_The Nature of Crystals: Diamond_
WE have seen that when the effects of movement overcome the forces
of mutual attraction, the atoms and molecules have an independent
existence and form a gas; and, further, that when the attractive forces
are somewhat stronger or the effects of movement are somewhat less,
the molecules may cling together and form a liquid. In this state we
suppose that the connections between the molecules are loose enough
to allow a molecule to change its position and its partners with
ease. We have now to consider a final state in which the attractive
forces have quite the upper hand. The bonds between the molecules
are more numerous, and it may be stronger: each molecule is tied to
its neighbors at more than one point of its structure, so that it is
riveted into its place, and in this way the _solid_ is formed.
Molecules differ very much from one another in their form and in the
forces which they exert on one another. When the forces are strong,
much movement is required to prevent them from binding the molecules
into the solid: in other words, the melting point is comparatively
high. Substances like diamond or tungsten, of which the filaments of
electric lamps are made, are so tightly bound together that they must
be raised to temperatures of several thousands of degrees centigrade
before the molecules are forced to release their hold. Such substances
as butter or naphthalene barely remain solid at ordinary temperatures;
others, again, like carbon dioxide, still more oxygen or hydrogen, must
be greatly reduced in temperature before solidification takes place.
It is all a matter of the balance between the two opposing agencies,
motion and mutual attraction, and it is easy to realize that the
melting points of substances may differ very widely from one another.
Furthermore, a molecule is not to be thought of as a body of vague
and uncertain form exerting a loosely directed attraction on its
neighbors. When two molecules are brought together they may or may
not draw tightly together: everything will depend on the way they
are presented to each other. Each molecule has a definite shape or
outline, we may say; though in using these words we must remember that
their meaning will require careful consideration when we look more
closely into the matter. The molecules join together as if there were
definite points of attachment on each, and the junction implied that
the proper points were brought together. The action between them is not
usually to be compared to the general attraction between two oppositely
electrified bodies, but rather to the riveting together of two parts of
a mechanical structure, such as two parts of an iron bridge. Just as
in the latter case the parts must be brought into the proper relative
positions so that the rivets can be dropped into their places, so we
find two molecules of a solid substance tend to arrange themselves so
that certain parts of one are fastened with considerable rigidity to
the proper corresponding parts of the other. There may be more than one
way in which molecules can be joined up, and in consequence different
structures may be formed out of the same molecules; for example, there
are different forms of sulphur, of quartz, and of many other things.
It often happens that one mode of arrangement is adopted at one
temperature, and a different mode at another temperature.
The consequence is that when the molecule contains many atoms, and is,
therefore, probably of complicated structure and curious form, the
solid that is formed by their union is of a lace-like formation in
space. We may compare it to a bridge formed of iron struts and stays;
which is a very empty structure, because each member is peculiar in
form, generally long and narrow, and is attached to the neighboring
members at definite points. Most organic substances, like naphthalene,
or one of the solid paraffins, have such a complicated character, and
the emptiness of the structure makes for a low density. Few organic
substances are much heavier than water. When the molecules are less
complicated, less irregular in outline, they may pack together more
closely; if the molecule contains one or two atoms only, like the
molecule of ruby, or iron pyrites, still more if it contains but one
atom, atom and molecule being then equivalent terms, as in the case of
gold or iron, then the packing may be very close and we have relatively
heavy substance.
The infinite variety in the properties of the solid materials we find
in the world is really the expression of the infinite variety of
the ways in which the atoms and molecules can be tied together, and
of the strength of those ties. We shall never thoroughly understand
the materials that we put to use every day, nor grasp their design,
until we have found out at least the arrangement of the atoms and
molecules in the solid, and are able to test the strength and other
characteristics of the forces that hold them together.
Now, within the last few years the discovery of the X-rays has provided
means by which we can look far down into the structure of solid bodies,
and observe in detail the design of their composition. We have advanced
a whole stage toward our ideal purpose--that is to say, toward the
position from which we can see why a material composed of such and such
atoms has such and such characteristics, density, strength, elasticity,
conductivity for heat or electricity, and so on; or, in other words,
reacts in such and such ways to electricity or magnetism, or mechanical
forces, or light or heat. How far our new powers will carry us, we do
not yet know; but it is certain that they will take us far and give us
a new insight into all the ways in which material things or structures
are handled, consciously or unconsciously, it may be in some industrial
process, or it may be in some action of a living organism.
The new process is especially applicable to the solid, and I hope to
describe it in this and the following chapters, which deal especially
with the solid state. It depends on the combined use of crystals and
X-rays, and we must give a little consideration to each of these
subjects. Let us take the crystal first.
Imagine a slowly cooling liquid to reach the stage of which I have
already spoken, when the heat motions have decayed so far that the
molecules or atoms begin to attach themselves rigidly together. They
will lay themselves side by side, so arranged that the attractions
of various points on the one for various points on the other are
satisfied as far as possible. We can imagine two molecules, already
tied together at one point, to swing about each other with diminishing
movements until at last a second tie is made, quite suddenly, perhaps.
Then it may be that a third tie is quickly made in the case of each
molecule, linking it to the other of the two, or to a third; and so it
becomes locked into position. Thus, as the liquid cools, molecule after
molecule will take its place with others already locked together, and
the solid grows.
