Batisivite,V<Subscript>8</Subscript>Ti<Subscript>6</Subscript>[Ba(Si<Subscript>2</Subscript>O)]O<Subscript>28</Subscript>, a new mineral species from the derbylite group

Batisivite has been found as an accessory mineral in the Cr-V-bearing quartz-diopside metamorphic rocks of the Slyudyanka Complex in the southern Baikal region, Russia. A new mineral was named after the major cations in its ideal formula (Ba, Ti, Si, V). Associated minerals are quartz, Cr-V-bearing diopside and tremolite; calcite; schreyerite; berdesinskiite; ankangite; V-bearing titanite; minerals of the chromite-coulsonite, eskolaite-karelianite, dravite-vanadiumdravite, and chernykhite-roscoelite series; uraninite; Cr-bearing goldmanite; albite; barite; zircon; and unnamed U-Ti-V-Cr phases. Batisivite occurs as anhedral grains up to 0.15–0.20 mm in size, without visible cleavage and parting. The new mineral is brittle, with conchoidal fracture. Observed by the naked eye, the mineral is black and opaque, with a black streak and resinous luster. Batisivite is white in reflected light. The microhardness (VHN) is 1220–1470 kg/mm² (load is 30 g), the mean value is 1330 kg/mm². The Mohs hardness is near 7. The calculated density is 4.62 g/cm³. The new mineral is weakly anisotropic and bireflected. The measured values of reflectance are as follows (λ, nm—R _max ^′ /R _min ^′ ): 440—17.5/17.0; 460—17.3/16.7; 480—17.1/16.5; 500—17.2/16.6; 520—17.3/16.7; 540—17.4/16.8; 560—17.5/16.8; 580—17.6/16.9; 600—17.7/17.1; 620—17.7/17.1; 640—17.8/17.1; 660—17.9/17.2; 680—18.0/17.3; 700—18.1/17.4. Batisivite is triclinic, space group P \(\overline 1\); the unit-cell dimensions are: a = 7.521(1) Å, b = 7.643(1) Å, c = 9.572(1) Å, α = 110.20°(1), β = 103.34°(1), γ = 98.28°(1), V = 487.14(7) ų, Z = 1. The strongest reflections in the X-ray powder diffraction pattern [d, Å (I, %)(hkl)] are: 3.09(8)(12\(\overline 2\)); 2.84, 2.85(10)(021, 120); 2.64(8)(21\(\overline 3\)); 2.12(8)(31\(\overline 3\)); 1.785(8)(32\(\overline 4\)), 1.581(10)(24\(\overline 2\)); 1.432, 1.433(10)(322, 124). The chemical composition (electron microprobe, average of 237 point analyses, wt %) is: 0.26 Nb₂O₅, 6.16 SiO₂, 31.76 TiO₂, 1.81 Al₂O₃, 8.20 VO₂, 26.27 V₂O₃, 12.29 Cr₂O₃, 1.48 Fe₂O₃, 0.08 MgO, 11.42 BaO; the total is 99.73. The VO₂/V₂O₃ ratio has been calculated. The simplified empirical formula is (V _4.8 ³⁺ Cr_2.2V _0.7 ⁴⁺ Fe_0.3)_8.0(Ti_5.4V _0.6 ⁴⁺ )_6.0[Ba(Si_1.4Al_0.5O_0.9)]O₂₈. An alternative to the title formula could be a variety (with the diorthogroup Si₂O₇) V₈Ti₆[Ba(Si₂O₇)]O₂₂. Batisivite probably pertains to the V ₈ ³⁺ Ti ₆ ⁴⁺ [Ba(Si₂O)]O₂₈-Cr ₈ ³⁺ Ti ₆ ⁴⁺ [Ba(Si₂O)]O₂₈ solid solution series. The type material of batisivite has been deposited in the Fersman Mineralogical Museum, Russian Academy of Sciences, Moscow.     

Middendorfite,K<Subscript>3</Subscript>Na<Subscript>2</Subscript>Mn<Subscript>5</Subscript>Si<Subscript>12</Subscript>(O,OH)<Subscript>36</Subscript> · 2H<Subscript>2</Subscript>O,a new mineral species from the Khibiny pluton,Kola Peninsula

