Thermal expansion,heat capacity,and entropy of MgO at mantle pressures

The pressure dependence of the Raman spectrum of forsterite was measured over its entire frequency range to over 200 kbar. The shifts of the Raman modes were used to calculate the pressure dependence of the heat capacity, C _v, and entropy, S, by using statistical thermodynamics of the lattice vibrations. Using the pressure dependence of C _v and other previously measured thermodynamic parameters, the thermal expansion coefficient, , at room temperature was calculated from = K _S (T/P) _S C _V/TVK _T, which yields a constant value of ( ln / ln V)_T= 6.1(5) for forsterite to 10% compression. This value is in agreement with ( ln / ln V)_T for a large variety of materials.At 91 kbar, the compression mechanism of the forsterite lattice abruptly changes causing a strong decrease of the pressure derivative of 6 Raman modes accompanied by large reductions in the intensities of all of the modes. This observation is in agreement with single crystal x-ray diffraction studies to 150 kbar and is interpreted as a second order phase transition.     

Pressure-volume-temperature behavior of fayalite based on static compression measurements at 400° C

Twenty-one energy-dispersive X-ray diffraction spectra for fayalite at 400° C constitute the basis for an elevated-temperature static compression isotherm for this important silicate mineral. A Murnaghan regression of the resulting molar volumes yields 103.8 GPa and 7.1 for the 400° C, room-pressure values of the isothermal bulk modulus (K ₀) and its first pressure derivative (K₀), respectively. When compared to the room-temperature static compression isotherm of Yagi et al. (1975), our 400° C value for K ₀ yields 5.4 ×10^–2 GPa/deg for (K/T)₀₀. When combined with literature volume data, our measurements indicate that the fayalite isochores are strongly concave toward the pressure axis [( ² T/P ² ) _v <>This is publication number 1125 of the School of Earth Sciences, Department of Geology and Geophysics, University of Minnesota, Minneapolis, MN 55455, USA     

P - V - T equation of state of stishovite to the mantle transition zone conditions

In-situ synchrotron X-ray diffraction experiments were conducted using the SPEED-1500 multi-anvil press of SPring-8 on stishovite SiO₂ and pressure-volume-temperature data were collected at up to 22.5 GPa and 1,073 K, which corresponds to the pressure conditions of the base of the mantle transition zone. The analysis of room-temperature data yielded V₀=46.56(1) ų, K_{T 0}=296(5) GPa and K _T =4.2(4), and these properties were consistent with the subsequent thermal equation of state (EOS) analyses. A fit of the present data to high-temperature Birch-Murnaghan EOS yielded (K_T /T) _P =–0.046(5) GPa K^–1 and = a + bT with values of a =1.26(11)×10^–5 K^–1 and b =1.29(17)×10^–8 K^–2. A fit to the thermal pressure EOS gives ₀=1.62(9)×10^–5 K^–1, ( K _T / T) _V =–0.027(4) GPa K^–1 and (²P /T ²) _V =27(5)×10^–7 GPa K^–2. The lattice dynamical approach by Mie-Grüneisen-Debye EOS yielded ₀=1.33(6), q =6.1(8) and ₀=1160(120) K. The strong volume dependence of the thermal pressure of stishovite was revealed by the analysis of present data, which was not detectable by the previous high-temperature data at lower pressures, and this yields ( K _T / T) _V 0 and q 1. The analyses for the fictive volume for a and c axes show that relative stiffness of c axis to a axis is similar both on compression and thermal expansion. Present EOS enables the accurate estimate of density of SiO₂ in the deep mantle conditions.     

