Joshua S.
Tse
a,
James
Grant
b,
Jonathan M.
Skelton
c,
Lisa J.
Gillie
*a,
Runliang
Zhu
d,
Giovanni L.
Pesce
e,
Richard J.
Ball
f,
Stephen C.
Parker
*b and
Marco
Molinari
*a
aDepartment of Chemistry, University of Huddersfield, Queensgate, Huddersfield HD1 3DH, UK. E-mail: M.Molinari@hud.ac.uk; L.J.Gillie@hud.ac.uk
bDepartment of Chemistry, University of Bath, Claverton Down, Bath, BA2 7AY, UK. E-mail: S.C.Parker@bath.ac.uk
cDepartment of Chemistry, University of Manchester, Oxford Road, Manchester, M13 9PL, UK
dCAS Key Laboratory of Mineralogy and Metallogeny, and Guangdong Provincial Key Laboratory of Mineral Physics and Materials, Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Guangzhou 510640, P. R. China
eDepartment of Mechanical and Construction Engineering, Northumbria University, Newcastle upon Tyne, NE1 8ST, UK
fDepartment of Architecture and Civil Engineering, University of Bath, Bath, BA2 7AY, UK
First published on 15th June 2023
The MgO–CO2–H2O system have a variety of important industrial applications including in catalysis, immobilisation of radionuclides and heavy metals, construction, and mineralisation and permanent storage of anthropogenic CO2. Here, we develop a computational approach to generate phase stability plots for the MgO–CO2–H2O system that do not rely on traditional experimental corrections for the solid phases. We compare the predictions made by several dispersion-corrected density-functional theory schemes, and we include the temperature-dependent Gibbs free energy through the quasi-harmonic approximation. We locate the Artinite phase (Mg2CO3(OH)2·3H2O) within the MgO–CO2–H2O phase stability plot, and we demonstrate that this widely-overlooked hydrated and carbonated phase is metastable and can be stabilised by inhibiting the formation of fully-carbonated stable phases. Similar considerations may apply more broadly to other lesser known phases. These findings provide new insight to explain conflicting results from experimental studies, and demonstrate how this phase can potentially be stabilised by optimising the synthesis conditions.
Measuring phase stability is essential to predicting which material phase will form under a given set of conditions, and hence for understanding and controlling the structure and resultant properties. This problem has drawn intensive research17 from both experiment and theory and across many fields of organic18 and inorganic chemistry.19–25 The stability of different phases is conceptually described by phase diagrams, which capture the relationships between equilibrium and metastable phases, the activities of component species, and external conditions including pressure, volume and temperature, in an elegant way that can be used to predict the nature and composition of a material.26,27
Whereas the major species in the MgO–CO2–H2O phase diagram, such as Magnesia and Magnesite, are relatively well studied, minor phases have received comparatively less attention. One such example is the Artinite phase, which was first observed by Brugnatelli in 190228 and is a naturally-occurring metastable phase formed at low temperature. The crystal structure of Artinite has been analysed using X-ray diffraction29 and the thermodynamic properties have been determined using calorimetry.30 A few studies have also examined the thermodynamic stability of Artinite at low temperature,31–33 but comparatively little is known on the stability of Artinite with respect to other phases in the MgO–CO2–H2O system. Given that the materials in this system are found under a wide range of conditions, both natural and anthropogenic, a better understanding of where this phase sits within the MgO–CO2–H2O phase diagram is potentially important to a range of disciplines.
