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ab initio Thermodynamics of Hydrated Calcium Carbonates and Calcium Analogues of Mg Carbonates: Implications for Carbonate Crystallization Pathways Anne M. Chaka ACS Earth Space Chem., Just Accepted Manuscript • DOI: 10.1021/ acsearthspacechem.7b00101 • Publication Date (Web): 16 Jan 2018 Downloaded from http://pubs.acs.org on January 20, 2018
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ACS Earth and Space Chemistry
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ab initio Thermodynamics of Hydrated Calcium Carbonates and Calcium
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Analogues of Mg Carbonates: Implications for Carbonate Crystallization Pathways
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Anne M. Chaka
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Pacific Northwest National Laboratory, P.O. Box 999, MS K8-96, Richland, WA 99352
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[email protected] 7
509-371-7104 (V)
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509-371-6354 (Fax)
9 10
Abstract
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Formation of calcium carbonate and its hydrates are important for a wide variety of
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geological, biological, and technological concerns. Recent studies have determined that
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formation of anhydrous crystalline calcite, aragonite, and vaterite can involve a complex
14
series of nonclassical pathways in which the hydrated polymorphs monohydrocalcite
15
(CaCO3•H2O), ikaite (CaCO3•6H2O), and amorphous calcium carbonate (ACC) play key
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roles and in some instances are stable or metastable endproducts. The stages of
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nucleation and crystallization along these pathways are not well understood, nor is how
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what is learned in an aqueous environment transfers to CO2-rich conditions. In this work
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ab initio thermodynamics based on density-functional theory and experimental chemical
20
potentials for H2O-rich and CO2-rich systems are used to determine the stability of
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calcium carbonate polymorphs as a function of environmental conditions. In water-
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saturated supercritical CO2, formation of ikaite and monohydrocalcite are both highly
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exothermic, yet metastable to calcite, and are therefore likely intermediates upon
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carbonation of CaO and Ca(OH)2 according to the Ostwald step rule. Hence low energy
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nonclassical crystallization pathways that utilize these intermediates are available for
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calcite formation in CO2-rich environments as well as aqueous systems, particularly in
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water-saturated systems even though water is less than only 1% by mass. Formation free
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energies calculated for Ca analogues of nesquehonite (MgCO3•3H2O), lansfordite
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(MgCO3•5H2O), hydromagnesite (Mg5(CO3)4(OH)2•4H2O), and pokrovskite
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(Mg2CO3(OH)2) are exothermic in both aqueous and water-saturated scCO2 from 273-373
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K, but they are always metastable with respect to the observed Ca minerals. Hence they
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may form prenucleation clusters, transient intermediates, or localized coordination
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arrangements trapped in hydrated ACC, but will never be observed in nature. The
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arrangement of CaCO3•6H2O complexes in ikaite is proposed as the structure of
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prenucleation clusters.
36 37
KEYWORDS: Ab initio thermodynamics, calcium carbonate, DFT, prenucleation,
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crystallization, ikaite, monohydrocalcite
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1.0 Introduction Carbonate formation is a complex process that is important for the global carbon
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cycle, biomineralization, abiotic geochemical systems, paleoclimate indicators,1 and
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industrial processes such as carbon sequestration,2 environmental remediation3, scale
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formation in oilfields and pipelines,4 properties of concrete and cement,5 and
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development of functional materials for microlenses and other applications.6 The early
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stages of nucleation and crystallization of carbonates are not well understood, and have
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recently been the focus of an increasing number of studies on non-classical, multistep
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pathways involving amorphous and hydrated crystalline precursors.7-16 Ca carbonate -
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being widespread in nature, the most common biomineral, and an important industrial
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material - has been the subject of intensive focus as a model system to study the influence
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of factors on the nucleation and growth of carbonates at the molecular level. These
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studies have focused exclusively on aqueous systems. How Ca carbonate polymorph
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formation changes in CO2-rich environments relevant to carbon capture and geochemistry
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has not yet been investigated.
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Ca carbonate and its polymorphs are important throughout the natural
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environment. Ca carbonate can exist in an anhydrous state (calcite, vaterite, or aragonite),
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hydrated (monohydrocalcite and ikaite), or amorphous form. Calcite is the most
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thermodynamically stable polymorph except in cold waters where ikaite becomes the
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most stable. Hence ikaite is important in geochemistry as a paleoclimate and fluid
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composition indicator,1, 17 for increasing the efficiency of the sea-ice carbon pump and
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adsorption of CO2,18 and as a precursor of tufa-like mounds of calcite19-20 and glendonite
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pseudomorphs.1, 21 Monohydrocalcite, although never the most stable Ca carbonate
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polymorph, is likely a widespread metastable intermediate and may warrant
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reconsideration in pathways of geological formations as secondary origin.8, 22
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Monohydrocalcite has been shown to transform to calcite or aragonite. 23-24
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Monohydrocalcite has also been found as a biomineralization endproduct and has been
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proposed as a remediation material for anion pollutants such as arsenate and phosphate.3
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More recently it has garnered considerable interest as an intermediate in the
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transformation of amorphous Ca carbonate (ACC) to calcite8, 22, 25-26, and as a model for
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ACC.27-28 Hence delineating the conditions under which both ikaite and
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monohydrocalcite form and transform is important for interpretation of the geological
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record and understanding carbon cycling and carbonate crystallization.
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Although growth of Ca carbonate can occur by classical nucleation and growth
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under certain circumstances, in the last decade evidence has been increasing that CaCO3
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crystallization can proceed through nonclassical means via an amorphous intermediate.
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The nonclassical transformation process from soluble Ca and carbonate ions to crystalline
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CaCO3 follows a complicated sequence of steps, the majority of which are not yet
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understood. The solution phase ions are hypothesized to condense into prenucleation
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clusters, which then aggregate to form ACC.7 The prenucleation clusters have proven
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challenging to detect. The only indication of prenucleation species has come from
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isolation of ~70 micron clusters by Gebauer and coworkers via analytical ultra
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centrifugation,7 and a shift in carbonate vibration frequency in in situ time-resolved
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Raman spectroscopy observed by Montes-Hernandez and Renard that did not correspond
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to ACC or calcite.16 In either case the structure of the prenucleation species could not be
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determined. Molecular simulation has played a significant role in developing models to
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understand the early stages of this process. In the molecular dynamics (MD) simulations
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by Tribello and coworkers a barrierless aggregation of primarily neutral bidentate ( )
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Ca2+ CO3-2 ion pairs formed.29 Small amounts of water was trapped kinetically as clusters
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assembled, but was not distributed to each Ca in an approximation of the
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monohydrocalcite structure. In contrast to the results of Tribello and coworkers, MD
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simulations performed by Demichelis and coworkers resulted in prenucleation aggregates
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forming polymeric chains of Ca and carbonate ions termed Dynamically Ordered
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Liquidlike Oxyanion Polymers (DOLLOPs).30 How the DOLLOP aggregates grow,
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reorganize, and reach a critical size, however, has not yet been determined.
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In contrast to the prenucleation species, ACC has been widely observed in nature
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and in the laboratory. ACC provides a low energy pathway for CaCO3 crystallization31 to
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calcite, aragonite or vaterite, and is typically the first phase formed in biomineralization
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processes and crystallization in the laboratory at high supersaturation.14 ACC has been
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detected in more than seven animal phyla and even some plants.32-3334-353637-38 Although
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not widespread in geological settings due to its proclivity to transform to crystalline
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forms, Dupuis and coworkers hypothesized that ACC is involved in the formation of
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essentially all new geological calcareous structures.39 ACC is considered a hydrated form
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of Ca carbonate with water content typically ranging from 0.5 to 1.4 moles of water per
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mole of CaCO3.11 Biogenic ACC is observed to have nominally a stoichiometry of
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CaCO3•H2O (15.25 wgt%).40-41 Dehydration of ACC results in crystallization whether in
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air, upon heating, or even in aqueous solution. 29, 42
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In 2010 Radha and coworkers determined that the order of transformations once ACC had precipitated follows the sequence of thermal stability: hydrous ACC (least
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stable) → anhydrous ACC → vaterite → aragonite → calcite (most stable),31 though
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small size for amorphous particles may invert this order. More recent results have shown
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the crystallization pathway can be even more complicated with crystalline polymorphs
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such as monohydrocalcite and ikaite playing a role.8, 14, 22, 26 Monohydrocalcite and ikaite
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can precipitate directly from solution or crystallize from ACC.8, 14 Recent work on
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CaCO3 crystallization by Rodriguez-Blanco and coworkers22, Blue et al.8, and others
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have underscored the importance of monohydrocalcite as another potentially important
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end-member phase for ACC transformation. Monohydrocalcite has also been observed as
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an intermediate between ACC and aragonite.3, 22, 24, 43 Ikaite has been reported
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infrequently as a metastable precursor in recent studies on CaCO3 crystallization, likely
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due to its low temperature stability and highly transient nature at warmer temperatures.
