Adsorption of H<Subscript>2</Subscript>O,NH<Subscript>3</Subscript> and C<Subscript>6</Subscript>H<Subscript>6</Subscript> on alkali metal cations in internal surface of mordenite and in external surface of smectite: a DFT study

Adsorption of H₂O, NH₃ and C₆H₆ on H- and alkali metal-exchanged structures of mordenite and on corresponding cations on the smectite layer is investigated by ab initio density-functional calculations. Proton or an alkali metal cation compensates one Al/Si framework substitution and resides in the extra-framework position of zeolite or above flat smectite layer close to the Al/Si substitution. Pronounced similarities between zeolite and smectite are observed in changes of the adsorption energies and location of the external cation with changing character of the external cation. Calculated adsorption energies exhibit the following trend: E(NH₃) > E(H₂O) > E(C₆H₆). Because of looser contact with the framework, zeolitic cations are stronger adsorption centers and calculated adsorption energies of zeolites are by ~20–30% larger than cations of smectites. The highest adsorption energy is calculated for H-exchanged structures and down the group of alkali metal cations a decrease of the adsorption energy is observed. Deviations from the smooth variation of the adsorption energy are caused by: (1) formation of strong hydrogen bonds in H-exchanged structures, (2) adsorption induced migration of the external Li⁺ cation, and (3) steric hindrances of the flat C₆H₆ molecule adsorbed on the cation in the cage of zeolite.     

Heterogeneous C<Subscript>16</Subscript>Zn<Subscript>8</Subscript>O<Subscript>8</Subscript> nanocluster as a selective CO/NO nanosensor: computational investigation

Density functional theory (DFT) calculations were employed to investigate the effects of adsorption of toxic carbon monoxide (CO) and nitrogen monoxide (NO) molecules on heterogeneous C₁₆Zn₈O₈ nanocage. A detailed analysis of the energetic, geometry, and electronic structure of various CO and NO adsorptions on the cluster surface was performed. It has been shown that CO molecule was adsorbed on the surface of the cluster resulting in more stable complex system, while NO molecule adsorption led to less stable system. These processes also changed the electronic properties of the cluster by reducing the HOMO/LUMO energy gap after adsorption process. Since this phenomenon led to an increment in the electrical conductivity of the cluster at a definite temperature, the C₁₆Zn₈O₈ was transformed to a stronger semiconductor substance upon the CO and NO adsorption. We believe that this research may be helpful in the several fields study such as sensor and catalyst investigation.     

Photocatalytic performance of TiO<Subscript>2</Subscript> and WO<Subscript>3</Subscript>/TiO<Subscript>2</Subscript> nanoparticles coated on urban green infrastructure materials in removing nitrogen oxide

This study investigated the performance of UV light active TiO₂ and UV–visible light active WO₃/TiO₂ nanoparticles as air purifying materials that can be potentially applied to urban green infrastructures such as rain gardens and pervious pavements. Using a laboratory-scale continuous gas flow photoreactor, the removal efficiency of gaseous nitrogen oxide (NO _x ) by two different photocatalytic nanoparticles coated on natural zeolites and pervious concrete blocks was evaluated. The results showed that the TiO₂- and WO₃/TiO₂-coated zeolites are excellent photoactive materials providing enhanced air purification function (~95% removal efficiency of NO _x ) under UV and UV–visible light irradiation, respectively. In contrast, both of the TiO₂- and WO₃/TiO₂-coated pervious concrete blocks showed a measurable NO _x removal (~60%) only under UV irradiation, whereas the visible light activity of the WO₃/TiO₂-coated concrete block was significantly reduced (~20%) mainly due to the decrease in the photocatalytic reaction sites for visible light. This study revealed the potential utility of photocatalytic nanoparticles in improving urban air quality, in the form of the surface component of various urban infrastructures.     

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.     

