Assessment of hydrogeochemical processes in a coastal region: Application of multivariate statistical model

Hydrogeochemical studies have been carried out in a coastal region, using multivariate statistical model, for better understanding the controlling processes that influence the aquifer chemistry. Two principal components (PC1 and PC2) are extracted from the data set of chemical variables (pH, TDS, Ca²⁺, Mg²⁺, Na⁺, K⁺, HCO ₃ ^? , Cl^?, SO ₄ ^2? , NO ₃ ^? and F^?), which account for 79% of the total variation in the quality of groundwater. The PC1 (salinity controlled process) includes the concentrations of TDS, Mg²⁺, Na⁺, K⁺, Cl^?, SO ₄ ^2? and NO ₃ ^? , while the PC2 (alkalinity controlled process) comprises the concentrations of pH, HCO ₃ ^? and F^?. The spatial distribution of PC scores identifies the locations of high salinity and alkalinity processes. The first process corresponds to the influences of geogenic, anthropogenic and marine sources, and the second one to the influence of water-soil-rock interaction. Thus, the present study shows the usefulness of multivariate statistical model as an effective means of interpretation of spatial controlling processes of groundwater chemistry.     

First principles quantum mechanical calculation of the electric dipole polarizabilities of the borate,carbonate, nitrate and related ions

Electric dipole polarizabilities have been calculated from first principles of quantum mechanics for the BO ₃ ^3? , CO ₃ ^2? , NO ₃ ^? series and for NO ₂ ^? and LiNO₃(g). Calculated trends in average polarizability and polarizability anisotropy in the BO ₃ ^3? -NO ₃ ^? series are in agreement with experiment and can be qualitatively interpreted in terms of the varying energies of the a₁′, a₂″ and e′ symmetry unoccupied MO's of the oxyanions. Embedding a CO ₃ ^2? ion in a D_3h symmetry array of divalent cations reduces both the average polarizability and its anisotropy, particularly when diffuse s and p functions are included in the calculation. Calculations on the gas phase LiNO₃ molecule and on the free NO ₃ ^? ion in the distorted geometry found in LiNO₃(g) allow us to separate polarizability contributions internal to the NO ₃ ^? and Li⁺ ions from those which arise from the Li⁺-NO ₃ ^? interaction. The Li⁺-NO ₃ ^? interaction term so obtained is much smaller than the NO ₃ ^? contribution but is in turn larger than the Li⁺ contribution, suggesting that the inclusion of this interaction term is essential for obtaining accurate results for ion pairs. Although static polarizabilities are in reasonable agreement with experiment for NO ₃ ^? the wavelength dispersion of the polarizability is underestimated by about a factor of two, apparently as a result of inadequacies in the quantum mechanical method. Calculated values are also presented for ¹⁴N NMR shieldings in the nitrogen oxyanions but these are in only qualitative agreement with the experimental values. Similarly, calculated values of magnetic susceptibility are in only qualitative agreement with experiment although trends along the BO ₃ ^3? -NO ₃ ^? series are properly reproduced.     

Optical absorption spectra of iron ions in vivianite

Absorption bands are determined in polarized optical spectra of vivianite Fe₃(PO₄)₂·8H₂O, recorded at room and low temperatures. These bands are caused by spin-allowed d-d transitions in structurally nonequivalent Fe _A ²⁺ (～11000 cm^-1 (γ-polarization) (and) ～12000 cm^-1 (β-polarization)) (and) Fe _B ²⁺ (～8400 cm^-1 (γ, α-polarization) and ～11200 cm^-1 (α-polarization)) ions. A charge transfer band (CTB) Fe _B ²⁺ +Fe _B ³⁺ →Fe _B ²⁺ +Fe _B ²⁺ (～15000 cm^-1) also determined, has polarizing features giving evidence of a change in the Fe _B ²⁺ -Fe _B ³⁺ bond direction, when compared with Fe _B ²⁺ -Fe _B ²⁺ . Bands of exchange-coupled Fe³⁺-Fe³⁺ pairs (～19400, ～20400, ～21300 and ～21700 cm^-1) which appear on oxidation of Fe²⁺ in paired Fe _B octahedra are also characterized.     