Pressure-volume-temperature behavior of γ-Fe2SiO4 (spinel) based on static compression measurements at 400° C

Thirteen energy-dispersive x-ray diffraction spectra for -Fe₂SiO₄ (spinel) collected in situ at 400° C and pressures to 24 GPa constitute the basis for an elevated-temperature static compression isotherm for this important high-pressure phase. A Murnaghan regression of these molar volume measurements yields 177.3 (±17.4) GPa and 5.4(±2.5) for the 400° C, room pressure values of the isothermal bulk modulus (K _{P 0}) and its first pressure derivative (K _{P 0}), respectively. When compared to the room-Tdeterminations of K _{P 0} available in the literature, our 400° C K _{P 0} yields -4.1 (±6.2)×10^-2 GPa/degree for the average value of (K/T) _{P 0} over the temperature interval 25° C<><400°>A five-parameter V(P, T) equation for -Fe₂SiO₄ based on simultaneous regression of our data combined with the elevated P-Tdata of Yagi et al. (1987) and the extrapolated thermal expansion values from Suzuki et al. (1979) yields isochores which have very little curvature [(² T/P ²) _v 0], in marked contrast to the isochores for fayalite (Plymate and Stout 1990) which exhibit pronounced negative curvature [(T/P ²) _v <0]. along=" the=">-Fe₂SiO₄ reaction boundary V_Rvaries from a minimum of approximately 8.3% at approximately 450° C to approximately 8.9% at 1200° C. Extrapolation of the fayalite and -Fe₂SiO₄ V(P, T) relationships to the temperature and pressure of the 400 km discontinuity suggests a V _R of approximately 8.4% at that depth, approximately 10% less than the 9.3% V _R at ambient conditions.     

The elasticity of the upper mantle orthosilicates olivine and garnet to 3 GPa

The elastic moduli of single crystals of pyrope-rich garnet and San Carlos olivine have been measured over a 3 GPa pressure range at room temperature. The combination of improved ultrasonic techniques and this large pressure range provide for more reliable characterization of the pressure dependence of acoustic wave velocities than has previously been possible. First and second pressure derivatives of the velocities have been determined within 1 percent and 10 percent respectively. The Hashin-Shtrikman bounds for the pressure dependences of the bulk and shear moduli of the garnet used in this study are; K = 173.6 GPa, K = 4.93, K = –0.28 GPa^–1, G= 94.9 GPa, G = 1.56, G = –0.08 GPa^–1 and the Hashin-Shtrikman least-upper bounds and greatestlower bounds for the pressure dependences of the bulk and shear moduli of the San Carlos olivine are K=129.8 GPa, K = 4.66, K= –0.15 GPa^–1, G = 77.8 GPa, G = 1.93, G = –0.11 GPa^–1 and K = 129.2 GPa, K = 4.63, K= –0.15 GPa^–1 G = 77.3 GPa, G=1.96, G = –0.11 GPa^–1 respectively. The determination of the room-pressure elastic moduli of this pyrope-almandine garnet removes the previously observed anomaly in the predictions of systematic treatments of variations of the elastic moduli of garnets with composition. The determination of the second pressure derivatives of the moduli of garnet and olivine illustrates the importance of these terms in extrapolations to higher pressures — with K/P for these crystals being reduced by 17 percent and 9 percent respectively over the 3 GPa pressure range.     

Mechanisms of the transformations between the α, β and γ polymorphs of Mg2SiO4 at 15 GPa

Data on the mechanisms of mantle phase transformations have come primarily from studies of analogue systems reacted experimentally at low pressures. In order to study transformation mechanisms in Mg₂SiO₄ at mantle pressures, forsterite () has been reacted in the stability field of -phase, at 15 GPa and temperatures up to 900° C, using a multianvil split-sphere apparatus. Transmission electron microscope studies of samples reacted for times ranging from 0.25–5.0 h show that forsterite transforms to -phase by an incoherent nucleation and growth mechanism involving nucleation on olivine grain boundaries. This mechanism and the resultant microstructures are very similar to those observed at much lower pressures in analogue systems (Mg₂GeO₄ and Ni₂SiO₄) as the result of the olivine to spinel () transformation. Metastable spinel () also forms from Mg₂SiO₄ olivine at 15 GPa, in addition to -phase, by the incoherent nucleation and growth mechanism. With time, the spinel progressively transforms to the stable -phase. After 1 h, spinels exhibit a highly striated microstructure along {110} and electron diffraction patterns show streaking parallel to [110] which indicates a high degree of structural disorder. High resolution imaging shows that the streaking results from thin lamellae of -phase intergrown with the spinel. The two phases have the orientation relationship [001]//[001] and [010]//[110] so that the quasi cubic-close-packed oxygen sublattices are continuous between both phases. These microstructures are similar to those observed in shocked meteorites and show that spinel transforms to -phase by a martensitic (shear) mechanism. There is also evidence that the mechanism changes to one involving diffusion-controlled growth at conditions close to equilibrium.     