For prediction and generation of phase diagrams, the “brute force” option is to use so-called global exploration methods to sample the potential-energy landscape, but this approach quickly becomes intractable as the number of variables (i.e. phases) increases.34–37 When data on experimentally-identified materials and their structures is available, there are alternative, cheaper methodologies using computer simulation that can be employed whose capabilities are often overlooked.21,38–42 The most accurate and reliable way of calculating phase diagrams, i.e. the current “gold standard” is to employ a consistent and accurate ab initio methodology to all the phases, so that the resulting predictions are independent of experimental thermodynamic data. It is however critical that the choice of methodology is appropriate to the system being studied (i.e. transferable across different material phases, which may display significant differences in chemical bonding), but also feasible given the available computational power. Transferability can be a particular challenge for systems such as MgO–CO2–H2O that display multiple types of bonding across the phase space. For example, the bonding between Mg and different ligands (e.g. hydroxyl groups, water molecules and carbonate anions) is strongly ionic, whereas the intramolecular bonding within the ligands is predominantly covalent, and some of the layered magnesium hydroxides may also display interlayer van der Waals dispersion interactions.
In this work, we compare a series of different approaches, all without the inclusion of experimentally derived corrections, to construct first-principles phase stability plots for the MgO–CO2–H2O system in order to study the thermodynamics of the under-explored Artinite phase. To account for the hierarchy of chemical bonding, we compare predictions made using density–functional theory with the popular PBE generalised-gradient approximation functional and three van der Waals corrected functionals used successfully in the literature for simulations of these materials.43–46 We also assess the impact of using the quasi-harmonic approximation to derive the temperature dependence of the Gibbs free energy. This comprehensive study allows us to compare the predictions made from ab initio thermodynamic models with different approximations, and to assess the accuracy and reliability of the different flavours of DFT for studying the hydrated and carbonated phases of magnesian and other mineral systems.
The vibrational frequencies and elastic-constant matrices were calculated using the finite-displacement routines implemented in VASP, the latter of which were used to calculate the bulk moduli by averaging the first nine elastic constants (c11:c33).57–59
For quasi-harmonic approximation (QHA) calculations, harmonic phonon calculations were performed using the Phonopy code60 on a set of 10 expansions and contractions around the equilibrium volume (approx. ±5%). The forces were determined in a 2 × 2 × 2 supercell for all phases apart from Brucite, for which we used a 3 × 3 × 2 expansion, with VASP as the force calculator. For calculating the thermal properties, the Brillouin zone was integrated by sampling with the following regular Γ-centred q-point meshes, which were converged individually for each structure: 30 × 30 × 30 for Artinite, Brucite, Hydromagnesite, Lansfordite and Nesquehonite, 36 × 36 × 36 for Periclase and 48 × 48 × 48 mesh for Magnesite. Details of the QHA free energy calculations are provided in the ESI.†
The phase stability plots where generated using SurfinPy 2.61,62 We note here several limitations in the procedure used here, viz.: (1) we do not account for the possibility of the coexistence of several phases, miscibility gaps, and the possible existence of different polymorphs (unless explicitly stated); (2) we similarly do not account for the possibility of unknown phases that may arise at high pressure; and (3) we do not account for the anharmonic effects that may play an important role at elevated temperature.
Physical properties of the two models including the predicted lattice parameters and elastic constants are presented in Table 1. The predictions for both Artinite structures made using all four DFT techniques give generally excellent agreement with available experimental measurements, with the notable exception of a 6% underestimation of the enthalpy of formation using PBE. This highlights the importance of accurately describing vdW interactions. For both Artinite structures the DFT methods including dispersion corrections predict a decrease in the cell volume compared to experiments. We also performed similar calculations on the other phases shown in Fig. 1, and structural data and predictions of the physical properties are given in the ESI† (Tables S1–S4).
