drops
of rain. When a ray of light goes into a raindrop and out again it is
bent through an angle of more than two right angles, so that to see a
rainbow one must have the sun at one’s back.
A little model may help to make this explanation clearer. The arc-lamp
at _S_ in the figure is the source, the eye is at _E_. Between _S_ and
_E_ is a stand on which an arm is mounted; the latter carries a glass
prism. The dimensions of the model are so adjusted that a ray of light
refracted by the prism falls on _E_. If the arm swings round _J_, the
eye continues to be illuminated. If there were prisms all around the
circle, the eye would see a circle of light round the central spot.
If for any reason the prisms tended to set themselves in certain
positions only, the halo would be incomplete. Something of this kind
actually happens. When a long prism falls through the air, the axis
tends to set itself horizontally. If, however, it has the tables at
the ends, as shown in Plate XVIII a, or if it is simply a
hexagonal table which may be considered as a very short prism, its
axis tends to become vertical, or, in other words, the table itself to
become horizontal.
[Illustration: Fig. 43.--Model showing the formation of the ice halo.
_S_, _J_, _E_ should be in the same straight line.]
This rather strange effect is in accordance with a well-known rule
concerning the movement of bodies through gases or liquids. They tend
to set themselves so as to offer as much opposition to the motion as
possible. If we make a packet of two or three letters or postcards, and
drop them from a height, holding them horizontally and taking the hand
quickly from underneath, they remain level throughout the fall. But if
we let them fall edge first, they subsequently turn over and over. When
we drop a white plate into the water, we see it swaying from side to
side, but always tending to the horizontal position. The consequence is
that the falling shower of ice crystals contains an undue proportion
of vertical and horizontal crystals. Those parts of the halo which lie
at the ends of the horizontal and vertical diameters are emphasized,
and are like bright spots on the ring; they are often spoken of as mock
suns.
It is easy to show the tendency of the “tea-table” forms to become
vertical as they fall. We make a number of models of ebonite and allow
them to fall in a tall jar full of water. A very tall jar is the
best, but even if the depth is not more than eighteen inches or so the
tendency is quite obvious.
[Illustration: Fig. 44.--Flat disks, and prisms some of which end in
disks falling through water in a tall jar.]
Curiously enough, some of the bodies tend to fall with the plate
leading the way, and some with the plate in the rear. The point was
examined mathematically by Besson, who showed that when the diameter
of the plate is small compared with the length of the prism, the plate
tends to go first, and vice versa. We can prove this by experiment; it
is best to hold the axis horizontally under the surface of the water
and then let go.
The whole of the vertical line through the center of the halo is often
illuminated also, but this is due to a different reason altogether; it
is caused by reflection at the flat surfaces of the snow crystals and
plates. Consequently the observer receives reflections of the sun from
snowflakes at all altitudes, but they must all lie in a vertical plane
through the sun. The bright vertical line is called a “sun-pillar.”
Ice when it forms quietly on a water surface exposed to the sky
crystallizes in a form analogous to that of the snow crystal, all the
six-sided figures being horizontal. That it does so is not generally
very obvious, though in books of Arctic exploration pictures are to be
found of table ice breaking up into six-sided vertical columns, like
the basalt columns of the Giant’s Causeway. It is also said that when
the ice on a lake breaks up, it first divides into vertical columns,
which for a time hold one another up; when, however, the ice begins to
move, the collapse is rapid and the lake clears quickly.
In the accounts given by Antarctic explorers, it is especially
mentioned that the ice on fresh-water lakes was found to be divided
into six-sided prisms, all standing upright on the surface. The planes
of separation were marked by lines of air bubbles. On the sea ice the
formation of the crystals led to an expulsion of the salt which was
deposited in the spaces between the crystals, and sometimes squeezed
out above the top surface. The prisms were nearly free from salt
inside, and fairly fresh water could be obtained if the outside layers
were first melted off. They were clear crystals, through which an
observer might look at the rocks underneath as through tubes.
