Carlin-type gold deposits in Qinling and some related problems

The sediment-hosted disseminated gold deposits in the Oinling region are of sedimentation-slight-metamorphic origin superimposed by hydrothermal reworking at moderate-low temperatures and are well comparable with the typical Carlin gold deposits in the United States.In view of the confusing concept concerning the “sediment-hosted”and “Carlin-type” gold deposits,the authors propose that the term“sediment-hosted gold deposit”should be used in a broad sense which encompasses at least the four subtypes,i.e.,the Carlin type,the metamorphic fine clastic type,the hydrothermal sedimentary type and the vein type.In oter words,the “Carlin-type”should not be used as a synonym for “sediment-hosted”but is recommended as a subtype under the general category of “sediment-hosted gold deposits”     

Dodging alligators,rattlesnakes, and backyard docks: a political ecology of sweetgrass basket-making and conservation in the South Carolina Lowcountry,USA

There is growing recognition among political ecologists of the need to examine shifting natural resource regimes and their effects on livelihoods in “First World” places. This emerging literature has variously examined the “Third World within,” the persistence of “subsistence activities” in the “First World,” and the “reterritorialization” of land tenure and access. However, much of this work has tended to focus on traditional extractive industries in the American West, indigenous claims to lands and resources in the U.S. and Canada, and non-timber resources on public lands. In contrast, we use a case study of African-American sweetgrass basket-makers, associated with the Gullah culture, in South Carolina’s lowcountry to examine the ways in which ongoing amenity-driven residential development is fundamentally reshaping resource access on private lands. Historically, basket-makers harvested the materials (primarily sweetgrass or Mulenbergia filipes) needed for their culturally important art form from accessible, rural, and privately held tracts of land in close proximity to their communities, but development pressures and changes in resident interpretation of property rights has decreased access to basket-making resources. The case is particularly illuminating, as it examines the emergence of ‘conservation subdivisions’ in the region and raises important questions about what “rural uses” and users are being conserved through responses to exurban, suburban, and urban development in formerly rural areas.     

Landslide Hazard Zonation using Remote Sensing and GIS: a case study of Dikrong river basin, Arunachal Pradesh, India

Landslides are among the most costly and damaging natural hazards in mountainous regions, triggered mainly under the influence of earthquakes and/or rainfall. In the present study, Landslide Hazard Zonation (LHZ) of Dikrong river basin of Arunachal Pradesh was carried out using Remote Sensing and Geographic Information System (GIS). Various thematic layers namely slope, photo-lineament buffer, thrust buffer, relative relief map, geology and land use / land cover map were generated using remote sensing data and GIS. The weighting-rating system based on the relative importance of various causative factors as derived from remotely sensed data and other thematic maps were used for the LHZ. The different classes of thematic layers were assigned the corresponding rating value as attribute information in the GIS and an “attribute map” was generated for each data layer. Each class within a thematic layer was assigned an ordinal rating from 0 to 9. Summation of these attribute maps were then multiplied by the corresponding weights to yield the Landslide Hazard Index (LHI) for each cell. Using trial and error method the weight-rating values have been re-adjusted. The LHI threshold values used were: 142, 165, 189 and 216. A LHZ map was prepared showing the five zones, namely “very low hazard”, “low hazard”, “moderate hazard”, “high hazard” and “very high hazard” by using the “slicing” operation.     

A pre-edge analysis of Mn K-edge XANES spectra to help determine the speciation of manganese in minerals and glasses

High-resolution manganese K-edge X-ray absorption near edge structure spectra were collected on a set of 40 Mn-bearing minerals. The pre-edge feature information (position, area) was investigated to extract as much as possible quantitative valence and symmetry information for manganese in various “test” and “unknown” minerals and glasses. The samples present a range of manganese symmetry environments (tetrahedral, square planar, octahedral, and cubic) and valences (II to VII). The extraction of the pre-edge information is based on a previous multiple scattering and multiplet calculations for model compounds. Using the method described in this study, a robust estimation of the manganese valence could be obtained from the pre-edge region at 5% accuracy level. This method applied to 20 “test” compounds (such as hausmannite and rancieite) and to 15 “unknown” compounds (such as axinite and birnessite) provides a quantitative estimate of the average valence of manganese in complex minerals and silicate glasses. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Impact of assimilation of ATOVS temperature and humidity and SSM/I total precipitable water on the simulation of a monsoon depression