Or it may be that a solid substance forms out of a solution in which
it has been dissolved. The solution evaporates and the molecules meet
one another more often, so that their association is encouraged. When
the liquid has entirely disappeared, the substance is all solid. If
the evaporation has been slow, the molecules as they wander on their
way through the solution come to places where already a few molecules
have tied themselves together, and join up with them, quietly and
deliberately arranging themselves before they finally settle down, or
refusing to take their places before they are presented to one another
in the right way.
We can well imagine that under such circumstances a regularity in the
arrangement will ensue. Suppose that a flat body, shaped like A, had
four centers of attraction, two positive and two negative, arranged as
shown. If we had to lay a number of such bodies on a flat surface, and
so join them together that a positive and a negative center lay always
close to each other, we might arrive at some such arrangement as is
shown in Fig. 26.
[Illustration: Fig. 26.]
Whatever arrangement we adopted we should naturally find in the result
a certain regularity, as in the figure. And apparently nature works
in some such way: the molecules lie side by side in an ordered array.
The point is of fundamental importance. Order and regularity are the
consequence of the complete fulfillment of the attractions which the
atoms or molecules exert on one another. When the structure has grown
to a size which renders it visible in the microscope, or even to the
naked eye, the regularity is manifest in the form of the solid body: it
is what we call a crystal. It is bounded by a number of plane faces,
often highly polished in appearance, so that the crystal has a certain
charm due partly to glitter and sparkle, partly to perfect regularity
of outline. We feel that some mystery and beauty must underlie the
characteristics that please us, and indeed that is the case.
[Illustration: Fig. 27.--Models illustrating screw structure.
A. One sort of peg: _i. e._, every peg is like every other, and all
point the same way. B_1 and B_2. In each of these there are two sorts
of peg: _i. e._, one lot of pegs pointing to the right and one to the
left. Two varieties of arrangement. C_1 and C_2. Three sorts of peg:
pointing in three different directions. The two arrangements C_1 and
C_2 give a right-handed and a left-handed screw, respectively.]
Nature is telling us how she arranges the molecules when given full
opportunity. There are but two or three in her unit of pattern, and
when the unit is complete it contains every property of the whole
crystal, because there is nothing to follow but the repetition of the
first design. Through the crystal, therefore, we look down into the
first structures of nature, though our eyes cannot read what is there
without the use, so to speak, of strong spectacles, which are the X-ray
methods. A few crystal forms are shown in Plate XIII.
[Illustration: PLATE XIII.
Crystalline forms.
A. Sulphur trioxide crystals which have grown from vapour in a glass
vessel. B. Erythritol crystal, grown from solution. C. Ammonium
chloride: ideal and distorted cubical crystals from solution containing
urea. Crystal forms: Quercite: Cocosite. E. Crystal forms: Alizarin;
Rubidium alum; Sodium chloride: Ammonium cobalt sulphate; Phthalic
acid. F. Ammonium chloride: fern-leaf crystals (octahedral) and cubical
crystals from solution containing urea.]
There are three stages in the arrangements of matter: the single atom
as we find it in helium gas; the molecule as it is studied by the
chemist; and the crystal unit which we now examine by X-ray analysis.
To take an example, there are the _atoms_ of silicon or of oxygen.
The _molecule_ of silicon dioxide contains one unit of silicon
and two units of oxygen, arranged, no doubt, in some special way.
Lastly, there is the substance quartz, of which the _crystal unit_
consists of three molecules of silicon dioxide, arranged, again, in a
special fashion which we now know has a certain screw-like character.
The quartz crystal contains an innumerable multiplication of these
units. Each of the units has all the properties of quartz, and, in
fact, is quartz; but a separate molecule of silicon dioxide is not
quartz. For example, one of the best-known properties of quartz is its
power of rotating the plane of polarization of light, and this property
is associated with the screw which is to be found in the crystal
unit. It takes three molecules to make the screw. If we insert pegs
into a round stick as in the figure, and make all the pegs the same
in every particular--that is to say, if our unit of pattern contains
one peg only--we may form an arrangement like _A_. With two pegs
to the unit of pattern we can make an arrangement like _B{1}_ or
_B{2}_. With three pegs to the unit of pattern we may make one
as in _C_, which may twist either of two ways, _C{1}_ or
_C{2}_, or, as it is generally said, may be either right-handed or
left-handed.
[Illustration: Fig. 27a.]
The X-rays actually tell us that the quartz unit contains three
molecules, and that they are arranged in a screw-like form, with which
facts the form of the quartz crystal is in complete agreement, because
there are two varieties in the form, as shown in Fig. 27 a. In
one there is a sequence in the faces x, s, r', which screw off to the
right, while in the other they go to the left. Such a dual arrangement
may be expected to be a consequence of the existence of the two kinds
of screw, though we do not yet know enough to enable us to guess why
these particular faces are prominent. Quartz or “rock crystal” was
called “Krystallos” by the Greeks; the name was given to ice also,
because the two substances were confused with each other. It is
appropriate, therefore, that we should use quartz as an illustration of
what is meant by crystal structure and the crystal unit.