There is a very beautiful way of observing the crystalline structure of
ice, which is described by Tyndall in his book on _Heat_.
[Illustration: Fig. 45.]
A slab of clear ice is placed in the rays from an arc-lamp and is
focused on the screen, as in Fig. 45. The heat of the lantern begins to
“undo” the crystals, which come to pieces in the order inverse to that
in which they were put together. Little six-rayed cavities appear and
grow, looking like flowers of six petals, and other cavities having a
fern-like form in which the fronds are inclined to the stem at an angle
of 60°. Soon the whole screen is covered with these “flowers of ice,”
as they are called; it looks like a beautiful carving in low relief.
[Illustration: Fig. 45 a.--This illustration of the “flowers
of ice” is taken from the original sketch in Tyndall’s _Heat_.
It represents a certain stage in the growth of the flowers; at a
later stage the whole screen is covered with interlacing figures.]
The ordinary commercial ice does not show the effect; there is a
specially prepared “plate ice” which is fairly satisfactory. But the
natural ice that is formed in the open at nighttime is far better than
anything frozen under the usual conditions of ice manufacture. Many
disappointing trials were made to prepare a satisfactory experiment.
After all, there was a kindly frost one night, and the next day a young
enthusiast rode out on his bicycle and collected from a pond a number
of pieces which showed the effect splendidly. It is clearly essential
that the ice should grow quietly; probably it is also a condition that
the water should lose heat quietly at one face, as the water of a pond
does on a still, frosty night.
A little black spot often appears in the center of the ice flower.
Tyndall was greatly interested in it, and explained its occurrence.
When the ice melts within the block and a cavity is formed, the water
due to the melting occupies less volume than the ice from which it
came. Perhaps it holds together at first in a highly strained condition
and fills as water the space it filled as ice. But if so the strain
must be very great; it breaks away from the ice and shrinks to its
natural volume. A vacuum is left, which acts as a tiny lens and
diffuses the light that crosses it. Hence the black spot, which implies
the absence of light going straight through the cavity.
The ice flowers can be seen in glacier ice, where they are produced
by the heat of the sun. When a glacier is formed by the contributions
of ice from tributary glaciers or from blocks that have fallen in on
the sides, the mass may consist of a pile of ice masses all frozen
together, each of them showing ice flowers. The orientation of the
flowers shows in each case the original lie of the block, for they
are always formed in planes which were once horizontal. In the figure
(Plate XX a), taken from an old volume by Agassiz, a section
of glacier ice shows well the various positions of the cavities--some
in full view, some on edge, and some in intermediate position.
Let us now turn to the analysis of the structure of the ice crystal
which X-rays have made possible. We must hope to find in it some
explanation for its form and other physical properties which we have
been considering. It turns out that the structure is something like
that of diamond: there is the same symmetrical arrangement of four
neighbors of like kind round every atom. In this case, it is the oxygen
atom that stands at the center of a tetrahedron, four other oxygen
atoms lying at the four corners. There are, however, certain minor
differences of structure. In the first place, in diamond the carbon
atoms join on to one another. In ice there are the hydrogens to be
placed. If we put one hydrogen between each pair of oxygens we shall
have a symmetrical arrangement in which the atoms are in the proper
numerical proportion. Every oxygen has four hydrogen neighbors, and
every hydrogen has two oxygen neighbors, which implies that there are
twice as many hydrogens as oxygens. A model showing the arrangement
under these conditions is illustrated in Plate XX b, c. The large balls
represent oxygen, the small represent hydrogen. It must be clearly
understood that the X-ray methods do not measure the size of the oxygen
atom, or of the hydrogen. All that they do is to find the distance
between the center of one oxygen and the center of an oxygen neighbor,
a distance which is the sum of the diameters of oxygen and hydrogen.
The oxygen atom may take ah the room, and the hydrogen none, because
the hydrogen atom is supposed to hand over its electrons to the oxygen
and be left a bare nucleus. No one can say how its size should then be
represented. In making a model we must adopt some sizes for the balls
which represent the atoms, and the model must be interpreted with the
corresponding reservation.