The present study explored the effect of assimilation of Advanced TIROS Vertical Sounder (ATOVS) temperature and humidity profiles and Spectral sensor microwave imager (SSM/I) total precipitable water (TPW) on the simulation of a monsoon depression which formed over the Arabian Sea during September 2005 using the Weather Research and Forecast model. The three-dimensional variational (3DVAR) data assimilation technique has been employed for the purpose of assimilation of satellite observations. Statistical scores like “equitable threat score,” “bias score,” “forecast impact,” and “improvement parameter” have been used to examine the impact of the above-mentioned satellite observations on the numerical simulation of a monsoon depression. The diagnostics of this study include verification of the vertical structure of depression, in terms of temperature anomaly profiles and relative vorticity profiles with observations/analysis. Additional diagnostics of the study include the analysis of the heat budget and moisture budget. Such budget studies have been performed to provide information on the role of cumulus convection associated with the depression. The results of this study show direct and good evidence of the impact of the assimilation of the satellite observations using 3DVAR on the dynamical and thermodynamical features of a monsoon depression along with the effect of inclusion of satellite observation on the spatial pattern of the simulated precipitation associated with the depression. The “forecast impact” parameter calculated for the wind speed provides good evidence of the positive impact of the assimilation of ATOVS temperature and humidity profiles and SSM/I TPW on the model simulation, with the assimilation of the ATOVS profiles showing better impact in terms of a more positive value of the “forecast impact” parameter. The results of the study also indicate the improvement of the forecast skill in terms of “equitable threat score” and “bias score” due to the assimilation of satellite observation.     

Multi-model multi-analysis ensemble weather forecasting on the grid for the South Eastern Mediterranean Region

Weather forecasting is based on the use of numerical weather prediction (NWP) models that are able to perform the necessary calculations that describe/predict the major atmospheric processes. One common problem in weather forecasting derives from the uncertainty related to the chaotic behaviour of the atmosphere. A solution to that problem is to perform in addition to “deterministic” forecasts, “stochastic” forecasts that provide an estimate of the prediction skill. A computationally feasible approach towards this aim is to perform “ensemble forecasts”. Indeed, in the frame of SEE-GRID-SCI EU funded project a Regional scale Multi-model, Multi-analysis ensemble forecasting system (REFS) was built and ported on the Grid infrastructure. REFS is based on the use of four limited area models (namely BOLAM, MM5, ETA, and NMM) that are run using a multitude of initial and boundary conditions over the Mediterranean. This paper presents the tools and procedures followed for developing this application at a production level.     

Chemodynamics of trace metal fractions in surface sediments of the Pandoh Lake,Lesser Himalaya,India

The seasonal variation in the trace metals’ concentrations (Cd, Co, Cu, Fe, Mn, Ni, Pb, and Zn) were investigated in surface sediments of the Pandoh Lake. The horizontal distribution of TC, TN, and TP reflects spatial and temporal differences in sedimentary organic production. The chemical sequential extraction of heavy metals was carried out by seven-step fractionation scheme (Leleyter and Probst in Int J Environ Chem 73:109–128, 1999). The significant concentrations of Ni and Cd were associated with “water soluble (Eua)” fraction in the monsoon and winter, respectively, while “exchangeable (Exch)” and “carbonate-bound (Carb)” fractions for Ni and Cd were abundant in winter and summer. The Cd, Cu, and Pb associated with “Exch” fraction in the summer season support their availability on exchange sites due to oxidized nature of surface sediments. Enrichment of Co, Fe, Mn, and Zn in “AFeO” fraction showed poor bioavailability, while Cd, Cu, and Mn in the monsoon, Co in the winter and summer, and Zn in the winter season showed significant “organically bound (Org)” fraction. The ANOVA was significant for chemical fractions of trace elements except “Carb” fraction of Pb and Zn and “CFeO” fraction of Pb. Factor analysis revealed that the “Eua”, “Exch”, and “Carb” fractions together control the metal enrichment of “MnO”, “AFeO”, and “CFeO” fractions in the summer season.     

