Monitoring a Mechanochemical Reaction Reveals the Formation of a New ACC Defect Variant Containing the HCO3– Anion Encapsulated by an Amorphous Matrix

Amorphous
calcium carbonate (ACC) is an important precursor in
the biomineralization of crystalline CaCO3. In nature,
it serves as a storage material or as a permanent structural element,
whose lifetime is regulated by an organic matrix. The relevance of
ACC in materials science is primarily related to our understanding
of CaCO3 crystallization pathways and CaCO3/(bio)­polymer
nanocomposites. ACC can be synthesized by liquid–liquid phase
separation, and it is typically stabilized with macromolecules. We
have prepared ACC by milling calcite in a planetary ball mill. Phosphate
“impurities” were added in the form of monetite (CaHPO4) to substitute the carbonate anions, thereby stabilizing
ACC by substitutional disorder. The phosphate anions do not simply
replace the carbonate anions. They undergo shear-driven acid/base
and condensation reactions, where stoichiometric (10%) phosphate contents
are required for the amorphization to be complete. The phosphate anions
generate a strained network that hinders ACC recrystallization kinetically.
The amorphization reaction and the structure of BM-ACC were studied
by quantitative Fourier transform infrared spectroscopy and solid
state 31P, 13C, and 1H magic angle
spinning nuclear magnetic resonance spectroscopy, which are highly
sensitive to symmetry changes of the local environment. In the firstand
fastreaction step, the CO32– anions
are protonated by the HPO42– groups.
The formation of unprecedented hydrogen carbonate (HCO3–) and orthophosphate anions appears to be the
driving force of the reaction, because the phosphate group has a higher
Coulomb energy and the tetrahedral PO43– unit can fill space more efficiently. In a competing secondand
slowreaction step, pyrophosphate anions are formed in a condensation
reaction. No pyrophosphates are formed at higher carbonate contents.
High strain leads to such a large energy barrier that any reaction
is suppressed. Our findings aid in the understanding of the mechanochemical
amorphization of calcium carbonate and emphasize the effect of impurities
for the stabilization of the amorphous phases in general. Our approach
allowed the synthesis of new amorphous alkaline earth defect variants
containing the unique HCO3– anion. Our
approach outlines a general strategy to obtain new amorphous solids
for a variety of carbonate/phosphate systems that offer promise as
biomaterials for bone regeneration.


INTRODUCTION
Mechanochemistry has become a tool for the synthesis of new inorganic, 1 organic, 2 and metalorganic compounds. 3 The product range can be extended by using small amounts of solvents or dispersants (liquid-assisted grinding), 4 ionic compounds (ion-and liquid-assisted grinding), 5 or polymers (polymer-assisted grinding) during grinding. 6 Ball-milling is an established strategy for producing out-of-equilibrium structures, and it can be employed for breaking down bulk materials to nano-size. 7,8 Defect formation on a large scale leads to an amorphization of crystalline solids. 9 Elemental germanium 10 or zeolites 11,12 show a loss of crystallinity during ballmilling, and changes of extended hydrate networks have been reported for Co3(PO4)2 × 8 H2O. 13 Ball milling can induce an alloying of metals 14 or polymorph changes (e.g., a transformation from the anatase to the rutile phase of TiO2). 15 Similarly, organic compounds mixtures of organic and inorganic compounds 16 undergo structural changes during mechanochemical treatment. This is of particular interest for pharmaceuticals as the higher solubility of amorphous phases enhances the uptake of drugs with poor water solubility. 17 Mechanochemistry is of particular interest for large applications due to its scalability and the reduced use of solvents, which make it a "green chemistry" technique. 18 Continuous mechanical stress during ball milling was proposed to trigger unusual reactivity and lead to the formation of transient phases that are different from those accessible in conventional solid state reactions. 19 There is limited evidence for or against this hypothesis. Ex situ studies, 20,21 where the reactants are converted and analyzed after the reaction, provide little information about intermediates, kinetics and dynamics during the mechanochemical reaction itself.