There is a second point of difference between diamond and ice which is
subtler and more difficult to realize; but it is worth while trying to
understand it. If the reader finds it too difficult to grasp, he may
leave it out without any fear of losing the thread of the story.
Suppose that we are looking down on the diamond model from above, and
we see a single puckered layer, as in Fig. 46, A. The carbon atoms are
marked as 1, if they lie directly on the base of the crystal, and as
1' if they are atoms which are somewhat raised above their neighbors
in the layer. Take another layer exactly like the first, and write 2
everywhere instead of 1, and place it on the first, so that each 2
comes over a 1'--that is to say, an atom in the lower level of the
second layer comes over an atom in the higher level of the first.
[Illustration: PLATE XX.
A. This is due to Agassiz. It shows that the mass of glacier ice is an
agglomeration of smaller blocks in which, when first laid down, the
ice flowers would be in a horizontal plane. The blocks have now been
heaved into various positions, and the flowers are seen some edgeways,
some in full face, and in various other positions. B. The model is made
of balls of two colours, the white representing oxygens and the black
hydrogens. C. A smaller section of the ice model, showing the grouping
of the oxygens and hydrogens.]
[Illustration: Fig. 46.--Arrangement of atoms in ice structure.]
This is what happens in diamond. The combination is shown in Fig. 46,
B, where 1'2 means that the atom 2 lies over the atom 1'. Now take a
third layer, which we may denote by using 3's, and lay this so that 3
comes over 2'. We then get the arrangement of Fig. 46, C, and when this
is repeated over and over again, in the same order 1 2 3 1 2 3, we get
the diamond structure.
If now we begin again with a layer of 1's, but take as the arrangement
of a layer of 2's that which is shown in Fig. 46, D--which, it must
be carefully observed, is not the same as before; the layer of 2's
has been turned round in its own plane through 180°--we then repeat
the first layer, and alternately have 1 and 2. This gives us the
arrangement of the oxygens in ice. The structure is complete when we
place a hydrogen between each pair of oxygens.
If we look at the picture of the ice model shown in Plate XX
b, we may be able to realize the arrangement. Why one crystal
should repeat continually a series of three layers, and the other of
only two, we cannot imagine.
If we now look at the model of the ice structure we can see in it
many interesting features which help to explain what we know of the
properties of ice. The hexagonal structure is there, of course, and
the emptiness of the model is surely connected with the lightness of
ice and the featheriness of snow. Ice floats on water; we can see that
the molecules of water when they join up in the crystal structure must
take up more room than before. We could obviously crush the model
together into a smaller space, and that is, no doubt, what happens
when ice melts under pressure. There is a well-known experiment which
illustrates the point. A block of ice is supported at its ends, and a
fine wire carrying heavy weights is slung over it, as shown in Fig. 47.
[Illustration: Fig. 47.--Wire cutting through ice (from Tyndall).]
The wire proceeds to sink slowly into the ice, but as it does so the
ice closes up behind it, and when, finally, the wire makes its way
right through the block and drops, with the weights, on the floor,
the block is still whole. It would seem that the pressure of the wire
on the block breaks down the structure of the ice, and some of the
molecules are set free. In other words, a certain quantity of ice is
melted under pressure and becomes water, which is squeezed out from
under the wire and slips round to the vacant space above it. There
it joins up again with the ice on either side. We can imagine the
molecules as settling into their places, because on either side there
is crystalline ice holding out hands to them.
[Illustration: Fig. 48.--Ice molds and the making of a cup (from
Tyndall).]
Crushed ice can be molded under great pressure into various shapes. We
may, for instance, make a crystal cup: we need two or three boxwood
molds of the proper shape. In one we can form the upper portion of the
cup, in another the stem, and in yet another the foot; then we join
them together into one piece by holding them into position for a few
moments. The molds we use in making the cup shown in Fig. 48 were once
used by Tyndall for the same purpose.