Expt. | optB86b-vdW | optB88-vdW | PBE-D3 | PBE | |||||
---|---|---|---|---|---|---|---|---|---|
Artinite A Mg2CO3(OH)2·3H2O | |||||||||
a | 6.30663 | 6.28 | −0.41% | 6.284 | −0.34% | 6.303 | −0.05% | 6.371 | 1.04% |
B | 6.23163 | 6.113 | −1.90% | 6.116 | −1.85% | 6.109 | −1.97% | 6.186 | −0.73% |
C | 16.56063 | 16.558 | −0.01% | 16.567 | 0.04% | 16.598 | 0.23% | 16.768 | 1.25% |
α = γ | 90.0063 | 90 | 0.00% | 90 | 0.00% | 90 | 0.00% | 90 | 0.00% |
B | 99.1063 | 97.77 | −1.39% | 97.75 | −1.41% | 97.87 | −1.29% | 98.69 | −0.46% |
Volume | 642.563 | 629.82 | −1.97% | 630.88 | −1.81% | 633.01 | −1.48% | 653.27 | 1.68% |
ΔHf | −2920.6064 | −2896.12 | −0.01% | −2943.26 | 0.01% | −2844.29 | −0.03% | −2738.62 | −0.06% |
B | 64.1 | 65.1 | 62.8 | 56.4 | |||||
c11 | 103 | 104 | 103 | 95 | |||||
c12 | 28 | 29 | 27 | 24 | |||||
c13 | 65 | 66 | 63 | 54 | |||||
c15 | 0 | 0 | 0 | 0 | |||||
c22 | 122 | 124 | 120 | 113 | |||||
c23 | 32 | 33 | 31 | 28 | |||||
c25 | 0 | 0 | 0 | 0 | |||||
c33 | 101 | 103 | 99 | 88 | |||||
c35 | 0 | 0 | 0 | 0 | |||||
c44 | 16 | 16 | 17 | 17 | |||||
c46 | 0 | 0 | 0 | 0 | |||||
c55 | 23 | 24 | 24 | 24 | |||||
c66 | 40 | 41 | 39 | 35 | |||||
Artinite B (Mg2CO3(OH)2·3H2O) | |||||||||
a | 6.30663 | 6.314 | −0.20% | 6.293 | −0.13% | 6.298 | 0.12% | 6.38 | 1.17% |
b | 6.23163 | 6.14 | −1.34% | 6.147 | −1.28% | 6.151 | −1.46% | 6.223 | −0.14% |
c | 16.56063 | 16.547 | −0.37% | 16.499 | −0.33% | 16.505 | −0.08% | 16.709 | 0.90% |
α = γ | 90.0063 | 90 | 0.00% | 90 | 0.00% | 90 | 0.00% | 90 | 0.00% |
B | 99.1063 | 98.06 | −1.22% | 97.94 | −1.23% | 97.93 | −1.10% | 98.84 | −0.31% |
Volume | 642.563 | 635.1 | −1.61% | 632.2 | −1.44% | 633.25 | −1.15% | 655.45 | 2.02% |
ΔHf | −2920.6064 | −2843.25 | −0.01% | −2895.72 | 0.01% | −2942.75 | −0.03% | −2738.57 | −0.06% |
B | 64.3 | 65.3 | 62.6 | 56.4 | |||||
c11 | 100 | 102 | 100 | 92 | |||||
c12 | 29 | 30 | 29 | 25 | |||||
c13 | 65 | 65 | 62 | 53 | |||||
c15 | 0 | 0 | 0 | 0 | |||||
c22 | 122 | 124 | 120 | 114 | |||||
c23 | 32 | 32 | 30 | 27 | |||||
c25 | 0 | 0 | 0 | 0 | |||||
c33 | 105 | 106 | 102 | 90 | |||||
c35 | 0 | 0 | 0 | 0 | |||||
c44 | 14 | 14 | 15 | 16 | |||||
c46 | 0 | 0 | 0 | 0 | |||||
c55 | 20 | 21 | 21 | 23 | |||||
c66 | 41 | 42 | 41 | 35 |
xMgO + yH2O + zCO2 → A | (1) |
δGT,p = μA − xμMgO − yμH2O − zμCO2 = 0 | (2) |
![]() | (3) |
![]() | (4) |
μMgO = μ0MgO | (5) |
μA = μ0A | (6) |
![]() | (7) |
δGT,p = ΔG0f − yΔμH2O − zΔμCO2 | (8) |
ΔG0f = yΔμH2O + zΔμCO2 | (9) |
ΔG0f = RT![]() | (10) |
We can therefore find the values of ΔμH2O and ΔμCO2 (or (pH2O)y and (pCO2)z) for which the Mg-rich phases are more or less stable than MgO. This procedure can be applied to all the solid phases to identify which is the most stable, provided that the free energy ΔG0f is known for each Mg-rich phase. These free energies can be calculated using eqn (11):
![]() | (11) |
In the harmonic model, the free energies are calculated from:
G(T) = U0 + Aphonon(T) = U0 + UZPE + Avib(T) | (12) |
![]() | (13) |
![]() | (14) |
![]() | (15) |
