# Role of Impurities in the Kinetic Persistence of Amorphous Calcium Carbonate: A Nanoscopic Dynamics View

Ayumi Koishi, Alejandro Fernandez-Martinez, Beatrice Ruta, Mónica Jiménez-Ruiz, Roberta Poloni, Devis Di Tommaso, Federico Zontone, Glenn Waychunas, German Montes-Hernandez

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Ayumi Koishi, Alejandro Fernandez-Martinez, Beatrice Ruta, Mónica Jiménez-Ruiz, Roberta Poloni, et al. Role of Impurities in the Kinetic Persistence of Amorphous Calcium Carbonate: A Nanoscopic Dynamics View. Journal of Physical Chemistry C, 2018, 122 (29), pp.16983-16991. 10.1021/acs.jpcc.8b05189 . hal-02402584

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The role of impurities on the kinetic persistence of
amorphous calcium carbonate: a nanoscopic dynamics view

<table><tr><td>Journal:</td><td>Journal of the American Chemical Society</td></tr><tr><td>Manuscript ID</td><td>Draft</td></tr><tr><td>Manuscript Type:</td><td>Article</td></tr><tr><td>Date Submitted by the Author:</td><td>n/a</td></tr><tr><td>Complete List of Authors:</td><td>Koishi, Ayumi; Univ. Grenoble Alpes, ISTerre<br>Fernandez-Martinez, Alejandro; CNRS, ISTerre<br>Ruta, Beatrice; European Synchrotron Radiation Facility,<br>Jimenez-Ruiz, Monica; Institut Laue-Langevin,<br>Poloni, Roberta ; Laboratoire de Science et Ingénierie des Matériaux et<br>Procédés (SIMaP),<br>Di Tommaso, Devis; queen Mary, University of London, School of Biological<br>and Chemical Sciences<br>Zontone, Federico; ESRF<br>Waychunas, Glenn; Lawrence Berkeley National Laboratory, Earth Sciences<br>Division<br>MONTES-HERNANDEZ, German; CNRS ISTerre,</td></tr></table>

SCHOLARONE™
Manuscripts
# The role of impurities on the kinetic persistence of amorphous calcium carbonate: a nanoscopic dynamics view

Ayumi Koishi,<fnref n="1" /> Alejandro Fernandez-Martinez,<fnref n="1" /> Beatrice Ruta,<fnref n="2" />,<fnref n="3" /> Monica Jimenez-Ruiz,<fnref n="4" /> Roberta Poloni,<fnref n="5" /> Devis di Tommasso,<fnref n="6" /> Federico Zontone,<fnref n="3" /> Glenn A. Waychunas,<fnref n="7" /> German Montes-Hernandez<fnref n="1" />

**ABSTRACT:** Amorphous calcium carbonate is found in the early stages of biomineral formation. Its moldability and its kinetic persistence against crystallization make it of potential interest to the development of biomimetic materials. The presence of water and of inorganic impurities such as Mg<fnref n="2" />⁺ has been reported to increase its kinetic stability. Yet, the precise mechanisms of stabilization as well as the link between structural dynamics and crystallization kinetics are still missing. Here, we report the vibrational and diffusive dynamics of water and other atomic constituents in a series of Mg<fnref n="2" />⁺-doped solid amorphous calcium carbonates revealed using coherent X-ray and incoherent neutron scattering. This unique combination of techniques presents a novel view on the nanoscopic dynamic behavior of these amorphous materials: the presence of Mg<fnref n="2" />⁺ results in a higher frequency of structural rearrangements within the material. However, this increased dynamic behavior does not translate into a higher crystallization kinetics due to a concomitant stiffening of the water hydrogen bond network.

## Introduction

Amorphous calcium carbonate (ACC) is a metastable precursor found during the formation of calcium carbonate bio-minerals.<fnref n="1" />⁻<fnref n="4" /> Calcifying organisms take advantage of the moldable character of ACC and of its exceptional kinetic persistence against crystallization in order to form their shell and skeleton structures, which bear intricate shapes and advanced functionalities.<fnref n="5" /> Given the potential of this amorphous precursor strategy in the field of biomimetics,<fnref n="6" /> particular attention has been devoted to obtaining a mechanistic understanding of the polymorph selection and the kinetic control during the crystallization process from ACC.<fnref n="7" />,⁸ Previous studies on biogenic ACC have revealed that the stability of the amorphous phase is strongly influenced by the presence of water<fnref n="5" /> and impurities (ranging from co-ions to organic molecules),⁹⁻¹¹ and interfacial and confinement effects.¹²,¹³ Among many factors, the role of water, known as key to structural stability¹⁴, and that of the Mg<fnref n="2" />⁺ ion, a common impurity,<fnref n="5" />,⁹ are the focus of our work.