When Tyndall showed these experiments he was proposing a theory of
the movement of glaciers, and employed them as an illustration of
his arguments. Tyndall, we may remember, devoted a great deal of
time to the measurement of glacier movements: he was interested in
them both from the scientific point of view and from his devotion to
mountaineering.
Glaciers descend from the snow-covered mountains, glide along the
valleys, and pour out into the plains almost as if they were fluid:
a very viscous, treacly fluid, because the motion is so slow--a few
inches a day or even less in some cases, many feet a day in others.
That which has always excited wonder and interest is the stateliness
of the motion, and the strange way in which a substance so brittle
and crystalline can flow like a river, can move round the corners of
a valley, or fall over a cliff and yet remain whole. In Tyndall’s
time much consideration was given to a theory which supposed that the
glacier melted internally in places where the strain was great, and
that the water thus formed slipped away, relieving the pressure. It
would freeze again, it was said, if it made its way into empty cracks
or spaces where there was no longer the pressure required to keep it
molten. Thus the glacier would, in a way, contract where compressed and
expand elsewhere, and so accommodate itself to its bed. The explanation
seems to offer difficulties when we think of the glaciers in the Arctic
or Antarctic which also flow, though the temperature is so low that no
conceivable pressure would bring about any melting.
It is possible that when we look a little more closely into the
behavior of a crystalline structure we shall find another way of
conceiving how the motion takes place: not so very different in reality
from the view that Tyndall maintained, but not so open to criticism.
There are many substances that can be made to flow like a glacier:
metals can be squirted through holes; wires can be drawn; plates can
be rolled. Even the surface of glass, or of a perfect crystal such as
Iceland spar, can be made to “flow,” as Sir George Beilby has shown.
Now all these things are crystalline; if we did not know it before,
the X-rays have emphasized the fact for us. And they are just as
crystalline after the flow as before. We shall see some examples when
we come to speak of the metals. The substance accommodates itself
to pressure, changing its shape as it does so. Whole layers of atoms
or molecules are momentarily uprooted from their places, ride over
the tops--so to speak--of the atoms on which they lie, and settle
down into a new position, or perhaps are kept on the move for some
time. When they settle down again for a moment the crystal is perfect
once more, and when they are uprooted, the bonds are broken as if
the substance was going to melt. This must be especially the case
when, as in ice, the substance contracts on melting, when the bonds,
breaking under pressure, let the atoms and molecules take up positions
in which less space is occupied than before. When a piece of metal is
bent or squeezed into a new form, the crystals of which it is made,
whether few or many, are “sheared”--that is to say, one part slides
on another part; and we can understand how many successive “shears”
can bring about any change of shape. So it may be in the case of ice:
both shearing and melting may be called into play during the change of
shape. The “shearing” of ice has often been observed. A block of ice
is cut from the ice that has formed naturally on the surface of the
water. If such a block is supported at its ends, and lies in the same
position which it had when it grew, it bends under a weight, just as a
beam would (Fig. 49, A).
[Illustration: Fig. 49.--A set of planks arranged as in A would bend
under a weight. Set up on edge as in B, they would bend far less. If
arranged as in C, stuck together by some very viscous substance, they
would yield gradually and continuously.]
If it is turned on its edge and placed so that the layers which were
horizontal are now vertical, and their plane is parallel to the line
joining the supports (Fig. 49, B), then the block yields very little
indeed. If the planes that were horizontal are perpendicular to the
line joining the support, they slide one on another, and the ice block
is altered in shape (Fig. 49, C). If under pressure and local melting a
few molecules are set sufficiently free to move as a liquid into a new
place, they will, as in the case of the wire, readily join on to the
ice structure on either side, simply because a place is always waiting
for them. But we can look on the effect in the general sense as due to
the movement of the planes over one another.
It is curious to see with what readiness pieces of ice join together.
If we rest one fairly flat piece on another for a few moments, we can,
keeping hold of the latter piece, turn the pair upside down, and the
added piece does not fall. When two pieces of ice are held together
under water, even warm water, they join together.
