Ab Initio Thermodynamic Model for Magnesium Carbonates and

Article pubs.acs.org/JPCA

Ab Initio Thermodynamic Model for Magnesium Carbonates and Hydrates Anne M. Chaka* and Andrew R. Felmy Pacific Northwest National Laboratory, P.O. Box 999, MS K8-96, Richland, Washington 99352, United States S Supporting Information *

ABSTRACT: An ab initio thermodynamic framework for predicting properties of hydrated magnesium carbonate minerals has been developed using densityfunctional theory linked to macroscopic thermodynamics through the experimental chemical potentials for MgO, water, and CO2. Including semiempirical dispersion via the Grimme method and small corrections to the generalized gradient approximation of Perdew, Burke, and Ernzerhof for the heat of formation yields a model with quantitative agreement for the benchmark minerals brucite, magnesite, nesquehonite, and hydromagnesite. The model shows how small differences in experimental conditions determine whether nesquehonite, hydromagnesite, or magnesite is the result of laboratory synthesis from carbonation of brucite, and what transformations are expected to occur on geological time scales. Because of the reliance on parameter-free first-principles methods, the model is reliably extensible to experimental conditions not readily accessible to experiment and to any mineral composition for which the structure is known or can be hypothesized, including structures containing defects, substitutions, or transitional structures during solid state transformations induced by temperature changes or processes such as water, CO2, or O2 diffusion. Demonstrated applications of the ab initio thermodynamic framework include an independent means to evaluate differences in thermodynamic data for lansfordite, predicting the properties of Mg analogues of Ca-based hydrated carbonates monohydrocalcite and ikaite, which have not been observed in nature, and an estimation of the thermodynamics of barringtonite from the stoichiometry and a single experimental observation. (MCO3),17,18 there is considerable evidence both from the geological record and recent laboratory experiments that there is a broad range of conditions under which hydrated carbonates will form.1,4,5,16,19−27 This is particularly true for magnesium carbonates, likely due to the highly hydrated character of Mg2+ ions in solution. Indeed, some watereven trace amounts appears to be essential for the carbonation reaction to occur in the presence of CO2.16,21,24,28−34 The geologically relevant Mg hydrate and carbonate minerals are periclase (MgO), magnesite (MgCO3), brucite (Mg(OH)2), nesquehonite (MgCO3·3H2O), lansfordite (MgCO3·5H2O), hydromagnesite Mg5(CO3)4(OH)2·4H2O), artinite (Mg2(CO3)(OH)2·3H2O), and dypingite (Mg5(CO3)4(OH)2·5H2O). There is spectroscopic evidence for several of these hydrated carbonates such as hydromagnesite and artinite on Mars as well, providing evidence for liquid water being at least transiently present on Mars at some time.35 The potential for successful geological sequestration of CO2 can be improved by obtaining fundamental understanding of the structure and bonding of carbonate mineral deposits and development of predictive simulations and thermodynamic

1. INTRODUCTION The thermal stability of hydrated magnesium carbonates is important for a wide variety of technological applications such as precursors for synthesis of complex nanostructures,1−3 industrial manufacturing based on crystallization separation processes,4−6 paints, paper, coatings, pharmaceuticals, nuclear waste isolation,6 and fire retardants.7,8 Recently interest has grown considerably because geological sequestration of carbon dioxide, the principle anthropogenic greenhouse gas, has been proposed as a strategy to mitigate climate change.9 The success of this approach is, in part, dependent upon the ability to form carbonate mineral phases with long-term stability under geological conditions. Sequestration approaches considered among the most viable involve injection of liquid or supercritical CO2 into reservoirs,10−12 deep saline aquifers,13,14 or geological formations. Magnesium−based minerals are an important focus for geological sequestration studies because (1) of their geological abundance (Mg is the seventh most abundant element, and MgO the fifth to seventh most abundant mineral in most regions of the earth’s crust,15 plus forsterite (Mg2SiO4) is the most abundant mineral in the earth’s mantle above a depth of 400 km), and (2) Mg oxides, hydroxides, and silicates are very reactive toward supercritical CO2.16 Although in general the thermodynamically most stable carbonates for divalent cations are the anhydrous forms © 2014 American Chemical Society

Special Issue: Kenneth D. Jordan Festschrift Received: January 9, 2014 Revised: March 24, 2014 Published: March 28, 2014 7469

dx.doi.org/10.1021/jp500271n | J. Phys. Chem. A 2014, 118, 7469−7488

The Journal of Physical Chemistry A

Article

Figure 1. Crystal structures of minerals investigated in this study. Mg atoms are green, oxygen red, carbon grey, and hydrogen white.

Hence development of a thermodynamic model that enables facile calculation of decomposition phase boundaries under a range of conditions will help to establish boundaries for interpretation of the solid state transformations that occur during thermal decomposition. This is particularly important for geochemistry, as many transformations will occur on geological time scales if thermodynamically allowed, but are kinetically too slow to be observed in the laboratory. Our objective is to develop a widely applicable thermodynamic framework capable of treating minerals and their solidstate transformations across a range of conditions relevant to geological conditions and to laboratory studies. The framework is based on ab initio electronic structure calculations on mineral crystal structures coupled to experimentally determined values for the chemical potentials of H2O and CO2 in the surrounding medium. The method can be applied to conditions not readily accessible by experiment. As ab initio calculations provide reliable structure and energy predictions for solid state substitutions, vacancies, and other nonstoichiometric defects or compositional variation, the ab initio thermodynamics (AIT) framework established here lays the groundwork for evaluation of transformations, transitional structures, and mechanistic pathways resulting from phenomena such as thermal decomposition and transport of species such as water, O2, and CO2 into and out of minerals (lansfordite transforming to nesquehonite upon standing, for example), leading to increased mechanistic understanding of solid state transformations with atomic resolution. Developing a reliable thermodynamic framework capability requires validated first-principles theoretical methods for treating a wide range of structures exhibited by the Mg minerals from the very simple rock salt structure of periclase46 to complex hydromagnesite. These structures are shown in Figure 1 and briefly described here. Magnesite crystallizes in the calcite structure, with alternating layers of Mg2+ ions and CO2− 3 groups. Brucite exhibits a layered structure of hexagonally arranged Mg ions and staggered antiparallel hydroxyl groups that do not engage in hydrogen bonding. Nesquehonite is a relatively open structure consisting of 2-dimensional ribbons of coplanar MgCO3 surrounded by water molecules, two-thirds of which are axially coordinated to the Mg ions and one-third hydrogen bonded to the carbonate groups along the edges of