Some studies have described the crystallization as a dissolution-reprecipitation process on the basis of isotopic tracing experiments¹⁵ or physico-chemical analyses of crystallization products.¹⁶ This view is related to the widely accepted understanding that the high dehydration energy of aqueous Mg<fnref n="2" />⁺ is a prominent kinetic barrier to calcite nucleation and growth from solution in the presence of Mg<fnref n="2" />⁺.¹⁷⁻¹⁹ Other studies, however, have reported that transformation of biogenic ACC to calcite during the sea urchin spicule growth proceeds without

an identifiable crystallization front.<fnref n="5" />,²⁰,²¹ This observation is consistent with the view that the crystallization mainly proceeds through solid-state transformations initiated by physisorbed water-mediated partial dissolution.²²,²³

A potentially important clue to the type of crystallization mechanism is the observation that biogenic ACC exists in both hydrous or anhydrous states, with the latter being the transient phase prior to crystallization.<fnref n="2" />⁻<fnref n="4" />,²⁴ Previous studies identified different “types” of water in hydrous ACC, typically named as mobile water or rigid structural water, bearing different degrees of restricted motion, of which the gradual loss contributes to the crystallization.²⁵⁻²⁷ An interesting observation made by Reeder et al. is that mobile water is in fact absent in close vicinity of carbonate groups in biogenic ACC from lobster gastrolitsh.²⁸ From this, the authors suggest that the mobile water component might facilitate the transport and structural rearrangement of the carbonate framework, which infers that the topological distribution of different types of water may be the key. Reflecting on this, Mg<fnref n="2" />⁺ may be able to regulate this structural rearrangement process to a non-negligible extent by affecting the water exchange dynamics,²⁹,³⁰ owning to its high barrier to dehydration as compared to Ca<fnref n="2" />⁺.³¹

Thermodynamic factors provide a basis for the crystallization pathway across a free-energy landscape for any given system. The way the system actually explores this landscape, however, is strongly influenced by kinetic factors such as how rapidly or readily ionic species diffuse and internal cluster

<footnote n="1">¹Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, XNRS, IRD, IFSTTAR, ISTERRE, Grenoble, France</footnote>

<footnote n="2">²Univ. Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, Villeurbanne, France</footnote>

<footnote n="3">³ESRF – The European Synchrotron, Grenoble, France</footnote>

<footnote n="4">⁴Institut Laue Langevin, Grenoble, France</footnote>

<footnote n="5">⁵SIMAP, CNRS and Univ. Grenoble Alpes, Grenoble, France</footnote>

<footnote n="6">⁶Queen Mary University of London, London, UK</footnote>

<footnote n="7">⁷Earth and Environmental Sciences Area, Lawrence Berkeley National Laboratory, Berkeley, United States</footnote>
structures relax⁷. Despite their relevance to crystallization processes, the experimental elucidation of such dynamic factors during crystallization remains scarcely explored. The foremost goal of the present study, therefore, is to establish a direct link between the dynamics of water molecules and other constituents of ACC and the crystallization kinetics. We examine this link in particular in relation to the role of Mg²⁺. Given its distinct dehydration energy, we hypothesize that Mg²⁺ enhances the persistence of ACC via the formation of a strong H-bonding network and, in doing so, creates a barrier to structural rearrangements, thus delaying crystallization.

The dynamic properties of water present in amorphous carbonates were investigated by directly probing the hydrogen bond dynamics using inelastic incoherent neutron scattering. This technique, successfully applied to the studies of hydrogenated materials and confined water³²⁻³⁴, is not limited by selection rules as in IR or Raman spectroscopy, and it is highly sensitive to intermolecular interactions of water molecules. To elucidate the structural relaxation dynamics of disordered systems such as amorphous carbonates, a derivative of dynamic light spectroscopy in the X-ray regime, X-ray photon correlation spectroscopy (XPCS), was employed. Thanks to the use of a partially coherent X-ray source and a two-dimensional detector, this technique enables capturing the spatial arrangements of individual scatterers providing a quantitative measure of the rate of collective structural relaxation and information about the nature of such dynamics. XPCS has been successfully used to describe the dynamic behavior of out-of-equilibrium systems such as metallic glasses³⁵ or colloidal systems.³⁶ It is here used for the first time to probe structural rearrangements within ACC and Mg²⁺-bearing amorphous carbonates.