In situ measurements, on the other hand, can provide real-time insight into a ball milling environment. [22][23][24] Time-resolved X-ray diffraction with synchrotron radiation (PXRD) is the method of choice for elucidating chemical reaction pathways by the structure determination of intermediates whose existence might be deduced only indirectly otherwise. Diffraction, however, provides meaningful information only for crystalline materials. Non-crystalline solids elude structural analysis with diffraction methods. Only local probes, such as vibrational (IR, Raman) and nuclear magnetic resonance (NMR) spectroscopy or total scattering 12,16 can aid in the structural analysis. Since solid state transformations are typically diffusion limited and therefore comparatively slow, a step by step analysis can be used to identify transient phases, where "snapshots" are taken at different stages of the reaction. 25, 26 We demonstrate the utility of this approach by unravelling the structure of non-crystalline intermediates from the mechanochemical reaction of calcium carbonate (CaCO3) and calcium hydrogenphosphate (monetite, CaHPO4).
Calcium carbonate is an important biomineral in ascidians and molluscs, and calcium phosphate is an essential constituent of vertebrate hard tissues (bone, dentine, enamel). [27][28][29] The corresponding amorphous polymorphs play a prominent role in biomineralization. 28,[30][31][32][33] The transition from amorphous to crystalline phases allows Nature to exert control through ion concentrations (with ion pumps) and organic matrices or molecules. 34 Many research groups have invested substantial efforts to achieve a deep understanding of the mechanism of biomineralization. 35 An application-oriented result of the crystallization mechanisms is the use of amorphous calcium carbonate and phosphate for bone grafting materials or nanocomposites. [36][37][38][39][40] There is a growing interest on the effect of impurities in the local structure of amorphous calcium carbonate (ACC) 41,42 and amorphous calcium phosphate (ACP). 43 Organisms control the metastability of ACC by incorporating additives (like Mg 2+ , PO4 3or water). 43 These impurities have strong effects on the local structure of ACC and ACP, and several studies have been carried out to investigate the effect of additives such as magnesium and phosphate ions on ACC. [40][41][42][43] The local structure in ACC is a matter of debate. 44 A "protostructuring" of ACC with respect to different crystalline CaCO3 polymorphs has been proposed, 45,46 and the concept of "polyamorphism" has been considered for biogenic ACC. 44 Although the short-range order in ACC is pH dependent 47 and OHgroups were found to be incorporated in ACC, 48 there are no indications for the presence of hydrogen carbonate (HCO3 -) ions in ACC or any hydrated CaCO3 polymorph. [49][50][51][52] The synthesis and stabilization of ACC have been pursued by freeze-drying, 53 with polymers 54 and proteins, 55 or foreign ions like Mg 2+ 56 and phosphate. 43 These approaches start from the Ca 2+ and CO3 2ion constituents in aqueous solution, and the crystallization process is stopped at the ACC stage by stabilizing the product kinetically.
Mechanochemical treatment of calcium carbonate has been studied before. [57][58][59][60] The transformation of calcite to its high-pressure polymorph aragonite has been reported in a mechanically operated mortar. 61 The reverse transformation from aragonite to calcite, the thermodynamically stable polymorph, was described later. 62 Likewise, vaterite can be transformed to calcite mechanochemically. 63,64 In an earlier study we have shown that amorphous CaCO3 could be prepared by ball milling only, when Na2CO3 (minimum 7.5 mol %) was added to stabilize a metastable ball-milled amorphous calcium carbonate phase (BM-ACC) by cationic defects. 65  The process of amorphization was studied ex situ by solid-state nuclear magnetic resonance (ssNMR) spectroscopy and Fourier transform infrared (FTIR) spectroscopy. The local structure of the amorphous compounds was probed by ssNMR spectroscopy. Complementary structural information about the local structure motifs revealing the coordination sphere for the alkaline earth cations was derived from the analysis of total scattering data using synchrotron radiation.
The molecular dynamics was derived from X-ray photon correlation spectroscopy (XPCS). An outstanding feature of the amorphous phases is their extraordinary stability and slow crystallization (up to several months), because ACC and BM-ACC crystallize within minutes in contact with humidity. 37,66,67 The evaluation of the XPCS data indicates the presence of a highlystrained system in BM-aCCP. This strain due to hydrogen-bonded HCO3groups leads to a large energy barrier that suppresses any further reaction.