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Yet it has also been shown to transform to ACC14, 44-45 and subsequently to vaterite. 23, 46-
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48, 15, 31
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Even though ACC is widely observed, its metastability, complexity, and
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variability has made structural characterization challenging despite a wide range of
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experimental techniques that have been applied.32-33, 45, 49-50 In a review by Cartwright and
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coworkers, Ca carbonate was described as exhibiting polyamorphism – amorphous
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polymorphism – for ACC as well as polymorphism for crystalline structures calcite,
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aragonite, and vaterite. The range of Ca-O coordination reported by EXAFS is from 5 to
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9.32, 35, 41, 51-53 On average EXAFS indicates approximately seven oxygen atoms in the Ca
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coordination shell with typical Ca – O distances between 2.40 and 2.50 Å, but with
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significant variation with materials from different sources.40, 54
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Spectra of amorphous materials without sufficient reference standards can be
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difficult to interpret. For example Michel and coworkers interpreted the 13C NMR of
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carbonate groups in ACC to be exclusively monodentate ( ) based on the similarity of
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the chemical shift with calcite, but did not examine ikaite as an NMR reference.54 Nebel
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and coworkers, however, also ran ikaite as an NMR reference and found that the ACC
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13
C chemical shift was very close to ikaite, which is exclusively bidentate ( ).49
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Therefore the 13C chemical shift is not sufficient to distinguish between and
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carbonate coordination. Malini and coworkers utilized classical MD simulations to
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generate models of ACC from four different starting points and obtained synchrotron X-
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ray scattering pair distribution functions (PDF) essentially identical to the experimental
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data from Radha et al11, despite significant structural differences. Hence a PDF is not
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sufficiently sensitive to discriminate between ACC structural candidates.
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Although considerable progress has been made in understanding nucleation and
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crystallization, several questions remain regarding the process of going from fully
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hydrated solution species to anhydrous crystalline structures. The changes in coordination
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experienced by Ca and the accompanying thermodynamics as it goes from the fully
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hydrated cation in solution to the monohydrated ACC and monohydrocalcite have not yet
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been delineated. The number of coordination environments known from the three
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anhydrous and two hydrated polymorphs is limited and does not encompass the range of
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what is observed in ACC let alone partially dehydrated species that may form precursors
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or transient intermediates. Hence there is a need to generate reasonable structural models
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for Ca-coordination beyond the known crystalline Ca carbonate polymorphs. MD
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simulations of anhydrous42, 55 and hydrated ACC40, 42, 56-58 are powerful in that they
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provide atomistic detail and dynamics, but the large system sizes required for simulation
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of ACC formation and crystallization makes sufficient time and length scales for
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configuration sampling problematic.
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To address this gap in configurations between the fully solvated cation and the
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monohydrate, we look to the type of hydrated structures formed by Mg carbonates. Ca
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and Mg exhibit the same oxide, hydroxide, and carbonate (calcite) structures, but
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completely different hydrated carbonate structures as shown in Figure 1. Not only is the
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stoichiometry complementary (mono- and hexahydrate for CaCO3, and di-, tri-, and
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pentahydrate for MgCO3 plus hydromagnesite and pokrovskite basic carbonates) but the
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local coordination chemistry is completely different, as shown in Table 1.
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Demichelis and coworkers raised the question as to why there are no Ca
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analogues of hydrated Mg carbonate polymorphs observed in nature or the laboratory.59
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The reason Mg does not crystallize in the monohydrocalcite and ikaite structures was
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determined by Chaka and Felmy using ab initio thermodynamics (AIT); the Mg-
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analogues of monohydrocalcite and ikaite were found to be thermodynamically less
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stable than the observed hydrated Mg carbonates due to Mg’s inability to accommodate
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the 8-fold coordination exhibited by the Ca carbonate hydrates. The thermodynamics of
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the Ca analogues, however, have not yet been determined. If these Ca analogues of
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hydrated MgCO3 minerals exhibit intermediate thermodynamic stability, then they may
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be reasonable models for transient metastable structures along the CaCO3
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dehydration/crystallization pathway. Formation of ACC is a nonequilibrium process and
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therefore examining other structures with different degrees of hydration may inform the
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ACC structure, even if they are highly metastable.
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In this work molecular modeling and ab initio thermodynamics are used to
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determine the structure and thermodynamics of the known hydrated Ca carbonate
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polymorphs and Ca analogues of hydrated Mg carbonates to determine their potential role
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in forming prenucleation clusters, transient intermediates, or local coordination
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arrangements of ACC in both aqueous and CO2-rich environments. Radha and coworkers
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raised the question whether hydrated ACC formation and crystallization studies are
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relevant to carbon sequestration because the higher temperatures that exist in geological
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reservoirs (~313 – 366 K) and high CO2 activity may preclude ACC’s formation.60 To
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address this issue the ab initio thermodynamics are calculated for the observed hydrated
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Ca carbonate polymorphs and Ca-analogues of Mg carbonates in CO2-rich environments
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relevant for carbon sequestration, including dry and water-saturated supercritical CO2
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(scCO2). In addition, ab initio thermodynamics is used to expand the range of
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thermodynamic data available for species such as calcite and monohydrocalcite beyond
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300 K.
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10 (a) Lime: CaO
(d) Nesquehonite: MgCO3•3H2O
(b) Portlandite: Ca(OH)2
(e) Lansfordite: MgCO3•5H2O
(c) Calcite: CaCO3
(f) Hydromagnesite: (g) Pokrovskite: Mg5(CO3)4(OH)2•4H2O Mg2CO3(OH)2
M1 M2
(i) Ikaite: CaCO3•6H2O
(h) Monohydrocalcite: CaCO3•H2O
191 192
Figure 1. Structures of Ca and Mg oxide, hydroxide, carbonate, and hydrated carbonates.
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Table 1. Number of Ca and Mg coordinated species in the hydroxide and carbonate polymorphs for
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observed and hypothetical mineral strutuctures.
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Calcite Aragonite62 Vaterite63-64 Monohydrocalcite65 Nesquehonite66 Lansfordite67 Ikaite68 Hydromagnesite69 Pokrovskite70
M1 M2
Cation Ca Ca Ca Ca Mg Mg Ca Mg, Ca Mg, Ca Ca Mg Mg Ca Mg, Ca Mg, Ca
#H2O 0 0 0 2 2 2 2 6 4 6 4 1 1 0 0
#OH 0 0 0 0 0 0 0 0 0 0 0 1 1 2 4
# − CO3 6 3 4 2 4 2 1 0 2 0 0 4 2 4 2
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# − CO3 0 3 2 2 0 1 2 0 0 1 1 0 2 0 0
Coordination 6 9 8 8 6 6 7 6 6 8 6 6 8 6 6
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2. Methodology Demichelis and coworkers examined how well a dozen DFT functionals
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reproduced the reaction energies for CaCO3 + nH2O → CaCO3•nH2O for
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monohydrocalcite (n =1) and ikaite (n = 6) at 298 K for which experimental data has
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been published, and pointed out the difficulties calculating the thermodynamics of liquid
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water and the non-ideal behavior of water vapor via ab initio means.59 Functionals that
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worked well for the anhydrous and low water carbonates (calcite, aragonite, and
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monohydrocalcite) did not work well for ikaite, and vice versa, primarily due to the
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differences in types of bonding and difficulties in treating liquids and vapors. Their work,
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our previous study,71 and that of Costa and coworkers72 underscored the importance of
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including dispersion into the DFT functional for these systems, as well as the necessity of
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utilizing corrections to the heat of formation.
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In this work the difficulties in treating liquids and vapors by ab initio means are
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circumvented by 1) choosing well-defined reference states for water and CO2 that are
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suitable for accurate calculations by DFT, namely isolated molecules at 0 K, and 2)
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utilizing experimental data for the free energies of water and CO2 in the vapor, liquid, or
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supercritical state at finite temperature and pressure. In addition, we apply corrections to
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the 0 K heats of formation for the carbonate solids. These corrections are necessary
214
because although errors for pairwise hydrogen bonding and M•••O ligand interaction
215
energies are small – on the order of 5 kJ/mol or less consistent with the known limitations
216
of DFT – these mineral systems are large and the errors have a cumulative effect.71
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Utilizing a 0 K reference state rather than 298 K enables the separation of error due to
218
cohesive energy versus the vibrational partition function at finite temperature.
