Spreadsheets to calculate <i>P–V–T</i> relations, thermodynamic and thermoelastic properties of silicates in the MgSiO₃–MgO system

<p>Modified equations of state (EoS) of forsterite, wadsleyite, ringwoodite, akimotoite, bridgmanite and post-perovskite based on the Helmholtz free energy are described using Microsoft Excel spreadsheets. The equations of state were set up by joint analysis of reference experimental data and can be used to calculate thermodynamic and thermoelastic parameters and <i>P–V–T</i> properties of the Mg-silicates. We used Visual Basic for Applications module in Microsoft Excel and presented a simultaneous calculation of full set of thermodynamic and thermoelastic functions using only <i>T–P</i> and <i>T–V</i> data as input parameters. Phase transitions in the MgSiO₃–MgO system play an important role in the interpretation of the seismic boundaries of the upper Earth’s mantle and in the D″ layer. Therefore, proposed EoSes of silicates in the MgSiO₃–MgO system have clear geophysical implications. The developed software will be interesting to specialists who are engaged to study the mantle mineralogy and Earth’s interior.</p

First Finding of High-Pressure Modifications of Na₂CO₃ and K₂CO₃ with sp³‑Hybridized Carbon Atoms

The transition from structures with classical [CO3] triangles to structures with [CO4] tetrahedra, corresponding to the transition from sp2 to sp3 hybridization of carbon atoms, is quite well established for alkaline earth carbonates CaCO3 and MgCO3. Here, using a crystal structure prediction technique, we show that alkali carbonates Na2CO3 and K2CO3 follow the same trend. Both compounds form isostructural sp3-hybridized phases, Na2CO3–C2/m and K2CO3–C2/m, which became thermodynamically stable at pressures above 125 and 150 GPa, respectively. The automated topological search through ICSD has shown that the found C2/m structures, as well as sp3-structures of CaCO3 and MgCO3 do not have topological analogs among silicates and phosphates. Transitions of Na2CO3 and K2CO3 to C2/m structures are realized without sufficient perturbation of the initial Na2CO3–P21/m and K2CO3–P1̅ structures and require relatively small atomic displacements of carbon and oxygen atoms. These transitions are realized through simple energy optimization. This indicates the absence or low height of the energy barrier. In the wide interval of pressures before the transition to the sp3 structures, carbon atoms of [CO3] triangles are gradually displaced from the plane defined by three oxygen atoms due to the interaction with the fourth oxygen atom. In the case of Na2CO3, the dihedral angle C–O–O–O describing the degree of this displacement increases from 5 to 12°, when the pressure increases from 60 to 127 GPa. At pressures above 130 GPa, the angle abruptly increases to the value of 31°, which corresponds to the formation of the sp3-hybridized phase Na2CO3–C2/m. Based on the examples of alkali and alkaline earth carbonates, we show that the transition from a sp2-hybridized [CO3] triangle to a sp3-hybridized [CO4] tetrahedron is realized when the fourth oxygen atom approaches the carbon atom at a distance less than 2.0 Å, which is usually realized at pressures of around 100 GPa. The stable structures with sp3-hybridized carbon atoms have not been found for Li2CO3 in the considered pressure range up to 200 GPa, and we show that the P63/mcm structure of this compound is stable in sp2 form up to a pressure of 700 GPa or even higher. This indicates that not all the structures of carbonates adopt sp3 form even at extreme pressures

Toward Analysis of Structural Changes Common for Alkaline Carbonates and Binary Compounds: Prediction of High-Pressure Structures of Li₂CO₃, Na₂CO₃, and K₂CO₃

The behavior of alkaline carbonates at high pressure is poorly understood. Indeed, theoretical and experimental investigations of the pressure induced structural changes have appeared in the literature only sporadically. In this article we use evolutionary crystal structure prediction algorithms based on density functional theory to determine crystal structures of high-pressure phases of Li₂CO₃, Na₂CO₃, and K₂CO₃. Our calculations reveal several new structures for each compound in the pressure range of 0–100 GPa. Cation arrays of all high-pressure structures are of the AlB₂ topological type. The comparison of cation arrays of ambient and high-pressure structures with that of binary A₂B compounds indicates an analogy between high-pressure behavior of alkaline carbonates and alkaline sulfides (oxides, selenides, tellurides), which under compression go through the following series of phase transitions: anti-CaF₂ → anti-PbCl₂ → Ni₂In → AlB₂. All structures presented in this trend are realized in the high-pressure trend of alkaline carbonates, although some intermediary structures are omitted for particular compounds

