page 402 note 1 Often, most of the oxides shown in an analysis were actually weighed as such. This has one advantage not often realized; it is not necessary to know the atomic weights used by the analyst in order to make use of the analysis. This may seem unimportant, but is not always so; thus in any analysis of an antimony mineral, Sb will probably be reported as the element after weighing as Sb₂S₃, and the percentage Sb reported will be appreciably different according as 120·2 or 121·76 is used as the atomic weight of Sb. A note on the weighing-forms and atomic weights employed is certainly desirable in any analysis having claims to high accuracy.

page 403 note 1 Where the impurity is adsorbed water, it is not really certain what density should be assumed for the water; however, a value of 1 is not likely to introduce appreciable error.

page 403 note 2 Most mineral analyses are primarily presented in a mixed form, mainly as oxides, but with some negative ions (F′, Cl′, S″), and ‘less 0 for’ these latter. To deduce the atomic ratio for oxygen a formal calculation of the percentage of oxygen is unnecessary; the molecular ratios of the several oxides are multiplied by the number of oxygen atoms in each oxide added, and the atomic ratio for any oxygen subtracted ‘for F′, Cl′, &c.’ subtracted from the sum.

page 403 note 3 These relations may seem too obvious to require stating, but instances could be cited from the recent literature where corrections for impurities have been wholly neglected and conversations have shown that the way in which a correction may be effected is often not understood.

page 403 note 4 Hillebrand, W. F. and Lundell, G. E. F., Applied inorganic analysis. New York, 1929.Google Scholar

page 403 note 5 Larsen, E. S., Amer. Journ. Sci., 1938, ser. 5, vol. 35, p. 94. [M.A. 7–183.]CrossRefGoogle Scholar

page 404 note 1 It must, of course, be remembered that these last, affecting the factor F, will necessarily affect all constituents equally or in the same direction, and cannot affect their distribution.

page 404 note 2 The low density makes the factor F low, but because water contains a larger percentage of oxygen than any other compound the oxygen percentage will be high, and as a general rule the latter effect will preponderate; as an illustration we may calculate the effect of 1 per cent adsorbed water on the apparent cell contents of quartz and of litharge: Si 2·951, O 6·002, H 0·199 (in place of Si 3, O 6); Pb 1·962, O 2·208, H 0·491 (in place of Pb 2, O 2) ; the effect is, of course, more marked the smaller the percentage of oxygen in the substance.

page 405 note 1 It is most unscientific for chemical analysis and optical, X-ray, or other physical data to be made on separate samples without explicit statement of the fact, and a careful check of the uniformity of the material studied is always desirable.

page 406 note 1 The electrical conductivity of some ionic crystals which show no excess of either component is probably due to vacant positions in both anion and cation lattices ; proof of this suggestion appears to be still incomplete, and the proportion of vacancies called for is very small (up to 0·02 per cent. in calcite).

page 406 note 2 The actual integer to be accepted may be decided on the basis of approximate unit-cell contents, based on an approximate density and cell-sides, or by extension from an isomorphous or isostructural compound.

page 406 note 3 Thus in evidence of the substitution of C for Ca in carbonate-apatites, it was shown that no basis of calculation of the analyses could be found requiring less of this substitution than 0·2 atom per unit cell. (This vol., p. 400.)

page 406 note 4 Recent work has shown that even so typically ionic a mineral as rock-salt may contain an excess of sodium ions, balanced only by free electrons; such excess is usually far less than the probable accuracy of the majority of analyses, but clearly an ionic balance need not always be quite exact.

page 407 note 1 The possibility that an ion may be replaced by one of a different charge without the creation of a lattice vacancy must not, however, be forgotten; neutrality could be maintained by interstitially accommodated ions or by a simultaneous parallel substitution among the ions of opposite sign.

page 407 note 2 Another possibility is that sulphur atoms may enter some of the metal positions, or vice versa. In any particular sulphide or similar mineral, calculations to an assumed basis can do no more than demonstrate variability and departure from a constant simple metal-sulphur ratio; the manner of this variation can only be profitably discussed on a basis of empirical cell contents, at least in the present state of our knowledge of such structures.

page 407 note 3 The exception is with minerals where the determination of the state of oxidation of such elements as Fe, Mn, or V is liable to be inaccurate from the nature of the mineral (e.g. staurolite). For such minerals Σ(cations) = const, will often be a more satisfactory mode of presentation

page 409 note 1 Except in this form of calculation, anionic and cationic charges or valencies must necessarily balance in analyses which are presented mainly in the form of oxides with an oxygen deduction for any ion reported; failure to balance simply indicates mistakes in calculation. In analyses of ionic minerals reported in terms of ions, failure of the positive and negative ions to balance may occur, and indicates inaccuracy of the analysis (lattice defect in the crystal is usually too minute to detect). Analyses of ‘atomic’ minerals, such as sulphides, rarely balance exactly.

page 409 note 2 The errors will balance only if both the constituents involved are weighed in the forms they are reported in or have the same conversion factor.

page 409 note 3 If the several other constituents are denoted by B _p O _q , their molecular weights by b, and the percentages present by y, oxygen will be low if Σy(n/am–q/bp) is positive.

page 410 note 1 The calculated density will be low if the mean equivalent weight of the oxides is less than that of the anion which is in deficit.

page 410 note 2 It is not always realized that the ‘ferrous iron’ determination is really no more than a determination of the amount of oxygen necessary to convert all the oxides present to that state of oxidation which is stable under the conditions of the determination. The allocation of the whole of the observed reducing power to FeO, or to FeO+V₂O₃, is often purely an arbitrary assumption, necessary because we have no means at present of detecting and determining other lower oxides such as Ti₂O₃, UO₂, or Cu₂O, or higher oxides such as Mn₂O₃ or Co₂O₃, which might conceivably be present. The term ‘net state of oxidation’ includes, of course, ‘available oxygen’ determinations in peroxidized minerals such as piedmontite, manganite, or minium.