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2.1 DFT The methodology employed in this work is the same as was developed and tested
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in prior work on hydrated Mg carbonates in water and in CO2-rich environments.71, 73
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Hence the overall methodology is summarized briefly here, followed by a more in depth
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treatment of the requirements for heats of formation correction for the Ca polymorphs.
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All calculations were performed using periodic all-electron density functional
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theory as implemented in the DMol3 program. For the real-space cutoff, values ranging
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from 5.1 to 3.5 Å were tested for a double-zeta plus polarization quality basis set with
228
respect to the ∆fH(0K) for calcite (CaCO3) and portlandite (Ca(OH)2). The difference in
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∆fH(0K) between the more accurate 5.1 and 3.5 Å is 2.7 kJ/mol for calcite and 4.0 kJ/mol
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for portlandite, which is negligible. An rcut of 4.3 Å was utilized for computational
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efficiency, as computational time scales as the cutoff radius r6. Converged k-point
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sampling using the Monkhorst-Pack74 methodology was used during lattice optimizations
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performed with the aid of unit cell stress. The generalized gradient approximation to the
234
density functional of Perdew, Burke, and Ernzerhof (PBE)75 was utilized plus an
235
empirical dispersion term in the Hamiltonian as developed by Grimme and first published
236
in 2006.76-77 Herein this method is abbreviated PBE-G06. Table S-1 in the Supporting
237
Information (SI) shows the magnitude of the dispersion energy in these systems, as well
238
as the total PBE-G06 energies and the zero-point vibrational energy (ZPE).To improve
239
the reliability of the vibrational partition function and how the chemical potential ∆µ
240
changes with finite temperature, it is important to ensure the phonon spectrum is
241
converged from a thermodynamic perspective. This involves running increasingly large
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13 242
unit cells and longer phonon wavelengths until the free energy converges at finite
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temperature. This is shown in Figure 2 for CaO and portlandite for which the JANAF78
244
tables provide thermodynamic data up to 1000 K. Both minerals require a 3x3x3 super
245
cell to converge the phonon spectrum. Calcite required a 2x2x1 super cell, but the
246
conventional unit cells for monohydrocalcite and ikaite were sufficiently large. 0
-20
-40 ∆µ (kJ/mol)
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ACS Earth and Space Chemistry
CaOExpt Expt CaO CaO CaO(1x1x1) (1x1x1) CaO(2x2x2) (2x2x2) CaO
-60
CaO(3x3x3) (3x3x3) CaO Ca(OH)2Expt Expt Ca(OH)2
-80
Ca(OH)2(1x1x1) (1x1x1) Ca(OH)2 Ca(OH)2(2x2x2) (2x2x2) Ca(OH)2
-100
Ca(OH)2(3x3x3) (3x3x3) Ca(OH)2 -120
247
0
200
400
600
800
1000 K
248
Figure 2. Changes in the calculated chemical potential with temperature due to the vibrational partition function for
249
CaO and Ca(OH)2 as a function of unit cell size compared to experimental data.78
250
2.2 Thermodynamic Reference States
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Since the enthalpy of a substance is not an absolute quantity like entropy,
252
reference states must be chosen for the enthalpy that ensures a consistent basis for
253
comparison. Thermodynamic tables typically use a standard state of 1 bar pressure and
254
298.15 K. Since DFT calculations are done at 0 K, that temperature becomes a more
255
convenient reference state for the ab initio thermodynamics framework. In this work
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formation energies at 0 K (∆fH) are calculated relative to the oxides, i.e. H2O, CO2, and
257
CaO, consistent with much of the geochemical literature. To facilitate comparison of
258
literature thermodynamic values with the DFT results, literature values given with respect
259
to the elements at 298 K are converted to ∆fH(0K) from the oxides, as shown in Table 2.
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Table 2
262
Thermodynamic values in J/mol for entropy and kJ/mol for all others. HFC is the Heat of
263
Formation Correction for ∆fH°(0K) from the oxides.
CaO1
S°(298)
∆fH°(298)
∆fG°(298)
H-H°(Tr)
∆µ(298-
∆fH°(0K)
∆fH°(0K)
∆fH°(0K)
HFC
Expt
Expt
Expt
Expt
0) Calc.
Expt
Expt
Calc.
Elements
Elements
Elements
Elements
Elements
Oxides
Oxides
Oxides
38.212
-635.089
-603.501
6.749
-631.760
N/A
N/A
N/A
83.387
-986.085
-898.421
14.160
-977.358
-106.677
-92.063
14.614
91.71
-1207.590
-1129.076
14.483
-1202.262
-177.351
-142.585
34.765
Monohydrocalcite
129.7
-1497.950
-1361.218
14.652
-1489.348
-225.516
-195.801
29.715
Ikaite79
310.4
-2971.710
-2541.131
38.596
-2928.997
-470.560
-508.238
-37.679
1
Portlandite 2
Calcite
79
264
1
S°(298), ∆fH°(298), ∆fG°(298), and H-H°(Tr) from JANAF.
265
2
S°(298), ∆fH°(298), and ∆fG°(298) from Konigsberger,79 and H-H°(Tr) from Staveley.80
266
3
S°(298), ∆fH°(298), and ∆fG°(298) from Konigsberger,79 and ∆µ(298-0) from PBE-G06 calculations.
267 268 269 270 271
For a mineral such as calcite for which the ∆fH°(298K) and ∆(H - H°(Tr)) values are known for 0 and 298 K, ∆fH°(0K) from the elements is calculated as follows: ° ° 0) = ∆ ) − − ° ) )− − ° ))0)} − ∆
° ) ° 0) − − ° ) − ° 0) − 1.5 ° ) − ° 0)
272
[Eq. 1]
273
where T = 298.15 K, calcite, Ca, and C are in the solid phase, and O2 is in the gas phase.
274
For monohydrocalcite and ikaite, however, the ∆(H - H°(Tr)) values are not known
275
because the heat capacity measurements between 0 and 298 K have not been done. In
276
these cases the PBE-G06 calculated partition function is used to determine the free energy
277
difference Δ between 298 and 0 K. These values under the ∆µ(298-0) heading and the
278
resultant ∆fH°(0K) values are shown in italics in Table 2. This methodology also enables
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15 279
extrapolation of thermodynamic values beyond measured values to higher temperatures,
280
which are tabulated in Tables 3-3 and S-4 in the SI. Table 2 also shows the PBE-G06
281
calculated ∆fH°(0K) values compared with experimental values, the difference termed
282
HFC for Heat of Formation Correction. Calculated data that include these corrections in
283
this work are termed PBE-G06-HFC.
284
For Ca analogues of the Mg minerals nesquehonite, lansfordite, hydromagnesite,
285
and pokrovskite, however, there are no thermodynamic data available. In these cases the
286
HFC value for the Mg minerals was employed for the Ca-analogues as an approximation.
287
To estimate the magnitude of this assumption, we examined magnesian calcite for which
288
∆fH°(0K) is known for both calcite and magnesite. In this system applying the HFC
289
correction for Ca to Mg in calcite results in an error on the order of 8.7 kJ/mol per Mg.
290
Although this error is not large, it should be noted when considering the AIT results.
291 292 293 294 295
2.2. Chemical potentials The chemical potentials for the molecular and crystalline species used in this work are obtained from , ") = # $%&',() + # +,- + Δ , ")
[Eq 2]
296
where # $%&',() and # +,- are calculated using the PBE-G06 level of theory. For water
297
and CO2, # $%&',() and # +,- are calculated as isolated molecules at 0 K. Total energies
298
and ZPE for crystalline structures are calculated using periodic boundary conditions, as is
299
Δ , ") from the vibrational partition function. For water (. ) and CO2 ( ), the
300
effects of temperature and pressure on the chemical potentials are obtained from
301
experimental data to circumvent the difficulties cited by Demichelis and coworkers.59 For
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16 302
the water-rich and ultra-high vacuum (UHV) systems, the thermodynamic data from the
303
JANAF tables are used. The free energies at the reference pressure of 1 bar presented in
304
the JANAF tables are converted to relevant pressures using the ideal gas law:
305
[Eq. 3]
306
Chemical potentials for water and CO2 in CO2-rich environments with varying
307
amounts of water, including the supercritical region, are based on the experiments and
308
thermodynamic model described in Springer et al., and incorporated into software
309
available from OLI.81 The values of the chemical potentials used in this study are
310
tabulated in Appendix A in Chaka and Felmy.73
311 312 313
2.2 Ab initio Thermodynamics The free energies of minerals calculated with respect to the formation reaction
314
from the oxides are a function of independent variables , . , and . For Ca
315
polymorphs, the energy of the crystalline phase is defined as:
316
$%&',() 23 /0&' , ", 1 ) = #0&' + #0&' − 1 , ") − 1 . , ") − 14 , ")
317
[Eq.4]
318
where ni are the coefficients of CaO, H2O, and CO2 in the stoichiometric formula for the
319
23 mineral, #0&' is the ZPE at 0 K plus the vibrational entropy and enthalpy at finite
320
temperature and pressure for the crystalline (xtl) mineral phase, and µi(T, p) is the
321
chemical potential of species i as described above.