Calcite and barite precipitation in CaCO<Subscript>3</Subscript>-BaSO<Subscript>4</Subscript>-NaCl and BaSO<Subscript>4</Subscript>-NaCl-CaCl<Subscript>2</Subscript> aqueous systems: kinetic and microstructural study

During the production of hydrocarbons from subterranean reservoirs, scaling with calcium carbonate and barium sulfate causes flux decline and dangerous problems in production facilities. This work is intended to study the effect of calcium ions on the precipitation of barium sulfate (barite); then, the effect of the formed barite on calcium carbonate crystallization. The conductometric and pH methods were used to follow the progress of the precipitation reaction in aqueous medium. The obtained precipitates were characterized by FTIR, RAMAN, SEM, and XRD. It was shown that Ca²⁺ in the reaction media does not affect the microstructure of barite even for higher calcium–barium molar ratio. It influences the precipitation kinetics and the solubility of barite by the formation of CaSO₄° ion pairing as a predominant role of complex formation (CaSO4) and the increase of the ionic strength. In Ca(HCO₃)₂-BaSO₄-NaCl aqueous system, experiments have showed that added or formed barite in the reaction media accelerates calcite precipitation. No effect on the microstructure of heterogeneous formed calcite which remain calcite shape. However the presence of carbonate ions affects slightly the microstructure of barite.     

Magnetic properties and neutron diffraction study of two manganese sulfosalts: monoclinic MnSb<Subscript>2</Subscript>S<Subscript>4</Subscript> and benavidesite (MnPb<Subscript>4</Subscript>Sb<Subscript>6</Subscript>S<Subscript>14</Subscript>)

Mn²⁺Sb₂S₄, a monoclinic dimorph of clerite, and benavidesite (Mn²⁺Pb₄Sb₆S₁₄) show well-individualized single chains of manganese atoms in octahedral coordination. Their magnetic structures are presented and compared with those of iron derivatives, berthierite (Fe²⁺Sb₂S₄) and jamesonite (Fe²⁺Pb₄Sb₆S₁₄). Within chains, interactions are antiferromagnetic. Like berthierite, MnSb₂S₄ shows a spiral magnetic structure with an incommensurate 1D propagation vector [0, 0.369, 0], unchanged with temperature. In berthierite, the interactions between identical chains are antiferromagnetic, whereas in MnSb₂S₄ interactions between chains are ferromagnetic along c-axis. Below 6 K, jamesonite and benavidesite have commensurate magnetic structures with the same propagation vector [0.5, 0, 0]: jamesonite is a canted ferromagnet and iron magnetic moments are mainly oriented along the a-axis, whereas for benavidesite, no angle of canting is detected, and manganese magnetic moments are oriented along b-axis. Below 30 K, for both compounds, one-dimensional magnetic ordering or correlations are visible in the neutron diagrams and persist down to 1.4 K.     

Experimental study of pure and mixtures of CO<Subscript>2</Subscript> and CH<Subscript>4</Subscript> adsorption on modified carbon nanotubes

In this work 3-[2-(2-aminoethylamino)ethylamino]propyl trimethoxysilane (TRI) was employed to functionalize MWCNT containing hydroxyl groups (OH-MWCNT), and the XRD, FTIR, TGA and CHNS elemental analysis techniques were used to characterize the resulted adsorbents. The characterization results for amine-MWCNT showed amine groups effectively attached to the surface of the MWCNT. The equilibrium adsorption capacity of pure CO₂ and CH₄ and their binary mixture on the pristine MWCNT, OH-MWCNT and amine-MWCNT was measured through a set of equilibrium adsorption experiments at 303.2 and 318.2 K. Capacities of all three types of adsorbents for CO₂ adsorption were higher than those for methane adsorption. Also, amine-MWCNT demonstrated better performance on CO₂ adsorption than the other two adsorbents, especially at low partial pressures. The capacity of amine-MWCNT for pure CO₂ adsorption was 2.5 and 4 times as much as those for pristine MWCNT and OH-MWCNT, respectively, at the temperature of 303.2 K and the pressure of 0.2 bar. The binary adsorption experiment revealed that CO₂/CH₄ selectivity for pristine MWCNT and amine-MWCNT in all molar fractions of CO₂ is about 1.77 and 7, respectively.     

