An interatomic potential model for carbonates allowing for polarization effects

An empirical model for investigating the behaviour of CaCO₃ polymorphs incorporating a shell model for oxygen has been created. The model was constructed by fitting to: the structure of aragonite and calcite; their elastic, static and high-frequency dielectric constants; phonon frequencies at the wave vectors [&frac; 0 2] and [0 0 0] of calcite; and vibrational frequencies of the carbonate deformation modes of calcite. The high-pressure phase transition between calcite I and II is observed. The potentials for the CO₃ group were transferred to other carbonates, by refitting the interaction between CO₃ and the cation to both the experimental structures and their bulk modulus, creating a set of potentials for calculating the properties of a wide range of carbonate materials. Defect energies of substitutional cation defects were analyzed for calcite and aragonite phases. The results were rationalized by studying the structure of calcite and aragonite in greater detail.     

Lattice dynamics of corundum

The short-range force constants and the contribution of the potential energy to the elastic constants have been calculated from explicit expressions for the elastic constants and for the optical frequencies. The large elastic constants of corundum are attributable to the contribution of the large short-range stretching forces. The frequencies of the phonon spectrum and the contribution of the potential energy to the frequencies have also been calculated based on a rigid-ion and polarizable-ion model. The effective charge of an oxygen ion is found to be ?0.955e. The electronic polarizability of an aluminium and oxygen ion is found to be 0.05 and 1.36 ų, respectively.     

Thermodynamic properties of CaCO3 calcite and aragonite: A quasi-harmonic calculation

A quasi-harmonic model has been used to simulate the thermodynamic behaviour of the CaCO₃ polymorphs, by equilibrating their crystal structures as a function of temperature so as to balance the sum of inner static and thermal pressures against the applied external pressure. The vibrational frequencies and elastic properties needed have been computed using interatomic potentials based on two-body Born-type functions, with O-C-O angular terms to account for covalency inside the CO₃ molecular ion. A good agreement with experimental data is generally shown by simulated heat capacity and entropy, while the thermal expansion coefficient seems to be more difficult to reproduce. The results obtained for aragonite are less satisfactory than those of calcite, but they are improved by using a potential specifically optimized on properties of that phase itself.     

Quantum-mechanical Hartree-Fock study of calcite (CaCO3) at variable pressure,and comparison with magnesite (MgCO3)

The static crystal energy of calcite and its structure configuration as functions of pressure were determined by ab initio all-electron periodic Hartree-Fock calculations (CRYSTAL code). Ca, O and C atoms were represented by 22, 18 and 14 atomic orbitals, respectively, in form of contracted Gaussian-type functions. Comparison between theoretical and experimental data was performed for binding energy, equilibrium unit-cell and bond lengths, bulk modulus and C ₃₃ and C ₁₁ + C ₁₂ elastic constants, and vibrational frequency of the symmetrical C-O stretching mode. The agreement is generally satisfactory. A larger compressibility is observed for structural parameters of calcite than for those of magnesite coming from a similar calculation. The Ca-O and C-O chemical bonding was characterized by electron density maps and by Mulliken atomic charges; these are discussed and compared to values determined by empirical fitting of Born-type interatomic potentials.     

Elasticity of single-crystal aragonite by Brillouin spectroscopy

The elastic constants of natural single-crystal aragonite (CaCO₃) have been measured by Brillouin spectroscopy at ambient conditions. The elastic constants C₁₁, C₂₂, C₃₃, C₄₄, C₅₅, C₆₆, C₁₂, C₁₃ and C₂₃ are 171.1±1.0, 110.1±0.9, 98.4±1.2, 39.3±0.6, 24.2±0.4, 40.2±0.6, 60.3±1.0, 27.8±1.6 and 41.9±2.0 GPa, respectively, for aragonite. The linear compressibilities of the a-, b- and c-axis for aragonite at ambient conditions were derived from our measured data to be 3.0±0.2, 4.2±0.2 and 7.3±0.6×10^–3 GPa^–1, respectively. The aggregate bulk and shear moduli for aragonite using the Voigt-Reuss-Hill (VRH) scheme are thus calculated to be 68.9±1.4 and 35.8±0.2 GPa, respectively. The value of bulk modulus is in remarkable contrast to the literature value of 46.9 GPa measured almost a century ago. Our new datum, however, is closer to that derived from recent atomistic simulation and static compression studies.     