## Methods

**Sample preparation.** A series of solid amorphous carbonates with stoichiometry Ca(1-x)MgCO₃ nH₂O (M = Mg, Sr and Ba) were synthetized as model systems to biogenic ACC under controlled conditions. A highly basic environment (pH ≈ 11-13) was employed in order to facilitate the precipitation of stable amorphous carbonates in large quantities, enabling neutron scattering studies. Using the same protocol, a previous study showed that the short range order of this basic ACC is similar to that of biogenic ACC except for the minor presence of hydroxyl groups.²⁸ The high pH synthesis methodology has also been used by other authors to determine the formation enthalpies of ACC and Mg²⁺-doped ACC, up to amorphous magnesium carbonate (AMC).³⁷⁻³⁹ A smooth transition in the short range order from ACC to AMC has been demonstrated by X-ray Pair Distribution Function analyses.³⁸

The synthesis procedure involves the rapid mixing of equimolar divalent cation and carbonate solutions (Table S1) followed by immediate quench with acetone and vacuum-filtration.³⁸ The mixture typically yields a pH of ≈11; for pure ACC, this was adjusted to ≈13 with NaOH to favor the precipitation of an amorphous basic calcium carbonate, yielding a long-term stability.⁴⁰ Prior to the synthesis, all glassware was cleaned with 20% HCl to remove any possible nucleation loci and rinsed thoroughly with ultrapure water. Glassware, as well as all the solutions used in the synthesis, were kept in a 4°C refrigerator before use to prevent crystallization upon mixing. Vacuum-filtered samples were verified to be amorphous by ATR-FTIR (Nicolet iS10; Supporting Figure S1). These measurements were also used to verify the absence of Ca and

Mg hydroxide precipitates, which are susceptible to precipitate at highly alkaline conditions.²⁵,²⁶,²⁸,⁴¹ Once filtered, solid samples were transferred to a dry desiccator and kept until analysis. Additionally, a fraction of each sample was dried at 80°C in a vacuum oven for one hour and then kept in a dry desiccator until analysis after the same verification by ATR-FTIR. The chemical compositions of the solid samples (x values) were obtained by ICP-OES (Varian 720ES) and the water contents (n values) were determined by thermogravimetric analyses as described later.

**Inelastic incoherent neutron scattering (IINS).** Hydrogen is a strong spin-incoherent scatterer with a distinguishably large incoherent scattering cross-section (Table S2). Given the relative abundance of ¹H relative to ²H (~10⁻⁴), the scattering by hydrogen can be considered mostly incoherent. Therefore, using an appropriate spectrometer, the so-called vibrational density of states of the excitation spectrum can be probed. This last provides precious information on the dynamical properties of the H-bonding network with minimum contributions from non-hydrogen-bearing components (Ca, CO₃ and Mg). In particular, the excitation energies between 300 and 1200 cm⁻¹ (≈ 37 – 148 meV) are sensitive to librational modes: intermolecular interactions of water molecules that probe the hindered rotational motions of the H-bonding network and are difficult to explore with other optical probes.⁴²

IINS measurements were performed at the Institute Laue-Langevin (ILL) in Grenoble, France, using the IN1-LAGRANGE (LAarge GRaphite ANalyser for Genuine Excitations) secondary spectrometer setup installed at the hot source of the high-flux reactor yielding an energy resolution ΔE/E of ~ 2-3%.⁴³ About 100 – 200 mg of solid samples were loaded in hollow aluminum sample holders and the data were collected in the range of excitation energy transfer between 21.5 and 195.3 meV at 10 K in order to decrease the Debye-Waller factor. Acquisitions lasted for an average of 5 hours per sample. The obtained intensity was normalized to the monitor counts and corrected for the monitor efficiency using the LAMP package provided by ILL. The background spectrum from the cryostat and an empty sample holder were measured separately and then subtracted from the raw IINS spectrum of the sample. To help with the interpretation of the IINS data, computational simulations were used to produce vibrational density of states (VDOS) for hydrated Ca²⁺ and Mg²⁺ as well as monohydrocalcite and compared to the experimentally obtained data (see Supporting Information section 2. Computational simulations methods).