Middendorfite, a new mineral species, has been found in a hydrothermal assemblage in Hilairite hyperperalkaline pegmatite at the Kirovsky Mine, Mount Kukisvumchorr apatite deposit, Khibiny alkaline pluton, Kola Peninsula, Russia. Microcline, sodalite, cancrisilite, aegirine, calcite, natrolite, fluorite, narsarsukite, labuntsovite-Mn, mangan-neptunite, and donnayite are associated minerals. Middendorfite occurs as rhombshaped lamellar and tabular crystals up to 0.1 × 0.2 × 0.4 mm in size, which are combined in worm-and fanlike segregations up to 1 mm in size. The color is dark to bright orange, with a yellowish streak and vitreous luster. The mineral is transparent. The cleavage (001) is perfect, micalike; the fracture is scaly; flakes are flexible but not elastic. The Mohs hardness is 3 to 3.5. Density is 2.60 g/cm³ (meas.) and 2.65 g/cm³ (calc.). Middendorfite is biaxial (?), α = 1.534, β = 1.562, and γ = 1.563; 2V (meas.) = 10°. The mineral is pleochroic strongly from yellowish to colorless on X through brown on Y and to deep brown on Z. Optical orientation: X = c. The chemical composition (electron microprobe, H₂O determined with Penfield method) is as follows (wt %): 4.55 Na₂O, 10.16 K₂O, 0.11 CaO, 0.18 MgO, 24.88 MnO, 0.68 FeO, 0.15 ZnO, 0.20 Al₂O₃, 50.87 SiO₂, 0.17 TiO₂, 0.23 F, 7.73 H₂O; ?O=F₂?0.10, total is 99.81. The empirical formula calculated on the basis of (Si,Al)₁₂(O,OH,F)₃₆ is K_3.04(Na_2.07Ca_0.03)_Σ2.10(Mn_4.95Fe_0.13Mg_0.06Ti_0.03Zn_0.03)_Σ5.20(Si_11.94Al_0.06)_Σ12O_27.57(OH)_8.26F_0.17 · 1.92H₂O. The simplified formula is K₃Na₂Mn₅Si₁₂(O,OH)₃₆ · 2H₂O. Middenforite is monoclinic, space group: P2₁/m or P2₁. The unit cell dimensions are a = 12.55, b = 5.721, c = 26.86 Å; β = 114.04°, V = 1761 ų, Z = 2. The strongest lines in the X-ray powder pattern [d, Å, (I)(hkl)] are: 12.28(100)(002), 4.31(81)(11\(\overline 4 \)), 3.555(62)(301, 212), 3.063(52)(008, 31\(\overline 6 \)), 2.840(90)(312, 021, 30\(\overline 9 \)), 2.634(88)(21\(\overline 9 \), 1.0.\(\overline 1 \)0, 12\(\overline 4 \)), 2.366(76)(22\(\overline 6 \), 3.1.\(\overline 1 \)0, 32\(\overline 3 \)), 2.109(54)(42–33, 42–44, 51\(\overline 9 \), 414), 1.669(64)(2.2.\(\overline 1 \)3, 3.2.\(\overline 1 \)3, 62\(\overline 3 \), 6.1.\(\overline 1 \)3), 1.614(56)(5.0.\(\overline 1 \)6, 137, 333, 71\(\overline 1 \)). The infrared spectrum is given. Middendorfite is a phyllosilicate related to bannisterite, parsenttensite, and the minerals of the ganophyllite and stilpnomelane groups. The new mineral is named in memory of A.F. von Middendorff (1815–1894), an outstanding scientist, who carried out the first mineralogical investigations in the Khibiny pluton. The type material of middenforite has been deposited at the Fersman Mineralogical Museum, Russian Academy of Sciences, Moscow.     

Oxyvanite,V<Subscript>3</Subscript>O<Subscript>5</Subscript>, a new mineral species and the oxyvanite-berdesinskiite V<Subscript>2</Subscript>TiO<Subscript>5</Subscript> series from metamorphic rocks of the Slyudyanka Complex,southern Baikal region

Oxyvanite has been identified as an accessory mineral in Cr-V-bearing quartz-diopside meta- morphic rocks of the Slyudyanka Complex in the southern Baikal region, Russia. The new mineral was named after constituents of its ideal formula (oxygen and vanadium). Quartz, Cr-V-bearing tremolite and micas, calcite, clinopyroxenes of the diopside-kosmochlor-natalyite series, Cr-bearing goldmanite, eskolaite-karelianite dravite-vanadiumdravite, V-bearing titanite, ilmenite, and rutile, berdesinskiite, schreyerite, plagioclase, scapolite, barite, zircon, and unnamed U-Ti-V-Cr phases are associated minerals. Oxyvanite occurs as anhedral grains up to 0.1–0.15 mm in size, without visible cleavage and parting. The new mineral is brittle, with conchoidal fracture. Observed by the naked eye, the mineral is black, with black streak and resinous luster. The microhardness (VHN) is 1064–1266 kg/mm² (load 30 g), and the mean value is 1180 kg/mm². The Mohs hardness is about 7.0–7.5. The calculated density is 4.66(2) g/cm³. The color of oxyvanite is pale cream in reflected light, without internal reflections. The measured reflectance in air is as follows (λ, nm-R, %): 440-17.8; 460-18; 480-18.2; 520-18.6; 520-18.6; 540-18.8; 560-18.9; 580-19; 600-19.1; 620-19.2; 640-19.3; 660-19.4; 680-19.5; 700-19.7. Oxyvanite is monoclinic, space group C2/c; the unit-cell dimensions are a = 10.03(2), b = 5.050(1), c = 7.000(1) Å, β = 111.14(1)°, V = 330.76(5)ų, Z = 4. The strongest reflections in the X-ray powder pattern [d, Å, (I in 5-number scale)(hkl)] are 3.28 (5) (20\(\bar 2\)); 2.88 (5) (11\(\bar 2\)); 2.65, (5) (310); 2.44 (5) (112); 1.717 (5) (42\(\bar 2\)); 1.633 (5) (31\(\bar 4\)); 1.446 (4) (33\(\bar 2\)); 1.379 (5) (422). The chemical composition (electron microprobe, average of six point analyses, wt %): 14.04 TiO₂, 73.13 V₂O₃ (53.97 V₂O_3calc, 21.25 VO_2calc), 10.76 Cr₂O₃, 0.04 Fe₂O₃, 0.01 Al₂O₃, 0.02 MgO, total is 100.03. The empirical formula is (V _1.70 ³⁺ Cr_0.30)_2.0(V _0.59 ⁴⁺ Ti_0.41)_1.0O₅. Oxyvanite is the end member of the oxyvanite-berdesinskiite series with homovalent isomorphic substitution of V⁴⁺ for Ti. The type material has been deposited at the Fersman Mineralogical Museum, Russian Academy of Sciences, Moscow.     