models to optimize the conditions for their formation and longterm stability. In addition, capture of CO2 on site at large point sources can lead to commercially viable forms of the hydrated carbonates hydromagnesite and nesquehonite for use as flame retardants and fillers.7 Although the MgO−CO2−H2O system has been extensively studied,17,22,27,36−38 thermodynamic data across the range of geologically relevant conditions is not available for most of the hydrated magnesium carbonate minerals. Industrial applications such as flame-retardants require even higher temperature thermodynamic data than geochemistry, yet values for nesquehonite, hydromagnesite, and artinite are only tabulated up to 300 K. In some cases, equilibrium phase boundaries can be experimentally determined in solution with high-pressure equipment, such the periclase-brucite equilibrium by Schramke and co-workers.39 Even so, the low solubility or poor stability of many minerals has resulted in contradictory measurements of solubility products and significant uncertainties in the calculation of chemical equilibria and phase transformations. For example, a recent review by Bénézeth and co-workers found that reported values for the solubility product of magnesite at room temperature varied from 10−10.3 to 10−5.1, necessitating new, more reliable measurements.37 Lansfordite is particularly challenging, as data from solution measurements are not available at 300 K. Those data that are available, however, exhibit a significant discrepancy with respect to the entropy. In addition, determination of phase boundaries from decomposition reactions is extremely difficult due to factors such as high reactivity,40 particle size variability,41 and kinetic limitations, particularly in the absence of catalytic water. For example, carbonation of MgO has been observed to occur at the (100) surface above the magnesite threshold equilibrium pressure of CO2,42 but the full solid state transformation to form bulk magnesite from periclase has not been observed even at high temperatures and CO 2 pressures.36 Advanced experimental techniques such as controlled rate thermal analysis43,44 and in situ X-ray spectroscopy45 are helping to elucidate the multiple stage decomposition mechanisms for complicated structures like nesquehonite and hydromagnesite, but they also reveal that experimental determination of a reversible equilibrium phase boundary is not kinetically feasible. 7470



Article

the ribbons.47,48 Lansfordite consists of a complicated arrangement of two Mg complexes hydrogen bonded to each other: Mg(H2O)6 and Mg(CO3)2(H2O)4.49 Hydromagnesite has the most complicated structure of all.50,51 The carbonate groups are arranged so that half lie roughly parallel to the (001) plane and the other half to the (100). Those in the (001) plane have one oxygen coordinated to two Mg atoms and the other two O are coordinated to one Mg atom and H-bonded to one water molecule. Those that are tilted slightly from the (001) plane have all three oxygens in the carbonate group coordinated to two Mg. Theoretical modeling of the hydrated and carbonated Mg minerals is challenging because these complicated structures exhibited by the hydrated Mg carbonates encompass a range of chemical bonding, from strong covalent and ionic interactions, to weaker hydrogen bonding and dispersion or van der Waals (vdW) interactions. Density-functional theory (DFT) has been established as the method of choice for studying bonding and structure in solids. The generalized gradient approximation (GGA) to DFT in particular has been successful over the past 15 years in describing strongly interacting systems52 such as MgO,53 Mg(OH)2,54 and MgCO3,55−57 as well as covalent and hydrogen bonded systems at ambient pressure.58−60 Recent studies, however, have highlighted the importance of including vdW interactions or dispersion for a wide range of organic,61−64 biological,65 and inorganic systems.52,65−73 Early work by Doll and Stoll utilized the coupled cluster method to elucidate that significant dispersion was present even in dimers of the alkali halides.68 More recently, Zhang and co-workers demonstrated the importance of vdW interactions in solids for the more covalent semiconductors as well as for predominantly ionic systems such as MgO and NaCl.52 For water-based systems, GGA alone has been shown by Santra and co-workers58 as well as Hirsch and Ojamäe60 to yield very good results for describing the low-pressure phases of ice. To accurately describe the full phase diagram of ice,58,74,75 however, particularly at high pressure,58 vdW interactionsalthough they do not dominate H-bondingbecome increasingly more important. Including vdW interactions also significantly improves the description of the structure and properties of liquid water.56,76−78 Dispersion has been shown to play a significant role in weakly bonded layered systems such as clays79 and layered double hydroxides such as brucite.67,80 Ugliengo and co-workers showed that adding dispersion to hybrid DFT improved the structural and cohesive descriptions of brucite, portlandite, and kaolinite.67 Exfoliation energies, i.e., the energy to separate the layers, were found to increase by including dispersion from −3.8 to −22.0 kJ/mol for brucite, −4.7 to −22.7 kJ/mol for portlandite, and −32.6 to −70.9 kJ/ mol for kaolinite, thus indicating the significant role of dispersion in the stabilization of these layered structures. Hence, any theoretical method used to investigate these systems needs to treat dispersion reasonably well, in balance with all other interactions. It has not yet been established whether adding dispersion to traditional DFT improves the reliability of calculations on hydrated mineral carbonates. In order to perform this assessment, the methodology utilized to add dispersion in these systems must be efficient, as the unit cell for hydromagnesite contains 74 atoms and lansfordite has 80. Unfortunately, seamless incorporation of vdW forces into DFT functionals or correlated wave function methods is currently prohibitively expensive for large periodic systems.52 However,