Ball Milling Reaction
The milling process was monitored ex situ using 1 H-and 31 P-single pulse excitation (SPE) magic angle spinning solid-state nuclear magnetic resonance spectroscopy ( 31 P-MAS-ssNMR) at 10 kHz and FTIR spectroscopy. The full width at half maximum (fwhm) of the NMR signals in crystalline solids is a sensitive measure of the uniformity of the local field 68 and thus suitable to follow the changes during the amorphization process.
The milling process of amorphous calcium carbonate/calcium hydrogen phosphate (aCCP 0.2) was stopped after 10 min, 30 min, 60 min, 240 min and 480 min.  shows the presence of residual water and (iii) the signals at 0.88 and 3.52 ppm are related to ethanol used in the washing step. These resonances remained unaffected even after drying the sample for 8 h at 40 °C in a vacuum oven ( Figure S1, Supporting Information). This indicates that the solvent molecules are encapsulated in nanocavities or in "grain boundaries" of the amorphous structure. Increasing the milling time leads to broadening of all signals, related with a loss of order and/or mobility. The appearance of a broad resonance at 11 ppm after 8 h of milling is attributed to changes in the 1 H environment leading to higher shielding of the phosphate proton or to a chemical reaction.  Figure 1c shows the X-ray powder diffractograms (XRPD) of the amorphous alkaline earth metal carbonate phosphates (x(carbonate)= 0.5) after 480 min of milling. The loss of all reflections associated with the starting crystalline components and the simultaneous appearance of modulations characteristic for amorphous materials reveal all samples to be "X-ray amorphous". However, the pure starting materials, MCO3 (M = Ca, Sr, Ba) and CaHPO4, cannot be amorphisized completely by ball milling (exemplary for CaCO3 Figure S2a, Supporting Information as well as the Quantification of the remaining crystalline proportion: Table S1). Transmission electron microscopy (TEM) images and the associated diffraction patterns for aCCP 0.5 confirm the complete lack of long-range order. The morphology of the particles (Figure 1d) is very different compared to amorphous carbonates precipitated from solution, 69 (Figure 2a-c). Therefore, we expect that the mechanism leading to amorphization is independent of the cation. However, the different Pearson hardness 72 of the alkaline earth cations (absolute values for Mg 2+ : =32.5; Ca 2+ : =19.7; Ba 2+ :=12.8) leads to slight shifts in the ν2 vibration mode to higher wavenumbers and to lower wavenumbers for the ν3 and ν4 vibration modes, which is consistent with the size of the cations. Therefore, the different charge density of the cations leads to different ionic bond strengths, and bands appear at different positions (i.e. vibrational energies, Table S1, Supporting Information).

Crystalline starting compounds and amorphous products
For crystalline monetite the bands of the νs-POH vibrational in-plane bending mode at 1348 and 1401 cm -1 overlap with the ν3 carbonate band (Figure 2d). 73 Surprisingly, the pronounced band of the νs P-O(H) stretch at 884.2 cm -1 in crystalline monetite cannot be detected in any of the amorphous products. Possible explanations are (i) strong shifts of the absorption maxima, (ii) strong signal broadening, or (iii) loss of intensity due to chemical transformation. Furthermore, the νs-PO stretch remained broadened in all samples, which is well known for amorphous phosphates. 43,74 The broad bands at about 3500 cm -1 are assigned to νs O-H stretching modes. All spectral bands show a significant broadening due to the loss of long-range order compared to those of the crystalline compounds. The bands at 2931 and 2853 cm -1 indicate that the dispersant medium cyclohexane is occluded in "nanocavities" of the amorphous product. The bands are characteristic for the asymmetric and symmetric C-H stretch of the CH2 groups in cyclohexane. 75 Phosphate Environment: 31

P NMR Spectroscopy
The ratio between the starting materials CaCO3 and CaHPO4 has a great effect on the structure of the amorphous products ( Figure 3a). The increase of the carbonate content for a milling time of 480 min results in a shift of the 31 P signal of the amorphous product to lower field. For carbonate mole fractions x > 0.3 the maximum of the 31 P signal at 1.6 ppm remains unchanged ( Figure 3b). Thus, the average phosphorus environment depends on the milling time ( Figure   1b) and the carbonate:hydrogen phosphate ratio, especially for low carbonate concentrations.
