The Crystallization Process of Vaterite Microdisc Mesocrystals via Proto-Vaterite Amorphous Calcium Carbonate Characterized by Cryo-X-ray Absorption Spectroscopy

: Investigation on the formation mechanism of crystals via amorphous precursors has attracted a lot of interests in the last years. The formation mechanism of thermodynamically meta-stable vaterite in pure alcohols in the absence of any additive is less known. Herein, the crystallization process of vaterite microdisc mesocrystals via proto-vaterite amorphous calcium carbonate (ACC) in isopropanol was tracked by using Ca K-edge X-ray absorption spectroscopy (XAS) characterization under cryo-condition. Ca K-edge X-ray absorption near edge structure (XANES) spectra show that the absorption edges of the Ca ions of the vaterite samples with di ﬀ erent crystallization times shift to lower photoelectron energy while increasing the crystallization times from 0.5 to 20 d, indicating the increase of crystallinity degree of calcium carbonate. Ca K-edge extended X-ray absorption ﬁne structure (EXAFS) spectra exhibit that the coordination number of the nearest neighbor atom O around Ca increases slowly with the increase of crystallization time and tends to be stable as 4.3 ( ± 1.4). Crystallization time dependent XANES and EXAFS analyses indicate that short-range ordered structure in proto-vaterite ACC gradually transform to long-range ordered structure in vaterite microdisc mesocrystals via a non-classical crystallization mechanism. Ca ions of the vaterite samples with di ﬀ erent crystallization times shift to lower photoelectron energy while increasing the crystallization times, indicating the increase of crystallinity degree of calcium carbonate. Based on the ﬁtting of the ﬁrst coordination shell of the Ca K-edge EXAFS spectra, the coordination numbers of neighbor atom O around Ca for vaterite samples increase from 3.4 ( ± 1.1) to 4.3 ( ± 1.4) with the increase of crystallization times. Crystallization time dependent XANES and EXAFS analyses exhibited the variation of local coordination environment of Ca ions during the crystallization process, which show the gradual transformation from proto-vaterite ACC with short-range ordered structure to well crystallized vaterite with long-range ordered structure. XANES and EXAFS analyses show that the coordination environment of our samples becomes gradually ordered via ACC precursor during the crystallization process in isopropanol. According to the XAS analysis, it is proposed that both solid–solid transformation and dissolution and recrystallization exist simultaneously in crystallization process. XAS analysis under cryo-condition (cryo-XAS) can be applied as a very useful method to study the crystallization mechanism.


Introduction
Calcium carbonate is one of the most abundant biominerals existing in nature, which is often applied as a crystallization model for the investigation of nucleation and crystal growth mechanism [1,2]. The polymorphs of calcium carbonate crystals include three anhydrous crystals: calcite [3], aragonite [4], and vaterite [5], and three hydrated crystal forms: calcium carbonate monohydrate, ikaite, and calcium carbonate hemihydrate [6]. In addition, there are a few amorphous calcium carbonate (ACC) phases with different water contents, which are important precursors in both biomineralization and bio-inspired crystallization systems [7][8][9][10][11][12]. Vaterite is the thermodynamically least stable phase of the three anhydrous crystalline phases. Different solvents and additives can induce the nucleation and crystallization of thermodynamically meta-stable vaterite. Vaterite crystals have been synthesized in aqueous solutions [13][14][15], alcohol-water mixed solvents [16,17], dimethyl formamide-water mixed was covered with Parafilm punched with seven needle holes and then put in a desiccator. A beaker containing 4 g of NH 4 HCO 3 was placed at the bottom of the desiccator as the source of CO 2 . A small bottle containing 20 mM H 2 SO 4 was also placed in the desiccator to absorb the NH 3 gas. After 24 h of reaction time, the white suspension in the beaker was transferred into a sealed bottle and stood for different times for crystallization at ambient condition. The precipitated CaCO 3 particles in the bottle were isolated by centrifugation, washed twice with isopropanol and then dried in a vacuum oven overnight at room temperature [33].

