STOICHIOMETRIC CALCULATIONS ON THE BASIS OF CRYSTAL LATTICES' ALEXANDER SILVERMAN Uniuersity of Pittsburgh, Pittsburgh, Pennsylvania
I N A paper on "The Silica-Alumina Relationship in G l a s ~ , "SaBord ~ and Silverman have shown that aluminum may enter the crystal lattice in fourfold coordination, replacing silicon. Boron, phosphorus, and other elements may be substituted for silicon similarly. In quartz andother minerals, silicon atoms are usually a t the centers of tetrahedra with an oxygen atom a t each of the four corners. The specialist in X-ray studies of crystal structure may refer to the "silicon ion" and the "oxide ion." Whether the silicon or its substituted aluminum unit is an atom or an ion, one atomic weight of silicon is displaced by one atomic weight of aluminum and, therefore, the old stoichiometric calculations based on the common valences of the respective elements should be abandoned in such cases. Alumina in the white sapphire is in sixfold coordination and has the normal valence of three, but in glasses and certain minerals it may have fourfold coordination. Structure of substances determines the kind of substitution-calculation which should be made, and the chemist should broaden his interpretation by including structure studies. In a glass the S i 0 tetrahedra ~ are not arranged as in crystals, but there is a random scattering of these tetrahedra, with holes here and there into which sodium ions or calcium ions may slip as in the production of a sodalime glass. Now, suppose that an aluminum atom replaces a silicon atom in one tetrahedron. The replacement is atom for atom, or ion for ion in the terms of the X-ray specialist. Although the substitution is atomic
(26.97 parts by weight of aluminum for 28.06 parts by weight of silicon), a normally trivalent ion has replaced . a tetravalent one in the lattice. If a sodium ion was located in one adjacent hole and a calcium ion in another, i t is now possible to substitute a second calcium ion for the sodium ion to make up for the unit of valence lost by the displaced silicon ion. In other words, while the substitution in one spot may be atom for atom and not equivalent, the total valence of the system remains unaltered. Although not of particular interest to the average chemist, the example cited accounts for the possibility of producing higher lime-containing sodalime glasses, when some alumina is substituted for silica in the glass batch, or mixture of raw materials. Isomorphons substitution, independent of valence, is not new to the chemist. He knows that arsenic, a Group V element, may replace sulfur, a Group VI element, in sulfides. Perhaps he is less familiar with some mineralogical fads which X-ray studies have cleared. Let us consider the mineral albite (soda feldspar), known to most of us by the formula NaAISisOs, and rewrite this NaSi(AISiZOs). By substituting one aluminum for one silicon (valence change 4 to 3), we can replace the sodium by a calcium (valence change 1 to 2) and get CaAL(AISizOs), better known as anorthite with the formula CaA12Siz08. Similar changes may be effected in potash feldspar by replacing potassium by barium when an aluminum atom replaces a silicon.' It is not the purposeof this paper to furnish an elaborate treatise. A principle is presented: Interested chemists can find numerous examples of "substituted" 'Contribution No. 441 from the Department of Chemistry. minerals in the literature on mineralogy and the atomic University of Pittsburgh. Paper presented before the Division structure of minerals.
of Chemical Education at the 102nd meeting of the A. C . S., Atlantic City, New Jersey, September 11. 1941. Paper presented before the Glass Division, American Ceramic Society, Conneaut. Pennsylvania. September 13, 1941.
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a B~nnoo."Atomic structure of minerals," Cornell University Press, Ithaca, N. Y., 1937, p. 230.