For low carbonate contents a shoulder appears at ~ -9 ppm which decreases with increasing carbonate content and disappears almost completely for x = 0.66, i.e. the 31 P resonance becomes symmetric.  Neutron diffraction studies on crystalline calcium hydrogen carbonate revealed the presence of two crystallographically distinct phosphate groups. 73 At ambient conditions one half of the phosphate groups exist as HPO4 2with one O-H group covalently bound to the central P atom while the other half has one proton in a symmetrically bridging hydrogen bond and one proton statistically distributed between two centrosymmetric positions. 73,77,78 The existence of two phasesan ordered low temperature and a disordered high temperature phase with a phase transition at about 280 K was suggested. 78 Furthermore, the increased 1 H linewidth in lowtemperature NMR spectra was assumed to result from a reduced proton mobility. 77 The increased temperature for longer milling times would induce disorder and enhance proton transfer, i.e. destabilize the hydrogen bonds. The applied mechanical force would most probably facilitate the transfer of the protons participating in destabilized hydrogen bonds (orange marked signals at -1.7 and -1.6 ppm, Figure 4a   Reference spectra of crystalline CaHPO4, Ca3(PO4)2 and Ca2P2O7 are presented in Figure 4b for comparison. Surprisingly, well defined resonances rather than one broad (amorphous) signal appear in all TEDOR spectra, which implies local order. The 31 P SPE reference spectrum is broadened inhomogeneously. In addition, the 31 P resonances in the TEDOR spectra (depending on the recoupling time) are shifted by up to 7.5 ppm up-and downfield with respect to the signals for crystalline CaHPO4. These differences -not typical for a simple amorphization -are associated with changes in the chemical (and electronic) environment of the phosphorus atoms when new bonds are formed.
In the TEDOR spectra of the aCCP sample (xCarbonate = 0.2) (Figure 4c) three resonances appear at 1.8, -2.6 and -9.1 ppm together with a shoulder at ~ -5.5 ppm. The broadened 31 P signal at -9.3 ppm and the shoulder at -5.5 ppm are in harmony with the shift range typical for crystalline Ca2P2O7. 79 Thus, it is likely that pyrophosphate was formed as an intermediate in a condensation reaction during the ball milling process. The other 31 P shifts are compatible with hydrogen phosphate or orthophosphate units from the reference spectra. A higher calcium carbonate content (aCCP = xCarbonate = 0.5) (Figure 4d) results in a loss of the signal at -9.1 ppm. All other resonances in the TEDOR spectra are shifted to lower field (i.e. at 0.3, ~2 and 4.0 ppm). By "diluting" the phosphate starting compound with carbonate the mean P-P distance increases, and a condensation reaction is less likely. In addition, new signals appear at low field, in agreement with the results of the 31

Carbonate Environment: 13 C NMR Spectroscopy
Ball milling leads to pronounced changes in the 31 P environments. The 13 C environment was probed as a function of the carbonate content and the alkaline earth metal using 13 C SPE, crosspolarization (CP) and heteronuclear correlation (HETCOR) NMR experiments, where two different types of nuclei are correlated via through-space dipole-dipole couplings. Figure 5a shows the SPE 13 C NMR spectra for aCCP, aSCP and aBCP (xCarbonate = 0.2)). Figure  The second broad resonance appears at ~162 ppm. Such chemical shifts have been reported by Nebel et al. 70 for sodium and potassium hydrogen carbonate. Although the existence of alkaline earth metal hydrogen carbonates is well known in solution, [80][81][82] there are no reports about alkaline earth metal hydrogen carbonate in the solid state. This is assessed from this resonance which is associated with the hydrogen carbonate chemical environment. Therefore, in line with the data of the 31 