X-ray Absorption Spectroscopy (XAS) Measurement
Crystallization time dependent XAS measurements were carried out using cyro-system at KMC-3 beamline in the Helmholtz Zentrum Berlin GmbH (HZB) [34], Germany. Ca K-edge information was collected in fluorescence mode under a liquid helium atmosphere at 30 K. The spot size of incident beam is 100 × 100 µm 2 . Several scans were collected and combined together as one spectrum to improve the signal-to-noise ratio. The original data were processed and optimized by deglitching, energy calibration, alignment, merging, normalization, and self-absorption correction using ATHENA software. Fitting of the optimized data for every sample was performed using ARTEMIS software. For the fitting of all coordination shells of Ca ions in calcium carbonate, we gradually increased the scattering paths with the increase of the radius distance. There was a slight variation for the choice of R range and k range. For the fitting of the first coordination shell of Ca ions in calcium carbonate, the experimental data including the proto-ACC, the vaterite samples with different crystallization time and the vaterite reference were fitted as one combined data set. The R range was 1.25~2.5 Å, the k range was 3~9.5 Å −1 .

Ca K-Edge X-ray Absorption Near Edge Structure (XANES) Spectra
Proto-vaterite ACC was synthesized as a precursor using gas diffusion method, which was then crystallized for 0.5, 1, 2, 4, 10, and 20 d, respectively. To simplify description, we term the calcium carbonate samples with different crystallization times, e.g., vaterite-0.5d means the sample was crystallized for 0.5 d while it may still contain a certain amount of proto-vaterite ACC. Herein, freshly prepared calcium carbonate samples with short crystallization times (from 0.5 to 4 d) were immediately characterized using XAS, while calcium carbonate samples obtained after long crystallization times (10 and 20 d) were prepared in advance for XAS measurement. Ca K-edge X-ray absorption near edge structure (XANES) spectra of CaCl 2 , proto-vaterite ACC, samples crystallized for different times and vaterite reference were shown in Figure 1. XANES spectra of other well crystallized calcium carbonate samples, calcite and aragonite were also performed as references ( Figure A1). XANES data for proto-vaterite ACC, sample crystallized for 10 d (vaterite-10d) and three well-crystalline reference crystals (calcite, aragonite, and vaterite) were shown in our previous work [33]. There are significant differences for the Ca K-edge XANES data of the three crystalline references of calcium carbonate, calcite, vaterite and aragonite, indicating that the local chemical environments around Ca ions of the different crystal phases are different from each other. CaCl 2 , proto-vaterite ACC, samples with different crystallization times, and vaterite reference show very similar Ca K-edge XANES spectra. It is obvious that the Ca K-edge peaks of calcium carbonate samples are broader than the peak of CaCl 2 . The spectra of proto-vaterite ACC and the samples at the early crystallization stage (0.5, 1, and 2 d) with less crystallinity degree are very similar to that of vaterite, indicating that proto-vaterite ACC and the partially crystallized samples have short-range ordered structure similar to that of vaterite. A pre-edge feature at 4043 eV can be seen from the XANES spectra of all the samples with different crystallization times, which is attributed to 1 s→3 d transition [7], similar to proto-vaterite ACC and vaterite reference. The transition from s orbitals to d orbitals is dipole-forbidden, which are not appeared in centrosymmetric coordination environment Crystals 2020, 10, 750 4 of 12 (calcite). The white line peak around 4053 eV is corresponding to the K-edge of Ca ions, which is due to 1s→4p transition [7]. A post edge feature appears at 4061 eV. The absorption edges of Ca of the samples with different crystallization times generally shift to low photoelectron energy, from 4052.90 to 4052.29 eV, while increasing the crystallization times from 0.5 to 20 d, indicating the increase of crystallinity degree of calcium carbonate [27]. In comparison, the absorption edge of vaterite reference is at 4051.5 eV.
Crystals 2020, 10, x FOR PEER REVIEW 4 of 12 seen from the XANES spectra of all the samples with different crystallization times, which is attributed to 1 s→3 d transition [7], similar to proto-vaterite ACC and vaterite reference. The transition from s orbitals to d orbitals is dipole-forbidden, which are not appeared in centrosymmetric coordination environment (calcite). The white line peak around 4053 eV is corresponding to the K-edge of Ca ions, which is due to 1s→4p transition [7]. A post edge feature appears at 4061 eV. The absorption edges of Ca of the samples with different crystallization times generally shift to low photoelectron energy, from 4052.90 to 4052.29 eV, while increasing the crystallization times from 0.5 to 20 d, indicating the increase of crystallinity degree of calcium carbonate [27]. In comparison, the absorption edge of vaterite reference is at 4051.5 eV.

