Locally dense finite lattice packings of spheres

We consider finite packings of unit-balls in Euclidean 3-spaceE ³ where the centres of the balls are the lattice points of a lattice polyhedronP of a given latticeL ³E³. In particular we show that the facets ofP induced by densest sublattices ofL ³ are not too close to the next parallel layers of centres of balls. We further show that the Dirichlet-Voronoi-cells are comparatively small in this direction. The paper was stimulated by the fact that real crystals in general grow slowly in the directions normal to these dense facets.The results support, to some extent, the hypothesis that real crystals grow preferably such that they need little volume, i.e that they are locally dense.Dedicated to A. Florian on the occasion of this 60th birthday     

Two isoperimetric inequalities with lattice constraints

Two isoperimetric inequalities with lattice constraints for arbitrary lattices in the euclidean plane are proved. They generalize previous results by Hadwiger et al. for the special lattice ^d (but all dimensionsd) to general lattices.     

A thermogravimetric study of the alunites of sodium, potassium and ammonium

Thermogravimetry in tandem with mass spectrometry has been used to characterise the thermal decomposition of synthetic alunites of potassium, sodium and ammonium. Three mechanisms of decomposition are observed (a) dehydration, (b) dehydroxylation and (c) desulphation. The thermal decomposition of the three alunites is different. For NH₄-alunite, an additional process of de-ammoniation is observed which occurs simultaneously with dehydration. Dehydroxylation takes place in a series of four steps. De-sulphation occurs for K-alunite at 680 °C in a single step in comparison with Na and NH₄ alunites where de-sulphation is observed in a series of four steps. The temperature of desulphation is cation dependent. The thermal decomposition is not completed until around 800 °C.