We may now go back to the consideration of the peculiar chain molecules
of carbon atoms which we referred to in the previous chapter. When
we considered the structure of the diamond, we saw that there was a
certain arrangement of the carbon atoms which was found everywhere
within it. It was an arrangement of six atoms in the form of a ring.
We saw that a similar arrangement formed the basis of the so-called
benzene ring, which is a molecule formed by fringing the six-sided
carbon ring with six hydrogen atoms; and that a very large number
of other important molecules were founded on the same arrangement,
the hydrogen atoms being replaced by various other atoms or groups of
atoms. The study of these molecules is the purpose of one of the great
branches of organic chemistry. The molecules form substances which are
called “aromatic,” because many of them have a fragrant smell.
There is a second great branch of organic chemistry, which deals with
substances of a different kind. They are called “aliphatic,” the word
implying that they are well represented by oils and fats. The chemist
has been able to prove that in this case the molecule is formed of a
chain of carbon atoms, to which various atoms, particularly hydrogens,
may be attached along its length and its end. The ring was obvious in
the diamond structure. It seems, from recent experiments, that we may
find the chain also in the diamond; so that the diamond contains the
essentials of both the great branches.
We considered a few examples of the ring in the last chapter, but left
the chain until now. The chain is formed of any number of links,
each of which, in general, is made out of one atom of carbon and
two atoms of hydrogen; and the ends are formed of various groups of
atoms, of which some are very common and give to the chain well-known
characteristics. In the simplest case the ends are formed of hydrogen
atoms, and we have then the hydrocarbon or paraffin molecule. The
symbol of pentane, for example, is written by the chemist as follows:
[Illustration]
Pentane is an inflammable liquid used in standard lamps--that is to
say, lamps which serve as a standard of comparison for other lamps,
because they burn with a steady and constant flame. The diagram is
intended to represent the way in which the various atoms are attached
to one another. Each carbon is joined to four other atoms. The carbon
atom cannot link up closely to more than four, so that the molecule
cannot be added to without first breaking it somewhere. It is said to
be saturated. In the diagram it is represented as lying altogether in
one plane, partly because of convenience of drawing, partly because
so little is known of its actual arrangement. One of the objects of
the X-ray analysis is to determine the relative positions of the atoms
in a molecule more accurately than has been possible hitherto, and
to measure the linear dimensions. In the case of these long-chain
molecules, the X-rays have recently had an unexpected success. In
order to express this additional knowledge, we really need a model or
a sketch in perspective; a model of the probable form of the pentane
molecule is shown in Plate XXI a.
Many members of the paraffin series are found mixed together in
petroleum wells. They are inflammable, because they readily break up
under the proper stimulus in the presence of oxygen, and the atoms
rush into fresh combinations, developing great heat in doing so. The
shortest member of the series contains only one link. It is a gas,
called methane or marsh gas, represented thus:
[Illustration]
It bubbles up from stagnant water containing vegetable matter in
decay. As the chain grows longer, the substance holds together better.
Pentane, with five links, is a liquid at ordinary temperatures and
boils at 36° C.; pentadecane, with fifteen links, boils at 257° C.,
while pentacosane, with twenty-five links, is solid at ordinary
temperatures and melts at 54° C. The long molecules are supposed to
have a tendency to lie side by side, like matches in a box; we shall
see that this view is strongly supported by the X-ray results. It may,
therefore, be expected that the longer they are, the greater the forces
required to tear them apart; so that for this reason alone the longer
the chain the higher its boiling point and melting point. As a class
they have no strong hold on one another: the boiling and melting points
are low. The cloak of hydrogens with which they are covered seems to
hinder their association with other molecules such as those of acids.
In fact, the word paraffin is derived from two Latin words meaning
“little” and “affinity.” But, as I have already said, they join up very
readily with oxygen under the proper circumstances.