adding a pairwise interatomic dispersion term to density functionals, termed DFT-D, is sufficiently computationally efficient to be used for large systems.73 DFT-D methods are pairwise approximations that neglect higher order, nonadditive many-body interactions, which recent work has shown to be negligible.58 Hence we evaluated two a posteriori empirical correction methods for the DFT-D dispersion interactions: Grimme (G06) that utilizes semiempirical fitting to experiment and/or post-Hartree−Fock binding energies to obtain a damped f(R)C6/r6 term,64,69,81 and Tkatchenko and Scheffler (TS), which employs mean-field ground-state electron density and free reference data scaled by self-interaction corrected TDDFT.82 These two DFT-D methods have demonstrated success for predicting the structure and cohesive energies for a wide range of systems, including low-pressure ice phases, ionic systems such as MgO, semiconductors, and biological systems.52,61,63−65,67,69,70,72,73 Recent work by Maschio and co-workers have found that the accuracy is good relative to localized MP2, and given the computational efficiency, DFT-D was determined to be the method of choice for 60 molecular crystals investigated.61 The objective of this work is to validate the theoretical methods and develop a predictive geochemical thermodynamic framework for mineral phase stabilities and transformations. We will employ parameter-free density functional theory to calculate the electronic and structural properties of Mg-based minerals and evaluate the need for semiempirical dispersion methods at 0 K, then extend the method of ab initio thermodynamics to obtain properties in equilibrium with gases and fluids at finite temperature and pressure. To our knowledge, the presentation of experimental thermodynamic data as a function of temperature at a range of pressures has not yet been done for the hydrated magnesium carbonates. Most of the theoretical work on carbonates in both quantum and classical molecular dynamics83−85 mineral arenas has focused on CaCO3, with a few electronic structure calculations on MgCO3,55,86,87 some involving high pressure.88,89 This work represents the first theoretical investigation of the hydrated carbonates of magnesium. The benchmarking of DFT for these compounds, including vdW forces, serves as a foundation for the ab initio thermodynamic framework, as well as for development of classical pair potentials by others. In this study, the framework is developed utilizing magnesium hydrate and carbonate minerals for which there are well-defined crystal structures and evaluated thermodynamic data. These minerals are periclase, magnesite, brucite, nesquehonite, and hydromagnesite, shown in Figure 1a−e. We develop a first-principles model on these known systems and compare with experimental thermodynamic data to assess the accuracy and uncertainty of the model. We then utilize the model for three different applications. The first is to resolve a discrepancy in entropy data for lansfordite and determine the thermodynamic properties and phase stability of lansfordite over a broad range of temperature and pressure in the absence of heat capacity measurements and H−H°(Tr) data. Then, to determine how the model would work for intermediate structures and metastable phases other than the methoddevelopment set, we consider the Mg analogues of the calciumbased minerals monohydrocalcite (CaCO3·H2O) and ikaite (CaCO3·6H2O) (shown in Figure 1g,h.), and show why they have never been observed in nature. Lastly, having the AIT framework for the series of MgCO3·nH2O with n = 1, 3, 5, and 6, enables development of empirical estimates of thermody7471



Article

at zero temperature, which is equivalent to the enthalpy under conditions where work due to pV is not significant. Therefore, the Gibbs free energy can be expressed as

namic quantities for minerals such as barringtonite with an intermediate number of water molecules (MgCO3·2H2O) even though the crystal structure has not yet been determined.

G(T , V , p , NaNb...NR ) = ETotal(T , V , p , NaNb...NR )

2. THEORETICAL METHODS 2.1. General. Periodic density-functional theory (DFT) calculations were performed with the Perdew, Burke, and Ernzerhof (PBE) generalized gradient approximation (GGA) to the exchange-correlation functional.90 All-electron calculations were carried out using the DMol3 code.91,92 Both double (v4.4) and triple numeric basis sets plus polarization (DNP and TNP, respectively), analogous to double/triple valence plus polarization, were tested. Lattice optimization calculations were converged with respect to k-points utilizing the Monkhorst− Pack93 scheme to sample the Brillouin zone. A real space cutoff of 4.4 Å was used. The two forms of DFT-D were tested in conjunction with the PBE functional and are referred to in the following text as PBE-G06 for the Grimme method of adding dispersion, and PBE-TS for Tkatchenko−Scheffler. The DFT-D corrections were calculated within DMol3 using the DFT Semi-Empirical Dispersion interaction Correction (SEDC) module by McNellis, Meyer, and Reuter.94 For benchmarking the DFTD methods, we include Ice XI (the proton-ordered structure most stable at 0 K) and dry ice (crystalline CO2) in addition to the minerals periclase, brucite, magnesite, nesquehonite, and hydromagnesite. 2.2. Methodology: Ab Initio Thermodynamics. In this section, we describe the thermodynamic formalism and how it is coupled with DFT total-energy calculations to calculate the free energy of mineral phases at finite temperature and pressure in geochemical and laboratory environments knowing only the structure. This is an extension of the methodology termed ab initio thermodynamics95,96 that has been applied successfully to describe the free energy of nonstoichiometric, reconstructed, and/or hydrated metal oxide surfaces,58,95,97−100 and defects and surfaces in semiconductors.101 The concept of Helmholtz free energy provides the link between the DFT total energy calculations ETotal and the Gibbs free energy G, under specific circumstances. The Helmholtz free energy F is a thermodynamic potential developed to measure useful work at constant temperature. It is defined as F  U − TS where U is the internal energy of the system, T the temperature, and S the entropy. At zero temperature, the DFT total energy corresponds to U, the internal energy of the system if the zero-point vibrational energy is neglected. Hence at 0 K when the TS term equals zero, the Helmholtz free energy for a system can be written as

+ Evib(T , V , NaNb...NR ) − TS(T , V , NaNb...NR )

with the vibrational contribution noted as E , which at 0 K is equal to EZPE. The ZPE is not always considered in theoretical computation of mineral energies. If a mineral structure contains hydroxyl groups or water molecules such as brucite, nesquehonite, and hydromagnesite, however, it is essential to include the ZPE, as their high frequency vibrational modes make a significant contribution to the ZPE as well as to the vibrational entropy at finite temperature. The C−O stretch in carbonate and CO2 has a lesser, but still significant, effect. To quantify these effects, the phonon spectrum was calculated within DMol3 using the frozen phonon method102 and two-point finite differences per atom with a step size of 0.01 ao to construct the mass-weighted Hessian matrix. Diagonalization of the Hessian yields the harmonic vibrational frequencies of the solid. ZPE values calculated using PBE-G06 are shown in Table 1. ZPE calculated Table 1. Total, Zero Point Vibrational, and Dispersion Energies from DFT Calculations per Stoichiometric Formula Unit in kJ/mol

H2O molecule H2O crystal CO2 molecule CO2 crystal periclase MgO brucite Mg(OH)2 magnesite MgCO3 nesquehonite MgCO3· 3H2O hydromagnesite Mg5(CO3)4(OH)2·4H2O lansfordite MgCO3·5H2O Mg analogue of monohydrocalcite MgCO3·H2O Mg analogue of ikaite MgCO3·6H2O

PBE-G06 ETotal

PBE-G06 EZPE

G06 EvdW

TS EvdW

−200614.18 −200535.53 −494855.07 −494832.00 −722928.28 −923540.16 −1217855.88 −1819664.09