Some features of twisting of the Earth in geological history: the tectonophysical aspect

In this work some examples of “twisting” of the Earth in the geologic past are given: displacement of the northern parts of the global submeridional structures to the west relative to their southern parts; the rotation of the “geodynamic pair” of Siberia-Laurentia in the Proterozoic; sinistral displacement of the Northern Hemisphere relative to the Southern Hemisphere after the collapse of the last Pangaea; the equatorial rotation of the continental plates; oblique orientation of the global network of planetary fracturing; an inclination of the axis of submeridional compression; sinistral “beveling”; the dextral “twisting” of Venus. All these examples confirm the idea of possible sinistral “twisting” of the Earth that has been proposed by many authors. The cause of such “twisting” is unclear, although it is likely connected with the Earth’s rotation around its axis. Some of these examples show that many paleomagnetic reconstructions can be usefully discussed in a tectonophysical aspect. Moreover, in connection with this data, the development of a new scientific field, called “paleomagnetic tectonophysics”, is possible.     

Using ALSM to map sinkholes in the urbanized covered karst of Pinellas County,Florida—2. Accuracy statistics

We apply the logic of clinical epidemiological studies to quantify the accuracy of mapping sinkholes by ALSM in the 750 km² Pinellas County. By such studies, a new diagnostic procedure is tested by comparing the diagnoses in a clinical trial to diagnoses on the same patients from a more reliable, but more elaborate and expensive procedure (“gold standard” in epidemiological context). A relatively undeveloped, 65 km² focus area where we have aerial photographs that are effectively contemporaneous with the ALSM flights serves as the “clinical trial”. The xy-locations in the focus area are the “patients” in the trial. The “diagnostic test” for having “sinkhole disease” is inclusion in a database of sinkhole polygons delimited by ALSM contours (“ALSM-alone”), as detailed in Part 1. The standard of comparison (“gold standard” would be an overstatement in the absence of geophysical testing) is inclusion in a database of sinkhole outlines derived by best judgment of conjunctive interpretation of ALSM and aerial photography. GIS intersections that indicate the sensitivity and specificity of the test (ALSM-alone) are 43 and 98.3%, respectively, and, in the focus area where the prevalence of “sinkhole disease” is 4.7%, the positive and negative predictive values are 55.5 and 97.2%, respectively. Over much of the rest of the county, where only the test can be applied, the prevalence of sinkholes is sufficiently small that it cannot be determined to be any different from zero given the paucity of interpreted sinkholes (positive diagnoses) and the low specificity of the test method. The conclusion, therefore, is that contemporaneous aerial photography is essential to compile an ALSM-derived database that aims to state that the given xy-points lay inside or outside of topographic depressions in the covered karst of west-central Florida.     

Synthetic “Cooperite”, “Braggite”, and “Vysotskite” in the system PtS-PdS-NiS at 1100°C, 1000°C, and 900°C

Summary ?Results of experimental investigations in the dry system PtS-PdS-NiS at 1100°C, 1000°C, and 900°C are presented. The phases observed at 1100°C are “cooperite” and a melt, at 1000°C “cooperite”, “braggite”, and a melt and at 900°C “cooperite”, “braggite”, “vysotskite”, Ni_1−xS, and a melt. At 1100°C the maximum solubility of Ni in ideal, Pd-free “cooperite” is 2.7 atomic per cent and the Pd-content limit in Ni-free “cooperite” is 12.8 atomic per cent. At 1000°C the maximum solubility of Ni in ideal, Pd-free “cooperite” is 3.3 atomic per cent and the Pd-content in Ni-free “cooperite” is 13.7 atomic per cent. The “braggite” composition ranges from Pt_0.56Pd_0.38Ni_0.06S and Pt_0.59Pd_0.41S in a Ni-saturated and Ni-free environment respectively to Pt_0.18Pd_0.80Ni_0.02S and Pt_0.14Pd_0.86S respectively. At 900°C the maximum Ni-content in ideal Pd-free “cooperite” is 3.1 atomic per cent and the Pd-limit in Ni-free “cooperite” is 12.5 atomic per cent. The “braggite” composition ranges from Pt_0.59Pd_0.29Ni_0.12S and Pt_0.60Pd_0.40S for a Ni-saturated and Ni-free environment respectively, to Pd_0.91Ni_0.09S and PdS respectively. The Ni-content in “braggite” and “vysotskite” increases slightly with increasing Pt/Pd ratios and is higher at 900°C than at 1000°C. Comparison of experimental trends with cooperite, braggite, and vysotskite analyses from the literature implies high temperatures of formation for Pt-Pd-Ni sulphides in placers if Ni-saturation is assumed.

