On the nonstoichiometry and point defects of olivine

This paper presents the point-defect thermodynamics for fayalite and olivine solid solutions (Fe _x Mg_1?x )₂SiO₄. By means of thermogravimetry, the metal-to-oxygen ratio of these silicates has been determined as a function of oxygen potential, compositionx and temperature. Experiments were performed in the range of 1,000° C≦T≦1,280° C and 0.2≦x≦1.0. It is found that V _Me ^″ , Fe _Me ^· and the associate {Fe′ _Si ^′ Fe _Me ^· } are the majority defects. With this knowledge it is possible to calculate the nonstoichiometry at given temperature as a function of \(p_{O_2 } \) and \(a_{SiO_2 } \) . The cation vacancy concentration shows a \(p_{O_2 }^{1/5} \) -dependence (forx≧0.2) and increases at givenT and \(p_{O_2 } \) almost exponentially with compositionx. In the composition range studied here, the silicates show an oxygen excess, and FeO is more soluble in the olivine than SiO₂.     

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.     

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.     

Double nuclear magnetic resonance and crystal chemistry at the lattice positions of diamagnetic atoms,both structural,and foreign

Double nuclear magnetic resonance (DNMR) with Jeener's pulsed sequence on proton and fluorine frequencies was used to investigate the electric quadrupole interactions of (i) ²³Na in Na₂Cd(SO₄)₂·2H₂O, B ₂ ⁰ =±218.5±1 kHz, B ₂ ² =±98±5 kHz, (ii) of ²³Na, which enter the crystal, CaF₂: Na⁺ (0.07 wt. %) B ₂ ⁰ =±85.7±0.5 kHz, trigonal position, and (iii) ²³Na which are near the foreign atom in NaF:Ca²⁺ (0.02 wt.%) B ₂ ⁰ =±86.7±0.5 kHz, tetragonal position. Some details of DNMR experiments are analyzed. The conditions for maximum transfer of a Zeeman energy to a dipole-dipole reservoir are described for multispin systems and some crystal hydrates. The angular dependence of the Hamiltonian containing the spherical tensor operators of second rank was obtained for all possible orientations of a local coordinate system relative to a laboratory system.     

Thermodynamics of plagioclase III: Spontaneous strain at the I\overline 1 - P\overline 1 phase transition in Ca-rich plagioclase

The lattice parameters of anorthites An₉₈Ab₂ and An₁₀₀ have been measured from 22 to 1100 K. The spontaneous strain arising from the \(I\overline 1 - P\overline 1\) displacive transition in An₉₈ follows second order Landau behaviour. The spontaneous strain (? _s) couples quadratically to the order parameter (Q ⁰) with ? _s∝Q ⁰²∝(T _c ^* ?T) and T _c ^* =530 K in An₉₈. This is in contrast to the tricritical behaviour observed in pure anorthite. These observations are consistent with a Landau model for the free energy of Ca-rich plagioclases in which Al/Si order and Na content renormalize the fourth order coefficient.     

A new Cu-rich variety of lyonsite from fumarolic sublimates of the Tolbachik volcano (Kamchatka, Russia) and its crystal structure

A new Cu-rich variety of lyonsite has been found from fumarolic sublimates of the Tolbachik volcano (Kamchatka, Russia). The empirical formula is Cu_4.33Fe _2.37 ³⁺ Ti_0.26Al_0.26Zn_0.07(V_5.85As_0.07Mo_0.07P_0.01S_0.01)O₂₄. The crystal structure was studied on single crystal using synchrotron radiation, R = 0.0514. The mineral is orthorhombic, Pnma, a = 5.1736(7), b =10.8929(12), c = 18.220(2) Å, V = 1026.8(2) ų, and Z = 2. The structural formula is (Cu_0.6Ti_0.3Al_0.3Fe _0.2 ³⁺ □_0.6)_Σ2Cu₂(Fe _2.2 ³⁺ Cu_1.8)_Σ4(V_5.8As_0.1Mo_0.1)_Σ6O₂₄. It is proposed to recast the simplified formula of lyonsite as Cu_3+x (Fe _4?2x ³⁺ Cu_2x )(VO₄)₆, where 0 ≤ x ≤ 1.     