55.00 67.54 29.91 30.88 13.51 68.51 51.14 252.80

−9.65 −66.58 −56.93 −62.72 −74.29 −96.49

−4.82 −55.96 −112.89 −106.14 −103.24 −118.68

−6597358.17

556.73

−371.47

−480.50

−2220901.63 −3191475.63

385.95 118.68

−126.40 −77.19

-

−1076182.61

462.17

−183.33

-

by PBE and PBE-TS exhibited negligible differences from PBEG06, e.g., less than 1 kJ/mol difference for nesquehonite, which has a significant ZPE of 253 kJ/mol. The ZPE contribution ranges from only 13.5 kJ/mol per formula unit for MgO to as high as 557 kJ/mol for hydromagnesite with ten O−H and 12 C−O bonds, thus underscoring the importance of including ZPE for accurate thermodynamics for these systems. This is consistent with the importance of ZPE shown by Zhang et al. for ionic and semiconductor solids,52 and Murray and Galli for the phases of ice.74 The vibrational contribution to the entropy at finite temperature is calculated from first-principles calculations, and is described in more detail in the online Supporting Information (SI). Formation energies at 0 K (ΔfH) are calculated relative to the oxides, i.e., H2O, CO2, and MgO. The enthalpy of a substance is not an absolute quantity like entropy. Therefore, reference states must be chosen for the enthalpy that ensures a

F(0 K, V , p , NaNb...NR ) = ETotal(0 K, V , p , NaNb...NR ) + Evib(0 K, V , NaNb...NR )

(2)

vib

(1)

The Gibbs free energy function is defined as G  H − TS for systems at constant temperature and pressure, where H is the enthalpy, T the temperature, and S the entropy. Enthalpy H is equal to U + pV, where U is the internal energy, p is the pressure, and V is the volume. For the range of geological pressures relevant to carbon sequestration, the carbonate minerals can be considered incompressible and the pV term ignored. Hence, as quantum mechanical calculations are done at constant volume, the DFT self-consistent total energy ETotal(T, V, p, Na Nb...NR) at composition NaNb...NR plus the zero-point vibrational energy (ZPE) give the internal energy U 7472



Article

Table 2. Lattice Parameters in Åa parameters MgCO3 a=b c Mg(OH)2 a=b c Ice XI a b c CO2 crystal MgO MgCO3·3H2O a b c β Mg5(CO3)4(OH)2·4H2O a b c β MgCO3·5H2O a b c β MgCO3·H2O a=b c MgCO3·6H2O a b c β a

exp

PBE

PBE-G06

PBE-TS

4.637,105 4.635(2)106 15.026

4.6892 (1.15%) 15.2323 (1.37%)

4.6585 (−0.39%) 14.9558 (−0.47%)

4.7677 (2.84%) 14.5031 (−3.48%)

3.150107 4.770

3.1916 (1.37%) 4.7598 (−0.24%)

3.1453 (−0.10%) 4.5925 (−3.73%)

3.1962 (1.51%) 4.5994 (−3.60%)

4.465108 7.8584 7.2922 5.6242109 4.212046

4.4294 7.6178 7.1726 6.0904 4.2345

4.3800 7.4836 7.0637 5.6587 4.1777

4.4419 7.8759 6.8721 5.6794 4.1567

7.7053(11)47 5.3673(6) 12.1212(11) 90.451(13)°

7.868 5.468 11.84 91.57

10.101(5)51 8.954(2) 8.378(4) 114.44°

10.28 (1.72%) 8.848 (−1.15%) 8.464 (0.91%) 113.77 (−0.71%)

10.11 (0.04%) 8.711 (−2.68%) 8.337 (−0.61%) 113.47 (−0.97%)

9.997 (−1.08%) 8.779 (−1.92%) 8.246 (−1.69%) 114.52 (−0.05%)

12.475849 7.6258 7.3463 101.762 monohydrocalcite (CaCO3·H2O)110 10.5536 7.5446 ikaite (CaCO3·6H2O)111 8.87 8.23 11.02 110.2

12.6865 (1.69%) 7.7144 (1.16%) 7.2496 (−1.32%) 102.270 (0.50%)

12.5157 (−0.02%) 7.5565 (−0.24%) 7.195 (0.11%) 102.048 (−0.11%)

12.3876 (0.05%) 7.8705 (0.30%) 7.1632 (−0.24%) 101.91 (0.07%)

(−0.80%) (−3.06%) (−1.64%) (8.29%) (0.53%)

(0.91%) (1.76%) (−3.33%) (−0.38%)

7.615 5.398 11.78 91.70

(−1.91%) (−4.77%) (−3.13%) (0.61%) (−0.81%)

(−1.17%) (0.58%) (−2.82%) (1.38%)

7.605 5.508 11.89 94.24

(−0.52%) (0.22%) (−1.15%) (0.98%) (−1.31%)

(−1.30%) 2.62% (−1.89%) (4.19%)

10.1914 7.3245 8.4883 7.3851 10.6012 110.28

Percent error indicated in parentheses.

the chemical potential μi (T, p) can be expressed as μi (0 K, 1 bar) + Δμi (T, p), where 0 K and p° = 1 bar is taken as the reference state, and Δμi (T, p) is the change in free energy from that reference state to the system at a given temperature and pressure. Δμi (T, p) includes the changes in free energy due to the TS term for solid, liquid, and gas phase species and the pV term for the gases at finite temperatures and pressures. The chemical potential for a given species at equilibrium will always be at a minimum. Since in this work the minerals are considered to be formed from the reaction of the oxides MgO, CO2, and H2O, the free energy of the mineral is treated as a function of the independent chemical potential variables μMgO, μCO2, and μH2O. The chemical potential of oxygen is treated as a dependent variable in this case. Hence the free energy of the crystalline mineral phase is defined as

consistent basis for comparison. For DFT calculations it is convenient to assign reference states for H2O, CO2, and MgO to be the molecules or crystalline solids at 0 K at a pressure of 1 bar. The details of how experimental data for ΔfH°(298 K) from the elements for the reference minerals was converted to ΔfH(0 K) from the oxides is given in the SI. To analyze the relative Gibbs free energy of carbonates and hydrates under a range of geologically relevant conditions, the dependence of the free energy on the chemical potentials of the components present in the material and in the environment (the surrounding solution and/or gas phases) must be considered. The chemical potential μ is defined as the change in the Gibbs free energy G of a system with respect to the number of particles or atoms of type Ni: μi (T , p , Ni) = δG(T , p)/δNi

(3)

Under equilibrium conditions at constant temperature and pressure, the chemical potential of a given atomic species in one phase is equal to that in all other phases. Thus, we have to add to eq 3 the term ∑μiNi, where μi is the chemical potential of atom-type i. The value of μi is determined by the environmental conditions such as partial pressure or concentration of a species containing the element i. At finite temperature and pressure,

Total,0K vib Gxtl(T , p , ni) = Extl + Extl − n1μMgO(T , p)

− n2μH O(T , p) − n3μCO (T , p) 2

2

(4)

where ni are the coefficients of MgO, H2O, and CO2 in the stoichiometric formula for the hydrated carbonate crystal, Evib xtl is 7473