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Zusammenfassung ?Synthetischer ,,Cooperit”, ,,Braggit” und “Vysotskit” im System PtS-PdS-NiS bei 1100°C, 1000°C und 900°C Ergebnisse experimenteller Untersuchungen im trockenen System PtS-PdS-NiS bei 1100°C, 1000°C und 900°C werden dargestellt. Bei 1100°C sind die Phasen “Cooperit” und Schmelze, bei 1000°C “Cooperit”, “Braggit” und Schmelze und bei 900°C “Cooperit”, “Braggit”, “Vysotskit”, Ni_1−xS und Schmelze stabil. Bei 1100°C ist die maximale L?slichkeit von Ni in idealem, Pd-freiem “Cooperit” 2.7 Atomprozent und der Pd-Gehalt in Ni-freien “Cooperit” liegt bei maximal 12.8 Atomprozent. Bei 1000°C ist die maximale L?slichkeit von Ni in idealem, Pd-freien “Cooperit” 3.3 Atomprozent und der Pd-Gehalt in Ni-freien “Cooperit” liegt bei maximal 13.7 Atomprozent. Die Zusammensetzung des “Braggits” variiert zwischen Pt_0.56Pd_0.38Ni_0.06S und Pt_0.18Pd_0.80Ni_0.02S in einem Ni-ges?ttigtem und zwischen Pt_0.59Pd_0.41S und Pt_0.14Pd_0.86S in einem Ni-freien Umfeld. Bei 900°C liegt die maximale L?slichkeit von Ni in idealem Pd-freien “Cooperit” bei 3.1 Atomprozent und der Pd-Gehalt in Ni-freien “Cooperit” liegt bei maximal 12.5 Atomprozent. Die Zusammensetzung des “Braggits” variiert zwischen Pt_0.59Pd_0.29Ni_0.12S und Pd_0.89Ni_0.08S in einem Ni-ges?ttigten und zwischen Pt_0.59Pd_0.40S und PdS in einem Ni-freien Umfeld. Der Nickelgehalt in “Braggit” und “Vysotskit” nimmt mit zunehmendem Pt/Pd Verh?ltnis zu und ist bei 900°C h?her als bei 1000°C. Ein Vergleich der experimentellen Trends mit Cooperit, Braggit und Vysotskit Analysen aus der Literatur weist auf eine Hochtemperaturbildung der Pt-Pd-Ni Sulfide in Seifenlagerst?tten hin, wenn man von Nickels?ttigung ausgeht.

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Received October 1, 1998;/revised version accepted September 7, 1999     

Geochemical studies on Dachang antimony ore deposit in Qinglong, Guizhou Province

The Dachang antimony deposit in Qinglong,Guizhou Province,is strictly controlled by the “Dachang Layer” which is a complex altered rock occurring at unconformity between the Permian Emeishan basalt and the Maokou limestone.Based on the studies of the hanging-and foot-wall rocks,the trace elements and REE contents of the rocks and ores and heavy placer minerals in the basalt,this paper is focused on the relations between these data and the “Dachang Layer”and its hanging- and oot-wall rocks.The author pointed out that the “Dachang Layer” and basalt are the source-beds of antimony;ilmenite and magnetite are the major mineral carriers of antimony.In the processes of halmyrosis and burial metamorphism of the “Dachang Layer” an basalt,antimony was mobilized along with the mobilization of iron and was preliminarily concentrated in the“ Dachang Layer”.     

Redox environment effect on redox sensitive elements in surface sediments of the Changjiang Estuary hypoxia zone

The grain size and element (including redox sensitive elements and terrigenous elements) concentration of surface sediments from the Changjiang Estuary hypoxia zone and its adjacent sea area were measured in this research. Based on the obtained data, the hypoxic environment’s influence on the distribution of elements in surface sediments was further studied. We believe that the “redox environment effect” greatly influences the distribution of the RSE, which reveals the “patchy enrichment pattern” offshore in the hypoxia zone, while the distribution of the terrigenous elements which shows the “stripped enrichment pattern” near shore is mainly affected by “granularity effects”. Due to the existence of the hypoxia zone of the Changjiang Estuary, the distribution of the RSE such as Mo, Cd and V in the study area exhibits the characteristics of “redox environment effects”. __________ Translated from Marine Geology & Quaternary Geology, 2007, 27(3):1–8 [译自: 海洋地质与第四纪地质]     