322 323
3.0 Results and Discussion
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17 324
The results are presented in two subsections. Section 3.1 describes the structures
325
of the Ca minerals and the Ca-analogues of Mg minerals presented in Figures 1 and 3 and
326
Table S-2 in the SI. Section 3.2 discusses the AIT results given in Figures 4-8 and Table
327
3.
328 329 330
3.1 Structures The issues to be discussed in this section are threefold, namely (1) how well does
331
the computational method used describe the observed mineral structures, (2) can the
332
structures provide insights into kinetic formation and transformation mechanisms in the
333
crystallization process, and (3) do the Ca-analogues of hydrated Mg carbonates provide
334
unique cation coordination environments that could be useful in interpreting experimental
335
spectra of prenucleation species and ACC.
336
The lattice constants for the observed Ca carbonate polymorphs and the
337
hypothesized Ca-analogues of Mg hydrated carbonates are shown in Table S-2. The
338
bond distances for the first Ca coordination shell are shown in Figure 3. In general, the
339
PBE-G06 level of theory describes the structures of the observed minerals with a high
340
degree of accuracy, with deviations in lattice constants being less than 1%. The
341
exceptions are the deviations for the c vector of calcite (-1.1%) and portlandite (-4.18%),
342
and the a and c vectors for ikaite at 1.34% and 1.22%, respectively, which are still quite
343
small. The portlandite structure is consistent with that calculated by Laugesen using the
344
PW91 functional.5 The structures and hydrogen bonding arrangement found for
345
monohydrocalcite and ikaite agree closely with the DFT results of Demichelis and
346
coworkers59 and Costa et al.82, as well as the neutron diffraction for monohydrocalcite by
347
Swainson65.
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18 348
Analysis of the carbonate polymorph structures can provide insight into the
349
likelihood of rapid crystallization, namely how closely does the cation coordination in the
350
solid state resemble solution speciation. Highly hydrated structures such as ikaite,
351
lansfordite, and nesquehonite would be expected to have a higher probability of kinetic
352
formation, even if not the most thermodynamically favored. The more
353
thermodynamically favored species –except at cold temperatures- are the less hydrated
354
species monohydrocalcite, pokrovskite, and hydromagnesite, plus the anhydrous calcite,
355
aragonite, vaterite, and magnesite. These latter species, however, exhibit high carbonate
356
coordination that is not favored in solution and thus require aggregation, dehydration, and
357
extensive rearrangement to form. This is evidenced in Mg carbonation experiments where
358
nesquehonite is rapidly precipitated, followed by slow transformation to hydromagnesite,
359
and an even slower transformation to magnesite.83-85 The thermodynamic stability
360
sequence in these experiments is nesquehonite (least stable) → hydromagnesite →
361
magnesite (most stable), and their order of appearance is consistent with the Ostwald step
362
rule.71, 73, 86 The Ostwald Step Rule – also termed the Ostwald-Lussac Rule of Stages –
363
postulates that the least stable phase crystallizes first, followed by successive
364
transformations into more stable phases. 87 Discussion of the structures as a function of
365
degree of hydration is as follows: ikaite (six), lansfordite (five), nesquehonite (three),
366
monohydrocalcite (one), hydromagnesite (one), and pokrovskite (half).
367
The hexahydrate ikaite structure is extensively hydrated with each Ca coordinated
368
to six water molecules and one carbonate group. The structure is stabilized by an
369
extensive hydrogen bonding network that was described by Demichelis and coworkers.82
370
At the PBE-G06 level of theory, the Ca-Oc distance is 2.443 Å, and the Ca-Ow distance is
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ACS Earth and Space Chemistry
19 371
on average 2.490 Å. This is in close agreement with synchrotron X-ray diffraction by
372
Lennie who found the mean Ca-O distance in ikaite to be 2.469(3) Å at 243 K.88 This
373
hydration structure around Ca in ikaite is nearly identical to the mean Ca-O distance of
374
2.46(2) Å for 8-fold Ca coordination in an aqueous environment determined by
375
Jalilehvand and coworkers using EXAFS, large-angle X-ray scattering, and ab initio
376
molecular dynamics.89-90 This supports the hypothesis that ikaite crystallizes out of
377
solution without changing its coordination environment or requiring water molecules to
378
be displaced in conditions that are saturated with respect to ikaite.
379
The pentahydrate lansfordite structure consists of two sixfold coordinated Mg
380
complexes hydrogen bonded together. One is a Mg(H2O)62+ complex and the other a
381
Mg(CO3)2 (H2O)42- complex. The carbonate groups are - coordinated as shown in
382
Figure 3e. The Ca analogue of lansfordite exhibited the same 6-fold coordination as the
383
Mg mineral, but with expanded M-O distances shown in Figure 3f. Ca-lansfordite may
384
form as a prenucleation aggregate if there is a sufficient population of hydrated
385
Ca(H2O)62+ and Ca(CO3)2 (H2O)42- complexes in solution. The free Ca2+ ion can
386
accommodate more than six water molecules in its solution coordination sphere, as
387
evidenced by theory and experiment, and has been observed to comprise a significant
388
fraction of the Ca2+ speciation.7 The dicarbonate Ca(CO3)2 (H2O)4+2- complex, however,
389
has to our knowledge not yet been considered as a potential Ca species in solution. As
390
shown in the next section, there are conditions under which the Ca-lansfordite analogue is
391
metastable with respect to CaO and Ca(OH)2 and thus according to the Ostwald Step
392
Rule may form as a transient intermediate. Hence an initial condensation aggregate for
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20 393
Ca carbonate may contain a significant fraction of Ca(H2O)6+2+ and Ca( - CO3)2
394
(H2O)4+2- complexes.
395
The trihydrate nesquehonite structure consists of a two-dimensional Mg carbonate
396
ribbon shown in Figure 3a surrounded by waters of hydration. Two water molecules
397
occupy the axial positions as shown in Figure 1d. The M-Ow distances from the cation to
398
the axial waters is lengthened from 2.069/2.095 for Mg to 2.323/2.340 Å for Ca. The
399
third water is not coordinated to Mg, but is hydrogen bonded to the carbonate groups and
400
axial water. This structure is discussed in more detail in Chaka and Felmy.71 The Mg is
401
six-fold coordinated by two and one carbonate groups within the plane of the
402
ribbon, plus two axial water groups. Replacement of Mg with Ca causes a significant
403
distortion of the ribbon due to a shifting of carbonate orientation to yield 7-fold
404
coordination, namely one of the carbonates becomes , shown in Figure 3b. These
405
Ca2+ carbonate ion pairs in the planar CaCO3 ribbon could readily be assembled from
406
ion pairs in solution, as shown by the circled ion pairs in Figure 3b. The axial waters
407
remain in place as the ribbon is assembled, but the planar Ca-coordinated water
408
molecules would be displaced.
409
Monohydrocalcite has a unique structure consisting of three three-fold screw axes
410
and nine formula units in the unit cell. Ca is eightfold coordinated with two water
411
molecules, two bidentate carbonate groups, and two monodentate carbonate groups
412
shown in Figure 3h. Each water molecule is coordinated to two Ca atoms, and hydrogen
413
bonded to two carbonate oxygens. One Ca-Ow bond is slightly longer than the other. The
414
low water content and coordination with four carbonate groups is not an arrangement that
415
would be found in solvated, dilute Ca ions due to an excess of negative charge.
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ACS Earth and Space Chemistry
21 416
Formation of monohydrocalcite would require significant aggregation of multiple Ca
417
carbonate ion pairs and displacement of almost all waters of hydration, and thus would be
418
kinetically challenging to form despite thermodynamic drivers.
