2.2 The notion of compositional space

There are large number of possible substitutions in the silicate minerals. Of these only a handful are important in as much as they describe the great proportion of the compositional range of the common rock forming silicates. These important substitutions occur in a wide range of mineral groups: for example, the substitution described above:


which is so common that it is given the special name Tschermak's substitution is important in pyroxenes, amphiboles and micas (three of the most common rock forming mineral groups). If we designate the standard compositions (or key comnponent) of the pyroxene (Mgvi2Siiv2O6), amphibole (Mgvi7Siiv8O22(OH)2) and mica (Kxii2Mgvi6Aliv2Siiv6O20OH4) groups by P, A and M respectively, then we can draw maps which show the compositional effect of the Tschermak substitution on each of these standard compostions:


Thekey component for each group has been awarded a point in compositional space upon which the Tschermak substitution works as a vector. Clearly, the extent of possible Tschermaks substitution in any mineral group is limited by the initial composition upon which it operates. Thus we cannot perform the Tschermak substitution more than twice in real pyroxenes before we run out of Si and Mg:


(It turns out that structural constraints limit the maximum Tschermaks substitution to much less than 1.0 in natural pyroxenes). We can continue to build up our picture of compositional space by adding other common substitutions, for example:


The updated maps of the compositional space for the three groups now look like this:

In these maps the axes bound a region of potential compositional variation in each of the groups. For example, the majority of common trioctahedral micas (or biotites) are defined by this exact mapping, shown below.

In reality the composition realm of many mineral groups, particularly the amphiboles, needs more than two substitutions acting on the key component. Although this is clearly difficult to draw on a 2-dimensional paper, the principles remain the same (the only difference between 3-dimensions and 4-dimensions is in our mind which is used to thinking about things in terms of geographical space. Compositional space can have many more dimensions than the 3-dimensions of our earthly geographical space). However, an important aspect of using substitutions in this way is that substitutions are common to many mineral groups, the only thing that differs is the starting composition (or key component) on which the substitutions operate. Moreover, a quick inspection of the starting composition should allow you, with some knowledge of the coordination number and valency of the various cations, to determine which substitutions are likely to operate in that particular group.

A baffling array of mineral names have been awarded to various points in the compositional space of the compositionally complex mineral groups such as the pyroxenes, amphiboles and micas. Most of these names were awarded before there was a clear idea of the nature of the substitution mechanisms which operated in these groups, and consequently there does not seem to be much rhyme or reason to these names. In the following weeks we will introduce the names of some important points in the compositional spaces of each of these mineral groups (and expect you to remember some of them). However, more importantly we hope (by presenting mineral compositional space as a series of common substitutions which operate on a single key component )that you will be able to predict the compositional realm of the mineral groups once you have learnt the one key component for each of the groups.