**X-ray photon correlation spectroscopy (XPCS).** XPCS takes advantage of a high flux coherent X-ray beam to register “speckle patterns” scattered by a disordered system. Thanks to the incoming coherent X-ray, the random diffraction pattern collected on a 2D detector is nothing but the exact spatial arrangement of the particles, or density domains in the probed size-range (see Supporting Figure S2 for representative speckle patterns). Therefore, if the particle positions were to fluctuate, so does the speckle pattern. Their temporal fluctuations in intensity thus provide information on the dynamics of structural rearrangements at the length scale defined by the experimental q range (q being the modulus of the momentum transfer, q = |q| = |kᵢ - kⱼ|). This is evaluated by computing the intensity autocorrelation function:

$$g^{(2)}(\Delta t, q) = \frac{\langle I(t, q)I(t + \Delta t, q) \rangle}{\langle I(t, q) \rangle^2} \quad (1)$$
where <...> denotes the ensemble average. This function simply provides the correlation between intensities of a given *q* region within the 2D detector separated by a lag time Δ*t*.

Data were collected at the ID10 Troïka beamline at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. Measurements were performed at ambient temperature and under active vacuum (~5 mbar) with an incident energy of 8.1 keV (λ = 1.53 Å) in a horizontal scattering geometry over a *q* range of 0.001 to 0.022 Å⁻¹. The coherent part of the incoming X-ray beam (10×10 µm) was selected by a pinhole placed right in front of the sample. The solid samples were loaded into steel gaskets with a 100 µm-wide hole, which was then mounted vertically in the vacuum chamber. 2D speckle patterns were recorded using a Maxipix photon counting area detector with 256×256 pixels (pixel size 55 µm). Acquisition times and the number of intensity attenuators were carefully adjusted to avoid beam damage to the samples, which was monitored by plotting two-time correlation functions (representative data shown in Supporting Information).⁴⁴ Accordingly, acquisition times of 0.04 s were chosen for most of the samples, with a sleeping time of 1.96 s between images, thus leading to a lag time Δ*t* of 2 s between subsequent speckle patterns. Only sample *x* = 0.35 was measured with a higher dose: 0.04 s acquisition times and 0.46 s sleeping time (Δ*t* = 0.5 s). The profile of the scattered intensity, *I*(*q*), was obtained from the same data by performing azimuthal averages of the 2D speckle patterns at different *q* values. Intensity autocorrelation functions, *g*⁽²⁾(*t*), were generated using the pyXPCS software provided by the ID10 beamline and fitted at a given *q* with a Kohlrausch–Williams–Watts (KWW) model:

$$g^{(2)}(t) = 1 + c * \exp(-2 * (t/\tau)^\beta) \quad (2)$$

where *c* is a set-up dependent contrast, *τ* is the structural ‘relaxation time’, i.e., the characteristic period of time for the system to attain a spatial arrangement different from that of a given initial time point, and *β* is a ‘shape factor’ referring to the nature of the relaxation processes. An ideal Brownian diffusive system will show an exponent of *β* = 1. Values of *β* < 1 are typically associated with dynamical heterogeneities in the sample, whereas values *β* > 1 are associated with stressed or ‘jammed’ systems.⁴⁵,⁴⁶

**Thermogravimetric and calorimetric analyses.** Samples were loaded in alumina crucibles and heated from 25 to 1100°C at 15°C/min under argon flow of 20 mL/min (Mettler Toledo TGA/DSC3+). The water content (*n* value) in each sample was quantified from the first weight loss step in the TGA curves and was further distributed into two types of water from the perspective of thermal stability, namely mobile and rigid. The assignment was operatively achieved by a rigorous determination of the first two inflection points found on the second derivatives of the TGA curves (see Supporting Figure S3 for detailed methodology).

## Results and Discussion

**Water dynamics.** The librational spectra shown in Figure 1 stem from the contributions of rock, twist and wag librational modes of water molecules in pure water and the Mg²⁺-doped ACC. Water in its liquid state shows a broad distribution of modes (Figure 1a, top) due to the disordered nature of the H-bonding network, while at 10 K the spectrum displays sharp features due to the formation of crystalline ice and to the degeneration of the librational modes.⁴⁷ Water in Mg²⁺-doped

ACC (Figure 1a bottom), on the contrary, displays broad features at 10 K. This indicates a distribution of modes (broken degeneracy) suggesting a heterogeneity of local hydrogen environments or structural disorder in the H-bonding network. Interestingly, this feature is proportional to the amount of Mg²⁺, as is best shown in the decreasing slope of the librational edge between 400 and 600 cm⁻¹ (Figure 1b).