57Fe Mössbauer spectroscopy and magnetization of cation-deficient Fe2TiO4 and FeCr2O4. Part I:57Fe Mössbauer spectroscopy

⁵⁷Fe Mössbauer spectra are presented for synthetic cation-deficient Fe₂TiO₄ and FeCr₂O₄ spinel particles (<1μm) at various temperatures. The spectra of ferrimagnetic cation-deficient Fe₂TiO₄ show characteristic features due to relaxation because of superparamagnetism and spin relaxation in the temperature range 5–294 K. At 5 K and 78 K, a superposition of at least two sextets is observed which appear to arise from Fe³⁺ onA-sites (Fe _A ³⁺ andB-sites (Fe _B ³⁺ ) of the spinal lattice with magnetic hyperfine fields at 5 K ofB _hf ((Fe _B ³⁺ )≈47.5 T andB _hf (Fe _B ³⁺ )≈51.0 T, respectively. Cation-deficient FeCr₂O₄ particles reveal at 78 K a fieldB _hf (Fe³⁺)≈46.9 T and exhibit relaxation spectra as a consequence of superparamagnetism in the temperature range 80 K - ～300 K. At 294 K, quadrupole splitting Δ(Fe _A ³⁺ )=0.92 mm/s and isomer shift δ(Fe _A ³⁺ )=0.29 mm/s (relative to metallic Fe) are measured. For both compounds the magnetic hyperfine fieldsB _hf are discussed in terms of supertransferred hyperfine fields involving vacancies and in the case of cation-deficient Fe₂TiO₄ also diamagnetic Ti⁴⁺ neighbours of the Fe ions.     

Thermodynamic data from redox reactions at high temperatures. II. The MnO-0Mn3O4 oxygen buffer,and implications for the thermodynamic properties of MnO and Mn3O4

The \(\mu _{O_2 } \) defined by the reaction 6 MnO+O₂ =2 Mn₃O₄ has been determined from 917 to 1,433 K using electrochemical cells (with calcia-stabilized zirconta, CSZ) of the type: Steady emfs were achieved rapidly at all temperatures on both increasing and decreasing temperature, indicating that the MnO-Mn₃O₄ oxygen buffer equilibrates relatively easily. It therefore makes a useful alternative choice in experimental petrology to Fe₂O₃-Fe₃O₄ for buffering oxygen potentials at oxidized values. The results are (in J/mol, temperature in K, reference pressure 1 bar); \(\mu _{O_2 } \) (±200)=-563,241+1,761.758T-220.490T inT+0.101819T ² with an uncertainty of ±200 J/mol. Third law analysis of these data, including a correction for the deviations in stoichiometry of MnO, impliesS _298.15 for Mn₃O₄ of 166.6 J/K · mol, which is 2.5 J/K · mol higher than the calorimetric determination of Robie and Hemingway (1985). The low value of the calorimetric entropy may be due to incomplete ordering of the magnetic spins. The third law value of Δ _r H _298.15 ⁰ is-450.09 kJ/mol, which is significantly different from the calorimetric value of-457.5±3.4 kJ/mol, calculated from Δ _f H _298.15 ⁰ of MnO and Mn₃O₄, implying a small error in one or both of these latter.     

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.     

Mössbauer,electrokinetic and refined lattice parameters study of synthetic manganoan lipscombite

Manganoan lipscombite (Fe _x ^/2+ , M _y ^/2+ ) Fe _3?(x ^+y)/3+ [OH)_3?(x+y)(PO₄)₂] was synthesized from pure chemicals. From the study of the Mn²⁺/Fe²⁺ atomic ratio by Mössbauer spectra, solubility, and electrokinetic properties, it was found that the crystal structure of lipscombite is not changed substantially by the manganese substitution. The unit cell parameters were determined from Guinier-Hägg X-ray diffraction patterns, which are identical for both synthetic ferrous-ferric and manganoan lipscombite. The two compounds crystallize in the tetragonal system with a=5.3020±0.0005 Å and c=12.8800±0.0005 Å.     

A finite temperature chandrasekhar model: Determining the parameters and calculation of the characteristics of degenerate dwarfs

We suggest a generalization of the standard Chandrasekhar model for degenerate dwarfs. We apply an equation of state for a degenerate ideal electron gas in the form of a Sommerfeld expansion in the parameter k _B T(r)/m ₀ c ². The radial temperature distribution T(r) is modeled taking into account the presence of the isothermal core. The model has four dimensionless parameters, two microscopic (the relativistic parameter at the stellar center x ₀ and the chemical-composition parameter ?? _e = A/Z) and two macroscopic (the dimensionless temperature T ₀ ^* = k _B T _c /m ₀ c ² and dimensionless radius ?? ₀ = R _c /R of the core, where R _c and R are the radii of the core and dwarf). We found x ₀, ?? _e , and T ₀ ^* for about 3000 DA white dwarfs, based on their masses, radii, and effective temperatures from the Sloan Digital Sky Survey Data Release 4; ?? ₀ was treated as a free parameter. The influence of temperature effects on the macroscopic characteristics is analyzed, in particular, the minimum mass and maximum radii of the stars. Based on our computed energy-radius dependence, we suggest an interpretation of the observed radius distribution for these dwarfs.     