Zn and Pb solubility and speciation in aqueous chloride fluids at T-P parameters corresponding to granitoid magma degassing and crystallization

The solubility of all possible Zn and Pb species in aqueous chloride fluids was evaluated by means of thermodynamic simulations in systems ZnO(PbO)-aqueous solution of NaCl (KCl, NaCl + HCl) within broad ranges of temperature (600–900°C), pressure (0.7–5 kbar), and chloride concentrations, under parameters corresponding to the crystallization and degassing of granitoid magmas in the Earth’s crust. Our simulation results demonstrate that the addition of Cl to the fluid phase in the form of Na(K)Cl and HCl significantly increases the concentrations of Cl-bearing Zn and Pb complexes and the total concentration of the metals in the solutions in equilibrium with the solid oxides. In Zn-bearing fluids, the Zn(OH) ₂ ⁰ , ZnOH⁺, and Zn(OH) ₃ ^? —hydroxyl complexes and the ZnCl ₂ ⁰ , and ZnCl⁺ chlorocomplexes, which are predominant at low Cl concentrations (C_Cl < 0.05–0.1 m) give way to ZnCl ₄ ^2? with increasing C_Cl, which becomes the predominant Zn species of the fluid at C_Cl > 0.1–0.5 m throughout the whole temperature range in question and pressures higher than 1 kbar. For Pb-bearing fluids, the T-P-X region dominated by the Pb(OH) ₂ ⁰ , and Pb(OH) ₃ ^? hydroxyl complexes is remarkably wider than the analogous region for Zn, particularly at elevated temperatures (≥700°C) in alkaline solutions. An increase in C_Cl is associated with an increase in the concentration and changes in the speciation of Pb chlorocomplexes: PbCl ₂ ⁰ → PbCl ₃ ^? → PbCl ₄ ^2? . The concentrations of Zn and Pb chlorocomplexes increase with increasing pressure, decreasing temperature, and decrease pH with the addition of HCl to the system. It is demonstrated that the solubility of ZnO at any given T-P-X in alkaline solutions with low chloride concentrations are lower than the solubility of PbO. The Zn concentration increases more significantly than with the Pb concentration with increasing C_Cl and decreasing pH, so that the Zn concentration in acidic solutions is higher than the Pb concentration over broad ranges of temperature, pressure, and Cl concentration. Chloride complexes of Zn (ZnCl ₂ ⁰ , and ZnCl ₄ ^2? ) and Pb (PbCl ₂ ⁰ , and PbCl ₃ ^? are proved to be predominant within broad T-P-X-pH ranges corresponding to the parameters under which magmatic fluid are generated. Our simulation results confirm the hypothesis that chlorocomplexes play a leading role in Zn and Pb distribution between aqueous chloride fluids and granitic melts. These simulation results are consistent with experimental data on the Zn and Pb distribution coefficients (D(Zn)^f/m and D(Pb)^f/m, respectively) between aqueous chloride fluids and granitic melts that demonstrated that (1) D(Zn)^f/m and D(Pb)^f/m increase with increasing Na and K chloride concentrations in the aqueous fluid, (2) both D(Zn)^f/m and D(Pb)^f/m drastically increase when HCl is added to the fluid, and (3) (D(Zn)^f/m is higher than D(Pb)^f/m at any given T-P-X parameters. The experimentally established decrease in D(Zn)^f/m and D(Pb)^f/m with increasing pressure (at unchanging temperature and Cl concentration) is likely explained by an increase in the alkalinity of the aqueous chloride fluid in equilibrium with granite melt and, correspondingly, a decrease in the Zn and Pb solubility in this fluid.     

Thermodynamics of plagioclase II: Temperature evolution of the spontaneous strain at the I\bar 1 \leftrightarrow P\bar 1 phase transition in anorthite

The temperature dependence of the lattice parameters of pure anorthite with high Al/Si order reveals the predicted tricritical behaviour of the \(I\bar 1 \leftrightarrow P\bar 1\) phase transition at T _c ^* =510 K. The spontaneous strain couples to the order parameter Q° as x _i∝S _xQ ⁱ Q°² with S _xQ ¹ =4.166×10^?3, S _xQ ² =0.771×10^?3, S _xQ ³ =?7.223×10^?3 for the diagonal elements. The temperature dependence of Q° is $$Q^{\text{o}} = \left( {1 - \frac{T}{{510}}} \right)^\beta ,{\text{ }}\beta = \tfrac{{\text{1}}}{{\text{4}}}$$ A strong dependence of T _c ^* , S _xQ ⁱ and β is predicted for Al/Si disordered anorthite.     

