Shear modulus, heat capacity, viscosity and structural relaxation time of Na2O–Al2O3–SiO2 and Na2O–Fe2O3–Al2O3–SiO2 melts

The configurational heat capacity, shear modulus and shear viscosity of a series of Na₂O–Fe₂O₃–Al₂O₃–SiO₂ melts have been determined as a function of composition. A change in composition dependence of each of the physical properties is observed as Na₂O/(Na₂O + Al₂O₃) is decreased, and the peralkaline melts become peraluminous and a new charge-balanced Al-structure appears in the melts. Of special interest are the frequency dependent (1 mHz–1 Hz) measurements of the shear modulus. These forced oscillation measurements determine the lifetimes of Si–O bonds and Na–O bonds in the melt. The lifetime of the Al–O bonds could not, however, be resolved from the mechanical spectrum. Therefore, it appears that the lifetime of Al–O bonds in these melts is similar to that of Si–O bonds with the Al–O relaxation peak being subsumed by the Si–O relaxation peak. The appearance of a new Al-structure in the peraluminous melts also cannot be resolved from the mechanical spectra, although a change in elastic shear modulus is determined as a function of composition. The structural shear-relaxation time of some of these melts is not that which is predicted by the Maxwell equation, but up to 1.5 orders of magnitude faster. Although the configurational heat capacity, density and shear modulus of the melts show a change in trend as a function of composition at the boundary between peralkaline and peraluminous, the deviation in relaxation time from the Maxwell equation occurs in the peralkaline regime. The measured relaxation times for both the very peralkaline melts and the peraluminous melts are identical with the calculated Maxwell relaxation time. As the Maxwell equation was created to describe the timescale of flow of a mono-structure material, a deviation from the prediction would indicate that the structure of the melt is too complex to be described by this simple flow equation. One possibility is that Al-rich channels form and then disappear with decreasing Si/Al, and that the flow is dominated by the lifetime of Si–O bonds in the Al-poor peralkaline melts, and by the lifetime of Al–O bonds in the relatively Si-poor peralkaline and peraluminous melts with a complex flow mechanism occurring in the mid-compositions. This anomalous deviation from the calculated relaxation time appears to be independent of the change in structure expected to occur at the peralkaline/peraluminous boundary due to the lack of charge-balancing cations for the Al-tetrahedra.     

Development of Local IDF-formula Using Controlled Random Search Method for Global Optimization

The aim of the study is to present the effective and relatively simple empirical approach to rainfall intensity-duration-frequency-formulas development, based on Controlled Random Search (CRS) for global optimization. The approach is mainly dedicated to the cases in which the commonly used IDF-relationships do not provide satisfactory fit between simulations and observations, and more complex formulas with higher number of parameters are advisable. Precipitation data from Gdańsk gauge station were analyzed as the example, with use of peak-overthreshold method and Chomicz scale for rainfall intensity. General forms of the IDF-function were chosen and the parameter calibration with use of CRS algorithm was developed. The compliance of the obtained IDFformulas with precipitation data and the efficiency of the algorithm were analyzed. The study confirmed the proposed empirical approach may be an interesting alternative for probabilistic ones, especially when IDFrelationship has more complex form and precipitation data do not match “typical” hydrological distributions.