We may now ask ourselves why, if the natural arrangement of molecules
is regular, we do not find all bodies in crystalline form. To this
we must answer that in the first place a large perfect crystal must
grow from a single nucleus. It is difficult to say what first arrests
the relative motion of two or three molecules of the cooling liquid,
joining them together and making a beginning to which other molecules
become attached. Perhaps it is a mere accident of their meeting;
perhaps some minute particle of foreign matter is present which
serves as a base, or some irregularity on the wall of the containing
vessel. If there are very many nuclei present in the liquid, very many
crystals will grow; and since they are not likely to be oriented to
one another when they meet, they will finally form an indefinite mass
of small crystals, not a single crystal. They may be so small that
to the eye the whole appears as a solid mass without any regularity
of form. In order that a large perfect crystal should be formed, the
arrangements must be such that the molecules find few centers on which
to grow. And they must grow, usually, very slowly and quietly, so
that each molecule has time to settle itself correctly in its proper
place. The molecules must have enough movement to permit of this
adjustment. These conditions are well shown in the methods which the
crystallographer employs for the growth of crystals. If, for example,
he is growing a large crystal of salt from a solution of brine, he will
suspend a minute, well-formed crystal in the brine, and he will keep
the temperature of the latter so carefully adjusted that the atoms of
sodium and chlorine are only tempted to give up their freedom when
they meet an assemblage of atoms already in perfect array--that is to
say, when they come across the suspended crystal. If the solution is
too hot, the suspended crystal will be dissolved in the unsaturated
solution; if it is too cold, crystals will begin to grow at many
points. Sometimes the liquid is kept in gentle movement so that various
parts of it are brought to the suspended crystal in due turn.
[Illustration: Fig. 28.--The thermostat.
The temperature of the bath in which stand the bottles containing the
growing crystals must be free from sudden and irregular variations, and
must be slowly lowered day by day. The temperature is maintained by an
electric heater: if it rises too high the current is turned off through
the expansion of the liquids in the large thermometer which also stands
in the bath. The rise of the mercury closes a circuit containing
an electromagnet which pulls the switch. The clock is all the time
lowering--very slowly--a wire to meet the mercury in the thermometer,
so that the temperature at which the heating coil is turned off is
being steadily diminished. The heater is at the bottom of the bath, and
a stirrer is just above it.]
The principal conditions are time and quiet, a solution of the salt
just ready to precipitate its contents, temperature and strength of
solution being properly adjusted for the purpose, the presence of a
small perfect crystal and the gentle movement of the solution past
it. We do not, of course, quite understand how these or some such
conditions come to be realized during the growth of a diamond or a
ruby; but we find them to be necessary in the laboratory when we
attempt to grow crystals ourselves.
When the conditions are fulfilled in part only, we may get a mass of
minute crystals in disarray; we may even find a totally irregular
structure--an amorphous substance, to employ the usual phrase. This
alone would account for the seeming rarity of crystals, and we
have also to bear in mind that many bodies are highly composite in
character, consisting of many substances each of which has its own
natural form. The X-rays show us that the crystal is not so rare as
we have been inclined to think; that even in cases where there is no
obvious crystallization. Nature has been attempting to produce regular
arrangements, and that we have missed them hitherto because our means
of detecting them have been inefficient. The regularity of Nature’s
arrangement is manifested in the visible crystal, but is also to be
discovered elsewhere. It is this regularity which we shall see to be
one of the foundation elements of the success of the new methods of
analysis.
Let us now turn to the consideration of the X-rays. The reason of their
ability to help us at this stage may first be given in general terms.
The X-rays are a form of light, from which they differ in wave length
only. The light waves which are sent out by the sun or an electric
light or a candle and are perceived by our eyes have a narrow range
of magnitude. The length of the longest is about a thirty-thousandth
of an inch, and of the shortest about half as much. These sizes are
well suited to the purpose for which we employ them. Let us remember
that when we see an object we do so by observing the alterations which
the object makes in the light coming from the source and reaching our
eyes by way of the object. Our eyes and brains have attained by long
practice a marvelous skill in detecting and interpreting such changes.
We may be unsuccessful, however, if the object is too small; and this
is not only because a small object necessarily makes a small change in
the light. There is a second and more subtle reason: the _nature_
of the effect is changed when the dimensions of the object are about
the same as the length of the wave, or are still less. Let us imagine
ourselves to be walking on the seashore watching the incoming waves.
We come in the course of our walk to a place where the strength of the
waves is less, and when we look for the reason we observe a reef out
to sea which is sheltering the beach. We have a parallel to an optical
shadow: the distant storm which has raised the waves may be compared
to the sun, the shore on which the waves beat is like the illuminated
earth, and the reef is like a cloud which casts a shadow. The optical
shadow enables us to detect the presence of the cloud, and the silence
on the shore makes us suspect the presence of the reef. Now the
dimensions of the reef are probably much greater than the length of the
wave. If for the reef were substituted a pole planted in the bottom of
the sea and standing out of the surface, the effect would be too small
to observe. This is, of course, obvious. Even, however, if a very large
number of poles were so planted in the sea, so that the effect mounted
up and was as great as that of the reef, the resulting shadow would
tell us nothing about each individual pole. The diameter of the pole is
too small compared with the length of the wave to impress any permanent
characteristic on it; the wave sweeps by and closes up again and there
is an end of it. If, however, the sea were smooth except for a tiny
ripple caused by a breath of wind, each pole could cast a shadow which
would persist for at least a short distance to the lee of the pole. The
width of the ripple is less than the diameter of the pole, and there is
therefore a shadow to each pole.