Hydrochemistry and pollution probability of selected sites along the Euphrates River, Western Iraq

The hydrochemistry of Euphrates River in the study area which extended from Hit to Al-Saqlawia was studied in order to determine the physical, chemical, and biological properties in addition to the radiation level. Thirty-one stations along the Euphrates River were chosen, 17 of them represented the Euphrates River itself, whereas the other stations are considered as point pollution sources which all empty their load directly in the Euphrates River with an average total discharge of 32 m³/s. Twenty-eight samples of the Euphrates water of both high- and low-flow periods were analyzed for cations (Ca²⁺, Mg²⁺, Na⁺, and K⁺), anions (SO ₄ ⁼ , Cl^?, CO ₃ ⁼ , HCO ₃ ^? , NO ₃ ^? , PO ₄ ^?3 ), H₂S boron, dissolved oxygen, biological oxygen demand, bacteriological tests, radiation levels in addition to physical parameters such as hydrogen number (pH), total dissolved solid, electrical conductivity, total suspended solid, and temperature. This study showed that the cations and anions during periods of high and low flows are within acceptable limit with exceptional Cl^?. Hydrochemical formula during the high flow was Na-Ca-Mg-Cl-SO₄, then it changed into Na-Ca-Mg-HCO3-SO₄-Cl during the low-flow period. The average output cations and anions at downstream (Saqlawiya area) was relatively higher than those of input at upstream (Hit area); this attributed to the natural and anthropogenic activities originated mainly from agricultural activity and population communities around the river. Radiation level for ²¹²Pb, ²¹⁴Pb, ⁴⁰k, ²²⁰Ac, and ²¹⁴Bi showed that the higher level of radiation is concentrated within sediment rather than in water, but the radiation in both is within acceptable limit.     

Characterization, classification, and determination of drinkability of some Algerian thermal waters

In this study, the physicochemical parameters (Conductivity, pH, Cl^?, HCO ₃ ^? , PO ₄ ^3? , SO ₄ ^2? , NO ₃ ^? , NO ₂ ^? , F^?, TH, Ca²⁺, K⁺, Mg²⁺, Na⁺, and DS) were determined for 41 samples collected from fourteen places in Algeria. The temperature of the thermal water samples at collection sites varied from 26°C to 86°C. pH values varied from 6.5 to 8.5 (i.e., from slightly acidic to moderately alkaline); 90.24% of the samples exhibited relatively high salinity (DS?=?550–5,500 mg L^?1). Total hardness measurements indicated these waters to be moderately hard. Forty-six percent of the samples are Na–Cl in character. The ratios Na⁺/Ca²⁺, Na⁺/Mg²⁺, and (Na⁺ + K⁺)/(Ca²⁺ + Mg²⁺) were high in 90.24% of the samples. This indicates the ion exchange process is important, which indicates that most of the Algerian thermal waters had developed over a long period at a depth sufficient to react with the rock. Statistical analyses of the physicochemical data gave positive correlation values, thereby enabling good interpretation of the results and revealing the composition of ions present in the thermal waters, as well as some information about their origin. The therapeutic properties associated with thermal waters encourage people at spas to drink the water they bathe in. Therefore, we examined the drinkability of these thermal waters. World Health Organization (WHO 1993) standards were used to evaluate the thermal water quality for drinking. With respect to hardness, the samples were classified as moderately hard (58.54% of the samples), very hard (36.58% of the samples), and soft (4.88% of the samples). The drinkability study shows that only 16 samples of the investigated waters were drinkable and thus could be consumed without special precaution.     

The effect of medium chemistry on the solubility and morphology of brushite crystals

An experimental study of the particulars of the solubility and crystallization of brushite Ca(HPO₄) · 2H₂O from aqueous solution in conditions of a variable pH (6.0–3.0) and the contents of impurity ions (K⁺, Na⁺, NH ₄ ⁺ , Mg²⁺, SO ₄ ^2? , CO ₃ ^2? ) has been conducted. It is established that brushite solubility markedly rises with a decrease in pH from 6 to 3 and slightly rises with an increase in Mg²⁺ and SO ₄ ^2? concentrations. The enrichment in K⁺, Na⁺, and NH ₄ ⁺ does not affect brushite solubility. The changeable chemistry of the medium results in variation of the synthetic crystal habit, from rhombic tabular to thickened prismatic crystals.     

