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Some years ago, in an extended paper upon the constitution of the silicates,' I proposed a formula for tourmaline which seemed to satisfy all known conditions. Recently Penfield and Foote? bave offered still another interpretation of the analyses, and support their views with a considerable weight of argument. The appearance of their paper has led me to rescrutinize the evidence more in detail than previously, and the result bas been to modify my formulæ in some particulars while retaining them in their general form.

According to Penfield and Foote all tourmaline may be represented as salts of the alumino-borosilicic acid Hj Al,B.Si,021, in which two hydroxyls are permanently linked to boron, leaving an available valency or basicity of nine. In my formulæ all tourmalines are derived from the similar acid 1/4A12B,Sic031, with all of the hydrogen atoms replaceable by bases. Upon bringing the two acids to the common basis of six silicon atoms, they compare as follows: Penfield and Foote

H164Al4xBjSi60.31%
Clarke

H 4A1,B:Sig021
Replacing aluminum by hydrogen, in order to show the ultimate acids,
these expressions become
Penfield and Foote...

H30B351,0314
Clarke

HB:Si;0.31 The small difference between the empirical formulæ is thus made evident, and it hardly amounts to more than the uncertainties in the analyses. In fact, the trustworthy analyses of tourmaline give ratios lying between and beyond both extremes, as the following formulæ, computed from Riggs's data, show: In these expressions fluorine has been assumed equivalent to hydroxyl. Pierrepont, black...

H29.47B2.4:Si:0:30.83
Paris, black.

H3073B2.6 Si.031.36
Stony Point, black.

H:30.23B3.02S16031.66 Auburn, colorless.

H29.26B2 77Si60.20.78 Brazil, red

H307,B2... Si.,031.646 Gouverneur, brown.

H28.36B24;Si 0:30.61 Hamburg, brown

H:30.X B3.06SiO32.14

2 Am. Jour. Sci., 4th series, Vol. VII, 1899, p. 97.

1 Bul). U. S. Geol. Survey No. 125, 1895.

The two analyses by Penfield and Foote, however, conform sharply to their formula, thus:

De Kalb, white...
Haddam Neck, green

H29.85B3.0;Si, 0.31.48
H.29. B3.0;Si-031.

The Gouverneur and Hamburg tourmalines represent the extreme range of variation; a variation which is too large to be safely set aside as due to analytical errors or to impurities in the material analyzed. Some of the formulæ approximate to mine, some to that of Penfield and Foote, and hence it seems probable that neither formula, without some qualification, can safely be taken as final.

In order to be satisfactory, a constitutional formula must fulfill several conditions. First, it must adequately express the composition of the compound in question, covering all of its variations. Second, it must be readily applicable to the full discussion of analyses, so that the dif. ferent isomorphous salts which are commingled in a mineral species can be separately identified and given reasonable expressions. Finally, it should indicate the relations between a species and the other min. erals with which it is allied, or into which it commonly alters. A formula can be fully adopted only when all of these conditions are satisfied. The third condition, which relates to function, is equally important with the other two.

With the tourmalines, the micas seem to be most nearly akin. In each group we have to consider comminglings of isomorphous molecules, and when tourmaline alters, a mica is commonly the product of the reaction. In composition, also, the two groups show an apparent parallelism. With the lithia mica, lepidolite, lithia tourmalines occur; with muscovite and biotite, the common iron tourmaline is associated; and the magnesian tourmalines, which show the minimum of alumiva in their composition, are similarly allied to phlogopite. This relationship, if it is real, should be suggested in the formulæ assigned to the several species.

To the commoner micas a simple series of formulæ can be easily given, thus:

Muscovite
Biotite
Phlogopite

Al2(SiO4)3KH,
Al(SO4)3Mg:KH,
Al (SiO4)3Mg:KH2;

and to these types, or mixtures of them, most micas are referable. The variations and exceptions have been considered elsewhere, and need not be discussed here.

With these fundamental molecules the corresponding salts of the tourmaline acid H,9B2SigO31, or H,,AlsBySię031 are structurally corre. lated. The subjoined formulæ are sufficient to make this point clear; and to render the splitting up of tourmaline, its alteration into mica, somewhat intelligible.

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In the acid, two hydrogen atoms are united with the orthoboric group, and twelve with the orthosilicate portion of the nucleus. Hence, to avoid repetition of the structural expression, the formula may be condensed into a linear form, as follows:

Al(Si04).(BO,), . BO3H, . H 2,

and this is applicable to the discussion of the analyses. For example, Riggs's analysis of the black magnesium tourmaline from Pierrepont, New York, corresponds to the following molecular mixture:

13. Al:(Si04)6(BO3)2 · BO:Ca . Mg H,
7. Al;(SiO4)ri(B02), . BO,Mg . Mg4H,
2. Al;(SiO4).( BO,)2 , B03NaAl Na H,

Comparing this with the analysis, and reducing the latter by union of like bases and recalculation to 100 per cent, we bave

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The result is evidently satisfactory. In dealing with titanium I have followed Penfield, regarding it as really Ti,O, and equivalent to alumina. The fluorine is treated as replacing hydroxyl, and is, there. fore, united with the water. It is possible, however, that fluorive may sometimes replace the group BO2, an equivalency which is strongly indicated in the cappelenite group of minerals.

The brown tourmaline from Gouverneur, New York, as analyzed by Riggs, also reduces to a similar mixture of molecules, and its composi. tion may be written thus:

5. Al(SiO4).(BO.): . BO3Ca . Mg,H1,
3. Als(Si04)6(BO3)2 . BO3Mg . Mg+H4,

2. Als(Si04)6(BO2)2 . BO3NaH . Al Na H4;
and the comparison between analysis and theory is as follows:

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By consolidating lime with magnesia the expressions for both tourmalines might be simplified; but in other cases this would not be warrauted.

In some tourmalines calcium seems rather to replace sodium, or else the group Nał, a probability which will appear later.

In these two tourmalines the theoretical silicon-oxygen ratio Si031 is assumed, in accordance with my original formula. We may now consider the cases in which that ratio is exceeded, with more or less approach to the formula proposed by Penfield and Foote. This condition is easily satisfied by regarding one of the component salts of tour. inaline as slightly basic, containing the bivalent group = Al-0-H or =Al-F as an essential factor. With this assumption, which recog. nizes the equivalency of hydroxyl and fluorine, the analyses reduce to the general type indicated in the two preceding examples. For instance, the white tourmaline from De Kalb, New York, has the following composition:

10. Als(SiO2)6(BO,)2 . BO3(A10H). Mg4H4.
20. Al(SiO2)6(BO3)2 · B03Ca . Mg,H4.

3. Als(Si04)6(BO3)2 . BO:3Naz. Al.Naz. For comparison the analyses by Penfield and Foote and by Riggs are available. In this case the minute quantities of titanium are ignored.

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The dark brown tourmalines from Orford, New Hampshire, and
Monroe, Connecticut, as analyzed by Riggs, also reduced to similar
form, and approximate to the mixture

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Here the divergence between the composition as found and as
calculated is evidently due to the low determinations of boric acid in
the analyses. Still the comparison is close.

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