Mineralogy

Ionic crystals’ structures are all based on a fundamental group of atoms (or, more accurately, ions) consisting of one silicon atom surrounded by four oxygens - the Si0₄-group, which is the “unit brick” of silicate structure. The oxygens are arranged at the four corners of a regular tetrahedron, with the silicon at its centre. Such groups can occur separately, or may be linked together in a number of ways by sharing oxygen atoms with adjacent groups, thus forming more complex structures. Metallic ions, such as Mg, Fe, Ca, etc., can be accommodated in the interstices of the structure; which of these will enter a given structure depends chiefly on their size and, to a lesser degree, on their ionic charge (or valency), matters which will now be discussed.

Ionic Radii

It is convenient to think of ions as spheres having a definite radius. When two ions are brought close together, a force of repulsion between them sets in abruptly when they are a certain distance apart and resists any closer approach. The distance between their centers is then taken as the sum of the radii of the two ions. In this way, the ions are treated as spheres in contact, and by various methods their radii can be measured. The following list of ionic radii is due largely to the work of V. M. Goldschmidt, J. A. Wasastjerna, and others; it is arranged so that the columns correspond to the groups of the Periodic Table, and ionic charge is indicated at the top of each column.

Notice particularly the large size of the oxygen ion (1.32) in comparison with relatively small positive ions (cations) such as Si, AI, Mg, and Fe. It is the spacing of the oxygens, which are closely packed together in a silicate crystal that largely controls the scale of the structure; the smaller cations are situated in the interstices between the oxygens. Other negative ions (anions), e.g. F-, Cl- -, S- -, are similarly large.

The hydrogen ion is exceptional in being extremely small; when bound to an atom of oxygen it becomes embedded, as it were, in the oxygen, and the resulting (OH)-ion has about the same radius as that of oxygen. We can think of the H-ion as a centre of positive charge without dimensions.

When one or more electrons are removed from a group of atoms bound together by homopolar bonds, a charged radicle is formed. Thus the carbonate ion, C0₃- -, has one carbon atom to which are attached three evenly spaced oxygen atoms, and it carries a double negative charge. The sulphate ion, 504- -, has four oxygens arranged at the corners of a tetrahedron around a central atom of sulphur. The shapes of these ions affect the type of crystal structure of their compounds. Thus in calcite the Ca-ions are situated at the corners of a rhombohedron and the CO₃-ions, represented by triangles in the figure, are arranged with their centres midway along the rhombohedral edges and lie in horizontal planes. Physical and optical properties parallel and perpendicular to these planes differ greatly.

Co-ordination

In ionic crystals each positive ion (cation) is surrounded by a number of negative ions, at a distance fixed by the sum of their radii. The number of negative ions around anyone cation is called the co-ordination number, and is determined by the ratio of the radii of the two kinds of ion. Thus in sodium chloride, the relative sizes of the sodium and chlorine ions are such that every sodium is surrounded by six chlorines arranged at the corners of a regular octahedron, a grouping known as 6-fold co-ordination. The metals aluminium, iron, magnesium and titanium, among others, are also found in 6-fold co-ordination.In silicate minerals, silicon always has four oxygen atoms arranged around it at the corners of a tetrahedron; the space left between the four oxygens packed together thus is just sufficient to accommodate the small silicon ion. Other cations which are found in 4-fold co-ordination are beryllium and zinc. An important feature of many silicate structures is that aluminium, already mentioned as having 6-fold coordination, can also play the role of silicon (because its ionic radius is only a little larger) and thus occur in 4-fold co-ordination. Aluminium is, because of its size, a borderline case and can occur in either 4- or 6- co-ordination.

Groups with co-ordination numbers from 7 to 12 are formed by large cations such as Na, Ca, K, Sr, Ba, and Zr, but these larger groups tend to be less regular than the smaller groups. The tetrahedral and octahedral groups (4 and 6- co-ordination) are very regular in their form, and in building crystals they are put together so that neighboring groups share corners, edges, or faces, and are thus linked together so as to build up the pattern.

Previously, crystals were defined as bodies bounded by usually flat surfaces, arranged in a regular manner expressing the internal arrangement of the atoms. The study of the arrangement of atoms within a crystal, that is, of atomic structure, has been made possible in recent years by new methods of analysis in which X-rays are employed. This advance dates from the discovery by Laué and others, in 1912, of the diffraction of X-rays by crystals. The first analysis was made in 1913 by W. L. Bragg, on crystals of sodium chloride (common salt).

X-rays are somewhat like light waves but have a much shorter wave-length (see p. 149), this being comparable to the distances between atoms in a crystalline solid. When a beam of X-rays falls on a crystal, it is scattered or diffracted by the layers of atoms within the crystal, in the same way that light waves are diffracted by an optical grating. In making an analysis of a crystal structure, the diffracted X-rays are allowed to fall on a photographic plate, and the resulting photograph shows a series of spots or lines which form a more or less symmetrical pattern. From measurements made on the photograph, the arrangement of the atoms in the crystal can be deduced and also the distances between them. Distances are expressed in Angstrom units; one Angstrom (Ã…)=10-8 em. The several methods of taking X-ray photographs of crystals or of powdered minerals cannot be discussed here, but the principle is broadly that outlined above; details can be found in books on the subject. We are more concerned with the results of X-ray analysis, as these have thrown a flood of light on the structure of crystals, and in particular of minerals, and have confirmed the classes of symmetry worked out in the past by crystallographers from a study of external form, as previously. X-ray analysis has been especially helpful in connection with the big group of mineral silicates, and in this field the work of many investigators has given us a considerable, though not yet complete, knowledge of their structures.

The Unit Cell

Every crystal consists of certain atoms or groups of atoms arranged in a three-dimensional pattern, which is repeated throughout the crystal. The smallest complete unit of pattern is called the unit cell, and the whole pattern is formed by stacking unit cells together. To take a simple example, in crystals of sodium chloride (NaCI) the atoms of N a and CI are arranged at the corners of a series of cubes, as shown in Fig. 68. The unit cell of sodium chloride contains four atoms of Na and four of CI, whose arrangement is exactly similar to that in every other unit cell of the substance. It is to be noted that the number of atoms in the unit cell of a particular mineral is not necessarily the same as in its formula, but is usually some simple multiple; for NaCI this multiple is four. Verify by counting the atoms in Fig. 68, allowing for some atoms belonging half to the unit cell shown there and half to adjacent cells. The array of points in space at which the pattern repeats is called the lattice.

Atomic Bonds

There are four main kinds of bond which hold together the atoms in different crystal structures; they are known respectively as the ionic or polar bond, the homopolar or co-valent bond, the metallic bond, and the residual or van de Waals bond. Correspondingly, crystals may be divided into four classes, each characterized mainly by one of the above four types of bond. The van der Waals bond is very weak in character and is present in all crystals. Nearly all the common minerals have ionic bonding.