In the QHA model, the harmonic approximation is modified to include the effect of volume changes due to thermal expansion at finite temperature. This is practically achieved by applying the harmonic approximation to a series of contracted and expanded unit cells about the equilibrium volume V0. Using this method, the Gibbs free energy is obtained at a specific temperature T and pressure p as:65
![]() | (16) |
For gaseous species, the standard free energy varies significantly with temperature, and as plane-wave DFT simulations are designed for condensed-phase systems we use experimental data to determine the temperature-dependent free energy term for the gaseous species:
G = U0 + UZPE + (H − H0(T) − TSexpt(T)) | (17) |
G = U0 + UZPE | (18) |
![]() | ||
Fig. 3 (a) Phase stability plot of Mg(OH)2 (Brucite), MgCO3 (Magnesite) and MgO (Periclase) constructed using experimental data. (b) Predicted phase stability plot including all Mg-rich phases calculated using optB86b-vdW and eqn (18) with both solid and gaseous phases at 0 K: MgO, MgCO3, Mg(OH)2 and MgCO3·5H2O. The solid and dashed white lines correspond to 1 bar pressure at 0 K and 298 K, respectively, and the white circles indicate atmospheric conditions of 400 ppm CO2 and 32 mbar of H2O at 298 K. |
For the experimental phase stability plot in Fig. 3(a), ΔG0f is calculated using the corrected enthalpies of formation defined in eqn (19), where ΔHexpt(298 K → 0 K) is the change in enthalpy from 298 K to 0 K. Thermodynamic data was taken from the NIST database,68 but experimental values are only available for these well studied phases.
δHexpt(0 K) = ΔHexpt(298 K) − ΔHexpt(298 → 0 K) | (19) |
This first test for a thermodynamic modelling strategy is to evaluate the relative stability of Mg(OH)2, MgO and MgCO3 following the procedure outlined in eqn (18). The triple point (where all three phases co-exist; Table 2) was calculated from the experimental data to be at ΔμCO2 = −1.18 eV and ΔμH2O = −0.83 eV, whereas using optB86b we predict the point to occur at ΔμCO2 = −1.27 eV and ΔμH2O = −0.66 eV. This is excellent agreement, with differences of only 0.08 eV for ΔμCO2 and 0.17 eV for ΔμH2O.
Temperature (K) | ΔμCO2 (eV) | ΔμH2O (eV) | p CO2 (bar) (298 K) | p H2O (bar) (298 K) | |
---|---|---|---|---|---|
Brucite Mg(OH)2, Magnesite MgCO3 and Periclase MgO triple point | |||||
Experimental | 0 | −1.18 | −0.83 | 10−10.9 | 10−6.1 |
optb86B | 0 | −1.27 | −0.66 | 10−12.4 | 10−3.1 |
Brucite Mg(OH)2, Magnesite MgCO3 and Lansfordite MgCO3·5H2O triple point | |||||
optb86B | 0 | −1.00 | −0.40 | 10−9.2 | 103.0 |
Due to the limited literature data on Lansfordite (MgCO3·5H2O) and Artinite (Mg2CO3(OH)2·3H2O), we are not able to include these phases on the experimental phase stability plot. However, at pCO2 = pH2O = 1 bar at 298 K (where the dashed white lines cross in Fig. 3(b)), the most thermodynamically stable phase is predicted to be Magnesite (MgCO3), whereas at pCO2 = pH2O = 1 bar at 0 K (where the solid white lines cross in Fig. 3(b)) the predicted stable phase is Lansfordite. This agrees well with both computational43 and experimental71 data.