The behavior of these chains is greatly altered if we take off an end
group and put on a different one. By substituting for one of the end
hydrogens a certain group, containing a carbon, two oxygens, and a
hydrogen, we get another highly important series of compounds called
the “fatty acids.” The group is known as the carboxyl group. Here again
the chain may be of any length.
[Illustration]
When there is only one carbon in it, the chemist represents it thus:
meaning that of the four bonds which carbon can exert, drawing four
other atoms to itself, one goes to a hydrogen, another to an oxygen
which carries a hydrogen, and two go to a separate oxygen, binding it
very tightly. This substance is formic acid, which is secreted by ants,
and has a very irritating action on the skin, as we all know. When
a fresh link is added to the chain, we have acetic acid, which gives
acidity to vinegar; in fact, the name is derived from the Latin word
for vinegar. The formula is now:
[Illustration]
Butyric acid has four carbons; it is the substance that gives to
rancid butter its peculiar taste and smell. Lauric acid has twelve
carbons, and is found in laurel oil and cocoanut oil. Myristic acid has
fourteen, and is found in the butters of mace and nutmeg. All these are
liquids. Palmitic acid, found in palm oil, has sixteen, and stearic has
eighteen. The last two are solids at ordinary temperatures. They are
used in the manufacture of stearine candles, and, slightly modified,
are the most important constituents of animal fat.
The alcohols constitute another of these chain series. They are formed
from the paraffins by taking off a hydrogen from one end and replacing
it by an oxygen and a hydrogen in combination. Thus, is the ordinary
alcohol.
[Illustration]
And so we may go on describing an immense number of substances, all
consisting of links of CH{2}, with varying terminations.
Sometimes one or more hydrogens are taken off the side of the chain and
replaced by other atoms or atom groups; sometimes there are further
complications. There is a fascination in the simplicity of the general
principle and in the wonderful variety and influence of detail. Why
should different plants or different animals, or different members of
the same plant or animal, contain these carbon chains of different
lengths, on which their own growth and properties and characteristics
greatly depend? Of course, the whole effect rests, in the first place,
on the properties of the carbon atom, and it is that which gives a
peculiar interest to the crystal forms of carbon, diamond, and graphite.
We may look again at the diamond model and ask ourselves whether we can
see any skeleton form of the chain, just as we saw the skeleton of the
ring. The model (Plate XIV a) shows that it can be cut into
chains of any length and of this form, in which the angle that recurs
at every bend can be calculated to be 109° 28'.
[Illustration: Fig. 50.--Chain from diamond.]
We might suppose this to be a simple form of the chain. We are only
speculating, of course, trying to imagine possible solutions of our
problems, which we may put to the test of experiment, and even when we
seem to have a success, not counting too much upon it. If this were
the chain, two hydrogens would naturally be attached to each carbon
at points which, with the two points of attachment of its carbon
neighbors, would make four points symmetrically arranged, like the four
points at which each carbon atom is attached to its four neighbors
in the diamond, as in Plate XXI a. This picture goes more
into details than the form of illustration generally employed by the
chemist; the latter is merely a representation on the flat, our new
figure is in three dimensions. And no doubt the true figure is in three
dimensions. The chemist has not drawn it so hitherto, because he has
had no direct evidence as to how he ought to do it. We are trying to go
one stage further, with some hesitation, because we are not perfect in
the interpretation of our new methods, though very hopeful as to their
value to us in the end.
In the last year or two we have been able to make accurate measurements
of the lengths of the chain molecules by means of the X-rays. The
discovery of the method arose from a curious accident. A certain
crystal was under examination by X-rays, and because it was liable to
suffer rapid deterioration from the moisture of the air, it was covered
over with a thin layer of the solid paraffin, which is generally used
in laboratories as an electric insulator. Certain reflections of the
X-rays were found which could not be reconciled with what was known.
[Illustration: PLATE XXI.
A. Model of a hydrogen chain, pentane, containing five carbon atoms.
The larger balls represent carbon atoms, the smaller hydrogens.
