AFM diagram

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).

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.

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. 

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. 

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. 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. 5. Schematic diagram of AFM setup for shear modulation measurement.

Figures 27-30 are diagrams of friction force versus load for different multilayer L-B hlms of the C5o-Pst hyperbranched polymer molecules obtained using AFM/FFM. The...

FIGURE 6.1 Diagram of AFM work principle. Reprinted with permission from Liu and... 

FIGURE 6.2 Diagrams of different AFM operating modes. (A) Contact mode and (B) dynamic mode for topographic imaging. (C) Force spectroscopy mode for interaction probing. Reprinted with permission from Liu and Wang (2010). 

Fig. 3. Total alkalis versus silica (TAS) and (b) AFM plot of Irvine and Baragar (1971), (c) modified Zr/Ti02-Nb/Y plot (Pearce, 1996) of Winchester and Floyd (1977), (d) Rock/chondrite-normalized REE diagram for rocks of amli-llica pluton and (e) rock/MORB-normalized spidergrams, (f) Th/Yb vsTa/Yb diagram.

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. 

Figure 15.6 is a schematic diagram of an AFM with an optical interferometer (Erlandsson et al., 1988). The lever is driven by a lever oscillator through a piezoelectric transducer. The detected force gradient F is compared with a reference value, to drive the z piezo through a controller. In addition to the vibrating lever method, the direct detection of repulsive atomic force through the deflection of the lever is also demonstrated. 

After the microfabricated cantilever was introduced (Albrecht and Quate, 1988), the optical beam deflection method was successfully applied in the repulsive-force mode, and atomic resolution on insulators as well as conductors has been achieved (Manne et ah, 1990 Meyer and Amer, 1990). A schematic diagram of the optical beam deflection AFM is shown in Fig. 15.8. An... 

AFM image of Cu adlayer on Au(lll) in copper perchlorate solution, showing close-packed structure with a rotation to the Au(lll) substrate, (b) Schematic of the incommensurate structure of the Cu adlayer. (c) ( J3 X y/3 )/ 30° structure of the Cu adlayer on Au(lll), in copper sulfate solution, (d) Schematic diagram of that structure. The open circle represents Au atom at the topmost layer, the hatched circle represents the Cu adatom. (Reproduced from Manne et al., 1991a, with permission.)... 

FIGURE 2.31 (a) STM image of a periodic array of C atoms on HOPG. (Courtesy of Prof. R.Reifenberger, Purdue University.) (b) Diagram of AFM. 

Figure 31-3 (A) Cryo atomic force (AFM) micrograph of molecules of the human immunoglobulin IgM. Courtesy of Zhifeng Shao, University of Virginia. (B) Schematic diagram. One-fifth of this structure is shown in greater detail in Fig. 31-4A. (C) Model based on earlier electron microscopic images. From Feinstein and Munn. 64(2...

Fig. 9. Block diagram of the frequency-modulation AFM feedback loop for constant amplitude control and frequency-shift measurement. Three physical observables are available frequency shift, damping signal, and (average) tunneling current.

Figure 5.17 Schematic diagram representing AFM imaging of partially-embedded starch granules.

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