Laihunite—A new iron silicate mineral

Laihuite reported in the present paper is a new iron silicate mineral found in China with the following characteristics:

1. This mineral occurs in a metamorphic iron deposit, associated with fayalite, hypersthene, quartz, magnetitc, etc.
2. The mineral is opaque, black in colour, thickly tabular in shape with luster metallic to sub-metallic, two perfect cleavages and specific gravity of 3.92.
3. Its main chemical components are Fe and Si with Fe³⁺>Fe²⁺. The analysis gave the formula of Fe Fe _1.00 ³⁺ ·Fe _0.58 ²⁺ ·Mg _0.03 ²⁺ ·Si_0.96O₄.
4. Its DTA curve shows an exothermic peak at 713°C.
5. The mineral has its own infrared spectrum distinctive from that of other minerals.
6. This mineral is of orthorhombic system; space group:C _2h ^/5 ?P2₁/c; unit cell:α=5.813ű0.005,b=4.812ű0.005,c=10.211ű0.005,β=90.87°.
7. The Mössbauer spectrum of this mineral is given, too.

     

Ephesite,Na(LiAl2) [Al2Si2O10] (OH)2: I. thermal stability and standard state thermodynamic properties

Ephesite, Na(LiAl₂) [Al₂Si₂O₁₀] (OH)₂, has been synthesized for the first time by hydrothermal treatment of a gel of requisite composition at 300≦T(° C)≦700 and \(P_{H_2 O}\) upto 35 kbar. At \(P_{H_2 O}\) between 7 and 35 kbar and above 500° C, only the 2M₁ polytype is obtained. At lower temperatures and pressures, the 1M polytype crystallizes first, which then inverts to the 2M₁ polytype with increasing run duration. The X-ray diffraction patterns of the 1M and 2M₁ poly types can be indexed unambiguously on the basis of the space groups C2 and Cc, respectively. At its upper thermal stability limit, 2M₁ ephesite decomposes according to the reaction (1) $$\begin{gathered} {\text{Na(LiAl}}_{\text{2}} {\text{) [Al}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{{\text{10}}} {\text{] (OH)}}_{\text{2}} \hfill \\ {\text{ephesite}} \hfill \\ {\text{ = Na[AlSiO}}_{\text{4}} {\text{] + LiAl[SiO}}_{\text{4}} {\text{] + }}\alpha {\text{ - Al}}_{\text{2}} {\text{O}}_{\text{3}} {\text{ + H}}_{\text{2}} {\text{O}} \hfill \\ {\text{nepheline }}\alpha {\text{ - eucryptite corundum}} \hfill \\ \end{gathered}$$ Five reversal brackets for (1) have been established experimentally in the temperature range 590–750° C, at \(P_{H_2 O}\) between 400 and 2500 bars. The equilibrium constant, K, for this reaction may be expressed as (2) $$log K{\text{ = }}log f_{{\text{H}}_{\text{2}} O}^* = 7.5217 - 4388/T + 0.0234 (P - 1)T$$ where \(f_{H_2 O}^* = f_{H_2 O} (P,T)/f_{H_2 O}^0\) (1,T), with T given in degrees K, and P in bars. Combining these experimental data with known thermodynamic properties of the decomposition products in (1), the following standard state (1 bar, 298.15 K) thermodynamic data for ephesite were calculated: H _f,298.15 ⁰ =-6237372 J/mol, S _298.15 ⁰ =300.455 J/K·mol, G _298.15 ⁰ =-5851994 J/mol, and V _298.15 ⁰ =13.1468 J/bar·mol.     

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.     

Radiological characterization of granitoid outcrops and dimension stones of the Variscan Corsica-Sardinia Batholith

This study focuses on the radiological characterization of granitoid outcrops and dimension stones using in situ gamma-ray spectrometry. Extensive measurements were performed on 210 granitoid outcrops of the Corsica-Sardinia Batholith. The large statistical sample allowed us to improve the analysis by considering a log-normal distribution of radioelements and propagating the uncertainties using Monte Carlo method. The activity concentrations of ⁴⁰K, ²²⁶Ra (²³⁸U) and ²³²Th in C-SB area were 1,177 _?304 ⁺⁴⁰⁸ , 60 _?23 ⁺³⁶ and 69 _?25 ⁺³⁸  Bq/kg (at 1σ uncertainty). The median abundance of K, U and Th on the Variscan C-SB was higher than the average values of the upper continental crust and was comparable with Variscan belt. This corresponds to an outdoor absorbed dose rate of 124 _?26 ⁺³³  nGy/h at 1σ uncertainty which is 3σ higher than the population-weighted average absorbed dose rate (60 nGy/h). Seven commercial granites (Rosa Beta, Ghiandone, Giallo San Giacomo, Rosa Cinzia, Grigio Malaga, Bianco Sardo and Grigio Perla) were investigated to characterize their radiological hazard through 147 measurements taken in 73 extractive quarries. All of the commercial granites were categorized as A2 material based on their activity concentration indices, excluding (at the 3σ level) any restriction on their utilization as superficial materials. Rosa Beta, Grigio Malaga, Grigio Perla and Bianco Sardo can also be used as bulk materials as they can be included in the A1 category. In the case of Ghiandone, Giallo San Giacomo and Rosa Cinzia, we are confident of an A1 classification only at the 1σ level.     