β(Mg0.9, Fe0.1)2SiO4: Single crystal structure,cation distribution,and properties of coordination polyhedra

The synthesis boundaries of the phase transformation; ++ in (Mg_0.9, Fe_0.1)SiO₄, have been clarified at temperatures to 2000° C and pressures up to 20 GPa in order to synthesize single crystals of high quality. A single crystal of (Mg_0.9, Fe_0.1)₂SiO₄ was grown successfully to a size of 500 m. The crystal structure has been refined from single-crystal X-ray intensities. The ferrous ions prefer M1 and M3 sites to over the larger M2 site. The volume change of all the occupied polyhedra does not contribute to the decrease of total volume in the transformation; rather it tends to increase the bulk volume through the expansion of occupied tetrahedra. The volume reduction in the phase transformations is accounted for by unoccupied polyhedra, with the octahedra contributory 60% and the tetrahedra 40% to the V of the transition. The volume change in the transformation is caused also partly by the volume decrease of MO ₆ (25%), partly the unoccupied tetrahedra (45%) and octahedra (30%).     

Mg tracer diffusion in synthetic forsterite and San Carlos olivine as a function of P,T and fO2

We present new experimental data on Mg tracer diffusion in oriented single crystals of forsterite (Fo₁₀₀) and San Carlos olivine (Fo₉₂) between 1000–1300° C. The activation energies of diffusion are found to be 400 (±60) kJ/mol (96 kcal/mol) and 275 (±25) kJ/mol (65 kcal/ mol) in forsterite and San Carlos olivine, respectively, along [001] at a fO₂ of 10^–12 bars. There is no change in activation energy of Mg tracer diffusion within this temperature range. Mg tracer diffusion in a nominally pure forsterite is found to be anisotropic (D_c > D_a > D _b) and a function of fO₂. This fO₂ dependence is different from that in olivine containing Fe as a major element, which suggests that the diffusion mechanism of Mg in forsterite is different from that in Fe-bearing olivine at least over some range of fO₂. The diffusion mechanism in nominally pure forsterites may involve impurities present below the limits of detection or alternately, Si or Fe³⁺ interstitial defects, Fe being present as impurity (ppm level) in forsterite. Pressure dependence of Mg tracer diffusivity in forsterite measured to 10 GPa in a multianvil apparatus yields an activation volume of approximately 1–3.5 cm³/ mol. It is found that presence of small amounts of hydrogen bearing species in the atmosphere during diffusion anneal (f_H2 0.2 bars, f_H20 0.24 bars) do not affect Mg tracer diffusion in forsterite within the resolution of our measurement at a total pressure of 1 bar. The observed diffusion process is shown to be extrinsic; hence extrapolation of the diffusion data to lower temperatures should not be plagued by uncertainties related to change of diffusion mechanism from intrinsic to extrinsic.     

Calibration of Al/Si order variations in anorthite

New single crystal diffraction data for natural and heat-treated anorthite crystals (Angel et al. 1990) allow the determination of their states of Al/Si order in terms of a macroscopic order parameter,Q _OD , for the transition. Numerical values ofQ _OD obtained from estimates of site occupancies are shown to vary with the scalar spontaneous strain, _s , as _s Q _OD ² , and with the ratio of the sums of typeb (superlattice) reflections and typea (sublattice) reflections asI _b/I _a Q _OD ² . An empirical calibration for pure anorthite is obtained giving varies between 0.92 and 0.87 in samples equilibrated at T1300° C, but then falls off relatively rapidly with increasing temperature, reaching 0.7 near the melting point ( 1557° C). The observed temperature dependence does not conform to the predictions of the simplest single order parameter models; coupling ofQ _OD withQ of the transition is suspeeted.     