Article

should be 4MgCO3·Mg(OH)2·4H2O. The Mineralogical Society of America’s Handbook of Minerology lists the formula as 4MgCO3·Mg(OH)2·4H2O. The DFT results confirm the stoichiometry of hydromagnesite as 4MgCO3·Mg(OH)2·4H2O, as the optimized lattice constants with four waters and atomic positions are consistent with experimental analysis of natural samples.50,51 DFT also affords analysis of the role of hydrogen bonding in the structures through precise positioning of the protons and electron lone pair orientation on oxygen atoms. For example, the existence of hydrogen bonding in hydromagnesite has been controversial. White had proposed in hydromagnesite that no hydrogen bonding between carbonate groups and water molecules existed based on analysis infrared spectra.117 From X-ray diffraction, Akao and Iwai deduced that the hydroxyl groups are not hydrogen bonded but are shared between three MgO6 octahedra.50 With respect to the water molecules in hydromagnesite, however, Akao and Iwai proposed that H2O molecules−as opposed to hydroxyl groups−do engage in hydrogen bonding; half the hydrogen atoms are hydrogen bonded to other water molecules, and half to oxygen atoms in carbonate molecules perpendicular to the (001) axis. Our calculations confirm this arrangement of hydrogen bonding proposed by Akao and Iwai (shown in Figure 2) in which the

the ZPE at 0 K plus the vibrational entropy and enthalpy at finite temperature and pressure for the mineral phase, and μi (T, p) is the chemical potential of species i obtained from μi (T , p) = EiTotal,0K + EiZPE + Δμi (T , p)

(5)

where and μMgO(T,p) are calculated from DFT, and ΔμH2O(T,p), and μCO2(T,p) are taken from experimental thermodynamic tables such as JANAF.103,104 It should be noted that the JANAF values used are the intrinsic changes in Gibbs free energy of a substance as it is heated from 0 to 1000 K at 1 atm pressure calculated from H−H°(Tr) and S values, and not the changes of free energies of formation, which is determined relative to the free energy changes of the elements. The DFT total energies used for all species at 0 K are given in Table 1. The chemical potential values used in ab initio thermodynamics require a shift in reference state from 298.15 K used in conventional thermodynamic tables to one that is directly linked to 0 K DFT calculations. For example, the chemical potential of molecules of water vapor or CO2 at temperature T and p° (1 atm) is calculated as follows: K ETotal,0 , i

EZPE i ,

Total,0K ZPE μi (T , p°) = Emol + Emol + ΔHg0K → T + T ΔS° 0K ETotal, mol

(6)

EZPE mol

where is the total energy and is the zero point vibrational energy from the DFT calculations per molecule of →T water, and ΔH0K and ΔS° are taken from thermodynamic g tables such as JANAF for the ideal gas. Note that ΔH here as well refers to the intrinsic enthalpy changes, i.e., H−H°(Tr), and not changes in heat of formation ΔfH°. μi(T,p) for pressures other than p° is calculated from the ideal gas law: ⎛ p⎞ Δμi (T , p) = Δμi (T , p°) + kBT ln⎜ ⎟ ⎝ p° ⎠

(7)

3. RESULTS AND DISCUSSION The first three subsections here focus on the results of benchmarking for structure, 0 K heat of formation, and finite temperature effects. Subsection 3.4 compares the calculated with experimental phase stabilities as a function of temperature for the MgO:magnesite:brucite:nesquehonite:hydromagnesite system. 3.1. Structures. The lattice and structural optimization results are shown in Table 2. The PBE-G06 method with the DNP basis set yielded the best results, with a mean absolute error of 1.06% for all lattice vectors, compared to PBE at 1.91% and PBE-TS at 2.44%. Not surprisingly, the largest error for PBE at 0.53 Å (8.3%) was for the crystalline CO2 lattice constant. For these mineral phases, the structures calculated with PBE-G06 represents a significant improvement over PBE alone, highlighting the importance of dispersion to obtain more accurate geometries. DFT calculations can be used to assess the accuracy of proposed stoichiometries where there is some ambiguity by predicting the crystal structure for differing stoichiometries and comparing them with the observed lattice. For example, a recent review by Hollingbery and co-workers highlighted the longstanding controversy over the stoichiometric formula for hydromagnesite, i.e., whether there are three or four water molecules.7 Langmuir in 195636 and Hancock and Rothon in 2003112 reported the formula as 4MgCO3·Mg(OH)2·3H2O, whereas Robie and Hemingway,113 Winchell and Winchell,114 Todor,115 and Botha and Strydom116 indicate the formula

Figure 2. Hydrogen bonding (HB) in hydromagnesite indicated by blue arrows between water molecules and carbonate groups perpendicular to the (100) plane, and between pairs of water molecules in columns in the (001) direction, but not between columns of water molecules.

hydroxyl groups are not hydrogen bonded, but all the water molecules are. Half of the H-bonds are between water molecules, and half between water molecules and carbonate oxygens perpendicular to the (001) axis. There are short and long hydrogen bonds between the water molecules and carbonate oxygens at 1.670 and 1.814 Å. Half of the carbonate groupsthose perpendicular to the (100) axisdo not experience hydrogen bonding, and are oriented to maximize the electrostatic interactions with Mg cations. Hence the complicated hydromagnesite crystal structure results from optimizing both electrostatic and hydrogen bonds to maximize stability. In general, a network of hydrogen bonding is a critical component in the stabilization of the diverse hydrated Mg carbonate structures. This type of network is illustrated for nesquehonite in Figure 3, looking down the (010) axis. The axially Mg-coordinated water molecules in one stack of MgCO3 ribbons are hydrogen bonded to carbonate oxygens in the staggered adjacent stack of ribbons on one side and to non-Mg7474



Article

Table 3. ΔHf(0 K) from the Oxides n1MgO + n2H2O + n3CO2 in kJ/mola

Figure 3. Hydrogen bonding network in nesquehonite. Single-pointed blue arrows indicate hydrogen bonding from hydrogen atoms on visible water molecules to carbonate molecules located behind those that are visible.

