682 
as to the nature of the equilibrium which determines 
the arrangement of the atoms in a crystalline element 
is of too simple a character. In 1912 Laue showed 
that on passing a narrow pencil of X-rays through a 
crystal plate the emergent rays were capable of form- 
ing a regular, geometrical pattern of spots upon a 
photographic plate placed to receive the emergent 
beam; the pattern of spots thus produced was in 
agreement with the symmetry of the direction in the 
crystal plate in which the beam was passed. This 
discovery was developed and very considerably ex- 
tended by Bragg, who was able to show that an X-ray 
beam undergoes reflection at the surface of a crystal 
plate. The interpretation of the novel results indicates 
that the homogeneous crystal structure acts upon the 
X-ray beam much as a solid diffraction grating might 
be expected to do, and that each deflected transmitted 
ray is a reflection from one set of parallel planes of 
atoms in the crystal, 
The experimental and theoretical study of the X-ray 
effects has been prosecuted with brilliant success by 
W. H. and W. L. Bragg, the result being that a 
method is now available which makes it possible to 
determine, with very great probability, the actual 
arrangement of the constituent atoms in crystal struc- 
ture. Sufficient time has not yet elapsed for the 
thorough exploitation of this new and fruitful field of 
research, but many data are available already for com- 
parison with the conclusions drawn from the con- 
sideration of the equilibria possible in crystal struc- 
tures; it is found that the two methods do not at 
once lead to identical conclusions. Thus, in accord- 
ance with the first method, the structure of the 
diamond would be indicated at some slight modifica- 
tion of the cubic closest-packed assemblage of equal 
spheres, the modification consisting in the main 
of a grouping of sets of atoms which leads to 
the partial cubic symmetry which the diamond 
apparently exhibits; one particular mode of group- 
ing which leads to the required result consists in 
supposing the carbon atoms formed into sets of four, 
tetrahedrally arranged, two oppositely orientated sets 
of such tetrahedral groups being distinguished. If 
each of these tetrahedral groups be replaced by a 
single point situated at the group-centre, the struc- 
ture which the Bragg experiments indicate for the 
diamond is obtained. 
The simple geometrical relationship which thus 
exists between the two suggested structures for dia- 
mond raises a suspicion that the particular form in 
which the assumption of equilibrium is stated re- 
quires qualification: that possibly the domain of the 
carbon atom when packed with others, as in the dia- 
mond, does not become converted into a rhombic 
dodecahedron, but into a polyhedron roughly tetra- 
hedral in shape. 
Leaving this particular point for the moment and 
turning again to Table I., it is seen that the binary 
compounds, like the elements, also tend to crystallise 
in the cubic or hexagonal systems; the axial ratios of 
the hexagonal binary compounds approximate very 
closely to the value, a: c=1: 1-6330, calculated for the 
closest-packed, hexagonal assemblage of equal spheres. 
The values ot c/a for all the known cases are: 
BeO — 1-6365, ZnO—1-6077, ZnS—1-6350, CdS — 1-6218, 
and AgI—1-6392. 
Assemblages representing the crystal structures of 
the cubic and hexagonal binary compounds may be 
derived from. the two closest-packed assemblages of 
similar spheres already described, by homogeneously 
replacing one half of the spheres by different ones of 
the same size. The degrees of symmetry presented 
by these arrangements are not so high as those of the 
unsubstituted assemblages; this is in accordance with 
NON2330, VOURG.|| 
NATURE 
[AUGUST 27, I914 
| the fact that the crystals themselves have not the full 
symmetry of the holohedral cubic or hexagonal system. 
Thus, on warming a hexagonal crystal of silver iodide, 
one end of the principal axis c becomes positively, 
and the other negatively, electrified. The axis c is 
thus a polar axis, having different properties at its 
two ends; this axis will be found to be polar in the 
model. Again, when hexagonal silver iodide is heated 
to 145°, it changes its crystalline form and becomes 
cubic; this so-called polymorphous change can be 
imitated in the hexagonal model by slightly shifting 
each pair of layers of spheres in the assemblage. 
A very close agreement thus exists between the 
properties of the assemblages deduced and the ob- 
served properties of those binary compounds which 
crystallise in the cubic or hexagonal systems. The 
remaining 12 per cent. or so are not, in general, 
pseudo-cubic or pseudo-hexagonal, and it is noteworthy 
that they comprise those binary compounds in which 
the two component elements have not the same lowest 
valency; amongst them are the substances of the 
compositions, PbO, FeAs, HgO, AsS, and CuO. 
On comparing the structures of the binary crystal- 
line compounds indicated by the foregoing method of 
consideration with those deduced by the Braggs, dis- 
crepancies are again obvious; again, however, the 
former assemblage is converted into the latter by re- 
placing groups of spheres by their group-centres. The 
relation thus rendered apparent is once more a sug- 
gestion that the type of equilibrium conditions origin- 
ally assumed is too simple. It will be seen, however, 
that the Bragg results furnish a proof of one part of 
the assumption made concerning equilibrium, namely, 
that each component atom operates separately; the 
discussion of the properties of crystals on the assump- 
tion that the crystal structure may be regarded as 
built up of similar mass-points, due to the mathe- 
matical physicists of the last century, therefore 1e- 
quires to be reopened. Thus, the Bragg structure of 
rock-salt is represented by dividing space into equal 
cubes by three sets of parallel planes and replacing 
the cube corners encountered along the directions of 
the cube edges by chlorine and sodium atoms alter- 
nately; each chlorine atom then has six sodium atoms 
as its nearest and equally distant neighbours. With 
which of the latter the one chlorine atom is associated 
to form a molecule of sodium chloride is not apparent 
from the nature of the crystal structure. 
Time need not be now occupied with the further 
discussion of the crystalline structure of simple sub- 
stances; until the discovery of the X-ray effects thus 
briefly described, no direct method of determining 
those structures was available, and, in view of the 
paucity of the experimental data, only the possibilities 
of arrangement could be considered in the light of 
the Barlow-Pope mode of treatment. It will, how- 
ever, be useful to review some of the results which 
accrue from this latter method of regarding the 
problem of crystal structure in general. : 
Taking the general standpoint, which is also in 
accordance with the Bragg results, that each com- 
ponent atom of a crystalline structure has a separate 
spacial existence, and premising that the atomic 
domains are close-packed in the assemblage in accord- 
ance with some particular type of equilibrium law, 
it becomes obvious that crystalline structure presents 
a volume problem. The law arrived at after a careful 
investigation of the subject—the so-called law of 
valency volumes—states that in a crystalline structure, 
the component atoms occupy domains approximately 
proportional in volume to the numbers representing 
the fundamental valencies of the elements concerned; 
the student of the subject of molecular volumes will 
hardly accept this conclusion without convincing evi- 