Uplift-related retrogression history of aragonite marbles in Western Crete (Greece)

In the low-grade, high-pressure (400°C, 10 kbar) metamorphic Phyllite-Quartzite Unit of Western Crete, widespread occurrences of aragonite marbles have been discovered recently. A sedimentary precursor is proved by relic structures (bedding, fossils). Partial or complete transformation of aragonite into calcite is ubiquitous. Compositional and microstructural features reflect the metamorphic history: (1) The high-pressure stage is documented by aragonite that is chemically characterized by incorporation of variable amounts of Sr and the lack of Mg. The most Sr-rich aragonite has about 9 wt% SrO (X _Sr ^arag =0.09). A compositional zoning observed in some aragonite crystals may be due to the prograde divariant calcitearagonite transformation in the system CaCO₃-SrCO₃. Because the parent rocks probably were Sr-poor calcite limestones, one can speculate that strontium has been supplied from an external source under high-pressure conditions. (2) During uplift, calcite replacing aragonite did not equilibrate with unreplaced aragonite. Disequilibrium is indicated by highly variable compositions of calcite crystals that show topotactic relations to the host aragonite. The calcite compositions range from that of the host aragonite (Sr-rich and Mg-free) to Mg-bearing and Sr-poor. (3) Calcite that recrystallized during retrogression is generally Sr-poor (mean value ofX _Sr<0.005), Mg-bearing (X _Mg0.010), and chemically homogeneous. Because practically no Sr remains in the calcite, an interaction with a fluid phase is indicated. In fine-grained calcite marbles rich in solid organic matter, microstructural features indicative of former aragonite may be present. (4) The last stage of retrogression is documented by the appearance of radiating aragonite in veins and nodules. This aragonite, which shows neither deformation nor retrogression, was probably formed metastably in a near-surface environment.     

Lattice dynamics of α-quartz including the effect of the width of the atomic electron distribution

On the basis of the polarizable-ion model (PIM) the effect of the width of the atomic electron distribution on the lattice dynamics of α-quartz was taken into account using the Birman method. The frequencies of optical mode, elastic constants and piezoelectric constants were reproduced using the parameters of this model (an effective charge z, a width parameter w, an electronic polarizability α, and force constants). The width parameter of oxygen atom was found to be about 0.59 Å, and the effective charge of the silicon atom 1.42 electron charges.     

Aragonite crystallization from strained calcite at reduced pressures and its bearing on aragonite in low-grade metamorphism

Aragonite, the dense form of CaCO₃, grew hydrothermally at 100–300° C and dry at 300–400° C at very low pressures from calcite strained by grinding. Nearly complete inversion to aragonite occurred in some runs with Ca-Mg chloride solutions at 0–2.4 kb and 100–200° C on strained calcite having a (10¯14) reflection with a half-width of 0.48° 2 Cu K. A little aragonite grew dry at one atm. from the ground calcite at 300–400° C in a few hrs. Simultaneous shear during recrystallization of calcite in a rotating squeezer resulted in significant aragonite at 300–400° C several kb. below the stability field. No inversion occurred in any ground calcite when previously annealed in CO₂ at 500° C for a few hrs. Thermochemical data show that at least 200 cal/mole of strain energy can be produced in calcite by mild deformation. This much stored energy would lower the pressure requirements of aragonite, relative to the strained calcite by more than 3 kb, and our observation that aragonite growth was faster than strain recovery of calcite indicates that aragonite can grow in nature at reduced pressures from strained calcite.Some experiments were also carried out on highly magnesian calcites with the thought that aragonite might also form at the expense of this metastable material. No aragonite was produced, but the possibility that this mechanism could be operative in nature cannot be discounted.The microtexture of aragonitic deformed marbles from NW Washington (prehnite-pumpellyite facies rocks, courtesy of J. A. Vance) as well as electron probe microanalysis of these rocks indicates that aragonite selectively replaced highly strained calcite. The calcite-aragonite transition is thus a questionable indicator of high-pressure in certain metamorphic rocks.     