419
In addition to kinetic difficulties in formation, the monohydrocalcite structure also
420
inhibits transformation. It’s structure is unique among the Ca and Mg carbonate hydrates
421
in that the water molecules are not in contact with each other. In all the other hydrated
422
Ca and Mg carbonate polymorphs - namely ikaite, nesquehonite, lansfordite, and
423
hydromagnesite - the water molecules form columns in the structures and hence are
424
readily able to diffuse out upon heating or exposure to dehydrating conditions. These
425
structures are thus capable of undergoing solid state transformations upon facile
426
dehydration. In contrast, water molecules in monohydrocalcite are trapped by
427
surrounding carbonate groups and Ca ions, and cannot readily diffuse out. Hence
428
monohydrocalcite would have to dehydrate and transform into calcite, aragonite, or
429
vaterite via a dissolution/precipitation mechanism. These structural considerations alone
430
thus provide an explanation for why Munemoto and Fukushi observed that
431
monohydrocalcite must first dissolve in order to transform to aragonite.24 This required
432
dissolution/precipitation process to transform monohydrocalcite into anhydrous Ca
433
carbonate can also explain the release of Mg from Mg-containing monohydrocalcite just
434
prior to calcite precipitation.8 It is also consistent with the observations by Jiménez-
435
López and coworkers that monohydrocalcite dissolves prior to precipitation of calcite as
436
carbonate concentration increases.91 The stability of monohydrocalcite is underscored by
437
the observation of Neumann and Epple who found monohydrocalcite to be stable in
438
artificial seawater at room temperature in a sealed vial for 3 months.28
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22 439
Hydromagnesite also has a 1:1 ratio of Mg:H2O, but one of five water molecules
440
is dissociated to form two hydroxides. In this structure each Mg is 6-fold coordinated by
441
one water molecule, one hydroxyl group, and four carbonate groups. In the Ca
442
analogue, the coordination sphere is considerably expanded with two of the carbonate
443
groups shifting to become and yielding an 8-fold coordinated structure shown in
444
Figure 3d. The M-Ow distance increases from 2.195 Å to 2.530 Å. The kinetic issues of
445
formation for hydromagnesite are comparable to monohydrocalcite discussed above. In
446
contrast to monohydrocalcite, however, water molecules are organized in columns that
447
provide diffusion pathways for facile dehydration. Hence hydromagnesite need not
448
transform by a dissolution/precipitation mechanism, but can undergo a solid state
449
transformation.
450
Pokrovskite has a 2:1 ratio of Mg:H2O, and all water is dissociated into hydroxyl
451
groups. The pokrovskite structure shown in Figure 1g has corrugated sheets of Mg and
452
hydroxyl groups stabilized by carbonate groups that are coordinated with Mg ions within
453
the same layer and between layers. Each carbonate group has oxygens that are
454
coordinated with one, two, and three Mg ions. There are two distinct type of metal sites,
455
M1 and M2 shown in Figure 3k, with M1 exhibiting two apical hydroxyl groups and four
456
carbonate groups, and M2 having two axial carbonate groups and four hydroxyl
457
groups. The structure is described in detail in Chaka.92 In the Ca analogue of
458
pokrovskite, the rigid coordination structure and metal placement does not allow for the
459
carbonate groups to shift from to ; hence they remain sixfold coordinated.
460
Formation of this complicated structure would be expected to require a high
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ACS Earth and Space Chemistry
23 461
concentration of cation and carbonate and low water, as well as a basic pH, and hence be
462
kinetically more difficult to form.
463
To summarize, the highly hydrated ikaite, Ca-lansfordite, and Ca-nesquehonite
464
structures have pathways of formation from solution that are expected to proceed with
465
low barriers due to similarities of ionic arrangements with the solvated cation. In contrast,
466
poorly hydrated species such as monohydrocalcite, Ca-hydromagnesite, and Ca-
467
pokrovskite require aggregation, extensive ionic rearrangement, and dehydration to
468
transform solution phase structures into the solid state, processes which can be expected
469
to have much higher kinetic barriers than simple ion assembly without rearrangement and
470
minimal or no dehydration. The thermodynamic attributes of these crystal structures are
471
discussed in the next section.
472
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Page 24 of 51
24 MCO3•3H2 O (b). Ca (a). Mg*
M5 (CO3 )4 (OH)2 •4H2O (c). Mg* (d). Ca
3.360 2.610
2.057 2.163
2.366
2.019
2.080
2.318
2.141
2.072
2.679
2.034
2.586 2.439 2.494 2.451
2.092
2.933
2.394
2.530
2.067
2.195
2.310
2.457
MCO3 •5H2 O (f). Ca
(e). Mg*
2.384 2.028!
2.084!
2.087! 2.087! 2.090! 2.089!
2.111!
2.111!
2.089!
2.090!
2.084! 2.028!
2.300
2.434
2.341
2.434
2.374
2.341 2.300
2.339 2.374
2.339
2.384
(c)!
MCO3 •6H2O
MCO3 •H2 O
2.360
2.050 2.079
2.204
(i). Mg
(h). Ca*
(g). Mg
2.106
2.421
2.455
2.400
2.223
2.642
2.468
2.136
2.437
(j). Ca*
2.503
2.444
2.223
2.532
2.468
2.384
2.139
2.516
2.629 2.403
2.139
2.013
2.442
2.189
2.526
2.189
2.464
M2 (CO3 )(OH)2 (l). Ca
(k). Mg* 1.998
2.085 2.067
2.105 2.172
2.104
2.047 2.032
2.313
2.277
2.097
2.224 2.476 2.590
2.002
2.291
2.328
2.245 2.263
2.204
M1
2.209
2.271 2.259
M2
2.439
M1
M2
473 474
Figure 3. Ligand arrangements for Ca (blue) and Mg (green) in the hydrated carbonates calculated by
475
DFT-G06. Observed structures are indicated by an asterisk (*). Bond distances in Å. Axial waters in
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25 476
the nesquehonite structures (a) and (b) not shown for clarity. Circles in (b) show arrangement of
477
bidentate ion pairs.
478 479 480
3.2 ab initio Thermodynamics In this section, the thermodynamic stability of the hydrated Ca carbonates and Ca-
481
analogues of Mg carbonate polymorphs is considered as a function of environmental
482
conditions across the range of . and from pure water to dry scCO2 to ultrahigh
483
vacuum (UHV). The specific states examined are: 1) ambient pressure where pCO2 is set
484
to the atmospheric concentration of 400 ppm, and pH2O is set to 32 mbar, the pressure
485
where the vapor chemical potential is equal to that of liquid water at 298 K; 2) high pCO2
486
conditions where pCO2 equals 1, 60, and 90 bar and water is either at saturation or trace
487
amounts (mole fraction χ is 10-9); and 3) UHV where pCO2 = pH2O = 10-4 mbar. The
488
high pCO2 range considered is limited to 275-375 K due to the availability of the
489
chemical potential data. It should be noted that scCO2 calculations up to 210 bar were
490
performed, but the results did not differ significantly from 60 and 90 bar and therefore are
491
not presented. Free energy phase diagrams are presented in Figure 4-8 phase boundary
492
temperatures in Table 3.
493 494 495 496 497 498
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26 499
Table 3. Phase Boundarya and Thermal Decomposition Temperatures (K) calculated by PBE-G06-
500
HFC.
Portlandite Ca(OH)2 → CaO+H2O
" = 1 bar ". = 32 :;? :bar
640.7
640.7
393.5
>1000 NA
814.0 NA
618.2 NA
267.7 653.7 667.3
267.7 551.8 493.0
174.6 390.0 386.8
Calcite
CaCO3 → CaO + CO2 CaCO3 ↔ Ca(OH)2
Monohydrocalcite
CaCO3•H2O → CaCO3 + H2O CaCO3•H2O → CaO + CO2 + H2O CaCO3•H2O ↔ Ca(OH)2
Ikaite
501
CaCO3•6H2O → CaCO3 + 6H2O 287.7 287.7 183.2 CaCO3•6H2O → CaO + CO2 + 6H2O 392.2 373.2 245.2 CaCO3•6H2O ↔ Ca(OH)2 354.4 334.7 221.5 CaCO3•6H2O ↔ CaCO3•H2O 292.1 292.1 185.1 Ca-Nesquehonite Analogue CaCO33H2O → CaO + CO2 + 3H2O 436.5 400.1 268.1 CaCO33H2O → CaCO3 + 3H2O 238.7 238.7 150.9 CaCO33H2O ↔ Ca(OH)2 373.7 333.5 227.9 CaCO33H2O ↔ CaCO3•H2O 222.3 222.5 138.0 CaCO33H2O ↔ CaCO3•6H2O 336.1 336.0 215.0 Ca-Lansfordite Analogue CaCO35H2O → CaO + CO2 + 5H2O 415.2 360.0 238.2 CaCO3H2O → CaCO3 + 5H2O 295.2 255.0 162.4 CaCO35H2O ↔ Ca(OH)2 374.6 312.2 208.5 CaCO35H2O ↔ CaCO3•H2O 302.6 251.6 159.2 CaCO35H2O ↔ CaCO3•6H2O 248.4 (463) (289) Ca-Hydromagnesite Analogue Ca5(CO3)4(OH)24H2O ↔ CaO 492.5 422.2 293.5 Ca5(CO3)4(OH)24H2O ↔ Ca(OH)2 315.9 230.1 178.5 Ca5(CO3)4(OH)24H2O ↔ CaCO3 NA NA NA Ca5(CO3)4(OH)24H2O ↔ 359.9 355.0 228.5 CaCO3•6H2O Ca-Pokrovskite Analogue Ca2CO3(OH)2→ CaO + CO2 + H2O 466.5 395.2 280.5 a Forward arrows → indicate a reaction that becomes thermodynamically favored at the temperature indicated.