Just so light waves sweeping over molecules much smaller than
themselves receive no impressions which can be carried to the eye and
brain so as to be perceived as the separate effects of the molecules.
And it is no use trying to overcome our difficulty by any instrumental
aids. The microscope increases our power of perceiving small things:
with its help we may, perhaps, detect objects thousands of times
smaller than we could perceive with the naked eye. But it fails when
we try to see things which are of the same size as the wave length of
light, and no increase in skill of manufacture will carry us further.
But the X-rays are some ten thousand times finer than ordinary light,
and, provided suitable and sensitive substitutes can be found for the
eyes, may enable us to go ten thousand times deeper into the minuteness
of structure. This brings us comfortably to the region of atoms and
molecules, which have dimensions in the various directions of the order
of a hundred-millionth of an inch, and this is also the order of the
wave lengths of X-rays. Broadly speaking, the discovery of X-rays has
increased the keenness of our vision ten thousand times, and we can now
“see” the individual atoms and molecules.
We must now connect the X-rays with the crystal, and again we may first
state the point in a broad way. Although the single molecule can now
affect the X-rays just as in our analogy the single pole can cast a
shadow of the fine ripples, yet the single effect is too minute. In the
crystal, however, there is an enormous number of molecules in regular
array, and it may happen that when a train of X-rays falls upon the
crystal the effects on the various molecules are combined and so become
sensible. Again, we may make use of an analogy. If a single soldier
made some movement with his rifle and bayonet, it might happen that a
flash in the sunlight, caused by the motion, was unobserved a mile away
on account of its small magnitude. But if the soldier was one of a body
of men marching in the same direction in close order, who all did the
same thing at the same time, the combined effect might be easily seen.
The fineness of X-rays makes it possible for each atom or molecule to
have some effect, and the regular arrangement of the crystal adds all
the effects together.
We may now consider more in detail the way in which the properties of
X-rays and crystals are combined in the new method of analysis. The
explanation is, perhaps, a little difficult, and I am trying to state
both what precedes and what follows the explanation in such a manner
that the explanation can be omitted by those who wish to leave it for
a time. It must, however, be mastered sooner or later by everyone who
wishes to make use of the new methods.
We have seen that the atoms and molecules of a crystal are in regular
array, and have even found reasons for expecting them to be so.
Suppose that we stand before the papered wall of a room and consider
the pattern upon it. It is a repetition of some unit (Plate XIV
b). Mark one particular point of the pattern whenever it
occurs; if a real marking is disallowed, a mental marking must suffice.
[Illustration: Fig. 29.--Space lattice.]
It will be found that the marks lie on a diamond- or rhombus-shaped
lattice, and that this lattice has the same form no matter what point
of the pattern has been chosen for the marking. The rhombus will
have different sizes and shapes in different wall-papers, though the
four sides will always be equal or, it may be, the rhombus will be
a rectangle, because no one could endure a wall-paper in which this
was not the case. The whole pattern of marked points may be called a
“lattice.” Each rhombus contains the substance of one whole unit of
pattern with all its details, and no more.
The arrangement in space of the units of the crystal is like the
arrangement on the wall of the unit of the wall-paper design, except
that the plane lattice is replaced by a “space lattice” (Fig. 29).
[Illustration: Fig. 30.--Size and dimensions of the unit cell of the
quartz crystal in hundred-millionths of a centimeter.]
Each little cell of the lattice is bounded by six faces, which are
parallel in pairs. The cell can have any lenghts of side and any
angles; its simplest and most regular form is that of a cube. Each cell
contains a full unit of pattern with all its details, and no more: it
is the crystal unit, which possesses all the qualities of the crystal,
however large the latter may be. In the case of quartz, for example, it
has the special shape that is shown in Fig. 30, and it contains three
molecules of silicon dioxide. This fact is readily determined by X-ray
methods, and also the size and dimensions of the cell, as we shall see;
but it is a far more difficult matter to discover the arrangement of
the atoms and molecules within the cell.
[Illustration: Fig. 31.--An atom group is associated with each point of
a lattice.]
Suppose that we were able to look into a crystal along one of the cell
edges of Fig. 29, and found ourselves able to represent what we saw
in some such way as is shown in Fig. 31. There is a grouping of atoms
associated with each point on the lattice, which grouping we represent
by the entirely imaginary set of circles in the figure. The form of the
grouping is of no account, nor its contents; it may contain any number
of atoms and molecules, but the essential point is that an exactly
similar group is associated with each point on the lattice, as in the
design of the wall-paper. Suppose a train of X-ray waves to strike the
crystal; in Fig. 32, A, they are represented by the line _WW_ and
the parallels to _WW_.
[Illustration: PLATE XIV.
A. Diamond model.
The model shows only the arrangement, and says nothing about the size
or shape of the carbon atom.
B. Wall-paper.
The unit cell is outlined in two ways: (a) by thick lines, (b) by
thin lines. The shape and content of the cell are exactly the same
in the two cases, although the corners of the two cells are chosen
differently.]
