Evolution of the isotopic composition of carbon and oxygen in a calcite precipitating H2O-CO2-CaCO3 solution and the related isotopic composition of calcite in stalagmites

The isotopic composition of carbon and oxygen in a calcite precipitating CO₂-H₂O-CaCO₃ solution is preserved in the calcite precipitated. For the interpretation of isotopic proxies from stalagmites knowledge of the evolution of δ¹³C and δ¹⁸O in the solution during precipitation is required. A system of differential equations is presented from which this evolution can be derived. Both, irreversible loss of carbon and oxygen from the solution with precipitation time τ and exchange of oxygen in the carbonates with the oxygen in the water with exchange time T are considered. For carbon, where no exchange is active, a modified equation of Rayleigh-distillation is found, which takes into account that precipitation stops at c_eq, the saturation concentration of DIC with respect to calcite, and that c_eq as well as the precipitation time τ is slightly different for the heavy and the light isotope. This, however, requires introducing a new parameter γ = (A_eq/B_eq)/(A₀/B₀), which has to be determined experimentally. (A_eq/B_eq) is the isotopic ratio for the heavy (A) and the light isotope (B) at both chemical and isotopic equilibrium and (A₀/B₀) is the initial isotopic ratio of the solution. In the case of oxygen, where exchange is present, the isotopic shifts are reduced with increasing values of the precipitation time τ. For τ ? T the solution stays in isotopic equilibrium with the oxygen in the water during the entire time in which precipitation is active. The isotopic ratios in a calcite precipitating solution R(t)/R₀ = (1 + δ(t)/1000) for carbon are plotted versus those of oxygen. R₀ is the isotopic ratio at time t = 0, when precipitation starts and δ(t) the isotopic shift in the solution after time t. These show positive correlations for the first 50% of calcite, which can precipitate. Their slopes increase with increasing values of τ and they closely resemble Hendy-tests performed along growth layers of stalagmites. Our results show that stalagmites, which grow by high supply of water with drip times less than 50 s, exhibit positive correlations between δ¹³C and δ¹⁸O along a growth layer. But in spite of this the isotopic composition of oxygen in the solution at the apex is in isotopic equilibrium with the oxygen in the water, and therefore also that of calcite deposited at the apex.