Geochemical characterization of groundwater from shallow aquifer surrounding Fetzara Lake N. E. Algeria

Hydrogeochemical investigations were carried out around Fetzara Lake, Northeast Algeria, to assess the quality of groundwater for its suitability for drinking and irrigation purposes. The groundwater chemistry is mainly controlled by the water?Crock interactions, but also influenced by other processes such as evapotranspiration and ion exchange. Groundwater samples collected, during two periods (1993 and 2007) from wells in the area were analyzed for pH, EC, TDS, Ca²⁺, Mg²⁺, Na⁺, K⁺, CO ₃ ^2? , HCO ₃ ^? , Cl^?, SO ₄ ^2? , and NO ₃ ^? . The chemical relationships in Piper??s diagram and Gibbs??s diagram suggest that groundwaters mainly belong to noncarbonate alkali type and Cl^? group and are controlled by evaporation dominance, respectively, due to the sluggish drainage conditions, greater water?Crock interaction, and anthropogenic activities. A comparison of the groundwater quality in relation to drinking water quality standards proves that most of the water samples are not suitable for drinking. US Salinity Laboratory??s and Wilcox??s diagrams and %Na⁺ used for evaluating the water quality for irrigation suggest that the majority of the groundwater samples are not good for irrigation.     

Submarine Groundwater Discharge-Derived Nutrient Loads to San Francisco Bay: Implications to Future Ecosystem Changes

Submarine groundwater discharge (SGD) was quantified at select sites in San Francisco Bay (SFB) from radium (²²³Ra and ²²⁴Ra) and radon (²²²Rn) activities measured in groundwater and surface water using simple mass balance box models. Based on these models, discharge rates in South and Central Bays were 0.3?C7.4?m³?day^?1?m^?1. Although SGD fluxes at the two regions (Central and South Bays) of SFB were of the same order of magnitude, the dissolved inorganic nitrogen (DIN) species associated with SGD were different. In the South Bay, ammonium (NH ₄ ⁺ ) concentrations in groundwater were three-fold higher than in open bay waters, and NH ₄ ⁺ was the primary DIN form discharged by SGD. At the Central Bay site, the primary DIN form in groundwater and associated discharge was nitrate (NO ₃ ^? ). The stable isotope signatures (??¹⁵N_NO3 and ??¹⁸O_NO3) of NO ₃ ^? in the South Bay groundwater and surface waters were both consistent with NO ₃ ^? derived from NH ₄ ⁺ that was isotopically enriched in ¹⁵N by NH ₄ ⁺ volatilization. Based on the calculated SGD fluxes and groundwater nutrient concentrations, nutrient fluxes associated with SGD can account for up to 16?% of DIN and 22?% of DIP in South and Central Bays. The form of DIN contributed to surface waters from SGD may impact the ratio of NO ₃ ^? to NH ₄ ⁺ available to phytoplankton with implications to bay productivity, phytoplankton species distribution, and nutrient uptake rates. This assessment of nutrient delivery via groundwater discharge in SFB may provide vital information for future bay ecological wellbeing and sensitivity to future environmental stressors.     

Characterisation and quality assessment of groundwater with a special emphasis on irrigation utility: Thirumanimuttar sub-basin, Tamil Nadu, India

Thirumanimuttar sub-basin is of particular importance in the study of groundwater quality due to the release of effluents from industries, agricultural, sewage and urban runoff, brining considerable change in water quality. An investigation was carried out by collecting a total of 194 groundwater samples for two seasons to decipher hydrogeochemistry and groundwater quality for determining its suitability for agricultural purposes. The water is neutral to alkaline in nature with pH ranging from 6.78 to 9.22 with an average of 7.37. Higher electrical conductivity (EC) was noted in NW and mid-downstream parts of the study area. Higher NO ₃ ^? was observed during post-monsoon (POM) due to the action of leaching and anthropogenic process. The piper plot reveals the dominance of Na⁺?CCl^? and Na⁺?CHCO ₃ ^? , mixed Ca²⁺?CNa⁺?CHCO ₃ ^? , mixed Ca²⁺?CMg²⁺?CHCO ₃ ^? and Ca²⁺?CSO ₄ ^? types of hydrogeochemical facies. Higher total hardness in the groundwater is due to the effect of dyeing and bleaching industries discharging effluents affects the quality of water. Residual Sodium Carbonate value indicates 56% of the samples are not suitable for irrigation purposes in both seasons. Higher sodium percentage is noted during PRM indicating the dominance of ion exchange and weathering. Higher sodium adsorption ratio was observed during POM indicating the effect of leaching and dissolution of salts into the aquifer matrix. USSL plot indicates 15% of samples record high salinity to medium sodicity. The Permeability Index indicates water is moderate to good for irrigation purposes. In general, groundwater in the study area is influenced by both natural and anthropogenic activities.     