When these waves strike the series of groupings strung along
_AA_--each grouping is now represented by a single dot--a new set
of similar waves will start from every grouping, though the wave as a
whole sweeps on, just as a row of posts planted in the sea would each
become the center of a disturbance when a wave passed by.
[Illustration: Fig. 32.--Reflection of X-rays.]
At a little distance from the row _AA_ these minor disturbances
link themselves together in a connected set of waves, represented by
the parallel lines _aa_. The effect is analogous to the reflection
of sound by a row of palings, or by a stretched piece of muslin. In all
cases the bulk of the wave goes on, but there is a reflected wave which
makes with the reflecting layer the same angle as the original waves.
The reflected waves form a simple train, the same as the original as to
wave length, but far weaker, of course: it might be thought that the
reflection would simply be a confused mass of ripples, but it is not
so. Quite close to the groupings there is some apparent confusion, but
a little farther along the track of the reflection the wavelets melt
into the steadily moving train _aa_, etc.
Behind the row of groupings strung along _AA_ there is another,
exactly like the first, which is strung along _BB_ (Fig. 32, B). The
original waves, which experiment shows to be very little impaired by
their passage over _AA_, sweep over _BB_ in turn, and again there is a
reflection represented by the group of parallel lines _bb_. Behind that
there is a row _CC_ forming a _cc_ train, a row _DD_ forming a _dd_
train, and so on.
As a rule the lines _aa_, _bb_, _cc_, do not coincide with one another.
But if the wave length of the rays, the distance between _AA_ and
_BB_ (which are really planes seen edgeways), and the angle at which
the waves meet _AA_, _BB_, are correctly adjusted to each other, then
the lines _aa_, _bb_, etc., do coincide with one another. In actual
practice thousands of reflecting planes come into play, and when the
reflections all fit together in this way exactly, the whole reflection
is strong. If the adjustment is incorrect as it is drawn in the
diagram, the reflections do not add together into a sensible effect;
some throw their crests, or what corresponds to the crests on a water
wave, into the hollows of other waves, and there is mutual interference
and annulment. The adjustment has to be exceedingly exact, because
there are so many reflecting planes, one behind the other. It is easy
to find a formula which expresses the condition for correctness of
adjustment, and therefore for reflection. The line _A'B'B_ must be
longer than _AB_ by a whole number of wave lengths. If λ is the wave
length, _d_ the distance between planes, or spacing, as it is usually
called, and θ the angle shown, then
_n_λ = A'B'B - AB = A'D - AB = DN = 2_d_sinθ,
where _n_ is any whole number.
It is not necessary, as I have stated already, for the reader to go
through the calculation just given, from which the fundamental equation
of the subject is derived.
The essential point is that if the direction of the original rays is
gradually altered with respect to the planes _AA_, _BB_,
etc., there will be _no_ observable reflection until the proper
inclination is reached; when this happens there is a sudden flash of
reflection. The angle of inclination is observed; and when, as is
always the case in crystal analysis, the wave length of the rays is
known, it becomes possible to measure the spacing.
[Illustration: Fig. 33.--The law of reflection of X-rays.]
The reflected rays cannot, of course, be detected by the eye, but they
can make their mark on a photographic plate and be observed in other
ways which need not be considered here. The instrument constructed
for the purpose of the experiment is called an X-ray spectrometer. It
measures the angles at which reflection occurs; and its observations
are used to determine spacings in the first instance, and in the second
the angles between the various planes of the crystal. For instance,
it gives not only the spacings between _AA_, _BB_, but also
between _PP_, _QQ_, (see Fig. 32, B) and the angle between
_AA_ and _PP_. It gives, in fact, the dimensions and form of
the unit cell.
It is, in general, a simple matter to find by experiment the density of
the crystal, and then we can find the weight of the matter contained
in the cell. Since we always know the weight of the molecule, it is
easy to find how many molecules go to the unit; as already stated, it
is always a very small number. Moreover, the observations of the X-ray
spectrometer give us some knowledge of the relative positions of the
molecules that make up the unit of pattern. They would tell us far
more than this if only we knew how to interpret them, but we are too
inexperienced as yet. We have found our Rosetta Stone, but are as yet
only learners of the new language.
The most important point to bear in mind is that the X-rays give us
the distance between any sheet on which the atom groups are spread,
and the next sheet, which is exactly the same as the first, on which,
therefore, another lot of atom groups is spread. This spacing is the
same thing as the distance between two opposite faces of the unit
cell. We can draw the cell in many ways by joining up different corners
of the space lattice. There are not only three spacings to be measured
in the crystal, but in reality any number of them; usually we are
content to determine a few of them.
In a few cases the crystal analysis has already been carried so far
that we know where every atom has its place in the unit of pattern.
To get so far we have made use not only of our X-ray analysis, but
of many facts of chemistry and physics. I shall not describe these
further details in any case; the general explanation I have given above
will serve as a sufficient indication of the methods that have been
followed. But I think we shall be interested in some of the results.
First of all let us take the diamond, which is a prince among crystals.
It is not only a beautiful and valuable gem, but in its structure
it teaches us many things concerning the most fundamental truths of
chemistry, particularly organic chemistry. Only one atom, that of
carbon, goes to the building of the diamond; but that atom is of
vital interest to us. It is a fundamental constituent of foods and
fuels, dyes and explosives, of our own bodies and many other things.