P NMR, it can be envisioned that (i) the carbonate group is protonated in an acid/base reaction by the hydrogen phosphate group or (ii) that this specific "hydrogen carbonate" (bicarbonate) environment is formed by reorganization during the milling process. The 13 C SPE spectra show a 7:1 ratio between the signals of amorphous calcium carbonate and the hydrogen carbonate. The hydrogen carbonate content in the samples increases drastically for the heavier group homologues SrCO3 (2.6:1) and BaCO3 (2.4:1). The fwhm for the resonance at ~162 ppm is 549 Hz for aCCP, 690 Hz for aSCP, and 703 Hz for aBCP. This correlates well with the increasing ionic radii of the alkaline earth metals (r(Ca 2+ ) = 99 pm; r(Sr 2+ = 113 pm; r(Ba 2+ ) = 135 pm). 83 The fraction of the hydrogen carbonate signal is significantly higher for samples with low mole fractions of calcium carbonate. To obtain more information about the distances between the protons and the carbonate group in the different samples, 2D HETCOR NMR spectra were recorded. The spectra with short contact times allow different proton environments around the 13 C nuclei and thus the carbonate ions to be resolved. The signal of the amorphous carbonate species at 168 ppm correlates strongly with a proton signal of 15.6 ppm (Figure 6b). This signal can be assigned to protons of hydrogen phosphates. In contrast, the signal of the hydrogen carbonate species at 162 ppm correlates weaker with the hydrogen phosphate signal. Furthermore, an additional proton signal at 12.4 ppm appears, which can be assigned to the hydrogen carbonate species. This is an indication that unreacted hydrogen phosphates enclose carbonate ions and hydrogen carbonate ions are surrounded by orthophosphate ions. This assumption becomes even more evident in the HETCOR spectra of aSCP and aBCP due to the higher hydrogen carbonate content (see Supporting Information).
The spectra with long contact times additionally reveal 1 H signals in the range of the entrapped solvents (especially cyclohexane). Therefore, the heteronuclear dipole-dipole coupling reaches to 1 H atoms of entrapped solvents in the grain boundaries.

Chemical Transformations during Ball-Milling: FTIR Spectroscopy
FTIR spectroscopy provides complementary information to solid state NMR spectroscopy on the chemical transformations of MCO3/CaHPO4 (M = Ca, Sr, Ba) during ball-milling. 13 C enriched samples of aMCP (M = Ca, Sr, Ba) were used to facilitate the assignment of the carbonate or phosphate bands in the FTIR spectra. The higher mass of the 13 C isotope shifts the carbonate bands to lower wavenumbers. 84 The difference between samples containing carbon in natural abundance and enriched with 13 C is displayed for aCCP for milling time of 480 min in Figure   7. The difference spectrum shows the bands assigned to (or affected by) the carbonate vibration modes. Particularly relevant are the bands at ~1640 and 850 cm -1 . The first is related to the (HO)CO2 stretch. 85,86 Since the ν2 (out of plane) mode of the carbonate ion is not degenerate, the associated band splits in two sub-bands. One of them at 862.7 cm -1 can be assigned to the amorphous calcium carbonate environment, the one at 828.2 cm -1 is associated with calcium hydrogen carbonate. Fitting the FTIR spectra for aCCP 0.5 revealed a ratio of 7:1 for the amorphous and hydrogen carbonate species (see Figure S11, Supporting Information) which perfectly matches the results from ssNMR. Unfortunately, a similar comparison was not possible for aCCP (xCarbonate = 0.2) due to the overlap with the νs P-O(H) stretch at 884.2 cm -1 .  13 C and with C in natural abundance for aCCP. The spectra show the essential bands at ~1640 and 850 cm -1 assigned to (or influenced by) the carbonate vibrations. The visualized ν4 vibration mode shows that the carbon atom has only a small influence on the position of these bands.