Tracing sources of carbon in urban groundwater using δ<Superscript>13</Superscript>C<Subscript>TDIC</Subscript> ratios

Total dissolved inorganic carbon (TDIC) and its stable isotope ratio δ¹³C_TDIC are used to trace the evolution of the carbon system of groundwater in three UK Permo-Triassic sandstone aquifers. Samples were collected from multilevel piezometers, open boreholes and sewer sampling points in the British Midlands (Nottingham, Birmingham and Doncaster) to evaluate both local and regional variations in δ¹³C_TDIC. δ¹³C samples of matrix and pore water have also been analysed in each aquifer to further constrain the interpretations. Combining δ¹³C_TDIC ratios with measurements of TDIC and pH clearly distinguishes the principal processes underlying the geochemical evolution of groundwater in Triassic sandstone aquifers, where processes can be both natural (e.g. carbonate dissolution) and anthropogenic (sewer-derived recharge). The paper shows that δ¹³C_TDIC resolves ambiguities that arise from the interpretation of TDIC and pH measurements in isolation. Field measurements demonstrate that, under natural conditions, the carbonate system evolves similarly in each aquifer. An open-system evolution during recharge largely saturates the groundwater with carbonate depending upon its availability in the sandstone matrix. The contribution of sewer exfiltration to urban recharge is readily distinguished by lower pH and higher TDIC values without significant changes in δ¹³C_TDIC.     

Thermodynamic properties,low-temperature heat-capacity anomalies,and single-crystal X-ray refinement of hydronium jarosite, (H<Subscript>3</Subscript>O)Fe<Subscript>3</Subscript>(SO<Subscript>4</Subscript>)<Subscript>2</Subscript>(OH)<Subscript>6</Subscript>

Crystals of hydronium jarosite were synthesized by hydrothermal treatment of Fe(III)–SO₄ solutions. Single-crystal XRD refinement with R₁=0.0232 for the unique observed reflections (|F_o| > 4_F) and wR₂=0.0451 for all data gave a=7.3559(8) Å, c=17.019(3) Å, V^o=160.11(4) cm³, and fractional positions for all atoms except the H in the H₃O groups. The chemical composition of this sample is described by the formula (H₃O)_0.91Fe_2.91(SO₄)₂[(OH)_5.64(H₂O)_0.18]. The enthalpy of formation (H^o_f) is –3694.5 ± 4.6 kJ mol^–1, calculated from acid (5.0 N HCl) solution calorimetry data for hydronium jarosite, -FeOOH, MgO, H₂O, and -MgSO₄. The entropy at standard temperature and pressure (S^o) is 438.9±0.7 J mol^–1 K^–1, calculated from adiabatic and semi-adiabatic calorimetry data. The heat capacity (C_p) data between 273 and 400 K were fitted to a Maier-Kelley polynomial C_p(T in K)=280.6 + 0.6149T–3199700T^–2. The Gibbs free energy of formation is –3162.2 ± 4.6 kJ mol^–1. Speciation and activity calculations for Fe(III)–SO₄ solutions show that these new thermodynamic data reproduce the results of solubility experiments with hydronium jarosite. A spin-glass freezing transition was manifested as a broad anomaly in the C_p data, and as a broad maximum in the zero-field-cooled magnetic susceptibility data at 16.5 K. Another anomaly in C_p, below 0.7 K, has been tentatively attributed to spin cluster tunneling. A set of thermodynamic values for an ideal composition end member (H₃O)Fe₃(SO₄)₂(OH)₆ was estimated: G^o_f= –3226.4 ± 4.6 kJ mol^–1, H^o_f=–3770.2 ± 4.6 kJ mol^–1, S^o=448.2 ± 0.7 J mol^–1 K^–1, C_p (T in K)=287.2 + 0.6281T–3286000T^–2 (between 273 and 400 K).     