Thermal equation of state of CaIrO<Subscript>3</Subscript> post-perovskite

The pressure–volume–temperature (P–V–T) relation of CaIrO₃ post-perovskite (ppv) was measured at pressures and temperatures up to 8.6 GPa and 1,273 K, respectively, with energy-dispersive synchrotron X-ray diffraction using a DIA-type, cubic-anvil apparatus (SAM85). Unit-cell dimensions were derived from the Le Bail full profile refinement technique, and the results were fitted using the third-order Birth-Murnaghan equation of state. The derived bulk modulus \( K_{T0} \) at ambient pressure and temperature is 168.3 ± 7.1 GPa with a pressure derivative \( K_{T0}^{\prime } \) = 5.4 ± 0.7. All of the high temperature data, combined with previous experimental data, are fitted using the high-temperature Birch-Murnaghan equation of state, the thermal pressure approach, and the Mie-Grüneisen-Debye formalism. The refined thermoelastic parameters for CaIrO₃ ppv are: temperature derivative of bulk modulus \( (\partial K_{T} /\partial T)_{P} \) = ?0.038 ± 0.011 GPa K^?1, \( \alpha K_{T} \) = 0.0039 ± 0.0001 GPa K^?1, \( \left( {\partial K_{T} /\partial T} \right)_{V} \) = ?0.012 ± 0.002 GPa K^?1, and \( \left( {\partial^{2} P/\partial T^{2} } \right)_{V} \) = 1.9 ± 0.3 × 10^?6 GPa² K^?2. Using the Mie-Grüneisen-Debye formalism, we obtain Grüneisen parameter \( \gamma_{0} \) = 0.92 ± 0.01 and its volume dependence q = 3.4 ± 0.6. The systematic variation of bulk moduli for several oxide post-perovskites can be described approximately by the relationship K _T0  = 5406.0/V(molar) + 5.9 GPa.     

Laboratory parallel-beam transmission X-ray powder diffraction investigation of the thermal behavior of nitratine NaNO<Subscript>3</Subscript>: spontaneous strain and structure evolution

Present work provides in-situ structural data at a fine temperature scale from RT to the melting point of nitratine, NaNO₃. From the analysis of log e ₃₃ versus log t plots, it is possible to prove that an univocal indication on the R \( \overline{3} \) c (low temperature, LT) → R \( \overline{3} \) m (high temperature, HT) transition mechanism cannot be obtained because of the relevant role played by the arbitrary assumptions required for defining the c ₀ dependence from temperature of the HT phase. This is due to the occurrence of excess thermal expansion for the HT phase. A significantly better fit for an Ising-spin structural model over a non-Ising rigid-body one has been obtained for the LT phase. Moreover, the Ising model led to a smooth variation of the oxygen site x fractional coordinate throughout the transition. The structure of the HT polymorph has been successfully refined considering an oxygen site at x, 0, ½, with 50% occupancy. Such model was the only acceptable one from the crystal chemical point of view as the alternative model (oxygen site at x, y, z with 25% occupancy) led to unrealistically aplanar \( {\text{NO}}_{3}^{ - } \) groups.     