Ca K-Edge Extended X-ray Absorption Fine Structure (EXAFS) Spectra
Extended X-ray absorption fine structure (EXAFS) analysis was also proceeded in order to better understand the neighbor environment of the calcium ions, coordination number, and the distance of Ca to neighbor atoms. Ca K-edge extended X-ray absorption fine structure (EXAFS) spectra of proto-vaterite ACC, samples with different crystallization times and vaterite reference were plotted in R space (Fourier transform magnitude) and k space in Figure 2. The EXAFS spectra of proto-vaterite ACC, vaterite samples with different crystallization times and vaterite reference were fitted separately according to the lattice parameters and space group of vaterite (hexagonal P3221) by using ARTEMIS, while FEFF was applied to calculate the EXAFS function for single scattering paths [35,36]. There are three energy-minimized structures having space groups P65, P3221, and P1121 [37] and it was noted that the P3221 variant of this structure also fitted their XRD data well, and was calculated to be only ~1 kJ/mol different in energy from the P6522 form [38]. The structures that have been proposed for vaterite are all based upon a common average structure with orientationally disordered carbonate groups [37]. The fitting results in R space of the four coordination shells of Ca ions including Ca-O1 (the first coordination shell), Ca-C (the second coordination shell), Ca-O2 (the third coordination shell), and Ca-Ca (the fourth coordination shell) are shown in Figure 2a, which are consistent very well with the experimental results when the R value is in between 2.0 and 3.5 Å . Considering that the proto-vaterite ACC precursors are composed of amorphous structures and don't own long-range order, only the first coordination shell close to the Ca ions, Ca-O1, can be fitted well by using vaterite crystal as reference.

Ca K-Edge Extended X-ray Absorption Fine Structure (EXAFS) Spectra
Extended X-ray absorption fine structure (EXAFS) analysis was also proceeded in order to better understand the neighbor environment of the calcium ions, coordination number, and the distance of Ca to neighbor atoms. Ca K-edge extended X-ray absorption fine structure (EXAFS) spectra of proto-vaterite ACC, samples with different crystallization times and vaterite reference were plotted in R space (Fourier transform magnitude) and k space in Figure 2. The EXAFS spectra of proto-vaterite ACC, vaterite samples with different crystallization times and vaterite reference were fitted separately according to the lattice parameters and space group of vaterite (hexagonal P3 2 21) by using ARTEMIS, while FEFF was applied to calculate the EXAFS function for single scattering paths [35,36]. There are three energy-minimized structures having space groups P6 5 , P3 2 21, and P112 1 [37] and it was noted that the P3 2 21 variant of this structure also fitted their XRD data well, and was calculated to be onlỹ 1 kJ/mol different in energy from the P6 5 22 form [38]. The structures that have been proposed for vaterite are all based upon a common average structure with orientationally disordered carbonate groups [37]. The fitting results in R space of the four coordination shells of Ca ions including Ca-O 1 (the first coordination shell), Ca-C (the second coordination shell), Ca-O 2 (the third coordination shell), and Ca-Ca (the fourth coordination shell) are shown in Figure 2a, which are consistent very well with the experimental results when the R value is in between 2.0 and 3.5 Å. Considering that the proto-vaterite ACC precursors are composed of amorphous structures and don't own long-range order, only the first coordination shell close to the Ca ions, Ca-O 1 , can be fitted well by using vaterite crystal as reference. The peak for the first coordination shell (Ca-O1) is strong in the EXAFS spectra (R space) of proto-vaterite ACC and vaterite-0.5d while the other peaks for the subsequent three coordination shells are barely distinguished. However, both the EXAFS spectra in R space of proto-vaterite ACC and vaterite-0.5d can be fitted well by using vaterite crystals, which indicates that short-range ordered atomic structure exists in the ACC and the very early crystallization stage (vaterite-0.5d). In comparison, the Ca K-edge EXAFS in R space of samples with crystallization times from 1 to 20 d show clearly a second peak, which are deduced to the second coordination shell (Ca-C) and the third coordination shell (Ca-O2). The third peak, deduced to the fourth coordination shell (Ca-Ca), can be clearly distinguished while the crystallization time was extended to 20 d, which is similar to vaterite reference. The Ca K-edge EXAFS spectrum in R space of vaterite-20d is very similar to that of vaterite reference, indicating that the sample crystallized for 20 d has high crystallinity degree.