Low-temperature heat capacities of MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript> and spinels of the MgCr<Subscript>2</Subscript>O<Subscript>4</Subscript>–MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript> solid solution

We present results from low-temperature heat capacity measurements of spinels along the solid solution between MgAl₂O₄ and MgCr₂O₄. The data also include new low-temperature heat capacity measurements for MgAl₂O₄ spinel. Heat capacities were measured between 1.5 and 300 K, and thermochemical functions were derived from the results. No heat capacity anomaly was observed for MgAl₂O₄ spinel; however, we observe a low-temperature heat capacity anomaly for Cr-bearing spinels at temperatures below 15 K. From our data we calculate standard entropies (298.15 K) for Mg(Cr,Al)₂O₄ spinels. We suggest a standard entropy for MgAl₂O₄ of 80.9 ± 0.6 J mol⁻¹ K⁻¹. For the solid solution between MgAl₂O₄ and MgCr₂O₄, we observe a linear increase of the standard entropies from 80.9 J mol⁻¹ K⁻¹ for MgAl₂O₄ to 118.3 J mol⁻¹ K⁻¹ for MgCr₂O₄.     

Theoretical studies of cation adsorption on hydroxylated α-A1<Subscript>2</Subscript>O<Subscript>3</Subscript> (corundum): electronic structure calculations

 The adsorption of alkali metal cations on a hydroxylated corundum surface was investigated using high-level electronic structure calculations, with both cluster Hartree–Fock and periodic density-functional theory approaches. The work concentrates on the structural aspects of binding sites with threefold oxygen coordination at the basal (0001) surface. It was found that adsorption at different sites can give rise to a wide range of adsorption energies, which strongly depends on the freedom of surface hydrogen atoms to adjust their positions. Alkali metal adions from Li⁺ to Cs⁺ were studied with the cluster method, periodic plane-wave pseudopotential calculations being carried out for K⁺ adsorption to validate the cluster results. A site above an octahedral interstice was found to be the least preferred for cation adsorption, despite having the lowest repulsion from surface aluminium atoms. The strongest adsorption was found over an aluminium atom in the second layer, because the hydroxyl groups could reorient towards the neighbouring octahedral interstices, and hence significantly decrease repulsion with the cation. The adsorption energy and the first three interlayer spacings parallel to the basal surface change systematically with ionic size for each adsorption site. Many of these trends extend to adsorption of Ca²⁺, Co²⁺ and Pb²⁺, which were also investigated, although a redistribution of 3d electrons in Co²⁺ results in strong adsorption even at an unfavourable site. The results suggest that it may be possible not only to predict adsorption behaviour for a wide range of elements, but also to use experimental measurements of interplanar separations to gain information about contaminated surfaces. Received: 29 April 2002 / Accepted: 23 October 2002 Acknowledgements The authors thank the Natural Environment Research Council for support in carrying out this work.     

The effect of slight to minor biodegradation on C<Subscript>6</Subscript> to C<Subscript>7</Subscript> light hydrocarbons in crude oils: a case study from Dawanqi Oilfield in the Tarim Basin,NW China