The effect of cobalt ion on nucleation of calcium-carbonate polymorphs

Cobalt, like Mg, may cause the precipitation of aragonite rather than calcite in aqueous solutions due to the adsorption and crystal poisoning of calcite by a hydrated ion. Solutions containing NaCl and CaCl₂, having the ionic strength and Ca content of seawater (35‰ salinity), were spiked with known amounts of CoCl₂. Calcium carbonate was precipitated by the addition of 0.7 ml of 1 M Na₂CO₃. All experimental runs were made at 25°C, and all products were examined by X-ray diffraction. At low concentrations of Co (< 5·^?4M) calcite and vaterite formed. At concentrations from 5·10^?4 M to 2·10^?3M, the products consisted of combinations of calcite and vaterite; aragonite and calcite; aragonite and vaterite; calcite, vaterite and aragonite. In solutions of 3·10^?3M CoCl₂, most precipitates were aragonite with only one sample containing a small amount of calcite. All precipitates from 5·10^?3M CoCl₂ solutions either contained aragonite or were amorphous. Solutions with concentrations of 1 · 10^?2M CoCl₂ produced only amorphous precipitates. All precipitates contained an amorphous violet phase, assumed to be basic cobaltous carbonate (2CoCO₃·Co(OH)₂·H₂O).     

High-temperature enthalpy at the orientational order-disorder transition in calcite: implications for the calcite/aragonite phase equilibrium

The enthalpy of calcite has been measured directly between 973 K and 1325 K by transposed-temperature- drop calorimetry. The excess enthalpy has been analysed in terms of Landau theory for this tricritical phase transition. The zero-point enthalpy and entropy allow estimates of the parameters a and C in the Landau expansion for free energy which expresses excess free energy G as a function of the order parameter Q and temperature T: G 1/2a(T _2c–T)Q ²+1/6CQ ⁶ with a=24 J·K·mol^-1, C = 30 kJ·mol^– T _c = 1260 ±5 K. The entropy of disorder below the transition has been formulated as a function of temperature allowing the calculation of the calcite/aragonite phase boundary when taking this extra entropy into account. There is remarkable agreement between the calculated equilibrium curve and previous experimental observations. The Landau theory predicts behaviour which fully accounts for the change in slope of the calcite/aragonite phase boundary, which is thus wholly due to the R¯3c –R¯3m transition in calcite.     