Electron paramagnetic resonance of PO 3 2− and SO 3 − radicals in anhydrite,celestite and barite: the hyperfine structure and dynamics

Electron paramagnetic resonance (EPR) measurements of natural anhydrite CaSO₄, celestite SrSO₄ and barite BaSO₄ have revealed the presence of PO ₃ ^2? and SO ₃ ^? radicals. Hyperfine structure from³³S has been detected and measured for the first time. Low-symmetry effects, which are manifested in noncoincidence of g and hyperfine axes, were observed for SO ₃ ^? . The dynamics of one of the two SO ₃ ^? types in anhydrite has been investigated. Variations of spin Hamiltonian parameters with temperature have been attributed to thermally induced jumps between the two magnetically inequivalent sites of this center.     

A theoretical study of bond distances,X-ray spectra and electron density distributions in borate polyhedra

The borate polyhedra BO ₃ ^3? , B(OH)₃, BO ₄ ^5? , and B(OH) ₄ ^? are studied using the ab initio and multiple scattering Xα quantum mechanical methods. The ab initio self-consistent-field (SCF) molecular orbital (MO) method, at the minimum basis set level, predicts equilibrium B-O distances within 0.04 Å of their average values in solids so long as the polyhedron charge is small. Orbital energies from double zeta basis set ab initio calculations and analogies with isoelectric compounds are used to assign the X-ray spectra of BO ₃ ^3? and to predict the valence region spectra of BO ₄ ^5? . Contour maps of the difference between molecular and superimposed free atom electron densities show charge buildup along the B-O bond which is only slightly smaller than that observed in CO ₃ ^2? .     

A dynamical model for the I\bar 1 - P\bar 1 phase transition in anorthite,CaAl2Si2O8

The non-ferroic triclinic to triclinic \(I\bar 1 - P\bar 1\) phase transition in anorthite is described in terms of the spontaneous onset of an order parameter η. A triclinic to triclinic phase transition can be driven by order parameters (representations) arising from the Γ, Z, X, U, V, R, Y, and T points of symmetry of the Brillouin zone. Each point leads to a set of two inequivalent representations and thus there is a total of sixteen inequivalent order parameters. However, only the R ₁ ⁺ representation is consistent with the change from the body-centered to primitive cell (increase of primitive cell size of two) and also with the origin of the two space groups (inversion center) being at the same position. The R ₁ ⁺ order parameter of the high symmetry triclinic phase \(P\bar 1_0\) (or equivalently \(I\bar 1\) ) causes a reciprocal lattice change and, in terms of the lower symmetry reciprocal lattice, the order parameter corresponds to the b^* point. This is consistent with experimentally observed x-ray diffuse scattering. Using induced representation theory, microscopic distortions compatible with the R ₁ ⁺ order parameter are obtained. Assuming a distortion in an arbitrary direction at the general 2(i) Wyckoff position (x₀,y₀,z₀) of \(P\bar 1_0\) (the higher symmetry phase) induced representation theory demands an opposite displacement at the position (x₀, y₀, z₀), an opposite displacement at (x₀+1,y₀+1,z₀+1), and the same displacement at ( \(\bar x\) ₀+1, \(\bar y\) ₀+1, \(\bar z\) ₀+1) of \(P\bar 1_0\) . This is also consistent with experiment. The presence of the weak c-type reflections above the transition is attributed to the fluctuating lower symmetry antiphase domains related by the translation (1/2, 1/2, 1/2).     