Light hydrocarbons (LHs) are one of the main petroleum fractions in crude oils, and carry much information regarding the genetic origin and alteration of crude oils. But secondary alterations—especially biodegradation—have a significant effect on the composition of LHs in crude oils. Because most of the LHs affected in oils underwent only slight biodegradation (rank 1 on the biodegradation scale), the variation of LHs can be used to describe more the refined features of biodegradation. Here, 23 crude oils from the Dawanqi Oilfield in the Tarim Basin, NW China, eleven of which have been biodegraded to different extents, were analyzed in order to investigate the effect of slight to minor biodegradation on C₆–C₇ LHs. The study results showed that biodegradation resulted in the prior depletion of straight-chained alkanes, followed by branched alkanes. In slight and minor biodegraded oils, such biodegradation scale could not sufficiently affect C₆–C₇ cycloalkanes. For branched C₆–C₇ alkanes, generally, monomethylalkanes are biodegraded earlier than dimethylalkanes and trimethylalkanes, which indicates that branched alkanes are more resistant to biodegradation, with the increase of substituted methyl groups on parent rings. The degree of alkylation is one of the primary controlling factors on the biodegradation of C₆–C₇ LHs. There is a particular case: although 2,2,3-trimethylbutane has a relative higher alkylation degree, 2,2-dimethylpentane is more resistant to biodegradation than 2,2,3-trimethylbutane. 2,2-Dimethylpentane is the most resistant to biodegradation in branched C₆–C₇ alkanes. Furthermore, the 2-methylpentane/3-methylpentane and 2-methylhexane/3-methylhexane ratios decreased steadily with increasing biodegradation, which implies that isomers of bilateral methyl groups are more prone to bacterial attack relative to mid-chain isomers. The position of the alkyls on the carbon skeleton is also one of the critical factors controlling the rate of biodegradation. With increasing biodegradation, Mango’s LH parameters K1 values decrease and K2 values increase, the values of n-heptane and isoheptane decrease, and the indices of methylcyclohexane and cyclohexane increase. LH parameters should be applied cautiously for the biodegraded oils. Because biodegraded samples belong to slight or minor biodegraded oils, the values of n-heptane and isoheptane from Dawanqi Oilfield can better reflect and determine the “Biodegraded” zone. When the heptane value is 0–21 and the isoheptane value is 0–2.6, the crude oil in Dawanqi Oilfield is defined as the “Biodegraded” zone.     

Vibrational and thermodynamic properties of Ni<Subscript>3</Subscript>S<Subscript>2</Subscript> polymorphs from first-principles calculations

We have calculated the compressional, vibrational, and thermodynamic properties of Ni₃S₂ heazlewoodite and the high-pressure orthorhombic phase (with Cmcm symmetry) using the generalized gradient approximation to the density functional theory in conjunction with the quasi-harmonic approximation. The predicted Raman frequencies of heazlewoodite are in good agreement with room-temperature measurements. The calculated thermodynamic properties of heazlewoodite at room conditions agree very well with experiments, but at high temperatures (especially above 500 K) the heat capacity data from experiments are significantly larger than the quasi-harmonic results, indicating that heazlewoodite is anharmonic. On the other hand, the obtained vibrational density of states of the orthorhombic phase at 20 GPa reveals a group of low-frequency vibrational modes which are absent in heazlewoodite. These low-frequency modes contribute substantially to thermal expansivity, heat capacity, entropy, and Grüneisen parameter of the orthorhombic phase. The calculated phase boundary between heazlewoodite and the orthorhombic phase is consistent with high-pressure experiments; the predicted transition pressure is 17.9 GPa at 300 K with a negative Clapeyron slope of −8.5 MPa/K.     

High-pressure Raman studies and heat capacity measurements on the MgSiO<Subscript>3</Subscript> analogue CaIr<Subscript>0.5</Subscript>Pt<Subscript>0.5</Subscript>O<Subscript>3</Subscript>

Raman spectroscopy and heat capacity measurements have been used to study the post-perovskite phase of CaIr_0.5Pt_0.5O₃, recovered from synthesis at a pressure of 15 GPa. Laser heating CaIr_0.5Pt_0.5O₃ to 1,900 K at 60 GPa produces a new perovskite phase which is not recoverable and reverts to the post-perovskite polymorph between 20 and 9 GPa on decompression. This implies that Pt-rich CaIr_1−xPt_xO₃ perovskites including the end member CaPtO₃ cannot easily be recovered to ambient pressure from high P–T synthesis. We estimate an increase in the thermodynamic Grüneisen parameter across the post-perovskite to perovskite transition of 34%, of similar magnitude to those for (Mg,Fe)SiO₃ and MgGeO₃, suggesting that CaIr_0.5Pt_0.5O₃ is a promising analogue for experimental studies of the competition in energetics between perovskite and post-perovskite phases of magnesium silicates in Earth’s lowermost mantle. Low-temperature heat capacity measurements show that CaIrO₃ has a significant Sommerfeld coefficient of 11.7 mJ/mol K² and an entropy change of only 1.1% of Rln2 at the 108 K Curie transition, consistent with the near-itinerant electron magnetism. Heat capacity results for post-perovskite CaIr_0.5Rh_0.5O₃ are also reported.     