Equation of state of synthetic qandilite Mg<Subscript>2</Subscript>TiO<Subscript>4</Subscript> at ambient temperature

Using a diamond-anvil cell and synchrotron X-ray diffraction, the compressional behavior of a synthetic qandilite Mg_2.00(1)Ti_1.00(1)O₄ has been investigated up to about 14.9 GPa at 300 K. The pressure–volume data fitted to the third-order Birch–Murnaghan equation of state yield an isothermal bulk modulus (K _T0) of 175(5) GPa, with its first derivative \(K_{T0}^{{\prime }}\) attaining 3.5(7). If \(K_{T0}^{{\prime }}\) is fixed as 4, the K _T0 value is 172(1) GPa. This value is substantially larger than the value of the adiabatic bulk modulus (K _S0) previously determined by an ultrasonic pulse echo method (152(7) GPa; Liebermann et al. in Geophys J Int 50:553–586, 1977), but in general agreement with the K _T0 empirically estimated on the basis of crystal chemical systematics (169 GPa; Hazen and Yang in Am Miner 84:1956–1960, 1999). Compared to the K _T0 values of the ulvöspinel (Fe₂TiO₄; ~148(4) GPa with \(K_{T0}^{{\prime }} = 4\)) and the ringwoodite solid solutions along the Mg₂SiO₄–Fe₂SiO₄ join, our finding suggests that the substitution of Mg²⁺ for Fe²⁺ on the T sites of the 4–2 spinels can have more significant effect on the K _T0 than that on the M sites.     

Magnetic fields and the $$\dot P - P$$ diagram for radio pulsars

Various mechanisms for the loss of angular momentum of neutron stars are analyzed. Theoretical predictions about the evolution of the period are compared with the observed distribution of pulsars on the log\(\dot P\)log(P) diagram. Pulsars with short periods (P≤0.1 s) cannot be fit well by any of the models considered. Their braking index is n=?1, which requires the development of a new braking mechanism. The evolution of pulsars with P>1.25 s is described by the law \(\dot P \propto P^2\), probably due to processes internal to the neutron stars. The observational data for pulsars with 0.1<P≤1.25 s can be fit with a hybrid model incorporating internal processes and magnetic-dipole losses. The magnetic fields in pulsar catalogs should be recomputed in accordance with the results obtained. For example, the magnetic fields obtained for two magnetars with P=5.16 s and P=7.47 s are B _s =1.7×10¹³ and 2.9×10¹³ G, which are lower than the critical field B_cr=4.4×10¹³ G. For a substantial fraction of pulsars, their characteristic ages \(\tau = P/2\dot P\) cannot serve as measures of their real ages.     

Zinclipscombite,ZnFe<Stack><Subscript>2</Subscript><Superscript>3+</Superscript></Stack>(PO<Subscript>4</Subscript>)<Subscript>2</Subscript>(OH)<Subscript>2</Subscript>, a new mineral species

Zinclipscombite, a new mineral species, has been found together with apophyllite, quartz, barite, jarosite, plumbojarosite, turquoise, and calcite at the Silver Coin mine, Edna Mountains, Valmy, Humboldt County, Nevada, United States. The new mineral forms spheroidal, fibrous segregations; the thickness of the fibers, which extend along the c axis, reaches 20 μm, and the diameter of spherulites is up to 2.5 mm. The color is dark green to brown with a light green to beige streak and a vitreous luster. The mineral is translucent. The Mohs hardness is 5. Zinclipscombite is brittle; cleavage is not observed; fracture is uneven. The density is 3.65(4) g/cm³ measured by hydrostatic weighing and 3.727 g/cm³ calculated from X-ray powder data. The frequencies of absorption bands in the infrared spectrum of zinclipscombite are (cm^?1; the frequencies of the strongest bands are underlined; sh, shoulder; w, weak band) 3535, 3330sh, 3260, 1625w, 1530w, 1068, 1047, 1022, 970sh, 768w, 684w, 609, 502, and 460. The Mössbauer spectrum of zinclipscombite contains only a doublet corresponding to Fe³⁺ with sixfold coordination and a quadrupole splitting of 0.562 mm/s; Fe²⁺ is absent. The mineral is optically uniaxial and positive, ω = 1.755(5), ? = 1.795(5). Zinclipscombite is pleochroic, from bright green to blue-green on X and light greenish brown on Z (X > Z). Chemical composition (electron microprobe, average of five point analyses, wt %): CaO 0.30, ZnO 15.90, Al₂O₃ 4.77, Fe₂O₃ 35.14, P₂O₅ 33.86, As₂O₅ 4.05, H₂O (determined by the Penfield method) 4.94, total 98.96. The empirical formula calculated on the basis of (PO₄,AsO₄)₂ is (Zn_0.76Ca_0.02)_Σ0.78(Fe _1.72 ³⁺ Al_0.36)_Σ2.08[(PO₄)_1.86(AsO₄)_0.14]_Σ2.00(OH)_{1. 80} · 0.17H₂O. The simplified formula is ZnFe ₂ ³⁺ (PO₄)₂(OH)₂. Zinclipscombite is tetragonal, space group P4₃2₁2 or P4₁2₁2; a = 7.242(2) Å, c = 13.125(5) Å, V = 688.4(5) ų, Z = 4. The strongest reflections in the X-ray powder diffraction pattern (d, (I, %) ((hkl)) are 4.79(80)(111), 3.32(100)(113), 3.21(60)(210), 2.602(45)(213), 2.299(40)(214), 2.049(40)(106), 1.663(45)(226), 1.605(50)(421, 108). Zinclipscombite is an analogue of lipscombite, Fe²⁺Fe ₂ ³⁺ (PO₄)₂(OH)₂ (tetragonal), with Zn instead of Fe²⁺. The mineral is named for its chemical composition, the Zn-dominant analogue of lipscombite. The type material of zinclipscombite is deposited in the Mineralogical Collection of the Technische Universität Bergakademie Freiberg, Germany.     