coordinated water molecules hydrogen bonded to carbonate oxygens on the other side. Each of these non-Mg-coordinated water molecules are hydrogen bonded to three water molecules and one carbonate group that are Mg-coordinated. The nesquehonite structure is relatively open with the symmetry equivalent, eclipsed axially coordinated water molecules along the (010) direction being 5.367 Å apart. The water molecules within this open structure are highly oriented to maximize hydrogen bonding and stabilize the structure. This pattern of oriented hydrogen bonding is reflected throughout the hydrated Mg carbonates. 3.2. Heats of Formation at 0 K. The DFT-D approach, in particular PBE-G06, has been shown to improve the structures of the minerals investigated in this study, but the impact on formation energy needs to be assessed as well. The contribution of the added dispersion component from both the Grimme06 and TS methods to the total energies from the self-consistent field (SCF) calculation is shown in Table 1. These total energies form the basis for the AIT predictions. For all crystalline species, the dispersion contribution to the total energy was significant, on the order of −60 to −115 kJ/mol per formula unit for periclase, brucite, magnesite, and nesquehonite, and −371.47 and −480.50 kJ/mol for hydromagnesite for the G06 and TS methods, respectively. With the exception of dry ice, the TS method yielded significantly higher vdW energies than the G06 method. Surprisingly, the dispersion contribution for brucite is not significantly different than for MgO, and is calculated by PBE-TS to be even 6.75 kJ/mol less than MgO. As dispersion is a minor component of hydrogen bonding, this is consistent with the lack of H-bonding in brucite’s structure, in which each oxygen is fully 4-fold coordinated to three Mg atoms plus the covalently bound hydrogen atom, and does not have electron lone pairs available to engage in hydrogen bonding with any neighboring hydroxyls if any were close enough to form a hydrogen bond. To assess the accuracy of the DFT-D methods for geochemical thermodynamics, we first compare heats of formation at 0 K rather than 298.15 K. This enables an assessment of DFT for the calculation of binding energies without compounding the potential error with that from the vibrational thermodynamics and entropy calculations. The results for the heat of formation calculations from the oxides at 0 K are shown in Table 3. Employing the PBE-G06 dispersion improves the formation energy for crystalline CO2, Mg(OH)2, MgCO3, and nesquehonite over conventional GGA. In general, PBE-G06 is better than PBE-TS for all species except for Ice XI. PBE-G06 overestimates the ΔfH(0 K) for Ice XI by −19.78 kJ/ mol per molecule of water, compared to −10.03 kJ/mol for PBE and −14.57 kJ/mol for PBE-TS, as shown in Table 3. Given that every water molecule exhibits four hydrogen bonds in the solid, this error is on the order of 5 kJ/mol per hydrogen

exp

PBE

PBE-G06

PBE-TS

CO2 crystal

−26.15

H2O crystal (Ice XI)

−58.86

Mg(OH)2

−79.70

−9.17 (16.98) −68.80 (−10.03) −71.69 (8.01) −78.83 (35.31) −254.05 (−8.59) −725.58 (28.46) -

−23.06 (2.99) −78.44 (−19.78) −76.32 (3.47) −87.90 (26.24) −252.89 (−7.33) −616.55 (80.57) −396.17 −117.75 −348.86

−22.77 (3.38) −74.78 (−14.57) −66.96 (12.74) −66.38 (47.76) −273.54 (−27.98) −536.47 (160.17) -

MgCO3

−114.14

MgCO3·3H2O

−245.46

Mg5(CO3)4(OH)2· 4H2O MgCO3·5H2O MgCO3·H2O MgCO3·6H2O

−696.64

a

-

-

-

Error with respect to experiment in kJ/mol shown in parentheses.

bond, which is consistent with the known limitations of DFT. For magnesite, the error is in the opposite direction; PBE-G06 improves the ΔfH(0 K) calculation over PBE, but still underbinds by 26 kJ/mol, or ∼4.4 kJ/mol per Mg···O interaction. (See Table 1S in the SI for average errors for PBE and PBETS.) These over binding errors for PBE-G06 in hydrogen bonding in Ice XI and under binding the electrostatic interactions in MgCO3 appear to cancel for nesquehonite, which has a net over binding error of only 7.33 kJ/mol. For PBE-TS, however, the 14.57 kJ/mol over binding of hydrogen bonding in Ice XI cannot compensate for the 47.76 kJ/mol under binding error in MgCO3, resulting in a net error of −27.98 kJ/mol in ΔfH(0 K) for nesquehonite. In hydromagnesite, the error per interaction is relatively small, but the over binding from the number of hydrogen bonds is not able to cancel the under binding from the number of carbonate groups in the formula unit, resulting in a net error of 16.11 kJ/mol in the ΔfH(0 K) for PBE-G06 normalized per Mg atom, or 80.37 kJ/mol for the entire formula unit. PBE alone does better in this case, with an over binding error of −5.69 kJ/mol. PBE-TS is much worse for hydromagnesite, with an under binding error of 32.02 kJ/mol. Overall, the PBE-G06 significantly improves the 0 K heats of formation over traditional DFT, and is consistently better than PBE-TS. The benefits of this analysis of the accuracy of the 0 K heats of formation compared to experimental data are 2-fold. First, although the errors are small for single pairwise atomic interactions, the cumulative impact for large unit cells such as hydromagnesite is significant. This identification and quantification of the error in heats of formation for these systems serves as a benchmark to drive further improvement in the fundamentals of density-functional theory. In the meantime, however, this analysis quantifies the modest improvements to the ab initio thermodynamics model from experimental data needed to increase the accuracy, which is hereafter referred to as PBE-G06-HFC for “heat of formation corrected”. Both the results for the PBE-G06-HFC and PBEG06 without heat of formation corrections are reported in the next section to assess the methodology for finite temperature effects. 3.3. Accuracy of Finite Temperature Thermodynamics. To determine how well the calculated phonon spectrum predicts the changes in enthalpy and entropy for the crystalline 7475



Article

function of temperature. The calculated thermodynamics for MgO underestimates Δμ by 3.6 kJ/mol at 700 K, but only 1.0 kJ/mol at 400 K. The least amount of experimental thermodynamic data are available for nesquehonite and hydromagnesite, both of which have a steep dependence of Δμ on temperature due to the large number of hydroxyl groups per formula unit. (The vibrational entropy increases more rapidly as a function of temperature for high frequency vibrations such as hydroxyl groups than for heavier atoms.) At 300 K, the highest temperature for which data are available, the calculated Δμ is underestimated by 5.2 kJ/mol for nesquehonite and 10.8 kJ/mol for hydromagnesite, which is relatively small. What is clear from Figure 4 is that the Δμ values are well separated for the different minerals, with the exception of magnesite and brucite, which track very closely. This separation is important for the reliability of predictions of relative stability of the different types of minerals as a function of temperature, and enables formulation of a crude “rule of thumb” via interpolation to estimate Δμ for species for which no experimental thermodynamic data or structural information is available. The Δμ per 100 degree increments is shown in Table 4. This type of approximation will be used in a subsequent section to estimate the thermodynamic properties of barringtonite, MgCO3·2H2O, for which the crystal structure has not been solved. 3.4. Mineral Phase Stability as a Function of Temperature: Comparison with Experiment for the MgO:Magnesite:Brucite:Nesquehonite:Hydromagnesite System. In this section we compare mineral stabilities as a function of temperature predicted from ab initio thermodynamics with the values from experimental data for periclase, magnesite, brucite, nesquehonite, and hydromagnesite. In this study we examined the thermal stability of Mg minerals for three conditions. The first condition has the reference pressures of pCO2 = pH2O = 1 bar. Ambient conditions comprise the second set with pCO2 = 400 ppm and the water partial pressure equal to the vapor pressure in equilibrium with liquid water at 298.15 K, i.e., pH2O = 32 mbar. The third condition corresponds to ultrahigh

