The Bond Valence Topological Model I: The bond-valence topological map of tourmaline from Forshammar, Sweden

Abstract The bond-valence topological graph represents a segment of the structure that can be chosen based on the studied phenomena. In bond-valence topological graphs, atoms or structural sites are vertices, and bonds are edges of graphs. Bond-valence topological graphs are weighted; therefore, bond-valence or bond-length values are attached to every edge of the graph. The bond-valence topological model (BVTM) is the specific structural fragment represented as a bond-valence topological graph with attached values of bond valences or lengths. Bond-valence topological models can be used to create a bond-valence topological map of real mineral structures. This map is a composite of BVTM added together, which, as a result, should have identical properties to the real structure. Tourmaline from Forshammar, Sweden, with the composition of X(Na0.707Ca0.045K0.008) Y,Z(Al6.554Mg2.192Fe0.174Ti0.024Mn0.004Zn0.002) TSi6O18 (BBO3)3V,W(OH3.464O0.507F0.028Cl0.001) was chosen for the bond-valence topological mapping because of the very low Fe and Mn content and relatively simple composition. The composition of tourmaline from Forshammar can be expressed as the sum of different ordered and disordered components: dravite, oxy-dravite, uvite, magnesio-foitite,magnesio-dutrowite, schorl and schorl-dravite. Two factors were used for testing them: (1) long-range structural stability and (2) local bond-valence stability. Due to long-range stability, ordered dravite, uvite, and magnesio-dutrowite can be considered unstable because they are positioned clearly in the region of unstable structures. Considering local bond-valence stability, ordered components including dravite, schorl-dravite, schorl, oxy-dravite, and magnesio-dutrowite can be considered unstable due to the large difference in the sum of bond-valence sum at various sites compared to their formal valence. The final topographic map of the bond valence showed that the examined tourmaline from Forshammar does not consist of ordered, but only of disordered components of these tourmaline end members, except ordered magnesio-foitite.