A new method to calculate end-member thermodynamic properties of minerals from their constituent polyhedra II: heat capacity, compressibility and thermal expansion

Thermodynamic calculations in petrology are generally performed at pressures and temperatures beyond the standard state conditions. Accurate prediction of mineral equilibria therefore requires knowledge of the heat capacity, thermal expansion and compressibility for the minerals involved. Unfortunately, such data are not always available. In this contribution we present a data set to estimate the heat capacity, thermal expansion and compressibility of mineral end‐members from their constituent polyhedra, based on the premise that the thermodynamic properties of minerals can be described by a linear combination of the fractional properties of their constituents. As such, only the crystallography of the phase of interest needs to be known. This approach is especially powerful for hypothetical mineral end‐members and for minerals, for which the experimental determination of their thermodynamic properties is difficult. The data set consists of the properties for 35 polyhedra in the system K–Na–Ca–Li–Be–Mg–Mn–Fe–Co–Ni–Zn–Al–Ti–Si–H, determined by multiple linear regression analysis on a data set of 111 published end‐member thermodynamic properties. The large number of polyhedra determined allows calculation of a much larger variety of phases than was previously possible, and the choice of constituents together with the large number of thermodynamic input data results in estimates with associated uncertainty of generally <5%. The quality of the data appears to be sufficiently accurate for thermodynamic modelling as demonstrated by modelling the stability of margarite in the CASH system and the position of the talc–staurolite–chloritoid–pyrope absent invariant point in the KMASH system. In both cases, our results overlap within error with published equivalents.     

Calibration of modelled mixing patterns in loess grain-size distributions: an example from the north-eastern margin of the Tibetan Plateau, China

Genetically meaningful decomposition (unmixing) of sediment grain-size distributions is accomplished with the end-member modelling algorithm. Unmixing of the loess grain-size distributions of a Late Quaternary loess–palaeosol succession from the north-eastern Tibetan Plateau indicates that the loess is a mixture of three end-members representing very fine sandy, coarse silty and medium silty loess. The unmixing approach potentially enables the unravelling of sediment fluxes from multiple dust sources, opening the way to significant advances in palaeoclimatic reconstructions from loess grain-size distribution data. However, as laser-diffraction size analysis is a volume-based technique, the proportional contributions of the modelled end-members might deviate (significantly) from weight proportions. Hence, calibration of the end-member volume proportions to weight proportions must be established before one can calculate the source-specific dust fluxes. This paper reports the findings of a sediment-mixing experiment which enables calibration of the modelled mixing patterns established for the Tibetan loess–palaeosol succession.     

A new method to calculate end-member thermodynamic properties of minerals from their constituent polyhedra I: enthalpy, entropy and molar volume

The thermodynamic properties of silicate minerals can be described as a linear combination of the fractional properties of their constituent polyhedra. In contrast, given the thermodynamic properties of these polyhedra, the thermodynamic properties of minerals can be estimated, where only the crystallography of the mineral needs to be known. Such estimates are especially powerful for hypothetical mineral end‐members or for minerals where experimental determination of their thermodynamic properties is difficult. In this contribution the fractional enthalpy, entropy and molar volume for 35 polyhedra have been determined using weighted multiple linear regression analysis on a data set of published mineral thermodynamic properties. The large number of polyhedra determined, allows calculation of a much larger variety of phases than was previously possible and the larger set of minerals used provides more confident fractional properties. The OH‐bearing minerals have been described by partial and total hydroxide coordinated components, which gives better results than previous models and precludes the need of a S–V term to improve estimates of entropy. However, the fractional thermodynamic properties only give adequate results for silicate minerals and double oxides, and should therefore not be used to estimate the properties of other minerals. The thermodynamic properties of ‘new’ minerals are calculated from a linear stoichiometric combination of their constituent polyhedra, resulting in estimates generally with associated uncertainty of <5%. The quality of such data appears to be of sufficient accuracy for thermodynamic modelling as shown for meta‐bauxites from the Alps and the Aegean, where the effect of Zn on the P–T stability of staurolite can be both qualitatively and quantitatively reproduced.     

Impact of water diversion on the morphological development of the Lower Yellow River

In this paper we carry out a theoretical analysis based on the general one-dimensional morphodynamic model for rivers in order to show how the morphological equilibrium of a fiver is influenced by water and sediment diversion/supply along the river. The results of the analysis show that large scale water diversions, like those along the Lower Yellow River, can cause the development of a convex riverbed profile in the long-term. Deposition will take place along the whole reach of the river, with an increasing deposition depth from downstream to upstream. The slope of the river bed increases from upstream to downstream. Furthermore, an analysis on the morphological time scale shows that this development in the Lower Yellow River will take a time period on the order of decades to centuries. The results of the analysis have been compared with observations in the Lower Yellow River. Since the second half of the 1980＇s large scale water diversions from the Yellow River have been taking place. The observations show that this has indeed led to significant sedimentation along the river.