The FTIR spectra confirm a proton transfer reaction associated with the formation of a chemical bond (HCO3 -) during ball-milling according to: Replacement monetite by tricalcium phosphate did not lead to complete amorphization (Supporting Information S2b). Thus, proton transfer is crucial for the amorphization. Remarkably, alkaline earth hydrogen carbonates in solid-state have not been reported so far although they are quite common in solution. Pyrophosphates were detected for aCCP (xCarbonate = 0.2) based on the band at 750 cm -1 . This band disappears for higher carbonate contents, in agreement with the NMR results (vide supra). Finally, the ν4 band at 683 and 727 cm -1 in aCCP (xCarbonate = 0. 5) shows no 13 C-related shift, although it can be clearly assigned to the carbonate ion. An explanation is that the ν4 mode is associated with displacements of the oxygen atoms. Therefore it is nearly independent from the mass of the carbon atom. The addition small amounts of alkaline earth carbonates lead to a significant decrease of the second moment. The curve is discontinuous, with two steps for calcium and strontium carbonates. This may be rationalized by a chemical reaction (rather than by a physical mixture of the components) for compositions of xCarbonate < 0.3. The curve suggests four different processes to occur: (i) Dilution of the phosphates, (ii) condensation reaction to pyrophosphates, (iii) protonation of carbonate and formation of orthophosphates and (iv) increase of the disorder.
Here,  is the gyromagnetic ratio of the nuclei studied, S the nuclear spin, rij the internuclear distance, 0 the Bohr magneton, and ℏ the Planck constant divided by 2. Due to the r -6 dependence, 90-95 % of the first two coordination spheres contribute to the second moment. 91 In systems containing abundant magnetically active nuclei of different kind both homo-as well as heteronuclear dipole-dipole couplings are present. Both interactions have an influence on the Hahn echo intensity, however, esp. for amorphous systems containing solvent molecules (in this case water and cyclohexane) these contributions are difficult to evaluate. Thus, our aim is to follow the trend in the Hahn echo signal intensity and relate it with the composition of the mixture of CaHPO4 and earth-alkali carbonates rather than investigating in detail the coupling contributions. Figure 8  X-ray total-scattering experiments were performed to probe the local structure of the amorphous products. GudrunX4 was used to calculate the pair distribution function (PDF) from this data. Figure 9a shows the PDFs of aCCP 0.5, aSCP 0.5 and aBCP 0.5 with seven significant peaks.
The first can be assigned mainly to the phosphorus-oxygen (phosphate ion) distance at 1.52 Å (Figure 9b: Peak 1). We assume that carbon-oxygen (carbonate ion) distances contribute to this peak as well. This can be explained by the shift of the peak to lower distance values depending on the amount of the starting material calcite and thus a higher ratio of carbonate (aCCP 0.1: 1.54 Å, aCCP 0.2: 1.54 Å, aCCP 0.5: 1.52 Å, aCCP 0.6: 1.50 Å). Further, the decrease of the height of the peak with increasing carbonate amount can be explained by the higher amount of the carbonate due to its less neighbor atoms compared to phosphate. However, the effective shift is small as the peak is a superposition of both, the P-O as well as the C-O distances, the latter contributing far less (in comparison to synthetic hydrous ACC: 1.25 Å, Figure S13, Supporting Information) because of the small atomic form factor of both carbon and oxygen which keep the contribution of the C-O pair small. Hoeher et al. 92 reported a C-O distance of 1.3 Å which could also be an explanation for the merged peak. The peak height is not only a measure of the coordination number, but also the total number and product of the atomic form factors. The peak at 3.12 Å for aCCP 0.5 can be assigned most probably to the metal-phosphorus distance (Figure 9a: Peak 3). Since the peak shifts depending on metal cations, a metal is involved in these pairs (aSCP 0.5: 3.26 Å aBCP 0.5: 3.50 Å). In the next peak at 3.66 Å for aCCP 0.5, phosphorus-metal, phosphorus-phosphorus and metal-metal distances are expected to have a large contribution (in comparison to crystalline monetite, Figure 9a: Peak 4). 