Preferred orientation in experimentally deformed limestone

Over sixty syntectonic deformation experiments in uniaxial compression have been done on fine-grained limestones in the stability fields of calcite I, calcite II and aragonite. X-ray techniques and spherical harmonic analysis of the data were used to determine preferred orientation quantitatively, and inverse pole-figures were derived for these axially symmetric specimens. They display in most cases strong preferred orientation which varies as a function of the experimental conditions, mainly temperature and pressure. At temperatures below 350° C recrystallization is lacking and flattened grains indicate that translation, twin gliding and kinking have been the dominant deformation mechanisms. The inverse pole-figure shows a maximum at c with a shoulder towards or a second maximum at e. This is in agreement with preferred orientation observed in experimentally deformed Yule marble and can be explained as the product of dominant twin gliding on e and translation gliding on r (Turner et al., 1956). At high temperatures (900–1000° C) strong grain growth (from 4 to 50 microns) indicates that the fabric recrystallized. Grains are equidimensional and clear with a marble-like texture. The inverse pole-figure shows a single maximum at r, and c-axes are oriented in a small circle around the axis of compression, ₁. Such a pattern of preferred orientation would be expected on thermodynamic grounds assuming that recrystallized grains will be oriented in such a way that the strain energy is a maximum (e.g. MacDonald, 1960). Decrease in confining pressure caused a decrease of the maximum at c and the formation of a secondary maximum at highangle positive rhombs in the inverse pole-figure. This can be interpreted as r translation dominating over e twinning. In all deformation experiments an equilibrium in preferred orientation was reached after 20 percent shortening. The strength of preferred orientation decreased with increasing temperature. Aragonite was produced within its hydrostatic stability field at temperatures above 500° C. Close to the phase boundary, coarse-grained textures showed preferred orientation with poles to (010) parallel to ₁. At higher pressures the fabric is fine-grained and [001] is aligned parallel to ₁. Evidence is given that the phase change from calcite to aragonite in these deformation experiments is a diffusive and not a martensitic transformation.Publication No. 1043, Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California.     

Theoretical studies of charge relaxation effects on the statics and dynamics of oxides

Inclusion of spherical charge relaxation in response to the long-range electrostatic potential (potential induced breathing, or PIB) gives improved results for the static and dynamic properties of oxides. PIB is a Gordon-Kim type model, in which the crystal charge density is estimated by overlapping ionic charge densities. No experimental data are used, except for the values of universal constants, and in this sense the results are from first principles. In contrast to earlier models which include some form of charge relaxation, we explicitly include the breathing effects on the self-energy and pair potentials in the model Hamiltonian. PIB is a many-body effect that couples the long-and short-range forces in a way that is not present in any other first principles or empirical models. It leads to the observed violations of the Cauchy relations for the elastic constants whereas central force rigid ion models cannot violate the Cauchy relations. PIB also reduces the predicted LO-TO splitting because the breathing effect introduces dynamical effective charges that are lower in magnitude than the ionic charges. Some results are shown and discussed for MgO (periclase), BeO (bromellite), Al₂O₃ (corundum), TiO₂ (rutile) and SiO₂ (quartz and stishovite).     

碳酸钙矿物低温化学合成及其同质多象转变矿物学机理研究

通过缓慢分解Ca²⁺-Mg²⁺-HCO₃^--Cl^--H₂O溶液和以菱锶矿(或碳钡矿、白铅矿)为晶种的附晶生长法,在0-90℃温度范围内定向合成了碳酸钙同质多象变体.矿物合成实验结果表明,随着温度升高,有利于亚稳态文石和不稳定六方方解石的生成;随着溶液中Mg²⁺离子浓度增大和Ca(HCO₃)₃溶液浓度减小,均有利于亚稳态文石的形成.以XRD和SEM技术为实验手段,详细研究了碳酸钙同质多象转变过程.结果显示:在流体参与的情况下,文石→方解石和六方方解石→方解石的同质多象转变速率很快,并且其转变的矿物学机理为溶解/再沉淀.     

Étude expérimentale de la réactivité du CO2 supercritique vis-à-vis de phases minérales pures. Implications pour la séquestration géologique de CO2