All the fitting results of Ca K-edge EXAFS in R space of proto-vaterite ACC and samples with different crystallization times from 0.5 to 20 d fit well with the experimental results. The R-factor values of the fittings are below 0.025, indicating relatively good fittings. Therefore, the proto-vaterite ACC and the partially crystallized samples at the early crystallization stage have the same short-range ordered structure with that of vaterite reference. The successive appearance of the second peak and the third peak in the Ca K-edge EXAFS spectra in R space with the extension of crystallization time indicates that the short-range ordered structures in the proto-vaterite ACC slowly transform to vaterite crystal with long-range ordered structure. In comparison, well crystallized calcite and aragonite show totally different EXAFS spectra in R space ( Figure A2). The peak for the first coordination shell (Ca-O 1 ) is strong in the EXAFS spectra (R space) of proto-vaterite ACC and vaterite-0.5d while the other peaks for the subsequent three coordination shells are barely distinguished. However, both the EXAFS spectra in R space of proto-vaterite ACC and vaterite-0.5d can be fitted well by using vaterite crystals, which indicates that short-range ordered atomic structure exists in the ACC and the very early crystallization stage (vaterite-0.5d). In comparison, the Ca K-edge EXAFS in R space of samples with crystallization times from 1 to 20 d show clearly a second peak, which are deduced to the second coordination shell (Ca-C) and the third coordination shell (Ca-O 2 ). The third peak, deduced to the fourth coordination shell (Ca-Ca), can be clearly distinguished while the crystallization time was extended to 20 d, which is similar to vaterite reference. The Ca K-edge EXAFS spectrum in R space of vaterite-20d is very similar to that of vaterite reference, indicating that the sample crystallized for 20 d has high crystallinity degree.
All the fitting results of Ca K-edge EXAFS in R space of proto-vaterite ACC and samples with different crystallization times from 0.5 to 20 d fit well with the experimental results. The R-factor values of the fittings are below 0.025, indicating relatively good fittings. Therefore, the proto-vaterite ACC and the partially crystallized samples at the early crystallization stage have the same short-range ordered structure with that of vaterite reference. The successive appearance of the second peak and the third peak in the Ca K-edge EXAFS spectra in R space with the extension of crystallization time indicates that the short-range ordered structures in the proto-vaterite ACC slowly transform to vaterite crystal with long-range ordered structure. In comparison, well crystallized calcite and aragonite show totally different EXAFS spectra in R space ( Figure A2). sinusoidal. For well-crystalline vaterite crystals (vaterite reference, vaterite-20d), every Ca 2+ ion and CO 3 2− ion are in a nearly identical environment apart from occasional defects and thermal vibrations [39]. The same local structures keep repeating. Finally, the signals of multiple ordered Ca ions are superimposed and show a non-sinusoidal spectrum. The higher order of the local atomic structures, the less sinusoidal shapes of the Ca K-edge EXAFS spectra in k space can be observed. The Ca K-edge EXAFS spectra in k space show a trend of less sinusoidal shape with the increase of crystallization time, which reveals that the ACC with short-range ordered structure is gradually replaced by crystalline structure with long-range ordered structure and the crystallinity degree of calcium carbonate increases while extending the crystallization time.
For the quantitative evaluation of the coordination environment, the EXAFS spectra of proto-vaterite ACC, vaterite samples with different crystallization times and vaterite reference were fitted as one combined data set while only the first coordination shell (Ca-O 1 ) was taken into account ( Figure 3). Ca K-edge EXAFS spectra for the first coordination shell provides atomic distribution of the nearest-scattering atom, O, around Ca. The EXAFS spectra in k space of samples with different crystallization times exhibit obvious glitch peaks when the k value is bigger than 8 Å −1 , illustrating that the data quality is poor at high k values (>8 Å −1 ). Thus, we only fitted the first coordination shell to obtain more reliable coordination number of Ca ions.