B. An X-ray spectrum of the hydrocarbon containing 18 carbons obtained
by the method shown in Fig. 52. (Müller.)
C. The model shows the arrangement of the sodium and chlorine atoms in
rock-salt: the dark balls represent sodium, the white chlorine, or vice
versa. Only _arrangement_ is shown: there is no attempt to show
the size or shape of the atom.]
It was found that they were due to the paraffin. The commercial
paraffin is a mixture of several of the fatty acid chains, and is
not suitable for accurate experiment. It happened, however, that a
certain enthusiastic student of organic chemistry, Doctor Le Sueur, had
prepared a great number of these chain substances in a pure state, and
these were fortunately available. Those and many others have now been
examined, with very interesting and, on the whole, simple results.
[Illustration: Fig. 51.--Diagrammatic arrangement of the molecules in
the layers of a substance like stearic acid, or a hydrocarbon such as
pentane.]
The particular method is a good example of the way in which the X-rays
can be used. A little of the solid substance is put on a piece of glass
and pressed flat: we will consider the significance of the pressing in
a moment. The substance is now, as it turns out, in layers parallel to
the glass. The molecules in each layer are more or less perpendicular
to it, and are linked together side by side. They may be represented
as in Fig. 51, in which three layers are drawn. Each layer is perhaps
a fifty-millionth of an inch thick, and the thickness is proportional
to the length of the molecule. When a beam of X-rays is passed through
such a sheet, composed of layers, a little is reflected by each layer,
just as would happen in the case of a beam of light passing through
a pile of glass plates. The principle of the experiment has already
been described on p. 152. Suppose _S_ is the source of X-rays, and
_P{1}_P{1}_ is the glass plate with its layers upon it. When the X-ray
beam along _SC_ falls on the plate at the proper angle, the reflection
from the different layers are all in step and the reflection is strong.
We may imagine the reflected ray going off on the line _CR{1}_, and
making its mark at _R{1}_ on the photographic plate _DD_. If the plate
is then turned round about the vertical line through _C_--the figure
shows the experiment in plan--reflection as a whole ceases, because
the separate reflections from the various layers get out of step and
destroy one another. But when the plate has been turned sufficiently,
another general reflection appears, because the reflections from
the different layers have got into step again. The first general
reflection comes when the particular reflection from one layer is
_one_ wave-length behind or in advance of the reflection from the
layers on either side of it; the next when there is a difference of two
wave-lengths, and so on. Consequently the photographic plate when it
is developed shows a whole series of such general reflections. Usually
the plate is turned so as to throw reflections both above and below the
line (Fig. 52).
[Illustration: Fig. 52.--The method of making the X-ray spectrum of
a hydrocarbon. The X-rays from _X_ pass through a limiting slit at
_S_, and if the layer, which has been pressed flat on the glass plate
_P{1}P{1}_ is at the proper angle for reflection, there is a reflection
pencil, _CR{1}_, which makes an impression on the photographic plate
at _R{1}_. If the plate is turned sufficiently there is another
reflection, _R{2}_, when the plate occupies the position _P{2}P{2}_ and
so on.]
A central mark _M_ is due to the direct action of the X-rays--this
part of the plate is usually shielded, so that the direct action is
not too strong--and all the different orders of reflection appear on
either side. An actual example showing the reflection of a paraffin
of eighteen carbons is shown in Plate XXI b. It was obtained
by Doctor Müller. It will be seen that the reflections are very well
marked. It is possible to measure their distance apart with accuracy,
and from this we calculate the thickness of one of the layers in the
reflecting material. We cannot be quite sure that the molecules stand
upright and perpendicular to the layer, but we have good grounds for
supposing so, which we need not enter into here. We find that the
length of the chain increases with perfect regularity as carbon links
are added to it. We actually find that many of them have exactly the
length we should expect if they were as represented in Fig. 50.
The whole series of experiments of this kind bears out the idea
that the chemist has formed as to the shape of these molecules: his
representation has been wonderfully correct. The X-rays have given
precision to the idea, suggesting also that the molecule must be drawn
in three dimensions, and at the same time measuring the length. I may
add that the sideways dimensions can be measured also.
