Harker diagrams

Major elements of Vico rocks display scattered distributions on Harker diagrams (Fig. 4.12). However, rocks from different periods of activity define more coherent groups, which suggest the occurrence of different magma types in the volcanic systems at various stages of activity. For... 

In the discussion of single and multiple isomorphous replacement (called SIR and MIR respectively), we have to this point tacitly assumed all things to be ideal. In reality this is never the case, certainly not in X-ray crystallography. In terms of Harker diagrams this means that for virtually all Fhki, the circles for the first heavy atom derivative and the second heavy atom derivative never really intersect the native circle at a common point. In the best of circumstances they come close, but for many hkl they don t. Figure 8.5c represents a more typical case, and Figure 8.5dhow we have traditionally dealt with it (for details, see Dickerson, 1968 Blundell and Johnson, 1976 Blow and Crick, 1959 Drenth, 1999). 

In practice, Harker diagrams, like those described in Figure 8.5 are not actually constructed. Instead, the probability of any phase on the circle being correct, given the structure amplitudes of two or more derivatives and the calculated structure factors of the heavy atoms, is computed at increments around the circle, say at every 5 or 10 degrees. Blow and Crick (1958) showed that the probablility formulation, given certain assumptions regarding the distribution of errors, for any reflection is... 

As with the isomorphous replacement method, the locations x, y, z in the unit cell of the anomalous scatterers must first be determined by Patterson techniques or by direct methods. Patterson maps are computed in this case using the anomalous differences Fi,u — F-h-k-i-Constructions similar to the Harker diagram can again be utilized, though probability-based mathematical equivalents are generally used in their stead. 

As with MIR, we do not actually draw Harker diagrams but compute and combine probability distributions. Phase determination by anomalous dispersion has a probability form very similar to that for MIR ... 

Figure 9.10 The centres for the phasing circles in this Harker diagram are based on the Friedel equivalent pair at the white line (or just on the short A side of the edge) and one equivalent for the minimum off (i.e. two wavelengths in total). The centres are well separated and non-collinear and the unique phase is well resolved. From Flelliwell (1984) with the permission of the Institute of Physics.

Figure 8.1. Univariant curves for the dissociation of calcite, magnesite, and dolomite in system CaO-MgO-CC>2. Compatibility diagrams are shown for each divariant area. F=CC>2, C=calcite, D=dolomite, M=magnesite, L=lime, P=periclase. (After Harker and Tuttle, 1955.)...

Figure 3. IS Harker variation diagrams for quartz-rich sandstone suites from eastern Australia (after...

---