Correlation analyses of effects of temperature on physical and mechanical properties of clay

In determining the physical and mechanical parameters of clay, it is sometimes necessary to determine them indirectly from other parameters since they cannot be measured directly from laboratory or field tests. In order to determine the effect of temperature on the behavior of clay, an indirect approach is used here by analyzing the changes of mass (\(\Delta m\)), density (\(\rho\)), porosity (\(\phi\)), P-wave velocity (\({v_p}\)), thermal conductivity (\(\lambda\)), specific heat capacity (c), resistivity (R) and uniaxial compressive strength (f) of clay from eastern China for a temperature range between 20 and 800 °C. The results indicate that temperature has a significant effect on these parameters. Comparisons between \(\Delta m\) and \(\rho\), \(\Delta m\) and \({v_p}\), \(\rho\) and \({v_p}\), \(\phi\) and \(\lambda\), \({v_p}\) and f, R and f show a linear change among these parameters,whereas the relationships among \(\Delta m\) and \(\phi\), \(\phi\) and \({v_p}\), \(\phi\) and R, \({v_p}\) and \(\lambda\), \(\phi\) and f are exponential. It is difficult to obtain these relationships by using regression analysis with high levels of accuracy. Further refinement is therefore required.     

A spindown mechanism for short-period radio pulsars

It is shown that a model with accretion in a “quasi-propeller” mode can explain the observed spindown of pulsars with periods P<0.1 s. The mean accretion rate for 39 selected objects is \(\dot M = 5.6 \times 10^{ - 11} M_ \odot /year\). If \(\dot M\) is constant during the pulsar’s lifetime, the neutron star will stop rotating after 10⁷ years. The mean magnetic field at the neutron-star surface calculated in this model, \(\bar H_0 = 6.8 \times 10^8 G\), is consistent to an order of magnitude with the values of H₀ for millisecond pulsars from known catalogs. However, the actual value of H₀ for particular objects can differ from the catalog values by appreciable factors, and these quantities must be recalculated using more adequate models. The accretion disk around the neutron star should not impede the escape of the pulsar’s radiation, since this radiation is generated near the light cylinder in pulsars with P<0.1 s. Pulsars such as PSR 0531+21 and PSR 0833-45 have probably spun down due to the effect of magnetic-dipole radiation. If the difference in the braking indices for these objects from n=3 is due to the effect of accretion, the accretion rate must be of the order of 10¹⁸ g/s.     

Electrical conductivity of NaCl-bearing aqueous fluids to 600 °C and 1 GPa

The electrical conductivity of aqueous fluids containing 0.01, 0.1, and 1 M NaCl was measured in an externally heated diamond cell to 600 °C and 1 GPa. These measurements therefore more than double the pressure range of previous data and extend it to higher NaCl concentrations relevant for crustal and mantle fluids. Electrical conductivity was generally found to increase with pressure and fluid salinity. The conductivity increase observed upon variation of NaCl concentration from 0.1 to 1 M was smaller than from 0.01 to 0.1 M, which reflects the reduced degree of dissociation at high NaCl concentration. Measured conductivities can be reproduced (R ² = 0.96) by a numerical model with log \(\sigma\) = ?1.7060– 93.78/T + 0.8075 log c + 3.0781 log \(\rho\) + log \(\varLambda\) ₀(T, \(\rho\)), where \(\sigma\) is the conductivity in S m^?1, T is temperature in K, c is NaCl concentration in wt%, \(\rho\) is the density of pure water (in g/cm³) at given pressure and temperature, and \(\varLambda\) ₀ (T, \(\rho\)) is the molar conductivity of NaCl in water at infinite dilution (in S cm² mol^?1), \(\varLambda\) ₀ = 1573–1212 \(\rho\) + 537 062/T–208 122 721/T ². This model allows accurate predictions of the conductivity of saline fluids throughout most of the crust and upper mantle; it should not be used at temperatures below 100 °C. In general, the data show that already a very small fraction of NaCl-bearing aqueous fluid in the deep crust is sufficient to enhance bulk conductivities to values that would be expected for a high degree of partial melting. Accordingly, aqueous fluids may be distinguished from hydrous melts by comparing magnetotelluric and seismic data. H₂O–NaCl fluids may enhance electrical conductivities in the deep crust with little disturbance of v _p or v _p/v _s ratios. However, at the high temperatures in the mantle wedge above subduction zones, the conductivity of hydrous basaltic melts and saline aqueous fluids is rather similar, so that distinguishing these two phases from conductivity data alone is difficult. Observed conductivities in forearc regions, where temperatures are too low to allow melting, may be accounted for by not more than 1 wt% of an aqueous fluid with 5 wt% NaCl, if this fluid forms a continuous film or fills interconnected tubes.     