502
Bidirectional arrows ↔ indicate a phase boundary between two minerals. Note, experimental temperatures for calcite
503
have been extrapolated above 298 K using ab initio thermodynamics.
504 505 506 507
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27 508 509
3.2.1 Ambient The ambient results are presented in two stages. Initially the impact of the heat of
510
formation correction for DFT on the thermodynamics of the Ca mineral species is
511
discussed, followed by the AIT of the Ca-analogues of the Mg minerals.
512
The AIT results for Ca carbonates, hydrates, and hydroxide under ambient
513
conditions (pH2O = 32 mbar, pCO2 = 400 ppm) are shown in Figure 4 for both the heat of
514
formation corrected (PBE-G06-HFC) and the uncorrected DFT (PBE-G06) methods.
515
The uncorrected DFT results yield qualitative results consistent with experimental
516
observations – that calcite is the most thermodynamically stable across most of the
517
temperature range until decomposition at high temperature, and ikaite is the most
518
thermodynamically stable at lower temperature. Portlandite is always metastable with
519
respect to calcite, and monohydrocalcite is always metastable with respect to the most
520
stable polymorph, which is ikaite at low temperatures and calcite at higher temperatures. 10 -10 -30 µCa (kJ/mol)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
ACS Earth and Space Chemistry
-50 -70 -90
-110 -130 -150
521 522
.
250
275
300
325
350
375
400 K
Figure 4. Comparison of PBE-G06 calculated free energies of Ca carbonate
523
minerals with (solid lines) and without (dashed lines) heat of formation
524
corrections (HFC).
525
The application of HFC brings the DFT results into quantitative agreement with
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28 526
experimental values. The HFC for calcite, monohydrocalcite, and portlandite all serve to
527
lower the energy by 34.77, 29.71, and 14.61 kJ/mol, respectively. Ikaite has the largest
528
HFC of all the polymorphs at -37.41 kJ/mol, which is not surprising as it has the largest
529
number of atoms in the stoichiometric formula. It should be noted that the HFC for
530
ikaite has the opposite sign of the other polymorphs due to the slight overbinding of
531
DFT-GGA for hydrogen bonds. Applying the HFC and thus increasing the stability of
532
calcite and decreasing the stability of ikaite results in shifting the temperature of their
533
phase boundary in liquid water under atmospheric pressure from 352.0 K to 287.7 K, a
534
much more realistic value. This lower temperature phase boundary is consistent with
535
ikaite’s utility as a paleothermometer for cold water conditions93 and the determination
536
that ikaite is the only Ca carbonate that precipitates in sea ice.44 The actual maximum
537
temperature for ikaite’s stability has been shown to depend upon conditions. In seawater,
538
the generally accepted maximum temperature for ikaite’s formation and persistence is
539
280 K.93 Ikaite was found to be stable up to 291 K in the presence of saccharose when
540
MacKenzie94 injected CO2 gas into a solution of CaO, following a method reported by
541
Pelouze in 1865.95 The maximum temperature limit for ikaite was raised to 297 K by
542
Brooks and coworkers when sodium hexametaphosphate was added during the mixing of
543
Na2CO3 and CaCl2.96 In the presence of triphosphate, Clarkson found ikaite would form
544
up to 298 K.14 The value of 287.7 K determined by AIT for the ikaite/calcite phase
545
boundary serves as a reference value that depends solely on the intrinsic free energy of
546
the solids, . and in the absence of solution kinetic effects and any added
547
compounds. For monohydrocalcite, including the HFC shifts the temperature at which it
548
becomes metastable with respect to calcite from 292.7 K to 267.7 K with HFC. Below
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29 549
this temperature, monohydrocalcite is more thermodynamically stable than calcite,
550
though not as favored as ikaite. pH2O = 32 mbar; pCO2 = 400 ppm 0
CaO
-20 -40 µCa (kJ/mol)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
ACS Earth and Space Chemistry
-60 -80
-100 -120 -140
551
275
295
315
335
355
375 K
552
Figure 5. AIT free energy phase diagram for Ca minerals (solid lines) and Ca-analogues of Mg minerals (dashed lines)
553
calculated using PBE-G06-HFC.
554
According to the Ostwald Step Rule, these sequences of thermodynamic stability
555
can provide insight into species that may be kinetically formed during carbonation
556
processes, along with the structural complexity analysis of the previous section.
557
Carbonation of portlandite slurries has been shown to occur readily upon brief exposure
558
to high pCO2.16 Portlandite is much more soluble than brucite, which would facilitate the
559
carbonation reaction.97 The AIT phase diagrams enable predictions of which polymorphs
560
are more stable than portlandite and thus may be observed upon portlandite’s dissolution
561
and subsequent carbonation. In an aqueous solution under atmospheric pressure with 400
562
ppm pCO2, the sequence of thermodynamic stability changes with temperature. Below
563
287.7 K the sequence of thermodynamic stability from lowest to highest (most stable) is
564
CaO → portlandite → monohydrocalcite → calcite → ikaite. Above 287.7 K ikaite
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Page 30 of 51
30 565
and calcite switch places, and above 292.1 K, ikaite switches with monohydrocalcite, to
566
result in the following sequence that holds up to 344.7 K: CaO → portlandite → ikaite
567
→ monohydrocalcite → calcite. Above 344.7 K, ikaite is less stable than portlandite,
568
and hence the thermal stability sequence is CaO → ikaite → portlandite →
569
monohydrocalcite → calcite. The thermodynamic sequence of metastability stages and
570
hence which phases may be observed during the crystallization process, change with
571
temperature under ambient conditions in water.
572
The results of the AIT calculations of the Ca-analogues of the Mg carbonate
573
minerals nesquehonite, hydromagnesite, lansfordite, and pokrovskite are shown in Figure
574
5. These results show clearly that formation free energies of these compounds from the
575
oxides are exothermic. These Ca-analogues, however, are highly metastable with respect
576
to the known minerals across the entire range of geologically relevant conditions,
577
consistent with the fact that they have never been observed in nature. In addition, they are
578
all predicted to decompose to CaO, H2O and CO2 between 360 – 422 K, much lower than
579
the observed polymorphs except for ikaite. The highly hydrated Ca-lansfordite and Ca-
580
nesquehonite are the lowest energy analogues primary due to the stabilization of
581
hydrogen bonding and nesquehonite’s ability to accommodate 7-fold coordination. The
582
least stable are the basic carbonate analogues Ca-hydromagnesite and Ca-pokrovskite,
583
which have much less structural flexibility to accommodate the larger size cation.
584
Although Ca-hydromagnesite exhibits 8-fold coordination, it has much less stabilization
585
from hydrogen bonding, and Ca-pokrovskite has none.
586 587
According to the Ostwald step rule, the sequence of thermodynamic stability provides an indication as to which phases may be observed during a carbonation of CaO
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ACS Earth and Space Chemistry
31 588
or Ca(OH)2 experiment and the series of dissolution/precipitation/transformation
589
reactions. This can include the Ca-analogues of Mg polymorphs. At 278 K the stability
590
sequence from least to most stable is: CaO → Ca-pokrovskite → Ca-hydromagnesite →
591
portlandite → Ca-lansfordite → Ca-nesquehonite → monohydrocalcite → calcite →
592
ikaite. Ikaite will certainly form and persist as it is both the most thermodynamically
593
stable as well as the most kinetically accessible from associated Ca2+ and CO32- ions in
594
solution. The Ca analogues of lansfordite and nesquehonite may also be kinetically
595
accessible, and condense as components of the prenucleation clusters that contribute to
596
ACC at lower temperatures.
