Computation of surface energies in an electrostatic point charge model: I. Theory

The attachment energies, the slice energies and the specific surface energies can be calculated in an electrostatic point charge model using the formula derived by Madelung for the potential introduced by an infinite row of equally spaced point charges. Power series are given for the Hankel function iH ₍₀₎ ⁽¹⁾ (iy) and Ψ(x)=d ln x!/dx. The logarithmic expression in the Madelung formula converges rapidly when applying a power series, which combines equally charged cations and anions. Besides the specific surface energy (γ ^hkl), the slice energy (E _s ^hkl ) and the attachment energy (E _a ^hkl ) can be considered as special categories of surface energies as they depend on surface configurations as well. The specific surface energy γ is the energy per unit area of surface needed to split the crystal parallel to a face (hkl). The attachment energy (E _a) is the energy released per mole, when a new slice of thickness d _hkl crystallizes on an already existing crystal face (hkl). The growth rate of the crystal face (hkl) is a function of its attachment energy. The slice energy (E _s) is the energy released per mole, when a new slice d _hkl is formed from the vapour neglecting the influence of edge energies. The lattice energy (E _c) which is the energy released per mole of a crystal crystallizing from the vapour, is given by the following relation: E _c=E _a+E _s.     

Sulphur content and sulphur isotope composition of orange and black glasses in Apollo 17 drive tube 74002/1

The sulphur contents and δ³⁴S values have been determined for the bulk and various grain size fractions of three $\text{74002}\text{1}$ lunar drive tube samples. The sulphur contents of the bulk samples ate much lower than those of other lunar soils. These samples, along with the surface orange soil 74220 analysed previously, show an increase of sulphur concentration with decreasing particle size which is more marked than for other soils and indicates that the orange and black glass droplets have a coating enriched in sulphur and other volatile elements.In sharp contrast with other soils, the orange and black glasses have slight positive δ³⁴S values for large particles while the smallest particle sizes show negative δ³⁴S values. This indicates that the coating of the glassy droplets is enriched in isotopically light sulphur. These observations favour the theory that the orange and black glasses were generated by a volcanic fire fountain.The anomalously high δ³⁴S values of the fine fractions of the core bottom sample, 74001-135, combined with the results of an acid leaching experiment, indicate that these fractions are contaminated, possibly by a mature soil of high sulphur content and relatively positive δ³⁴S value.     

Non-axial planar S1 cleavage in the Hawick Rocks of the Galloway area,Southern Uplands,Scotland

S₁ cleavage in the Hawick Rocks of the Galloway area is non-axial planar, cutting obliquely across the F₁ folds in a predominantly clockwise sense. Individual S₁ cleavage planes within cleavage-fans in F₁ folds strike clockwise, locally anti-clockwise, of axial surfaces, and the mean plane to the S₁ cleavage-fans dips predominantly more steeply than the axial surface. F₁ folds investigated at scattered localities in Silurian and Ordovician rocks north of the Hawick Rocks are also transected by the S₁ cleavage, indicating that non-axial planar S₁ cleavage is widespread in the Southern Uplands. The S₁ cleavage is a composite fabric. Objects deformed within sandstones and tuffs indicate oblate strain. F₁ fold plunge varies from NE to SW and fold hinges locally are markedly curvilinear. Steeply plunging and locally downward-facing F₁ folds are present along the southeast margin of the Hawick Rocks. The non-axial planar S₁ cleavage relationships persist in the steeply plunging F₁ folds. Synchronous development of the non-axial planar S₁ cleavage and the variably plunging F₁ folds is proposed.     