Characteristics of motions in the 2D isosceles three-body problem with unequal masses

We analyze the general 2D isosceles three-body problem for various ratios ? of the mass of the central body to the mass of each of the other two bodies. We set the initial conditions using two parameters: the virial coefficient k and the parameter \(\mu = \dot r/\sqrt {\dot r^2 + \dot R^2 }\), where \(\dot r\) is the relative velocity of the two outer bodies and \(\dot R\) is the velocity of the central body relative to the center of mass of the outer bodies. We compare statistical dependences between evolutionary parameters of triple systems with various values of ?, and analyze the k and μ dependences of the number of crossings of the center of mass of the triple system by the central body and the lifetime of the system. We construct the functions R_max(r_max), where r_max and R_max are the maximum achievable distances between the outer bodies, and between the central body and the center of mass of the outer bodies in the triple system. The parameter ? proves to be the most important parameter of the problem, and determines the relationship between the measures of the regular and stochastic trajectories. However, there exist “seeds” of stochasticity, even at small ?～10^?2. The measure of the stochastic orbits increases with ?; when ?≥10, virtually the entire region of the initial conditions corresponds to stochastic trajectories.     

Phase diagram and thermodynamic properties of AIPO<Subscript>4</Subscript> based on first-principles calculations and the quasiharmonic approximation

We calculated the phase diagram of \(\hbox {AlPO}_{4}\) up to 15 GPa and 2,000 K and investigated the thermodynamic properties of the high-pressure phases. The investigated phases include the berlinite, moganite-like, \(\hbox {AlVO}_{4},\, P2_1/c\), and \(\hbox {CrVO}_{4}\) phases. The computational methods used include density functional theory, density functional perturbation theory, and the quasiharmonic approximation. The investigated thermodynamic properties include the thermal equation of state, isothermal bulk modulus, thermal expansivity, and heat capacity. With increasing pressure, the ambient phase berlinite transforms to the moganite-like phase, and then to the \(\hbox {AlVO}_{4}\) and \(P2_1/c\) phases, and further to the \(\hbox {CrVO}_{4}\) phase. The stability fields of the \(\hbox {AlVO}_{4}\) and \(P2_1/c\) phases are similar in pressure but different in temperature, as the \(\hbox {AlVO}_{4}\) phase is stable at low temperatures, whereas the \(P2_1/c\) phase is stable at high temperatures. All of the phase relationships agree well with those obtained by quench experiments, and they support the stabilities of the moganite-like, \(\hbox {AlVO}_{4}\), and \(P2_1/c\) phases, which were not observed in room-temperature compression experiments.     

High-pressure thermo-elastic properties of beryl (Al<Subscript>4</Subscript>Be<Subscript>6</Subscript>Si<Subscript>12</Subscript>O<Subscript>36</Subscript>) from ab initio calculations,and observations about the source of thermal expansion

Ab initio calculations of thermo-elastic properties of beryl (Al₄Be₆Si₁₂O₃₆) have been carried out at the hybrid HF/DFT level by using the B3LYP and WC1LYP Hamiltonians. Static geometries and vibrational frequencies were calculated at different values of the unit cell volume to get static pressure and mode-γ Grüneisen’s parameters. Zero point and thermal pressures were calculated by following a standard statistical-thermodynamics approach, within the limit of the quasi-harmonic approximation, and added to the static pressure at each volume, to get the total pressure (P) as a function of both temperature (T) and cell volume (V). The resulting P(V, T) curves were fitted by appropriate EoS’, to get bulk modulus (K ₀) and its derivative (K′), at different temperatures. The calculation successfully reproduced the available experimental data concerning compressibility at room temperature (the WC1LYP Hamiltonian provided K ₀ and K′ values of 180.2 Gpa and 4.0, respectively) and the low values observed for the thermal expansion coefficient. A zone-centre soft mode \( P6/mcc \to P\bar{1} \) phase transition was predicted to occur at a pressure of about 14 GPa; the reduction of the frequency of the soft vibrational mode, as the pressure is increased, and the similar behaviour of the majority of the low-frequency modes, provided an explanation of the thermal behaviour of the crystal, which is consistent with the RUM model (Rigid Unit Model; Dove et al. in Miner Mag 59:629–639, 1995), where the negative contribution to thermal expansion is ascribed to a geometric effect connected to the tilting of rigid polyhedra in framework silicates.     