Hydrochemical characteristics of groundwater in the plains of Phalgu River in Gaya, Bihar, India

Assessment of groundwater quality is essential to ensure sustainable use of it for drinking, agricultural, and industrial purposes. The chemical quality of groundwater of Gaya region has been studied in detail in this work to delineate the potable groundwater zones. A total of 30 groundwater samples and 2 surface water samples were collected in and around Gaya district of Bihar. The major cations follow the trend: Ca²⁺?>?Mg²⁺?>?Na⁺?>?K⁺. The domination of calcium ions in the groundwater is due to weathering of rocks. The K⁺ ranged between 0.2 and 47.95 ppm, suggesting its abundance the below desired limit; but some samples were found to be above permissible limit. K⁺ weathering of potash silicate and the use of potash fertilizer could be the source. The major anions abundance followed the order HCO ₃ ^? ?>?Cl^??>?SO ₄ ^2? ?>?NO ₃ ^? ?>?PO ₄ ^3? . Dissolution of carbonates and reaction of silicates with carbonic acid accounts for the addition of HCO ₃ ^? to the groundwater and oxidation of sulphite may be the source of SO ₄ ^2? . Principal component analysis was utilized to reflect those chemical data with the greatest correlation and seven major principal components (PCs) representing >80 % of cumulative variance were able to interpret the most information contained in the data. PC1, PC2 and PC3 reflect the hydrogeochemical processes like mineral dissolution, weathering and anthropogenic sources. PC4, PC5, PC6 and PC7 show monotonic, random and independent relationships.     

Major ion composition and seasonal variation in the Lesser Himalayan lake: case of Begnas Lake of the Pokhara Valley, Nepal

The Begnas Lake in the Pokhara Valley is one of the threatened habitats in Nepal. The major ion chemistry explains the status of most of the inorganic nutrients and their possible sources. However, the earlier studies mostly cover limnological investigations, and phytoplankton and zooplankton diversity. Thus, the present study has been conducted to investigate the geochemical processes and to examine the seasonal variation of chemical composition within Begnas Lake. The results showed that SO ₄ ^2- , PO ₄ ^3- , and NO ₃ ^- increased compared with the previous values. The domination of Ca²⁺, Mg²⁺, and HCO ₃ ^- explains the influence of carbonate weathering on the major ion concentration. In general, pH and dissolved oxygen decreased with the depth of water-column, while electric conductivity, total dissolved solids, HCO ₃ ^- , Cl^-, H₄SiO₄, K⁺, Mg²⁺, Ca²⁺, Mn²⁺, and Fe increased. Among the cations, the predominance of Ca²⁺ and Mg²⁺ as characterized by high (>0.6) (Ca²⁺ + Mg²⁺)/(Tz⁺) and (>0.8) (Ca²⁺ + Mg²⁺)/(Na⁺ + K⁺) equivalent ratios, also suggests prevalence of carbonate weathering. The low value of (Na⁺ + K⁺)/Tz⁺ ratio shows deficiency of Na⁺ and K⁺, suggesting low contribution of cations via aluminosilicate weathering. The C-ratio suggests a proton source derived both from oxidation of sulfide and dissolution and dissociation of atmospheric CO₂ during different seasons. Though the major hydro-chemical parameters are within permissible limit, the increase in trophic state of the lake suggests that inherent biogeochemical processes make the limiting nutrients available, rendering eutrophic effect. Therefore, further comprehensive studies incorporating sediment–water interaction ought to be carried out to explain the ongoing phenomena and curb the eutrophication process in the lake.     

On the least-squares fit of small and great circles to spherically projected orientation data

Given the direction cosines a _i ^′ = (a ₁ ⁱ , a ₂ ⁱ , a ₃ ⁱ )corresponding to a set of pspherically projected fabric poles, an initial estimate x′ = (x₁, x₂, x₃, x₄)for the angular radius x₄,and direction cosines of the center of the least-squares small circle which minimizes the sum of the squares of the angular residuals $$r = \sum\limits_p {\left[ {x_4 - \cos ^{ - 1} \left( {a_1^i x_1 + a_2^i x_2 + a_3^i x_3 } \right)} \right]} ^2 $$ can be iteratively improved by taking x_j+1 = x_j + Δxwhere x_j is the value of xat the jth iteration and $$\Delta x = - H_j^{ - 1} \left[ {q_j + x_j \left( {x'_j H_j^{ - 1} x_j } \right)\left( {q_j - x'_j H_j^{ - 1} q_j } \right)} \right],$$ where As an initial approximation for xwe have found it convenient to ignore the fact that the data are constrained to lie on the surface of the reference sphere and to use the parameters of a least-squares plane through the given poles. Generalization of this approach to fitting variously constrained great and small circles is easily made. The relative merits of differently constrained fits to the same data can be tested approximately if it is assumed that the errors in the location of the poles are isotropic and normally distributed. It is thus possible to statistically assess the relative significance of conflicting structural models which predict different geometrical patterns of fabric elements.     