As noted above, one of our aims is to evaluate the thermodynamic stability without requiring experimental data for the condensed phases, not least as comparison with experiment is then a rigorous check on the reliability. Nevertheless, inclusion of experimentally-derived corrections does represent a valuable tool for demonstrating the viability of DFT for modelling a given system as shown in Chaka et al.43 Comparing the performance of the different DFT methods, we find that optB86b-vdW gives the most accurate representation of the thermodynamics, as the triple point between the Brucite (Mg(OH)2), Magnesite (MgCO3) and Periclase (MgO) phases is closest to the experimental one.
We choose a temperature range between 273 K and 373 K, i.e. where liquid water is present, which are appropriate conditions for industrial6 and nuclear waste reprocessing5 applications, for construction materials,8,72 and for catalysis.2–4 The vibrational entropy of the Mg-rich phases is included in the calculation of ΔG0f for Δμ = −2 to +1 eV, with entropies for the solid phases calculated using eqn (13)–(15) and entropies for gaseous species taken from the NIST database.68
We showed in the previous two sections that optB86b-vdW provides a good description of the experimental phase stability plot of the well-characterised Mg-rich phases, and that the predicted phase stability plots obtained using the different DFT methods are all shifted relative to each other. We therefore consider here only the results obtained with optB86b-vdW, but as before the phase stability plots predicted using the other DFT techniques are available in Fig. S3–S5 (ESI†) for comparison.
We organise the results in this section into three parts, showing first the free energies of Mg-rich phases at different pCO2 as a function of temperature at constant pH2O = 1 bar, followed by the phase stability plots as a function of pCO2 and pH2O at a fixed T = 298 K, and finally the phase stability as a function of pCO2 and temperature at constant pH2O.
At ΔμCO2 = −1 eV (low CO2 pressure, pCO2 = 10−17 bar) and ΔμH2O = 0 eV (pH2O = 1 bar) the most thermodynamically stable phase is predicted to be Brucite (Mg(OH)2) (Fig. 4a and b). Using optB86b and the QHA free energies, Artinite shows no phase transitions at low CO2 pressure, identified by intersections of its free-energy curve with other compounds, over the temperature range modelled. Increasing the temperature stabilises phases that contain less water per Mg2+ ion, due to the evaporative loss of H2O.
The harmonic free energies predict that at ΔμCO2 = ΔμH2O = 0 eV, corresponding to standard conditions with pCO2 = pH2O = 1 bar, MgCO3 is the most thermodynamically stable phase at all temperatures (Fig. 4c),43,71 whereas the QHA predicts that Lansfordite becomes the most stable phase at 277 K (Fig. 4d). If the formation of MgCO3 is kinetically inhibited, which has been demonstrated experimentally,73 then the metastable Hydromagnesite (Mg5(CO3)4(OH)2·4H2O) phase becomes the most stable above 295 K. Under these conditions Artinite has two phase boundaries at 321 K (Artinite Mg2CO3(OH)2·3H2O/Nesquehonite MgCO3·3H2O) and 314 K (Artinite Mg2CO3(OH)2·3H2O/Lansfordite MgCO3·5H2O) (Fig. 4c). The 332 and 320 K predicted using the QHA free energies are shifted to slightly higher values (Fig. 4d).
We also compared the phase stability plots under atmospheric conditions for the different DFT techniques (Fig. S3–S5, ESI†), which all show very similar features to the phase stability plots computed under standard conditions. The predicted phase transition temperatures are tabulated in Tables S5–S7 (ESI†).