Computation of surface energies in an electrostatic point charge model: II. Application to zircon (ZrSiO4)

The attachment energies, the slice energies and the specific surface energies can be calculated in an electrostatic point charge model using the formula derived by Madelung for the potential introduced by an infinite row of equally spaced point charges. Power series are given for the Hankel function iH ₍₀₎ ⁽¹⁾ (iy) and (x)=d ln x!/dx. The logarithmic expression in the Madelung formula converges rapidly when applying a power series, which combines equally charged cations and anions. Besides the specific surface energy ( ^hkl), the slice energy (E _s ^hkl ) and the attachment energy (E _a ^hkl ) can be considered as special categories of surface energies as they depend on surface configurations as well. The specific surface energy is the energy per unit area of surface needed to split the crystal parallel to a face (hkl). The attachment energy (E _a) is the energy released per mole, when a new slice of thickness d _hkl crystallizes on an already existing crystal face (hkl). The growth rate of the crystal face (hkl) is a function of its attachment energy. The slice energy (E _s) is the energy released per mole, when a new slice d _hkl is formed from the vapour neglecting the influence of edge energies. The lattice energy (E _c) which is the energy released per mole of a crystal crystallizing from the vapour, is given by the following relation: E _c=E _a+E _s.     

Effects of different crystal faces on the surface charge of colloidal goethite (α-FeOOH) particles: an experimental and modeling study

The surface charge of colloidal particles is usually determined by potentiometric titration. These acid-base titrations make it possible to measure the pH of point-of-zero charge (pzc) for oxide minerals. This macroscopic property is the most important parameter used in surface complexation modeling to reproduce experimental data. The pzc values of goethite reported in the literature vary between 7.0 and 9.5. Carbonate adsorption and/or surface morphology are thought to account for this wide range.We demonstrate a procedure for the removal of the carbonate ions that initially adsorb on goethite and strongly affect the titration curves and pzc determination. We also investigated the crystal-face-specific reactivity of two morphologically different goethites. The z-profiles obtained from atomic force microscopy (AFM) images showed that the goethite with the smallest specific surface area (S = 49 m²/g, denoted G49) exhibits 70% of the (001) face, whereas this value is only 30% for the goethite with largest specific surface area (S = 95 m²/g, denoted G95). This morphologic difference results in slightly different pzc values: 9.0 for G49 goethite and 9.1 for G95 geothite. These experimental pzc values have been correlated with multisite complexation calculations using both the full-site and the 1-pK approaches. We used the full-site approach to consider all of the configurations of hydrogen bond interactions with surface site. The resulting mean charges gave estimated pzc values of 8.9 and 9.2 for the (001) and (101) faces, respectively. Considering these theoretical pzc values for individual faces and the face distributions obtained from AFM analysis, the calculated pzc values are in full agreement with the experimental pzc values. However, this morphologic difference is more expressed in surface charge values than in the pzc values. Indeed, the surface charge of G49 goethite is much higher than that of G95 goethite, and the 1-pK calculations make it possible to fit the titration data satisfactorily.     

Role of degree of saturation in denitrification of unsaturated sand specimens

Nitrate contamination of groundwater arises from anthropogenic activities, such as, fertilizer and animal manure applications and infiltration of wastewater/leachates. During migration of wastewater and leachates, the vadose zone (zone residing above the groundwater table), is considered to facilitate microbial denitrification. Particle voids in vadose zone are deficient in dissolved oxygen as the voids are partially filled by water and the remainder by air. Discontinuities in liquid phase would also restrict oxygen diffusion and therefore facilitate denitrification in the vadose/unsaturated soil zone. The degree of saturation of soil specimen (S _r) quantifies the relative volume of voids filled with air and water. Unsaturated specimens have S _r values ranging between 0 and 100 %. Earlier studies from naturally occurring nitrate losses in groundwater aquifers in Mulbagal town, Kolar District, Karnataka, showed that the sub-surface soils composed of residually derived sandy soil; hence, natural sand was chosen in the laboratory denitrification experiments. With a view to understand the role of vadose zone in denitrification process, experiments are performed with unsaturated sand specimens (S _r = 73–90 %) whose pore water was spiked with nitrate and ethanol solutions. Experimental results revealed 73 % S _r specimen facilitates nitrate reduction to 45 mg/L in relatively short durations of 5.5–7.5 h using the available natural organic matter (0.41 % on mass basis of sand); consequently, ethanol addition did not impact rate of denitrification. However, at higher S _r values of 81 and 90 %, extraneous ethanol addition (C/N = 0.5–3) was needed to accelerate the denitrification rates.     