Crystals 2020, 10, x FOR PEER REVIEW 6 of 12 Figure 2b exhibited a k 3 -weighted χ(k) spectra of proto-vaterite ACC, samples with different crystallization times and vaterite reference. The Ca K-edge EXAFS spectrum in k space of proto-vaterite ACC looks like a modulated sinusoid, but the signals of well-crystallized vaterite crystals are less sinusoidal. For well-crystalline vaterite crystals (vaterite reference, vaterite-20d), every Ca 2+ ion and CO3 2− ion are in a nearly identical environment apart from occasional defects and thermal vibrations [39]. The same local structures keep repeating. Finally, the signals of multiple ordered Ca ions are superimposed and show a non-sinusoidal spectrum. The higher order of the local atomic structures, the less sinusoidal shapes of the Ca K-edge EXAFS spectra in k space can be observed. The Ca K-edge EXAFS spectra in k space show a trend of less sinusoidal shape with the increase of crystallization time, which reveals that the ACC with short-range ordered structure is gradually replaced by crystalline structure with long-range ordered structure and the crystallinity degree of calcium carbonate increases while extending the crystallization time.
For the quantitative evaluation of the coordination environment, the EXAFS spectra of proto-vaterite ACC, vaterite samples with different crystallization times and vaterite reference were fitted as one combined data set while only the first coordination shell (Ca-O1) was taken into account ( Figure 3). Ca K-edge EXAFS spectra for the first coordination shell provides atomic distribution of the nearest-scattering atom, O, around Ca. The EXAFS spectra in k space of samples with different crystallization times exhibit obvious glitch peaks when the k value is bigger than 8 Å 1 , illustrating that the data quality is poor at high k values (>8 Å 1 ). Thus, we only fitted the first coordination shell to obtain more reliable coordination number of Ca ions.  The EXAFS amplitude (proportional to the coordination number) of proto-vaterite ACC and vaterite samples with different crystallization times were fitted as a portion of the EXAFS amplitude of Crystals 2020, 10, 750 7 of 12 the vaterite reference, giving the relative occupation of the first shell, as compared to the reference sample. The distance of Ca and O of the first coordination shell (Ca-O 1 ) is Reff+alpha*Reff. The radial distances from Ca to O of the first coordination shell are the same for all samples due to using the combined fitting method and finally the fitting R value is 2.38 Å. The R-factor value of the fitting is 0.023. The Ca K-edge EXAFS spectra and the fitting results for the first coordination shell (Ca-O 1 ) are presented in Figure 3. The fitting results (N, the coordination number; R, the radial distance of the first coordination shell; σ 2 , the Debye-Waller factor) are summarized in Table 1. The N of the samples at the early crystallization stages from 0.5 to 2 d increased from 3.4 (±1.1) to 3.7 (±1.1), very close to that of proto-vaterite ACC (3.5 (±0.8)). The N of vaterite-4d (4.3 (±1.1)) and vaterite-20d (4.3 (±1.4)) are obviously higher than those at early crystallization stages (0.5-2d), 3.4 to 3.7 (±1.1). Therefore, the coordination numbers of vaterite samples crystallized for different times generally increase from 3.4 (±1.1) to 4.3 (±1.4) with the increase of the crystallization time from 0.5 to 20 d, while the coordination number of vaterite reference is 6. The N of vaterite-10d is 3.7 (±0.9), lower than that of vaterite-4d (4.3 (±1.1)). We assume that the N value of vaterite-10d is not very precise. A possible reason is that the signal to noise ratio of the EXAFS spectrum of vaterite-10d is not very high, which might decrease the fitting quality. The Debye-Waller factor (σ 2 ) shows the mean square disorder of the distance to the neighboring atom [8]. The Debye-Waller factors of proto-vaterite ACC, vaterite samples with different crystallization times are all smaller than 0.01 Å 2 and similar to each other.