78 The shift to lower P-P distances compared to crystalline monetite (3.91 Å) indicates changes in the phosphorous coordination sphere and most probably a stressed and distorted system. Furthermore, a variety of different interatomic distances contribute to the higher peaks (4.3 Å, 6.3 Å and 9.42 Å, Figure 9a: Peak 5,6,7), mainly metal-metal distances. The PDF fade out early and become virtually flat at ~10 Å indicating a total lack of translational coherence. The PDF of aSCP and aBCP are in Figure S14 (supporting information).  Table 1). 41 Furthermore, and similar to synthetic hydrous ACC, the shape factor shows extremely high values. In comparison, Brownian molecular motion has a value of one. This is a strong indication for a dynamically highly strained system. 93 Table 1. Fitted parameters () obtained from the intensity auto-correlation functions measured at the start of the experiment, i.e., minimizing the effect of vacuum and related water loss. Relaxation times for the aCCP 0.2 sample cannot be determined precisely, only lower boundary can be established. behavior was observed for ball-milled ACC ( Figure 10). This can be explained for ACC by the loss of small amounts (few weight %) of water during the measurement due to an active vacuum. These minor changes in the mass of water cannot be detected by the static structure factor S(q), but they can have a large impact on the dynamics. DTA/TG measurements ( Figure S15

Reactions and Mechanisms
The 1 H-13 P TEDOR spectrum (see Figure 4a) reveals that only the environment of one phosphorous atom in pure CaHPO4 is significantly affected (loss of the 31 P resonance at -1.6 ppm) during the ball milling process, whereas the other resonance signal is only broadened. As a result of a condensation reaction, a signal at -5.5 ppm (typical for pyrophosphates) appears in the 1 H-31 P TEDOR spectrum. Based on the structural and spectroscopy data the following scenario may be derived for the sequence of events in the ball-milling reaction between CaHPO4 and MCO3 (M = Ca, Sr, Ba) for different ratios xCarbonate ( Figure 11).
The first -and fast -reaction is a proton transfer resulting in a local charge disorder. This forces the system to reorganize. The carbonate anions act in this step as proton acceptors (bases), the hydrogen phosphates act as proton donors (acids). The formation of hydrogen carbonates and orthophosphates (i.e. higher Coulomb energy, the tetrahedral unit can fill space more efficiently) appears to be the driving force of the reaction. Additionally, a second -and slow -condensation reaction to pyrophosphates occurs, which competes with proton transfer. Although the energy balance of pyrophosphate formation from two equivalents of hydrogen phosphate (2HPO4 2--> P2O7 4-+ H2O) may not be strongly disfavored, the kinetics is slow. 94 It has been suggested that crystalline monetite has an ordered low temperature phase (space group 1) and a disordered high temperature phase (space group 1). 78  sons are: (i) At higher dilution the mean distance between two HPO4 2groups (and therefore contact probability and time) decreases. Therefore, it is much less likely that two hydrogen phosphate ions will be able to stay in contact long enough and react. (ii) The formation of orthophosphates (PO4 3-) in the acid-base reaction between CO3 2and HPO4 2preceding pyrophosphate condensation leads to an even stronger dilution effect. (iii) The highly-strained system leads to such a large energy barrier that any reaction is suppressed.

Conclusions
In conclusion, we have explored the formation of amorphous anhydrous alkaline earth car-  Synthesis of Calcium Pyrophosphate. Loaded in a corundum jar, monetite (7.35 mmol) was heated to 800 °C in a horizontal tube furnace oven for 8 h (5 °C/min). Afterward, the resulting product was grinded.
The solution was degassed with an argon stream for 30 minutes. Under argon atmosphere and vigorous stirring 13 C enriched Na2CO3 (2 mmol) was added to the solution. The reaction solution was stirred for one hour. Afterward, the precipitate was separated by centrifugation and washed with water and ethanol. The product was dried in vacuo.