<figure><img src="image_3.png" /><figcaption>Figure 1. (a) Librational region of the generalized vibrational density of states (GDOS) for water at 300 and 10 K (top) and Mg²⁺-doped ACC at 10 K (bottom) for *x* = 0 (pure ACC), 0.08, 0.35, and 0.7. The intensity is normalized to the unity within the 300 to 1200 cm⁻¹ range. Thick lines represent data smoothed over 20 points for better visualization. The red arrow indicates the frequency range where the stiffening of H-bonds is displayed (see text). (b) Slope of the librational edge from 400 to 600 cm⁻¹ as a function of Mg²⁺ content.</figcaption></figure>

At higher frequencies (from ~600 to 1100 cm⁻¹, the so-called librational region), the positions and the intensities of the modes are sensitive to the local H-bond environment.⁴⁷,⁴⁸ Our DFT calculations successfully show that the structural water in monohydrocalcite exhibits well-defined librational spectra with discrete modes comparable to experimental data (Supporting Figure S4). Despite the lack of discrete modes in amorphous carbonates, we observed a relative increase of the higher frequency modes above 850 cm⁻¹ that is proportional to the Mg²⁺/Ca²⁺ ratio (red arrow in Figure 1a bottom), pointing to an increase in the stiffness of the H-bonds. This observation was further confirmed by DFT simulations of hydrated Ca²⁺ and Mg²⁺ ions (Supporting Figure S5), thus strongly supporting the existence of stiffer H-bonding networks when Mg²⁺ is present. This stiffening can be associated to the high dehydration energy of Mg²⁺, reflected in the frequency of exchange events in the hydration water, which is three orders of magnitude lower than that of Ca²⁺.²⁹ Other type of divalent ion inclusions, such as Sr²⁺ or Ba²⁺, are also known in biogenic ACC.⁴⁹,⁵⁰ However, these ions did not demonstrate any stiffening effect (Supporting Figure S6), which could be due to their larger ionic size and the subsequent lability of water from their first hydration shell. These results therefore highlight the fact that Mg²⁺ acts as a stronger center of charge, contributing to the formation of localized and stiff H-bonding networks within amorphous carbonates. To further understand the role of
Mg²⁺ in association to the stiffening, we determined the thermal stability of water present in the amorphous samples by identifying, in a purely operational way, two types of water, namely mobile and rigid (see Supporting Figure S3 for the detailed methodology). The former represents adsorbed or surface-bound water, whereas the latter can be regarded as structural water.²² Figure 2 shows that, besides the anticipated increase of the total water content with increasing Mg²⁺/Ca²⁺ ratio, the fraction of rigid, structural water increases more significantly than mobile water as Mg²⁺/Ca²⁺ ratio increases. This non-negligible presence of structural water can be related to the local stiffening of H-bonding induced by Mg²⁺. This in turn may indeed have contributed to the kinetic persistence of Mg²⁺-doped ACC (Supporting Figure S7) which is also in agreement with previous studies both in air and in solution.³⁸,⁵¹,⁵²

<figure><img src="image_4.png" /><figcaption>Figure 2. Water contents in Mg²⁺-doped ACC for x = 0 (pure ACC), 0.08, 0.35, and 0.7 and the distribution into mobile and rigid structural components, determined by TGA analysis.</figcaption></figure>