solids as a function of temperature, we compare the theoretical results with the experimental free energies for MgO, brucite, magnesite, nesquehonite, and hydromagnesite. Because many of the unit cells of minerals in this study are small, such as brucite, it is important to test for convergence of phonon spectra with unit cell size to ensure adequate capture of the lower frequency, longer period phonons. For all species, the 1 × 1 × 1 conventional unit cell was sufficient for phonon convergence with the exception of brucite, whose small unit cell size required a 2 × 2 × 2 supercell. Increasing the size of the supercell further had a negligible effect on the force constants, consistent with the findings of Jochym and co-workers on brucite.54 As can be seen in Figure 4, the calculated Δμ values

Figure 4. Comparison of experimental (dashed lines) versus calculated (solid lines) values for the changes in free energy, i.e., the chemical potential Δμ in kJ/mol, from 0 K to the indicated temperatures for the benchmark minerals.

are in very good agreement with experiment over a broad temperature range. In general, the calculated values for Δμ are smaller (less negative) than the experimental values. The closest agreement is with brucite and magnesite, with underestimation errors of less than 2 kJ/mol per formula unit even at 700 K. The contribution of the two hydroxyl groups in brucite imparts essentially equivalent changes in enthalpy and entropy as the single carbonate group in magnesite as a

Table 4. Average Slopes per 100-degree Intervals Representing the Changes in Free Energy in kJ/mol Relative to the Oxides as a Function of Temperature Calculated from DFT Corrected for the Heat of Formation (PBE-G06-HFC) Except for Barringtonite (MgCO3·2H2O)a MgCO3

Mg(OH)2

pCO2 = pH2O = 1 bar 0−100 K 11.67 14.76 100−200 K 14.86 17.17 200−300 K 15.15 17.17 300−400 K 15.24 17.08 pCO2 = 400 ppm; pH2O = 32 mbar 0−100 K 14.57 21.23 100−200 K 17.66 23.64 200−300 K 18.04 23.64 300−400 K 18.14 23.54 pCO2 = pH2O = 10−7 bar 0−100 K 25.09 28.17 100−200 K 28.27 30.59 200−300 K 28.56 30.59 300−400 K 28.66 30.49 a

Mg5(CO3)4 (OH)2·4H2O

MgCO3·H2O

MgCO3·2H2O

MgCO3·3H2O

MgCO3·5H2O

MgCO3·6H2O

23.45 28.66 29.43 29.33

26.24 31.45 31.84 35.99

42.84a 52.20a 53.16a 57.60a

49.79 62.33 64.16 64.84

73.23 92.92 96.29 97.55

84.23 108.16 112.60 114.53

31.55 36.67 37.53 37.44

35.70 40.72 41.20 45.35

57.31a 66.48a 67.64a 72.08a

64.94 77.19 79.41 80.08

94.27 113.47 117.23 118.58

108.07 131.51 136.53 138.46

47.57 52.87 53.55 53.45

53.07 58.28 58.66 62.81

87.61a 96.87a 97.93a 102.28a

103.43 115.69 117.81 118.49

153.70 173.39 176.67 178.02

178.11 202.04 206.48 208.41

Values for barringtonite (MgCO3·2H2O) are interpolated. 7476



Article

vacuum (UHV) or an inert atmosphere with pCO2 = pH2O = 10−7 bar. The free energies of formation from the oxides were calculated as a function of these three different partial pressures of CO2 and H2O at 100-degree intervals from 0 to 1000 K, and compared with experimental data. In the cases of nesquehonite and hydromagnesite, for which experimental data are only available up to 300 K, the free energy at higher temperatures was extrapolated nonlinearly, using the Δμ values from the DFT vibrational calculations corrected to align with the known experimental data from 0 to 300 K. These ab initio extensions of the experimental data for nesquehonite and hydromagnesite are indicated by dotted lines in Figures 5a, 6a, and 7a. Although the extrapolation appears linear at the scale presented, there is a slight curvature as is apparent in Figure 4 and Table 4. The

Figure 6. Free energy phase diagrams in kJ/mol as a function of temperature for pCO2 = 400 ppm and pH2O = 32 mbar, the saturation vapor pressure for water at 298 K. BR = brucite; M = magnesite; HM = hydromagnesite; NQ = nesquehonite. (a) From experimental data. (b) Calculated free energies using the corrected PBE-G06-HFC. (c) Calculated free energies using PBE-G06.

DFT calculations allow us to estimate thermodynamic data more accurately than a linear extrapolation at higher temperature where no experimental data are available. The free energies as a function of temperature for both calculated and experimental data are shown in Figures 5−7. In these diagrams, the blue horizontal line at 0 kJ/mol represents the free energy of MgO. The temperature at which the line for the free energy of a mineral phase crosses the MgO reference represents the point at which the phase becomes unstable and decomposes to generate the oxide. When the free energy line for a mineral phase crosses the line for any other phase, it indicates the temperature for the phase boundary between them under the specified conditions. For example, when a hydrated mineral such as nesquehonite or hydromagnesite crosses the line for magnesite, the cross point indicates the

Figure 5. Free energy phase diagrams in kJ/mol as a function of temperature for pCO2 = pH2O = 1 bar. BR = brucite; M = magnesite; HM = hydromagnesite; NQ = nesquehonite. (a) From experimental data. (b) Calculated free energies using the corrected PBE-G06-HFC. (c) Calculated free energies using PBE-G06. 7477