A sulphur isotopic study of the Navia gold belt (Spain)

The Navia gold belt is located in the West Asturian-Leonese Zone of the Iberian Variscan Orogen. The host rocks of the mineralization are quartzites, sandstones and black shales of Cambro-Ordovician age. The gold belt extends along 35 km and has five major veins: Penedela, Encarnita, Fornaza, Carmina and S. Jose. The ores belong to at least four associations having contrasting mineralogies and textures. The δ³⁴S values for individual mineral phases reflect the polyphase metallogenic history. The older association (Stage 1) is Fe-Mn-rich and is made up of spessartine, grunerite-dannemorite and quartz, with magnetite, pyrrhotite and chalcopyrite as metallic phases. The mineralization of Stage 1 is followed by the As-rich Stage 2 with quartz, arsenopyrite and pyrite. The δ³⁴S values for pyrite range from 14.9 to 19.9 per mil (n = 16), and for arsenopyrite from 13.2 to 17.3 per mil (n = 7). The observed isotopic homogeneity likely implies isotopic equilibrium at the scale of the gold vein. Stage 3 contains a coarse-grained base metal sulphide-rich association. The δ⁴S values for sphalerite range from 16.4 to 20.6 per mil (n= 16), and for galena from 17.0 to 18.7 per mil (n = 11). δ³⁴S_sp > δ³⁴S_gl suggests that the sulphur isotopic fractionation of the ore-forming system had reached equilibrium. The youngest crosscutting mineral association (Stage 4) consists of Pb-Sb sulphosalts, bornite, electrum and quartz. The δ³⁴S values for sulphosalts range from 9.7 to 15.8 per mil, showing the lightest results of the Navia sulphides.The relatively tight clustering of δ³⁴S values of the Au-related sulphides, and the results of fluid inclusions and paragenetic studies, can be interpreted to indicate that the hydrothermal fluids of the last three stages were dominated by H₂S. In the H₂S predominant field, sulphide minerals precipitating from solutions would exhibit δ³⁴S values similar to the δ³⁴S_ΣS value of the ore fluid. The heavy δ³⁴S_ΣS of the Navia fluids is consistent with leaching of sulphur from the host rocks. The main sulphur source could be diagenetic pyrite from the siliciclastic rocks of the Cabos and Luarca Formations, which exhibit δ³⁴S values from 8.3 to 21.2 per mil. An additional sulphur-source in Stage 3 would be the leaching of disseminated sphalerite and galena present in Cambrian carbonates.     

Sound velocity and density of liquid Ni68S32 under pressure using ultrasonic and X-ray absorption with tomography methods

A new experimental setup for simultaneous P-wave velocity (V_P) and density (ρ) measurements for liquid alloys is developed using ultrasonic and X-ray absorption methods combined with X-ray tomography at high pressures and high temperatures. The new setup allows us to directly determine adiabatic bulk moduli (K_S) and to discuss the correlation between the V_P and ρ of the liquid sample. We measured V_P and ρ of liquid Ni₆₈S₃₂ up to 5.6 GPa and 1045 K using this technique. The effect of pressure on the V_P and ρ values of liquid Ni₆₈S₃₂ is similar to that of liquid Fe₅₇S₄₃. (Both compositions correspond to near-eutectic ones.) The obtained K_S values are well fitted to the finite strain equation with a $K_{{\text{S}}_0}$ value (K_S at ambient pressure) of 31.1 GPa and a dK_S/dP value of 8.44. The measured V_P was found to increase linearly with increasing ρ, as approximated by the relationship: V_P [m/s] = 1.29 ρ [kg/m³] – 5726, suggesting that liquid Ni–S follows an empirical linear relationship, Birch's law. The dV_P/dρ slope is similar between Ni₆₈S₃₂ and Fe₅₇S₄₃ liquids, while the V_P–ρ plot of liquid Ni–S is markedly different from that of liquid Fe–S, which indicates that the effect of Ni on Birch's law is important for understanding the V_P–ρ relation of planetary and Moon's molten cores.     

