VECTOR REPRESENTATION OF SOME MINERAL COMPOSITIONS IN THE AENIGMATITEGROUP, WITH SPECIAL REFERENCE TO HOGTUVAITE

Aenigmatite-group compositions conform to the general formula A2B6T6O2 0, where [8]A cations are Na and Ca, [6]B are Fe2+, Fe3+, Mg, Al, Cr, Ti, and Sb5+, and [4)T are Si, Al, B, and Be in named end-members. The se include the sodic minerals aenigmatite, krinovite, and wilkinsonite , and the calcic minerals rhonite, serendibite, dorrite, welshite, and hogtuvaite (a new Be-bearing end-member: Grauch et al. 1994). Graphic al representation of the compositional relations among these phases is made possible by the vector method, which has recently been applied t o a number of other mineral groups. The fundamental principle is that a chemical displacement such as CaAl(NaSi)-1, having both direction an d magnitude, can be thought of as a vector of unit length and arbitrar y orientation. Compositional relations are simplified by condensing on vectors of isovalent substitution, such as Fe3+Al-1 and Fe+Mg-1. In v ector diagrams, bound vectors are attached to a point and show the rel ations among basis and derived vectors. The corresponding free vectors generate the accessible compositional range (e.g., triangle, quadrila teral, or pentagon), starting from an initial formula or composition ( additive component of J.B. Thompson, Jr.). When this approach is used on the aenigmatite group, the compositions of the main minerals are de rived from that of aenigmatite by application of the basis vectors CaA l(NaSi)-1, Al2(MgTi)-1, and Al2(MgSi)-1. Hogtuvaite is derived by BeSi Al-2 acting on rhonite, and welshite by AlSbBe(MgTiSi)-1 acting on hog tuvaite. Other theoretical end-members can be generated by the vector method; in the aenigmatite group, many are probably unstable with rega rd to a mixture of clinopyroxene plus olivine or spinel, especially if they lack Ti or excess Al.