EXPLORATION OF THE MINERAL WORLD BY X-RAYS 443 
strong bonds in the tetrahedral groups, and the relatively weak links which 
bind the chains together. 
These minerals are divided into two great classes, the pyroxenes and 
amphiboles. They are distinguished by their cleavage. ‘Fhe cleavages 
cross each other at about 90° in the pyroxenes, and 56° in the amphiboles. 
The reason for this difference was discovered by Warren, and his explanation 
is illustrated in Fig. 5. 
All pyroxenes are based on single chains of tetrahedra, all amphiboles 
on double chains, two chains being linked side by side to form a kind of 
tape. In the figure, we are looking at the chains end on, and it will be seen 
that the amphibole chains have a much more oblong cross-section. ‘The 
consequence is that the cleavage cracks, in avoiding cutting the chains, 
cross each other more obliquely in the amphiboles. 
(c) Mica.—Sheets of mica cleave with extreme ease. A sheet can be 
split again and again into thinner lamelle in an apparently endless way. 
The model of mica which I have here shows its structure, first analysed 
by Pauling. The main feature is a series of sheets of tetrahedra, each 
tetrahedron being linked by three corners to neighbours to form a hexagonal 
network. ‘Two such sheets are then linked together by Al, Mg, or Fe 
octahedra to form a composite sheet. It is these double sheets which are 
so immensely strong, and enable mica to be cleaved so easily, because 
each is only fastened to its neighbours on either side by the weak attractions 
of potassium atoms lying between them. 
The perfection of the mica cleavage is a truly remarkable phenomenon. 
It runs along the plane where the potassium atoms are situated, and may 
run for a centimetre or more without deviating from this plane by a single 
atom. We can show this, as Friedel first pointed out, by growing crystals 
of (NH,)I on the mica. The ammonium atoms in NH,I happen to have 
precisely the same arrangement as the K atoms in mica, both in shape and 
scale. In consequence, the NH,lI crystals all grow in parallel orientation 
on the mica. The grain of the pattern in. successive molecular sheets of 
mica points alternately to right and left of its symmetry plane, hence the 
little crystals of NH,I also point to right or to left depending on which 
type of sheet forms the top surface of the mica. If they all point the 
same way, the top sheet must be the same all over the surface. Fig. 6 
shows a mica surface in two steps, all the crystals pointing one way on 
one side and in the reverse direction on the other. 
The ‘grain’ is less marked in micas (biotite, phlogopite) with the 
formula K(Mg, Fe);(AISi;0,))(OH)., than in micas (muscovite) with the 
formula KAI,(A1Si,0,))(OH),; hence in the former case the NH,I crystals 
point indifferently in either direction. 
The mica-like sheets form the basis also of the clay minerals. ‘These 
are single sheets of tetrahedra with an active side of vertices and an inactive 
side of bases. ‘The clay minerals are little hexagonal spangles, a kind of 
mineral ‘ leaf-mould’ formed by the breakdown of other rocks. ‘Their 
curious chemical and physical properties, so important to the soil, are the 
result of their platy character. 
(d) Felspar——This is the most important mineral of the earth’s crust. 
We are familiar with it as a main constituent of granite. It is composed 
of Si and Al tetrahedra linked by every corner in every direction, a three- 
dimensioned latticework of tetrahedra. ‘The bulky atoms Na, K, Ca are 
immeshed in its interstices. 
We may only refer here to two of its interesting properties. In the 
first place, if we make a structure of tetrahedra linked by all their corners 
in this way, it is geometrically impossible to fit octahedra on to it. In 