The structure of the diamond is remarkably simple, though, like all
constructions in space, it is difficult to comprehend quickly. We are
so accustomed to drawings on the flat, paper and pencil are so handy,
that our minds easily grasp the details of a plane design. But we
cannot draw in space; we can only construct models at much cost of time
and energy, and so our power of conceiving arrangements in space is
feeble from want of practice. A few have the natural gift, and some,
being crystallographers, have trained themselves to think in three
dimensions. Most of us find a great difficulty in our first efforts to
realize the arrangements of the atoms and molecules of the crystal.
Nevertheless, the diamond structure shown in Plate XIV a will
become clear at the cost of a little consideration. The black balls
represent carbon atoms, in respect to position only, not in any way as
to size and form, of which we know very little. Every carbon atom is
at the center of gravity of four others; these four lie at the corners
of a four-cornered pyramid, or tetrahedron, and the first carbon
atom is, of course, at the same distance from each of them. We have
reason to believe that the ties between the atoms are very strong, and
there is only one form of tie throughout the whole structure. In its
uniform simplicity and regularity we can surely see the reason why the
diamond is placed in the highest class on the scale of hardness. If
it is pressed against any other crystal it is the atoms of the latter
that must give way, not the atoms of the diamond. The diamond has a
cleavage plane. In the figure it is parallel to the plane of the table
on which the model stands; there are four such planes, one parallel to
each face of the four-faced pyramid. The model can be turned over so
as to rest on any one of the four faces, and looks exactly the same
in each position. The distance between the centers of two neighboring
carbons is 1.54 Ångstrom units; this unit is the hundred-millionth of
a centimeter. It does not seem surprising that this particular plane
should be the cleavage plane, because it cuts straight across the
vertical connections between the horizontal layers that appear in the
figure. Each of the layers may be described as a puckered hexagonal
network.
[Illustration: PLATE XV.
(_By courtesy of Joseph Asscher & Cie._)
A. The Cullinan diamond split into three pieces.
It was originally as large as a small fist.
(_By courtesy of Joseph Asscher & Cie._)
B. The table and tools used for splitting the diamond.]
The crystal may, of course, be considered as an arrangement of layers
parallel to any one of the four faces of the tetrahedron, not merely
the face on which the model happens to stand.
The existence of this cleavage is well known to diamond cutters, who
save themselves much labor by taking advantage of it. In the Tower of
London are shown the tools wherewith the great Cullinan diamond was
split during its “cutting.” Plate XV a shows the diamond in
three pieces; and XV b the tools used in splitting it. It is
possible to cleave a diamond in yet another plane, which contains any
one edge of the tetrahedron and is perpendicular to the other edge; but
the operation is difficult and rarely used.
When we consider the diamond construction we cannot but notice the
striking appearance, in every part of the model, of an arrangement of
the carbon atoms in a ring of hexagonal--or six-sided--form. If we take
one of these rings out from the model, it has the appearance of Plate
XVI b, 2: a perfect hexagon when viewed from above, but not a
flat ring.
Now the ring of six carbon atoms has already a famous place in
chemistry. No one has ever seen the ring: it is too small. But the
chemist has inferred its existence by arguments which are most
ingenious and most interesting. Even those of us who are not chemists
may find no great difficulty in acquiring some understanding of them.
For instance, it was well known in the middle of last century that
certain molecules could be formed in which the fundamental structure
consisted of carbon atoms in a row or chain, and that hydrogen atoms
could be attached to the various carbon atoms in such a way that every
carbon atom had four other atoms attached to it. That was known because
the molecule could not be made to take on any more hydrogens: it was
full, or, as the chemists say, “saturated,” because a single carbon
atom is “saturated” when it has four other atoms attached to it, as,
for example, in marsh gas or methane (CH{4}). The relative
number of carbons and hydrogens was exactly what would be expected
on this hypothesis. With six carbon atoms there ought to be fourteen
hydrogen atoms, as the diagram shows, and this is found by experiment
to be the case. These substances are called the “paraffins” (see the
latter part of the next chapter), the various members of the series
having different numbers of carbons in the chain. The particular
substance shown in the figure is called hexane.
Now in 1825 Faraday isolated a certain substance from the residue found
in gas retorts, which he called bicarburet of hydrogen; it is now known
as benzene. A few drops of Faraday’s first preparation are preserved as
an historical treasure in the Royal Institution.
[Illustration: Fig. 34.--Hexane.]
The molecule of this substance contains six carbon like hexane, and
six hydrogen atoms. It can be made to take on six more hydrogen
atoms, twelve in all, but no more, and the new molecule then behaves
chemically like hexane in respect to most of its properties. But it
cannot have the same structure as hexane, because it has two hydrogen
atoms less. The riddle was solved in 1867 by Kekulé, who suggested that
the framework of benzene is a ring, not a chain, of six carbon atoms;
we may think of it as derived from the chain of Fig. 34 by the removal
of the two hydrogen atoms at the ends and a bending of the chain round
until the two ends meet and are joined up. We then have the structure
shown in Fig. 35. Its chemical name is hexahydrobenzene. Benzene
itself has only one hydrogen at each corner of the hexagon.
