Mathematical Aspects of the Periodic Law

We review different studies of the Periodic Law and the set of chemical elements from a mathematical point of view. This discussion covers the first attempts made in the 19th century up to the present day. Mathematics employed to study the periodic system includes number theory, information theory, order theory, set theory and topology. Each theory used shows that it is possible to provide the Periodic Law with a mathematical structure. We also show that it is possible to study the chemical elements taking advantage of their phenomenological properties, and that it is not always necessary to reduce the concept of chemical elements to the quantum atomic concept to be able to find interpretations for the Periodic Law. Finally, a connection is noted between the lengths of the periods of the Periodic Law and the philosophical Pythagorean doctrine.Comment: 20 pages, PDF fil

Environmental controls on the petrology of a late holocene speleothem from Botswana with annual layers of aragonite and calcite

A carbonate stalagmite from Drotsky's Cave in northwestern Botswana consists of alternating layers of calcite and aragonite. Layer counts and radiocarbon ages indicate that the calcite-aragonite pairs are annual layers representing about 1500 years of deposition. The annual layering probably resulted from highly seasonal rainfall. Comparison of the uppermost layers of the speleothem with meteorological records shows that precipitation of CaCO3 in Drotsky's Cave was controlled by climate. Thickness of calcite layers correlates with rainfall, suggesting that calcite precipitation was largely dependent on the quantity of water supplied to the speleothem. By contrast, thickness of aragonite layers correlates with temperature, although variation in temperature cannot explain greater aragonite abundance on the sides of the speleothem compared to its center. Mg/Ca ratios in calcite layers increase upward to the bases of overlying aragonite layers, and analyses of cave waters suggest that fluid Mg/Ca ratios reach levels sufficient to cause aragonite precipitation. Increasing evaporation, which caused greater ionic strength and supersaturation, resultant increasing Mg/Ca ratios in the fluid, and perhaps increasing temperature probably combined to cause aragonite precipitation. Detailed petrographic analysis suggests that each annual cycle of CaCO3 precipitation began with relatively intense fluid flow, sometimes sufficient to dissolve some of the underlying aragonite before precipitation of calcite. Calcite precipitation under a thick fluid layer allowed euhedral crystals to form at first but thinning of the fluid to a film allowed only flatly terminated calcite crystals by season's end. As fluid flow diminished, increasing evaporation, increasing Mg/Ca ratios in the fluid, and perhaps increasing temperature combined to cause aragonite precipitation to begin, particularly on the sides of the speleothem. In some years, fluid flow diminished to the point that dust accumulated on aragonite surfaces before the onset of the next year's precipitation