Survival of the thinnest: rediscovery of Bauer’s (1898) ichthyosaur tooth sections from Upper Jurassic lithographic limestone quarries,south Germany

During the late Early Cretaceous, the shallow-water domains of the western Tethys are characterized by the widespread deposition of Urgonian-type carbonates rich in rudists, corals and other oligotrophic, shallow-marine organisms. In the Helvetic Alps, the Urgonian occurrences have been dated by ammonite biostratigraphy as Late Barremian and Early Aptian. For the more proximal occurrences in the western Swiss Jura, a recent age model based on bio-, chemo- and sequence stratigraphy has been proposed, which allows for an improved correlation with the Helvetic counterparts. In order to corroborate the recently proposed age model for the Jura, a set of well-preserved rhynchonellids collected from five different lithostratigraphical formations and members (“Marnes bleues d’Hauterive”, “Marnes d’Uttins”, basal marly layers within the “Urgonien Jaune”, “Marnes de la Russille”, “Urgonien Blanc”) has been analysed for its strontium–isotope ratios (⁸⁷Sr/⁸⁶Sr). In addition, K–Ar dating was performed on well-preserved glauconite grains from two different levels (“Marnes d’Uttins” and a basal layer within the “Urgonien Jaune”). The correlation of the Sr–isotope data set with a belemnite-based, ammonite-calibrated reference curve provides an age model which is coherent with recently published ages based on calcareous nannofossil biostratigraphy and the correlation of trends in chemo- and sequence stratigraphy. K–Ar dating on well-preserved glauconite grains from the “Marnes d’Uttins” and lowermost part of the “Urgonien Jaune” delivered ages of 127.5 ± 2.3 and 130.7 ± 2.6 Ma, respectively. Whereas the age of the glauconitic level near the base of the “Urgonien Jaune” is chronostratigraphically meaningful, the K–Ar age of the “Marnes d’Uttins” appears too young relative to the presently used time scale. This may be related to rejuvenation of the K–Ar chronometer due to post-depositional Ar loss, most likely during hardground formation. The ages obtained here confirm the Late Barremian age for the onset of the Urgonian platform, an age which is conform with ages obtained in the Helvetic Alps and elsewhere along the northern Tethyan margin.     

Precise temperature monitoring in boreholes: evidence for oscillatory convection? Part II: theory and interpretation

In the previous part of this work (Cermak, Safanda and Bodri, this volume p.MMM) we have described experimental data and quantified the heterogeneity features of the microtemperature time series. The spectral analysis and the local growth of the second moment technique revealed scaling structure of all observed time series generally similar and suggested the presence of two temperature forming processes. The longer-scale part can be attributed to the heat conduction in compositional and structural heterogeneous solid rocks, further affected by various local conditions. Short-scale temperature oscillations are produced by the intra-hole fluid convection due to inherent instability of water column filling the hole. Here we present how the observational evidence is supported by the results of the computer simulations. The exact modes of intra-hole convection may be different, ranging from quasi-periodic (“quiescent”) state to close of turbulence. As demonstrated by numerical modeling and referred on laboratory experiments, at higher Rayleigh numbers the periodic character of oscillation characteristic for “quiescent” regime is superseded by stochastic features. This so called “oscillatory” convection occurs due to instability within the horizontal boundary layers between the individual convectional cells. In spite of the fact that the basic convective cell motion is maintained and convection is characterized by slow motion, the oscillatory intra-hole flow and corresponding temperature patterns exhibit typical features of turbulence. The idea of boundary layer instability as a source of stochastic temperature fluctuations could explain many distinct features of borehole temperatures that previously cannot be interpreted.     