Additional Information
The data that support the plots within this paper and other findings of this study are available from the corresponding authors on request. Table S1, quantification of the ball-milled precursors; Table 2, shifts of the carbonate vibration bands; Table S3, chemical shifts of TEDOR signals; Figure S1, TEM images of aSCP and aBCP 0.5; Figure S2, XRPD patterns of reference samples; Figure S3, Best Fits of SPE NMR and FTIR spectra, Figure S4, results of thermogravimetric (DTA and TGA) studies, Figure S5, ex situ TGA plots; Figure S6,     The quantification is based on the FTIR data. For ball-milled calcite the band of the ν 2 vibration mode was fitted using a bimodal pseudo Voigt function. The area ratio of the function is shown in Table S1 for the amorphous and crystalline phase. To quantify portion of ball-milled monetite the band of the ν P-O vibration mode at ≈1000 cm -1 was fitted for the crystalline, ball-milled and amorphous phases. The full width at half maximum (FWHM) of the crystalline phase was set to "100% crystalline" and the FWHM of the amorphous phase to 0%. The ratios are in good agreement with the XRPD patterns ( Figure S8).     Figure S3. Comparison of the best fits (blue line) of the FTIR (left) and 13 C SPE (right) spectra. The ratio of the areas of the bimodal pseudo Voigt fits correspond to the carbonate to hydrogen carbonate ratio (top: aCCP, middle: aSCP, bottom: aBCP). S13 Figure S4. 31 P spin echo decay of aCCP 0.5 (left) with the corresponding static Hahn echo delay spectra (right). The solid line shows the best fit using the Gaussian function (equation 1). S14 Figure S5. Pair distribtuion function of hydrous ACC (from previous study). Figure S64. Pair distribtuion function of aSCP 0.2 (red) and aBCP 0.2 (blue). The PDFs show clear broad peaks beyond 10 Å. This proves a higher crystallinity in comparison to the aCCP samples. S15 Thermogravimetric and differential thermal analysis DTA and TGA measurements were performed on samples of aXCP 0.2 and 0.5. The first endothermic effect at ≈ 91°C is caused by surface-bound solvents, e.g. cyclohexane, ethanol and water. This is supported by the observed mass changes (< 1%). The second endothermic effect at about 220 °C (depending on the cation) shows the evaporation of entrapped solvent (specifically cyclohexane), and it is followed with a significant weight loss. We assume that the solvents are encapsulated in cavities between grain boundaries of the amorphous phase. The thermal energy increases the diffusion. This can lead to cracking of grain boundaries and a rapid release of the gaseous solvent. In samples with a mol fraction x = 0.2 this occurs at higher temperatures for the heavier alkaline earth cations. As shown by Zhang et al. 1 hydrogen bonded hydroxyl groups have a large impact on the thermal stability of phases. Therefore, we assume that due to the higher hydrogen carbonate content (aCCP<aSCP<aBCP, Figure S10) more hydrogen bonded hydroxyl groups are present, which leads to the observed higher thermal stability. A small endothermic effect occurs at ~500°C. Thermally induced crystallization to calcite, tricalcium phosphate and several polyphosphates occurs at ~600°C. The mass loss at higher temperature is due to decarboxylation of calcium carbonate.

Thermogravimetric analysis of samples subject to vacuum
Ex situ TGA measurements were performed to investigate the vacuum stability of the samples ( Figure S14). In accordance with the XPCS data, the aCCP (0.2) sample shows a significant change under vacuum. This is another indication that hydroxyl groups (with hydrogen bonds) are either broken or reorganized. In contrast, the water loss of sample aCCP (0.5) is less affected by the vacuum treatment. This is consistent with the less extent of sample aging observed in XPCS experiments. Figure S76. TGA traces under vacuum (blue line) and normal pressure (black line) for aCCP (0.2) (a, left) and aCCP 0.5 (b, right). The mass loss for aCCP 0.2 occurs at lower temperature (T = 9°C) under vacuum conditions. S18 Figure S87. Vibrational region of the generalized VDOS for water at 300 K in aCCP for (left) x Carbonate = 0.2 and (right) x Carbonate = 0.5. The intensity is normalized to the unity within the 2500−3500 cm −1 range. Black lines represent data for aCCP in air, blue lines for aCCP under vacuum conditions. S19

X-ray Photon Correlation Spectroscopy.
A high-flux coherent X-ray beam is used to detect time-dependent intensity fluctuations of the "speckle pattern", which directly relates to local dynamics, e.g. rearrangement of particles and density fluctuations in the probed volume. 2 The spatial size of the dynamics depends on the experimental q value, the scattering vector. The q-dependent intensity fluctuations are evaluated with the following autocorrelation function, which is a measure of the similarity of the intensity with itself after a lag time .
In order to obtain information about the dynamics of the system, the autocorrelation curve is fitted with the Kohlrausch-Williams-Watts model.
The parameter c is the setup-dependent contrast, is the structural relaxation time and is the shape factor of the curve.