Bavenite is an orthorhombic calcium beryllium aluminosilicate, a ≈ 23.2, b ≈ 5.0, c ≈ 19.4 Å, V ≈ 2250 Å3, Z = 4, that crystallizes in the space group Cmcm. The crystal structures of 24 bavenite samples from various localities worldwide were refined to R1 values from 2.4 to 7.5% based on ∼1330 unique reflections collected with Mo-Kα X-radiation on a Bruker P4 CCD single-crystal diffractometer. The composition of each crystal was determined by electron microprobe analysis. There is extensive solid-solution in bavenite according to O(2)OH– + T(4)Si4+ + T(3)Be2+ ⇌ O(2)O2– + T(4)Al3+ + T(3)Si4+, such that the general formula may be written Ca4BexSi9Al4–xO28–x(OH)x, where x ranges from 2.00 to ∼3.00 a.p.f.u. Small amounts of additional Be may be incorporated into bavenite via the substitution T(3)Be + O(2)OH– + Na + T(4)Si2 ⇌ T(3)Si + O(2)O2– + Ca + T(4)Al2. Local (short-range) bond-valence considerations indicate that Short-Range Order (SRO) should be extensive in the bavenite structure, and this is confirmed by Fourier Transform Infrared (FTIR) spectroscopy in the principal OH-stretching region and by 27Al Magic Angle Spinning Nuclear Magnetic Resonance (MAS NMR) spectroscopy. Short-range bond-valence considerations indicate that the T(3)–T(4)–T(3)–T(4) rings of the framework can incorporate any short-range arrangement of cations consonant with their site populations [T(3) = Be,Si; T(4) = Si,Al], and 27Al MAS NMR spectroscopy confirms this, showing the presence of the local clusters T(3)Be–T(4)Al–T(3)Be, T(3)Si–T(4)Al–T(3)Be and T(3)Si–T(4)Al–T(3)Si. Incorporation of Be at the T(3) site is accompanied by local replacement of O2– by (OH)– at the O(2) site and hydrogen bonding to the adjacent O(3) anion; the latter promotes Be → Si substitution at the T(3) tetrahedron adjacent in the b direction. T(3)–T(4)–T(3)–T(4) rings link in the c direction through a T(3)–(1)–(3) linkage [T(1) = Si]. Local bond-valence considerations show that occupancy of both T(3) tetrahedra by Be violates the valence-sum rule, and that the linkage T(3)Be–T(1)Si–T(3)Si provides the constraint whereby Be does not exceed 3 a.p.f.u. in bavenite when incorporated via the substitution O(2)OH– + T(4)Si4+ + T(3)Be2+ ⇌ O(2)O2– + T(4)Al3+ + T(3)Si4+.

The hyalotekite group has been approved by the Commission on New Minerals, Nomenclature and Classification of the International Mineralogical Association (memorandum 57–SM/16). The general formula of the minerals of the hyalotekite group may be written as: A2B2M2[Si8T4O28]W where A = Ba2+, Pb2+ or K+; B = Ba2+, Pb2+ or K+; M = Ca2+, Y3+ or REE3+; T = Si4+, B3+ or Be2+; and W = F– or □ (where REE = rare-earth elements and □ = vacancy).

Four minerals are currently known in this group: hyalotekite, Ba4Ca2[Si8B2(SiB)O28]F, triclinic, I$\bar 1$; khvorovite, Pb2+4Ca2[Si8B2(SiB)O28]F, triclinic I$\bar 1$; kapitsaite-(Y), Ba4(YCa)[Si8B2B2O28]F, triclinic, I$\bar 1$; and itsiite Ba4Ca2[Si8B4O28]□, tetragonal, I$\bar 4$2m.

We explore the possible end-member compositions within this group by conflating the properties of an end-member with the stoichiometry imposed by the bond topology of the hyalotekite structure-type and the crystal-chemical properties of its known constituents. There are two high-coordination sites in the hyalotekite structure, A and B, and occupancy of each of these sites can be determined only by crystal-structure refinement. If these two sites are considered together, there are 19 end-member compositions of the triclinic structure and six end-member compositions of the tetragonal structure involving A and B = Ba2+, Pb2+, K+; M = Ca2+, Y3+, REE3+; and T = Si4+, B3+, Be2+. There is the possibility for many other hyalotekite-group minerals, and two potential new minerals have been identified from data in the literature.

The main difficulty in the quantitative mineral analysis of rocks is connected with the variable nature of the mineral species. In the present paper a combined method (and a corresponding computer program) is proposed, which practically overcomes this difficulty. This method is based on linear equations, which are a combination of the chemical mass-balance equations with those of the quantitative X-ray diffractometry, and can perform (completely or partly) both the quantification and the chemical characterization of the minerals on several rock samples simultaneously, demanding only easily accessible initial information, such as: (i) major element (oxide) compositions for the samples; (ii) qualitative mineral composition of the samples; (iii) X-ray intensities for one or few nonoverlapped reflections of the crystalline minerals (not necessarily of all): (iv) some characteristic data for the phases (i.e., chemical composition data), if these are accurately known. Where it is possible the minerals may be expressed via end members. The samples may contain amorphous phases and/or phases without X-ray data. From the general case some very simple partial cases are derived, demanding less initial information. This method has the following advantages over the previous ones of similar philosophy: (i) drastic reduction of the number of required samples; (ii) sufficiency of equations for any analytical problem; (iii) possibility of performing partial analysis when a complete one is impossible; (iv) possibility of using the same end member in more than one solid solution. Analysis examples are given.