Who are the resident stakeholders in a flood project? A spatial analysis of resident stakeholders

The importance of public participation has been discussed and well understood for some time, and many people have moved beyond the development of ideas to putting them into practice. During the past few years, stakeholder theory, one of the most popular theories originating from the field of business management, has been attracting immense attention due to its utility in raising representativeness in government. For instance, Hemmati (Multi-stakeholder process for governance and sustainability: beyond deadlock and conflict. Earthscan, London, 2002) argued that multi-stakeholder processes (MSPs) might be effective methods toward generating better policy options under the current democratic paradigm. In real life, however, stakeholder theory often has not been appropriately adopted in the field of environmental management. Sometimes, planners, prompted by the difficulty of identifying stakes, have used the term “stakeholders” as roughly synonymous with “participants”, thus impairing the content of stakeholder theory. Different from previous work in the field of flood management, we propose an original approach, the spatial analysis of a flood project for resident stakeholders (SAFPRS), to identify resident stakeholders in a flood project, rather than merely improving the weakness of stakeholder identification. Hopefully, this approach might ameliorate the current situation in Taiwan, where some important stakeholders have been too easily excluded in the execution of flood projects.     

Predicting Lahar-Inundation Zones: Case Study in West Mount Pinatubo, Philippines

This paper demonstrates techniques for pre-eruption prediction of lahar-inundation zones in areas where a volcano has not erupted within living memory and/or where baseline geological information about past lahars could be scarce or investigations to delimit past lahars might be incomplete. A lahar source (or proximal lahar-inundation) zone is predicted based on ratio of vertical descent to horizontal run-out of eruptive deposits that spawn lahars. Immediate post-eruption distal lahar-inundation zones are predicted based on “pre-eruption” distal lahar-inundation zones and on spatial factors derived from a digital elevation model. Susceptibility to distal lahar-inundation is estimated by weights-of-evidence, by logistic regression and by evidential belief functions. Predictive techniques are applied using a geographic information system and are tested in western part of Pinatubo volcano (Philippines). Predictive maps are compared with a forecast volcanic-hazard map through validation against a field-based volcanic-hazard map. The predictive model of proximal lahar-inundation zone has “true positive” prediction accuracy, “true negative” prediction accuracy, “false positive” prediction error and “false negative” prediction error that are similar to those of the forecast volcanic-hazard map. The predictive models of distal lahar inundation zones have higher “true positive” prediction accuracy and lower “false negative” prediction error than the forecast volcanic-hazard map, although the latter has higher “true negative” prediction accuracy and lower “false positive” prediction error than the former. The results illustrate utility of proposed predictive techniques in providing geo-information could be used, howbeit with caution, for planning to mitigate potential lahar hazards well ahead of an eruption that could generate substantial source materials for lahar formation.     

Miocene tectonics of the Maramures area (Northern Romania): implications for the Mid-Hungarian fault zone

The interplay between the emplacement of crustal blocks (e.g. “ALCAPA”, “Tisza”, “Dacia”) and subduction retreat is a key issue for understanding the Miocene tectonic history of the Carpathians. Coeval thrusting and basin formation is linked by transfer zones, such as the Mid-Hungarian fault zone, which seperates ALCAPA from Tisza-Dacia. The presented study provides new kinematic data from this transfer zone. Early Burdigalian (20.5 to ∼18.5 Ma) SE-directed thrusting of the easternmost tip of ALCAPA (Pienides), over Tisza-Dacia is linked to movements along the Mid-Hungarian fault zone and the Periadriatic line, accommodating the lateral extrusion of ALCAPA. Minor Late Burdigalian (∼18.5 to 16 Ma) NE-SW extension is interpreted as related to back-arc extension. Post Burdigalian (post-16 Ma) NE–SW shortening and NW–SE extension correlate with “soft collision” of Tisza-Dacia with the European foreland coupled with southward migration of active subduction. During this stage the Bogdan-Voda and Dragos-Voda faults were kinematically linked to the Mid-Hungarian fault zone. Sinistral transpression (16 to 12 Ma) at the Bogdan-Voda fault was followed by sinistral transtension (12–10 Ma) along the coupled Bogdan-Dragos-Voda fault system. During the transtensional stage left-lateral offset was reduced eastwards by SW trending normal faults, the fault system finally terminating in an extensional horse-tail splay.     

Calculation of the configurational entropy of Al, Si in layer silicates using the cluster variation method

Entropies of Al-Si in layer silicates have been calculated using a series of CVM approximations for the honeycomb lattice. The parameters of the models have been constrained by ²⁹Si NMR data. The results of low order approximations such as “pair” and “star” have been rejected because of their low accuracy at high Al/(Al+Si) ratios. Reasonably accurate results have been achieved with the help of the “hexagon” and “star-hexagon” approximations. Received: 31 October 1997 / Revised, accepted: 17 April 1998