[Illustration: Fig. 35.--Hexahydrobenzene.]
The carbon chain and the carbon ring are the foundations of the two
great divisions of organic chemistry. Chain molecules are found not
only in the paraffins, but in fats, oils, soaps, and many other
important groups of substances. The ring is the basis of many thousands
of known molecules, including dyes and explosives, drugs such as
quinine and saccharine, and so on.
The conception of the closed hexagonal ring leads at once to a
simple and beautiful explanation of a number of remarkable chemical
observations, of which we will consider one example. The benzene
molecule consists of the hexagonal ring of carbon atoms, with one
hydrogen at each corner. Each carbon atom has only three neighbors in
this molecule: it can take on a fourth, so that on the whole there
is room for six more atoms or groups of atoms, to be tied on at the
corners, and these can be added. But the benzene molecule can exist
contentedly enough without them.
[Illustration: PLATE XVI.
A. The layers of the graphite crystal.
(_a_) and (_c_) are similar in all respects, but (_b_)
is like (_a_) when turned round through two right angles in its
own plane about any such vertical line as is drawn in the figure.
B. Possible forms of the benzene ring (see p. 164).
No hydrogens are shown.]
Taking the benzene molecule as it is, chemists find that they have
the power to alter its constitution, pulling off one or more of the
hydrogen atoms, and substituting other atoms or groups of atoms. In
a well-known and important case, a single hydrogen is removed and
replaced by a group consisting of one carbon and three hydrogen atoms,
known as the methyl group.
[Illustration: Fig. 36.--Toluene.]
The new molecule has the structure shown in Fig. 36, and is known as
toluene, a very important substance, a liquid at ordinary temperature.
A second hydrogen can be removed from the ring molecule and replaced,
let us say, by an atom of bromine; the new substance is known as
bromotoluene. It is very remarkable that when this has been done three
different substances are obtained, all having the same composition,
_viz._, the six carbon atoms, four hydrogen atoms, one bromine
atom, and one methyl group which we will presume remains intact. How
are we to explain the existence of these three, endowed with different
properties, yet all having the same constitution? The ring hypothesis
gives an immediate answer. There are three ways and no more of making
the substitutions, which are shown in the figure. The bromine atom may
be next to the methyl group, or next but one, or next but two.
[Illustration: Fig. 37.--Bromotoluene.]
The three molecules have different shapes, and therefore may be
expected to have different properties; and there is no doubt that
there are actually the three different substances. Chemists have even
been able to tell which is which. Many other similar examples could be
given, but this one will suffice as an illustration of the significance
of position as well as of composition, the three molecules differing
only in the relative positions of the two things substituted. The
methods of X-ray analysis are peculiarly fitted to deal with such
differences as these, because they measure the dimensions of the unit
of pattern into which two or more molecules are packed, and can detect
the effects of altering the _shape_ of the molecule. A little work
of this kind has already been done.
It is very interesting to observe that in the case of chain molecules
the number of carbon atoms is found to vary within wide limits;
butyric acid, the substance characteristic of rancid butter, contains
four carbon atoms, while palmitic acid, found in palm oil and other
places, contains sixteen (see the latter part of the next chapter).
On the other hand, the ring molecule of six carbon atoms occurs far
more frequently than any other. It must be the easiest to form and the
strongest in construction. Now the diamond, the only crystal, except
graphite, which consists of carbon atoms only, is full of hexagonal
rings. It is natural to suppose that the reason for the ring of six is
to be found in the diamond structure. But the basis of the latter is
simply the principle according to which each carbon atom is surrounded
by four others symmetrically arranged round about it. The two lines
which join a carbon atom to two of its neighbors are inclined to each
other at an angle readily calculated to be 109° 28'. If in certain
circumstances it is the rule that the junction of two carbon atoms with
a third must always be made so as to show this angle, see Fig. 50, then
the shortest ring that will close up contains six carbon atoms. (A
model may be made to illustrate the point. Wooden balls of sufficiently
regular form can be obtained in large numbers, being used in the
manufacture of large buttons. Four holes are drilled at the proper
places on each ball, and gramophone needles are used as connections.
Models of diamond, and many forms of ring and chain molecules, can
then be put together.) Five carbon atoms in one plane nearly make a
ring, because the angle of a pentagon is 108°. But if the angle is to
be 109° 28' it is necessary to take six, and to arrange them in the
puckered form of Fig. XVI b, 2. Whether the benzene ring is
actually puckered under all circumstances, or is sometimes flat, in
which case the angle is 120° (Plate XVI b, 1), or even has the
shape shown in Plate XVI b, 3, which is another form based
on the tetrahedral angle, we find it difficult at present to say with
any certainty. Experimental evidence is accumulating, but is not yet
decisive as to this particular point; perhaps all three forms occur.
Meanwhile, many facts emerge in the course of the work which are
definite and very interesting.