Carbon dioxide sequestration in deep aquifers and depleted oilfields is a potential technical solution for reducing green-house gas release to the atmosphere: the gas containment relies on several trapping mechanisms (supercritical CO₂, CO_2(sc), dissolution together with slow water flows, mineral trapping) and on a low permeability cap-rock to prevent CO_2(sc), which is less dense than the formation water, from leaking upwards. A leakproof cap-rock is thus essential to ensure the sequestration efficiency. It is also crucial for safety assessment to identify and assess potential alteration processes that may damage the cap-rock properties: chemical alteration, fracture reactivation, degradation of injection borehole seals, etc. The reactivity of the host-rock minerals with the supercritical CO₂ fluid is one of the potential mechanisms, but it is altogether unknown. Reactivity tests have been carried out under such conditions, consisting of batch reactions between pure minerals and anhydrous supercritical CO₂, or a two-phase CO₂/H₂O fluid at 200?°C and 105/160 bar. After 45 to 60 days, evidence of appreciable mineral-fluid reactivity was identified, including in the water-free experiments. For the mixed H₂O/CO₂ experiments, portlandite was totally transformed into calcite; anorthite displayed many dissolution patterns associated with calcite, aragonite, tridymite and smectite precipitations. For the anhydrous CO₂ experiments, portlandite was totally carbonated to form calcite and aragonite; anorthite also displayed surface alteration patterns with secondary precipitation of fibrous calcite. To cite this article: O. Regnault et al., C. R. Geoscience 337 (2005).     

The solubility of calcite and aragonite in seawater of 35%. salinity at 25°C and atmospheric pressure

The solubilities of synthetic, natural and biogenic aragonite and calcite, in natural seawater of 35%. salinity at 25°C and 1 atm pressure, were measured using a closed system technique. Equilibration times ranged up to several months. The apparent solubility constant determined for calcite of 4.39(±0.20) × 10^?7 mol² kg^?2 is in good agreement with other recent solubility measurements and is constant after 5 days equilibration. When we measured aragonite solubility we observed that it decreased with increasing time of equilibration. The value of 6.65(±0.12) × 10^?7 mol² kg^?2, determined for equilibration times in excess of 2 months, is significantly less than that found in other recent measurements, which employed equilibration times of only a few hours to days. No statistically significant difference was found among the synthetic, natural and biogenic material. Solid to solution ratio, contamination of aragonite with up to 10 wt% calcite and recycling of the aragonite made no statistically significant difference in solubility when long equilibration times were used.Measured apparent solubility constants of aragonite and calcite are respectively 22( ± 3)% and 20( ± 2)% less than apparent solubility constants calculated from thermodynamic equilibrium constants and seawater total activity coefficients. These large differences in measured and calculated apparent solubility constants may be the result of the formation of surface layers of lower solubility than the bulk solid.     

The role of magnesium in the crystal growth of calcite and aragonite from sea water

The seeded precipitation (crystal growth) of aragonite and calcite from sea water, magnesium-depleted sea water, and magnesium-free sea water has been studied by means of the steady-state disequilibrium initial rate method. Dissolved magnesium at sea water levels appears to have no effect on the rate of crystal growth of aragonite, but a strong retarding effect on that of calcite. By contrast, at levels less than about 5 per cent of the sea water level, Mg has little or no effect on calcite growth. Extended crystal growth on pure calcite seeds in sea water of normal Mg content resulted in the crystallization of magnesium calcite overgrowths, containing 7–10 mole % MgCO₃ in solid solution. This suggests that the rate inhibition by Mg is due to its incorporation within the calcite crystal structure during growth, which causes the resulting magnesian calcite to be considerably more soluble than pure calcite. The standard free energy of formation of 8.5 mole% Mg calcite calculated on this assumption is in good agreement with independent estimates of magnesian calcite stability.From the work of Katz (Geochim. Cosmochim. Acta37, 1563–1586, 1973), Plummer and Mackenzie (Amer. J. Sci. 273, 515–522, 1974), and the present paper, it can be predicted that the most stable calcite in Ca-Mg exchange equilibrium with sea water contains between 2 and 7 mole%MgCO₃ in solid solution. Likewise, calcites containing more than 8.5 mole% MgCO₃ are less stable, and those containing less than 8.5 mole% MgCO₃ are more stable than aragonite plus Ca and Mg in sea water.     