Spatial variations of groundwater vulnerability using cluster analysis

An investigation on quality of groundwater has been carried out in the river basin of Varaha located in Visakhapatnam District, Andhra Pradesh to find out the factors that are responsible for spatial variations of water vulnerability. The study area is underlain by the Precambrian rocks of Eastern Ghats over which the Recent Formations occur. Groundwater is a prime source for drinking and irrigation. The quality of groundwater is fresh and brackish with dominance of the latter. Groundwater samples are categorized into two major clusters A and B, using the dendrogram of cluster analyses. Out of these two major clusters, five sub-clusters I to V in the pre-monsoon season and six sub-clusters I to VI in the post-monsoon season are identified. The sub-clusters I to IV of pre-monsoon and I to V of post-monsoon seasons of the cluster A are characterized by less mineralized groundwater compared to those of V of pre-monsoon and VI of post-monsoon seasons of the cluster B, which represent highly mineralized groundwater. The low to high mineral content follows gradually from upstream to the downstream area, being higher in post-monsoon season in both the clusters A and B, depending upon the source, mineral dissolution, and precipitation, solubility and leaching of ions, ion exchange and adsorption processes. Spatial distributions of the sub-clusters give clues to understand the factors that cause variations of groundwater vulnerability at a specific site, vis-a-vis local and regional lithological and non-lithological influences. As a result, the quality of groundwater on a regional scale changes from Na⁺ > Mg²⁺ >Ca²⁺ > K⁺: HCO ₃ ^? > Cl^? > SO ₄ ^2? > NO ₃ ^? > F^? in the cluster A to Na⁺ > Mg²⁺ >Ca²⁺ > K⁺: Cl^? > HCO ₃ ^? > SO ₄ ^2? > NO ₃ ^? > F^? in the cluster B, following the topography. The classification of the area into the zones of relative groundwater vulnerability with respect to drinking water quality of the chemical composition of the sub-clusters helps the planners to identify the specific locations, where the inferior quality of groundwater can occur, for taking the remedial measures.     

Ab initio calculations of 17O and nT NMR parameters (nT=31P, 29Si) in H3 TOTH3 dimers and T 3O9 trimeric rings

NMR shieldings (σ) and electric field gradients (eq) are calculated using ab initio methods at the O and T nuclei (where T=P, Si) in two different types of molecules-TH₃ dimers, i.e. H₃SiOSiH₃ and H₃POPH ₃ ²⁺ , and TO₄ trimeric rings, i.e., Si₃O ₉ ^6- and P₃O ₉ ^3- , which serve as models for assessing the effects of polymerization, bond length and bond angle variation on the NMR properties of polymerized silicates and phosphates. In agreement with earlier ab initio studies on H₃SiOSiH₃ we confirm that σ(²⁹Si), σ(³¹P), σ(¹⁷O) and eq(¹⁷O) all decrease as θ(SiOSi) decreases in the range from 180° to 100°. However, correction for artifacts due to distant core electrons leads to a considerably reduced value for the anisotropy in σ ^O, bringing it into better agreement with estimated experimental values. The qualitative change in σ(²⁹Si) with θ(SiOSi) can be understood on the basis of changes in the energies of the highest energy occupied MO's and consequent variations in their contributions to the paramagnetic part of the shielding. For H₃POPH ₃ ²⁺ we calculate a larger value of eq^O than for the analog Si compound but the same type of variation of σ(¹⁷O) with θ(TOT). The change in σ(³¹P) with θ(POP) is, however, calculated to be much smaller than in the Si case and a maximum is predicted for intermediate angles. For the trimeric rings we obtain energy optimized geometries in good agreement with x-ray structural data, with T-O terminal distances systematically shorter than the T-O bridging distances. Calculated σ(T) anisotropies are also in good agreement with experiment and can be simply related to the calculated structure. After correction for distant core effects we obtain a change in σ(³¹P) between PO ₄ ^3- and P₃O ₉ ^3- in reasonable agreement with experiment.