Elastic behavior of vanadinite,Pb<Subscript>10</Subscript>(VO<Subscript>4</Subscript>)<Subscript>6</Subscript>Cl<Subscript>2</Subscript>, a microporous non-zeolitic mineral

The high-pressure behavior of a vanadinite (Pb₁₀(VO₄)₆Cl₂, a = b = 10.3254(5), c = 7.3450(4) Å, space group P6₃/m), a natural microporous mineral, has been investigated using in-situ HP-synchrotron X-ray powder diffraction up to 7.67 GPa with a diamond anvil cell under hydrostatic conditions. No phase transition has been observed within the pressure range investigated. Axial and volume isothermal Equations of State (EoS) of vanadinite were determined. Fitting the P–V data with a third-order Birch-Murnaghan (BM) EoS, using the data weighted by the uncertainties in P and V, we obtained: V ₀ = 681(1) Å³, K ₀ = 41(5) GPa, and K′ = 12.5(2.5). The evolution of the lattice constants with P shows a strong anisotropic compression pattern. The axial bulk moduli were calculated with a third-order “linearized” BM-EoS. The EoS parameters are: a ₀ = 10.3302(2) Å, K ₀(a) = 35(2) GPa and K′(a) = 10(1) for the a-axis; c ₀ = 7.3520(3) Å, K ₀(c) = 98(4) GPa, and K′(c) = 9(2) for the c-axis (K ₀(a):K ₀(c) = 1:2.80). Axial and volume Eulerian-finite strain (fe) at different normalized stress (Fe) were calculated. The weighted linear regression through the data points yields the following intercept values: Fe _a (0) = 35(2) GPa for the a-axis, Fe _c (0) = 98(4) GPa for the c-axis and Fe _V (0) = 45(2) GPa for the unit-cell volume. The slope of the regression lines gives rise to K′ values of 10(1) for the a-axis, 9(2) for the c-axis and 11(1) for the unit cell-volume. A comparison between the HP-elastic response of vanadinite and the iso-structural apatite is carried out. The possible reasons of the elastic anisotropy are discussed.     

Atomistic model of diopside-K-jadeite (CaMgSi<Subscript>2</Subscript>O<Subscript>6</Subscript>-KAlSi<Subscript>2</Subscript>O<Subscript>6</Subscript>) solid solution

Atomistic model was proposed to describe the thermodynamics of mixing in the diopside-K-jadeite solid solution (CaMgSi₂O6-KAlSi₂O₆). The simulations were based on minimization of the lattice energies of 800 structures within a 2 × 2 × 4 supercell of C2/c diopside with the compositions between CaMgSi₂O₆ and KAlSi₂O₆ and with variable degrees of order/disorder in the arrangement of Ca/K cations in M2 site and Mg/Al in Ml site. The energy minimization was performed with the help of a force-field model. The results of the calculations were used to define a generalized Ising model, which included 37 pair interaction parameters. Isotherms of the enthalpy of mixing within the range of 273–2023 K were calculated with a Monte Carlo algorithm, while the Gibbs free energies of mixing were obtained by thermodynamic integration of the enthalpies of mixing. The calculated T-X diagram for the system CaMgSi₂O₆-KAlSi₂O₆ at temperatures below 1000 K shows several miscibility gaps, which are separated by intervals of stability of intermediate ordered compounds. At temperatures above 1000 K a homogeneous solid solution is formed. The standard thermodynamic properties of K-jadeite (KAlSi₂O₆) evaluated from quantum mechanical calculations were used to determine location of several mineral reactions with the participation of the diopside-K-jadeite solid solution. The results of the simulations suggest that the low content of KalSi₂O₆ in natural clinopyroxenes is not related to crystal chemical factors preventing isomorphism, but is determined by relatively high standard enthalpy of this end member.     

