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A further note On the presentation of chemical analyses of minerals1

Published online by Cambridge University Press:  14 March 2018

Max H. Hey
Max H. Hey*
Affiliation:
Department of Mineralogy, British Museum (Natural History).
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Extract

Suppose that in the study of a mineral we have determined the cell-dimensions and the density, and made a ehemienl analysis. From these we can readily calculate the empirical unit-cell contents, which will usually approach integral values and so suggest a probable formula.

But the calculated empirical unit-cell contents, being based on chemical and physical data subjeet to experimental error, will be subjeet to numerous sources of error, and in any serious study it is very desirable to have some rough idea of the probable limits of error. Unfortunately, this is a matter of considerable complexity, but the following suggestions may be of assistance, though they will doubtless be considerably improved on.

Type
Research Article
Information
Mineralogical magazine and journal of the Mineralogical Society , Volume 30 , Issue 227 , December 1954 , pp. 481 - 497
Copyright
Copyright © 1954, The Mineralogical Society

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References

page 481 note 1 Hey, M.H., Min. Mag., 1939. vol. 25, p. 402 CrossRefGoogle Scholar.

page 481 note 2 The specific gravity must, of course, be corrected for all known impurities, including hygrosct)pic water; and due allowance must be made for uncertainties in the amount of impurity and in the uniformity of its distribution when assessing the probable error in the specific gravity, δD.

page 482 note 1 It may be of interest to consider shortly the addition of errors. Where errors are not independent, we can usually say definitely that a positive error in one factor, say 3a, will be associated with a positive error in another, 3b, and a negative error in a third, 3c, and so on; and the total error is clearly obtained by simple addition with due regard to sign, (3a + 3b —3c….). But when the errors are independent, we do not know how their signs are to be associated—-a positive error Sa may be associated with a positive 3b, or equally likely with a negative 3b. If two positive or two negative errors are associated, the total error will be but if one is positive and the other negative, the total will be Since we do not know the distribution of signs, our best estimate of the probable error will be somewhere between these values, and it can be shown that the best estimate will in fact be

page 483 note 1 A slightly different arrangement is, of course, necessary with minerals such as halides, sulphides, &c. ‘

page 483 note 2 Here and subsequently, the symbol δp is used for an error arising from the errors in the physicM data; for errors arising from the chemical analysis alone the symbol 3c is used, and for the total error from both sources, δ.

page 484 note 1 IIillebrand-Lundelt, Applied inorganic analysis. New York and London, 1929. pp. 874.887, 2nd edn. 1953, pp. 3.6; compare Sehleeht, W.G., Anal. Chem. 1951, vol. 23, p. 1568 Google Scholar. H.W. Fairbairn et M., Bull. U.S. Geol. Survey no. 980,1951; It. Fairbairn, W. and SchMrer, J.F., Amer. Min., 1952. vol. 37, p. 744.Google Scholar Groves, A.W., Silicate analysis, 2nd edn., London, 1951, pp. 224-236.Google Scholar

page 486 note 1 Strictly speaking, the errors added in finding E(metals) will not all be truly independent, since the total error in all the oxides is necessarily (100 — S±δi);and 8ihas already been incorporated in δF.

page 487 note 1 The assumption that the errors of separation are independent is only likely to be serious when two of the oxides concerned in any particular separation, wrongly taken as independent, differ widely in oxygen percentage-—e.g. Yt20. and Ce203.

page 487 note 2 The percentages of oxygen in the principal mineral-forming oxides are listed in table V.

page 492 note 1 More exactly if his less than about 5% and S+hdoes not depart seriously from 100%, the simpler expression is adequate. It is perhaps appropriate to mention here that the density correction for x% of an impurity of density dis where Dcis the corrected and Dothe observed.

page 497 note 1 If the frequencies of observations in the ranges A—0-50 to .4 —0-40, A —0-40 to A —0-30,…, A+O40 to .4 + 0-50 are all equal, then a random sample of nobservations will have a probability pof giving a sum wA ± A /10, where pis the coefficient of G(x)