Computer simulations of the structural and physical properties of the olivine and spinel polymorphs of Mg2SiO4

The aim of the work presented is to develop a computer simulation technique which will predict the structure and physical properties of forsterite and ringwoodite, the major mantle-forming polymorphs of Mg₂SiO₄. The technique is based upon energy minimization, in which all structural parameters are varied until the configuration with the lowest energy is achieved. The lattice energy and physical properties (e.g. elasticity and dielectric constants) are calculated from interatomic potentials, which generally include electrostatic and short-range terms. We investigate several types of traditional potential models, and present a new type of model which includes partial ionic charges and a Morse potential to describe the effect of covalency on the Si-O bond. This new form of potential model is highly successful, and not only reproduces the zero-pressure structural, elastic and dielectric properties of forsterite and ringwoodite, but also accurately describes their pressure dependence.     

非等轴颗粒付林图解

非等轴颗粒付林图解由直线a=1、b=1、a=b和曲线a2b=1、ab2=1分割成10个微区,并对应于不同的e_x、e_y、e_z组合和应变类型。这些直线和曲线分别对应于特殊的e_x、e_y、e_z组合和岩石应变类型。岩石的应变类型有18种。函数a.b的表征方程有4种类型,并分别表征直线a=1/k₁和b=1/k₂所分割的4个区间。a,b表征方程的确定取决于岩石总的变形行为。此图解可用于非等轴颗粒标志体应变测量和应变类型的确定和图示,文章给出了应用实例.      

Modelling of structural and elastic changes of forsterite (Mg2SiO4) under stress

The method of crystal static deformation, including inner strain effects, was applied to calculate the structure configuration and the elastic constants of forsterite under anisotropic and isotropic pressure. A Born type interatomic potential is used, with optimized atomic charges and repulsive radii; SiO₄ tetrahedra are approximated as rigid units. Computations were carried out in the range 1–8 GPa, with steps of 1 GPa, for the three uniaxial stresses τ₁, τ₂, τ₃ and for pressure p. By interpolation of results, interatomic distances and elastic tensor components are shown to depend quadratically on stress. A non-linear behaviour generally appears above 4 GPa; the importance of inner strain and non-linear effects is analyzed. Mg-O bond lengths and O-O edges of coordination polyhedra respond differently to anisotropic and to isotropic stresses, according to the topological features of the structure. Elastic and structural results for hydrostatic pressure are compared to experimental literature data, discussing the range of validity of the rigid body approximation for SiO₄ groups.     

Aragonite in California Glaucophane Schists, and the Kinetics of the Aragonite--Calcite Transformation

Coleman & Lee's discovery that aragonite is a widespreadmetamorphic mineral in California glaucophane schists is confirmedand amplified. Methods of microscopic distinction between aragonite,calcite, and dolomite, including a universal-stage technique,are described. Further data are recorded regarding the paragenesisof aragonite-bearing glaucophane and lawsonite schists. Carbonatesin the greenschist facies are found to be exclusively calciteand dolomite. In many Californian metamorphic aragonites partialinversion to calcite has been observed. This appears to be anequal-volume replacement in which an a axis and an edge [f:f] of calcite—both directions of Closest spacing of Ca⁺⁺ions—commonlyare parallel to of the crystal axes a, b, and c of aragonite. The problem of survival of metamorphic aragonite through a necessarilylong period of post-metamorphic unloading is approached by experimentalexploration of the kinetics of the aragonite calcite transformation.It is found that Californian aragonite could survive unloadingfrom a depth of 20 km if the linear temperature gradient were10? C per km, but not appreciably higher. Available experimentaldata are consistent with crystallization of aragonite, jadeite,and lawsonite at depths of 20–30 km if a gradient of 10?C per km is assumed. The corresponding conditions of the glaucophane-schistfacies (T = 2OO?-3OO? C, P = 6000-9000 bars) are attributedessentially to deep burial in regions (subsiding geosyn-clines)of unusually low temperature gradient (10? C per km).