597
The basic carbonates Ca-hydromagnesite and Ca-pokrovskite are the most
598
metastable of the hydrates. Given their high energies, complicated structures, and high
599
degree of carbonate coordination, Ca-hydromagnesite and Ca-pokrovskite are not likely
600
to be formed in the highly hydrated initial stages of prenucleation from solution. In the
601
later stages of aggregation and dehydration, however, they may form and become trapped
602
in local regions of ACC. There is indeed evidence of hydroxyl groups in ACC. NMR has
603
indicated that in addition to water bound to Ca, a small fraction (~7±3%) of hydrogen
604
was present as rigid OH groups.54 Some of this may be due to regions in ACC with a
605
structure similar to Ca-hydromagnesite or Ca-pokrovskite. Ca-hydromagnesite has a
606
Ca:H2O ratio of 1:1, and pokrovskite has 1:0.5, both of which are in the range of the
607
observed hydration stoichiometry of ACC. It should be noted that Ca-pokrovskite’s
608
stoichiometry can also be written as CaCO3•Ca(OH)2. The atomic coordinates of these
609
structures are given in Table S-5,7 in the SI to assist with spectroscopic interpretation.
610
At a higher temperature such as 353 K in an aqueous environment the Ca-
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Page 32 of 51
32 611
analogues are more destabilized relative to the observed Ca minerals with a stability
612
order of: Ca-lansfordite → CaO → Ca-pokrovskite → ikaite → Ca-hydromagnesite →
613
Ca-nesquehonite → portlandite → monohydrocalcite → calcite. Carbonation of CaO
614
might result in a very transient formation of ikaite, but at this high a temperature ikaite is
615
likely to dehydrate quickly to form monohydrocalcite or calcite via an amorphous
616
intermediate. Carbonation of portlandite would not go through an ikaite intermediate, as
617
it is higher in energy, but would likely go directly to monohydrocalcite, ACC, or
618
anhydrous CaCO3.
619
4.2.3. AIT in scCO2
620
The thermodynamics of the Ca carbonates and hydrates have not yet been
621
measured in CO2-rich conditions, which is most relevant for carbon sequestration.
622
Although scCO2 injected below ground or in above ground processing plants is dry, it is a
623
superfluid that can migrate extensively through rock and extract considerable amounts of
624
water. Even though the amount of water in saturated scCO2 is small (less than 1% by
625
weight) it exhibits the full reactivity of liquid water. Hence water in the CO2 liquid and
626
supercritical phases must be considered as well.98 The AIT results for scCO2 are
627
presented in two stages. First, the thermodynamics of observed Ca minerals are
628
discussed in both saturated and trace water conditions. In the second stage, the
629
thermodynamics of the Ca-analogues of Mg minerals are presented only for the saturated-
630
water case, as they become very unstable in the absence of water.
631
The results for the AIT of the observed Ca carbonate polymorphs in high pCO2 are
632
shown in Figure 6 for water-saturated and for trace (χ = 10-9 mole fraction) water
633
conditions. As expected, calcite is the lowest energy polymorph across the 275-375 K
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33 634
temperature range under all high pCO2 conditions. This contrasts with the ambient
635
conditions with 400 ppm pCO2, where ikaite becomes lower in free energy than calcite at
636
287.7 K. 1 bar pCO2 100
CaCO3•6H2O (tr)
µCa (kJ/mol)
-50
50
0
0
-50
-50
-100
-100
Ca(OH)2 (s)
-100
-150
-150 275
637
325
375
90 bar pCO2
100
50
CaO
0
60 bar pCO2
100
50
-150 275
325
375
275
325
375 K
638
Figure 6. Free energies of Ca carbonate minerals under high-pCO2 with water saturation (s, solid lines) and trace (tr,
639
dashed lines) water. 1 bar pCO2 10
µCa (kJ/mol)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
ACS Earth and Space Chemistry
CaO
Water Saturated 10
-10
-10
-30
-30
-50
-50 Ca(OH)2
-70
-70
-90
-90
-110
-110
-130
-130
-150
640
90 bar pCO2
-150 275
325
375
275
325
375 K
641
Figure 7. Free energies of Ca carbonate minerals (solid lines) and Ca-analogues of Mg minerals (dashed lines) in
642
water-saturated pCO2 at 1 and 90 bar.
643
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34 644
For trace water conditions - effectively dry CO2 indicated by the dashed lines in
645
Figure 6 - calcite is by far the most stable, becoming slightly more stable (-136 to -143
646
kJ/mol) as pCO2 increases from 1 to 90 bar. The order of stability is ikaite → CaO →
647
portlandite → monohydrocalcite → calcite. Free energies of formation of calcite,
648
monohydrocalcite, and portlandite are well-separated by 50-75 kJ/mol at 300 K, yet still
649
sufficiently stable to be lower in energy (more stable) than CaO with the exception of
650
portlandite at higher temperature at 1 bar pCO2. Ikaite, however, is extremely unstable
651
under dry conditions with an endothermic free energy of formation of 138 kJ/mol,
652
making it less stable than CaO across the entire temperature range. In Figure 6 the free
653
energy for ikaite under trace water conditions is so high in energy it is off the scale and
654
not shown.
655
In a water-saturated high pCO2 environment, the relative stability of the Ca
656
polymorphs changes dramatically from the trace-water series to CaO → portlandite →
657
ikaite → monohydrocalcite → calcite. In equilibrium with water, the free energy of
658
ikaite is lowered (made more stable) to a point where ikaite and monohydrocalcite are
659
essentially isoenergetic at -131 and -129 kJ/mol at 1 bar respectively, and slightly lower
660
in energy at 90 bar at -138 and -137 kJ/mol. Hence ikaite and monohydrocalcite are both
661
likely precursors to calcite at low temperatures. Ikaite would likely be formed first as
662
structural simplicity favors fast formation. Upon standing, however, thermodynamics will
663
drive ikaite to dehydrate and convert to monohydrocalcite or ACC, followed by
664
transformation to calcite. Monohydrocalcite’s transformation will likely occur via a
665
dissolution/precipitation process due to the lack of diffusion channels for water as
666
previously discussed. As the temperature increases, ikaite destabilizes more rapidly than
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35 667
monohydrocalcite and calcite, as would be expected due to entropy favoring free over
668
bound water.
669
Experimentally, carbonation of portlandite occurs rapidly.16 Montes-Hernandez
670
and Renault used in situ Raman spectroscopy to observe the transformations that
671
occurred upon exposure of a portlandite slurry to a pCO2 of 50 bar at 298 K. Within the
672
first five minutes Ca carbonate clusters and/or ACC was observed as well as an
673
unidentified species referred to as a complex carbonate, prior to growth of vibrational
674
modes consistent with calcite. The complex carbonate vibrational mode peaked at 1073
675
cm-1. The ab initio thermodynamics predicts that ikaite may be a transient intermediate
676
under these conditions. The ikaite Raman spectrum obtained by Coleyshaw and
677
coworkers is consistent with the complex carbonate intermediate, as the carbonate
678
vibrational mode was observed at 1072 cm-1.23
679 680 681
3.2.4. AIT of Ca analogues of Mg carbonate polymorphs As shown by the dashed lines in Figure 7, under high pCO2 water-saturated
682
conditions between 275 and 375 K the Ca analogues of nesquehonite and lansfordite are
683
more stable than portlandite but less than ikaite, monohydrocalcite, and ikaite. There are
684
no significant differences as pCO2 increases from 1 to 90 bar. The exothermic formation
685
energy of lansfordite indicates that the fully hydrated Ca2+ ion as well as the Ca( -
686
CO3)2 (H2O)4+2- complex may form in water-saturated scCO2 as portlandite or CaO
687
dissolves. In carbonation experiments of the Mg minerals brucite and forsterite, water in
688
scCO2 has been shown by Loring and coworkers to form films at surfaces and surround
689
ions as they are solvated rather than be uniformly dispersed in the supercritical fluid as
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Page 36 of 51
36 690
isolated molecules.99 Hence it is conceivable that hydrated complexes such as ikaite’s
691
Ca( - CO3) (H2O)6+, and Ca-lansfordite’s Ca( - CO3)2 (H2O)4+2- and Ca(H2O)6+2+
692
species will form and contribute to prenucleation clusters, followed by dehydration and
693
formation of monohydrocalcite, ACC, and calcite.
694 695 696
3.3. UHV The thermal stabilities of the Ca carbonate polymorphs UHV conditions where
697
pH2O and pCO2 are equal to 10-4 mbar is shown in Figure 8 and Table 3. This state also
698
corresponds to an inert atmosphere at higher pressures such as may be employed in
699
thermal decomposition experiments. Under UHV conditions, the relative stabilities of
700
the Ca polymorphs and Ca-analogues of Mg polymorphs follow the same general trends
701
as under ambient conditions, albeit at much lower temperatures. Ikaite is the most stable
702
below 183.2 K, and calcite above that until it decomposes at 618.2 K. Monohydrocalcite
703
will decompose to calcite and water at 174.4 K. Portlandite is remarkably stable up to
704
393.5 K upon which it decomposes to CaO and water. The Ca-analogues of Mg
705
polymorphs are highly metastable, decomposing at very low temperatures under UHV
706
conditions.