The H-bond network comprises three different types of interactions: 1) H₂O-H₂O, 2) H₂O-Ca²⁺/Mg²⁺ and 3) H₂O-CO₃²⁻. A plausible hypothesis to explain the enhanced structural disorder in the H-bonding network and the increased kinetic persistence of Mg²⁺-bearing amorphous carbonates as compared to pure ACC is a stiffening of H-bond network in the close vicinity to Mg²⁺ (H-bond type 2). Whether this stiffening extends to the whole water network needs further discussion. A study by Sen et al.,⁵³ as well as some previous studies,⁵⁴ demonstrated that there is a strong H-bond interaction between the water molecules and the carbonate units, with the latter experiencing significant structural distortion that is uniformly distributed within ACC, which in turn hinders crystallization due to steric frustration. The authors added, however, that this distortion is independent of the presence of Mg²⁺, except that the increased amount of water molecules could allow a closer packing, and thus a stronger interaction of water molecules and carbonate units. Others studies, on the other hand, suggested that the lower molar volume of Mg²⁺ as compared to Ca²⁺ introduces structural distortions (strain) in the host CaCO₃ structures that effectively inhibit crystallization or formation of periodic ordering, independently of cation-hydration effects.⁵⁵,⁵⁶ Mg-doped amorphous calcium carbonates have been described as forming a solid-solution kind of structure in the region of low Mg content (x < 0.5), and an heterogeneous mixture of Mg-rich and Ca-rich domains at high Mg content (x > 0.5).³⁸ The fact that Mg²⁺-doped carbonates show an enhanced kinetic persistence in the whole compositional range (Supporting Figure S7), and that no partial crystallization or segregation of CaCO₃ is observed, leads to the hypothesis that the Mg²⁺-induced stiffening of the H-bond network extends beyond the first Mg²⁺ hydration shell and can thus affect the H-bonding of type 1 and 3.

**Dynamics of structural relaxation.** According to the classical nucleation theory, the rate of nucleation, Jn, takes the form:

$$J_n = A e^{-\frac{\Delta g}{k_B T}} \quad (3)$$

with the pre-exponential term A being the kinetic factor and the argument of the exponential function being the thermodynamic factor where Δg_n is the nucleation barrier (for details see Supporting Information section 3. Classical nucleation theory). The activated character of the nucleation process implies that not all attempts are necessarily successful in overcoming the energetic barrier and that the system will undergo a certain number of conformational or structural rearrangements before a crystal is nucleated within the amorphous matrix. The frequency of structural rearrangements is actually one of the substantial factors dictating the kinetics of nucleation. The relaxation dynamics probed by XPCS provide a quantitative measurement on the frequency of these structural rearrangements and is therefore a good probe for the underlying dynamics. Our experimental set-up covered small scattering angles corresponding to distances of ~25 to 630 nm. The observed relaxation dynamics are therefore not probed at the atomistic-scale, yet they cover a range that corresponds to density fluctuations within individual particles of amorphous carbonates with a typical size range in the order of tens to hundreds of nanometers³⁸,⁵⁷. To this point, we would like to stress that preliminary XPCS measurements made at the atomistic-scale (i.e., high q) revealed extremely fast relaxation dynamics that were technically inaccessible with the 2D detector employed. This highly dynamic character of the amorphous carbonates contrasts with the dynamic regimes present in other amorphous and glassy systems such as covalent or metallic glasses, which exhibit relaxation times that are at least four orders of magnitude larger.⁵⁸,⁵⁹

Figure 3a shows a representative time-evolution of g⁽²⁾(Δt,q) for the pure ACC (x = 0) averaged every 33 minutes over the duration of a measurement. A significant slowing down of the relaxation dynamics—aging—was observed with time, and similar trends were found in all the other samples (Supporting Figure S8a). The aging nature is best demonstrated by the evolution of τ values (Figure 3b) and seemingly it could indicate the onset of crystallization. Strikingly, however, the corresponding time-evolution of the intensity profiles over the full q range (i.e. static structure, S(q)) displays no apparent change over time (Figure 3c). This surprising phenomenon was common in all the amorphous carbonates examined in the present study (Supporting Figure S8b). Additional test measurements were performed to verify and exclude the possibility of an artefact induced by the X-ray beam (Supporting Figure S9). The aging in our amorphous carbonates could instead be explained by the partial dehydration due to the active vacuum during the course of the measurements. Indeed, ex-situ TGA measurements performed on samples subject to the same vacuum conditions showed a very small dehydration, in the order of 1 - 2% w/w (Supporting Figure S10). Such minor dehydration may nevertheless suffice to trigger subtle struc-
tural changes, imperceptible in the static structure factor, S(q), as pointed out by Giordano and Ruta.³⁵ The authors demonstrated that structural change of metallic glasses as minor as 1% in the lattice parameter was responsible for significant changes in the relaxation dynamics (one order of magnitude). It is also to note that the interpretation proposed above is consistent with simulation results by Wallace et al.⁶⁰ showing that the self-diffusion of Ca²⁺ within the amorphous structure decreases monotonically as the samples are dehydrated.