Chemistry of some Pb-(Cu,Fe)-(Sb,Bi sulfosalts from France and Portugal. Implications for the crystal chemistry of lead sulfosalts in the Cu-poor part of the Pb2S2-Cu2S-Sb2S3-Bi2-Bi2S3 system

Electron microprobe analysis of Pb-Cu(Fe)-Sb-Bi sulfosalts from Bazoges and Les Chalanches (France), and Pedra Luz (Portugal), give new data about (Bi, Sb) solid-solution and incorporation of the minor elements Cu, Fe or Ag in jaskolskiite, and in izoklakeite-giessenite and kobellite-tintinaite series. Jaskolskiite from Pedra Luz has high Sb contents (from 17.9 to 20.7 wt.%), leading to the extended general formula: Cu _x Pb_2+x (Sb_1–y Bi _y )_2–x S₅, with 0.10 x 0.22 and 0.19 y 0.41. Fe-free, Bi-rich izoklakeite from Bazoges has high Ag contents (up to 2.2 wt. %), leading to the simplified formula Cu₂Pb₂₂Ag₂(Bi, Sb)₂₂S₅₇; in Les Chalanches it contains less Ag content (1.2 wt.%), but has an excess of Cu that gives the formula: Cu_2.00 (Cu_0.49Ag_1.18)_=1.67Pb_22.70(Bi_12.63Sb_8.99)_=21.62S_57.27.In tintinaite from Pedra Luz, the variation of the Fe/Cu ratio can be explained by the substitution: Cu + (Bi, Sb) Fe + Pb; Fe-free kobellite from Les Chalanches has a Cu-excess, corresponding to the formula Cu_2.81Ag_0.54Pb_9.88(Bi_10.37Sb_5.21)_=15.38S_35.09. Eclarite from the type locality, structurally related to kobellite, shows a Cu excess too. In natural samples of the kobellite homologous series, Fe is positively correlated with Pb, and its contents never exceed that of Cu. Ag substitutes for Pb, together with (Bi, Sb). Taking into account the possibility of Cu excess, but excluding formal Cu²⁺ and Fe³⁺, general formulae can be written:     

Structural relaxation in silicate melts and non-Newtonian melt rheology in geologic processes

The timescale of structural relaxation in a silicate melt defines the transition from liquid (relaxed) to glassy (unrelaxed) behavior. Structural relaxation in silicate melts can be described by a relaxation time, , consistent with the observation that the timescales of both volume and shear relaxation are of the same order of magnitude. The onset of significantly unrelaxed behavior occurs 2 log₁₀ units of time above . In the case of shear relaxation, the relaxation time can be quantified using the Maxwell relationship for a viscoelastic material; _S = _S/G (where _S is the shear relaxation time, G is the shear modulus at infinite frequency and _S is the zero frequency shear viscosity). The value of G known for SiO₂ and several other silicate glasses. The shear modulus, G , and the bulk modulus, K , are similar in magnitude for every glass, with both moduli being relatively insensitive to changes in temperature and composition. In contrast, the shear viscosity of silicate melts ranges over at least ten orders of magnitude, with composition at fixed temperature, and with temperature at fixed composition. Therefore, relative to _S, G may be considered a constant (independent of composition and temperature) and the value of _S, the relaxation time, may be estimated directly for the large number of silicate melts for which the shear viscosity is known.For silicate melts, the relaxation times calculated from the Maxwell relationship agree well with available data for the onset of the frequency-dependence (dispersion) of acoustic velocities, the onset of non-Newtonian viscosities, the scan-rate dependence of the calorimetric glass transition, with the timescale of an oxygen diffusive jump and with the Si-O bond exchange frequency obtained from ²⁹Si NMR studies.     