Interaction of longitudinal surface settlements for twin tunnels in shallow and soft soils: the case of Istanbul Metro

Increasing demands on infrastructures increases the attention on shallow soft ground tunneling methods in urbanized areas. Especially, in metro tunnel excavations, it is important to control the surface settlements observed before and after excavation, which may cause damage to surface structures. To solve this problem, earth pressure balance machines (EPBMs) have widely been used throughout the world. This study focuses on surface settlement measurements, the interaction of twin tunnel surface settlement, and the relationship between shield parameters and surface settlement for parallel tunnels using EPBM shields in clay and sand soils. In this study, the tunnels were excavated using two EPBMs. The tunnels were 6.5 m in diameter, as twin tubes with a 14 m distance from center to center. The EPBM in the first tube followed about 100 m behind the other tube. Segmental lining with 1.4 m of length was employed as a final support. The results from this study showed that (1) the most important parameters for the maximum surface settlements are the face pressure and backfill; (2) in twin tunnel excavation with EPBM for longitudinal profile, the settlement rate reached its peak value when the shield came to the monitoring section and this peak value continued until the shield passed the monitoring section; (3) every shield affected the other tunnel’s longitudinal surface settlement profile by approximately 35–36.8 %; (4) S _A, S _B and S _C values were found to be 38.0, 35.8 and 26.2 %, respectively for an EPBM, and (5) ensuring good construction quality is a very effective way to control face stability and minimize surface settlement.     

The structural evolution of the Northern Hastings Block and southern Nambucca Block,southern New England Orogen,eastern Australia

The Hastings Block is a weakly cleaved and complexly folded and faulted terrain made up of Devonian, Carboniferous and Permian sedimentary and volcanic rocks. The map pattern of bedding suggests a major boundary exists that divides the Hastings Block into northern and southern parts. Bedding north of this boundary defines an upright box-like Parrabel Anticline that plunges gently northwest. Four cleavage/fold populations are recognised namely: E–W-striking, steeply dipping cleavage S₁ that is axial surface to gently to moderately E- or W-plunging; F₁ folds that were re-oriented during the formation of the Parrabel Anticline with less common N–S-trending, steeply dipping cleavage S₂, axial surface to gently to moderately N-plunging F₂ folds; poorly developed NW–SE-striking, steeply dipping cleavage S₃ axial surface to mesoscopic, mainly NW-plunging F₃ folds; and finally_, a weakly developed NE–SW-striking, steeply dipping S₄ cleavage formed axial surface to mainly NE-plunging F₄. The Parrabel Anticline is considered to have formed during the D₃ deformation. The more intense development of S₂ and S₃ on the western margin of the Northern Hastings Block reflects increasing strain related to major shortening of the sequences adjacent to the Tablelands Complex during the Hunter–Bowen Orogeny. The pattern of multiple deformation we have recorded is inconsistent with previous suggestions that the Hastings Block is part of an S-shaped orocline folded about near vertically plunging axes.     

Estimates of the second dissociation constant of H2S from the surface sulfidation of crystalline sulfur

The adsorption of hydrogen sulfide (Γ_H2S) and protons (Γ_H⁺) on the surface of crystalline sulfur was investigated experimentally in H₂S-bearing solutions at temperatures of 25, 50, and 70°C, NaCl concentrations of 0.1 and 0.5 mol/dm⁻³ and log C_H⁺ values in the range −2.3 to −5. At all temperatures, the dominant process on the surface of the sulfur was deprotonation, and the average values of Γ_H2S were very close to the highest values determined for Γ_H⁺. This finding, combined with the lack of detectable proton adsorption in H₂S-free solutions, suggests that proton adsorption/desorption on the surface of sulfur occurs through formation of ≡ S − H₂S complexes in the presence of H₂S.We propose that this complexation represents sulfidation of the sulfur surface, a process analogous to hydroxylation of oxide surfaces, and that the sulfidation can be described by the reaction: ≡ S + H₂S = ≡SSH₂⁰ β° The deprotonation of the ≡ SH° complex occurs via the reaction: ≡ SSH₂⁰ = ≡SSH⁻ + H⁺ β⁻ Values of 2.9, 2.8, and 2.9 (± 0.23) were obtained for −log β⁻ at 25, 50, and 70°C, respectively. These data were employed to estimate the second dissociation constant for hydrogen sulfide in aqueous solutions using the extrapolation method proposed by Schoonen and Barnes (1988) and yielded corresponding values for the constant of 17.4 ± 0.3, 15.7, and 14.5, respectively. The value for 25°C is in very good agreement with the experimentally determined values of Giggenbach (1971) at 17 ± 0.1; Meyer et al. (1983) at 17 ± 1; Licht and Manassen (1987) at 17.6 ± 0.3; and Licht et al. (1990) at 17.1 ± 0.3.     