<figure><img src="image_5.png" /><figcaption>Figure 3. Aging dynamics. (a) Representative time-evolution of the intensity auto-correlation functions over the course of the measurement for ACC at q = 0.021 Å⁻¹ (d ~ 30.5 nm). (b) Corresponding time-evolution of the intensity profile for ACC, i.e. static structure factor S(q), for the full q range measured (0.001 ≤ q ≤ 0.023 Å⁻¹). (c) Relaxation time τ and (d) shape factor β as a function of the experimental time for Mg²⁺-doped ACC at x = 0 (pure ACC), 0.35, 0.7 and 1 (pure AMC). Note the sample x = 0.35 was measured under slightly different conditions (see text).</figcaption></figure>

The observed stronger H-bonding network induced by the presence of Mg²⁺, and the enhanced kinetic persistence of Mg²⁺-bearing amorphous carbonates, seemed to provide a strong suggestion that the Mg²⁺-bearing samples should exhibit slower relaxation dynamics than pure ACC. Remarkably, the XPCS data demonstrate the opposite trend as shown in Figure 4 and as summarized in Table 1. These data clearly demonstrate that the relaxation time τ is smaller for Mg²⁺-doped ACC. In other words, the number of structural rearrangements per unit of time (1/τ) is higher for Mg²⁺-doped amorphous carbonates, with a non-linear proportionality to the Mg²⁺ and water contents (Figure 4b). In addition, the rate of aging reflects the persistence of AMC and Mg²⁺-bearing amorphous carbonates in comparison to that of ACC (Figure 3b): the time-evolution of the measured relaxation times (τ) shows that ACC displays the most dramatic changes, with a five-fold increase. Mg²⁺-bearing samples are thus less prone to age, a fact related to their stability and/or kinetic persistence as opposed to that of pure ACC.

<figure><img src="image_6.png" /><figcaption>Figure 4. (a) Normalized intensity auto-correlation functions at q = 0.021 Å⁻¹ (d ~ 30.5 nm) for Ca(1-x)MgₓCO₃ nH₂O with x = 0, 0.7 and 1. Fitted data are shown in solid lines. (b) Frequency of structural rearrangement (ω = 1/τ) as a function of Mg²⁺ and water contents.</figcaption></figure>

Besides the aging phenomena and the unexpectedly dynamic character of the structural relaxation that is enhanced in presence of Mg²⁺, our data suggest that the nature of such relaxation seem to be subject to internal stresses. The first indicator is the compressed decay (shape factor β > 1) of the autocorrelation functions, g²(Δt,q), in all of our amorphous samples, which, in addition, increases proportionally to the Mg²⁺ content (Table 1) and to the aging time (Figure 3d). The second indicator is the dependence of the relaxation time τ on q, which displays proportionality to q⁻¹ (Supporting Figure S11). This has previously been shown to be indicative of ballistic dynamics which can accompany β > 1 for systems bearing internal stresses,⁶¹ in contrast to ideal Brownian diffusive systems (refer to Supporting Information section 3 for details). These results infer that: (i) the partial dehydration under active vacuum is accompanied by an increase in the stress within the hydrated amorphous solids; and (ii) that the presence of Mg²⁺ in the structure is what introduces internal stresses. As suggested by studies on metallic glasses⁶²,⁶³ and discussed earlier, the origin of the observed stress could be due to the structural distortion known in the CO₃²⁻ unit coordinated to water molecules as discussed earlier. The stiff H-
bonding network imposed by Mg²⁺ could possibly be an additional factor leading to internal stress.

<table><caption>**Table 1. Fitted parameters (τ, β) obtained from the intensity auto-correlation functions**</caption><thead><tr><th colspan="4">Ca<sub>1-x</sub>Mg<sub>x</sub>CO<sub>3</sub>·nH<sub>2</sub>O</th></tr><tr><th>x</th><th>n</th><th>τ (s)</th><th>β</th></tr></thead><tbody><tr><td>0</td><td>1.08</td><td>470 ± 39</td><td>1.54 ± 0.17</td></tr><tr><td>0.7</td><td>1.96</td><td>350 ± 6</td><td>1.76 ± 0.05</td></tr><tr><td>1</td><td>1.99</td><td>166 ± 4</td><td>1.97 ± 0.09</td></tr></tbody></table>