At ΔμCO2 = 0.6 eV (high CO2 pressure, pCO2 = 1010 bar) and ΔμH2O = 0 eV (pH2O = 1 bar) the most thermodynamically stable phase at all temperatures is predicted to be MgCO3 (Fig. 4e), as with pCO2 = pH2O = 1 bar (Fig. 4e and f). When the formation of MgCO3 is inhibited, at T < 290 K Lansfordite (MgCO3·5H2O) is predicted to be the second most stable phase, with Nesquehonite (MgCO3·3 H2O) favoured between 308–316 K, and Mg5(CO3)4(OH)2·4H2O favoured only at T > 316 K. At high pCO2 Artinite has one phase boundary at 364 K (Artinite Mg2CO3(OH)2·3H2O/Lansfordite MgCO3·5H2O). Increasing the temperature results in phase transitions associated with the loss of one H2O per MgO unit. Again, we see a similar trend using the QHA where the phase transition temperatures are shifted ∼5–10 K higher compared to those computed using the harmonic free energies.
Temperature (K) | ΔμCO2 (eV) | ΔμH2O (eV) | p CO2 (bar) (298 K) | p CO2 (bar) (298 K) | |
---|---|---|---|---|---|
Brucite Mg(OH)2, Magnesite MgCO3, Periclase MgO triple point | |||||
HA | 298 | −0.76 | −0.20 | 10−13.4 | 10−3.4 |
QHA | 298 | −0.76 | −0.20 | 10−13.4 | 10−3.5 |
Brucite Mg(OH)2, Magnesite MgCO3, Lansfordite MgCO3·5H2O triple point | |||||
HA | 298 | −0.52 | 0.05 | 10−9.1 | 100.9 |
QHA | — | — | — | — | — |
Brucite Mg(OH)2, Magnesite MgCO3, Artinite Mg2CO3(OH)2·3H2O triple point | |||||
HA | — | — | — | — | — |
QHA | 298 | −0.33 | 0.23 | 10−5.8 | 104.1 |
Brucite Mg(OH)2, Artinite Mg2CO3(OH)2·3H2O, Lansfordite MgCO3·5H2O triple point | |||||
HA | — | — | — | — | — |
QHA | 298 | −0.40 | 0.26 | 10−7.0 | 104.6 |
Brucite Mg(OH)2, Artinite Mg2CO3(OH)2·3H2O, Magnesite MgCO3 triple point | |||||
HA | — | — | — | — | — |
QHA | 298 | −0.29 | 0.24 | 10−5.1 | 104.2 |
Testing the validity of these phase stability plots using experimental techniques is challenging, as changing the pressure of one reference state independently can be difficult to achieve in practice. One method is to put MgCO3 under vacuum and decrease the pressure of both CO2 and H2O simultaneously, which would probe a diagonal line on the phase stability plot. The pressure at which MgCO3 transforms to MgO could then be determined and compared to the modelling results. Alternatively, the phase stability plots could be changed to show the effect of temperature and pCO2, which we consider in the following section.
Fig. 6 compares our calculated phase stability plots as a function of temperature and ΔμCO2 at a fixed ΔμH2O = 0 eV (pH2O = 1 bar), computed using the harmonic and quasi-harmonic free energies, and either including all the Mg-rich phases or with the formation of MgCO3 inhibited. Comparable phase stability plots obtained using the other functionals can be found in Fig. S7 and S8 (ESI†).