A stable isotope study of the Palaeoproterozoic Tallberg porphyry-type deposit,northern Sweden

The Tallberg deposit is situated in the Skellefte District in northern Sweden. It is a Palaeoproterozoic equivalent of Phanerozoic poryphyry-type deposits. The mineralization is situated within the Jörn granitoid complex and is associated with intrusive quartz-feldspar porphyries. The granitoids are coeval with mainly felsic volcanic rocks hosting several massive sulphide deposits. The alteration is generally of a mixed phyllic-propylitic type, but areas or zones associated with high gold grades exhibit phyllic alteration. Ore minerals are pyrite, chalcopyrite, sphalerite, magnetite, and trace amounts of molybdenite. In this stable isotope study, quartz, sericite, and chlorite from the alteration zones were sampled. The magmatic quartz has a ¹⁸O composition of + 6.2 to +6.7 whereas the quartz in the hydrothermal alteration zones have values ranging from +7.5 to +10.6. The calculated temperatures for this fractionation range from 430° to 520°C. The sericites have ¹⁸O ranging from +4.6 to +8.2 (average +6.6) and D -31 to -54 (average -41). Chlorites range from ¹⁸O +4.2 to +7.7 and D from –34 to –44. The range of ³⁴S of 11 pyrite samples is +3.8 to +5.5 with an average of +4.6 ± 0.5, suggesting a relatively homogeneous sulphur source, probably of magmatic origin. Modelling waters in equilibrium with the minerals indicates early magmatic fluids with ¹⁸O of 6.5. This fluid mixed with a low ¹⁸O and high D fluid, which is tentatively identified as seawater. The ¹⁸O signature of sericite and chlorite also indicates significant water-rock exchange, explaining the positive ¹⁸O values for the waters in equilibrium with the hydrated minerals.     

Unilateral ARMA processes on a square net by the herringbone method

Because multidimensional ARMA processes have great potential for the simulation of geological parameters such as aquifer permeability, it was important to resolve which of two proposed alternative methods should be used for determining the two-dimensional weighting parameter, , for a unilateral ARMA (1, 0) process on a square net. Practical simulations demonstrates that the correct formulation is: =₁₀/(1+ ₁₀ ² where _r,s is the correlation between lattice points at lagsr and s. When the simulations are performed with correlations of 0.8 or more a residual bias was detected which was found to be caused by a difference in the variance between the one- and two-dimensional models. This can be rectified by modifying the two- dimensional model as follows: z_ij=(z_{i–1, j} + z_{i, j–1}) + a_ij where ²=1/(1 + ₁₀ ² ).     

Pervasive rehydration of granulites during exhumation – an example from the Pulur complex, Eastern Pontides, Turkey

Summary High-grade gneisses from the Pulur complex in NE Turkey bear evidence for biotite-dehydration melting at 820°C and 0.7–0.8GPa, melt segregation and near-isothermal decompression to 0.4–0.5GPa. During further exhumation, the rocks underwent secondary pervasive rehydration at temperatures between 400 and 230°C and fluid pressures between 0.3 and 0.1GPa. Metamorphic peak conditions are dated at 331–327Ma, while hydrothermal retrogression occurred significantly later at 315–310Ma under static conditions. During the rehydration event, primary high-grade mineral assemblages including garnet, cordierite, sillimanite, spinel, biotite, plagioclase and ilmenite were extensively replaced by muscovite, paragonite, margarite, corundum, diaspore, chlorite, kaolinite, pumpellyite, prehnite, epidote, titanite, anatase, pyrite and chalcopyrite. Secondary mineral assemblages indicate that the infiltrating fluids were characterized by low fO₂, very low X_CO2 (<0.002), variable activities of Ca²⁺, K⁺, Na⁺ and H⁺ and relatively high activities of H₂S and CH₄. Quartz veins that might have acted as pathways for the fluids are rare. Ubiquitous veinlets consisting of (i) albite, (ii) chlorite+calcite+quartz or (iii) K-feldspar+calcite+quartz were formed after the pervasive rehydraton event by precipitation from aqueous solutions that were somewhat richer in CO₂.     