Discussion
Proto-vaterite ACC was successfully obtained in isopropanol by using a gas diffusion method. Despite the existence of short-range ordered structure in ACC can be confirmed according to characterization techniques such as XAS, solid state NMR [7], it remains a puzzle how the short-range ordered structures in ACC form [40]. According to our previous work, we proposed that proto-vaterite ACC nanoparticles aggregate in isopropanol and then vaterite nuclei form and start to grow via the condensation of proto-vaterite ACC nanoparticles and form vaterite microdisc mesocrystals [33], a typical mesocrystallization process [26,41]. The formation of proto-vaterite ACC instead of other kinds of ACC in isopropanol might be related to the stabilization of isopropanol for vaterite. And, the crystallinity degrees of vaterite samples increase with the increase of crystallization times according to the TEM, powder X-ray diffraction (PXRD), and fourier transform infrared spectroscopy (FTIR) results [33]. In this work, XAS characterizations for ACC and samples crystallized for different times were carried out under cryo-condition. Ultra-low temperature plays an important role in quenching crystallization of samples under irradiation of high energy X-ray beam, which limits the variation of structure phases. Therefore, cryo-XAS can exhibit the real structural information. XANES and EXAFS analyses in this article further show the gradual transformation from proto-vaterite ACC with short-range ordered structure to well crystallized vaterite with long-range ordered structure with the increase of crystallization times. XANES spectra show that the absorption edges of the Ca ions of the vaterite samples with different crystallization times shift from 4052.90 to 4052.29 eV while increasing the crystallization times from 0.5 to 20 d, indicating the increase of crystallinity degree of calcium carbonate. EXAFS fitting results show that the coordination numbers of neighbor atom O around Ca in the first coordination shell increase from 3.4 (±1.1) to 4.3 (±1.4) with the increase of crystallization times from 0.5 to 20 d, which supports the above solid-solid transformation pathway. Instead of the first coordination shell (Ca-O 1 ), the peaks of the other three coordination shells (Ca-C, Ca-O 2 , Ca-Ca) gradually appear with the increase of crystallization times. The short-range ordered structure in proto-vaterite ACC transform slowly to long-range ordered structure in vaterite. Then, the formed vaterite nanoparticles turn into vaterite microdisc mesocrystals through oriented attachment and secondary nucleation. It is suggested that both solid-solid transformation and dissolution and recrystallization exist simultaneously in crystallization process. Due to the low solubility of calcium carbonate in isopropanol, we propose that solid-solid transformation from proto-vaterite ACC to vaterite microdisc mesocrystals is the primary crystallization pathway, a mesocrystallization process, while dissolution and recrystallization are the minor pathways. The coordination number of O atoms in the first coordination shell for vaterite-20d (4.3 (±1.4)) is lower than vaterite reference (6). A possible reason is that the interaction between OH − group and Ca 2+ ions may result in a reduction in the fitted coordination number [7]. In addition, the multiple scattering paths may increase peak amplitudes. Ignoring multiple scattering could potentially lead to a slight underestimation of the amplitude of the EXAFS signal and thus the calculated coordination number is lower than the real systems [30].

Conclusions
The formation process of vaterite microdisc mesocrystals via proto-vaterite ACC was tracked by using Ca K-edge XAS characterization under cryo-condition at 30 K in this work. Ca K-edge XANES spectra show that the absorption edges of the Ca ions of the vaterite samples with different crystallization times shift to lower photoelectron energy while increasing the crystallization times, indicating the increase of crystallinity degree of calcium carbonate. Based on the fitting of the first coordination shell of the Ca K-edge EXAFS spectra, the coordination numbers of neighbor atom O around Ca for vaterite samples increase from 3.4 (±1.1) to 4.3 (±1.4) with the increase of crystallization times. Crystallization time dependent XANES and EXAFS analyses exhibited the variation of local coordination environment of Ca ions during the crystallization process, which show the gradual transformation from proto-vaterite ACC with short-range ordered structure to well crystallized vaterite with long-range ordered structure. XANES and EXAFS analyses show that the coordination environment of our samples becomes gradually ordered via ACC precursor during the crystallization process in isopropanol. According to the XAS analysis, it is proposed that both solid-solid transformation and dissolution and recrystallization exist simultaneously in crystallization process. XAS analysis under cryo-condition (cryo-XAS) can be applied as a very useful method to study the crystallization mechanism.  (a) (b) Figure A2. Ca K-edge extended X-ray absorption fine structure (EXAFS) spectroscopy of three references, vaterite, calcite, aragonite plotted in R space (Fourier transform magnitude) (a) and k space (b). Figure A2. Ca K-edge extended X-ray absorption fine structure (EXAFS) spectroscopy of three references, vaterite, calcite, aragonite plotted in R space (Fourier transform magnitude) (a) and k space (b).
Crystals 2020, 10, x FOR PEER REVIEW 10 of 12 (a) (b) Figure A3. Ca K-edge extended X-ray absorption fine structure (EXAFS) spectra for the first coordination shell of three references, vaterite, calcite, aragonite plotted in R space (Fourier transform magnitude) (a) and k space (b).  Figure A3. Ca K-edge extended X-ray absorption fine structure (EXAFS) spectra for the first coordination shell of three references, vaterite, calcite, aragonite plotted in R space (Fourier transform magnitude) (a) and k space (b).