The crystal structure of alumoklyuchevskite,K<Subscript>3</Subscript>Cu<Subscript>3</Subscript>AlO<Subscript>2</Subscript>(SO<Subscript>4</Subscript>)<Subscript>4</Subscript>

The crystal structure of the unstable mineral alumoklyuchevskite K₃Cu₃AlO₂(SO₄)₄ [monoclinic, I2, a = 18.772(7), b = 4.967(2), c = 18.468(7) Å, β = 101.66(1)°, V = 1686(1) Å] was refined to R ₁ = 0.131 for 2450 unique reflections with F ≥ 4σF _hkl. The structure is based on oxocentered tetrahedrons (OAlCu ₃ ⁷⁺ ) linked into chains via edges. Each chain is surrounded by SO₄ tetrahedrons forming a structural complex. Each complex is elongated along the b axis. This type of crystal structure was also found in other fumarole minerals of the Great Tolbachik Fissure Eruption (GTFE, Kamchatka Peninsula, Russia, 1975–1976), klyuchevskite, K₃Cu₃Fe³⁺O₂(SO₄)₄; and piypite, K₂Cu₂O(SO₄)₂.     

Experimental determination of liquidus H<Subscript>2</Subscript>O contents of haplogranite at deep-crustal conditions

The liquidus water content of a haplogranite melt at high pressure (P) and temperature (T) is important, because it is a key parameter for constraining the volume of granite that could be produced by melting of the deep crust. Previous estimates based on melting experiments at low P (≤0.5 GPa) show substantial scatter when extrapolated to deep crustal P and T (700–1000 °C, 0.6–1.5 GPa). To improve the high-P constraints on H₂O concentration at the granite liquidus, we performed experiments in a piston–cylinder apparatus at 1.0 GPa using a range of haplogranite compositions in the albite (Ab: NaAlSi₃O₈)—orthoclase (Or: KAlSi₃O₈)—quartz (Qz: SiO₂)—H₂O system. We used equal weight fractions of the feldspar components and varied the Qz between 20 and 30 wt%. In each experiment, synthetic granitic composition glass + H₂O was homogenized well above the liquidus T, and T was lowered by increments until quartz and alkali feldspar crystalized from the liquid. To establish reversed equilibrium, we crystallized the homogenized melt at the lower T and then raised T until we found that the crystalline phases were completely resorbed into the liquid. The reversed liquidus minimum temperatures at 3.0, 4.1, 5.8, 8.0, and 12.0 wt% H₂O are 935–985, 875–900, 775–800, 725–775, and 650–675 °C, respectively. Quenched charges were analyzed by petrographic microscope, scanning electron microscope (SEM), X-ray diffraction (XRD), and electron microprobe analysis (EMPA). The equation for the reversed haplogranite liquidus minimum curve for Ab_36.25Or_36.25Qz_27.5 (wt% basis) at 1.0 GPa is \(T = - 0.0995 w_{{{\text{H}}_{ 2} {\text{O}}}}^{ 3} + 5.0242w_{{{\text{H}}_{ 2} {\text{O}}}}^{ 2} - 88.183 w_{{{\text{H}}_{ 2} {\text{O}}}} + 1171.0\) for \(0 \le w_{{{\text{H}}_{ 2} {\text{O}}}} \le 17\) wt% and \(T\) is in °C. We present a revised \(P - T\) diagram of liquidus minimum H₂O isopleths which integrates data from previous determinations of vapor-saturated melting and the lower pressure vapor-undersaturated melting studies conducted by other workers on the haplogranite system. For lower H₂O (<5.8 wt%) and higher temperature, our results plot on the high end of the extrapolated water contents at liquidus minima when compared to the previous estimates. As a consequence, amounts of metaluminous granites that can be produced from lower crustal biotite–amphibole gneisses by dehydration melting are more restricted than previously thought.     

Thermoelastic properties of chromium oxide Cr<Subscript>2</Subscript>O<Subscript>3</Subscript> (eskolaite) at high pressures and temperatures

A new synchrotron X-ray diffraction study of chromium oxide Cr₂O₃ (eskolaite) with the corundum-type structure has been carried out in a Kawai-type multi-anvil apparatus to pressure of 15 GPa and temperatures of 1873 K. Fitting the Birch–Murnaghan equation of state (EoS) with the present data up to 15 GPa yielded: bulk modulus (K _0,T0), 206 ± 4 GPa; its pressure derivative K′_0,T , 4.4 ± 0.8; (?K _0,T /?T) = ?0.037 ± 0.006 GPa K^?1; a = 2.98 ± 0.14 × 10^?5 K^?1 and b = 0.47 ± 0.28 × 10^?8 K^?2, where α _0,T  = a + bT is the volumetric thermal expansion coefficient. The thermal expansion of Cr₂O₃ was additionally measured at the high-temperature powder diffraction experiment at ambient pressure and α _0,T0 was determined to be 2.95 × 10^?5 K^?1. The results indicate that coefficient of the thermal expansion calculated from the EoS appeared to be high-precision because it is consistent with the data obtained at 1 atm. However, our results contradict α ₀ value suggested by Rigby et al. (Brit Ceram Trans J 45:137–148, 1946) widely used in many physical and geological databases. Fitting the Mie–Grüneisen–Debye EoS with the present ambient and high-pressure data yielded the following parameters: K _0,T0 = 205 ± 3 GPa, K′_0,T  = 4.0, Grüneisen parameter (γ ₀) = 1.42 ± 0.80, q = 1.82 ± 0.56. The thermoelastic parameters indicate that Cr₂O₃ undergoes near isotropic compression at room and high temperatures up to 15 GPa. Cr₂O₃ is shown to be stable in this pressure range and adopts the corundum-type structure. Using obtained thermoelastic parameters, we calculated the reaction boundary of knorringite formation from enstatite and eskolaite. The Clapeyron slope (with \({\text{d}}P/{\text{d}}T = - 0.014\) GPa/K) was found to be consistent with experimental data.     