Dynamics of the α-β phase transitions in quartz and cristobalite as observed by in-situ high temperature 29Si and 17O NMR

Relaxation times (T₁) and lineshapes were examined as a function of temperature through the - transition for ²⁹Si in a single crystal of amethyst, and for ²⁹Si and ¹⁷O in cristobalite powders. For single crystal quartz, the three ²⁹Si peaks observed at room temperature, representing each of the three differently oriented SiO₄ tetrahedra in the unit cell, coalesce with increasing temperature such that at the - transition only one peak is observed. ²⁹Si T₁'s decrease with increasing temperature up to the transition, above which they remain constant. Although these results are not uniquely interpretable, hopping between the Dauphiné twin related configurations, ₁ and ₂, may be the fluctuations responsible for both effects. This exchange becomes observable up to 150° C below the transition, and persists above the transition, resulting in -quartz being a time and space average of ₁ and ₂. ²⁹Si T₁'s for isotopically enriched powdered cristobalite show much the same behavior as observed for quartz. In addition, ¹⁷O T₁'s decrease slowly up to the - transition at which point there is an abrupt 1.5 order of magnitude drop. Fitting of static powder ¹⁷O spectra for cristobalite gives an asymmetry parameter () of 0.125 at room T, which decreases to <0.040 at=" the=" transition=" temperature.=" the=" electric=" field=" gradient=" (efg)=" and=" chemical=" shift=" anisotropy=" (csa),=" however,=" remain=" the=" same,=" suggesting=" that=" the=" decrease=" in="> is caused by a dynamical rotation of the tetrahedra below the transition. Thus, the mechanisms of the - phase transitions in quartz and cristobalite are similar: there appears to be some fluctuation of the tetrahedra between twin-related orientations below the transition temperature, and the -phase is characterized by a dynamical average of the twin domains on a unit cell scale.     

Mössbauer study of a California desert celadonite and its pedogenically-related smectite

Celadonite from the northwestern Mojave Desert area of California was examined by detailed Mössbauer spectroscopy at temperatures from 10 K to 400 K. In addition to the predominant Fe³⁺ doublet with isomer shift 0.4 mm s^–1 and quadrupole splitting 0.4 mm s^–1, another Fe³⁺ doublet with 0.4, 1.2 mm/s and two Fe²⁺ doublets with 1.1, 1.7, 2.7 mm s^–1 at 300 K were distinguished. The minor Fe³⁺ component is ascribed to dehydroxylated surface sites. Most of the remaining Fe(90%) is M2 cis-OH octahedral in an ordered M⁺–M²⁺ array. However, about 10% is M1 trans-OH Fe²⁺. Isomer shift vs. T gives Debye temperatures of 570 K for Fe³⁺ in M2 and 380 K for both Fe²⁺ sites, indicating greater vibrational freedom for Fe²⁺. Quadrupole splitting vs. T for Fe²⁺ gives a valence electronic energy splitting of 760 cm^–1 between the ground and first excited state for M2. The M1 sites have a more drastic variation in vs. T which indicates not only a lower first excited state but a rhombic distortion at these sites. A proposed explanation is a neighboring M2 site vacancy. The soil clay formed from this celadonite, which is mostly Fe-rich smectite, was also studied by Mössbauer spectroscopy. About half the Fe²⁺ has been oxidized in the clay, but the isomer shifts and quadrupole splittings are essentially the same as in the original celadonite. A texture orientation in the clay absorber was detected by measuring the absorber at 55° to the source radiation. This texture effect produces asymmetric doublets in the usual 90° measurement.     

Compression of α-MnS (alabandite) and a new high-pressure phase

The compressibility of -Mns (alabandite) was determined by x-ray analysis using a Mao-Bell type diamond anvil cell. The zero pressure bulk modulus (K₀) is 74±2 GPa with the pressure derivative of the bulk modulus (K_o) fixed at four. Allowing (K_o) to vary yielded a statistically better fit with K₀ = 88±6 GPa and k₀ = 2.2±0.6. Our data combined with the data of McCammon (1991) gave K_o = 73±1 GPa with k_o fixed at four. A fit with k_o allowed to vary yielded k_o = 75±2 GPa and k_o = 3.7±0.4. Alabandite transformed from the B1 structure (NaCl-type) to an unknown high-pressure phase at 26 GPa. The high-pressure phase has lower than hexagonal symmetry and it is stable to at least 46±4 GPa.Also affiliated with the James Franck Institute, University of Chicago     

