The AFM diagram

It has been shown above that there are a variety of processes which can produce similar-looking trends on major element variation diagrams. It is important therefore to discover the extent to which these several processes might be distinguished from one another and identified. 

One approach is to try to calculate the composition of the materials added to or caleulatioru subtracted from a ma a and to quantify the amount of material involved. This may be done using an extract calculation, a device described in some detail by Cox era/. (1979). 

The amount of L2 is proportional to the distance X—Lj The amount of X is proportional to the distance Li-L2 

Addition-subtraction diagram for rocks A and B. The back-projection of trends for AI2O3, CaO, TiOj, NajO and K2O arc reduced to zero and converge at SiO 41.5 %. MgO and FeO values at SiO 41.5 % indicate the composition of the olivine removed from, rock A to produce composition B (after Cox et al., 1979). 

Ail extract calculation for a partial melting trend will not resolve into exact mineralogical constituents, whereas one based on a fractional crystallization trend should resolve exactly. Unfortunately these observations may not be as useful as they first appear, for Cox et al. (1979) point out that extract calculations are inexact when the minerals plotted show complex solid solution and that there are statistical uncertainties in fitting a straight line to a trend on a variation diagram. Thus in practice the differences between the effects of partial melting and fractional crystallization will be difficult to observe because of the imprecision of the method. 

---

Table 1.11a. Major-element compositions (%) used for the example of olivine fractionation in the AFM diagram of Figure 1.10.

Figure 1.10 The liquid line of descent upon olivine removal from basalt in the AFM diagram using equations (1.4.3) and (1.4.4). Olivine has a fixed composition (data from Tablel.lla). Each open circle indicates removal of 5 percent olivine.

A third consequence of percentage formation is that subcompositions, frequently used in variation diagrams such as the AFM diagram, do not reflect the variations present in the parent data-set. Aitchison (1986 — Table 3.1) shows that the correlation coefficient between pairs of variables varies substantially in subsets of a data-set and that there is no apparent pattern to the changes. In addition, subcompositions have variances which shqw different rank orderings from those in the parent data-set. For example, in the subset of data AFM (Na20+K20, MgO) the variances may be A > F > M, but in the parent data-set the variances may be F > A > M. 

Fig. 1. Schematic diagram illustrating the mechanical instability for (a) a weak spring (spring constant k) a distance D from the surface, experiencing an arbitrary surface force (after [19]) and (b) the experimentally observed force-distance curve relative to the AFM sample position (piezo displacement) for the same interaction.

Fig. 2.50. Plot of amphibole compositions on the Al203-Fe0 -Mg0 (AFM) diagram, together with the compositional range of amphibole in the hydrothermally metasomatized basalt from midocean ridges (Shinozuka et al., 1999).

By also using the LASIP procedure, grafted PS-b-PI and PBd-b-PS block copolymers have been prepared (Fig. 7) [72]. Using silane and thiol-DPE initiators, polymerization was carried out on the SiOx and Au surface by sequential addition of monomers. Typically, after allowing this first reaction to reach completion, the second monomer was added to the living anion, and polymerization of the second block was allowed to proceed. The polymerization was also investigated by SPS [80], AFM, ellipsometry, FT-IR, and XPS. The schematic diagram for the reaction on Au surfaces and the formation of the block copolymers is shown in Fig. 6. The results are summarized in Table 2. 

No detailed studies on the CaO-AljOj-SiOj-HjO system at ordinary temperatures have been reported, but, based largely on considerations of solubility products, Dron (D23) suggested the main features of a probable metastable equilibrium diagram, a modified form of which is shown in Fig. 6.7. The diagram indicates the metastable coexistence of CH, C-S-H and C4AH19, and that stratlingite cannot coexist with CH. In cement pastes, the AFm and AFt phases appear to accommodate some silicon the extents of these substitutions, and the related question of the scale on which the hydrated phases are mixed, are considered in Sections 7.2 and 7.3. 

On an AFM diagram (Fig. 16) all the minerals from iron-formations proper fall into a narrow and clearly defined field, while the rock-forming minerals of the associated iron-rich shales from BIF of Superior type (chamosite, ripidolite and other chlorites, garnets and some biotites) form another broader and less clear-cut field. These two fields do not overlap, which indicates the isochemical character of metamorphism and the limited mobility of the main rock-forming minerals, at least within individual layers and bands of the iron-formations and shales. The chemical composition of stilpnomelane occupies an intermediate position both in iron content and in alumina content. However, a high content of potassium (up to 2.2% K2O), an element not typical of most BIF, is necessary for the formation of this mica. 

Most audiors use oxide wt % when plotting data on an AFM diagram but in a few cases atomic proportions are used and it is not always clear which method has been adopted. The shape of the trend is amilar in each case but the position of the atomic proportions plot is shifted away from the Fe apex relative to the position of the oxide plot for the same data (see Barker, 1978). 

Barker (1978) advocated plotting mineral compositions on an AFM diagram in addition to rock compositions to assess mineralogical control of magmatic processes. However, this approach can only be semiquantitadve since the lever rule.(see below), which works well in bivariate plots, cannot be applied because of the disparate proportions of the compositions before projection. Thus AFM diagrams cannot be used in petrogenetic studies to extract quantitative information about... 

Fig. 3 Germination of phosphate crystals AFM results showing adsorbed colloidal particles on aluminum after treatment in an activation bath these particles are believed to be the nucleation sites for crystal growth, as shown in the schematic diagram. (After [10].)...

Following the expressions in Eqs. (4.86), (4.87), (4.88) and (4.89) it is obvious that by manipulating the wire radius one can control the phase diagram (e.g. EE, AFM and FM phase transition temperatures) and corresponding spontaneous polarization and magnetization in the EuTiOs nanowires. 

Schematic diagram of the AFM showing the auxiliary STM used for detecting movement of the atomic force cantilever. Source Reprinted with permission from Woodruff DP, Delchar TA, Modern Techniques of Surface Science, Cambridge University Press, Cambridge, 460, 1994. Copyright 1994, Cambridge University Press.

Fig. 4 shows the schematic diagram of the setup of SMM. A DC-biased AC voltage Ft =Fbc +Fac sincot is applied to a conductive AFM tip, which is normally held 20-30 nm away from the sample surface by monitoring the oscillating electric force on the tip with the second harmonic frequency 2co. 

---