Under standard pH2O and CO2-rich conditions, using the optB86b functional and the harmonic free energies, Lansfordite (MgCO3·5H2O) is metastable below ∼310 K, above which Nesquehonite (MgCO3·3H2O) becomes the more thermodynamically-stable phase. This prediction compares well with the work of Hill et al.71 and Schott et al.,74 who predict the transition to occur at 283 K. Further evidence for the existence of this transition is provided by Ming et al.80 who observed that MgCO3·5H2O crystals dehydrate to MgCO3·3H2O at 285 K under atmospheric pH2O and pCO2. However, our modelling predicts these transitions to occur at higher pCO2 and at temperatures of 308/312 K based on the harmonic and QHA energies. This phase transition was also investigated in a computational study by Chaka et al.,43 who obtained a transition temperature of ∼340 K but countered this by applying an experimental correction to the free energy of MgCO3·5H2O. This is possibly an indication of the shortcomings of the description of van der Waals forces in DFT in general, and of the treatment in the DFT+D2 method used in that study specifically.
There is debate in the literature about the thermodynamic stability of Artinite Mg2CO3(OH)2·3H2O. Our ab initio phase stability plots predict a small stability region for Artinite at low temperature (Fig. 6c), which is only found in some of the experimental studies.74,75 Using the QHA free energies increases the stability of this phase over a broader range of temperatures (Fig. 6d). We note however that the complexity of the Artinite structure that arises from the random distribution of the CO32− and H2O ligands is only partially considered in this study, as we use a single model structure. A random distribution would give some additional configurational entropy that would further stabilise Artinite. This is consistent with the work of Schott et al.,74 which suggests that Mg2CO3(OH)2·3H2O is stable at low temperatures and low pCO2. We also note that there are multiple entropy values for Mg2CO3(OH)2·3H2O in the literature.31,71,74 This makes it difficult to compare unambiguously our predictions to experiments, but, as our ab initio phase stability plots do not require any experimental corrections for the solid phases, and are therefore not biased towards particular sets of measurements, we can consider them truly predictive. With this in mind our results confirm that Mg2CO3(OH)2·3H2O is likely to remain a rare phase and one deserving of future investigation, but the favourable comparison between our predicted phase stability plots and literature data suggests that our predictions may be accurate enough to identify the synthesis conditions required to form specific Mg-rich phases.
However, we highlight a key assumption of our methodology, namely that the vibrational properties of the different phases are purely harmonic. This assumption may lead to deviation from experiment under some conditions, particularly at elevated temperature. On the other hand, using the quasi-harmonic approximation to account for thermal expansion, as we have done in the present study, did not significantly change the results despite a ten-fold increase in the computational cost.81 Despite these potential shortcomings, a key advantage of this thermodynamic framework is that it can be used unambiguously to compare the DFT functionals and the different techniques to account for entropy. It could also be used with a global-exploration structure search to identify potential unknown phases and place them on the phase stability plots. Similarly, although this work examines the MgO–CO2–H2O system, the methodology is completely general and could be applied to a wide variety of other systems, subject to choosing an appropriate theoretical description for treating the compounds in the system under study.
Our methodology has several advantages over alternatives, viz.: (1) it can identify overlooked materials that may be stable under specific conditions of temperature and partial pressures of water and carbon dioxide; (2) it can be used to identity competing and metastable phases, such as Artinite; and (3) it does not rely on the availability and accuracy of solid-phase experimental thermodynamic data. The latter in particular means that the present results can inform the future development of synthetic strategies to target and selectively stabilise specific phases of interest.
Our theoretical results also show that the inclusion of van der Waals dispersion corrections to density–functional theory is necessary to accurately predict the thermodynamic properties of the MgO–CO2–H2O system. Such corrections are particularly important for phases that display large numbers of hydrogen bonds, such as Artinite. On the other hand, applying the quasi-harmonic approximation does not lead to a significant improvement in the accuracy of our predictions over the harmonic approximation. Finally, we note that a potential limitation of our study is that we do not fully treat the disorder in Artinite, because of the limitations of our ab initio calculations, which may provide additional (entropic) stabilisation. Future work on this system should therefore consider applying classical molecular dynamics or Monte Carlo simulations to better take disorder into account.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3cp00518f |
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