Mendigite,Mn2Mn2MnCa(Si3O9)2, a new mineral species of the bustamite group from the Eifel volcanic region,Germany

A new mineral, mendigite (IMA no. 2014-007), isostructural with bustamite, has been found in the In den Dellen pumice quarry near Mendig, Laacher Lake area, Eifel Mountains, Rhineland-Palatinate (Rheinland-Pfalz), Germany. Associated minerals are sanidine, nosean, rhodonite, tephroite, magnetite, and a pyrochlore-group mineral. Mendigite occurs as clusters of long-prismatic crystals (up to 0.1 × 0.2 × 2.5 mm in size) in cavities within sanidinite. The color is dark brown with a brown streak. Perfect cleavage is parallel to (001). D _calc = 3.56 g/cm³. The IR spectrum shows the absence of H₂O and OH groups. Mendigite is biaxial (–), α = 1.722 (calc), β = 1.782(5), γ = 1.796(5), 2V _meas = 50(10)°. The chemical composition (electron microprobe, mean of 4 point analyses, the Mn²⁺/Mn³⁺ ratio determined from structural data and charge-balance constraints) is as follows (wt %): 0.36 MgO, 10.78 CaO, 37.47 MnO, 2.91 Mn₂O₃, 4.42 Fe₂O₃, 1.08 Al₂O₃, 43.80 SiO₂, total 100.82. The empirical formula is Mn_2.00(Mn_1.33Ca_0.67) (Mn_0.50 ²⁺ Mn_0.28 ³⁺ Fe_0.15 ³⁺ Mg_0.07)(Ca_0.80 (Mn_0.20 ²⁺)(Si_5.57 Fe_0.27 ³⁺ Al_0.16O₁₈). The idealized formula is Mn₂Mn₂MnCa(Si₃O₉)₂. The crystal structure has been refined for a single crystal. Mendigite is triclinic, space group \(P\bar 1\); the unit-cell parameters are a = 7.0993(4), b = 7.6370(5), c = 7.7037(4) Å, α = 79.58(1)°, β = 62.62(1)°, γ = 76.47(1)°; V = 359.29(4) ų, Z = 1. The strongest reflections on the X-ray powder diffraction pattern [d, Å (I, %) (hkl)] are: 3.72 (32) (020), 3.40 (20) (002, 021), 3.199 (25) (012), 3.000 (26), (\(01\bar 2\), \(1\bar 20\)), 2.885 (100) (221, \(2\bar 11\), \(1\bar 21\)), 2.691 (21) (222, \(2\bar 10\)), 2.397 (21) (\(02\bar 2\), \(21\bar 1\), 203, 031), 1.774 (37) (412, \(3\bar 21\)). The type specimen is deposited in the Fersman Mineralogical Museum, Russian Academy of Sciences, Moscow, registration number 4420/1.     

Pressuremeter Modulus and Limit Pressure of Clayey Soils Using <Emphasis Type="Italic">GMDH</Emphasis>-Type Neural Network and Genetic Algorithms

Pressuremeter modulus (\(E_{M}\)) and limit pressure (\(P_{L}\)) are used for the calculation of the settlement and bearing capacity of foundation respectively. As the determination of these parameters from pressuremeter test (PMT) is relatively time-consuming and expensive, various empirical correlations have been proposed to correlate the \(E_{M}\) and \(P_{L}\) to other soil parameters. For the existing equations are incapable of estimating these PMT parameters well, in present research group method of data handling type neural network is used to estimate the \(E_{M}\) and \(P_{L}\) of clayey soils. The \(E_{M}\) and \(P_{L}\) were modeled as a function of three variables including the moisture content (\(\omega\)), plasticity index and corrected SPT blow counts (\(N_{60}\)). A database containing 51 data sets have been used for training and testing of the models. The performances of proposed models are compared with those of existing empirical equations. The results demonstrate that appreciable improvement with respect to the other correlations has been achieved. At the end, sensitivity analysis of the obtained models has been performed to study the influence of input parameters on model outputs and shows that the \(N_{60}\) is the most influential parameter on the PMT parameters.