APRIL 2, 1914] 
NATURE 
125 
the wave-length of the X-radiation, the spacing of the 
planes, and the proper angle of incidence. If we 
always use the same rays, and measure the angles at 
which they are reflected by the different faces of a 
crystal, natural or prepared, we discover the relative 
spacings of the many systems of planes which can 
be drawn regularly through the atoms of the crystal; 
and hence the actual arrangement of the atoms can 
be deduced. It is in this way that the structure is 
analysed. 
Let us first consider some details of the reflection 
effect. The theory is not entirely strange to us, for 
Lord Rayleigh carefully investigated a “strictly 
analogous phenomenon twenty-five years ago; this 
was the brilliant coloration of crystals of chlorate of 
potash. When white light falls on these crystals 
there is a strong selective reflection of rays the wave- 
lengths of which are confined within very narrow 
limits. R. W. Wood has prepared crystals which 
reflect waves the limits of which are no wider apart 
than the two D lines of sodium. Rayleigh showed 
that the effect was due to the existence of regularly 
spaced twinning planes parallel to the reflecting sur- 
face. He pointed out the analogy to other physical 
problems in sound, and in a Friday evening discourse 
at the Royal Institution he illustrated the effect by 
reflecting a high-pitched note by a series of parallel 
muslin sheets stretched tight and evenly spaced. 
Rayleigh showed that in these and parallel cases the 
reflection must be total provided the number of planes 
was sufficiently great, no matter how feeble the re- 
flection from each plane. In the present case the 
wave-lengths of X-rays are many thousands of times 
smaller than the waves of light which Rayleigh used; 
and the crystal planes being at atomic distances from 
each other are also many thousands of time closer 
than the twinning planes of chlorate of potash. 
It is found that pencils of homogeneous X-rays 
suitable for use in the experiment, are contained in 
the general mass of radiation issuing from an X-ray 
bulb. The antikathode of the bulb emits ‘‘lines’’ or 
rays of definite wave-length which are characteristic 
of the material of which it is made. 
The platinum antikathode gives a spectrum contain- 
ing five sharply defined and intense lines which stand 
out well from the general radiation. The osmium 
spectrum appears to have five similar triplets instead 
of the five lines of the platinum, the head of each 
triplet coinciding with a platinum line. Several 
substances ranging in atomic weight from silver down 
to calcium emit similar spectra consisting each of two 
strong lines, increasing regularly in wave-length as 
the atomic. weight decreases. A large number of 
these have been photographed by Moseley. Bulbs 
having rhodium or palladium antikathodes have been 
exceedingly useful in the crystal analysis, as they last 
well, their line spectra are very intense, and the wave- 
lengths are of convenient magnitude. The principal 
rhodium line is really double; and it will serve to 
illustrate the surprising exactness of the reflection 
effect when it is stated that the two constituents are 
just separated by reflection at the cleavage face of the 
diamond. The glancing angles are then 8° 35’ and 
8 39. 
Let us next consider the application of these prin- 
ciples to the determination of crystal structure. We 
take first, naturally, the large class of cubic crystals 
which are not only of high importance, but also of 
the most simple construction. 
The atoms of a crystal can be arranged in the form 
of a repeated group or pattern. Each group is to be 
supposed to contain as few atoms as possible con- 
sistent with the requirement that the whole crystal 
can be built by packing these groups together, all 
the groups being similar and similarly oriented. If a 
NO. 2318, VOL. 93| 
point is chosen similarly in each group it serves to 
indicate the position of that group relative to other 
groups. An arrangement of points chosen in this 
way shows the basal structure of the crystal, and is 
known as a “space lattice.” 
There are three space lattices which give cubic 
cHatacter to crystals.. In the first the representative 
points are placed at the corners of a cube; the whole 
lattice consistine of a repetition of this arrangement 
in all directions in space. In the second there are 
representative points at the corners of a cube, and the 
centre of the cube; in the third at the corners of a 
cube and at the middle points of the faces. The three 
are called the cubic, the centred cubic, and the face- 
centred cubic respectively. 
These three types of lattice can be at once distin- 
guished from each other by the X-ray method. Sup- 
pose we consider three important types of plane which 
may be drawn through the atoms of a cubic crystal, 
that is to say, planes perpendicular to (a) a cube edge, 
(b) a face diagonal, (c) a cube diagonal. If we draw 
a diagram or build a model we find readily that the 
relative spacings of the three sets are different in the 
different crystals, and this causes corresponding differ- 
ences in the angles of reflection of some standard line. 
Proceeding on these lines we come at once to a case 
of great importance. Rock-salt or sodium chloride 
and sylvine or potassium chloride have long been 
known to be of similar construction, though the nature 
of the construction has been uncertain until now. 
X-ray analysis shows, however, that the former crystal 
has the characteristics of the third class of lattice, 
and the latter of the first. Moreover, it appears that the 
elementary group or pattern contains the same number 
of atoms in each case. There is one obvious way of 
explaining these facts. Suppose that we place chlorine 
atoms at the corners of a cube and at the centres of 
the faces and sodium atoms at the middle points of 
the edges of the cube and at the cube centre, and take 
this to represent the structure of rock-salt. Potassium 
chloride may be derived from sodium chloride by re- 
placing the chlorine atoms of the structure by potass- 
ium. Now it appears from a number of mutually 
supporting indications that the contribution of an 
atom to the reflection effect depends on its atomic 
weight only. The atoms of potassium and chlorine 
are of very nearly the same weight, and can be looked 
on as equivalent. If this is done the structure of 
potassium chloride is in effect the simple cubic. But 
there is a great difference between the weight of 
sodium and chlorine, and the face-centred arrange- 
ment of the chlorine atoms taken separately gives its 
character to the whole rock-salt structure. All this 
agrees with experiment. But there is more. The 
presence of the sodium atoms amongst the chlorine, 
arranged as a matter of fact on a face-centred lattice 
of their own, modify the purely face-centred character 
of the spectra, and experiment shows that the modi- 
fication is exactly such as theory predicts. 
It is impossible in a short account to describe in 
full the work that has or can be done. Moreover, 
description is difficult without the aid of a plentiful 
supply of diagrams or models. It will be sufficient 
to say that the examination of the positions of the 
spectra, and especially of the relative intensities of 
the different orders give information which is gradu- 
ally being interpreted. The simpler crystals have 
already been analysed, and the structure of many of 
the more important cubic crystals is known. The 
more complex structure of the calcite series has been 
determined, and something has been discovered of the 
still more difficult structures of sulphur and of quartz. 
It must be remembered that in all these cases com- 
plete analysis requires not merely the determination 
of the lattice, but, what is far more difficult, the 