External seismic stability of vertical geosynthetic-reinforced soil walls using pseudo-static method

Analysis of external stability of vertical geosynthetic-reinforced soil (GRS) walls is very important in the seismic prone zone. The scope of this paper is to obtain required minimum reinforcement length, L _min, for external seismic stability of vertical GRS walls by pseudo-static limit equilibrium method. Then, L _min can be calculated to resist sliding, eccentricity, and bearing capacity failure modes. The parameters considered include both horizontal and vertical seismic coefficients (k _h and k _v ), surcharge load (q), wall height (H) and the properties of retained backfill, GRS, and foundation soil. Results show that L _min against sliding failure mode, L _min,S , increases more quickly than that against the other two failure modes with the increase in k _h , q, or unit weight of retained backfill, γ _b , while L _min,S decreases more quickly than that against the other two failure modes with increase in friction angle of retained backfill, ? _b , or unit weight of GRS, γ _r . For the different failure modes, the effect of k _v on L _min is not identical with the change of k _h , and in addition, L _min/H will tend to remain unchanged with the increase in H. In general, L _min against bearing capacity failure mode, L _min,BC, is larger than L _min against the other two failure modes. However, L _min,BC will be less than L _min against eccentricity failure mode, L _min,E , for k _h exceeding 0.35, or friction angle of foundation soil, ? _f , exceeding 37°, and L _min,BC will also be less than L _min,S for friction angle of GRS, ? _r , being no more than 26°.     

Cone penetration-induced pore pressure distribution and dissipation

The excess pore water pressure distribution (u) induced by the penetration of a piezocone into clay and its dissipation behaviour have been investigated by laboratory model tests, theoretical analysis and numerical simulation. Based on the results of the tests and the analysis, a semi-theoretical method has been proposed to predict the piezocone penetration-induced pore pressure distribution in the radial direction from the shoulder of the cone. The method can consider the effect of the undrained shear strength (s_u), over-consolidation ratio (OCR) and rigidity index (I_r) of the soil. With a reliably predicted initial distribution of u and the measured curve of dissipation of pore water pressure at the shoulder of the cone (u₂), the coefficient of consolidation of the soil in the horizontal direction (c_h) can be back-fitted by analysis of the pore pressure dissipation. Comparing the back-fitted values of c_h with the values directly estimated by a previously proposed method indicates that the previously proposed method can be used reliably to estimate c_h values from non-standard dissipation curves (where u₂ increases initially and then dissipates with time).     

Lattice dynamics of pyrite FeS2 — polarizable-ion model

Lattice dynamical calculations of the pyrite FeS₂ were performed using the polarizable-ion model (PIM) with different sets of short-range force constants. Not until the mean deviations between the observed and the calculated phonon energies become smaller than 3 cm^-1, the true force field can be established. In the case of only slightly greater deviations, the force fields computed differ strongly being without any physical meaning. The results are discussed with respect to the force constants K _i , F _i , and H _i , the effective dynamic charges and polarizabilities of the atoms involved, and the eigenvectors and potential energy distributions of the phonon modes. The most important short-range force constants are K ₁ (Fe-S stretching): 0.5 N cm^-1, K ₂ (internal stretching of the S₂ units): 1.0 N cm^-1, F ₁ (Fe^....Fe stretching): 0.2 N cm^-1, which indicate repulsive interactions of Fe atoms due to the occupied t _2g orbitals despite the relatively large Fe?Fe distances of 383 pm, and F ₂ and F ₃ (both intermolecular S₂?S₂ interactions): 0.2 N cm^-1. The great TO/LO splittings of some of the IR allowed phonon modes (species F _u) are caused by the large polarizabilities (2.4^.10⁶ and 3.3^.10⁶ pm³) of the atoms involved rather than by their effective charges (Fe: 0.2 e).     