Given the isotropic character of the amorphous carbonates, and the lack of recognizable higher order or hierarchical structural arrangements, the dynamic behavior observed here at the nanoscale can be extrapolated to the atomic scale. Relaxation times can therefore be interpreted as the lifetimes of a given structural configuration. A link can then be established between the number of structural rearrangements per unit of time (ω) and the crystallization kinetics. Under these considerations, let us closely examine the kinetic term A in eq. (3). The idea behind is that in a (metastable) amorphous system, when the nucleation barrier is high enough compared to the thermal energy, the metastable state of the system contains thermal fluctuations that are well described by a Boltzmann distribution. Sometimes, some of these fluctuations will reach and overcome the critical size, leading to crystallization. The kinetic term A may adopt various forms depending on the nature of the nucleation event (see Supporting Information section 3)⁶⁴,⁶⁵, though qualitatively speaking, it includes 1) the number of trials (formation of critical clusters) to overcome the nucleation barrier per unit of time (ω), 2) the probability that these trials are successful or not (Zeldovich factor, Z), and 3) the number of sites per unit of volume where the clusters can be formed (C₀).⁶⁵ In nucleation processes within disordered materials, such as the case here, the ‘coherent diffusivity’ measured by XPCS is an adequate representative of the physical mechanisms underlying the crystallization process, as it integrates both the self-diffusion of molecular or ionic species within the solid and their relative diffusivity (refer to Supporting Information section 3). Here, it is to note that whether water acts as a mediator (via partial or interfacial dissolution – reprecipitation) or not (in a solid state reaction) is of no relevance, since both processes would lead to structural rearrangements that are probed with XPCS. A direct proportionality can thus be established between the nucleation rate, Jₙ, and the XPCS-determined number of structural re-arrangements per unit of time (ω):

$$J_n \propto A e^{-\frac{\Delta g}{K_B T}} \propto \omega Z C_0 e^{-\frac{\Delta g}{K_B T}} \quad (4)$$

This rationalization in eq. (4) can be used to interpret our experimental data in terms of the different physically meaningful factors. Given the slower nucleation rate observed in Mg²⁺-bearing systems, their faster dynamics (higher ω) have to be compensated by the other factors, provided that the Mg²⁺-bearing ACC are less prone to crystallize. The strong H-bonding network induced by the presence of Mg²⁺ is hypothesized as the main reason behind this increased kinetic persistence. The internal stress revealed by XPCS measurements and the stiffening of H-bonds shown by IINS are probably two

manifestations of the same phenomenon: an enhancement of the H-bond stiffness of the water network that results in a decrease of the success rate of nucleation trials (Z), and thus lowers the crystallization rate of Mg²⁺-bearing amorphous carbonates.

## Conclusion

The unique combination of coherent X-ray and incoherent neutron scattering techniques has provided a novel way to describe the mechanism by which the inclusion of Mg²⁺ increases the kinetic persistence of amorphous carbonates. Neutron scattering experiments probing the dynamics of H-bonding network have shown a stiffening of the intermolecular bonds. Unexpectedly, this stiffening is accompanied by an increase of the coherent diffusivity within the Mg²⁺-bearing amorphous carbonate samples (translated as enhanced structural rearrangements), and to an internally stressed structure, probably due to the molecular deformations induced by the strained Mg²⁺ environment. It is proposed that the addition of the highly bonded Mg²⁺ hydration water to the amorphous systems causes local stresses that impede crystallization. Future experiments will be devoted to ascertain the universality of this stabilization mechanism, using other types of additives.

## ASSOCIATED CONTENT

### Supporting Information.

The Supporting Information is available free of charge at http://pubs.acs.org.XXX

## AUTHOR INFORMATION

### Corresponding Author

*Alex.Fernandez-Martinez@univ-grenoble-alpes.fr

### Present Address

¹Ayumi Koishi
Department of Civil and Environmental Engineering, Princeton University, Princeton, New Jersey 08544, United States

## ACKNOWLEDGMENT

Gaston Garbarino and Alexander Van Driessche are thanked for constructive discussions and experimental help. A.K. acknowledges the French Ministry of Higher Education, Research and Innovation for the doctoral fellowship. A.F.-M. acknowledges the CNRS program EC2CO for financial support. TGA was funded from Labex OSUG@2020 (investissements d'avenir; ANR10 LABX56). The ESRF and ILL facilities are thanked for beamtime allocation.

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