Isomorphism

It is to be noted frequently that the results of a mineral analysis do not agree with the theoretical composition of the mineral as calculated from its formula. Further, it often happens that the analysis of different specimens of the same mineral will show marked variations in the proportions of the different elements present. If the material analyzed was pure and the analysis accurately made, these variations are commonly to be explained by the principle of isomorphism (derived from two Greek words meaning “same” and “form”). To make clear what is meant by this term, it will be best to consider some illustrative examples. Sphalerite, for instance, is a mineral which shows in its different specimens a wide range in color, from white through brown to black.

With a corresponding variation in composition. In column I is given an analysis of white sphalerite from Franklin Furnace, N. J., in column II is given an analysis of a brown sphalerite from Roxbury Conn., and in column III that of a black sphalerite from Felsobánya, Rumania.

It will be noted that in the three analyses there is a progressive increase in the percentages of iron present and a corresponding decrease in the amount of zinc. It would appear as if the iron had replaced a portion of the zinc in the mineral and was playing he same part as the zinc in the molecule. Further, if the atomic ratios are derived from each analysis by the method described in the preceding division, it will be found that in analyses II and III the series of numbers do not show any rational relations to each other. But, if the numbers derived in each case from the percentages of the different metals present are combined, their sum will equal the number derived from the percentage of the sulfur. In other words, the number of atoms of zinc plus sulfur. The formula of sphalerite could therefore be written R”S, where R” equals chiefly zinc, with smaller amounts of iron and other metals. Another way of expressing the same thing would be (Zn, Fe)S. In this case the iron is said to be isomorphism with the zinc, since it has the power to replace the zinc in the mineral in varying proportions without changing its molecular structure or crystal form.

The garnets form a series of minerals with the same crystallization and general physical properties, but show quite a wide variations in chemical composition. Consider the following analysis of an almandine garnet:

Percentages   Molecular weights   Ratio SiO2 = 35.92 ÷ 60.4 = 0.594 Al2O3 = 19.18 ÷ 102.2 = 0.187 Fe2O3 = 4.92 ÷ 159.8 = 0.030 FeO = 29.47 ÷ 71.9 = 0.409 MnO = 4.80 ÷ 71.0 = 0.067 MgO = 3.70 ÷ 40.36 = 0.091 CaO = 2.38 ÷ 56.1 = 0.042     100.37

It is a silicate containing chiefly ferrous and aluminium oxides but with smaller amounts of manganese, magnesium, calcium and ferric oxides. If the ratio of the series of oxides to each other in the molecule is obtained, it is seen that it is not a rational one. But if the ratio numbers of the similar oxides are combined, that is, the number from the al2O3 with that from the Fe2O3, and that from the FeO with those from the MnO, MgO and CaO, it will be found that the relationship of the different groups of radicals can be expressed as SiO2 : Al2O3 + Fe2O3 : FeO + MnO + mgO +Ca O = 3 : 1 : 3.  From this it is seen that some of the possible Al2O3 has been replaced by isomorphous Fe2O3, and that a part of the FeO has been replaced by the isomorphism oxides of MnO, MgO and CaO . The formula for this garnet might be written, therefore, as 3R”O.1R2”’O3Sio2 or R3”R2”’(SiO4)3, in which R” = Fe, Mn, Mg and Ca, and R”’ = Al and Fe.