We may now go back to the curious point that we get much better X-ray
reflections if the material is pressed on to the glass plate. It seems
likely that it naturally forms flakes, and in each flake the molecules
are perpendicular to the flake. They join together side by side, as
I have already said, and hold together much better in this union than
one flake holds to another. This last linking is affected by the ties
at the ends of the molecules, and these are much weaker. It is exactly
the same effect as we found in graphite, where flakes held together
strongly as flakes, but slid easily on one another. It is this that
gives the greasy, slippery feeling both to the greases and fats and
to graphite. When pressure is applied to the material, the layers
are squeezed flat, just as when graphite is rubbed on a surface, and
the X-ray reflections are good because the layers are made to lie
regularly. When the material is melted and cooled again, the layers
are broken up, and though, no doubt, they are formed again, they lie
irregularly; the X-ray reflection is then poor. We find the same effect
in the case of gold leaf, as we shall see in the next chapter.
There is another curious property of the long-chain molecules which
is worth our consideration. The paraffin chain has hydrogens at both
ends. Each flake is one molecule thick. But in the case of the fatty
acids (p. 202), the X-rays show that there are two molecules in the
layer, end to end. This is, indeed, to be expected, because it is known
that a carboxyl group has a tendency to join up with another of its
own kind. Consequently the chains attach themselves together in pairs,
forming a chain of double length, the ends of which are hydrogen; the
two carboxyl groups are in the center. This result is obtained from the
X-ray measurements. Here again the X-rays confirm a chemical conclusion
and throw a fresh light upon it.
There is a type of crystal structure which, differing entirely from
those that we have considered already, is of such great importance that
we must not pass it by. The crystals of ordinary salt are good examples.
Sometimes, as we have already seen, a molecule is formed from two
atoms, of which one, being greedy for an additional electron, has
satisfied itself at the expense of the other atom. The latter, before
the transference, has held one electron in a loose binding. For
example, chlorine has seventeen electrons: two in an innermost shell
or coating, and eight in the next shell. In the outer shell there are
seven, and the chlorine atom exerts a great force, tending to complete
the shell, which when full contains eight. It will then present the
external appearance of argon. Sodium has eleven electrons normally:
two in the innermost shell, and eight in the next, but only one in the
outer shell instead of the seven in chlorine. The sodium atom has no
tight hold on this odd electron, so the chlorine takes it. The sodium
atom then has the external appearance of a neon atom (p. 82).
The two atoms are now charged electrically; the chlorine is negative,
because it has one negative charge over and above its proper number,
and the sodium is positive, because it has one too few. The governing
principle in the growth of the crystal is the attempt on the part of
the atoms to satisfy as fully as possible the mutual attraction of the
positive sodiums and the negative chlorines. The system of packing
which nature adopts is that in which each chlorine is surrounded by
six sodiums, and _vice versa_. It is shown in Plate XXI c. It is
very simple--a cubic arrangement in which each of the lines of atoms
that are parallel to the edges consists of sodium and chlorine atoms
alternately. The white balls may represent chlorine and the black
sodium, or _vice versa_. It is because of this arrangement that salt
crystallizes from brine in cubic form. The crystals are not necessarily
cubes, but are rectangular blocks, all faces of which are of the same
type. The frequent differences between their sizes and appearances are
merely accidents of growth.
Very many crystals are built on this principle: in particular all the
salts of the metals, in which the metal has lost one or more electrons,
and the remainder of the molecules, as a group, has gained them. The
resulting structure is not always so simple as that of salt, because,
for instance, the group may be more irregular in outline than the
single chlorine. In calcite, the metal atom calcium loses two electrons
to the group CO{2}, and the result is the rhomb of Iceland
spar. It is still true that each metal atom is surrounded by six
negatively charged bodies, and each of the latter by six metal atoms;
the crystal is no longer rectangular, because the CO{2} group
is not round.