The sulphur isotope systematics of the Taolin lead-zinc ore deposit,China

Sulphur isotope data from coexisting sulphides and sulphates from the Taolin Pb-Zn ore deposit have been used to estimate the temperatures of sulphur mineral precipitation. The data indicate that sulphide was the dominant sulphur species in solution at high temperatures and that sulphate was dominant at low temperatures. Also the data show that the δ³⁴S value of total sulphur in solution was close to zero at high temperatures (~325°C) but had high positive values (+15%.) at low temperatures (~250°C). We interpret this phenomenon in terms of the effects of mineral precipitation on the isotopic composition of the solution. The increase in the δ³⁴S value of total sulphur with decreasing temperature was brought about by the removal from the system, by precipitation, of isotopically light sulphides.     

Theoretical growth morphology of whewellite CaC2O4·H2O

The morphological theory of Hartman and Perdok (1955, 1956) allows to deduce the character of a growth form {hkl} on the basis of structural data alone. Its application to the structure of whewellite leads to the identification of forms {100}, {010}, {021}, {011}, {12 \(\bar 1\) } and {121} which show during the growth a flat surface profile (flat forms F). These forms occur very frequently in the crystals we grew from pure aqueous solutions at supersaturation β≦1,90. Other forms, {001} and {10 \(\bar 1\) }, possibly show a double character (F or S, where S stays for related faces showing a stepped profile during the growth) according to the bonds assumed within some periodic bond chains (PBCs). Alternative ways of bonding water molecules lead to different structures of the same PBC. The different energy corresponding to these structures may explain the complex morphology of both natural and synthetic crystals grown at high β values.     

Research on probability integration parameter inversion of mining-induced surface subsidence based on quantum annealing

Probability integral method is an official prediction method for mining subsidence in China. However, how to obtain the probability integral method parameters based on the measured data is the premise of realizing the accurate prediction of the probability integral method. Simulated annealing (SA) is an effective nonlinear optimization algorithm that has recently been introduced into the mining subsidence field to obtain the parameters of the probability integration method. To solve the problems of slow convergence speed and easily falling into the local optimal solution in the method of parameters inversion in probability integral method based on SA (MPIPIMSA), the method of parameters inversion in probability integral method based on quantum annealing (MPIPIMQA) is proposed by combining the quantum fluctuation mechanism and simulated annealing theory. The simulation experimental results show that MPIPIMQA is superior to MPIPIMSA in the accuracy and stability of parameters, and MPIPIMQA has a stronger anti-interference ability for local losing observation points, random errors and gross errors in observation data. Finally, the parameters of probability integral method for the 1414(1) working face of the Guqiao Coal Mine in Huainan mining area were obtained by using MPIPIMQA, namely, q?=?0.9916, tanβ?=?1.9277, b?=?0.4190, θ?=?84.3381, S_u = ??7.3715, S_d = ??14.7126, S_l = 59.0695, and S_r = 32.6381, and the fitting error is 106.8863 mm. The research results have important reference values for accurate inversion of probability integral parameters.     

Influence of Infiltration of Sodium Chloride Solutions on SWCC of Compacted Bentonite–Sand Specimens

The degree of saturation of compacted bentonite buffer in deep geological repositories is subject to alterations from infiltration of groundwater and heat emanated from the waste canisters. The matric suction (ψ)–degree of saturation (S _r ) relations of unsaturated clays is represented by soil–water characteristics curves (SWCC) that are influenced by soil structure, initial compaction condition and stress history. Infiltration of groundwater besides increasing the degree of saturation can also alter the pore water chemistry; the associated changes in cation hydration and diffuse double layer thickness could impact the micro-structure and matric suction values. This study examines the influence of infiltrating sodium chloride solutions (1,000–5,000 mg/L) on the transient ψ–S _r relations of compacted bentonite–sand specimens. Analysis of the ψ–S _r plots, and X-ray diffraction measurements indicated that infiltration of sodium chloride solutions has progressively less influence on the micro-structure and SWCC relations of bentonite–sand specimens compacted to increasingly higher dry densities. The micro-structure and SWCC relations of specimens compacted to 1.5 Mg/m³ were most affected, specimens compacted to 1.75 Mg/m³ were less affected, while specimens compacted to 2 Mg/m³ remained unaffected upon infiltration with sodium chloride solutions.     

