APPENDIX

It is impossible to determine the amount of Fe³⁺ and H₂O in amphiboles by microprobe analysis. Therefore, for calculation of amphibole formula, it is assumed, in general, that amphibole contains O₂₂(OH,F,Cl)₂ instead of 24 (O, OH, F, Cl) or 23 oxygen (Robinson et al., 1982).

The amount of Fe³⁺ can be arbitrarily calculated with several different assumptions, which include the assumption of all Fe as Fe²⁺ (all-Fe²⁺ method), adjustments of cations to 13 except Ca + Na + K (13eCNK method) and to 15 except Na + K (15eNK method), or the method proposed by Holland and Blundy (1994) (H&B method). Thus, we cannot uniquely calculate such important parameters for the terminology of amphibole (e.g., Leake et al., 1997) as Fe³⁺, Al^IV, Al^VI, and A-site occupancy. This indicates the difficulty in comparing data from different literature in which the formula of amphiboles was calculated with different methods.

For the discussion of amphibole chemistry in this paper, we first calculated the cation numbers on a 23-oxygen basis. Then, we recalculated Fe³⁺ with the 13eCNK, 15eNK, and H&B methods. We discarded the results (two of 187 analyses) if either Fe²⁺ or Fe³⁺ were calculated to be negative or if Ca was allocated to either the M3 site or A-site. After these treatments, we compared the results by the different methods to choose appropriate formula by the following procedures.

Figure AF1 is (Na + K)_A-site vs. Al^IV plots calculated by 13eCNK, 15eNK, and H&B methods. Also plotted are (Na + K)_A-site calculated with the all-Fe²⁺ method. The plot of (Na + K)_A-site with the all-Fe²⁺ method is the narrowest and falls very close to the pargasite-tremolite join. On the other hand, the results of 13eCNK are strongly scattered and show a shift toward lower Na + K and/or higher Al^IV directions. The results of 15eNK are plotted in a rather close position to the (Na + K)_A-site calculated with the all-Fe²⁺ method, and those of the H&B method are plotted in the middle between the all-Fe²⁺/15eNK results and 13eCNK results.

Cosca et al. (1991) compared the results provided by the several methods with amphiboles from amphibolites and granulites of the Grenville Orogen of Ontario. Their examinations indicate that the 13eCNK method provided the best results. Following their results, we evaluated our data with the assumption that the 13eCNK method provides the best formula. If so, the wide scatter of the 13eCNK results should not be accidental but meaningful. If this is true, the apparent tight distribution of (Na + K)_A-site calculated with the all-Fe²⁺ method to the pargasite-tremolite join would have to be accidentally given by incomplete microprobe analyses or inappropriate corrections. We do not think this is the case. The tight distribution of the (Na + K)_A-site data to the pargasite-tremolite tie line is more likely to be true than the wide and nonsystematically scattered results of the 13eCNK method. Figure AF2 shows Fe³⁺/(Fe²⁺ + Fe³⁺) vs. Mg# (100 x Mg/[Mg + Fe²⁺ + Fe³⁺]) and Fe³⁺/(Fe²⁺ + Fe³⁺) vs. Si. At a given Mg# and/or Si values, plots of Fe³⁺/(Fe²⁺ + Fe³⁺) ratios calculated with the 13eCNK method are strongly scattered. It is not easy to explain these large dispersions. It is possible that there was pervasive but incomplete later-stage oxidation or an analytical problem, but it is most likely that the dispersion is an artifact of the correction scheme.

Based on these examinations, we have concluded that the 13eCNK method does not yield good results for our purposes in this research. The order of priority we took is 15eNK, all-Fe²⁺, H&B, and then 13eCNK methods. All the data accepted here are those calculated with the 15eNK (39 analyses) or all-Fe²⁺ methods (146 analyses). These procedures resulted in rather low Fe³⁺/(Fe²⁺ + Fe³⁺) ratios. Average, standard deviation, maximum, and minimum values of the Fe³⁺/(Fe²⁺ + Fe³⁺) ratio of 39 analyses calculated using the 15eNK method were 0.0439, 0.0326, 0.1315, and 0.0001, respectively.