Site classification of Pondicherry using shear-wave velocity and horizontal-to-vertical spectral ratio

Site classification studies play a vital role in earthquake hazard assessment since in situ ground conditions substantially affect the characteristics of incoming seismic waves during earthquakes. Flat areas along the coast and rivers generally consist of thick layers of soft clay and sand. Such deposits amplify certain frequencies of ground motion, thereby attributing to an increase in the damage due to an earthquake. Hence, site classification studies have been carried out using shear-wave velocity, ground response, and corresponding amplification at 83 locations in Pondicherry, a coastal city in India. The present study is aimed at estimating the shear-wave velocity through multichannel analysis of surface waves and to compute the average shear-wave velocity (V _S ³⁰ ), stiffness, and N values using empirical relations. Further, site-response studies (horizontal-to-vertical spectral ratio) were conducted to estimate the ground-response frequencies and corresponding amplifications through Nakamura technique. From the results, the study area was classified into three types, i.e., C-class: with V _S ³⁰ in the range of 360–760 m/s, D-class: with V _S ³⁰ in the range of 180–360 m/s, and E-class: with V _S ³⁰  < 180 m/s following the National Earthquake Hazard Reduction Programme norms (BSSC in NEHRP recommended provisions for seismic regulations for new buildings and other structures (FEMA 450), part 1: provisions. Building Seismic Safety Council for the Federal Emergency Management Agency, Washington, 2003). Finally, a site classification map for Pondicherry region has been prepared, which can be used in urban planning and strengthening of existing structures against future earthquakes.     

Thermodynamic properties of Zn(Al,Cr)2O4 spinels at high temperatures and pressures

Three Al-Cr exchange isotherms between Zn(Al, Cr)₂O₄ spinel and (Al, Cr)₂O₃ corundum crystalline solutions have been studied experimentally at 900°, 1100°, and 1300° C, at a total pressure of 25 kbar. Employing data on the equation of state of corundum (Chatterjee et al. 1982), the experimental results were evaluated thermodynamically. It was found that the thermodynamic mixing properties of Zn(Al, Cr)₂O₄ spinels are best described in terms of a symmetric Margules equation. The T- and P- dependence of the Margules Parameter, W _G ^Sp , and of ΔG^* of the exchange reaction, 1/2 ZnAl₂O₄ + 1/2 Cr₂O₃ = 1/2 ZnCr₂O₄+1/2 A1₂O₃, are found to be ΔG ^*=1493?2.869·T+0.0081·P and W _G ^Sp (J/mol)=23456+0.0386·P, with T given in K and P in bar.     

Interdiffusion of NaSi—CaAl in peristerite

The ‘average’ interdiffusion coefficient ( \(\bar D\) ) for NaSi—CaAl exchange in plagioclase for the interval from An₀ to An₂₆ was estimated from experimentally determined homogenization times for peristerite exsolution lamellae. The average spacing between adjacent (unlike) lamellae is 554±77 Å. Dry heating in air at 1,100°C for 98 days produced no change in the exsolution microstructure; thus \(\bar D\) (dry)<10^?17 cm²/s. This limit is consistent with the recently reported ‘average’ \(\bar D\) (dry) values for the Huttenlocher interval (An_70–90) at this temperature. At 1.5 GPa with about 0.2 weight percent water added the ‘average’ diffusion coefficient from 1,100°C to 900°C is given by: \(\bar D\) (wet)=18 _?15 ⁺¹⁰⁸ (cm²/s) exp (?97±5 (kcal/mol)/RT), where R is the gas constant, and T is °K. This \(\bar D\) (wet) at 1,100°C is more than three orders of magnitude greater than \(\bar D\) (dry) for Na- and Ca-rich plagioclases.     

The ionic conductivity in high-pressure polymorphs of calcite

Ionic conductivity of polycrystalline calcite containing varying amounts of PO ₄ ^3? ions was measured in the pressure range of 1–6 GPa and at room temperature. Electrical conductivity increased with pressure corresponding to the phase transition of calcite I to calcite II. The conductivity in calcite III decreased exponentially with pressure. Calculated activation volumes of the conductivity varied with PO ₄ ^3? content in the range of 0.94–5.34 cm³/mol. This variation corresponded to the lattice parameter change of calcite I due to PO ₄ ^3? incorporation and indicated the contribution of CO ₃ ^2? -vacancies associated with PO ₄ ^3? ions to the conductivity.