The remarkable substance graphite is, like diamond, composed of carbon
atoms only. It is much lighter, its density being 2.30 nearly; the
density of diamond is 3.52. Clearly, some rearrangement of the atoms
has taken place in which the spacings between the atoms have on the
average materially increased. The X-rays show that the increase has
taken place entirely in one direction. There are layers in graphite as
in the diamond structure (Plate XVI a). To one looking down
on a layer from above it presents the same appearance of a hexagonal
network; and moreover the side of the hexagon is almost exactly the
same in length. But the distance between layer and layer has been
greatly increased, and it is this change which has made the substance
so much lighter. Recent experiments seem to show that the layers have
been flattened out, so that each carbon is now surrounded by three
atoms in its own plane. If the ties between the atoms in each layer
have altered at all, they have at least not lost in strength; on the
other hand, the ties between layer and layer are greatly weakened. For
these reasons the layers slide over one another very easily, and at the
same time each layer is tough in itself. It is the existence of these
two conditions that makes graphite so good a lubricant; not only is the
readiness to slip of importance, but also the fact that the layer does
not easily break up into powder. When one slips on the black-leaded
hearthstone, some of the layers are clinging to the stone and some to
the sole of one’s boot; it is these layers that slide on one another.
It is very curious that a single change--whose real nature is, however,
a mystery--should convert the substance which is chosen as the type of
hardness into one of the most efficient lubricators we possess.
Another set of facts which also supports the idea that the ring is a
real thing, having dimensions which can be measured and allowed for,
is to be found in the comparison of two crystals, naphthalene and
anthracene. These substances are of the greatest importance in the
dye industry, the former being used in the manufacture of artificial
indigo, the latter in the manufacture of alizarin, which is the active
constituent of madder.
[Illustration: Fig. 38.--Naphthalene and anthracene.]
Naphthalene is a common substance; to most of us it is no doubt
familiar in the form of the white, strongly smelling balls which we
put into drawers to keep the moth away. If naphthalene is dissolved
in ether, and the solution allowed to dry off gradually, the crystals
are readily formed. In general appearance they resemble the crystals
illustrated in Plate XIII d.
The chemist finds that naphthalene consist of a double benzene ring
which we draw as in Fig. 38, A; anthracene is based on a treble ring,
Fig. 38, B. When crystals of the two substances are subjected to X-ray
analysis, it is found that the unit of pattern contains two molecules
and that the shape of the cell which contains the unit is as shown in
Fig. 39. The dimensions of the cells are given below the figures. If
the two cells are compared with each other, it is noteworthy that along
two of the edges the cells are very nearly the same size, but that
there is a great difference in respect to the third.
[Illustration: Fig. 39.--Unit cells of naphthalene and anthracene,
drawn to the same scale. Figures in Ångstrom units: see p. 156.
OA OB OC
Naphthalene 8.34 6.05 8.69
Anthracene 8.58 6.02 11.18]
The natural inference is that the double and treble ring molecules
lie parallel to _OC_ in the two cases, and that the difference
between 11.18 and 8.69 is to be ascribed to the extra length of the
molecule. The anthracene contains one more ring than diamond, which
gives it the extra length, 2.49. Now if we measure the width of the
ring as it occurs in diamond, it is found to be 2.50. Thus we again
find support for the view that the ring has a definite form, and
nearly constant dimensions; so that we have something to guide us in
trying to discover the structure of a crystal of which the ring forms
part. The X-rays tell us the size and form of the unit cell, and how
many molecules it contains, as well as certain information about the
relative positions of the molecules. If we know the size, more or less
accurately, of the ring or rings which form part of the molecule, we
can set out on the investigation of the structure, knowing that bodies
of definite dimensions have to be fitted into cells of definite shape.
Work of this kind is extraordinarily interesting, since it gives us new
knowledge of the arrangements of the atoms in the organic molecules
and of the forces that bind the atoms in the molecule and the molecule
in the crystal. It is a new field of inquiry, in which some results
are definite and clear, others more obscure and difficult to interpret
until greater experience has been obtained.
The organic molecule appears to us so far as a light rigid framework,
in itself tightly held together, but weakly joined to its neighbors in
the crystal. Organic substances are nearly always light, not very much
heavier than water. The fact that the density of naphthalene is only
1.15 shows the emptiness of its structure. Even the diamond is full
of holes, like a sponge. If the holes were filled up by other carbon
atoms, the density of the diamond would be doubled, for each hole is
just large enough to take one more carbon atom, and there are as many
holes as there are atoms.
[Illustration: Fig. 40.--Showing mutual relations of three naphthalene
molecules and parts of others.]
The weakness of the bonds that join molecule to molecule is the cause
of the softness of the organic crystal and of the ease with which
it can be melted. For the same reason naphthalene “sublimes”: it
evaporates while in the solid state. Whole molecules are flung off
from the solid, and form a vapor which may crystallize again in a
cooler part of the containing vessel.
Naphthalene and anthracene are flaky in structure: they have, as it is
said, a well-developed cleavage. The dotted lines show the cleavage
plane; clearly the molecules break away from one another more easily at
the ends than at the sides. In each flake the molecules stand nearly
upright, like corn leaning over in the wind.
The general conclusion to which we are led by these considerations is
that the “benzene ring” is a real material object of definite form
and dimension, which is built into crystalline structures with little
alteration of form. We must now go on to consider the “chain” molecule:
the basis of as great a section of organic chemistry as that which
rests on the ring. As this chapter is already long enough, we can
consider the chain in our next chapter, in addition to the ice crystal,
which will be our main subject.