Mean and turbulent velocity measurements of supersonic mixing layers

The behavior of supersonic mixing layers under three conditions has been examined by schlieren photography and laser Doppler velocimetry. In the schlieren photographs, some largescale, repetitive patterns were observed within the mixing layer; however, these structures do not appear to dominate the mixing layer character under the present flow conditions. It was found that higher levels of secondary freestream turbulence did not increase the peak turbulence intensity observed within the mixing layer, but slightly increased the growth rate. Higher levels of freestream turbulence also reduced the axial distance required for development of the mean velocity. At higher convective Mach numbers, the mixing layer growth rate was found to be smaller than that of an incompressible mixing layer at the same velocity and freestream density ratio. The increase in convective Mach number also caused a decrease in the turbulence intensity ( _u /U).List of Symbols a speed of sound - b total mixing layer thickness betweenU ₁ – 0.1U andU ₂ + 0.1U - f normalized third moment ofu-velocity,f u ³/(U)³ - g normalized triple product ofu ² v,g u ² v/(U)³ - h normalized triple product ofu v ², h uv' ²/(U)³ - l _u axial distance for similarity in the mean velocity - l _u axial distance for similarity in the turbulence intensity - M Mach number - M _c convective Mach number (for ₁=₂),M _c (U ₁–U ₂)/(a ₁+a ₂) - P static pressure - r freestream velocity ratio,rU ₂/U ₁ - Re unit Reynolds number,Re U/ - s freestream density ratio,s ₂/ ₁ - T _t total temperature - u instantaneous streamwise velocity - u deviation ofu-velocity,u u–U - U local mean streamwise velocity - U ₁ primary freestream velocity - U ₂ secondary freestream velocity - U average of freestream velocities, ¯U (U ₁ +U ₂)/2 - U freestream velocity difference,U U ₁ –U ₂ - v instantaneous transverse velocity - v deviation ofv-velocity,v v – V - V local mean transverse velocity - x streamwise coordinate - y transverse coordinate - y ₀ transverse location of the mixing layer centerline - ensemble average - ratio of specific heats - boundary layer thickness (y-location at 99.5% of free-stream velocity) - similarity coordinate, (y –y ₀)/b - compressible boundary layer momentum thickness - viscosity - density - standard deviation - dimensionless velocity, (U –U ₂)/U - 1 primary stream - 2 secondary stream A version of this paper was presented at the 11th Symposium on Turbulence, October 17–19, 1988, University of Missouri-Rolla     

Complexation of Gold(III)-Chloride at the Surface of Hematite

The acid/base properties of the hematite/water interface and surfacecomplexation with gold has been studied by potentiometric titrations in thefour component system H⁺ – FeOH –AuCl ₄ ^- – Cl^-. Equilibrium measurementswere performed in NaCl media at 298.2 K. In the evaluation of equilibriummodel from experimental data the constant capacitance model was applied. Theacid/base properties were investigated in 0.1 M NaCl in the range 2.6 pH 7.4. The resulting intrinsic constants for protonation anddeprotonation of hydroxyl groups at the surface were log _1,1,0,0(int) ^s = 7.10 ± 0.06 andlog _{-1,1,0,0(int)} ^s = - 7.80 ±0.06. The density of proton active surface sites was 2.85nm^-2 and the specific capacitance 2.5 C V^-1 m^-2. In the investigation of surface complexation of gold, thepotentiometric titrations were performed in the range 2.0 pH 10.2.Titration data was supplemented with analysis of Au in the aqueous phase byatomic absorbance spectrometry. The equilibrium model proposed consists ofthe following monodentate surface complexes: FeOHAuCl₃(log _0,1,1,-1 ^s = 1.45 ± 0.03),FeOHAuCl₂OH (log _-1,1,1,-2 ^s = -3.89 ± 0.02), FeOHAu(OH)₃ (log _-3,1,1,-4 ^s = -21.94 ± 0.05). Aslightly better fit could be obtained by assuming formation of a bidentatecomplex with the composition(FeO)₂Au(OH)H₂O. However, based onstructural arguments this complex was rejected.