Sulphur isotopic investigation of lower carboniferous vein deposits of the British Isles

Similar characteristics and age data suggest that the Pb + Zn vein deposits hosted by Lower Palaeozoic and Vendian strata of the British Isles form a genetically related group, coeval with the Lower Carboniferous carbonatehosted base-metal deposits of Ireland. Sulphur isotopic data demonstrate that there were separate sulphide and sulphate sulphur sources for the vein minerals. ³⁴S values from minerals in individual vein systems are consistent but there is a large variation between deposits, revealing distinctive local sulphur sources. The data suggests that sulphide sulphur (total range of values of ³⁴S_H2S of -6.5 to 18.62) was derived from the underlying strata while the sulphate (baryte) sulphur source (³⁴S_baryte mainly in the range 12 to 24) was groundwater or surface water that mixed with rising hydrothermal fluids in the upper reaches of the veins.     

Morphological evolution of dissolving feldspar particles with anisotropic surface kinetics and implications for dissolution rate normalization and grain size dependence: A kinetic modeling study

With previous two-dimensional (2D) simulations based on surface-specific feldspar dissolution succeeding in relating the macroscopic feldspar kinetics to the molecular-scale surface reactions of Si and Al atoms ( [Zhang and Lüttge, 2008] and [Zhang and Lüttge, 2009]), we extended our modeling effort to three-dimensional (3D) feldspar particle dissolution simulations. Bearing on the same theoretical basis, the 3D feldspar particle dissolution simulations have verified the anisotropic surface kinetics observed in the 2D surface-specific simulations. The combined effect of saturation state, pH, and temperature on the surface kinetics anisotropy has been subsequently evaluated, found offering diverse options for morphological evolution of dissolving feldspar nanoparticles with varying grain sizes and starting shapes. Among the three primary faces on the simulated feldspar surface, the (1 0 0) face has the biggest dissolution rate across an extensively wide saturation state range and thus acquires a higher percentage of the surface area upon dissolution. The slowest dissolution occurs to either (0 0 1) or (0 1 0) faces depending on the bond energies of Si-(O)-Si (Φ_Si-O-Si/kT) and Al-(O)-Si (Φ_Al-O-Si/kT). When the ratio of Φ_Si-O-Si/kT to Φ_Al-O-Si/kT changes from 6:3 to 7:5, the dissolution rates of three primary faces change from the trend of (1 0 0) > (0 1 0) > (0 0 1) to the trend of (1 0 0) > (0 0 1) > (0 1 0). The rate difference between faces becomes more distinct and accordingly edge rounding becomes more significant. Feldspar nanoparticles also experience an increasing degree of edge rounding from far-from-equilibrium to close-to-equilibrium. Furthermore, we assessed the connection between the continuous morphological modification and the variation in the bulk dissolution rate during the dissolution of a single feldspar particle. Different normalization treatments equivalent to the commonly used mass, cube assumption, sphere assumption, geometric surface area, and reactive surface area normalizations have been used to normalize the bulk dissolution rate. For each of the treatments, time consistence and grain size dependence of the normalized dissolution rate have been evaluated and the results revealed significant dependences on the magnitude of surface kinetic anisotropy under differing environmental conditions. In general, the normalized dissolution rates are strongly dependent on grain size. Time-consistent normalization treatment varies with the investigated condition. The modeling results suggest that the sphere-, cube-, and BET-normalized dissolution rates are appropriate under the far-from-equilibrium conditions at low pH where these normalizations are time-consistent and are slightly dependent on grain size.