Article

to temperature is due to the slower rate of increase in free energy of the solid phase relative to the gas and liquid phases in equilibrium with the solid. This is primarily due to entropy. The vibrational entropy of the water and hydroxyl groups, and to a lesser extent the carbonate groups, in the solid phase increase as a function of temperature. In isolation, this increase in entropy would lower the chemical potential and the free energy (make it more negative) of the solid phase. When equilibrium with the environment is considered, however, the entropy of the free water and CO2 molecules increases faster with temperature due to the additional rotational and translational entropy than for bound water and carbonate groups in the mineral phase. The greater the number of bound water molecules, the steeper the slope and lesser stability with increasing temperature. Hence in Figures 5−7, for example, the increase in slope with respect to temperature as a function of hydration can be easily seen, where nesquehonite with three water molecules has the steepest slope, and brucite and hydromagnesite have the least. Although hydromagnesite has formally 5 water molecules in its formula unit (4 water molecules and two hydroxyls), it also has 5 Mg, so the Mg:H2O ratio is 1:1. Across the range of temperature shown in Figures 5−7, the most stable phases have the lowest free energy. For the five minerals for which experimental data are available, nesquehonite is overwhelmingly the most stable phase at 0 K with a free energy of formation of −245.46 kJ/mol from the oxides, compared to −139.33 kJ/mol for hydromagnesite, −114.14 kJ/ mol for magnesite, and −79.70 kJ/mol for brucite. Nesquehonite is the most stable due to the enthalpy contribution from the binding energy of the three water molecules. As temperature increases, magnesite becomes the most stable phase, followed by MgO. Under all three conditions the nesquehonite → MgCO3 → MgO sequence of stability as temperature is increased from 0 K is the same, but the phase boundary temperatures exhibit dramatic shifts. At the reference pressures of pCO2 = pH2O = 1 bar, nesquehonite is the most stable phase up to a temperature of 319.3 K (46 °C). This is consistent with experiments by Hänchen and co-workers conducted at pCO2 = 1 bar at 298 K where only nesquehonite was observed from mixing Na2CO3 with MgCl2 solutions.22 Under ambient conditions, the phase boundary temperature between nesquehonite and magnesite is lowered considerably from 319.3 to 268.8 K. The equilibrium shifts as the water chemical potential is lowered from 1 bar to 32 mbar, thus favoring the anhydrous magnesite phase over nesquehonite with three water molecules in its stoichiometry. The lower pCO2 does not have a significant effect on the temperature of the nesquehonite:magnesite phase boundary because each structure incorporates the same number of carbonate groups. In aqueous solutions at or near ambient pCO2, however, many experiments have observed nesquehonite rather than magnesite forming up to 313−323 K (40−50 °C), well above the magnesite phase boundary temperature.20,23,25,31,118,119 This precipitation of metastable nesquehonite can be understood in terms of the high hydration energy of Mg2+ ions in solution that kinetically inhibits the formation of anhydrous magnesite.120,121 This high water binding energy of Mg2+ also accounts for the stability of nesquehonite at very low temperatures, even under UHV conditions. As can be seen in Figure 7a and Table 5, the nesquehonite:magnesite phase boundary temperature at pH2O = pCO2 = 10−4 mbar shifts

Figure 7. Free energy phase diagrams in kJ/mol as a function of temperature for pCO2 = pH2O = 10−7 bar. BR = brucite; M = magnesite; HM = hydromagnesite; NQ = nesquehonite. (a) From experimental data. (b) Calculated free energies using the corrected PBE-G06-HFC. (c) Calculated free energies using PBE-G06.

thermodynamic decomposition temperature with respect to dehydration, and the mineral becomes thermodynamically unstable with respect to magnesite. These temperatures are indicated in Table 5 and by the vertical lines in the expanded inserts in each figure. Values at the 0 K intercept represent the heats of formation from MgO(c), CO2(g), and H2O(g). These values were normalized per Mg atom to reflect balanced equations for reaction energies between phases, which means the formation energy for hydromagnesite is the reaction energy for 5MgO + 4CO2 + 5H2O → Mg5(CO3)4(OH)2·4H2O divided by 5. Qualitatively, the calculated and experimental results show the expected trend of decreasing stability of hydrated and carbonated minerals at higher temperatures and lower pressures. The steepness of the positive slopes with respect 7478



Article

Table 5. Phase Boundary and Thermal Decomposition Temperatures (K)a pCO2 = 400 ppm pH2O = 32 mbar

pCO2 = pH2O = 1 bar

Mg(OH)2 → MgO+H2O MgCO3 → MgO + CO2 MgCO3 ↔Mg(OH)2 MgCO3·3H2O → MgCO3 + 3H2O MgCO3·3H2O → MgO + CO2 + 3H2O MgCO3·3H2O↔ Mg(OH) Mg5(CO3)4(OH)2·4H2O ↔ MgCO3 Mg5(CO3)4(OH)2·4H2O ↔ Mg(OH)2 Mg5(CO3)4(OH)2·4H2O ↔ MgO Mg5(CO3)4(OH)2·4H2O↔MgCO3·3H2O MgCO3·5H2O → MgCO3 + 5H2O MgCO3·5H2O → MgO + CO2 + 5H2O MgCO3·5H2O → MgCO3·3H2O MgCO3·5H2O↔ Mg5(CO3)4(OH)2·4H2O MgCO3·5H2O↔ Mg (OH)2 monohydrocalcite Mg analogue MgCO3·H2O → MgCO3 + H2O MgCO3·H2O → MgO + CO2 + H2O MgCO3·H2O ↔ Mg (OH)2 MgCO3·H2O ↔ MgCO3·3H2O MgCO3·H2O ↔ Mg5(CO3)4(OH)2·4H2O MgCO3·H2O ↔ MgCO3·5H2O ikaite Mg analogue MgCO3·6H2O → MgCO3 + 6H2O MgCO3·6H2O → MgO + CO2 + 6H2O MgCO3·6H2O ↔ Mg (OH)2 MgCO3·6H2O ↔ MgCO3·3H2O MgCO3·6H2O ↔ Mg5(CO3)4(OH)2·4H2O MgCO3·6H2O ↔ MgCO3·5H2O

expb

DFTHFC

DFT

expb

542 674

554 685

531 531

452 488

319 413 376 253 460 501 341

309 406 362 241 438 499 332 328 390 355 343 360 31

379 418 384 324 348 442 398 418 437 475 435 420 228

269 335 302 222 339 393 283

378 241 439 none 396 277 338 305 247 283 0

pCO2 = pH2O = 10−4 mbar

DFTHFC

DFT

expb

DFTHFC

464 494 584 261 330 291 214 321 390 277 277 320 300 288 294 25

445 381 180 321 339 308 288 257 347 332 355 360 404 366 345 190

285 378

293 381

168 224 204 128 264 275 181

378 262 463 none 469 305

300 173 369 none 332 235

338 309 232 302 none

280 251 210 238 0

Ab Initio Thermodynamic Model for Magnesium Carbonates and

Recommend Documents