707
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37
0
pH2O = pCO2 = 10-4 mbar CaO
-50 µCa (kJ/mol)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
ACS Earth and Space Chemistry
-100
-150
-200 100
200
300
400K
708 709
Figure 8. Free energies of Ca carbonate minerals (solid lines) and Ca-analogues of Mg minerals (dashed lines) under
710
UHV conditions.
711 712 713
3.4. Implications for Prenucleation Although it is metastable relative to calcite, the structure and thermodynamics of
714
ikaite have implications for the prenucleation clusters observed by Gebauer and
715
coworkers7 as well as Montes-Hernandez and Renaud.16 Ca carbonate in solution has
716
been found to resemble the ikaite structure with each Ca coordinated to six water
717
molecules and one bidentate carbonate group as shown in Figure 3j and discussed Section
718
3.1. Ikaite is 52% water by weight, with the bidentate Ca2+ CO32- ion pair dipoles
719
arranged linearly as shown in Figure 9. Adjacent rows of dipoles are oriented in opposing
720
directions to ensure a nonpolar structure. The dipoles are separated by 4.118 Å due to the
721
coordinated waters in between, and provide an electrostatic driving force for alignment of
722
the complexes in solution. We postulate that this driving force – and significant
723
exothermic heat of formation for ikaite in water-saturated conditions with high carbonate
724
concentration – is sufficient for the ion pairs in solution to self-organize into the ikaite
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Page 38 of 51
38 725
arrangement and form clusters. At lower temperatures these clusters can grow and
726
precipitate out as ikaite. At higher temperatures they will dehydrate and lead to
727
formation of ACC, monohydrocalcite, and ultimately anhydrous Ca carbonate. This
728
mechanism can provide a low energy pathway for formation of ACC and CaCO3
729
polymorph crystallization in aqueous solutions with added carbonate and in water-
730
saturated liquid and scCO2.
731
a c b
4.118 Å
b c
732 733
a
Figure 9. Arrangement of Ca2+ and CO32- ion pairs in ikaite. Water molecules not shown for clarity.
734 735
4.0 Conclusions
736
Understanding how Ca carbonate coordination and energies change successively
737
from the fully hydrated structures to the minimally and fully dehydrated stages provides
738
insight into the underlying mechanisms of carbonate crystallization. AIT calculations
739
show that in water-saturated scCO2 nonclassical low energy pathways are available for
740
calcite formation. The formation energies of the hydrated Ca carbonate polymorphs
741
monohydrocalcite and ikaite are exothermic even at temperatures up to 373 K. Even
742
though they are metastable with respect to calcite, they can form as transient (ikaite) or
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ACS Earth and Space Chemistry
39 743
persistant (monohydrocalcite) intermediates upon carbonation of Ca(OH)2 or CaO. Hence
744
formation of CaCO3•6H2O complexes are kinetically as well as thermodynamically
745
feasible in water-saturated scCO2. We postulate that these CaCO3•6H2O complexes
746
aggregated in the ikaite arrangement are one of the major constituents of the
747
prenucleation clusters observed by Gebauer et al.15 and Montes-Hernandez and
748
coworkers16 in aqueous systems, and can occur in scCO2 as well. Ikaite is likely to form
749
rapidly as its coordination structure is exhibited in solution and its crystallization is
750
essentially an alignment and ordering of solution complexes. This same structure enables
751
facile water diffusion and dehydration in all directions. Upon dehydration ikaite has been
752
shown to result in formation of ACC, monohydrocalcite, vaterite, and calcite under other
753
conditions21, 45-46, 48, 100, and is likely to do so in CO2-rich environments as well.
754
In aqueous systems with 400 ppm pCO2, ikaite is a likely intermediate for
755
carbonation of Ca(OH)2 at low temperatures. As carbonate concentration is increased in
756
aqueous solution towards a chemical potential equivalent to pCO2 of 1 bar as in
757
concentrated carbonate solutions, the ikaite stability is dramatically increased and
758
becomes a more likely intermediate across the temperature range from 273 to 373 K.
759
Ikaite or prenucleation clusters with the ikaite structure become more susceptible to rapid
760
dehydration the higher the temperature. This dehydration can lead directly to formation
761
of ACC, or crystalline monohydrocalcite, vaterite, or calcite.
762
The monohydrocalcite structure is complicated and more difficult to form than
763
ikaite despite being more thermodynamically favored. There is no direct relationship
764
between a solution Ca carbonate ion complex and monohydrocalcite coordination, thus it
765
is unlikely to comprise a significant fraction of the prenucleation clusters in solution.
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40 766
Once a critical mass of aggregated carbonate and Ca ions has developed with most of the
767
waters of hydration removed, monohydrocalcite can form and trap water in its structure
768
since there is no clear diffusion pathway out of the crystal. Monohydrocalcite is therefore
769
likely to persist much longer until transforming via a dissolution/precipitation mechanism
770
in both aqueous and CO2-rich systems. The free energy of monohydrocalcite is likely to
771
be a lower bound for ACC with a comparable water content, as bond distances and angles
772
are less than ideal in amorphous systems. As ACC dehydrates, calcite becomes a lower
773
bound for its free energy.
774
Nature exhibits a gap with respect to intermediate degrees of hydration for Ca
775
carbonate minerals, but not for Mg. Yet understanding intermediate stages of hydration
776
and sampling a greater variety of coordination environments can provide insight into the
777
nucleation and crystallization process. Formation energies of the Ca analogues of Mg
778
carbonate minerals are exothermic in both aqueous and water-saturated CO2-rich
779
systems, though in general metastable with respect to the observed Ca carbonate
780
polymorphs. In the carbonation process it is reasonable to postulate that the polymorphs
781
that most closely resemble structures in solution, namely Ca-lansfordite and Ca-
782
nesquehonite, may also play a role in the initial formation of prenucleation clusters or as
783
rapidly transforming intermediates. This progression would be consistent with Ostwald’s
784
Step Rule. Ca-hydromagnesite and Ca-pokrovskite have complicated structures with no
785
direct relationship to solution complexes, and hence are not expected to constitute an
786
early phase or highly hydrated prenucleation cluster. Given that the cation:water ratio is
787
less than one for both Ca-hydromagnesite and Ca-pokrovskite, their local Ca coordination
788
structure may appear in low-water ACC and account for the rigid OH groups observed by
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ACS Earth and Space Chemistry
41 789
NMR. Atomic coordinates for all the Ca-analogues of hydrated Mg carbonates are
790
provided in the SI so that these structures can be factored into a fit for a PDF or EXAFS
791
spectral interpretation.
792
Although solution thermodynamics, kinetics, surface reactivity and enthalpy, and
793
deposition/dissolution mechanisms have a great influence on the precipitation of
794
carbonates, understanding the bulk thermodynamics and structure-property relationships
795
provides a framework for understanding processes that are too fast, too slow, or two
796
difficult to measure in the laboratory or on geological timescales.
797 798
Acknowledgments:
799
This work was supported by the U.S. Department of Energy, Office of Basic Energy
800
Sciences, Division of Chemical Sciences, Geosciences & Biosciences, the Geosciences
801
Research Program. This research was performed using the computing facilities at
802
EMSL, a national scientific user facility sponsored by the U.S. Department of
803
Energy's Office of Biological and Environmental Research and located at Pacific
804
Northwest National Laboratory (PNNL), and PNNL Institutional Computing. PNNL
805
is a multiprogram national laboratory operated for DOE by Battelle.
806 807
Supporting Information contains tables of the 1) Total, ZPE, and dispersion energies
808
for all species in this work (Table S-1); 2) Optimized lattice constants of Ca carbonate
809
minerals and Ca-analogues of Mg carbonate minerals (Table S-2)
810
3) Free energies of portlandite, calcite, monohydrocalcite, and ikaite up to 1000 K at 1
811
bar and UHV conditions (Table S-3), as well as water-saturated conditions for pCO2 = 1,
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42 812
60, and 90 bar (Table S-4); and 3) Atomic coordinates for the Ca-analogues of hydrated
813
Mg carbonate structures (Tables S-5, 6, and 7).
814 815 816 817
REFERENCES (1) Swainson, I. P.; Hammond, R. P., Ikaite, CaCO3•6H2O: Cold Comfort for Glendonites as Paleothermometers. Am. Mineral. 2001, 86, 1530-1533.
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ACS Earth and Space Chemistry
Ca(OH)2 (xtl)
-70
CaCO 3•6H 2O Prenucleation clusters
-90
CaCO3 •6H2 O (xtl)
-110
ACC•H 2O
CaCO3 •H2 O (xtl) CaCO3 (xtl)
-130 -150
1097
275
325
375K
ACS Paragon Plus Environment