Hydrothermal Synthesis and Structure Solution of Na₂Ca(CO₃)₂: “Synthetic Analogue” of Mineral Nyerereite

Crystals of Na₂Ca­(CO₃)₂, the structural analogues of mineral nyerereite, were synthesized using hydrothermal technique at 1 kbar and 450 °C. The crystals are transformational twins formed at the transition from the high-temperature hexagonal modification to the low-temperature orthorhombic modification. The structure was solved and refined to <i>R</i> = 0.059 in <i>P</i>2₁<i>ca</i> (No. 29) space group with <i>a</i> = 10.0713(5) Å, <i>b</i> = 8.7220(2) Å, and <i>c</i> = 12.2460(4) Å. The only structural analogue of the synthesized crystal is the high-temperature modification of K₂Ca­(CO₃)₂, which can be considered as a disordered analogue of Na₂Ca­(CO₃)₂. Structural analogues among borates and other classes of compounds have not been found. Based on group–subgroup analysis, we propose the structures of high- and intermediate-temperature modifications of Na₂Ca­(CO₃)₂. The relations of the determined structure with other polymorphs of Na₂Ca­(CO₃)₂ have also been considered

High-Pressure–High-Temperature Study of Benzene: Refined Crystal Structure and New Phase Diagram up to 8 GPa and 923 K

The high-temperature structural properties of solid benzene were studied at 1.5–8.2 GPa up to melting or decomposition using multianvil apparatus and <i>in situ</i> neutron and X-ray diffraction. The crystal structure of deuterated benzene phase II (<i>P</i>2₁/<i>c</i> unit cell) was refined at 3.6–8.2 GPa and 473–873 K. Our data show a minor temperature effect on the change in the unit cell parameters of deuterated benzene at 7.8–8.2 GPa. At 3.6–4.0 GPa, we observed the deviation of deuterium atoms from the benzene ring plane and minor zigzag deformation of the benzene ring, enhancing with the temperature increase caused by the displacement of benzene molecules and decrease of van der Waals bond length between the π-conjuncted carbon skeleton and the deuterium atom of adjacent molecule. Deformation of benzene molecule at 723–773 K and 3.9–4.0 GPa could be related to the benzene oligomerization at the same conditions. In the pressure range of 1.5–8.2 GPa, benzene decomposition was defined between 773–923 K. Melting was identified at 2.2 GPa and 573 K. Quenched products analyzed by Raman spectroscopy consist of carbonaceous material. The defined benzene phase diagram appears to be consistent with those of naphthalene, pyrene, and coronene at 1.5–8 GPa

Aragonite-II and CaCO₃‑VII: New High-Pressure, High-Temperature Polymorphs of CaCO₃

The importance for the global carbon cycle, the <i>P</i>–<i>T</i> phase diagram of CaCO₃ has been under extensive investigation since the invention of the high-pressure techniques. However, this study is far from being completed. In the present work, we show the existence of two new high-pressure polymorphs of CaCO₃. The crystal structure prediction performed here reveals a new polymorph corresponding to distorted aragonite structure and named aragonite-II. In situ diamond anvil cell experiments confirm the presence of aragonite-II at 35 GPa and allow identification of another high-pressure polymorph at 50 GPa, named CaCO₃-VII. CaCO₃-VII is a structural analogue of CaCO₃-<i>P</i>2₁/<i>c</i>-l, predicted theoretically earlier. The <i>P</i>–<i>T</i> phase diagram obtained based on a quasi-harmonic approximation shows the stability field of CaCO₃-VII and aragonite-II at 30–50 GPa and 0–1200 K. Synthesized earlier in experiments on cold compression of calcite, CaCO₃-VI was found to be metastable in the whole pressure–temperature range