Compressibility of strontium orthophosphate Sr<Subscript>3</Subscript>(PO<Subscript>4</Subscript>)<Subscript>2</Subscript> at high pressure

High pressure in situ synchrotron X-ray diffraction experiment of strontium orthophosphate Sr₃(PO₄)₂ has been carried out to 20.0 GPa at room temperature using multianvil apparatus. Fitting a third-order Birch–Murnaghan equation of state to the P–V data yields a volume of V ₀ = 498.0 ± 0.1 Å³, an isothermal bulk modulus of K _T  = 89.5 ± 1.7 GPa, and first pressure derivative of K _T ′ = 6.57 ± 0.34. If K _T ′ is fixed at 4, K _T is obtained as 104.4 ± 1.2 GPa. Analysis of axial compressible modulus shows that the a-axis (K _a  = 79.6 ± 3.2 GPa) is more compressible than the c-axis (K _c  = 116.4 ± 4.3 GPa). Based on the high pressure Raman spectroscopic results, the mode Grüneisen parameters are determined and the average mode Grüneisen parameter of PO₄ vibrations of Sr₃(PO₄)₂ is calculated to be 0.30(2).     

Elasticity and equation of state of Li<Subscript>2</Subscript>B<Subscript>4</Subscript>O<Subscript>7</Subscript>

A single crystal X-ray diffraction study on lithium tetraborate Li₂B₄O₇ (diomignite, space group I4₁ cd) has been performed under pressure up to 8.3 GPa. No phase transitions were found in the pressure range investigated, and hence the pressure evolution of the unit-cell volume of the I4₁ cd structure has been described using a third-order Birch–Murnaghan equation of state (BM-EoS) with the following parameters: V ₀  = 923.21(6) ų, K ₀  = 45.6(6) GPa, and K′ = 7.3(3). A linearized BM-EoS was fitted to the axial compressibilities resulting in the following parameters a ₀  = 9.4747(3) Å, K _0a  = 73.3(9) GPa, K′ _a  = 5.1(3) and c ₀  = 10.2838(4) Å, K _0c  = 24.6(3) GPa, K′ _c  = 7.5(2) for the a and c axes, respectively. The elastic anisotropy of Li₂B₄O₇ is very large with the zero-pressure compressibility ratio β _0c /β _0a  = 3.0(1). The large elastic anisotropy is consistent with the crystal structure: A three-dimensional arrangement of relatively rigid tetraborate groups [B₄O₇]²⁻ forms channels occupied by lithium along the polar c–axis, and hence compression along the c axis requires the shrinkage of the lithium channels, whereas compression in the a direction depends mainly on the contraction of the most rigid [B₄O₇]²⁻ units. Finally, the isothermal bulk modulus obtained in this work is in general agreement with that derived from ultrasonic (Adachi et al. in Proceedings-IEEE Ultrasonic Symposium, 228–232, 1985; Shorrocks et al. in Proceedings-IEEE Ultrasonic Symposium, 337–340, 1981) and Brillouin scattering measurements (Takagi et al. in Ferroelectrics, 137:337–342, 1992).     

First-principles-based calculations of the CaCO<Subscript>3</Subscript>–MgCO<Subscript>3</Subscript> and CdCO<Subscript>3</Subscript>–MgCO<Subscript>3</Subscript> subsolidus phase diagrams

 Planewave pseudopotential calculations of supercell total energies were used as bases for first-principles calculations of the CaCO₃–MgCO₃ and CdCO₃–MgCO₃ phase diagrams. Calculated phase diagrams are in qualitative to semiquantitative agreement with experiment. Two unobserved phases, Cd₃Mg (CO₃)₄ and CdMg₃(CO₃)₄, are predicted. No new phases are predicted in the CaCO₃–MgCO₃ system, but a low-lying metastable Ca₃Mg(CO₃)₄ state, analogous to the Cd₃Mg(CO₃)₄ phase is predicted. All of the predicted lowest-lying metastable states, except for huntite CaMg₃(CO₃)₄, have dolomite-related structures, i.e. they are layer structures in which A _m B _n cation layers lie perpendicular to the rhombohedral [111] vector. Received: 6 May 2002 / Accepted: 23 October 2002 Acknowledgements This work was partially supported by NSF contract DMR-0080766 and NIST.